.1 .I. m it >5 _LlBRARY M'Chlgan State University This is to certify that the dissertation entitled Characterization of Retention Behavior of Hybrid Stationary Phases presented by Amber Michelle Hupp has been accepted towards fulfillment of the requirements for the Doctoral degree in Chemistry Mambo mam Major Professor‘s Signature 51912000: v Date MSU is an Affirmative Action/Equal Opportunity Employer PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProj/Acc&Pres/ClRC/DateDue.indd A n I. 9"" CLL‘J‘:) ............................................................... 161 Retention factor for each solute on XBridge C18 (A), XBridge Shield RP18 (B), bridged-ethylene hybrid (C) in methanol as a function of mobile phase modifier. pure methanol (3), triethylamine (iii), acetic acid (fl), acetyl acetone (55333). Solutes defined in Table 5.1. Negative retention factors are indicated by * ............................... 179 xiv figure 5.2 Redo-c oiate figure 5.3 Isa”? 5.4 :33 5.5 :31: 5,5 Sh EiC Rpfg lE tact-on of "no: ( ). acetc ac 5.1 .............. 83933 for each 300 b'c'ged—e'." 3.5338 112,»: .‘e' SKEWS a'e r1: ‘3' Retect on fay; RP'E (8). am; incision of r~~ tref‘ffarnne t 35515 as: " T5336 5.1 ....... Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Reduced plate height for each solute on XBridge C13 (A), XBridge Shield RP13 (B), and bridged-ethylene hybrid (C) in methanol as a function of mobile phase modifier. pure \methanol (E), triethylamine (23:), acetic acid (g), acetyl acetone (3:53;). Solutes defined in Table 5.1 ............................................................................................... 182 Skew for each solute on XBridge C18 (A), XBridge Shield RP18 (B), and bridged-ethylene hybrid (C) in methanol as a function of mobile phase modifier. pure methanol (E), triethylamine (iiii), acetic acid (3%), acetyl acetone (353:2?22‘23). Solutes defined in Table 5.1 Negative skews are indicated by * .............................................................. 185 Retention factor for each solute on XBridge C18 (A), XBridge Shield RP18 (B), and bridged-ethylene hybrid (C) in acetonitrile as a function of mobile phase modifier. pure acetonitrile (E), triethylamine (:313), acetic acid (fi), acetyl acetone (335355.52?) pyridine (:3), acetic acid with triethylamine (iiiiéiE). Solutes defined in Table 5.1 ..................................................................................... 194 Reduced plate height for each solute on XBridge C13 (A), XBridge Shield RP18 (B), and bridged-ethylene hybrid (C) in acetonitrile as a function of mobile phase modifier. pure acetonitrile (I), triethylamine (iiif), acetic acid (E), acetyl acetone (1?) pyridine (K), acetic acid with triethylamine (3.3933). Solutes defined in Table 5.1 ..................................................................................... 197 Skew for each solute on XBridge C18 (A), XBridge Shield RP13 (B), and bridged-ethylene hybrid (C) in acetonitrile as a function. of mobile phase modifier. pure acetonitrile (H), triethylamine (‘1’), acetic acid (fl), acetyl acetone (3:33), pyridine (8), acetic acid with triethylamine (T331). Solutes defined in Table 5.1 ..................................................................................... 200 XV lNTROD tt. introduction Raisers-do’ase cn'i .‘fin‘n‘avfl ah . fi . I v Sui: 3’; NC meth-CCS Ag A , . 2363181018? onas. 22'.“ on ...i mechaosm -s r 52.13% aoc mm "3. 28 t -‘.t:.1'C"g?5 3150 he';‘. 33’7” ",h « c r .3 ases n. In 5.31.». v v or: bta'tc fig aqd C l‘ .1 . i my .' tal.‘ of the a " :37 Per. J If”? C c CHAPTER 1 INTRODUCTION AND BACKGROUND 1.1. Introduction Reversed-phase chromatography is the most widely used of all liquid chromatographic methods [1,2]. In reversed-phase liquid chromatography (RPLC), the stationary phase is a nonpolar material while the mobile phase is a relatively more polar solvent. The separation of a series of solutes is governed by the retention mechanism of the phase. Thus, a deep understanding of the retention mechanism is necessary in order to maximize the beneficial contributions and minimize the detrimental contributions to the separation. This understanding is also helpful to guide the development of commercially available stationary phases with better performance. Understanding and controlling the stationary phase synthesis is essential to understanding and determining the retention mechanism for a separation. The stationary phase is synthesized onto a solid support particle, commonly silica, by monomeric or polymeric surface modification [3,4], as shown in Figure 1.1. Monomeric synthesis involves the reaction of monofunctional silanes with silanol sites on the silica surface (Figure 1.1A). Monomeric phases are sterically limited with only half of the available silanol groups being covalently modified by the alkyl chain. Polymeric synthesis involves the reaction of di- or trifunctional silanes with silica in the presence of water. If water is included in the reaction slurry, the synthesis is referred to as solution polymerization (Figure 1.13). Alternatively, if water is added to the silica surface prior to the introduction of the SrOH ' ”nu, __ ‘iKE'Tr‘ y “:L. |Eb c. “f- Sj'ttk‘eq ‘ Zc'dpfi ! v 4 I. A‘Cah‘ y Si-O-Si(CH3)2R g Si-OH ClSi(CH3)2R Si'O'SKCHabR = ' SI'OH Si—O-Si(CH3)2R Si-OH Si-O-Si(CH3)2R \ R “Si’OHS/iR Si-OH Si\ O ‘ HOgR SOSR ._ - Ir 0 3'0” Cl SiR O I HO-Si-O-S/i-R 3 HO-Si-O'Si-R ——> o ‘ Si-OH ”20 CI gR ' Si-O-Si-R/ - ,u- o ._ S'-OH O -/ 3"R ' ,8)? Si-OSiOH HO R s 03%;: I- . .- / Si-O-Sj—R , Sic-33% H20 CI3SIR O Si-O-Si-R ,0 Si—O'Sj-R o Si-O-Si-R o / Figure 1.1. Synthesis schemes for stationary phases. A) monomeric synthesis B) polymeric synthesis: solution polymerization C) polymeric synthesis: surface polymerization. Adapted from Sander, Pursch, and Wise [3]. ., he syhess IS "3 :3.ng gytoesls rescits afaze '32th more slaWO‘ ’ESTSC'M-Dfi RPLC stat 0" run: a 9 ' -..~. Heme-ate so" A. | y '49.» 1" ‘ ' U V» l: aqc the stat 0“ :- ‘a"'“.?y 'esc‘ts from c “‘ an ' m: I. 53"" q r n ~ Udv‘ -1 . ~.. 1‘1: ‘ . comb oaton of t i ‘2 l". “- we s‘a’ o“ ‘ \ !afiy “h... rilétflfi r ‘ v 93 Coat siianr .335: Sal.» ‘(r C) Vusys |ay lnIEra ‘2“. .‘,' 7‘. :: . 'u b a e pP-marfly ,F‘S C ‘ Q: LC {JP-.339 that S 53.33?- 3" ~ JED O COth 3 m (41.35, .36 , ' Beggar's? \ v. '] [Tifir' ":33 'rt . .L‘m'q wtan lS’q F. c‘2r we. COP-rim ‘. 'II I l '0') E’d . “ ammm g.“ Pa' as l "7925': '5) and ,, HQ'Qt i silane, the synthesis is referred to as surface polymerization (Figure 1.1C). Polymeric synthesis results in higher bonding densities of the alkyl chain at the surface, with more silanol groups being covalently linked to alkyl chains. The most common RPLC stationary phases are derivatized with C18, followed by C8, and phenyl. The bulk retention mechanism is partition because the stationary phase consists of a permeable surface where the solute can completely dissolve in both the mobile and the stationary phases. Interaction with the stationary phase predominantly results from dispersion forces, however other interactions, such as dipole induction and orientation, ion-dipole, and hydrogen-bonding can occur as well. The combination of these interactions will influence the solubility of the solute in the stationary phase and thus, influence its retention. However, after derivatization, residual silanol groups may remain at the surface of the underlying particle. Solutes may interact with the weakly acidic silanol groups (Si-OH) and weakly basic siloxane groups (Si-O-Si) of the underlying silica. These interactions are primarily responsible for the adsorption mechanism [5-8]. Thus, a typical RPLC phase that should have a bulk partition-like retention mechanism may have some contribution from solute adsorption at residual silanols. The adsorption mechanism has several features that distinguish it from the partition mechanism. First, the stationary phase consists of an impermeable, solid surface. Common stationary phases include inorganic materials such as silica and alumina, as well as organic materials such as poly(styrene- divinylbenzene) and porous graphitic carbon. Most of these adsorbents are 'e:s:ge:cocs. having so ‘51:“; ‘ grows general. :cwor-accestor tB': 2222239.» iteractoos, an‘l ”33:75. toe-'9 .s o‘te" ...:~.a: gems of the $15; .' 3' "goes. Also. becacs P c a." .Wecrtaosms '3 p heterogeneous, having surface sites with different functional groups. These functional groups generally exhibit strong and selective interactions, including proton donor-acceptor (Bronsted acid-base) and electron donor-acceptor (Lewis acid-base) interactions, among others [9]. As a consequence of these strong interactions, there is often a fixed stoichiometry between the solute and the functional groups of the stationary phase, most frequently 1:1, but occasionally 2:1 or higher. Also, because the stationary phase is a solid with a fixed surface area, there are a limited number of surface sites. Consequently, the solute molecules are in competition for the surface sites and may be displaced by more strongly interacting species. These features of the adsorption mechanism make it distinctly different from the partition mechanism. The partition and adsorption mechanisms are the most widely observed retention mechanisms in RPLC [9], and may occur individually or in combination with one another. When a combination of mechanisms occurs by specific and deliberate design, it is generally beneficial to the resulting separation. However, when a combination occurs unintentionally or by accident, it is generally detrimental to the separation. Thus, in RPLC, efforts to reduce solute-silanol interactions that occur by an adsorption mechanism are important. Silica is by far the most widely used solid support for liquid chromatography. A number of other solid supports, such as zirconia, titania, and polymeric phases, have been used. However, silica is superior to other supports in terms of efficiency, rigidity, and general performance. Thus, in recent years, a large number of improvements to silica-based phases have been made that . .’ h AAOr-m "5'" “3&9 1.39 ‘95" ‘ ...U v t . . _ . L- 15336.33“- D‘v'i‘I 5 ' 'V l a .a- A 4 ‘ ' '33:,w LNC'LP‘L ES tra‘ C . i -r uu‘.V . KM— mpAA l ,- .535." ' ' A n r- ." £‘ I I‘ "U 63 Mid ~ We [nte'actoo c‘T I313 ”if‘" .w'oora: a; a : rm“— ‘U - --v i ’6 LX736"! “g ' in. A -‘~: '1' “‘ ' ‘fF " n v». t! 01 L'e be“. [we mDVO'V‘ET-E" b ‘ .. Huts 0f SEharaO {E- S l .:’ r 31'] Sica * :‘fie‘ke .‘QMRQFAJ “I, UV dklure [I ‘15!- 'q a «.8 For 1“ < :: .': “A?“ ESL-3““ £75229" c c ‘5‘1lv'1,t€:"‘. .3 O] 81-53 )‘E’ ‘ he ‘2‘ I “ 'r'tE'te ‘33:. directly reduce the detrimental interaction of solutes with residual silanols. For instance, high purity silica, introduced in the 1980’s, reduces peak tailing from metallic impurities that are known to affect of the acidity of the silanol sites [10,11]. In addition, endcapping with trimethylsiloxane and using trifunctional and sterically-hindered monofunctional silanes in the derivatization steps provide decreased interaction of solutes with the underlying support [12,13]. Likewise, phases incorporating a polar embedded group in the alkyl chain have been used to shield the underlying support in an effort to reduce peak tailing while modifying the selectivity of the separation [14-16]. The improvements made on silica supports have significantly influenced the types of separations that can currently be performed. Nevertheless, problems with silica-based materials continue to exist at high and low pH, extreme temperature, and for solutes that are more likely to adsorb to residual silanol groups. For this reason, a new type of support material based on a hybrid organic - inorganic particle has been developed and widely used as an RPLC stationary phase. This bridged-ethylene hybrid (BEH) particle (Figure 1.2) is synthesized by the co-condensation of tetraethyoxysilane with 1,2- bis(triethoxysilyl)ethane [17]. These support particles have the mechanicat strength of silica yet the high pH stability of polymeric particles [17,18]. In addition, the ethylene bridge in the backbone is thought to decrease the number of silanols available to bind to basic solutes. Despite the wide number of useful applications for this phase, only a small number of studies have attempted to characterize its retention behavior. /o m. /o i\ \C,i\ OrtS/C SIO H /Oumz /O H i\ i\ OiiSltOIISIO / / O O H i\ i\ OIISIIOIISIIO / / O O H i\ . i\ OIISIIOiiSIIO /O /O H i\ i\ OrlSIIOlSer / 2 / \0 Why \0 wife... «to / H / O O H .\ .\ / o o \ \O/ O OILSIOIIS H O O \/ \/ Figure 1.2. Bridged-ethylene hybrid (BEH) support its d§sse"atcrt exact-.3" .n RPLC. St. a": sued. Toe 'ete'2'. "IIOA ”1"" --- AUDI . if] a: In. ,H' 5"” .g F'Hv‘ . "i! G :.C a”: K ”E h tbs chazter t' un' ‘- a A, , '3'?) Som”a'z \- b --..~ .,., ' " '3375'TIJC a'tc .( r n... I Vital-h... “'3‘” a - 4.33 a; ‘yv S PE" L Therm°difnam fiemqua'h ( - i“J1lslln‘r ”S A ”1533?" n' . '“nve Sia- ~33 . ..s Tns w :5.“ 2:333? ' ‘v I [U,2lr‘} ‘h . re tfiemnfl J“ ' ‘1‘::‘:.'A .h"'.)‘"_~fi O f 3783: ‘ 3:5M',‘ ‘. . rd ll", ‘H j- t E ‘- v.~- _ ' '«3‘; . Eat? in. .x ' '€:' ‘ S‘fl’TEr This dissertation examines the fundamental properties that govern a separation in RPLC. Stationary phases built on both silica and hybrid supports are studied. The retention processes are quantitated using thermodynamic and kinetic theory. in addition, various experimental methods for extracting thermodynamic and kinetic parameters from solute zone profiles are evaluated. In this chapter, the fundamental theories of thermodynamics and kinetics are briefly summarized and the experimental methods of determining thermodynamic and kinetic parameters are described. The application of these methods to the partition and adsorption retention mechanisms in liquid chromatography is reviewed [19]. 1.2. Thermodynamic and kinetic theory Thermodynamic information provides an understanding of the energies of interaction between the solute and the mobile and stationary phases. This information is intrinsically related to retention and selectivity. Kinetic information provides an understanding of the rates of mass transport and surface interaction processes. This information is intrinsically related to the efficiency or plate height. Both thermodynamic and kinetic information are necessary to optimize resolution [9,20]. The thermodynamics and kinetics of solute transfer between the mobile and stationary phases in liquid chromatography can be treated in several ways. Most commonly, the retention process is treated as if it were analogous to a chemical reaction. For a partition mechanism, this may be represented as a simple first-order reaction 90—- ‘ .. - ,1 - -m-t or matte rX] Cs. we: ~13“ acsccton mecca" asecooco'c‘er 'ea (0 X ——(__—‘>X (1.1) m s for a solute (X) distributed between the mobile (m) and stationary (3) phases. For an adsorption mechanism, where the number of stationary phase sites (S) is limited, a second-order reaction is more appropriate Xm +S—(_—:'2XS (1.2) or Xm+DS(_—:_—>XS+Dm (1.3) where D is a displacing agent that is added to the mobile phase. If the concentrations of stationary phase sites and the displacing agent are sufficiently large, these mechanisms may be treated as pseudo-first—order reactions. The treatment of the retention process as a chemical reaction involves a rather simplistic view. First, chemical reactions occur in homogeneous solution and the reactants have relatively well defined energies and diffusion distances between them. The chromatographic system is intrinsically heterogeneous at the macroscopic level, as it involves two immiscible phases. Moreover, the phases themselves are also heterogeneous at the microscopic and molecular levels. The bulk mobile phase composition may be substantially different from that near the surface of the stationary phase or in the pores of the stationary phase support. The stationary phase may have several different types of retention sites or even different retention mechanisms. Because of these heterogeneities, the energy of the solute in the mobile and stationary phases is not as well defined as in a chemical reaction. Second, given sufficient time, the chemical reaction can 3.323.183? equai a": era’s 'errari corsta' it :3? wet-er 3:" 936 :.‘_-‘:7-:-:o"-c:c.":s. at" E is artiste vow. to: '1:*'Aq . ' ‘\ l P \l ‘” 4 iv U 'S De‘u tqt ‘ I. 4 n.‘ ‘ ' v: wide of the Va'cuc ‘ ‘ e“, “'3" ; v1 VI U lake C an 4 v ‘4 u 'v .-'."!.nam.lc a”C Kr F- 5,. “‘3 “0336 aha: A V” V 2.3:”? “N5 .. 4.5.33 (X:) T ‘9 1 5:50” v i d ‘8‘: aVE'afia 133”» “J 3’)” . i. "Jose i 3‘» ‘2- “l 'i-Cf‘vr mate thef‘fi .:--., ‘3 {2* - ' .22.!" 1 EH ‘ Dy a fag i“ . gt‘ee‘u +1”; istfn Jr. :4“ «as: L. an”: t 5“», ‘ :2; achieve a state of equilibrium in which the rates of the forward and reverse reactions are equal and the activities (or concentrations) of the products and reactants remain constant. The chromatographic system, by virtue of dynamic flow, can never achieve this macroscopic state of equilibrium but may, under suitable conditions, achieve a microscopic condition of steady state [20]. Despite this simplistic view, the treatment of liquid chromatography as a chemical reaction is prevalent as it provides considerable insight to the rank and magnitude of the various contributions to the retention mechanism. If the retention process is considered as a chemical reaction, then an energy coordinate diagram (Figure 1.3) can be used to explain the analogous thermodynamic and kinetic contributions. In this diagram, the solute transfers from the mobile phase (Xm) to the stationary phase (XS) through a high-energy transition state (X1). The thermodynamic parameters, e.g. the change in molar enthalpy (AH) and molar volume (AV), are characterized by the difference between the final and initial states. These thermodynamic quantities represent the weighted average value in all of the available states in the heterogeneous stationary and mobile phases, respectively. The kinetic aspects of the retention event can be described by using transition-state theory. The transfer from mobile to stationary phase is characterized by a fast equilibrium between the mobile phase and transition state with pre-equilibrium constant Kmx. followed by a rate-limiting step between the transition state and the stationary phase with rate constant ksm. The kinetic parameters, e.g. the activation enthalpy (AHim) and activation volume (Avim), l Nl.‘l‘&(-5Y :LCéL' €19.13 qufh- "1:“ Se ('h i ENERGY REACTION COORDINATE Figure 1.3. Energy coordinate diagram depicting the transfer of solute X from the mobile phase (m) to the stationary phase (5). Associated thermodynamic and kinetic parameters are described in the text. 10 JS‘BC to em: cats t6 r we“, ‘v A A A . .: :6? . cm Ship-"c"! I all AfiaA‘Aat ' v I p 3:. w 3.0 I K‘s a v ‘5‘):Jnamc aqc ( all '47. Thermodynamic "‘ I‘fifi ‘ \ - h . A. LWWV‘ a .‘\ UVV “ "Fra ‘ ,- ' M ‘I v" Ir‘r‘ffin VI “.13 d h: a . ”3 may be an" 73-.“ My i Z ..t.. lie phage fa. .tltu 9 Of] the 'T‘Cr ‘4” .le equ; ‘ ”h” s‘; 3 v r ‘ 8 he 6" dds P .‘ v :5: i".\ ‘V r b 978% {ls-5,; U can be used to elucidate the kinetic description of the retention event. For the transfer from stationary to mobile phase, the pre-equilibrium constant Ks; and rate constant kms are used to determine the activation enthalpy (AHSI) and activation volume (AVst). These kinetic quantities represent a weighted average of all available paths between the final and initial states. The derivation of these thermodynamic and kinetic quantities is described in the following sections. 1.2.1 . Thermodynamic theory As noted above, equilibrium is not attained due to the dynamic nature of the chromatographic system. However, at the microscopic level, steady-state conditions may be achieved in which the activity of the solute in the mobile and stationary phases (am and as, respectively) achieves a constant value k=$=kp (1.4) 8m where K is the equilibrium constant, k is the retention factor, and B is the phase ratio. The phase ratio is defined as the volume of the stationary phase divided by the volume of the mobile phase. The equilibrium constant is related to the change in molar Gibbs free energy (AG) by In K = SEE (1.5) RT where R is the gas constant and T is the temperature. The Gibbs free energy is related to the changes in molar enthalpy (AH) and molar entropy (AS) by the Gibbs-Helmholtz equation [21] 11 flail-T38 " . .u s f , t 23:42:..4.O"l 0 Ema. an}: . y ' ' 31:5" 3.59 ”‘02? 5’1": 0 u o n ; M.’,~ - vr'iC 39 in mO'.a' (Ih:m ‘ 1* - T Ca :78 'efier‘t r; C '= it fair. a shoe m Want?" ‘7- ~=al wta as ' "’3' WWW 51¢” of tre . .1: Or an enflf‘?p Vim. 'r . ' H W’ifin th ' Ere ‘Q . d .‘ our of H S" .- '.‘:-M ' .s ix. "1. 6: t'h » L £6 P. SV'UI; \. p ' in l'" V b. qaWCe-r V .. AG=AH—TAS (1.6) By substitution of Equation 1.6 into Equation 1.5, the retention factor can be related to the molar enthalpy and molar entropy as -AH AS I k=l K—l =— ——| 1.7 n n nB RT + R nB ( ) The change in molar enthalpy can be determined by graphing the natural logarithm of the retention factor versus inverse temperature at constant pressure. This will yield a slope that is related to the change in molar enthalpy, and an intercept that contains information about the change in molar entropy and the phase ratio. When the phase ratio is known, the molar entropy can be determined from the intercept. However, the phase ratio is often not known and accurate determination of the molar entropy is not possible. The phase ratio and the molar entropy must be independent of temperature for accurate determination of the molar enthalpy. The change in molar enthalpy will be positive for an endothermic transfer and negative for an exothermic transfer of the solute from mobile to stationary phase. Although there are some noteworthy exceptions, most successful separations in liquid chromatography involve an energetically favorable exothermic process. The change in molar entropy will be positive when there is a favorable dissipation of energy through an increase in the number or distribution of microstates. This most commonly occurs through a change in volume or concentration, leading to a change in configurational entropy, as the solute is transferred from the mobile to stationary phase. The change in molar enthalpy is defined as [21] AH = AE+PAV (1.8) 12 rare LE :5 the or; we ant: P as 1"! :fi! "4‘33 ‘0 .h-5. .. ~ .1 A v I; ” . -. h-“ u . Q.“ ‘ v I (S h . U .- ‘ I - A- btve'fin “ a t:-:“_ ~. ~1> ' ZS tip-t In ‘,E C“ -.; ' C e. P! ' s 'Q'fl “59 a \— C: ‘c._ “ M‘- ~_th'. ' .- r -u'} where AE is the change in molar internal energy, AV is the change in molar volume, and P is the pressure. Substitution of Equation 1.8 into Equation 1.7 yields ‘AE—PAV+§§—mp (1% RT RT R lnk= The change in molar volume can be determined by graphing the natural logarithm of the retention factor versus pressure at constant temperature. This will yield a slope that is related to the change in molar volume, and an intercept that contains information about the molar internal energy, molar entropy, and phase ratio. These parameters must be independent of pressure for accurate determination of the molar volume. The change in molar volume includes the difference in volume that the solute occupies in the mobile and stationary phases, the possible change in volume of the phases, and the difference in solvation of the solute between phases. 1.2.2. Kinetic theory Kinetic information provides a deeper understanding of the retention mechanism than does thermodynamics alone. There are two common approaches to describe the kinetic behavior. The first approach, consistent with the thermodynamic treatment, is to consider the retention process as a chemical reaction. The general principles of chemical kinetics are then applicable [21]. The second approach, commonly used in chemical engineering, is to characterize the rates at which the individual mass transfer processes occur. Each of these approaches provides a valuable and complementary description of the retention process and will be described herein. 13 If the 'etent on p * Ca 13”.? 3330'-..) to -. 76. it" aqc‘ kpls are t O ‘23.: ”l to "" M‘v I h 'H'H-‘ vua, v t): v "'25 pm ._ .W rat 0! TIC: L): :14 ”M “I” h . :5"‘“"3W D ase 23:31: 2.: ‘fl .. a! 0’ 3'9 re:dte€‘ 2' u! "R 3y r. .. w 1“...“ I ,5 7‘. .. .64 an of the???- F.‘ 3:), 'C. c.1- VSSEQ by t ‘:A‘ If the retention process is treated as a first-order or pseudo-first-order reaction according to Equation 1.1, k Xm<-:%)—Xs (1.10) ms then ksm and kms are the corresponding rate constants for solute transfer from mobile to stationary phase and from stationary to mobile phase, respectively. These designations for the rate constants will be used throughout this dissertation, regardless of the retention mechanism (partition, adsorption, etc.). These are “lumped” rate constants, i.e. they comprise all contributions to the kinetic behavior including the sorption/desorption event, diffusion in the mobile and stationary phases, diffusion in pores and stagnant layers, interfacial resistance to mass transfer, etc. The rate constants, which reflect the kinetic behavior, are related to the retention factor, which reflects the thermodynamic behavior, by k='—‘§m (1.11) ms The detailed kinetic parameters can be elucidated by applying a combination of thermodynamic and transition-state theories. The rate constant ksm is expressed by the Arrhenius equation [21] as 451m ksm = A1m exp RT (1.12) where Aim is the pre-exponential factor and AE1;m is the activation energy for the transfer from mobile to stationary phase. By rearrangement, 14 AE’M . . '1”... 2 1n A'bm - DI +1 . ' l ‘1. r‘ rmnn' “536130116 :8 33 cc 3733313211 ‘16'Scs 1".. ;:;e‘:'1al %s re:a.ed tc Tram acct: t"e _: Q .89 r-,~ .,_. V q ‘4 V 332’?) p" age~ 5519 ciassca.‘ ' . I 3i w ‘10?) VOELTIC- :5 fins. 1°“ .t W3 5 2: i' Ea \- E'GtEC to the a log" 0; ,‘C . P 31" \v avt'aI‘On e v.54; 5:23. d." ‘ v0: m 'U .'e‘ T “S“ ‘a h "- than VLOIT‘Ie ‘r ‘1 ' 9'7?) t... vy 5‘3“ '. 40' m u _e V a 5‘ I a ' u. "u 1 ~ ‘0 déic. AEim RT ln ksm =InA1m— (1.13) The activation energy can be determined by graphing the natural logarithm of the rate constant versus inverse temperature at constant pressure. This will yield a slope that is related to the activation energy, and an intercept that contains information about the pre-exponential factor. The activation energy represents the energetic barrier that must be overcome for the solute transfer from mobile to stationary phase. Using classical thermodynamic relationships, the activation energy is given by A51", = AHtm + RT —I=Av,tm (1.14) By substitution of Equation 1.14 into Equation 1.13 AHtm + RT - PAVim RT In ksm =lnA1m— (1.15) The activation volume can be determined by graphing the natural logarithm of the rate constant versus pressure at constant temperature. This will yield a slope that is related to the activation volume, and an intercept that contains information about the activation enthalpy and pre-exponential factor. The activation enthalpy and pre-exponential factor must be independent of pressure for determination of activation volume. The activation volume represents the volumetric barrier that must be overcome for the solute transfer from mobile to stationary phase. The activation enthalpy can then be calculated from the activation energy and activation volume via Equation 1.14. In a similar manner, the rate constant kms can be used to determine the activation energy (AE5)), activation volume (AVst), 15 - - I 2': amazon er‘trac) 2236 These krtetCI (surefire rec. 'E .5'333’13'Tilc desr' " V» ,I A7659? 8: p '33: “I": "VSOPWM hkoq e la! a ,4 ng Se; ‘32:!“ M:L T. ‘3 "“ math 4. e thOds fOr t1 ~s $5.310r1 a: ' ‘ l and activation enthalpy (AHSI) for the solute transfer from stationary to mobile phase. These kinetic quantities provide a detailed description of the energetic and volumetric requirements of the retention process that complement the thermodynamic description. Another approach, which is more common in the engineering literature, is to evaluate the individual mass transfer processes that contribute to band broadening. Miyabe and Guiochon [22] have identified four primary mass transfer processes: axial dispersion, external mass transfer, intraparticle diffusion, and sorption/desorption kinetics. Axial dispersion is broadening that occurs in the bulk mobile phase, including axial diffusion and multiple paths through the packed bed. External mass transfer occurs as the solute moves from the bulk mobile phase through the thin stagnant film at or near the particle surface. lntraparticle diffusion occurs as the solute diffuses into the pore of the particle. This process consists not only of solute diffusion through the mobile phase in the pore, but also surface diffusion on the wall of the particle. Finally, as the solute sorbs to and from the surface, slow mass transfer arises from the sorption/desorption event. These mass transfer processes are considered as individual and separable contributions to the overall broadening and rate constant. The mathematical treatment of this approach will be described in Chapter 1.3.3.2.1. 1.3. Methods for thermodynamic and kinetic studies This section reviews the traditional methods for characterization and evaluation of thermodynamic and kinetic parameters for a separation [19]. 16 1.3.1. Perturbatio HIM-ed n g...” c— '1‘ C re I'fi\~" vi with: .5 VVV “no I. g 2.3... a") phase “I- n A‘ r: ‘“ ~cs'0q is a Stanton of t: l".A:v I v.’V’e more“: '-* W ions .6' ‘f‘nl: _ 5 ’ I-' CW l 6"";th ’"ter-K- E...- : :3? 0%} C: 2. it; M‘Ch tin EI‘EC Heqfic :35" “0'36 “f :5" 1.3.1. Perturbation methods Among the available methods for evaluation of thermodynamic and kinetic parameters, perturbation methods play an important role [23,24]. Perturbation methods represent the simplest approach, wherein the solute, mobile phase, and stationary phase of interest are contained in a small, static cell. A fast perturbation is applied to the equilibrium in order to alter the activity or concentration of the solute in the mobile and stationary phases. The perturbation may be achieved by rapidly changing conditions such as temperature, pressure, or dipole moment. After perturbation, the rate of relaxation of the system to the new conditions is monitored, followed by mathematical extraction of the equilibrium and rate constants. The advantage of the perturbation methods is their simplicity, where thermodynamic and kinetic behavior can be measured without interference from flow contributions. The measured rate constants consist of the sorption/desorption process and diffusional contributions to mass transfer. One of the limitations of these methods is that they require perturbation, during which the actual thermodynamic and kinetic behavior of the system is altered. Hence, the determined values of equilibrium and rate constants are neither those of the initial state nor those of the final state after perturbation. In order to minimize the required perturbation, the equilibrium constant should be as close to unity as possible. This ensures the greatest change in activity or concentration for a given perturbation of the system. In addition, the perturbation must be applied uniformly to the entire system and with sufficient speed that it does not contribute to the observed kinetic behavior. Although these methods 17 3: re?) promisng. t‘" are?) limited. €3.11. Temperature j The lemce'atc'l 3752131 methods 5:. :'2a. lactating re' 5T5?) Ctafige an: 3' ,“n. - fl] 0075181! I ‘P. 0- r d, Ind-L3" nfi .‘«\_‘_ V wu-Q.‘ d‘ T."C.:.I “‘5qu n, . T 9413:; b I':*: fl J are very promising, their application to chromatographic systems has been relatively limited. 1.3.1.1. Temperature jump method The temperature jump method is the most versatile and useful of the perturbation methods. This method is based on the concept that chemical equilibria, including retention processes, are usually associated with a non-zero enthalpy change and, thus, are temperature dependent. The shift in the equilibrium constant depends on the change in molar enthalpy according to Equation 1.16 (aan) _ AH (1.16) m P ‘W The temperature pulse can be induced by Joule heating [25-28], dielectric heating [29], or optical heating [30]. The instrument is relatively simple to construct and the speed of heating is sufficient for a wide range of inorganic, organic and biochemical equilibrium reactions. 1.3.1.2. Pressure jump method The pressure jump method is based on the concept that chemical equilibria, including retention processes, display a more or less marked dependence on pressure. The shift in the equilibrium constant depends on the change in molar volume according to Equation 1.17. (aan] _—AV (1.17) T 6P _RT The pressure pulse can be produced either by a sudden application or a sudden release of pressure in the system. The pressure jump method does not have as 18 Ice 3 range of :23. "’31 ripper oi react rise-area ms metfisc' ' rage: spe-::es. dice tr £3.13. Dipole jump r T'le 6305.6 j‘c'T ’.:".57i5 in me Q'OL e:sr:.ton after DWI .‘e eerie ai‘Tzrzty of ”5.22136 .n sole: :1: ‘a‘ent as well as tr itssbb. Bea 5:321:25 cross sec 5113: . k l ic:- SFECIS: ii‘le S d': 33h L J W (Dr CO wide a range of application as the temperature jump method because of the limited number of reactions that exhibit a sufficiently large pressure dependence. However, this method has been beneficial for the study of sorption/desorption of charged species, due to their relatively large changes in molar volume [31]. 1.3.1.3. Dipole jump method The dipole jump method is based on the change in dipole moment induced by photoexcitation. Many chromophores exhibit different dipole moments in the ground and excited states as a consequence of electronic redistribution after photoexcitation. This change in dipole moment can influence the relative affinity of the solute for the mobile and stationary phases [32]. The net change in solubility is dependent upon the magnitude of the change in dipole moment as well as the absorption cross section and fraction of molecules in the excited state. Because high photon flux may be required to ensure large absorption cross sections, due care must be taken to avoid thermal heating. In addition, excited-state reactions of the solute must be avoided. In the absence of these effects, the shift in the equilibrium constant depends on the change in solute activity (or concentration) according to Equation 1.4. 1 .3.2. Shallow bed method The shallow bed method can be considered as an intermediate between perturbation methods and chromatographic methods. In this method, the stationary phase particles are packed in an extremely short (“zero length”) column. The experiments may be performed in two ways: sorption (uptake) or desorption (release) methods. In the sorption method, a mobile phase solution 19 :s'eerigliesclut ‘i: :‘25't'aten oi the sc‘ 'ieetsobton. If the ays'mmdng the p ”a an L’iaS layer ll. '.: Jud .eie Drmsses tenet sore-ton rate 5 treasxemeq] : x9. ant ' h 08cf -.s 3.3905 4 mQIEr :~ ~ u,“ L ‘ 158.; l Ulicflls ‘ "C“; J?’ .' (4‘ ~I-:" “F “c.3‘l.“ ”q if]: containing the solute flows through the shallow bed at a high linear velocity. The concentration of the solute in the effluent solution is nearly identical to that in the influent solution. If the linear velocity is sufficiently high, the stagnant diffusion layer surrounding the particle will be thin. Hence, the time required for diffusion through this layer will be small compared to the time required for the slow intraparticle processes. As a result, the intraparticle processes will determine the observed sorption rate. After a certain time, the flow is stopped and the amount of solute that has been sorbed is measured by eluting it out of the shallow bed. This measurement provides a single point on the sorption curve. This experiment is then repeated for varied sorption times to construct the complete sorption rate curve. An alternative approach that is less time-consuming and labor-intensive is the desorption method. In this method, the shallow bed is pre-equilibrated by flow of a mobile phase solution containing the solute. To initiate the experiment, the flow is abruptly shifted to a solute-free mobile phase, which causes the solute to be desorbed from the bed. By detecting the eluted solute concentration as a function of time, the desorption curve can be constructed from a single experiment. Specifically speaking, the concentration C(t) is a function of the instantaneous molecular desorption rate of the solute (dn;(t) / dt) and of the flow rate (F) as follows C (t) = w (1.18) After integration, the desorption rate curve is constructed as 20 We 3653's? 0" rate u-Q to extract the 'e ‘33. Chromatograp Ca'omatoeg'ar .een‘t'ig them-G” v' .;. I! Q H II a. ~|a§ 0" mei‘xs his; :73th the Ci ‘. puma" I v v' I .abbem lit-A615 I . . “9'33"" 'C met‘ 13.1. Frontal mell ah n i ' l. ,pta- ana ‘, x. "‘ ‘ 'vxv'q macaq- 'igi .rlec Conlz'ibOL .. .l- .n JEIO'Y‘res SE = gradually W :5: zest-on of tfe r Weta'it Emmi of sol "tr ‘3”: Donal of t' .‘EZ; 13 30'? n,(t)=F[C(t)dt (1.19) The desorption rate curve is then fit by nonlinear regression to different theoretical models, such as the linear driving force model and spherical diffusion model, to extract the rate constants [33-36]. 1.3.3. Chromatographic methods Chromatographic methods are the most widely used methods for determining thermodynamic and kinetic behavior of the system. In contrast to perturbation methods, chromatographic methods are dynamic with mobile phase flowing though the column at all times. In this way, the contribution of flow phenomena to the zone profile cannot be neglected. The two most common chromatographic methods are frontal and impulse methods. 1.3.3.1. Frontal method In frontal analysis, the column is pre-equilibrated with the mobile phase. A solution containing a known concentration of solute in the mobile phase is introduced continuously. As the solute sorbs onto the stationary phase, the column becomes saturated and the concentration of solute eluting from the column gradually increases, forming a characteristic breakthrough curve. The mean position of the breakthrough curve can be related to the concentration and equilibrium constant of the solute as well as the sorption capacity of the column. The amount of solute sorbed is calculated from the breakthrough curve providing a single point of the isotherm. This process is repeated for progressively increasing concentrations of the solute to construct the complete isotherm. 21 To obian k" .2... I ., E .: :1. 1a...es of t“ 5:. 3.11 153-teem Inn ‘6. ,, .11“, my] CL'I‘ES ~= mt .5 peter“; '5‘ 3cm ‘1» "1"" .16 1590?: : 1'] Ta» 4 ‘I "3'2“"! ‘ : 11“ "g or D,“ ?- ‘ .. :N. Tish“ u‘ L'r '. ‘E:-. To obtain kinetic information, theoretical breakthrough curves are numerically calculated for each concentration step. These theoretical curves use different values of the rate constant in the transport model, together with the equilibrium isotherm determined from the breakthrough data. The theoretical breakthrough curves are then compared to the experimental ones. The rate coefficient is determined in such a way that the best agreement is observed between the theoretical and experimental breakthrough curves. In this approach, it is assumed that the rate constant remains constant during each concentration step in the frontal analysis measurement and that this rate constant corresponds to the average concentration of each step [22]. 1.3.3.2. Impulse method The impulse method is generally performed by injecting a small volume of the solute onto the column. The elution of the solute zone is monitored by on- column or post-column detection. The retention factor and rate constants can be extracted by any of the following models. 1.3.3.2.1. Plate height model In this model, the thermodynamic and kinetic parameters are determined from the mean and the broadening of the zone profile, respectively. The broadening or plate height may be determined in a variety of ways, but the most accurate method uses statistical moments as they make no assumptions about the shape of the zone profile. The first and second statistical moments (M1 and M2, respectively) are calculated from the zone profile as 22 1' Gill-Ill. 1231 H [Camel III Cill is tne c< vs tie meat ' 1.3 l'fi’. p2; * is the vargar fl (that ~1le ( 5) IS 3: {20‘ _ [can dt M1 7—011)? (1.20) _ ] C(t)(t — M1)2dt _ * [C(t) dt 2 (1.21) where C(t) is the concentration as a function of time. The first moment represents the mean retention time and is related to the retention factor by _M1 ‘to to k (1.22) where to is the elution time for a non-retained compound. The method of calculating kinetic rate constants is derived by extrapolation of Giddings’ work [20]. The plate height in the length domain (HL) can be related to the peak variance or second moment in the time domain by 2 HL = ELL‘ = __MN2'12L (1.23) where 02 is the variance and L is the column length. The mass transfer term for slow kinetics (Cs) is derived from the generalized nonequilibirum theory of Giddings [20] and is given by _ 2k CS—(lka—k- (1.24) ms Thus, 2 km: 2'2” and ksm= “2“ (1.25) (1+k) dHL (1+k) dHL 23 res-11:5 the Iznear 3'31; tp.11 slow mass As at cusses '1 22:5 7:931 cont'.:..: axes". he eats: 2e where u is the linear velocity and dHL is the contribution to the plate height arising from slow mass transfer, and is described in more detail in Chapter 3.2.1. As discussed in Chapter 1.2.2, Miyabe and Guiochon have evaluated the plate height contributions to various mass transfer processes [22]. In their approach, the statistical moments can be further elucidated as L M=—6 1.26 1 u o ( ) 2L M2 =—u-(58x + 5f + 5d) (1.27) where 80 is a dimensionless retention parameter given by 60 :8” +(1—eu)(s+pK) (1.28) The contributions to M2 from axial dispersion (63).), external mass transfer (5f), and intraparticle diffusion (8d), respectively, are given by Sax =[D—5] 8% (1.29) U a,=(1—.c, ) Bi (8+pK)2 (1.30) “ 3kf R2 2 6d=(1_EU)[153 ](s+pK) (1.31) e where EU and a are the inter and intraparticle porosities, pp is the density of the Packing material, RF) is the particle radius, DL is the axial dispersion coefficient, kf is the external mass transfer coefficient, De is the intraparticle diffusivity, and K is 24 r;- e“ 'IIC’AL'T] Ci .3.qu 1 1| II ‘F-‘N NF‘, m“ tilt-ll 3U) S 'd .3. II L Zu 1' 3K.) ‘.F to .9- P‘o'ont -. " U a u. . s f‘ )4 aerate-a or cat 1": 3‘ mass fire A. 'N . 1: e'm . “son 006 43‘. “-53 CO’ Eumfiq ‘C :1": 2".»- d “e ‘ . fie n 1 3“ ‘-__ "e-1 v - ~1 ‘.Viy' A I l a» "-9. a 5.- . ’.:“ g ' the equilibrium constant. Under conditions where the rate of sorption/desorption is negligibly small, the plate height can be written as H=[M_§-](L]=D_§+§g+§g (1.32) M1 2“ U 50 5o The different parameters that are related to mass transfer processes can be estimated or calculated based on the above equations. For example, the external mass transfer coefficient, diffusion coefficient in the mobile phase, and pore diffusion coefficient can all be estimated, and the diffusion coefficient in the stationary phase can thus be calculated. The plate height model assumes that all contributions to variance, both symmetric and asymmetric, that are not directly attributable to fast processes such as axial dispersion arise from slow kinetics. There are several potential sources of error in this method. First, this method requires that the solute concentration be within the linear region of the isotherm, such that it does not contribute to the variance. Second, this method relies on the accurate calculation and subtraction of all fast mass transfer terms, which is difficult for packed columns in liquid chromatography. Empirical estimations of these parameters will introduce errors. Moreover, any extra-column contributions to variance, including those from the injector, detector, connectors, etc., must be accurately calculated and subtracted. Again, there are no theoretical methods for the calculation of these parameters, so empirical estimations are necessary. 25 1332.2. Expone If an Incre 1.3.3.2.2. Exponentially modified Gaussian (EMG) model If an incremental length of the chromatographic column is considered, then zone broadening can arise from multiple paths, diffusion, and mass transfer processes that are fast relative to the time spent in the incremental length. These processes contribute to the symmetric broadening, which is described by a Gaussian function 2 A t—tg C t = ex —O.5 — 1.33 () flag 9 [ Cg J ( ) where A is the area, tg is the retention time of the Gaussian component, and 09 is the standard deviation of the Gaussian component. In addition, zone broadening can arise from mass transfer processes that are slow relative to the time spent in the incremental length. These processes contribute to the asymmetric broadening. For a partition or adsorption mechanism that can be considered as a first-order or pseudo-first-order reaction, this contribution is given by an exponential function 1' C(t) = Aexp[fl] (1.34) where T is the standard deviation of the exponential component. The zone profile observed at the end of the total column length is the convolution of the Gaussian and exponential contributions, i.e. the multiplication of the functions and integration within each incremental length. This convolution is given by the exponentially modified Gaussian (EMG) equation 26 2 Ga :1 lflz—exp .. 3 2: 2:4 . :1 . tame pro e 5 2:55.31 parane: I . . n-A q ‘q. ‘ i an as C‘ and \Vd ~ V» n ”TC 2155 "m 339m611 flu . 1‘ {KL}- 9\ : 0.1 :nfr'. “4:. F'rst *h .53. m, a3” of (s, Er~ L .5.K‘ 3 LA I.“ In ‘ .1 n, ‘43 \.. . .~;~‘.‘~ ‘K.J rah.“ La‘ "14' h) I": C(t)=iexp[fi+i‘£i] [ear—t9 — 69 ]+1] (1.35) 21 212 t J2cyg J21 The zone profile is fit to the EMG equation by nonlinear regression to extract the regression parameters (A, t9, 09, I). From these parameters, the retention time tr is calculated as t, =tg+r (1.36) and the corresponding retention factor is calculated as k =%0_ (1.37) The method of calculating kinetic rate constants from the EMG model is derived by extrapolation of Giddings’ work [20,37]. The mass transfer term for slow kinetics in the partition or adsorption mechanism is given by Equation 1.24. By rearrangement, the rate constants are given by 2 kms = 2'20 and ksm = 2k :0 (1.38) ‘1' T The EMG model assumes that all contributions to asymmetric broadening (r) arise from slow kinetics. There are several potential sources of error in this method. First, this method requires that the solute concentration be within the linear region of the isotherm, such that it does not contribute to the asymmetry. Second, any extra-column contributions to asymmetry must be minimized or eliminated. In practice, this is achieved by detection at several points along the chromatographic column and subtraction of the parameters determined at each detector [37]. It is noteworthy that the EMG method does not require a priori 27 A" h‘ I 'H 2176.01 1‘1 1E . I. :ITB-C—GIJT‘I". Cl 13.3.2.3. Gidd B) "1163' Te”=‘:al tree 5" '5. . ‘pnt \ 3""31' fir «- il V "v‘ I‘u '3..~'*- 1, H . . we. hr )- 1... V.-c W a . “tan 0. "8-. _ . -~ . ‘3‘ Q t ‘9 0 tr ‘." . diff-3"" w [b " l‘ t..- :::§ 'n, '. Ge Blc.f‘l I» F d C N m. a ‘h‘ I. 'Ilu ‘1 Y‘ " .CmeA Iv estimation, whether by theoretical or empirical means, of symmetric column or extra-column contributions to broadening. 1.3.3.2.3. Giddings model By means of stochastic theory [20], Giddings derived a model suitable for theoretical treatment of the adsorption mechanism under first-order or pseudo- first-order conditions C(x) = A7 ,M 11(2IJR) exp(—yx — yk) (1.39) where I1 is a modified Bessel function of the first kind, and y is a dimensionless constant, equal to the product of the desorption rate constant (km) and the elution time of a non-retained compound (to). After conversion from the time domain (t) to the retention factor domain (x), the zone profile is fit by nonlinear regression to Equation 1.39. From the regression parameters (A, k, y), the corresponding retention factor and rate constants are calculated. The Giddings model assumes that all contributions to symmetric and asymmetric broadening arise from slow kinetics. There are several potential sources of error in this method. First, this method requires that the solute concentration be within the linear region of the isotherm, such that it does not contribute to the broadening. Second, this method requires that column contributions from multiple paths and diffusion in the mobile and stationary phases be negligible. Moreover, any extra-column contributions, including those from the injector, detector, connectors, etc., must also be negligible. Unlike the 28 1139-1 and . .AAA AA” "H' . 3" .——, ‘1 ...‘...-.~ 1. u‘... 13.3.2.4. Nonllnl All of l' ‘,;'~".."-.H2M- ll ltd! .U ‘HC ppppp “I : A > . Kc, ‘-_'n - : q ‘i N d'ln V c. a 5- m. " .. “-3 : L’:. H. J1 3‘. ‘ a.- a plate height and EMG methods, there is no a posteriori method to correct for these contributions. 1.3.3.2.4. Nonlinear chromatography models All of the impulse methods described above are suitable for thermodynamic and kinetic measurements within the linear region of the isotherm. However, some mechanisms such as adsorption have stationary phases with a limited number of sites that may be easily overloaded. Hence, it is desirable to be able to evaluate their behavior under nonlinear conditions. A convenient method to extract thermodynamic and kinetic information from frontal profiles was reported by Thomas [38] and later modified for elution zone profiles by Wade et al. [39]. This model was derived for mechanisms that can be considered as second-order sorption and first-order desorption reactions (Equation 1.2) under linear and nonlinear conditions. This theoretical model is given by _ ._A‘Y_ — — (Ml1(27\/1&))9Xp(-YX -Yk) C(x) ’ (Koo ] (1 exp( YKCO D 1- T(yk,yx)(1— exp(—yKCO )) (1'40) where T(u,v)=e‘Vje-‘IO(W)dt (1.41) 0 and lo and I1 are modified Bessel functions of the first kind and Co is the initial concentration. After conversion from the time domain (t) to the retention factor domain (x), the zone profile is fit by nonlinear regression to Equation 1.40. From 29 re regression pa- “ ”"1""fi Hrrx n‘ "j ‘51 u 9' '98.. separate". 1 ca .31 (l3 93 relental s "5235 a“c' the '5 ‘s..~u\ 3.5:"‘a". q'n ' I )- 356 7-3133 these I 3‘? ". ul I .: :vr‘e Uh. ‘ 33.12"». ... .9? meofifir‘. ‘ [U‘lu 01%? WON -.=.~: . *9 710"; b a. , ‘9‘ (Ia . ._; ash up :5 or 2.; the regression parameters (A, k, y, KCo), the corresponding retention factor and rate constants are obtained. The Thomas model assumes that all contributions to symmetric and asymmetric broadening arise from nonlinear isotherms and slow kinetics, which is a combination of mass transfer and sorption/desorption processes. There are several potential sources of error in this method. First, this method assumes the kinetics and the isotherm to be Langmuirian. Second, this method requires that column contributions from multiple paths and diffusion in the mobile and stationary phases be negligible. Moreover, any extra-column contributions, including those from the injector, detector, connectors, etc., must also be negligible. Unlike the statistical moment and EMG methods, there is no a posteriori method to correct for these contributions. Other nonlinear chromatography models have been reviewed by Golshan- Shirazi and Guiochon [40,41]. Among those that provide both thermodynamic and kinetic information are the reaction-dispersive and transport-dispersive models. The reaction—dispersive model presumes that sorption/desorption kinetics are slow relative to the fast kinetics of mass transfer. The transport- dispersive model presumes that mass transfer kinetics are slow relative to the fast kinetics of sorption/desorption. These simplifications allow numerical solution of the general rate model for comparison of theoretical and experimental zone profiles. 30 1.4. Previous ir Although a . ha y Q"F“n 0 fl ‘ , K I (1‘ UOVi I.” 4 a I ‘ 1:="‘A VUVU to 388C; 5. .'= 'JiPer‘t, H v] we 3:8 u ‘.l Q ”\vv‘IQfl ' Dy ~:. .‘ “‘u a .131 [43 , 1.4. Previous investigations Although a wide range of stationary phases are available, the vast majority of reversed-phase separations are performed with alkyl-bonded silica phases. These phases are based on dispersion (London) forces [9], the most universal of all interactions, and hence are broadly applicable. Although many studies have added insight and attempted to definitively characterize the retention mechanism, many questions and controversies still remain. The following section serves to review the thermodynamic and kinetic studies that have provided a better understanding of the underlying processes of retention in regards to the properties of the alkyl-bonded phase and support, properties of the mobile phase, and solute structure and concentration [19]. 1.4.1. Fundamental studies of the retention mechanism For many years, there has been a lively debate concerning the retention mechanism in reversed-phase liquid chromatography. Many models have been developed to describe the retention mechanism, some of which are directly and others indirectly based on thermodynamic concepts. Models that are directly based on thermodynamics include the general solution or solubility parameter model reviewed by Tijssen et al. [42] and the solvophobic model developed by Horvath et al. [43,44]. Models that are indirectly based on thermodynamics include the lattice models developed by Martire and Boehm [45] and by Dill [46]. Classification of the retention mechanism as partition or adsorption is one of the most important issues in RPLC. A theoretical perspective was provided by Dill [46], who developed lattice models for both the partition and adsorption 31 13315153115. In 213316 ueCertyo rested USI'TQ s ""9 of the sol; I‘LSC' l'n'e'a"? A '1‘ vs V .m'AOA . TM ”that one 75” 33131?) Q4 rated end and 3‘31. As the b 5.1.... , J:‘C"ec to def V :1. “hate! Y 81 . 5‘3“?“ 'a’lt meC" ('5‘. F. I .. \Xplell’lmoh’ cWe .55: a In P“ C0713. ‘F '52., .. ‘ ‘1'Nv’ehzg i'vqps V l.._ '53“ c ‘ Uhe.q‘.r a: of a mechanisms. In both mechanisms, the surface consisted only of alkyl chains and the underlying silica support was not considered. Solute retention was predicted using simple, thermodynamically related parameters: the entropy of mixing of the solute, the configurational entropy of the bonded chain, and the contact interactions of the solute with the solvent and bonded chain. This model predicted that the extent of partitioning becomes more important with increasing chain length. Solute molecules have the lowest concentration near the proximal or bound end and the highest concentration near the distal or free end of the chain. As the bonding density increases and space between the chains becomes more restricted, adsorption becomes more important. In fact, partition is predicted to decrease to zero as the chains reach their maximum density of approximately 8.1 pmollmz. However under most typical conditions, the predominant mechanism for long-chain alkylsilicas, particularly octadecylsilica, is likely to be partition or partition-like in nature. Experimental studies have also been used to examine the partition and adsorption mechanisms In reversed-phase liquid chromatography. In a study by Tan and Carr [47], liquid-liquid extraction was used as a model of a true partition system and compared with monomeric octylsilica and octadecylsilica phases. The alkylbenzenes were used as model solutes in order to determine the change in free energy of a methylene group (AAG) in each system. The ratio of the change in free energy of a methylene group for transfer from the mobile phase to bulk hexadecane to that for transfer from the mobile phase to the stationary phase was calculated. Values of this ratio that are close to unity denote a 32 M1 meshes 5 met. phase ch; I35 dose to up '3, 551131 70 is .‘r :éts3'fsf'ateo the ‘55 C'\'3"i~"?ie: ~33" r A 91 81 1‘15 ~‘- ;F}~\F’ C Np C 1v- as .A \Q ' 9 3.98 VJQ'F 433.: - N “as 9': VI 83333”), .;- 5m” .3.~ ”13:1“ 1 J ‘ (oi the \ kl \ :' 3'3 '33., ‘:v Q C S! \ 7‘ . ‘.:): "' Eemnn '.‘Jr 3‘ ‘ L 5'5'57‘39» '1. a C x. 1 3,. partition mechanism, where the methylene group can be fully embedded in the bonded phase chain. For both octylsilica and octadecylsilica, the observed ratio was close to unity when the concentration of methanol in the mobile phase was less than 70 °/o, indicating a partition-like mechanism. Tan and Carr [47] further demonstrated that shorter chains have larger ratios ranging from 2.2 to 1.5 for methylsilica to hexylsilica, indicative of a more adsorption-like mechanism. Moreover, phases with a low bonding density of 0.6 pmol/m2 have significantly higher AAG ratios of 1.8 to 2.0, while those with higher bonding densities of 1.4 and 2.3 pimol/m2 have smaller and approximately equal ratios of 1.3. These results confirmed the predictions of the lattice model of Dill [46]. Later studies by Park et al. [48] examined polymeric phases ranging from methylsilica to octadecylsilica. The ratios were closer to unity for polymeric phases than for the corresponding monomeric phases. This implies that polymeric phases act more like bulk hexadecane and exhibit a more partition-like mechanism than do monomeric phases. For all stationary phases examined in these studies, larger AAG ratios were observed when the concentration of methanol in the mobile phase was greater than 70 %. The authors suggested that this did not necessarily imply that adsorption was dominant under these conditions but, instead, that the structure of the bonded phase may be different or that methanol may be more soluble in the stationary phase at higher concentrations. These studies demonstrate that the retention of a nonpolar solute with both monomeric and polymeric alkylsilica phases is more similar to a partition-like mechanism than an adsorption-like mechanism. 33 The driving ‘ 21 arse from he statuary/phase. ' usea' on the gee rage in free eee T1::zéulzl'iase. Tn matron of a 53”. L‘s 13.": der ‘v‘l’aais 3'9; This m 3‘9] ’- 3:139. 1101161 6 The driving force for the separation is an important issue in RPLC, as it can arise from interactions of the solute with the mobile phase and/or with the stationary phase. The solvophobic model developed by Horvath et al. [43,44] is based on the general concept that the predominant contribution to the net change in free energy of retention arises from processes taking place in the mobile phase. The model includes changes in free energy arising from the formation of a cavity in the solvent, the reduction in free volume of the solute, and the van der Waals and electrostatic interactions between the solute and solvent [49]. This model has been very successful in predicting trends in retention, particularly those upon a change in mobile phase composition and solute structure. However, this view was challenged in a critical study by Carr et al. [50], which demonstrated that interactions with the stationary phase contribute more greatly to the free energy of retention than was previously thought. In order to separate the mobile and stationary phase contributions, partition coefficients for solute transfer were measured from the gas phase to water (as a model of the mobile phase), and from the gas phase to hexadecane (as a partition model of the stationary phase). The partition coefficients to water were relatively small and decreased with increasing chain length of the alkylbenzene. In contrast, the partition coefficients to hexadecane were substantially larger and increased with increasing chain length. The corresponding changes in molar free energy, calculated from Equation 1.5, exhibited similar trends. The average free energy for transfer of a methylene group was 0.67 kJ/mol from gas phase to water, -2.53 kJ/mol from gas phase to hexadecane, and -3.20 kJ/mol from water to 34 Iexac'euate. tease are 55' :ase aid: 5“ TIT- S ‘1‘: :e-‘ge h in ,,e shes gc§hfl :. .3331'115 ‘ n- 1” R «6 d- \ H H\- .5.- ‘ . ‘:E l“ ‘h 1]) hexadecane. Thus, the attractive interactions of the solute with the stationary phase are significantly greater than the repulsive interactions with the mobile phase and, hence, constitute the predominant contribution to their retention. This work was extended by Ranatunga and Carr [51], who determined the change in free energy for transfer of a methylene group as a function of the mobile phase composition. For all mobile phases examined (40 to 100 "/0 methanol-water and acetonitrile-water), the changes in molar free energy were positive. In other words, the transfer of alkylbenzenes from the organic mobile phase to the gas phase was an energetically unfavorable event. The contributions of molar enthalpy were unfavorable and slightly greater than the favorable changes in molar entropy. In all cases, however, the mobile phase contributions were significantly less than the stationary phase contributions. These studies conclusively demonstrate the predominant role of the stationary phase in the retention mechanism of reversed-phase liquid chromatography. 1.4.2. Effect of alkyl chain length and bonding density Many studies have been performed to elucidate the role of the bonded phase in the retention process. Some of these studies have focused on discerning the effect of alkyl chain length and bonding density, whereas others have examined the effect of the synthetic method. Krstulovic et al. [52] examined a series of silica bonded phases with alkyl chain lengths varying from 1 to 18. With increasing chain length, a small but systematic increase in the logarithm of selectivity (a = k2/k1) for a homologous series of alkylbenzenes was observed in both methanol-water and acetonitrile- 35 late hob'le phase: mic-.19 extractc :5 311,1 chain 33' :7.cec more deta oi the at; $5331? WOITIOIOCQUS U fume nuhoer Sieve-c oer-ween. s 5956 "1‘ M w between ‘ “2‘53 that us use. 1 q. 75 3011.59 “58 SUM ‘ “105mg“. V' V‘ TE‘M-e . - . 3.1..6 ~le the c 5‘. I . C. 3' We 51810113 i‘“! A} ”‘5 '.:" r . ' “he $01719 _ «‘5» CC :1: A 'Q U u.) ,' .. e EXa~ .4 '.::zfl‘l‘ds ' £3 17".. I :ZM‘F. :VLS SC? 2 . «s 13‘“ ‘:: .I‘H ":Lrs'l' water mobile phases. This effect, which was not observed in similar studies of liquid-liquid extraction (partition), was attributed to the more ordered structure of the allql chain after it was immobilized on the silica support. Tchapla et al. [53] provided more detailed measurements of retention factor and selectivity as a function of the alkyl chain length. They found that the methylene selectivity for several homologous series decreased in a stepwise manner near a critical value of carbon number for each particular stationary phase. The decrease was observed between solutes with 4 and 8 carbons for a hexylsilica phase, yet was observed between 12 and 18 carbons for an octadecylsilica phase. The authors noted that this decrease in selectivity occurred when the length of the alkyl chain of the solute was equal to or exceeded that of the stationary phase. This seemed to suggest that the partition mechanism involves a vertical penetration of the solute into the stationary phase. When the solute carbon number is less than that of the stationary phase, all carbon atoms are able to intercalate and interact directly with the corresponding carbon atoms of the stationary phase. However, when the solute carbon number is greater, the remaining carbon atoms cannot enter the stationary phase and, thus, undergo weaker dispersive interactions. Hence, solutes with carbon number greater than the chain length of the stationary phase are less retained and exhibit lower selectivity. Tchapla et al. [54] further examined the temperature dependence of butadecylsilica and octadecylsilica phases. The van’t Hoff plots showed linear behavior for all homologous series under all conditions in the temperature range of 298 to 338 K. Extrapolation of the data from the van’t Hoff plot showed two convergent points 36 rl~i-.pr12- ‘I “flaw-Me.“ fl $9599.11: l ‘u- up\h-J' ‘O'AA-Afib ’ iv- vJ~UU ‘.‘FF‘A’d ‘va I v" ;-.."n "a - ’ '5... a ' flfi-g‘ 55-4. - u ,‘ $.55“ ‘v .'~ D u - A... c! ,A . u ('5'; :‘1 u" 3“ O A \ [J‘- ‘Vi'l CPI—t J :2 k H _~.~‘ ' 2_:-:' C. 5 ‘v A. -'.._‘. . ‘i A“. 'v . b {'1 x. 5 ‘ . (.u-C‘h I U 7» b. ‘\ 21". ’v d‘ u where the critical value for all homologous series was observed at carbon number 12 - 13 for the butadecylsilica phase, and carbon number 14 — 15 for the octadecylsilica phase. From these plots, the change in molar enthalpy decreased while the change in molar entropy increased with increasing solute carbon number in the homologous series. However, a discontinuity was observed in each plot at the same critical carbon numbers cited above. All of these trends were viewed to be consistent with the previous explanation of vertical insertion of the solute into the stationary phase, where changes in both enthalpy and entropy were altered at the critical carbon number. These studies suggest a consistency in the retention mechanism of alkylsilica stationary phases. Miyabe and Guiochon [55] studied the kinetic properties of silica bonded phases with alkyl chain lengths ranging from 1 to 18 carbons. By using the plate height model, they determined the intraparticle diffusion (Equation 1.31) and the components of pore diffusion and surface diffusion for homologous alkylbenzenes. From the measured values of the surface diffusion coefficient, they calculated a hypothetical surface diffusion coefficient normalized for the carbon content of the stationary phase. A simple model was derived that permitted estimation of surface diffusion coefficients under different experimental conditions with an accuracy of approximately i 20 %. These results confirm that the kinetic behavior arising from surface diffusion was similar for alkylsilica materials with varying alkyl chain length. 37 The 0030’ Tet sol Cflical 1r seamed the pa vases 11 th ooh (_) 22.) 8 (D ' 11 C ) (I) 7.2:: {a . v. 31 U III {JR‘ ‘VI 3' 2' "1‘9 36‘s Ty. 47:3: QIWate') 2:":- 073 art 217-'03:“ Se: The bonding density of alkylsilica stationary phases is another parameter that is of critical importance to the retention mechanism. Sentell and Dorsey [56] examined the partition coefficient for a series of monomeric octadecylsilica phases with bonding densities of 1.6 to 4.1 pmoI/mz. They found that the partition coefficient increased linearly with bonding density up to 3.1 pmol/mz, whereafter it began to decrease. This trend was observed for a variety of aromatic solutes (ethylbenzene, biphenyl, p-terphenyl, naphthalene), mobile phases (methanol-water and acetonitrile-water), and temperatures (298 to 313 K). In the low density region (< 3.1 pmol/mz), the alkyl chain order or packing structure had little effect on solute retention, whereas in the high density region (> 3.1 pmol/mz), the chain packing was constrained and interfered with the solute partitioning into the phase. These results confirmed the prediction of the lattice model of Dill [46], as discussed previously. Sentell and Dorsey [57] subsequently compared the selectivity of monomeric octadecylsilica phases as a function of bonding density. When the mobile phase composition was held constant (55 % methanol-water), all changes in selectivity were attributed to free energy contributions arising from solute interactions with the stationary phase. For a homologous series of alkylbenzenes, the methylene selectivity was nearly constant at 1.96 i 0.03 for all bonding densities from 1.74 to 4.07 pmol/mz. However, for a homologous series of polycyclic aromatic hydrocarbons (PAHs), the phenyl selectivity increased in an approximately linear manner from 7.05 to 8.18 with increasing bonding density. This increase was attributed to an increase in shape selectivity for the solutes (benzene, biphenyl, and p-terphenyl) as the 38 twang dehsty ll'lC use oosewatohs. fee-.11 ahhetat or set) and hop; uPAhs. The s "31:557ar PAHs p 53"36' 31d ‘r'l'se 3173911 1] 01 [El'a'g ‘Z‘IIE‘.'9r [OT 00". 357-33353 10 1 5:- JEA'Q :3 .6 Of DO” 350's n' . v “e. .. d 35’: by Cc. ‘.I. '..‘ ”‘H’t v’ [ P V 5. ‘ ' 9918: \‘_ 7 .--£ . on . '7' .hc. V bonding density increased and the alkyl chains became more ordered. Based on these observations, selectivity was determined for a series of four-ring PAHs with different annelation structure. A distinct correlation was observed between selectivity and bonding density that was related to the length-to-breadth ratio of the PAHs. The selectivity was also determined for the series of planar and nonplanar PAHs previously identified for stationary phase characterization by Sander and Wise [58]. For bonding densities from 1.74 to 3.56 pmol/mz, the selectivity of tetrabenzonaphthalene and benzo[a]pyrene was approximately 1.7. However for bonding densities of 3.60 and 4.07 pmol/mz, the selectivity decreased to 1.56 and 1.63, respectively. Concurrently, a change in elution order was observed for benzo[a]pyrene and phenanthro[3,4-c]phenanthrene, indicative of a significant change in the stationary phase structure. The authors suggested that the shape selectivity observed for these monomeric octadecylsilica phases could be due to ordering of the alkyl chains rather than the degree of polymerization or thickness of the stationary phase. More detailed thermodynamic studies of the effect of bonding density were performed by Cole and Dorsey [59] using alkylbenzenes, nitroalkanes, and small PAHs as model solutes. The van’t Hoff plots were linear for all solutes on monomeric octadecylsilica phases with bonding densities of 1.60 and 2.84 umol/mz. On these phases, the change in molar enthalpy for benzene was —3.07 and -2.19 kcal/mol, respectively, and the change in molar entropy for benzene was -6.36 and -2.61 cal/mol K, respectively. Phases with bonding densities of 3.06 to 4.07 umol/m2 were also examined, however linear van’t Hoff plots were 39 u asserted owe :e‘sh hereased ‘Angg ‘ .,,,_ ‘C- 1" I “v at of t." l ’ a p,‘ 9 1.413868- T :5 n1 . 2 L""IQIFI'] T I? “in , -":S: ‘y’ r‘ a‘ :31”. (r "éTCara . V“ "g" 2:1-3.3:” a NO 5. .‘A H. ‘ .5: ”5 U;, Event 8 not observed over the temperature range from 273 to 358 K. As the bonding density increased, both AH and AS became less negative. This suggested that the entropic contribution became more significant than the enthalpic contribution as the bonding density increased. The chromatographic values for AH and AS were compared to thermodynamic values for dissolution of liquid benzene in water reported by Gill and Wadso (AH = 0.497 kcal/mol, AS = —13.8 cal/mol K at 298 K) [60]. Here, AH and AS represent the transfer from the nonpolar environment (benzene) to the polar environment (water), so the sign should be opposite that of the chromatographic system. When this was considered, Cole and Dorsey concluded that the thermodynamic values obtained for the chromatographic system were similar to those for dissolution. Other investigators have examined the effect of the synthetic method by which the alkylsilica stationary phase is prepared. Rimmer et al. [61] synthesized a series of bonded phases, tridecylsilica to octadecylsilica, using monomeric, solution polymerized, and surface polymerized methods on the same silica support. Each alkyl chain length was synthesized by each method to yield 20 different phases. The monomeric phases had similar bonding densities of 1.19 to 3.64 pmol/mz. The solution polymerized phases had slightly higher bonding densities of 4.21 to 5.92 umol/mz. The surface polymerized phases had the greatest variation in bonding density from 1.90 to 7.97 pmol/mz. The phases were compared with respect to methylene selectivity, shape selectivity, and band broadening. No significant chromatographic differences were found to result from the different synthetic routes, other than the changes in bonding density 40 Ani-A h ll '::...I.";9d asore 2.1.:enzenes. we zest). In contra 25755591! from I. 2.54 in 501.1 oe- esoe n reign: nu \ N1 .4 ‘1',“ . Inn-‘7‘ 'H 5..‘ . 4: ‘.:-9n, ‘V‘y of PA.r 1‘ . , . "'V'i‘fiar; d ' y C D ‘0. I ‘2‘,“13‘PQ‘ . tuttf'cc" v.', 3‘ . 33513., mentioned above. The methylene selectivity, measured with homologous alkylbenzenes, was observed to increase slightly from 1.28 to 1.71 with bonding density. In contrast, selectivity for tetrabenzonaphthalene and benzo[a]pyrene decreased from 1.67 for a monomeric heptadecylsilica phase (3.56 pmol/mz), to 0.64 for a solution-polymerized heptadecylsilica phase (5.50 umol/mz), to 0.19 for a surface-polymerized heptadecylsilica phase (7.28 pmol/mz). The concomitant inversion in retention order indicated a significant change in the stationary phase structure. To further understand the influence of the synthetic method, Jinno et al. [62] examined the temperature dependence of monomeric octadecylsilica, monomeric octadecylsilica with endcapping, polymeric octadecylsilica, and diphenylsilica phases. The van’t Hoff plots for PAHs on the monomeric octadecylsilica phases and the diphenylsilica phase were linear in the temperature range from 298 to 473 K, yet showed very high curvature on the polymeric phases. The selectivity was calculated for each solute pair at each temperature on each of the stationary phases. The authors concluded that polymeric phases were more capable of discriminating the planar/nonplanar character of PAHs than monomeric phases. This distinction was more marked with polymeric phases synthesized from trichlorosilanes than those synthesized from dichlorosilanes. This selectivity decreased with temperature, with a critical point between 313 and 333 K, which coincided with the temperature range where a phase transition was proposed to occur. 41 The 0 TE ,4- 'A‘I " Jr. Abe OI Ink ..|\ «S A\‘ u." I‘- . +9.33“ ' u .. i. :02. “' v as U 5‘- The occurrence of a phase transition has frequently been proposed for alkylsilica phases, particularly those with long alkyl chains, high bonding density, and polymeric synthesis method. Wheeler et al. [63] reviewed the published literature in this area derived from calorimetric, spectroscopic, and chromatographic studies. The primary chromatographic evidence of a phase transition has been the nonlinear nature of van’t Hoff plots. Nonlinearity suggests that the change in molar enthalpy is not constant with temperature and, hence, that the heat capacity at constant pressure (ACp = (a AH/a T)p) is also not constant [64]. A change in heat capacity is the clearest indication of a phase transition. Morel and Serpinet [65-67] directly confirmed this conclusion using differential scanning calorimetry and NMR spectroscopy. The transition temperature was observed to increase with the length and density of the alkyl chains bonded to the silica surface. By using adiabatic calorimetry, Van Miltenburg and Hammers [68] demonstrated that the phase transition is actually second order and extends over a broad temperature range from 70 to 310 K for octylsilica and from 150 to 305 K for octadecylsilica phases. This second-order phase transition is viewed as an order-disorder transition, rather than a traditional solid-liquid or melting transition. An ordered alkyl chain consists of all trans carbon-carbon bonds and the degree of disorder is indicated by the number and position of gauche bonds. The ordered state, in which the contact area between adjacent alkyl chains is maximized, is enthalpically preferred but entropically unfavored. In contrast, the highly disordered state, in which the chains have a great conformational diversity with many gauche bonds, is entropically preferred 42 :tt entealpicai‘. regressrrely, be ssemsccpy in. - tie Qegn p's: :e y: mal e reach: eg r 751‘ at he eat-re MSG if? '1 (fl but enthalpically unfavored. The phase transition is thought to occur progressively, beginning at the distal or free end of the alkyl chain then gradually prevailing to the proximal or bound end. Sander et al. [69] confirmed by FTIR spectroscopy that the bonded alkyl chains contain several gauche bonds at 317 K, with high probability of occurrence at the distal end and very low probability at the proximal end. The degree of disorder is comparable to that of the corresponding n-alkane coated in a thin film on the silica surface, but less than that of the n-alkane in bulk solution. McGuffin and Lee [70] compared the thermodynamic and kinetic behavior of a polymeric octadecylsilica phase (5.4 umoI/mz) in the vicinity of the transition temperature (318 K). The retention factors for a homologous series of fatty acids (C10 to C22) increased systematically with carbon number by approximately two orders of magnitude. The retention factors for C10 to C22 decreased by 84.4 to 99.6 %, respectively, as temperature was increased from 293 to 333 K. Hence, the phase transition had a significant effect on thermodynamic behavior. The increase in retention factor with carbon number was accompanied by changes in the rate constant for transfer from mobile to stationary phase by approximately one order of magnitude and the rate constant for transfer from stationary to mobile phase by approximately three orders of magnitude. Hence, the transition from stationary to mobile phase seemed to have the greatest effect on kinetic behavior. The characteristic time (t = 1/(kms + ksm)) increased with carbon number for C10 to C13 fatty acids, but remained relatively constant thereafter. This. is consistent with the mechanism described by Tchapla et al. [53,54], 43 iee'eie the solute :ae‘tm number g 333% into the :seze'a‘ale to hr in SubSBC'. Eager of PAH :c‘ezecylsica or 35538 We gen. tease. However *5? geee'afly sr :‘eg “WC-ZS. it v, .4. C1 N " HE" M for 1 -;‘!*I "5" A“ so 333% «.e ll 'ate ‘5‘». n .S’Ld s V Ix C "‘35: ' Ste'fiali l“ 'i‘Jg‘a vulucfi y. “u 'i 'r “468: .~. “Va-('14 ‘ “S 818 31;, wherein the solutes insert vertically in the stationary phase. Hence, solutes with carbon number greater than that of the stationary phase (C18) inserted the same distance into the stationary phase and had comparable kinetic behavior. Above the transition temperature, the rate constants increased significantly and were comparable to those for monomeric octadecylsilica phases. In subsequent studies, Howerton and McGuffin [37] compared the kinetic behavior of PAHs on monomeric (2.7 pmol/mz) and polymeric (5.4 umol/mz) octadecylsilica phases. The rate constants for transfer from mobile to stationary phase were generally larger for the polymeric phase than for the monomeric phase. However, the rate constants for transfer from stationary to mobile phase were generally smaller for the polymeric phase than for the monomeric phase. In other words, it was faster and more facile for solutes to enter, but slower and more difficult for them to exit the polymeric stationary phases with higher bonding density. All solutes on both monomeric and polymeric phases showed a decrease in rate constants as the retention factor was increased. Finally, a number of studies have examined the effect of other synthetic methods that modify the stationary phase structure. Vervoort et al. [71] compared six different octadecylsilica stationary phases, including polymeric phases, sterically protected phases, phases with bidentate bonded alkyl chains and embedded polar groups, as well as those synthesized with high-purity silica. Based on linear van’t Hoff plots, it was concluded that basic pharmaceutical compounds showed no change in retention mechanism over the temperature range from 280 to 360 K. The degree to which each compound interacted with 44 . - v. - Ii .5 w «L, ”d a e _iu. . Ab ., . U G» t... r .t. r nay q H. N uv 7.5 r it 'B.: «AW ,3; A v A_v 9 s a w aw» Q. . e a .. .3 A 3 5.. iiiii fit a. 3. .3 A" . _ F A~d .N i J RAJ Q a M b I u . av. nay tn, . .3 M: .3 . I... a . u . Mu. mi; . e mi ~ .. z. u... ~ w a . i. t... I \I ’ ~.\t - u _U .\u the stationary phase depended on the stationary phase properties. For example, neutral compounds (benzene, phenol) showed similar AH values on each stationary phase, whereas the more basic compounds (nortriptyline) showed more negative AH and AS values on the polar embedded phases and those synthesized with high-purity silica. Neue et al. [72,73] classified these various octadecylsilica materials using graphs of In k1 versus ln kg and graphs of In (11 versus In (12 where 1 and 2 correspond to two different stationary phases. This idea was previously introduced by Vailaya and Horvath [74]. Layne [75] has similarly compared conventional, polar-embedded, and polar-endcapped octadecylsilica phases by using various selectivity values for nonpolar, polar, and hydrogen-bonding solutes. These studies illustrated the importance of the synthetic method and the incorporation of polar groups, particularly for the separation of acidic and basic solutes. 1.4.3. Effect of support The underlying solid support also has a very significant influence on retention in reversed-phase separations. As noted in the previously-discussed studies, the most common support material is silica. Sander and Wise [76] compared bonded phases prepared on 22 silica materials with differing particle shape, diameter, density, surface area, and pore diameter. They observed large variations in bonding density on the silica materials when performed under the same synthetic conditions, 1.26 to 2.78 umol/m2 for monomeric octadecylsilica phases and 2.57 to 5.35 pmol/m2 for polymeric octadecylsilica phases. Two parameters were found to have the greatest influence: pore diameter and silica 45 :eteatnent wit"- ?llls we most siaeale the rete we‘re. of tetr 7.33. The att'ec fest often we; M :a ptases in add for size and ts det' tSec-eeieal st; 33:53? 00 the r 33‘56 5} a me: it? :ec'easec' a: “g The Co pretreatment with acid or base. Differences in retention factor and selectivity of PAHs were most pronounced for these parameters on the polymeric phases. For example, the retention factor of benzo[a]pyrene varied from 1.56 to 13.60 and the selectivity of tetrabenzonaphthalene and benzo[a]pyrene varied from 0.62 to 1.33. The authors concluded that the underlying silica substrate has a great effect, often unpredictable and uncontrollable, on retention and selectivity of alkylsilica phases. In addition, much attention has been drawn to the adsorptive nature of silica and its detrimental effect on the partition mechanism of alkylsilica phases. In a seminal study, Nahum and Horvath [77] examined the effect of the silica surface on the retention factor and change in molar enthalpy for dibenzo—18- crown-6 in a methanol mobile phase. The retention factor was greatest on silica and decreased progressively on octadecylsilica with 5 % and 12 % carbon loading. The corresponding changes in molar enthalpy were determined to be -8.797, -8.433, and -7.356 kcal/mol, respectively. If partition was the predominant mechanism here, then retention and molar enthalpy should increase with carbon loading. However, if adsorption was dominant, then the phase with the highest carbon loading should have the lowest concentration of residual adsorptive sites and, thus, the smallest effect of these sites on retention. Hence, the retention of hydrogen bonding solutes such as the crown ethers was shown to be largely controlled by the underlying silica support, even with high carbon loading of the bonded phase. In a two-part review by Nawrocki [5,6], the nature 46 tee sic mousse ar A9nn .5 ~U 3.33278 8. “.0. c— F ‘.:, ““I'H-J . pi i' ha .‘ ‘55:». , d ‘VU r U & ~§ Flaw“ . c. "‘V. .‘l N! l a g”..~= ‘ u. g. $.15. -... V “I. .. . J M u q , ~ ' . u! D“ ‘Q ‘ ‘VJ!‘:R f: 'b‘k‘ c r‘F- .h’~§ 5‘ c : p ‘H u 1 ‘ c- . I in- \- V 2 E: 7' “r- - ng .: ‘ Q .j»;. »‘ h...- L C -‘F uh.- ‘. g" ‘v . F of the silica adsorption sites was discussed and several methods for their blockage and removal were reviewed and compared. Although the most common underlying support is silica, many other supports such as zirconia, titania, and synthetic polymers have been used. Zirconia supports are more stable than silica supports, and can handle extremes of pH and temperature that silica cannot. However, complete coverage of the surface is essential to avoid deleterious adsorption. Li and Carr [78,79] have performed a number of studies on Zirconia-based reversed-phase systems. Changes in molar enthalpy were determined for alkylbenzenes on polybutadiene- coated (PBD) Zirconia in a temperature range of 313 to 373 K. The values ranged from -2.07 to -4.00 kcal/mol for benzene to n-pentylbenzene, respectively, and are similar to those reported for octadecylsilica phases. The enthalpy of transfer of a methylene group for the PBD-zirconia phase (-0.39 kcal/mol) was comparable to those for octadecylsilica phases (-0.27 and -0.41 kcal/mol) as well. In fact, the hydrophobic selectivity of the PBD-zirconia was found to be comparable to conventional bonded phases [78]. A temperature study by Guillarme et al. [80] compared the thermodynamic behavior of octadecyl- and PBD-zirconia with octadecylsilica phases. Over a limited temperature range of 298 to 353 K, the van’t Hoff plots were linear for alkylbenzenes and other solutes on all phases. Over a wider temperature range of 298 to 473 K, however, distinct differences were observed. Typical silica- based phases showed linear van’t Hoff plots for both methanol-water and acetonitrile-water mobile phases. However, slight curvature in the van’t Hoff 47 nth. ‘ 20‘s was ocser late mobile or 'ate' meste pr. lee eet Cue to :tscue the true 'c-re ceta'ied 31%] [81]. plots was observed for Zirconia-based phases with pure water and acetonitrile- water mobile phases, while a linear relationship was observed with methanol- water mobile phases. The authors demonstrated that the curved van’t Hoff plots were not due to changes in the system pressure with temperature, which could obscure the true temperature dependence of retention. A confirming study with more detailed thermodynamic measurements was performed by Coym and Dorsey [81]. They observed curvature in the van’t Hoff plots for nonpolar aromatic solutes on PBD-zirconia using a pure water mobile phase. From these plots, the changes in molar enthalpy were found to be significantly more negative (exothermic) at high temperature than at low temperature. For example, the change in molar enthalpy for toluene was reported to be -5.7 kJ/mol in the temperature range of 288 to 328 K and -31.3 kJ/mol in the temperature range of 398 to 448 K. The authors attributed the differences in molar enthalpy to a change in the hydrogen-bonding network in water that influences the solvation of the solute. In spite of this large difference in molar enthalpy, the retention factors were significantly smaller in the high temperature range than in the low temperature range. Organic-inorganic hybrid supports have seen increasing use in the past several years. While the hybrid phase has been employed in numerous experiments, only a few studies have made an effort to provide a thermodynamic characterization of the material [82,83] and kinetic characterization has not been reported. A thermodynamic evaluation of a C13 hybrid phase was performed as a function of temperature from 423 to 473 K in an aqueous mobile phase using 48 . I ' r-I-‘Afiaf‘ ’3' a I‘ ' i‘ . ”flute _ I eghn3 4 (l’ (I) --h alkyl benzenes and aromatic alcohols [82] and substituted anilines [83]. Linear van’t Hoff plots were obtained and negative changes in molar enthalpy were reported for all solutes. Further investigation of toluene at a wider temperature range from 303 to 473 K yielded a change in slope of the van’t Hoff plot near 370 K. Solid state NMR of the dry stationary phase indicated that no change in the stationary phase structure occurred [82]. However, the change in slope in the low temperature region (AH = -17.6 kJ/mol) was half that of the slope in the high temperature region (AH = -33.5 kcal/mol). This observation was similar to that seen by Coym and Dorsey [81] with PBD-zirconia, where the difference was attributed to a change in the hydrogen-bonding network with temperature. Additional studies have investigated the effect of alkyl chain length on a hybrid support material containing a polar embedded group in the chain. O’Gara et al. [84] investigated the retention of nonpolar, polar, and basic compounds on a series of phases ranging from C8 to C18. Retention increased from C8 to C16 but decreased for the C13 length, similar to silica-based materials. Tailing of the basic compounds was studied as a function of chain length and surface concentration. Tailing was independent of chain length, but decreased with increasing bonding density for a set of C13 phases. These studies suggest that the hybrid material may be quite similar to silica materials. However, a direct comparison of hybrid and silica has not yet been performed. 1 .4.4. Effect of mobile phase composition Whereas the contributions of the alkylsilica stationary phase clearly predominate [50,51], the contributions of the mobile phase also greatly influence 49 l V {-3. \iUU~\- a an." .i [AvU IV D ~ he" to rip AFR?!“ 4" yt' ’5 A ”Mr“ {H .;.hl\ $IW MW ”new Nu~ Mud “V.“ 5 flu .D4 .4 .v\ ~ uhw ”I A v a a A: . . . a: fiJ «L... .3 .1 a v ._ _. l. «S . .v. .6: a... w: 2. ~ .. 2. ~ 3 ‘5... s I. . . .3. P u .Av . w p e . . e a. . u u . P. . . u— u ‘9- .. up. u .HA. “Wu Hunt: - .‘o- usw -. \- a a. u 5’. ..n . e. ._ e. . retention and selectivity of reversed-phase separations. To elucidate these contributions, many investigators have varied the type and composition of the mobile phase to examine changes in the thermodynamic and kinetic behavior. The most common mobile phases in RPLC are aqueous mixtures of methanol, tetrahydrofuran, or acetonitrile. These solvents are chosen to enhance acid, base, or dipole interactions, respectively, and hence can influence the selectivity. To influence the retention, the proportion of water in the mobile phase is varied. The effect of water on retention has been investigated extensively. Grushka et al. [85] studied the effect of water on retention factor, selectivity, and the concomitant changes in molar enthalpy and entropy. As the water content was increased, the retention factors for a series of alkylbenzenes increased and the methylene selectivity increased. The selectivity was found to be more strongly dependent on the mobile phase composition than on the temperature. Values for AH became more negative as the water content increased, ranging from -1.82 to -4.39 kcal/mol in 90 % methanol-water and ranging from -2.06 to -6.21 kcal/mol in 80 % methanol-water for ethylbenzene to dodecylbenzene, respectively. The differential change in molar enthalpy (AAH) per methylene group was determined as -0.267 and -0.405 kcal/mol in 90 % and 80 % methanol-water, respectively. Therefore, it is energetically more favorable for the solute to be in the stationary phase as the water content of the mobile phase is increased. Cole et al. [86] investigated the role of the mobile phase by means of van’t Hoff plots for benzene. When water-rich mobile phases of protic solvents (e.g., 50 QQ'FAP‘I‘ I It. 5‘ UI' 27.193 0t «5* . p «é'fl a v-Iv .U V‘ a4 1" <6 L. (I) (I) 4', ~ v as g v " 5" \1 p.- Q .. ~ g. g. \ fl ‘5 S ' who. I '3" ..;e t ‘.:,‘F a I; .- iv: methanol-water and propanol-water) were used, the van’t Hoff plots were highly curved over the temperature range from 268 to 353 K. The values of AH were positive for temperatures from 268 to 293 K and negative for temperatures from 303 to 353 K. When mobile phases with aprotic solvents (e.g., acetonitrile-water) were used, the van’t Hoff plots were more nearly linear. The authors concluded that the hydrophobic (solvophobic) mechanism may be reasonable for protic solvents, but is not adequate to explain the retention mechanism in other situations. A related mobile phase effect was observed by Sentell et al. [87] through the examination of retention and selectivity for several homologous series consisting of alkylbenzenes, phenylenes, and PAHs. The selectivity changed more with temperature for methanol-water than for acetonitrile-water mobile phases. This was attributed to the hydrogen-bonding capability of the methanol-water mobile phases, which led to a more structured mobile phase. It is noteworthy that the graphs of the logarithm of selectivity versus inverse temperature were linear and the reported values for the differential change in molar enthalpy (AAH) and molar entropy (AAS) per methylene and phenyl groups were negative over all temperature ranges. Sander and Field [88] examined the retention behavior of N,N-diethylaniline and 2-propylbenzene on an octadecylsilica phase over a wide range of methanol-water compositions. The change in molar enthalpy values for both solutes, although all negative, increased with an increase in the methanol concentration. That is, the transfer became less favorable for higher concentrations of methanol. The change in molar entropy for both solutes, although negative, slightly increased with an 51 ‘Mnnn Q" ‘ \ 4 new... .1 ‘3'.- (I) W.- (D r ‘9’ cg. ‘: .u‘ h .‘ a“ t ‘Y‘, I .‘Q h § v I“-\- U ‘ ' ‘1 ~‘ ‘ . ‘0 h g C' « -I r V . ‘0 .‘ x“ q . 9.1 ,. U \ \ ‘vr‘h \‘h .._ . increase in the methanol concentration. The enthalpy term was found to be the predominant contribution to retention. Barman and Martire [89] examined the effect of methanol-water and ethanol-water composition on the retention of a series of alkylbenzenes by using a semi-empirical relationship between the retention volume and the temperature and mobile phase composition. Through graphs of the logarithm of retention volume versus the volume of fraction of water in the mobile phase, the enthalpic contribution was found to be greater and opposite the entropic contribution. That is, as the volume fraction of water was increased, the enthalpic contribution to the retention volume systematically increased, while the entropic contribution systematically decreased for xylenes, ethyltoluenes, and diethylbenzenes. In all cases, the enthalpic term was the predominant contribution to retention. Wu et al. [90] examined the thermodynamic behavior of methanol-water and acetonitrile-water mobile phases as a function of pH. The mobile phase type and composition greatly affected both the retention and selectivity of piperazine diastereomers. The neutral form of the diastereomers is predominant at pH 6.4, whereas the protonated form of the diastereomers is predominant at pH 3.0. At both pH values, the logarithm of the retention factor decreased monotonically with an increase in methanol-water or acetonitrile-water composition. However, the logarithm of the diastereomeric selectivity showed interesting behavior as a function of the mobile phase composition. For methanol-water systems at pH 6.4, the selectivity decreased linearly with composition. For acetonitrile-water systems at pH 3.0 and 6.4 and for methanol-water systems at pH 3.0, the 52 :25: eg tom 2 I A . I , , ‘CCQI at 0"! "acre gees ”‘P‘PSV 135'f . . \. vvl‘v 3.. in“. . "A ""v - '1’ | 7 Id \- 'fia. n.~ .. , my” ‘ ‘G :.\.c_ r "v H I‘."" ‘. l ~3- f‘a Udhq- ""C .C '.A I. ~ .A ' ' au 2.- f‘ v. . U VI 5 . . .A“ s. e Q‘ \- .5. v 1’ . Q N 3'28"“ “'2‘: l-_ I. I ’2 I“ *l 9 h L selectivity initially increased, reached a maximum value, and then decreased with composition. The authors suggested that the retention mechanism is complex, passing from a region that is dominated by selective solvation of the piperazine moiety at low concentration of the organic modifier to a region that is dominated by more general solvent strength effects at high concentration of the organic modifier. Through examination of the temperature behavior, the thermodynamic behavior of the mobile phases was also found to differ. At pH 3.0, the slope of the van’t Hoff plot was negative for both methanol-water and acetonitrile-water mobile phases. This was attributed to a change in the pKa of the piperazine diastereomers with increasing temperature, which favored the neutral form that was more highly retained. At pH 6.4, where the neutral form was already predominant, the behavior of the two mobile phases was distinctly different. The logarithm of the retention factor decreased with increasing temperature In methanol-water but slightly increased in acetonitrile-water. The slope of the logarithm of the selectivity factor versus inverse temperature was positive in the methanol-water system, suggesting that the retention process was enthalpy- dominated. In contrast, the slope was slightly negative in the acetonitrile-water system, suggesting that the retention process was entropy-dominated. Compared with the thermodynamic effects, relatively little work has been done to elucidate the kinetic effects of the mobile phase. Miyabe et al. [91] studied the effect of the organic modifier on retention and mass transfer kinetics for an octadecylsilica phase. The equilibrium constant increased with the surface area of the alkylbenzene solutes for mobile phases of 50 % tetrahydrofuran- 53 laze. 7 7.- IR“:- “ JI ' .3“ u) 3 In t: In . (u 1. cu) 1.. \ I. q'] . - (in: .' J ”UK . - Q \ ”‘.‘e‘r '- _ «a § ; ~Al-u .~ VI,‘ ‘1 .A .. h- "f \ R! h \ ‘8 .- A, A 'U N ‘\.- L:- Q - u I t- v 5“- H N . 9 “NA water, 70 % methanol-water, and 70 % acetonitrile—water. In addition, the relative importance of the individual mass transfer processes was evaluated. Axial dispersion (Sax) contributed around 30 %, fluid to particle mass transfer (8f) contributed from 30 to 40 °/o, and intraparticle diffusion (6d) contributed from 30 to 35 %. Since each of these mass transfer processes contributed approximately equally to the second moment, none could be neglected. Among the contributions to intraparticle diffusion, surface diffusion was shown to be more significant than pore diffusion. The surface diffusion coefficient was correlated to the molar volume of the solute through the use of an empirical equation. As the solute volume increased, the surface diffusion coefficient increased. The effect of the organic modifier was also observed, where the surface diffusion coefficient increased in the order methanol < tetrahydrofuran < acetonitrile. As this order is different from the order of retention strength, this suggests that the mobile phase has a different effect on surface diffusion than on retention. Based on these studies, the type and concentration of organic modifier as well as the type and concentration of buffer and pH have a significant effect on thermodynamic behavior. Presumably, these parameters also have a significant effect on kinetic behavior, however much work remains to be done in this area. 1 .4.5. Effect of solute structure and concentration The retention mechanism is dependent not only on the characteristics of the mobile and stationary phases, but also on the solute structure and properties. Many solutes are helpful for characterization of the retention process, particularly homologous series of aliphatic and aromatic solutes. These series provide 54 information about the contributions to retention and selectivity from an individual methylene or benzene group. McGuffin and Chen [64] determined the changes in molar enthalpy and molar volume for a homologous series of saturated fatty acids. On a monomeric octadecylsilica phase (2.7 umol/mz), the change in molar enthalpy ranged from -1.7 to -4.2 kcal/mol for C10 to C22. respectively. The differential change in molar enthalpy (AAH) per ethylene group was relatively constant at -0.41 i 0.02 kcal/mol. This suggests that each ethylene group contributes equally to the retention process from an energetic perspective. On a poymenc oca ecy snica p ase . umo m , e c ange In mo ar en apy was I ' td I'l' h (54 V 2)th h ' l thl much greater and ranged from -10.6 to -30.5 kcal/mol for C10 to C22, respectively. The differential change in molar enthalpy per ethylene group was relatively constant at -3.65 i 0.13 kcal/mol, approximately an order of magnitude greater than that on the monomeric phase. The changes in molar volume were similarly distinctive and informative. On the monomeric phase, the changes in molar volume ranged from 1.9 to -4.3 mL/mol for C10 to C22, respectively. A positive change indicates that the solute occupies greater volume in the mobile phase than in the stationary phase, whereas a negative change indicates the converse. The differential change in molar volume (AAV) per ethylene group was -1.0 i 0.4 mUmol, which confirmed that each ethylene group contributes equally to the retention process from a volumetric perspective. On the polymeric phase, the changes in molar volume ranged from -27.1 to -104 mL/mol for C10 to C22, respectively. This change in molar volume is a significant proportion of the total 55 ar v: in)!" '5 I . 5 AA '3?- WI“ luau-A U . I. a—\ Alta al- C T -- M. c 41.. 2. ~ . u A U . O .\ 2d . C n * ~ A‘. “Hub i R :— .11 .\. . . a a : _ . I 7 h... u . .3 “.0 ‘ M ‘.'A a... U ‘V‘ A5» a: a.» in 1. \ a. N.»- molar volume, which is approximately 201 to 441 mL/mol for C10 to C22, respectively. The differential change in molar volume per ethylene group was -14.1 i 2.8 mL/mol, approximately an order of magnitude greater than that on the monomeric phase. These studies provide a clear indication of the thermodynamic contributions of the methylene group to retention. The kinetic contributions to retention for the homologous fatty acids on the polymeric octadecylsilica phase were examined by McGuffln and Lee [70]. In this study, the retention factor increased logarithmically and the rate constants decreased logarithmically with increasing carbon number. The rate constants from mobile to stationary phase decreased by approximately one order of magnitude, while the rate constants from stationary to mobile phase decreased by approximately three orders of magnitude for C10 to C22. I-Ience, under most conditions, the transfer from stationary to mobile phase was the rate-limiting step in the retention mechanism. The concomitant changes in activation enthalpy from mobile phase to transition state showed small variations, but was roughly constant with increasing carbon number. In contrast, the activation enthalpy from stationary phase to transition state increased monotonically with carbon number and was approximately two-fold larger than the activation enthalpy from mobile to stationary phase. These activation: enthalpies were also substantially greater than the net change in molar enthalpy. Hence, it is likely that the solutes do not enter and leave the stationary phase in a single step (as shown in Figure 1.3), but rather in a stepwise or progressive manner. When considered as a progressive process, the average increase in activation enthalpy was 1.6 i 0.6 56 --,- MA (La .iUI A0! we." , v y; 'Gn\ a... pr \" "" ; (v ID. a, A vi» I a. v‘ F»! f (I) (f' I "i kcal/mol per ethylene group, which is energetically feasible within the chromatographic system. The activation volume from mobile phase to transition state increased monotonically by 11 i 4 mL/mol per ethylene group. The activation volume from stationary phase to transition state was approximately two-fold larger, and increased by 24 i 9 mL/mol per ethylene group. These activation volumes were also substantially greater than the net change in molar volume. Again, this suggests that the solutes do not enter and leave the stationary phase in a single step, but rather in a stepwise or progressive manner. Zhao and Carr [92] examined the thermodynamic contributions of the methylene group for several nonpolar homologous series. The differential change in molar free energy (AAG) per methylene group was determined for alkylbenzenes, alkylacetates, alkylphenones, alkylanilines, and nitroalkanes. The AAG values were very similar, ranging from 0.303 to 0.322 kcal/mol, with an average deviation of $0.007 kcal/mol. Hence, the authors concluded that the terminal functional group of the homologous series has little effect on the net retention of the methylene group for alkylsilica phases. More detailed studies by Chen et al. [93] evaluated the changes in molar enthalpy and entropy for an extensive set of solutes. For homologous alkylbenzenes, p-alkylphenols, p- alkyliodobenzenes, p-alkylacetophenones, and p—alkylanilines, AH became systematically more negative as the alkyl chain length was increased. Although there were small variations between these homologous series, the differential change in molar enthalpy for the methylene group ranged from 1.69 to 1.91 kJ/mol, with an average deviation of 10.09 kJ/mol. In addition, the intercept of 57 '5 in; (”I i "“ ”Kw - . - I an.” .. ., OR "-a. 9 Que F‘ .A, ‘v'up -v . I» ‘.fi . 3 "N... In... J - l N the van’t Hoff plot became more negative with increasing alkyl chain length. These values were also relatively similar, ranging from 0.224 to 0.314. Hence, the terminal functional group of the homologous series appeared to have little effect on the enthalpic and entropic contributions to retention of the methylene group for alkylsilica phases. Carr et al. [94] examined the retention behavior of more polar functional groups, such as methoxyl, methyl ester, aldehyde, nitro, and cyano. Unlike methylene groups, these polar groups exhibited different values for the change in molar free energy in the chromatographic system and in a liquid-liquid extraction system using hexadecane as a model of the stationary phase. This suggests that a simple partition mechanism may not be sufficient to describe the retention of polar functional groups. Moreover, unlike methylene groups, the interactions of the polar groups with the mobile phase were energetically favorable and much greater than their interactions with hexadecane. This observation may suggest that the retention process is, in fact, driven by the mobile phase for polar groups. However, these interactions are not solvophobic, as suggested in the model of Horvath et al. [43,44], but solvophilic in nature. Chen et al. [93] examined the changes in molar enthalpy and entropy for substituted benzenes. These values provide insight into the enthalpic and entropic contributions for individual functional groups. For solutes with a more negative change in molar enthalpy than benzene, their functional groups have a more energetically favorable interaction with the stationary phase or, equivalently, a less favorable interaction with the mobile phase. The most negative values were observed for chloro, 58 Prflflffi Ir \9‘ ' ass "6 1 “‘7 (I, 1“ AAQA. ll IIIf ‘- via. l '. “A.” J- v.‘ - 'fi- \ _\ '4 uhg‘,‘ (I) r" . AA. r "r U I h. h" c , w,‘ I - '\ -A‘M- ’- I ~ '25". '- h‘2o ’ "Ur" ' \ r‘» I (L) bromo, iodo, and phenylketone functional groups. Conversely, for solutes with a less negative change in molar enthalpy than benzene, their functional groups have a more energetically favorable interaction with the mobile phase or, equivalently, a less favorable interaction with the stationary phase. The least negative values were observed for hydroxyl, methylenehydroxyl, and methylketone functional groups. Similar insight can be gained from the entropy term, provided that the accessible phase ratio remains constants for these solutes. For solutes with a more negative change in this term than benzene, their functional groups have a less favorable entropic contribution to retention. The most negative values were observed for amide, hydroxyl, nitrile, methylenehydroxyl, and phenylketone functional groups. Conversely, solutes with a less negative change in this term than benzene will have a more favorable entropic contribution. For these experimental conditions, no solutes had a less negative value than benzene. In other studies, homologous series that vary in the number and position of benzene groups have been examined. McGuffin and Chen [64] determined the changes in molar enthalpy and molar volume for a series of PAHs. On a monomeric octadecylsilica phase (2.7 umol/mz), the change in molar enthalpy for the homologous series of phenanthrene, chrysene, and picene ranged from -0.8 to -2.9 kcal/mol. The change in molar enthalpy per benzene group was not constant, which suggests that each additional benzene group did not contribute equally to the retention process from an energetic perspective. Benzo[a]pyrene, with the same number (five) of aromatic rings but a more condensed structure 59 :ear eel - A ~ .nu bv‘. ln9pa!r - d I w I “y. l .’P 4:- ,A' let, \ ”‘2' p~\ y o l~n~ I ,4 :f' '“Uagh A ' n’:“ no, “ a r' h (H I n K‘ ‘- 4 .' ,q ‘V‘u - ‘8. ‘- d ‘H '1' 4" . than picene, had a slightly less negative change in molar enthalpy of —2.2 kcal/mol. The nonplanar PAHs, phenanthro[3,4-c]phenanthrene and tetrabenzonaphthalene, have significantly less negative changes in molar enthalpy than would be expected based on their six-ring structure. In fact, they are more comparable to the three- and four-ring homologous PAHs. On a polymeric octadecylsilica phase (5.4 umol/mz), the changes in molar enthalpy were significantly greater, but exhibited the same trends as the monomeric octadecysilica phase. The changes in molar volume were similarly distinctive and informative. On the monomeric phase, the change in molar volume for the cata-annelated homologous series of phenanthrene, chrysene, and picene ranged from -1.9 to -3.1 mUmol. The change in molar volume per benzene group was not constant, which suggests that each additional benzene group did not contribute equally to the retention process from a volumetric perspective. Benzo[a]pyrene, with the same number (five) of aromatic rings but a more condensed annelation structure than picene, had a slightly less negative change in molar volume of -2.1 mL/mol. In contrast, the nonplanar PAHs, phenanthro[3,4—c]phenanthrene and tetrabenzonaphthalene, exhibit positive changes in molar volume. Hence, these solutes occupy a greater volume in the stationary phase than in the mobile phase. On the polymeric phase, the changes in molar volume were greater, but exhibited the same trends as the monomeric octadecysilica phase. These studies, as well as others [87,93,95], provide a clear indication of the thermodynamic contributions of the benzene group to retention. 60 Th 5.4-5- " I’M. J. 0...?qu n v “‘9. 9A.;- » .3 Is: A) ' Y. _J ,_.r In Li: J (I) . e \ ‘O‘ "b t.» ‘1‘ Al The kinetic contributions to retention for the PAHs on the polymeric octadecylsilica phase were examined by Howerton and McGuffin [37]. The rate of transfer for the three-ring PAH phenanthrene and the six-ring nonplanar PAHs phenanthro[3,4—c]phenanthrene and tetrabenzonaphthalene were very fast and, in fact, were greater than the capabilities of the chromatographic measurement method (2400 5'1). For the remaining PAHs, the rate constants decreased with increasing ring number and increased for more condensed annelation structure. The transfer from mobile to stationary phase was the rate-limiting step for the monomeric octadecylsilica phase, whereas the transfer from stationary to mobile phase was the rate-limiting step for the polymeric octadecylsilica phase. The concomitant changes in activation enthalpy increased with ring number and decreased for more condensed annelation structure. A more detailed examination of the effect of annelation structure was reported by Howerton and McGuffin [87]. The activation enthalpies and volumes were substantially greater than the net changes in molar enthalpy and volume. As noted previously, this suggests that the solutes do not enter and leave the stationary phase in a single step, but rather in a stepwise or progressive manner. The thermodynamic and kinetic behavior of nitrogen-containing PAHs (NPAHs) has also been elucidated on a polymeric octadecylsilica phase by McGuffin et al. [96]. The retention factors for the NPAHs were smaller than those for the parent PAHs in methanol mobile phase, while the converse was true in acetonitrile. In fact, retention factors for aza-PAHs increased by approximately an order of magnitude in acetonitrile compared to methanol. This was attributed 61 ’53 re "‘ au . fl 5 Olson- d ‘9‘,“ 'v' V Ha, “I A ~ U v . c and :- f in Lt. a .2 .c .\. . a: v... . hi 9 - “fix-b N i A.‘ u fit A .u u .C Q. e .a.. -» 9 . q.- to the ability of the NPAHs to interact only weakly with residual silanol groups on the silica surface in the protic solvent, but much more strongly in the aprotic solvent. In general, the NPAHs had more negative changes in molar enthalpy than their parent PAHs owing to this adsorption. It is noteworthy, however, that the changes in molar enthalpy were relatively comparable in the two mobile phases. For example, benz[a]acridine had AH values of -6.6 i 0.1 kcal/mol in methanol and -8.3 i 2.1 kcal/mol in acetonitrile. Hence, the differences in thermodynamic behavior were attributed to changes in the intercept (e.g., molar entropy or phase ratio) rather than the slope (e.g., molar enthalpy) of the van’t Hoff plot. The kinetic behavior was equally dramatic, with rate constants differing by two to four orders of magnitude in the two mobile phases. For example, the rate constants for transfer of benz[a]acridine from mobile to stationary phase were 47 and 1.3 x 10'2 s’1 in methanol and acetonitrile, respectively, at 303 K. The corresponding rate constants for transfer from stationary to mobile phase were 80 and 2.9 x 10'3 5'1, respectively. In nearly all cases, the latter process was the rate-limiting step of the retention mechanism. These results clearly indicate the importance of adsorption on the underlying support in alkylsilica phases. Further studies with aqueous mobile phases and additives are desirable for more thorough characterization. The effect of solute concentration on kinetic behavior was examined by Miyabe and Guiochon [97] for an octadecylsilica phase. From the estimation of plate height, the axial dispersion coefficient was found to increase linearly with increasing concentration in the range of 0 to 102 g/mL of 4-(2-methyl-2- 62 Plr'F'I‘ b VIU~ tn;- .. ._->-fl'l ' «a. ' t r I 9!- ‘.‘P'Vefl (V .. y. Inc-no . (D (n § - ’- VA l’l cl" (1' propyl)phenol. The mass transfer rate constant was also found to increase linearly with concentration. Among the kinetic contributions to the rate constant, the sorption/desorption and external mass-transfer processes were negligibly small and intraparticle diffusion was dominant. Moreover, among the contributions to intraparticle diffusion, surface diffusion was shown to be much more significant than pore diffusion. Hence, the authors concluded that the concentration dependence of the rate constant arises primarily from the surface diffusion coefficient. This concentration dependence of the surface diffusion coefficient was explained by the chemical potential driving force model. These results are significant because they clearly indicate the important role of surface diffusion processes in the kinetic behavior of alkylsilica phases. 1.5. Conclusions Alkylsilica stationary phases operate predominantly by a partition mechanism, where the solute interacts more strongly with the stationary phase than with the mobile phase. The underlying support plays an important role in both the thermodynamic and kinetic behavior, often leading to a combined partition — adsorption mechanism. As the alkyl chain length and bonding density increase, the changes in molar enthalpy increase and kinetic rate constants decrease. The mobile phase composition, likewise, influences the changes in molar enthalpy by means of the water content and the type of organic modifier. The kinetic behavior is influenced by the organic modifier and its effect upon the surface diffusion coefficient. Finally, the solute structure provides a broad view of the retention mechanism from both a thermodynamic and kinetic perspective. 63 r' H ”-5 J i NJ --,A 1 5 ‘ ‘vv ~n‘q' '4 u— a.- D‘PQ-P p\- u U-- .. A a: b — -5" a -n~-_ ‘\— . l_,__ I“. At _- ' .1. 9“.»- 'v This deep understanding of the retention mechanism in liquid chromatography is necessary in order to maximize the beneficial contributions and minimize the detrimental contributions to the separation. While a vast amount is known about silica-based materials, little is known about hybrid-based materials. Thus, the goal of this research is to investigate hybrid stationary phases using thermodynamic and kinetic properties. Experimental methods to extract thermodynamic and kinetic information from zone profiles will be developed and compared in Chapter 3. The effect of temperature and mobile phase will be examined in Chapter 4 and the effect of mobile phase modifiers will be examined in Chapter 5. These investigations will lead to a better understanding of the retention processes on hybrid stationary phases. 64 1.6. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [15] [17] [18] References L.R. Snyder, J.J. 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Miyabe, G. Guiochon, Anal. Chem. 72 (2000) 5162-5171. 69 an]. Do- a n— A ‘.. .gc CHAPTER 2 EXPERIMENTAL METHODS 2.1 Introduction This chapter details the experimental methods used for the subsequent research. Column preparation and packing are discussed, along with physical properties of the stationary phases, followed by the two chromatographic systems utilized throughout the research. 2.2 Column preparation and packing In order to accurately determine thermodynamic and kinetic information regarding a separation, a well-behaved and well-characterized chromatographic column is needed. To this end, capillary columns that are packed in-house are used throughout this research. An optically transparent, fused-silica capillary is used for the column. Detection windows are created by burning off the, polyimide coating on the outside of the capillary, followed by removal of the charred residue with high purity methanol (Burdick and Jackson Division, Honeywell). The column is terminated with a quartz wool frit. The stationary phase is packed using the slurry method, as columns packed by this method have uniform packing across the diameter and length of the column [1]. To do this, the stationary phase is suspended in a solvent that prevents immediate precipitation. The slurry is stirred for 0.5 hours and subsequently transferred to a metal reservoir connected between a single-piston reciprocating pump (Model 114M, Beckman Instruments) and the prepared fused-silica capillary. The reservoir is brought to a high pressure (4000 psi) in an effort to quickly load the stationary 7O I”- m! __ '6‘ \gr I“ ‘ “n "v‘,. : H v . A :|_'_~no . v ‘ “A i- ’.:-«r ‘ Vw‘ - “‘~o- 1").‘ "L‘ § I ‘ - \- ‘4 e I I I. “Eh: \- H I! H 7 \ 9'. “ CPA H i d 5“ L'- "1 N. - a ‘ .A. "U (_ phase into the capillary column; packing is usually complete in less than twenty minutes. The highest pressure is maintained for three to five hours and gradually lowered to 1000 psi overnight. The lower pressure allows the packed bed to compress, removing any voids left during the initial packing step. The efficiency or plate height (H) of each column is investigated using a well-behaved series of coumarin-Iabeled fatty acid solutes (Figure 2.1). After separation, the zone profile for each solute is fit to the Gaussian function (Equation 1.33). The fit equation is regenerated in Microsoft Excel where the first and second statistical moments are calculated (Equations 1.20 and 1.21), followed by the calculation of plate height (Equation 1.23). For an efficient column, the plate height should be close to two times the particle diameter of the packing material. If an inefficient column is produced, the slurry density and solvent can be adjusted in an effort to improve the column efficiency. In addition, the column porosity can be useful for column characterization as it gives an indication of the void space between particles relative to the total column volume. The interparticle porosity (cu) can be calculated from 83 _ 180 ML 2 _ 2 (1‘3u) dP AP (2.1) where p is the linear velocity, 1] is the solvent viscosity, dp is the particle size, and AP is the pressure drop along the column. Typically for randomly packed spheres, su will be 0.38. The total porosity (ST) is the sum of the inter- and intraparticle porosities. Many porous, silica particles have intraparticle porosities of 0.5 [2]. Thus, 81' for a typical, silica-based porous particle is 0.88. 71 H3CO o 0 Figure 2.1. C10 coumarin-labeled fatty acid. 72 “FF i.“ F: ~A. .’A~ .6 2.3 Stationary phases Several different stationary phases were used throughout the course of the research. For the first investigation (Chapter 3), a polymeric octadecylsilica phase custom synthesized by Lane Sander at the National Institute of Standards and Technology was employed. This packing material is characterized by a 5.5 pm particle size, 190 A pore size, and 240 m2/g surface area (IMPAO 200, PO Corp.). It is prepared by reaction of the silica support with triethoxyoctadecylsilane at a bonding density of 5.4 pmol/mz. This phase was packed in an acetone slurry to yield of a plate height of 15 pm and an interparticle porosity of 0.44. For the subsequent investigations (Chapters 4 and 5), three organic — silica hybrid phases were used. The bridged-ethylene hybrid (BEH) support is prepared by the co-condensation reaction of tetraethoxysilane and 1,2- bis(triethoxysilyl)ethane. The alkyl-bonded phases are then produced through derivatization of the hybrid support. Each phase is endcapped with trimethylchlorosilane. An illustration of the phase chemistry is given in Figure 2.2. The C13 phase (Figure 2.2A) is prepared by reaction of the hybrid support with a trifunctional silane at a bonding density of 3.06 pmollmz. It is characterized by a 5.2 pm particle size, 141 A pore size, and 189 m2/g surface area (XBridge C13, Waters Corporation). This phase is packed in an acetone slurry to yield of a plate height of 10 um and an interparticle porosity of 0.39. Another C13 phase (Figure 2.2B) contains a carbamate (polar) group embedded 73 = ”‘5 if) u-i‘a fig-vat Um I :fllni ,[3- LS . a 1.“ hr. 'V 577‘ ‘1- 2 _ .— C(t)=—®—exp A22 +A1 t erf t A1 — A2 +1 (3.16) 2A3 2A3 A3 J2A2 J2A3 where erf is a statistical error function. The zone profile is fit to the EMG equation by nonlinear regression (PeakFit, Jandel Scientific) to extract the regression parameters, A0, A1, A2, A3. From these parameters, the retention time (tr) is calculated as tr = A1 +A3 (3.17) and the corresponding retention factor is calculated from Equation 3.1. The rate constants are calculated by (3.18) This method of determining the rate of transfer between mobile and stationary phases by adjusting an exponential equation on the tail of an asymmetric peak has been justified by Vidal-Madjar and Guiochon [13] and applied extensively by McGuffin et al. [6,14-17]. In the EMG method, any extra-column contributions to asymmetry must be minimized or eliminated. This can be accomplished by detection at several points along the chromatographic column with subtraction of the parameters determined at each detector. Thus, Equations 3.1 and 3.18 become k = At. -Ato (3.19) A10 2k Ato 2k2 A10 k = d k - (3.20) ms AAg sm Mg 87 .AL A -13 .aanc 32.3. 7 1"5'0 where Atr is the difference in the retention time and AA32 is the difference in A32 between two on-column detectors. 3.2.3. Thomas nonlinear chromatography model The Thomas method describes the concentration (C(x)) as ( _A_1 I 2 A1X ex -X - A1 \ A0 [ A3 X 1 A2 p A2 C(x) = 1— exp[ D (3.21) A1 X A3 (1‘Tl33'xéll“e*pl7§l]j where T(u,v) = exp(—v)jexp(—x) lo (Wfix (3.22) 0 and lo and I1 are modified Bessel functions of the first kind. After conversion from the time domain (t) to the retention factor domain (x), the zone profile is fit by nonlinear regression to Equation 3.21 (PeakFit, Jandel Scientific). From the regression parameters (A0, A1, A2, and A3), the corresponding retention factor and rate constants are obtained as shown k = A1 (3.23) 1 k A k = and k = — = ———1— ms Azto 3m A2to A2to (3.24) For accurate calculation of retention factor and rate constants, any extra-column contributions, including those from the injector, detector, connections, etc., must be negligible. However, unlike the moment and EMG models, there is no a posteriori method to correct for these contributions. 88 3.3. M 3.3.1. R1 in» I i an ' u .‘Inv’ 3.3. Methods 3.3.1. Reagents A series of fatty acids (Sigma) ranging from C10 to 020 are derivatized with 4-bromomethyl-7-methoxycoumarin (Sigma), as shown in Figure 2.1 [18]. Individual fatty acid derivatives are isolated and purified using a conventional- scale octadecylsilica column (ODS-224, Applied Biosystems) with methanol mobile phase [19]. The resulting fractions are evaporated in a stream of dry nitrogen at 313 K and are redissolved in high-purity methanol (Burdick and Jackson Division, Honeywell) at a concentration of 5 x 10“1 M. 3.3.2. Experimental system The solutes are separated on a capillary liquid chromatography system with multiple on-column detectors as illustrated in Figure 2.4. The stationary phase is a silica-based C18 material (IMPAQ 200, PO Corp.) described in Chapter 2.3 and the mobile phase is methanol. The sample is split between the capillary column and a 50 pm i.d. fused-silica capillary (0.6 m length, Polymicro Technologies). A 20 pm i.d. fused-silica capillary (2 m length, Polymicro Technologies) is attached post-column to serve as a restrictor. The length of the restrictor is systematically decreased to adjust the flow rate along the column while maintaining constant pressure. The separation was performed in constant temperature (303 K) and pressure (4000 psi) mode. 3.3.3. Data analysis After separation, the solute zone profiles are individually extracted from the chromatogram and then analyzed. In preliminary studies, several models 89 were 313' 3233531 «can»; c r- - . 1.1—grid 7» Pl“; A 3.11.169. H Algae... ‘ l.l ivviua 1:6Ah6q' "Fin YE . ~ I I v . t V ‘. .51; in 1 "' W 51 in ., “v- t r!) x ~ '.:", . n n- ‘ 0' "F I \I . . I u N. -\ ‘ d n “a .- .- .\_ were examined for experimental data analysis. Each profile was fit by nonlinear regression to the Gaussian and Giddings functions (Equations 1.33 and 1.39, respectively) by a commercially available program (Peakfit v4.14, SYSTAT Software, Inc.). The Gaussian model assumes a symmetric peak shape, while the Giddings model assumes negligible column contributions from multiple paths and diffusion in the mobile and stationary phases; both assumptions are not valid for all solutes in this experiment. The Gaussian model contained nonrandom residuals with correlation coefficients ranging from 0.990 to 0.813 for C10 to C20, respectively. The Giddings model also produced nonrandom residuals with correlation coefficients ranging from 0.990 to 0.830 for C10 to 020, respectively. Due to the poor quality of fit, these models were not used for further analysis of the zone profiles. Other models that can account for asymmetric peak shapes were then evaluated and determined to be more suitable. For the plate height method, the profile is fit to an asymmetric double sigmoidal function (ADS) y: __ A0 A _ 1— _ 1 A - (3.25) x—A1+—22 x—A1——22— 1 ex — 1 ex — + 9 A3 + 9 A4 — .—l L _l where A0 is the amplitude, A1 is the peak center, and A2, A3, and A4 are peak widths. A commercially available program (Tablecurve v2.02, SYSTAT Software, Inc.) is used to fit the zone profile. The fit equation is regenerated in Microsoft Excel, from which the statistical moments are calculated. This method produces high quality fits (correlation coefficients ranging from 0.999 to 0.979), reduces noise, and allows control of peak integration limits. In this work, the integration 90 1:; are lder: 'ec'essxon. of l with) (:05 139? to W; '5!“ 3‘4 ”the d limits are identified at 0.1 °/o of the maximum peak height, as the error in the calculation of the moments, particularly the second moment, has been proven small under these conditions [20]. Each profile is also fit by nonlinear regression to the EMG and Thomas functions (Equations 3.16 and 3.21, respectively) by a commercially available program (Peakfit v4.14, SYSTAT Software, Inc.). The regression of the zone profiles to each of these equations is excellent, with correlation coefficients ranging from 0.999 to 0.941 for the EMG equation and 0.998 to 0.942 for the Thomas equation. However, each of the models fits the zone profile differently. As shown in Figure 3.1, the EMG model overestimates the peak maximum and tail and underestimates the region around the mean, while the Thomas model behaves in the opposite manner. The high correlation coefficients result from the average of positive and negative error in both the EMG and Thomas models. The ADS fit is most accurate, however it lacks physical and chromatographic significance. 3.4. Results and discussion 3.4.1. Retention factor The retention factors at each on-column detector at a representative linear velocity are plotted in Figure 3.2. These retention factors are not corrected for extra-column effects. For all methods, the retention factor increases slightly as a function of column length. For example, for the C15 fatty acid, the retention factor increases by 4.8 % for the statistical moment, 4.6 °/o for the EMG, and 3.5 % for the Thomas methods. To further examine the effect of distance on retention factor, the difference method was used, as this method corrects for extra-column 91 TIL mo< .T Iv 32 +113 0.2m .T i V 3.81 .QEo mood Lo b_oo_m> Lama: m «m. Bum bum.— um_mnm_-c:mE:oo $0 35 Lo m_w>_mcm co_mm2mom in 2:9“. 2:5 m2: am, «we mm? GNP wFF err err «FF OFF p p p _ b b - 92 5v 80 iv M=0 8V 20 iv so Ev NFo Lev so 2.8 Sod Lo $8.9 .85. m a .385 Emacs 9: £3) 623328 995 9203 83:22 on... .8536 99.? 8:03 583 cascmumm " oofiiofio 995 9083 5:56. of. .8566 399 8303 88m... cozcouom umwd 2:9... Es mozEma om mm om mv ow mm om mm om _ |F _ I. _ _ _ F.O o l 1 6 11 «w m m “a .. _. E 4 «F l! 14 W H. )1 o f to W 4. I I ‘1 L m 0 o 0 LL 1 0.. mm cor 94 .0. ONo .I. so .0. so .4. so E. No .9. so 3.50 m8... .5 3.029, as... m .m .385 8&9: o... 5.; 86.8.8 93.5 2083 coucofi: of. .85qu m:m.o> nouoa 86$ cozcouom "Ow.” 959.... E5. moonE om mm om mv ow mm om. mm om _ L - |hl _ _ — Fuo 9 #1 ll 8 n. U Lm. Ln. 8 r _. m...— 4 «r at ld m H. o o 61 8 m 4.. I” i + in W .. .. t -s m. o c c a oow 95 A «Mi-Afr ._ _ active)! " An. A guru “ Int. 3., V Inn”. ‘5. no ‘- ".11. . r I (i) 5!.) ll’ ‘ eh I a? variance. The retention factors are calculated between detectors 4 and 1 (35.1 cm), detectors 4 and 2 (29.6 cm), and detectors 3 and 2 (24.1 cm), as summarized for the EMG model in Table 3.1. As the distance between the detectors increases, there is no significant change in the retention factor (0 to 1.4 %). This decrease in the variation relative to 4.6 % (Vida supra) illustrates the advantage of using the difference approach. Because the retention factor is a measure of thermodynamic conditions, the constancy along the column implies that steady state has been achieved and reliable extraction of the kinetic information can occur. Representative values for the retention factor calculated by difference (between detectors 4 and 1) at each velocity are summarized for each model in Tables 3.2 - 3.4. Retention factors are quite similar for all models and show the same trends with velocity and carbon number. The retention factor decreases with increasing linear velocity for all solutes. It may be noted that at any velocity, the solute transfers between the stationary and mobile phases toward equilibrium. At higher velocities, equilibrium conditions are more difficult to achieve because the mobile phase is moving faster, yet the stationary phase remains immobile, which leads to a decrease in retention. The effect is most apparent for solutes with longer alkyl chains, which on average spend a longer time in the stationary phase. For example, using the statistical moment model, the retention factor for C10 decreases by approximately 13 %, whereas the retention factor for C20 decreases by approximately 26 % as the velocity is 96 Table 3 #9" Cal 3‘ Table 3.1: Retention factors as a function of length (L). The retention factors were calculated with the EMG difference model at a linear velocity of 0.088 cm/s. Carbon Retention factor, k Number L4-L1= L4—L2= L3—L2= 35.1 cm 29.6 cm 24.1 cm 10 0.38 0.38 0.38 12 0.74 0.74 0.74 14 1.50 1.50 1.51 16 3.19 3.18 3.21 18 6.60 6.58 6.67 20 12.4 12.4 12.5 97 de m._._. 03 QNF m.N_. 0N 8... NE moo 23 new 8 2% SN m5 Ra mom 8 as m: Es m3 m3 3 so... is is 2.0 o; NF s3 R... and and and 2 £5 8”... u a sea 82. u a 2.8 8:... u a «.5 «8... u a sec 9...... u a .352 w . c0950 x .808 53:23. .s 95 3 £98.06 8928 858:6 E .25.: E88... 9: 5.3 83.8.8 2oz. £08m. 5:55. on... .3. 3623 .59... Lo cozoca a mo mEow bum. oo_onm_-c_.mE:oo .2 298.. 5.533. "N.” 22¢ d'mi33r— oo.w m. E. V.NF m.N_. N.m_. ON 05.3 mfim 006 5.0 mod 2‘ 3N mad. mfm wwd 30m 9 FN._. mVé omé vmé mmé E. 9 mmd Ed 35.0 mud mud NF 9 vmd nmd and and and or £Eo mend u 3 EEO 92.6 n 3 £80 awed u 3 350 «mod n 3 £38 236 u 3 39:32 :3th x .368 Caz—Bumm— 4 can v @5693 $928 85.2% 3 .89: 0.2m m£ 53> 85.8.8 So; 9903 83:92 9:. .3 a_oo_o> :85. p6 5:82 m 8 flow Ema nm_mnm_-c:mE:oo .2 2903 5:551 a.» min... 98 m. : 3F mfl 9N? om :m, mg 8.0 NE a; 2 EN :3 m; mg m3 8 Re 31 w: 84 v3 3 8.0 Ed NS NS Ed E 3.0 mg Bo Bo and 8 £50 3...... u 3 £60 33 n 3 «EB 83. n 3 «Eu ~85 u 3 £50 35.: u a .3232 :3th 100 x .3303 30:323. .v .98me 3m .258 3:55... 9: 53> 39330.8 903 3:938 29 ms... .3 360.9 .85. he cozoca m mm mEom >33 cm_mnm_-c_._mE:oo .5. 990m... cozcflmm 3.» 2an 21‘s": aw N no ‘V uu' u‘ 92 £4" “1““! ‘.‘f'hk I‘m: 't. . (.4. 7"“. '. . 1.7."!- I 5 2! increased. Thus, a change in linear velocity plays a more significant role retention of solutes that are highly retained. The retention factor increases logarithmically with an increase in carbon number, as shown in Figure 3.3. Each additional ethylene group systematically adds to the interaction of the solute with the stationary phase, causing the solute to become more retained as the carbon number increases. The retention factors for each solute calculated with each model are within 3 % of one another at all velocities, except the Thomas model at the highest velocity. At a linear velocity of 0.368 cm/s, values for the Thomas model differ by 0 to 9.4 % from those for the moment and EMG models. Overall, each model provides reasonably consistent thermodynamic information 3.4.2. Kinetic rate constants While retention factors provide information about the equilibrium or steady-state chromatographic behavior, rate constants provide information about the non-equilibrium and kinetic behavior. The rate of solute transfer between mobile and stationary phases depends not only on the chemical structure of the solute, but also on the experimental conditions. Thus, the distance the solute has traveled along the column, the velocity of the mobile phase, and the chemical structure of the solute are important with regard to their impact on the rate of solute transfer. 3.4.2.1. Effect of column length If the system is at steady state, both the thermodynamic and kinetic properties should remain constant with distance. The preceding investigation of 101 2:5 god so 3629, .85 m a 289: A: $59: Eqfiv 0.2m .on Emacs 9: 5_>> 8530.8 who; 990$ c0558.. 9:. .5353: .898 999 8503 .683 concoumm and 239". mum—>52 zOmm d1 .00 r I F F O 5'; (,,S) SUU>1 lNViSNOO 31w 00.. 105 .O. ONo .I. so .0. so .1206. N5 .0. so 2.8 8o... .0 362? .85. m. a 8.02.8 emu 9.9 .8308 $89.... 05 5.3 855.92. 92> 3:928 39 on... .8566 w3m5> 0050... 299.8 9mm ”UV.” 9.30.“. .50. mozfima 00 mm om 03 03 mm 00 mm 0N — b h n + — _ FO-O - P... w I. _.3 O O N S tr I. w ? O 0 l0 .1. X DH M” I? m w iii \3 ml lul i ll 1 -2 t... 00.. 106 Table 3.5: Rate constants calculated as a function of length (L). The constants were determined with the EMG difference method using data collected at a linear velocity of 0.088 cm/s. Carbon Rate constant, kms(s-1) Rate constant, ksm (3“) Number L4-—L1= L4—L2= L3-L2= L4-L1= L4—L2= L3-L2= 35.1 cm 29.6 cm 24.1 cm 35.1 cm 29.6 cm 24.1 cm 10 22 19.5 26.9 8.4 7.4 10.2 12 11 10.6 9.7 7.8 7.8 7.2 14 3.6 3.3 4.3 5.3 5.0 6.5 16 1.3 1.2 1.5 4.1 3.9 5.0 16 0.35 0.34 0.34 2.3 2.3 2.3 20 0.16 0.15 0.17 ‘. 1.9 1.9 2.1 0.0 0.. : NN N0 0F E 000.0 11 3 N0 N0 0.5 0.0 ..F E 0050 H 3 N0 v.0 ...0 0.0 0.0 .0: 000.0 N 3 ...N NN NV V0 08 N000 fl 3 0... n... 0.0 0.0 NF 000.0 N 3 0... 0N N.» 0F 00 0v E 000.0 N 3 N00 00.0 00 0.0 0v E 00rd 00.0 50.0 0N 0.0 0? m E 000.0 "3 0F.0 0.3.0 0... 0..V 50 F. N000 fl: ...m. any. 4:30.50 23. ...m. 2:. .Efimcoo 35m. 0 ...0 0m 0rd 0w 00.0 0? 0.0 3. 0F 0. -- or E 0W0L0 .03E3z 1 :2.th 9 new v 8900.00 5023.. 00:200.... >3 _ovoE .5505 05 05m: 086.328 8.82, mESmcoo 2m... 0:... .3. >._oo.m> 50.... .o c0525.. a ma 3.0m >59. 00.33.555.38 .5. «3:528 93. "0.0 San... 108 N...» 00 0. F 04 00.0 00.0 5.0 0 .0 00.0 00.0 0w 0.5 0.0 0.0 0.. 050 0.. 3.0 00.0 00.0 5.0 0. 0.0 0.0 :4 0.0 0; :0 0.0 04 0.. 00.0 0. 0. 0.0 0.0 0.0 00 N. 0.0 0.0 0.0 0.. .3 0. S 0.0 0.0 :0 00 0F 3 0.0 0.0 .9 -- 0w 0.0 0... >0 -- 00 mm 0F t or 0.E0 0E0 0E0 0E0 .E0 m.E0 0E0 0E0 0E0 3E0 000.0 03.0 000.0 «00.0 000.0 000.0 03.0 000.0 «00.0 000.0 ..0 E3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 a 2 :0900 ...0. sax 0:000:00 0.0m. ...0. «Ex 4:80:00 000”. .F 0:0 0 20.00.00 c0050.. 00:00.50 .5 .0005 0.20 05 0:.0: 00.0.0200 003 9:90:00 0.0: 0: .. ..s. b.00_0> .005. .0 500:... 0 00 00.00 >00. 00.000_-:_._0E:00 :0. 9:20:00 0.0m. "...0 030k 109 NV ..0 0N NN 0.. 0.0 0.N 0.N n... 0. .. 0N N0 00 0N 0N FN or 0.0 0.V ...0 ...0 0r 0N 0? N.. or 0.0 0.0 0V 0.0 ...0 NN 0.. NN t V.. N? I. t N_. N0 0.0 0K V.. N.. 0.0 5.0 0H N0 0F 0.. 3 0.. v.0 N_. V.V NV >0 0.0 N0 0— 0.. 0.. 0.0 0.0 0.. m}: \E E E E W\ao ”New mug—m W32” flNEM 000.0 009.0 000.0 N000 0.00 000.0 02.0 000.0 N000 0V00 ..0 E3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 fl 3 .II 3 fl 3 fl 3 a Z COENU . -0. Eu: 3:000:00 000m. _. ...0. 23. 3:30:00 0.0m. .V 80000 .0 .0005 0050:... 05 0:.03 00.0.0200 002. 3:90:00 0.0: 0:... ..3. b.00_0> .005. .0 500:3. 0 00 00.00 >00. 00.000.505.300 .0. 00:00:00 0.0m. "0.0 030... 110 calculated with each of the models show an overall increase with an increase in velocity. Bujalski experimentally investigated the diffusion-film thickness around an octadecylsilica particle using the shallow-bed technique [21]. As the flow .rate was increased from 2.2 to 3.9 cm/s, the diffusion-film thickness decreased from 0-51 to 0.44 pm. If the stagnant mobile phase layer is thinner at higher velocities, the solute may be able to traverse through the layer faster. This suggests that the decrease in the thickness of the stagnant mobile phase layer surrounding the particle could cause kms and ksm to increase with velocity, as observed in the present study. Although the rate constants calculated using each of the three models show the same overall trends, their magnitudes vary. For example, if km for the C16 fatty acid is considered, values range from 0.98 to 4.7 3'1 for the statistical moment model, from 0.45 to 4.1 s'1 for the EMG model, and from 2.7 to 9.6 3'1 for the Thomas model for a linear velocity range of 0.045 cm/s to 0.368 Cm/s. lf k$an for the same solute is then examined, values range from 3.2 to 11 s'1 for the moment model, from 1.5 to 9.9 3'1 for the EMG model, and from 8.9 to 25 s'1 for the Thomas model. The observed differences in rate constants demonstrate the intrinsic capabilities and limitations of each model. For instance, rate constants for the C10 fatty acid could not be obtained at most velocities using the moment method. In this method, the rate constants are calculated directly from dHL, the corrected plate height. If the sum of the theoretical A, B, and Cm terms in Equations 3.10 to 3.13 is larger than the observed plate height, an overcorrection 111 will occur that causes dHL and the rate constants to be negative and, thus, indeterminate. This is common for very narrow peaks, as the theoretical correction terms overestimate the experimental zone profile. This effect is an outcome and ultimate limitation of the moment model. Additionally, several assumptions of the Thomas model limit its ability to accurately calculate kinetic rate constants. First, as stated previously, the model assumes that all contributions to broadening arise from nonlinear isotherms and slow kinetics of adsorption/desorption. However, the concentrations used in this study are well within the linear region of the isotherm and the mechanism of retention is purely partition. Second, the method assumes column contributions to variance from multiple paths and diffusion are negligible. However, in a packed column, these processes will be present and most assuredly wili affect the peak broadening. Last, it should also be noted that the rate constants from the Thomas model are given only at the last on-column detector, while the moment and EMG models are calculated by taking the difference between the first and last detector. There is no direct way to use the difference approach with the Thomas model. Thus, any values calculated from the Thomas model inherently include extra-column contributions, which could lead to incorrect values for both thermodynamic and kinetic parameters. 3.4.2.3. Effect of solute carbon number The rate of transfer between mobile and stationary phases is controlled by several factors related to the solute structure and properties. These factors primarily include the solute affinity for the mobile and stationary phases, diffusion 112 in the stagnant mobile phase layer, diffusion in the stationary phase, and interfacial resistance to mass transfer. Each of these factors is dependent upon the solute carbon number and will affect the kinetic behavior. Rate constants for solute transfer from the stationary to mobile phase (kms) decrease with higher carbon number. However, the magnitude and rate of change are different for each model. For the statistical moment model, the rate constants for the C10 fatty acid could not be determined successfully due to overcorrection, as previously discussed. For the other solutes, the rate constants decrease over two orders of magnitude on going from C12 to C20. The EMG model shows a decrease in rate constant of over three orders of magnitude. For the same solute, rate constants from the moment model are consistently larger than those from the EMG model. Rate constants from the Thomas model also decrease with carbon number. However, inconsistencies in this general trend are prevalent throughout the data. That is, the contribution to the rate constant from each additional ethylene unit is relatively constant for both the moment and EMG models, while it is not constant for the Thomas model, as seen in a graph of the logarithm of kms versus carbon number (Figure 3.5A). Rate constants for solute transfer from mobile to stationary phase (ksm) decrease with increasing carbon number for the moment and EMG models, but increase for the Thomas model. Again, the contribution to the rate constant from each additional ethylene unit is relatively constant for both the moment and EMG models, while it varies for the Thomas model (Figure 3.5B). 113 mm 0.08 000.0 E b_oo_0> 000:: 0 .0 .2009: .4. 0089; 0.0.5. 0.2m ..Ov 0.0.09: 050: 00003200 0.03 0.00.0000 0.0.. 0:... 0000.5: 0090.0 m:w.0> 00020 000%. 0:09: o. b05006 EB. 000.008 0.01 ”<06. 0.50.". mums—DZ ZOmm<0 ON 0.. we .1. N_. 0.. m — P P — — — Foo ,, m T F :1— n O O N a S Il— - V N I- x. - is -3 w 0 \Qfl. 02. 114 0.80 000.0 .0 b_oo_0> 00:: 0 .0 0000.: .4. 00Eo:.r 0:0..D. 05E ..0. .:0EoE 050: 0003200 0.02. 00:90:00 00: 0: ._. 00:5: :0900 0:0:0> 00020 000:0 30:30.0 9 0:00.: EB. E0080 0.01 "mm.” 050.". mmmEDZ ZOmm<0 NN 0m 0.. 0r 3 NF 0.. 0 _ p _ _ _ F . F.O m r .. ..... n O O N S 0 H l - V - .. N - 1. ... N. m - or m \Qfl. 00. 115 . q 1‘- 3.5. Conclusions This study is the first to validate and compare theoretical methods to extract retention factors and kinetic rate constants from experimental data. In this experiment, the effect of column length, linear velocity, and solute chain length have been evaluated. Overall, values for the retention factor are similar for each model. Retention factors are constant with distance, decrease with velocity, and increase with solute carbon number. However, the values for the kinetic rate constants differ for each model. The statistical moment and EMG models show the largest variation in rate constant as a function of distance. However, the variation decreases substantially when the rate constants are calculated by difference between two detectors. The moment and EMG methods by difference are more reliable than the Thomas model at one detector. As a function of velocity and carbon number, the moment and EMG models show more consistent and reliable trends in rate constants, as compared with the Thomas method. Problems with the Thomas model could be related to the inherent assumptions that broadening arises due to nonlinear isotherms and slow kinetics, and that all column and extra-column effects are negligible. However, due to the nature of the model, extra-column effects cannot be eliminated using the difference approach. Based on these results, the statistical moment and EMG models yield reasonable values for retention factors and rate constants in an experimental liquid chromatographic system. 116 3.6. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [15] [1 7] [18] [19] [20] [21] References J.C. Giddings, Dynamics of Chromatography Part 1 Principles and Theory, Marcel Dekker, New York, 1965. K. Miyabe, G. Guiochon, Adv. Chromatogr. 40 (2000) 1-113. X. Li, A.M. Hupp, V.L. McGuffin, Adv. Chromatogr. 45 (2007) 1-88. J.F. Wheeler, T.L. Beck, S.J. Klatte, L.A. Cole, J.G. Dorsey, J. Chromatogr. A 656 (1993) 317-333. R.P.J. Ranatunga, P.W. Carr, Anal. Chem. 72 (2000) 5679-5692. X. Li, V.L. McGuffin, J. Chromatogr. A 1203 (2008) 67-80. J.J. van Deemter, F .J. Zuiderweg, A. Klinkenberg, Chem. Eng. Sci. 5 (1956) 271 -289. H. Purnell, Gas Chromatography, John Wiley & Sons, New York, 1962, 117-164. J.C. Giddings, R.A. Robinson, Anal. Chem. 34 (1962) 885-890. J.C. Giddings, Anal. Chem. 35 (1963) 2215-2216. K. Miyabe, G. Guiochon, J. Sep. Sci. 26 (2003) 155—173. C.R. Wilke, P. Chang, A.l.Ch.E. 1 (1955) 264-270. C. Vidal-Madjar, G. Guiochon, J. Chromatogr. 142 (1977) 61-86. V.L. McGuffin, C. Lee, J. Chromatogr. A 987 (2003) 3-15. 8.8. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-3548. 8.8. Howerton, V.L. McGuffin, J. Chromatogr. 1030 (2004) 3-12. V.L. McGuffin, S.B. Howerton, X. Li, J. Chromatogr. A 1073 (2005) 63-73. V.L. McGuffin, R.N. Zare, Appl. Spectrosc. 39 (1985) 847. S.-H. Chen, Ph.D. Dissertation, Michigan State University, East Lansing, Michigan, 1993. SB. Howerton, C. Lee, V.L. McGuffin, Anal. Chim. Acta 478 (2003) 99- 110. R. Bujalski, Ph.D. Dissertation, University of Alberta, Edmonton, 2005. 117 APPENDIX 3A.1 COMPARISON OF VARIOUS APPROACHES TO THE PLATE HEIGHT MODEL USING STATISTICAL MOMENTS 3A.1. Introduction As discussed in Chapter 3.2.1, the plate height model accounts for contributions to band broadening from multiple paths, diffusion, and mass transfer. Accurate estimation of each band broadening term is essential to the model. While the multiple paths (A) and longitudinal diffusion (Bm, BS) terms are straightfonNard, a variety of alternative methods have been proposed for the mass transfer contribution to broadening in the mobile phase (Cm). Therefore, in this work, several different methods for determining the mass transfer term, including classical and modern, are evaluated and compared. In this appendix, each method is developed to utilize the difference approach. The difference between two on-column detectors is used to subtract extra-column contributions to broadening. 3A.2. Classical kinetic approaches The corrected plate height (dHL) is derived by subtraction of the classical contributions to broadening, such as the A, Bm, BS, and Cm terms (Equation 3.9). In this appendix, the values for A, Em, and BS are fixed (Equations 3.10 — 3.12), while those for Cm are compared. That is, the calculated plate heights only differ in their expression for Cm. The van Deemter [1] form of the mass transfer contribution to plate height in a packed column can be expressed as 118 H c k2 d3 U (3A 1) = u : . van Deemter m 100(1+ k)2 Dm where u is the linear velocity calculated by difference (u = AL/Ato), k is the retention factor calculated by difference (Equation 3.14), (ID is the particle diameter, and Dm is the diffusion coefficient in the mobile phase. Based on the model originally developed by Golay [2] for open tubular columns, Purnell [3] developed the following expression for the mass transfer contribution to plate height 2 d2u x(1+6k+11k )] p (3A-2) HPumell = Cmu =[ 96(1 + k)2 D m where X is a factor equal to 0.05. In this approach, the packed column is treated as a bundle of open tubes of the same nominal diameter. An alternative equation was developed by Giddings [4], in which a single adjustable parameter, 0, is used to represent the first parenthetical term. dg u HGiddings = Cmu = (DD— (3A-3) m TYPical values for (0 range from 0.5 to 5. Later, Giddings challenged the idea that each of the sources of broadening is independent and concluded that multiple paths and mass transfer in the mobile phase are coupled to one another [5]. Giddings expressed this Coupling as 1 1 —1 HGiddings coupling = [K + 6‘?) (3A-4) m 119 where A is the multiple paths term (Equation 3.10) and Cm is the Giddings contribution to mobile phase mass transfer (Equation 3A.3). Each of the mass transfer terms (van Deemter, Purnell, Giddings, and Giddings coupling) can be directly subtracted from the plate height (Equation 3.9) in order to obtain the corrected plate height. 3A.3. Modern kinetic approaches More recently, Miyabe and Guiochon have investigated the individual mass transfer processes that contribute to band broadening [6]. This method does not use the classical expressions for A, Bm, BS, and Cm. Instead, contributions from axial dispersion (Sax) external mass transfer (81:) and intraparticle diffusion (5d) are estimated from the experimental data and used to calculate a corrected plate height. The sorption equilibrium constant (K) is derived from AM1 —Ato AL \_= — K 3A.5 1 ‘3 [Us )pp ( ) where s is the interparticle void fraction, pp is the density of the packing material, and us is the superficial velocity. In addition, AM is the first statistical moment 30d Ato is the elution time of a non-retained component, both calculated by difference, and AL is the distance between two on-column detectors. The values for e and the porosity of the packing material (2p) are estimated from Ato using At0 = [A—L](e+(1-8)sp) (3A-6) us 120 The value of K is subsequently obtained from the slope of a plot of the left side of Equation 3A.5 versus AL/us. This equilibrium constant is used to characterize the thermodynamic behavior of the system. The plate height is calculated from AM AL H = 2 3A.7 [(AM1)2][2U5] ( ) where AM2 is the second statistical moment calculated by difference. The contribution from external mass transfer is calculated from R 2 _ P Of — (1 — 8)[‘3K—f](8p + 93K) (3A.8) where Rp is the particle radius and kf is the external mass transfer coefficient. This coefficient is given by 1/3 1/3 Wit") i—“s‘lpl iD—mi s po n dp Where 1] and p are the viscosity and the density of the mobile phase, respectively. The diffusion coefficient of the solute (D...) is determined from the Wilke—Chang equation [7]. A dimensionless retention parameter (50) is estimated from Equation 3A.10 and subsequently used in Equation 3A.11 to afford Informmion about the contributions from axial dispersion and intraparticle diffusion. 5o = a +(1—e)(sp + ppK) (3A.10) 121 8 D 5 H__f = _L_ _d 3A.11 I 5%] [HIM ‘ ’ From a linear correlation of (H — 8f/602) versus 1/us, 8d can be determined from the intercept. The axial dispersion coefficient (DL) can be identified from the slope, and subsequently, be used to calculate sex as 58,, = [9L2] 55 (3A.12) us It should be noted that the value for 83x is indirectly dependent on the value for Of, according to Equation 3A.11. Finally, the corrected plate height is calculated by dHL =H______ (3A.13) 3A.4. Comparison of plate height models In an effort to accurately determine the plate height for the purposes of kinetic measurement, each of the aforementioned models are examined and compared. Representative values for each mass transfer term and the corresponding corrected plate height are given in the following tables with r(aspect to varying solute carbon number and linear velocity. The solutes are COUmarin-labeled fatty acids ranging from C10 to Czo. The linear velocity is Varied from 0.045 — 0.368 cm/s. All other experimental details are given in Chapter 3.3. As seen in Table 3A.1, the van Deemter and Purnell contributions to mass transfer are small and similar in magnitude to one another. For both, the Contribution increases with increasing carbon number and increasing linear 122 Table 3A.1: Mass transfer contributions to plate height according to van Deemter and Purnell calculated using Equations 3A.1 and 3A.2, respectively. Hvan Deemter = 6m u I"lPurnell = cm H Carbon (x 10'6 cm) (x 10'6 cm) Number u = u = u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 0.319 2.18 0.551 4.23 12 0.804 5.42 0.866 6.46 14 1.69 1.13 1.34 9.82 16 2.83 1.98 1.90 14.1 18 3.82 28.2 2.37 18.1 _ 20 4.51 34.6 2.69 21.1 123 velocity. However, each contribution is 5 orders of magnitude less than the combined contribution from the A, Bm, and Bs terms. Therefore, the subtraction of Cm yields equivalent corrected plate heights for both equations, as seen in Table 3A.2. Negative values for the corrected plate height indicate overcorrection from the A, 8..., and BS terms, where the correction is larger than the original plate height. Rate constants cannot be calculated from negative plate heights. The Giddings mass transfer terms for w = 0.5 and 5 are summarized in Table 3A.3. The Giddings correction increases with increasing carbon number and increasing linear velocity. The term is an order of magnitude smaller for co = 0.5 compared to co = 5. At 0 = 5, the Giddings contribution is the same order of magnitude as the combined contribution from the A, 8..., and Bs terms. This results in overcorrection of the plate height for several solutes, as seen in Table 3A.4. When 0 is decreased to co = 0.5, the corrected plate height increases, which is due to a smaller correction for the Cm term. Although the Giddings mass transfer term is one order of magnitude lower for (o = 0.5 than 0) = 5 (Table 3A.3), the corrected plate height is relatively similar at the slowest linear velocity (Table 3A.4). In contrast, at the fastest linear velocity, the corrected plate heights for the tWo values of 0 are substantially different. At the slowest linear velocity, the Corrected plate heights for the Giddings equation for both values of co are similar In Magnitude to those calculated using the van Deemter and Purnell equations (Table 3A.2). However, at the fastest linear velocity, only the corrected plate 124 Table 3A.2: Corrected plate height (dHL) using van Deemter and Purnell Equations 3A.1 and 3A.2, respectively. dHL (cm) Carbon van Deemter Purnell Number u = u = u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 -0.0010 0.0032 -0.0010 0.0032 12 0.0014 0.0035 0.0014 0.0035 14 0.0059 0.0099 0.0059 0.0099 16 0.0164 0.0322 0.0164 0.0322 18 0.0394 0.0375 0.0394 0.0375 20 0.0477 0.0685 0.0477 0.0686 125 Table 3A.3: Mass transfer contributions to plate height according to Giddings Equation 3A.3. C rb HGiddings = 0m u (X 10.3 cm) a on _ _ Number 0) - 5 a) - 0.5 u = u = u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 2.05 16.9 0.205 1.69 12 2.17 17.9 0.217 1.79 14 2.29 18.9 0.229 1.89 16 2.40 19.8 0.240 1.98 18 2.51 20.7 0.251 2.07 20 2.62 21.6 0.262 2.16 126 Table 3A.4: Corrected plate height (dHL) using Giddings Equation 3A.3 dHL cm) Carbon Giddings, 0 = 5 Giddings, 0 = 0.5 Number u = u = u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 -0.0030 -0.0136 -0.0012 0.0016 12 -0.0008 -0.0144 0.0012 0.0017 14 0.0037 -0.0090 0.0057 0.0080 16 0.0140 0.0124 0.0162 0.0303 18 0.0370 0.0168 0.0392 0.0355 20 0.0451 0.0470 0.0474 0.0664 127 heights for the Giddings model for 0) = 0.5 are similar to those calculated using the other models. Since 0 represents the retention factor dependence of the mass transfer term, a value of 0.5 appears to be more similar to the k dependence of the van Deemter and Purnell equations. The values for the Giddings coupling contribution calculated using Equation 3A.4 are summarized in Table 3A.5. These values are a combination of the contribution from both A and Cm terms. Values for the Giddings coupling contribution increase with increasing carbon number and increasing linear velocity. The term is smaller for 0 = 0.5 compared to 0 = 5. The corrected plate heights for the Giddings coupling method are summarized in Table 3A.6. The coupling method yields no negative or overcorrected plate heights. However, the plate heights for the Giddings coupling method are approximately half the magnitude of those from the van Deemter and Purnell equations. The modern method advocated by Miyabe and Guiochon [6], summarized in Equations 3A.5 — 3A.13, is quite different from the classical approach to the plate height model. Values for the corrected plate height are shown in Table 3A.7. The corrected plate height increases with increasing carbon number yet, in contrast to the classical models, decreases with increasing linear velocity. Corrected plate heights for the Guiochon method are one to two orders of magnitude larger than those for the classical models. Some overcorrection, primarily due to axial dispersion, is observed for narrow peaks. The parameters in this method are determined from the flow rate, rather than the linear velocity (AL/Ate), and errors may arise from inaccuracies in the flow rate measurement. 128 Table 3A.5: Mass transfer contributions to plate height according to Giddings coupling Equation 3A.4. I"lGIddings coupling = cm u (x 10.3 cm) Carbon Number 0) = 5 (D: 0.5 u = u '.: u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 0.7154 1.033 0.1725 0.6664 12 0.7299 1.036 0.1812 0.6817 14 0.7426 1.039 0.1893 0.6951 16 0.7544 1.042 0.1971 0.7076 18 0.7648 1.044 0.2044 0.7187 20 0.7744 1.046 0.2113 0.7289 129 Table 3A.6: Corrected plate height (dHL) using Giddings coupling Equation 3A.4. dHL (cm) Carbon 0 = 5 0 = 0.5 Number u = u = u = u = 0.045 cmls 0.368 cmls 0.045 cmls 0.368 cmls 10 0.0000 0.0008 0.0005 0.0012 12 0.0009 0.0009 0.0015 0.0013 14 0.0029 0.0035 0.0034 0.0038 16 0.0074 0.0122 0.0080 0.0126 18 0.0178 0.0141 0.0183 0.0144 20 0.0214 0.0255 0.0219 0.0259 130 Table 3A.7: Corrected plate height (dHL) for modern kinetic method. dH': (CURL Carbon Guiochon Number u = u = 0.045 cmls 0.368 cmls 10 -0.027 0.005 12 0.021 0.002 14 0.140 0.020 16 0.377 0.100 18 0.857 0.110 20 1.018 0.203 131 3A.5. Discussion It is important to note that most of the methods examined in this appendix yield comparable values for the corrected plate height and, hence, comparable kinetic rate constants. However, the number of variables and the accuracy with which they are known can limit the accuracy of each method. The van Deemter equation is straightforward, having no adjustable parameters. The Purnell equation generates comparable values to the van Deemter equation, however, it relies on a proportionality constant (X) that dictates the magnitude of the mass transfer term. While the Giddings mass transfer equation is straightforward, it also relies on a proportionality constant (0). Depending upon the magnitude of this constant, it can cause an overcorrection in the plate height for some solutes at some flow rates, making it less useful in practice. The Giddings coupling theory, with a similar adjustable parameter, provides corrected plate heights that are approximately half the magnitude of the other classical models. On the other hand, the modern approach developed by Miyabe and Guiochon yields corrected plate heights that are substantially larger than those from the classical methods. This method is more challenging to use, as it relies on experimentally derived values for numerous variables. Thus, after investigation of each method, the van Deemter equation is deemed most suitable for these chromatographic conditions and, thus, was selected for primary use in the study in Chapter 3. 132 3A.6. References [1] [2] I3] [4] I5] [6] [7] J.J. van Deemter, F.J. Zuiderweg, A. Klinkenberg, Chem. Eng. Sci. 5 (1956) 271-289. M.J.E. Golay, Gas Chromatography, Butterworths, London, 1958. R.H. Perrett, J.H. Purnell, Anal. Chem. 35 (1963) 430-439. J.C. Giddings, Dynamics of Chromatography Part 1 Principles and Theory, Marcel Dekker, New York, 1965. J.C. Giddings, Nature 187 (1960) 1023-1024. K. Miyabe, G. Guiochon, J. Sep. Sci. 26 (2003) 155-173. C.R. Wilke, P. Chang, A.l.Ch.E. 1 (1955) 264-270. 133 4.1 EA ll! 0" 5‘- b“ CHAPTER 4 THERMODYNAMIC AND KINETIC CHARACTERIZATION OF A BRIDGED-ETHYLENE HYBRID C13 STATIONARY PHASE 4.1 Introduction Silica-based supports remain the most widely used materials for reversed- phase liquid chromatography (RPLC) separations. However, a number of improvements have been made to these phases in recent years that address chromatographic problems related to the silica support [1-7]. These improvements have significantly influenced the types of separations that can currently be performed. Nevertheless, problems with silica-based materials continue to exist at high and low pH, extreme temperature, and for basic solutes interacting with residual silanol groups. For this reason, a support material based on a hybrid organic — inorganic particle has been developed and widely used as an RPLC stationary phase. This bridged-ethylene hybrid (BEH) particle is synthesized by the co-condensation of 1,2-bis(triethoxysilyl)ethane with tetraethoxysilane (Figure 1.2) [8]. This support particle has the mechanical strength of silica yet the pH stability of polymeric particles [8,9]. In addition, the ethylene bridge in the backbone is thought to decrease the number of silanols available to bind to basic solutes. The hybrid phase has been employed in many studies under numerous experimental conditions. However, only a few reported studies afford thermodynamic information about the hybrid material [10,11] while no studies provide kinetic information. A thermodynamic evaluation of a C13 hybrid phase was performed as a function of temperature (423 to 473 K) in an aqueous mobile 134 phase using alkyl benzenes and aromatic alcohols [10] and substituted anilines [11]. Linear van’t Hoff plots were obtained and negative changes in molar enthalpy were reported. Further investigation of toluene at a wider temperature range (303 to 473 K) was performed. A change in slope of the van’t Hoff plot near 370 K was seen and was attributed to a change in the conformation of the stationary phase in the presence of the mobile phase [10]. Nevertheless, a direct comparison to silica-based materials was not performed and has not been reported in the literature. Nitrogen-containing polycyclic aromatic hydrocarbons (NPAHs) are an interesting set of basic compounds that have been thoroughly investigated on silica-based materials [12,13]. NPAHs are commonly found in tobacco smoke [14,15], automobile exhaust [16], fossil fuels [17,18], and even lake sediment [19], and have been identified as carcinogens [20]. RPLC has proven useful for the separation of complex NPAHs. Their asymmetric peak shapes make them a suitable set of solutes for examination of the thermodynamic and kinetic behavior of hybrid stationary phases. The goals of this research are as follows: (1) to separate a series of NPAHs and their parent polycyclic aromatic hydrocarbons (PAHs) using a hybrid C13 packing material, (2) to observe the effect of temperature on thermodynamic and kinetic behavior, (3) to examine the effect of protic and aprotic mobile phase on thermodynamic and kinetic behavior, and (4) to compare specific thermodynamic and kinetic parameters to silica-based C13 phases in an effort to identify the retention mechanism of the hybrid C13 material. 135 4 4.2 Theory The determination of thermodynamic and kinetic contributions to retention requires a synthesis of traditional thermodynamic and transition state theories [21,22]. In this evaluation, the transfer between mobile and stationary phases is treated as a chemical reaction. The thermodynamic and kinetic theory utilized within this chapter was explained in Chapter 1.2. 4.3 Methods 4.3.1 Reagents As shown in Figure 4.1, two PAHs and six nitrogen-containing NPAHs are chosen to study the effect of nitrogen position, ring number, and annelation structure on the thermodynamics and kinetics of retention. Pyrene, benz[a]anthracene, 1-aminopyrene (Sigma-Aldrich), 1-azapyrene, 4-azapyrene, benz[a]acridine, dibenz[c,h]acridine, and dibenz[a,j]acridine (Institute fiir PAH Forschung) are obtained as solids and dissolved in high-purity methanol and acetonitrile (Burdick and Jackson Division, Honeywell) to yield standard solutions with concentrations between 10'3 M and 10'5 M. A non-retained marker, 4- bromomethyl-7-methoxycoumarin (Sigma), is added to each solution at a concentration of 10'3 M. 4.3.2 Experimental system The solutes are separated on a capillary liquid chromatography system with multiple on-column detectors as illustrated in Figure 2.4. The stationary phase is a hybrid-based C13 material (XBridge C18, Waters Corporation) described in Chapter 2.2. The mobile phase consists of methanol or acetonitrile. 136 NH2 Pyrene 1-Aminopyrene 1 -Aza pyrene ‘ Benz[a]anthracene Dibenz[c,h]acridine Dibenz[a,j]acridine FFQUI'e 4.1. Structures of the polycyclic aromatic hydrocarbons (PAHs) and ~%TEQen-substituted polycyclic aromatic hydrocarbons (NPAHs) examined in this Y. 137 The sample is split between the capillary column and a fused-silica capillary (50 pm i.d., Polymicro Technologies), resulting in an injection volume of 10 nL. A fused-silica capillary (20 pm i.d., Polymicro Technologies) is attached post-column to serve as a restrictor. The temperature was varied from 283 to 313 K (i 0.1 K), while the pressure was maintained at 2000 psi. 4.3.3 Data analysis After separation, the zone profile for each solute is extracted from the chromatogram. Each profile is fit by nonlinear regression to a combination of Gaussian (Equation 1.33) and asymmetric double sigmoidal (Equation 3.25) equations using a commercially available program (Peakfit v4.14, SYSTAT Software). This method produces high quality fits (correlation coefficients ranging from 0.999 to 0.956), reduces noise, and allows control of peak integration limits. The fit is regenerated in Microsoft Excel, from which the statistical moments are calculated. In this work, the peak boundaries are identified at 0.1 % of the maximum peak height, as the error in the calculation of the statistical moments has been proven small at this integration limit [23]. The data are analyzed using the plate height model (statistical moment model) as described in Chapter 3.2.1. 4.4 Results and discussion The choice of mobile phase has been shown to be very relevant to separation behavior on silica-based stationary phases [12]. In this study, both protic (methanol) and aprotic (acetonitrile) solvents are evaluated. The methanol mobile phase can form hydrogen bonds with the NPAHs, inhibiting their ability to 138 adsorb at silanol sites. Methanol can also form hydrogen bonds with silanol sites in the hybrid support, displacing or competing with the NPAHs. In these ways, methanol reduces the interactions of the NPAHs with silanol sites. However, acetonitrile cannot undergo hydrogen—bonding interactions, and, therefore retention behavior under such conditions is of interest. 4.4.1 Methanol mobile phase Figure 4.2 shows a representative set of chromatograms. In methanol, 3 neutral solute, such as pyrene (Figure 4.2A) has a symmetric peak shape. However, a basic solute, such as 4-azapyrene (Figure 4.28) has a tailing peak shape. The peak shape for pyrene is representative of benz[a]anthracene, 1- aminopyrene, and dibenz[c,h]acridine. The peak shape for 4-azapyrene is representative of the remaining NPAHs. 4.4.1.1 Thermodynamic behavior 4.4.1.1.1 Retention factor Table 4.1 summarizes the retention factors for the PAHs and NPAHs. For the most part, retention factors for the NPAHs are notably smaller than those for the parent PAHs. The retention factors for 1-aminopyrene and 4-azapyrene are smaller by 76 % and 20 "/0 than pyrene, respectively. In addition, the retention factor for benz[a]acridine is smaller by 45 % than benz[a]anthracene. This decreased retention behavior is due to the increased polarity of the NPAHs relative to the PAHs and is consistent with a partition mechanism. This behavior was also observed with stationary phases built on silica supports [12]. In addition, retention increases with the number of aromatic rings and less 139 .. .3 00200050: 0. .::0E:oo >xo:.0E-n-_>:.0EoEoB-v. 03:08 0E: 0.o> 0:... .0000:a 0.59: .v. mom. 0.5.8.000 0:0 .v. 000. .o:0:.0E :_ 0:006 .o wEmcmofiEoEo 02.0.:00050m ”0 00.000050: 0. .::0E:oo >xo:.0E-\.-_>:.0EoEo:0-v. .0008 0E: 29 0: ._. .0000:0 0:08: C. mom. 0.5.8.000 0:0 O. 000. .o:0:.0E :_ 0:00.800-.. .0 08000900800 0>..0.:000:00m "0N6 050.". .55. 0.2: 04 00 mm 00 em on 0. N. L p _ — n _ — 0.5.8.8... -- W090: It -- J .l). 141 Table 4.1: Retention factor (k) and change in molar enthalpy (AH) for PAH and NPAH solutes in methanol (2000 psi). Values in parentheses have large errors and are given for illustrative purposes only. Solutes: pyrene (P), 1-aminopyrene (1AmP), 1-azapyrene (1AzaP), 4-azapyrene (4AzaP), benz[a]anthracene (B[a]A), dibenz[a,j]acridine benz[a]acridine (B[a]Ac), (D[aj]Ac), dibenz[c,h]acridine (D[ch]Ac) Retention factor, k Molar Solute Enthalpy T = 288 K T = 313 K AH (kcallmolL P 0.78 0.55 -2.5 i 0.1 1AmP 0.15 0.13 -1.4i0.1 1AzaP 0.62 0.82 (3.1 i 1.4) 4AzaP 0.45 0.44 (1.6 i 1.1) B[a]A 0.92 0.62 -3.0 i 0.1 B[a]Ac 0.43 0.34 -1.6 i 0.1 D[aj]Ac 0.92 0.51 4.0 i 0.3 D[ch]Ac 1.80 1.02 4.3 i 0.2 condensed annelation structure. These trends are again, consistent with a partition mechanism and with phases built on silica supports. Table 4.1 demonstrates the effect of temperature. Retention factors decrease significantly (13 — 45 %) with increasing temperature, except for 1- azapyrene and 4-azapyrene, which fluctuate, yet increase (32 %) or remain the same with temperature, respectively. A decrease in retention factor with temperature is expected under a partition-dominated mechanism. 4.4.1.1.2 Molar enthalpy Figure 4.3 displays a representative graph of the logarithm of the retention factor versus inverse temperature (van’t Hoff plot). The graph for each solute in Figure 4.3A is linear (R2 = 0.973 —- 0.997) and the slope is positive. A linear graph indicates that the change in molar enthalpy is constant over the temperature range of the study (283 — 313 K), which suggests that there is no significant change in retention mechanism in this region. A positive slope indicates a negative change in molar enthalpy, suggesting the transfer from mobile to stationary phase is an enthalpically favorable process. The graph of 1- azapyrene and 4-azapyrene in Figure 4.38 is roughly linear (R2 = 0.554 and 0.346), however the slope is negative. A negative slope indicates a positive change in molar enthalpy, suggesting the transfer from mobile to stationary phase is not enthalpically favorable. This will be discussed in more detail in the following paragraph. The change in molar enthalpy is calculated from the slope of Figure 4.3, according to Equation 1.7, and is summarized for all solutes in Table 4.1. The 143 .0. 350.823.9339 ..O. 0:.0:00....0.N:00.0 ..I. 0:.0:00.0.~:00 ..D. 0:000.:.:0.0.~:00 ..U. 0:038:80; ..O. 0:030 000:0 0:008 .0:0:.08 .0. 05.0.0080. 00:08. 0:0:0> 0.00. 00000.0. .0 :0000 0208000000.”. "<0... 0.50.". ..-0. 0-9 x . 000200020: . 00.0 00.0 0.9.0 0V0 00.0 00.0 0N0 0N0 m ...0 _ L . . p . . v.0 T I+ +1 O I. II- + - + III-II Il'iII % l: I. a N oil 0 H. 0] -. m I... V 3 l O a 0.. 144 .4. 0008.00.00-.. ..4. 0:08.000- F 000:0 0:008 .0:0:.08 ..o. 05.0.0080. 00:08. 0:0:0> 00.00. 5000.0. .0 :00... 0>_.0.:000._00m_ "mm... 0.50.". ..-v. 0-0. x . 0002000sz F 00.0 00.0 04.0 as...” 00.0 00.0 00.0 00.0 0.0 _ _ . . P . _ P.O HOLOVd NOIlNEIiEH 0.. 145 changes in molar enthalpy are least negative for 1-aminopyrene and benz[a]acridine, followed by pyrene and benz[a]anthracene, and become even more negative for dibenz[a,j]acridine and dibenz[c,h]acridine. These trends indicate that the change in molar enthalpy becomes more negative with increasing ring number and with less condensed annelation structure. These trends also were observed on silica-based stationary phases and have been discussed in depth previously [12,24]. The change in molar enthalpy may be attributed to the depth to which each PAH can penetrate into the stationary phase. The proximal regions, where the alkyl group is bound to the silica surface, are highly ordered with all trans carbon - carbon bonds. As the distance from the surface increases, there are more gauche bonds and greater disorder [25-27]. The more condensed PAHs, such as pyrene, probe only the distal regions of the alkyl chain, while less condensed PAHs, such as benz[a]anthracene, penetrate more deeply into the ordered regions of the alkyl chain. Therefore, the change in molar enthalpy becomes more negative the farther the PAH can access in the inner region of the stationary phase. The change in molar enthalpy is positive for 1—azapyrene and 4- azapyrene, corresponding to the negative slope in the van’t Hoff plot. However, the slopes of these curves have large uncertainties. Despite the uncertainty in the measurement, some discussion of this interesting behavior is warranted. At high temperature, the alkyl chains of the stationary phase become more fluid like, making the surface of the underlying particle more accessible. It is possible that at the higher temperatures used in this study, 1- and 4—azapyrene are able to 146 access the underlying particle more easily. In this case, these solutes may be able to adsorb more strongly at the residual silanol sites. Thus, the retention mechanism for these solutes changes over the temperature range investigated. A change in molar enthalpy is not meaningful when two separate processes, in this case a change in retention mechanism, are occurring. 4.4.1.2 Kinetic behavior Thermodynamics provides information about steady-state behavior for the change between mobile and stationary phases; however it does not fully explain the retention mechanism. By considering a transition state, the pseudo-first order rate constants and activation energies can be calculated with the equations developed in Chapter 1.2.2. These values help to quantify the kinetic aspects of mass transfer between the mobile and stationary phases as a function of solute structure. These data provide information about the retention mechanism that would not be available from thermodynamic data alone. 4.4.1.2.1 Rate constants Table 4.2 summarizes the rate constants for the PAHs and NPAHs. At 288 K, benz[a]anthracene, 1-aminopyrene, and dibenz[c,h]acridine undergo the fastest rate of mass transfer, followed by pyrene, benz[a]acridine, and dibenz[a,j]acridine, with 1-azapyrene and 4-azapyrene having the slowest rate of transfer. 1-Azapyrene and 4-azapyrene are given only as an indication of their slow rate of transfer; the kinetic values are not reliable based on the uncertainty in the experimental measurement for those solutes. The rate-limiting step for dibenz[c,h]acridine is the transfer from stationary to mobile phase, since the 147 Table 4.2: Rate constants (kms and ksm) for PAH and NPAH solutes in methanol. Solutes defined in Table 4.1. Rate constant, km, (5'1) Rate constant, ks". (5'1) Solute T=288K T=313K T=288K T=313K P 0.69 220 0.53 120 1AmP 27 -- 4.1 - 1AzaP 0.005 0.003 0.003 0.003 4AzaP 0.009 0.01 0.006 0.006 B[a]A 500 -- 460 -- B[a]Ac 0.03 0.09 0.02 0.03 D[aj]Ac 0.03 0.96 0.04 0.49 DEhJAC 8.1 500 15 180 148 retention factor (k = ksm/kms) is greater than one. in contrast, the rate-limiting step for all other solutes is the transfer from mobile to stationary phase, since the retention factor is less than one. The rate constants for the four-ring NPAHs are notably smaller than those for their parent PAHs, with the exception of 1-aminopyrene. 1-Azapyrene and 4- azapyrene have rate constants that are two orders of magnitude smaller than pyrene. In addition, the rate constant for benz[a]acridine is five orders of magnitude smaller than benz[a]anthracene. In this case, the nitrogen in benz[a]acridine can adsorb to silanol groups causing a decrease in the rate constant compared to its parent PAH. This effect was not observed in the thermodynamic data, however, kinetic information provides a more sensitive indication of the retention mechanism. Table 4.2 demonstrates the effect of temperature on rate constants. The rate constants for most solutes increase significantly, while the rate constants for 1-azapyrene and 4-azapyrene decrease with increasing temperature. Some rate constants are not provided for 1-aminopyrene and benz[a]anthracene at the highest temperature due to overcorrection of the plate height for these narrow peaks. According to Equation 3.9, if the sum of the theoretical A, B, and C terms is larger than the observed plate height, an overcorrection will occur that causes the corrected plate height and the rate constants to be negative and, thus, indeterminate. This is common for very narrow peaks, where the theoretical correction terms overestimate the width of the experimental zone profile. An increase in rate is expected with an increase in temperature due to increased 149 diffusion coefficients and enhanced fluidity of the stationary phase. An increase in kinetic energy due to increased temperature allows the alkyl chains to become more labile, which in turn allows the solutes to diffuse in and out of the stationary phase more freely. 4.4.1.2.2 Activation energy Figure 4.4 shows a representative graph of the logarithm of the rate constant from stationary to mobile phase (kms) versus the inverse temperature. The graph does not contain information for 1-azapyrene and 4-azapyrene, due to uncertainty in the measurement, or for 1-aminopyrene, due to the narrow peak shape. Of those shown, the graph for each solute is roughly linear (R2 = 0.442 — 0.980) and the slope is negative. A negative slope is indicative of a positive energy barrier for mass transfer. The activation energy is calculated from the slope of this graph, according to Equation 1.13, and is summarized in Table 4.3. The activation energies are positive for all solutes listed. The activation energy for the transfer from stationary phase to transition state (AEts) is greater that that from mobile phase to transition state (AEmi). These data indicate that it is easier for the solutes to enter the stationary phase than to exit. With the exception of benz[a]acridine, all solutes seem to have a similar energy barrier, which suggests they encounter a similar barrier at the interface between mobile and stationary phases. In addition, the activation energies are similar to those reported on silica-based materials [12,24]. 150 AOV 059.602.3209“. .AOV 0c_n_._00=.0_Nc0n_u .AIV 052803200 ADV 0509535200 .AOV 0:093 00ch 0:09: 032.9000 .3 0.30.0QE9 00.02: 0:0.0> 290.50 000. 96 500.6 039500.501 #6 052". AL. m.2 x v 00:200.”.sz F mom 8.0 3m 9% mom com mum 8.0 2.0 Sod ) b r ‘_ o 151 - 5.0 m 3 no 0 N_ es 1 F .0 V N” '— wufll - or s Q. z.oor coo _. Table 4.3: Activation energy (AEtm and AEts) for PAH and NPAH solutes in methanol. Solutes defined in Table 4.1. Activation Energy Solute A5,.“ 135;, (kcal/mol) ikcallmol) P 37 i 4 39 i 4 B[a]A 30 i 11 33 i 10 B[a]Ac 2 i 3 6 i 3 D[aj]Ac 17 i 3 21 i 4 D[ch]Ac 25 i 5 29 i 4 152 4.4.2 Acetonitrile mobile phase Figure 4.2 shows a representative set of chromatograms in acetonitrile mobile phase. In acetonitrile, a neutral solute, such as pyrene (Figure 4.2A) has a tailing peak shape. However, a basic solute, such as 4-azapyrene (Figure 4.28) has a more pronounced tailing peak shape. The peak shapes for benz[a]anthracene and 1-aminopyrene remain symmetric in acetonitrile. The peak shape of pyrene is representative of the peak shape for dibenz[c,h]acridine. The peak shape for 4-azapyrene is representative of the remaining NPAHs. 4.4.2.1 Thermodynamic behavior 4.4.2.1.1 Retention factor Table 4.4 summarizes the retention factors for the PAHs and NPAHs. When compared to the methanol mobile phase (Table 4.1), almost all solutes demonstrate an increase in retention factor in acetonitrile. Benz[a]anthracene and dibenz[c,h]acridine show a decrease in retention in acetonitrile. Since acetonitrile is less polar than methanol, the retention factor would be expected to decrease if the partition mechanism were dominant. Thus, the observed increase in retention factor suggests that for many solutes, the adsorption mechanism is contributing more greatly to retention in acetonitrile than in methanol. The increase in retention factor going from methanol to acetonitrile is moderate for pyrene (5 %), but is more substantial for the other solutes (50 — 69 %). In addition, retention factors for the NPAHs are very similar to or larger than those for the parent PAHs, also suggesting that the adsorption mechanism is dominant for these solutes in acetonitrile. 153 Table 4.4: Retention factor (k) and change in molar enthalpy (AH) for PAH and NPAH solutes in acetonitrile (2000 psi). Solutes defined in Table 4.1. Retention factor, k MOI?" Solute Enthalpy T = 288 K T = 313 K AH (kcallmol) P 0.82 0.52 -3.5 i 0.2 1AmP 0.23 0.16 -2.7 i 0.1 1AzaP 1.33 0.58 (-6.8 i 3.1) 4AzaP 0.93 0.47 —4.4 i 0.5 B[a]A 0.78 0.47 -3.7 i 0.1 B[a]Ac 0.71 0.33 -5.9 i- 0.4 D[aj]Ac 1.56 0.76 -6.0 i 0.5 D[chlAc 1.64 0.91 4.4 i 0.2 154 Table 4.4 demonstrates the effect of temperature on retention factor. Retention factors decrease significantly with increasing temperature. In fact, for the same change in temperature, the change is more significant in acetonitrile than in methanol. 4.4.2.1 .2 Molar enthalpy Figure 4.5 displays a representative graph of the logarithm of the retention factor versus inverse temperature (van’t Hoff plot). The graph for each solute in Figure 4.5A is linear (R2 = 0.978 — 0.999) and the slope is positive. The positive slope indicates a negative change in molar enthalpy, suggesting the transfer from mobile to stationary phase is an enthalpically favorable process. The graph of 1- azapyrene and 4-azapyrene in Figure 4.58 is roughly linear (R2 = 0.573 and 0.929), however due to the uncertainty in the measurement, the thermodynamic and kinetic information for these solutes is unreliable and is given for illustrative purposes only. Table 4.4 summarizes the change in molar enthalpy for all solutes. The change in molar enthalpy is least negative for 1-aminopyrene, followed by pyrene, benz[a]anthracene, and dibenz[c,h]acridine. The most negative change in molar enthalpy occurs for benz[a]acridine and dibenz[a,j]acridine. These trends indicate that the change in molar enthalpy does not consistently become more negative with increasing ring number and with less condensed annelation structure, as would be seen in a partition mechanism. The changes in molar enthalpy are more negative in acetonitrile than in methanol for most solutes by 1.0 - 4.3 kcal/mol. This change in molar enthalpy is consistent with adsorption in 155 AOV 0528032286 .AOV 0Eu:om:.£~c0n_u .AIV 0:6:00H0fic0n ADV 0:000_£:0H0_Nc0n .AOV 0c0§quEmé .AOV 0:030 00050 0.59: 0_E_:9000 ..8 003900;.0“ 0m_0>:_ 0:0.0> .200.— co=c0u0h ho £005 0209:0850”. "<90 059". Ex ”-9 x V 0035.00sz F mm.m omd mvd ovd mmd omd mm...” omd mfim — L _ F _ — h v.0 i HOlOVd NOILNELBH or 156 .4. 0.003030% AG. 0.00.303; 00ch 0:09: 0:55.000 .0. 0.30.0900. 00.02.. 0:0.0> .900. 5.200. .6 £005 02.950050”. "mmé 0.5m."— rv. ”-2 10032000sz F 00.0 om...” 01m 9%. 00m 80 00m 80 £0 _ _ _ P _ F — F.o H 2.. '— a N \‘\‘\ u T r _. m T 3 I... V O l— 0 no 0.. 157 an aprotic solvent [12]. However, the change in molar enthalpy is comparable in acetonitrile for benz[a]anthracene and dibenz[c,h]acridine (a difference of 0.1 - 0.7 kcal/mol). This suggests that the partition mechanism is still important for these solutes, such that the less polar mobile phase, acetonitrile, competes more effectively than methanol with the nonpolar stationary phase. These solutes are suspected to have less basic character, due to lack of nitrogen (benz[a]anthracene) and sterically-hindered nitrogen placement (dibenz[c,h]acridine), and, hence, less adsorption at residual silanol sites. The difference in molar enthalpy for acetonitrile compared to methanol is directly a result of the difference in retention factor. That is, the slopes of the van’t Hoff plots for the two solvents are comparable to one another. This behavior is unlike that seen on silica-based materials, where the molar entropy contributed more to the difference in retention factor than the molar enthalpy. In this study, the intercept of the van’t Hoff plots are very similar for acetonitrile and methanol, which suggests that the entropy term: does not change significantly with solvent. 4.4.2.2 Kinetic behavior 4.4.2.2.1 Rate constants Table 4.5 summarizes the rate constants for the PAHs and NPAHs. In acetonitrile, benz[a]anthracene and 1-aminopyrene undergo the fastest rate of transfer, followed by pyrene, benz[a]acridine, dibenz[a,j]acridine, and dibenz[c,h]acridine, which are three orders of magnitude slower. 1-Azapyrene and 4-azapyrene have the slowest rate of transfer, an order of magnitude slower 158 Table 4.5: acetonitrile. Solutes defined in Table 4.1. Rate constants (kms and km) for PAH and NPAH solutes in Rate constant, kms (3'1) Rate constant, ksm (3'1) Solute T=288K T=313K T=288K T=313K P 0.03 0.16 0.02 0.08 1AmP 1.1 -- 0.24 -- 1AzaP 0.002 0.005 0.002 0.003 4AzaP 0.003 0.002 0.003 0.002 B[a]A 8.4 4.7 6.2 2.1 B[a]Ac 0.03 0.02 0.02 0.003 D[aj]Ac 0.01 0.02 0.01 0.02 D[ch]Ac 0.03 0.05 0.05 0.04 159 than the majority of the solutes. 1-Azapyrene and 4-azapyrene are given only as an indication of their slow rate of transfer. As previously stated, the kinetic values for those solutes are not reliable based on the uncertainty in the experimental measurement. The rate constants in acetonitrile are one to four orders of magnitude smaller when compared to those in methanol. The differences in the rate constants result from the increased ability of the NPAHs to interact with available silanols on the hybrid support. The aprotic solvent, acetonitrile, does not interact with the silanol sites as does the protic solvent, methanol. Therefore, the rate constants between the mobile and stationary phases are substantially slower. Table 4.5 demonstrates the effect of temperature on the rate constants. The rate constants for most solutes increase significantly, while the rate constants for 4-azapyrene, benz[a]anthracene, and benz[a]acridine decrease with increasing temperature. An increase in rate is expected with an increase in temperature due to increased diffusion coefficients and enhanced fluidity of the stationary phase. An increase in kinetic energy as a consequence of increased temperature allows the alkyl chains to become more labile, allowing easier access for the solutes. 4.4.2.2.2 Activation energy Figure 4.6 shows a representative graph of the logarithm of the rate constant versus the inverse temperature. The graph does not contain information for 1-azapyrene and 4-azapyrene, due to uncertainty in the measurement, or for 1-aminopyrene, due to its narrow peak shape. Of those 160 .0. 05280332090 ..9. 0c.u:om=.0.~:0£0 ..I. 052830.200 ..DV 0c0omE.c0.0.Nc0n ..O. 0:030 00ch 0:00.: 0.3.5.000 .5. 05.00080. 0202: 030.? 0:00:00 0.0.. 96 £005 0>=0E0m0a0m 6a. 0.39". .3. 02 x V 003200020: F 000 8.0 04.0 9% mm...” 80 mg 8.0 2.0 p . _ _ _ _ r Foo.o ..o.o '— .Pd 3 O O N S -F I. V N II— 0» -or m; S. .2: ooow 161 shown, the graph for almost all solutes is roughly linear (R2 = 0.525 - 0.970) and the slope is negative. A negative slope is indicative of a positive energy barrier for mass transfer. The rate constants for benz[a]anthracene fluctuate with temperature and, therefore, the slope is not linear. The activation energy is calculated from the slope of this graph, according to Equation 1.13, and is summarized in Table 4.6. The activation energies are positive for pyrene and dibenz[a,j]acridine. The activation energy is negative for the other solutes, however, due to uncertainty in the measurement these values are likely not meaningful. For pyrene and dibenz[a,j]acridine, the activation energy for the transfer from stationary phase to transition state (AEts) is greater that that from mobile phase to transition state (AEtm). These data indicate that it is easier for the solutes to enter the stationary phase than to exit. This behavior is similar to that seen in methanol. 4.5 Conclusions In this study, the thermodynamic and kinetic behavior of NPAHs was examined in reversed-phase liquid chromatography. The parent PAHs are separated primarily by the partition mechanism with the octadecyl groups, but some minor interaction with the silanol groups can occur through the aromatic system. In methanol mobile phase, the retention factors for the NPAHs are less than those for the parent PAHs. This is consistent with a partition mechanism, where retention decreases as the polarity of the solute increases. In addition, the trends of retention with ring number and annelation structure are consistent with the partition mechanism. However, the kinetic rate constants indicate that 162 Table 4.6: Activation energy (sz1.m and AE¢S) for PAH and NPAH solutes in acetonitrile. Solutes defined in Table 4.1. Activation Energy Solute AEtm AEts (kcallmol) (kcallmol) P 9 i 2 12 i 2 B[a]A (-17 i 10) (-14 i 10) B[a]Ac (-11 i 2) (--2 i 1) D[aj]Ac 4 i 1 10 i 1 D[ch]Ac (-0.9 i 2) 3 i 2 163 adsorption at silanol sites could play a role, as they are significantly smaller for the NPAHs than for the parent PAHs. The different thermodynamic and kinetic behavior in the presence of the aprotic solvent acetonitrile provides an interesting picture of the retention process. Methanol is able to hydrogen bond with both the NPAH solutes and the underlying silanols, which causes a reduction in the number of available silanols. Acetonitrile cannot hydrogen bond in this way to shield interactions of the solute with the underlying particle. Thus, the retention factors for the NPAHs are larger than those in methanol. Moreover, the retention factors for the NPAHs are more similar to or larger than those for the PAHs, suggesting the adsorption mechanism is likely dominant for the NPAH solutes. The changes in molar enthalpy for the NPAHs are slightly more negative than for the PAHs and are sufficient to account for the small changes in retention factor. If the change in molar enthalpy was not sufficient to account for the change in retention factor, a change in entropy or the phase ratio would be responsible, according to Equation 1.7, as was the case for silica-based C18 [12]. However, for the hybrid support, there does not seem to be a significant change in the molar entropy or phase ratio for acetonitrile. The kinetic behavior also reflects the increased role of adsorption, as the rate constants are one to four orders of magnitude smaller than those in methanol. The thermodynamic and kinetic behavior of the solutes on this hybrid phase is similar in nature to those built of silica supports [12]. The retention factors in both mobile phases are smaller for the same set of solutes under 164 similar conditions than on the silica phases. The rate constants in methanol are faster, while those in acetonitrile are slower on the hybrid phase compared to the silica phase. The change in molar enthalpy is less negative for the hybrid phases compared to the silica phases for the same solutes. However, the bonding density of the hybrid phase is more similar to the bonding density of the monomeric phase than the polymeric phase used in previous studies [21,28]. When this monomeric silica phase is considered, the changes in molar enthalpy are more consistent to the hybrid phase in this study. The thermodynamic and kinetic information provide a clearer description of the retention mechanism of NPAHs on hybrid supports in reversed-phase liquid chromatography. 165 4.6 [1] [2] [3] [4] [5] [5] [7] [8] [9] [10] [11] [12] [131 [14] [15] [16] [17] References J.W. Dolan, LCGC North America 23 (2005) 470-475. T.V. Koval'chuk, U. Lewin, V.N. Zaitsev, W. Engewald, J. Anal. Chem. 54 (1999)115-121. J.J. Kirkland, J.L. Glajch, RD. Farlee, Anal. Chem. 61 (1989) 2-11. N. Sagliano, T.R. Floyd, R.A. Hartwick, J.M. Dibussolo, N.T. Miller, J. Chromatogr. A 443 (1988) 155-172. J. Layne, J. Chromatogr. A 957 (2002) 149-164. U.D. Neue, Y.-F. Cheng, 2. Lu, B.A. Alden, P.C. Iraneta, C.H. Phoebe, K. Van Tran, Chromatographia 54 (2001) 169-177. J.W. Coym, J. Sep. Sci. 31 (2008) 1712-1718. K.D. Wyndham, J.E. O'Gara, T.H. Walter, K.H. Glose, N.L. Lawrence, B.A. Alden, G.S. lzzo, C.J. Hudalla, P.C. Iraneta, Anal. Chem. 75 (2003) 6781- 6788. J.E. O'Gara, K.D. Wyndham, J. Liq. Chromatogr. Relat. Technol. 29 (2006) 1025-1045. Y. Liu, N. Grinberg, K.C. Thompson, R.M. Wenslow, U.D. Neue, D. Morrison, T.H. Walter, J.E. O'Gara, K.D. Wyndham, Anal. Chim. Acta 554 (2005) 144-151 . S. Shen, H. Lee, J. McCaffrey, N. Yee, C. Senanayake, N. Grinberg, J. Clark, J. Liq. Chromatogr. Relat. Technol. 29 (2006) 2823-2834. V.L. McGuffin, S.B. Howerton, X. Li, J. Chromatogr. A 1073 (2005) 63-73. H. Colin, J.-M. Schmitter, G. Guiochon, Anal. Chem. 53 (1981) 625-631. 81.. Van Duuren, J.A. Bilbao, C.A. Joseph, J. Natl. Cancer Inst. 25 (1960) 53. M. Dong, I. Schmeltz, E. Jacobs, D.J. Hoffman, J. Anal. Toxicol. 2 (1978) 21. E. Sawicki, J.E. Meeker, M.J. Morgan, Arch. Environ. Health 11 (1965) 773. J.M. Schmitter, H. Colin, J.L. Excoffier, P. Arpino, G. Guiochon, Anal. Chem. 54 (1982) 769-772. 166 l.-. fil [18] [19] [20] [21 ] [22] [23] [24] [25] [25] [27] [28] C. Borra, D. Wiesler, M. Novotny, Anal. Chem. 59 (1987) 339-343. S.G. Wakeham, Environ. Sci. Technol. 13 (1979) 1118. J.C. Arcos, M.P. Argus, Chemical Introduction of Cancer, Academic Press, New York, 1974. SB. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-35448. V.L. McGuffin, C. Lee, J. Chromatogr. A 987 (2003) 3. SB. Howerton, C. Lee, V.L. McGuffin, Anal. Chim. Acta 478 (2003) 99. SB. Howerton, V.L. McGuffin, J. Chromatogr. 1030 (2004) 3-12. C.J. Orendorff, M.W. Ducey Jr., J.E. Pemberton, J. Phys. Chem. A 106 (2002)6991. M.W. Ducey Jr., C.J. Orendorff, J.E. Pemberton, L.C. Sander, Anal. Chem. 74 (2002) 5576. MW. Ducey Jr., C.J. Orendorff, J.E. Pemberton, L.C. Sander, Anal. Chem. 74 (2002) 5585. V.L. McGuffin, S.-H. Chen, J. Chromatogr. A 762 (1997) 35-46. 167 CHAPTER 5 EFFECT OF MOBILE PHASE MODIFIERS ON PEAK SHAPE USING BRIDGED-ETHYLENE HYBRID STATIONARY PHASES 5.1 Introduction As demonstrated in Chapter 4, nitrogen-containing polycyclic aromatic hydrocarbons (NPAHs) exhibit severely tailing peak shapes under typical reversed-phase liquid chromatographic (RPLC) conditions. This phenomenon is believed to arise from interaction of the solute with two types of sites: one with a high population yet a weak interaction (C18) and another with a low population yet a strong interaction (residual silanols and metals). The weak interaction site is kinetically fast and contributes only to symmetric broadening, while the strong interaction site is kinetically slow, and can lead to asymmetric peak shapes. Many investigators have shown that peak shape can be controlled by reducing the interaction of the solute with such sites [1 ,2]. A common way to reduce tailing caused by surface sites is the use of mobile phase modifiers. A mobile phase modifier can act to reduce tailing in several ways: 1) it can interact with the solute, reducing the ability to interact with the slow site, 2) it can permanently block the slow site, or 3) it can displace the solute from the slow site. Several types of modifiers have been used to reduce the influence of residual surface silanols in silica-based supports. An acidic modifier, such as an alkylsulfonic acid [3,4], can sometimes improve peak shape, however, for many solutes, an improvement is not seen [4,5]. Basic modifiers, containing a form of amine, have proven more useful for eliminating tailing peak shapes of basic analytes [4,6-14]. A pivotal study by Bij et al. focused on 168 -- _- reducing the silanophilic interaction of the solute with surface silanol sites using water and amines as silanol masking agents [7]. This study was the first to demonstrate that silanophilic interaction could be eliminated by blocking surface silanols and by masking the solute itself. A number of different types of amines, including primary, secondary, and tertiary amines [9,13], and amines with various alkyl chain lengths [8,12,13] have been investigated. However in many cases, a simple tertiary amine, such as triethylamine, is sufficient to decrease peak tailing caused by interactions with surface silanol groups [6.10.13]. In addition, the combination of acid and base modifiers is commonly used in chiral chromatography to improve both retention and peak shape [3,14,15], although the mechanism of interaction for the modifiers has only been studied by a relatively small number of authors [16]. In addition to silanol sites, metals in the underlying stationary phase can cause deleterious effects. Metals increase the acidity of nearby silanols, which greatly affects the peak shape [17,18]. In addition, the concentration of the metal in the stationary phase was found to be relevant to both retention and peak asymmetry [19]. Therefore, a large effort has been made toward the removal of metals from stationary phase materials, however, many phases still contain trace amounts of various metals. Thus, a mobile phase modifier, acting as a metal chelating agent, could be used to prevent complexation of the amine solutes with the metals [20,21]. Alternatively, stationary phase production has been altered to allow for phases that limit interaction with metal and silanol sites. For instance, phases 169 have been developed with a lower number of accessible silanol sites, decreased metal content, and the incorporation of a polar functional group embedded in the C18 phase to limit interaction with metal and silanol sites [22-24]. In addition, the organic-inorganic hybrid materials are synthesized to have a lower number of silanol sites than traditional silica [25,26]. Regardless, peak tailing is still observed for these hybrid materials, as seen in Chapter 4. This chapter aims to further evaluate and understand the causes of peak tailing in hybrid stationary phases. The goals of this research are as follows: (1) to separate a series of NPAHs and their parent polycyclic aromatic hydrocarbons (PAHs) using hybrid packing materials, (2) to investigate the effect of the underlying particle on retention and peak shape, (3) to evaluate the effect of a polar embedded group in the C18 chain, and (4) to elucidate the effect of typical modifying agents on the retention and peak shape of the NPAHs. 5.2 Methods 5.2.1 Reagents As shown in Figure 4.1, two PAHs and six nitrogen-containing NPAHs are chosen to study the effect of nitrogen position, ring number, and annelation structure on retention, broadening, and peak asymmetry. Pyrene, benz[a]anthracene, 1-aminopyrene (Sigma-Aldrich), 1-azapyrene, 4-azapyrene, benz[a]acridine, dibenz[c,h]acridine, and dibenz[a,j]acridine (Institute ftir PAH Forschung) are obtained as solids and dissolved in high-purity methanol and acetonitrile (Burdick and Jackson Division, Honeywell) to yield standard solutions 170 with concentrations between 10'3 M and 10'5 M. A non-retained marker, 4- bromomethyI-7-methoxycoumarin (Sigma), is added to each solution at a concentration of 10'3 M. Acetic acid, acetyl acetone (Aldrich), triethylamine (Spectrum), and pyridine (Fisher) are separately added to fresh methanol and acetonitrile mobile phases (Burdick and Jackson Division, Honeywell) at a concentration of 0.2 % (v/v). In the case where two mobile phase modifiers are added, the concentration of each modifier is 0.2 %. 5.2.2 Experimental system The solutes are separated by capillary liquid chromatography with one on- column detector as illustrated in Figure 2.3. The stationary phases are the hybrid-based materials (XBridge C13, XBridge Shield RP13, and bridged-ethylene hybrid (BEH) support, Waters Corporation) described in Chapter 2.2. The mobile phase consists of methanol or acetonitrile with 0.2 % modifier. The sample is split between the capillary column and a fused-silica capillary (50 pm i.d., Polymicro Technologies), resulting in an injection volume of 10 nL. The temperature was not controlled (ambient), while the pressure was maintained at 2000 psi. 5.2.3 Data analysis After separation, the zone profile for each solute is extracted from the chromatogram. Each profile is fit by nonlinear regression to a combination of Gaussian (Equation 1.33) and asymmetric double sigmoidal (Equation 3.25) equations using a commercially available program (Peakfit v4.14, SYSTAT Software). This method produces high quality fits (correlation coefficients ranging from 0.999 to 0.956), reduces noise, and allows control of peak 171 integration limits. The fit is regenerated in Microsoft Excel, from which the statistical moments are calculated. In this work, the peak boundaries are identified at 0.1 % of the maximum peak height, as the error in the calculation of the statistical moments has been proven small at this integration limit [27]. The statistical moments are calculated based on the regenerated fit by c 1:] (t)tdt (5.1) [C(t)dt C(t)(t - M )"dt ,, =I 1 (5.2) [ C(t)dt where C(t) is the solute concentration as a function of time and n is the order of the moment. Values for M1, M2, and M3 describe the mean retention time, variance, and asymmetry, respectively. To evaluate the retention and peak shape, the retention factor (k), reduced plate height (h), and skew (s) are calculated as k = (M1?) (5.3) H M I. ":5": 22 (5.4) p M1dp S: N? (5.5) where to is the elution time of a non-retained solute, H is the plate height, and dp is the particle diameter. Each calculated parameter (k, h, 3) represents a 172 normalized value for a statistical moment (M1, M2, M3, respectively). which quantitatively describes retention and peak shape behavior for the separation. 5.3 Results 5.3.1 Methanol mobile phase 5.3.1.1 Without modifier Table 5.1 summarizes the retention factor, reduced plate height, and skew for each solute on each stationary phase in pure methanol mobile phase. 5.3.1.1.1 XBridge C13 The retention factors for each neutral PAH are larger than those for the related NPAHs. This behavior is consistent with the partition mechanism where the polarity of the NPAHs is increased relative to the PAHs. This behavior was also observed on silica-based supports [28,29]. In addition, solute structure plays an important role in retention. Retention factor increases with number of rings and decreases with more condensed annelation structure, again consistent with the partition mechanism. The reduced plate height is a measure of the broadening of the peak. The reduced plate heights for XBridge are near 2 for the majority of solutes, which corresponds to plate heights that are roughly 2 times the particle diameter (H z 10 pm). That is, for these solutes, the broadening is only caused by typical on-column processes such as multiple paths, diffusion, and fast mass transport. The solutes with larger reduced plate heights are 1- and 4-azapyrene and benz[a]acridine, each with a nitrogen atom placed on the outside of the ring 173 8.0 0.0 80.0 8.. 00 $3 5.0 00 003 2.5.0 8.0 0... 80.0 03 NF 8:. 8.0 ...0 0.0.0 2.0.0 8.0 0.0 5.0.0 .00 9. 08.0 00.0 o? 80.0 2.0.0 8.0 0.0 08.0 8.0 ...0 000.0 8.0 0.0 00.0 $0.0 8.0 0.0 03.0 3... 80 000.0 80 80 000.0 .024 8.0 0.0 000.0 .00 80 .000 0.1. .0 000.0 .05 8.0 0.0 80.0 8.0 E 08.0 00.0 mm 00.0 .53 8.0 0.0 08.0 50 S 90.0 8.0 00 000.0 a. m .. x m P. v. m .. c. .8052... :00 3%. .2020 00.2.0.2 20 00.2.0.2 635.0. 052.00.90.28... 630.0. 2.2.82.0.280 630.0. 8.2.8.00ch .303. 0c000.5c0.0.~c0n .3020. 020.300.1309.: 0:05.000; ..n....<_.. 000309.200-.. ..n.. 0:030 “005.0m 005.00... 305.3 0005. 0.30:. .0:050E .0. .0. 30.0 0.0 .3. 5.0.0: 0.0.0 000300. .9. .500. 00500.0". 3.... 030... 174 structure. This behavior suggests that, not only the nitrogen, but also its location in the ring structure, influences the broadening. The skew describes the asymmetry of a peak, where a positive value indicates a tailing peak and a negative value implies a fronting peak. A larger value for the skew indicates a more asymmetric peak. The skew for several solutes (pyrene, benz[a]anthracene, and dibenz[a,j]acridine) is equal to zero, indicating a symmetric peak shape. The skew is positive for the other solutes, indicating a tailing peak shape. For the most part, solutes with positive skew values have a nitrogen located on the outside edge of the ring structure, leaving the nitrogen accessible to interact with surface silanols or other slow sites. It is important to note that large values for the reduced plate height correspond with large positive values for the skew. However, reduced plate height and skew do not correspond with retention factor. That is, positive skews are observed for solutes with both small (4-azapyrene) and large (dibenz[c,h]acridine) retention. This implies that solute structure rather than solute retention is the important factor controlling broadening and asymmetry. 5.3.1.1.2 XBridge Shield RP13 The retention factors on XBridge Shield are comparable in magnitude to those on XBridge (Table 5.1). Neutral or neutral-like solutes (pyrene, benz[a]anthracene, and dibenz[c,h]acridine) are slightly less retained, while 1- aminopyrene and dibenz[a,j]acridine are slightly more retained than on XBridge. The differences in retention are due to the carbamate group in XBridge Shield. That is, as the polarity of the phase increases (due to the carbamate group), 175 polar compounds become more retained, consistent with the partition mechanism. However, retention factors for 1- and 4-azapyrene are comparable, suggesting their behavior is more consistent with the adsorption mechanism. In addition, the addition of the carbamate group reduces the number of carbons in the alkyl chain to 15 (as seen in Figure 2.2), which can also cause a difference in retention for solutes governed strictly by the partition mechanism. Reduced plate heights for XBridge Shield are 60 to 80 % larger than those of XBridge, except for benz[a]acridine which is 70 % smaller. All solutes have reduced plate heights greater than 2, with benz[a]anthracene and 1-aminopyrene having the smallest reduced plate heights. The skews are larger for most solutes on XBridge Shield compared to those on XBridge. The skew is largest for 4—azapyrene and pyrene, indicating they are the most tailing solutes. The skew is next largest for the acridine compounds, followed by 1-azapyrene. The skew for 1-aminopyrene and benz[a]anthracene are equal to zero, indicating symmetric peak shape. When the two C13 phases are compared, an interesting trend is observed as a function of retention factor. A larger retention factor on one phase corresponds to a smaller reduced plate height and skew. For example, the retention factor for pyrene is larger on XBridge than on XBridge Shield, however the reduced plate height and skew are smaller on XBridge. This behavior is observed for all solutes except for 1-aminopyrene, 4-azapyrene, and dibenz[a,j]acridine, which show the opposite trend. 176 The addition of the polar embedded group affects the broadening and asymmetry. For the solutes in this study, the polar embedded group does not improve the peak shape, as it is intended. If the slow site is located in the hybrid support, the polar embedded group does not adequately block it. Furthermore, the creation of additional slow sites may occur when the polar embedded group is included in the phase. This will be discussed in more detail in Section 5.4.5. 5.3.1.1.3 Bridged-ethylene hybrid (BEH) particle Several solutes (pyrene, benz[a]anthracene, 1-aminopyrene, and dibenz[c,h]acridine) are non-retained on the bridged-ethylene hybrid (BEH) support. These solutes are the neutral solutes, the amine, and a solute with a sterically-hindered nitrogen. The other solutes, 1- and 4-azapyrene, benz[a]acridine, and dibenz[a,j]acridine are retained on BEH. These retained solutes have similar nitrogen placement, each having a nitrogen atom located on the outside edge of the ring structure, leaving the nitrogen accessible to interact with surface silanols or other slow sites. Reduced plate heights on BEH range from 4.6 - 6.3 for both retained and non-retained solutes. In addition, all values for the skew are equal to zero, indicating symmetric peak shapes on the underlying support. It is interesting to note that solutes retained on BEH correspond to the same solutes that exhibit peak tailing on the C18 derivatized phases. This suggests that retention on the underlying particle, not asymmetry on the underlying particle, contributes to the asymmetry on the C13 derivatized phases. This hypothesis will be discussed in more detail in Section 5.4. 177 5.3.1.2 Effect of mobile phase modifiers The effect of each modifier in methanol mobile phase is examined as a function of retention factor, reduced plate height, and skew. Detailed information on the change in each parameter is given in Appendix 5A.1. Figure 5.1 shows the effect of mobile phase modifier on retention factor. The retention factor does not change substantially with the addition of any modifier for any of the phases. In general, acetic acid causes a decrease in retention, with several negative retention factors. On BEH in methanol mobile phase, the retention factor does not decrease with any mobile phase modifier. Figure 5.2 shows the effect of mobile phase modifier on reduced plate height. A reduced plate height equal to 2 is shown by a black line on the graphs. None of the mobile phase modifiers cause a universal decrease in the reduced plate height towards the ideal value of h = 2. While triethylamine causes a decrease in plate height for XBridge, an increase is observed for XBridge Shield, and no change is seen for BEH. Acetic acid seems to have little effect on the reduced plate height for all phases, while acetyl acetone causes an increase in plate height for the C18 phases but causes no significant change for BEH. Figure 5.3 shows the effect of mobile phase modifier on skew. Overall, only acetic acid causes a reduction in skew. For many solutes the skew becomes negative, indicating a fronting peak shape. This behavior is also observed on BEH. In some cases, a small decrease in skew is observed, however, a reduction in skew for all solutes does not occur. In addition, acetyl acetone seems to increase the skew for many solutes on the C13 phases. 178 .. .5 00.00.00. 0.0 0.0.00. 00500.0. 02.0002 ...0 0.00... 0. 000000 00.3.0w AEA. 000.000 .3000 ...0... 0.00 05000 ...0... 00.0.0350... A.. 60050... 0.00 000.000. 0005. 0:000. .0 02.00:. 0 00 ..000500. 0. 0.0 0000mx 00 0.0.00 0000 .0. .0.00. 00500.00. "(...m 0.50.". 2.5.0 2.0.0 $0.0 $0.0 002.. 002. 00.5 n. WW2“. W . . 5.0 A A . A .. A .. A a A A . - 3 a M. W. A . m. A. l— . O a < 0. 179 .. >0 00.00.00. 0.0 0.0.00. 00500.0. 02.0002 ...m 0.00H 0. 005.00 0228 ..xx. 000.000 3.000 ..§. 0.00 05000 ...0“... 00.0.0350... ..I. 60050:. 0.00 005.00... 00000 0:000. .0 00500:. 0 00 .000500. 0. 0.0m 0.0.0w 000.3? 00 0.3.00 0000 .0. .0.00. 00500.01 ”m fin 0.00.“. 2.5.0 2.0.0 2.0.0 $0.0 002.. 002. 02. 0 A. - 3.0 A A A A A A a A -3 a A m A u 0 N J.— v 0 l— -. O H. m. o. 180 ..0 00.00.00. 0.0 0.0.00. 00000.0. 02.0002 .. m 0.00... 0. 000000 00.28 A . 000.000 .3000 Ag. 0.00 00000 ..A.... . 00500.50... _Al. .00050E 0.30 000.000. 00000 0__00E .0 000003. 0 00 .00050E 0. 1mm 00 0.3.00 000.0 .0. .900. 00000.02 .0.. m 0.30.". 2.5.0 2.0.0 20.0 <0.0 002... 002. 02. 0 HOlOVd NOLLNBJEIH or 181 («>( 00000 0_.00E .0 02.003. 0 00 6000.00. 0. 20 0 0..mx 00 0.3.00 0000 .0. .0900 0.0.0 0003000. .. 0'5 “.9 8- d—l .3A 0 D: ”E 00 “95 “’0 2E 3; i.|.o. «>0 00.00.00. 0.0 0300.0 02.0002 .F .0 0.00... 0. 000 ..00 00.28 A... .. 000.000 3.000 .A 0.00 00000 A . 00.E0..A0.0... A! 6000.00. 0.30 .0 ..00E 00000 0:000. .0 02.003. 0 00 6000.00. 0. 0.0 0.00..mx 00 0.3.00. 0000 .0. 300w .. A ~ .\ .\ .\ .\ n .\ A A .\ A . -. . a A 311:? ximmzw’mr nwauuu‘rumwr‘n t"‘\ §;: :::L I :§,\:§:: :.l$\:'1.l;\:|‘::I,‘,§,i,:;§,i:k¢§§ ' '-‘ :‘J‘l‘ulwul H 1“!" . IS1YPFI'I"I‘1TWW " ‘J‘g‘ WH‘J.' gul'hfi'm'yK’:fi' m'?.yiltfii ‘I‘P‘I‘I‘P r‘r r. .r‘r‘r‘r‘r‘i.t.7. f‘ r‘r.r r.’ AWN» WW; wfiwhme‘h }_ l ' ' ‘I‘ V \' \ \ \' \ \‘ \ \ \1 _- . . ,—r r rr r ..... re ‘yr_ > r Yr . .- 4 - 4 ‘ r .' . . _‘ ’ .............................................. A w V 1’fi T Y (4w Y ~ 1 x V v 4. 1ww-r \ r Y 1 1 ‘ ‘ ‘ \.‘ \ \ \ \ \- \ \ NI 9, K \ .\ \ x x \ v - u «WU, unfit-31W": 13W u’rfctszn'w '3' :*: P *0'0’1'5'u' "r"\"'fi’h'\*i'i'¥r i ;1 “14!; ;§;§: \,§,‘!C,§,‘,i)~;t’| ‘g‘ 0 \;~[!,\ 0 ~ 100 10~ 186 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac p ined in Table 5.1. l. Solutes def // / Xx? :l. acetvl acetone ( ass;- di- ic aci l.acet u A A V V 5 s A A V V \ Skew for each solute on XBridge Shield RP18 in methanol as a function of mobile phase modifier. oure methanol (Ell. triethvlaminel Figure 5.38 :— .. 3 00.865 0.0 02.000 02.0002 ...m 030... 0_ 000000 00.2om QR. 000.000 3.000 Ag. 200 2.000 Am“... 05.003500. .A . _0000.0E 050 00500.: 00000 0__0oE .0 02.00:. 0 00 6000.00. 0_ 1mm 00 0.200 0000 00.3005 ”00.0 0..: E 2an 2.0.0 90.0.0 0.0.0 002.. 002. 0.05 0 — \r . p L p . h - Fo.o u _no 187 MEN'S o. 5.3.2 Acetonitrile mobile phase 5.3.2.1 Without modifier Table 5.2 summarizes the retention factor, reduced plate height, and skew for each solute on each stationary phase in pure acetonitrile mobile phase. 5.3.2.1.1 XBridge C13 The retention factors for most solutes are larger in acetonitrile (Table 5.2) than in methanol mobile phase (Table 5.1), yet are smaller for benz[a]anthracene and dibenz[c,h]acridine. In addition, the retention factors for 1- and 4-azapyrene are larger than that of their parent PAH, pyrene. Since acetonitrile is less polar than methanol, the retention factor is expected to decrease under a partition- dominated mechanism, as observed for benz[a]anthracene. However, the solutes with increased retention are likely dominated by an adsorption mechanism. The increase is small for pyrene (2 %), but larger for the other solutes (38 — 70 %). The increase in retention is consistent with silica supports, however, the increase is less pronounced on the hybrid phases than that reported on the silica phases (320 — 850 %) [29]. In addition, the role of annelation structure is different in acetonitrile mobile phase, with pyrene and benz[a]anthracene having equivalent values for retention factor. The reduced plate heights are larger in acetonitrile than in methanol, indicating increased broadening. The reduced plate height is largest for 1- and 4—azapyrene, followed by dibenz[a,j]acridine, and pyrene. The first three of these solutes are expected to have larger plate heights than the other solutes due to the accessible nitrogen in the ring structure. 188 00.0 0.0 000.0 00.0 E 0000 00.: 000 000. . 2.00.0 00.0 0. 000.0 0... 000 000.0 00.0 0000 0000 03.0.0 00.0 . . 000.0 3.0 E 0000 00.0 000 0.00 2.0.0 00.0 0.0 000.0 00.0 00 000.0 00.0 000 0000 <.0.0 00.0 00. 000.0 00.0 000.. 0000 00.0 000: 000.0 0003. .0.. 00. .000 00.. 000 .000 00... 0000 000.0 0005 00.0 E 000.0 E... 00. 000.0 00.0 00 0E0 055 00.0 0.0 0 .00 E. : 000 000.0 00.0 000. 000.0 0 0 0 0. 0 0 0. 0 0 0. 0.000302 :00 200 0.0.00 00000.. M:0 00.0000. ...0 9000 s 000000 00.200 000005 .80.? 00000 0:00... 20009000 00. A0. 3000 000 .A0. .0900 0.0.0 000000. A... 00.00. 0o_.00.0m "a... 0.00... 189 The skew is larger for all solutes in acetonitrile than in methanol. Thus, all solutes, both NPAHs and PAHs exhibit more asymmetric peak shapes in acetonitrile. The largest skew occurs for 4-azapyrene and dibenz[c,h]acridine, while the smallest skew occurs for benz[a]anthracene and benz[a]acridine. This is interesting behavior, as dibenz[c,h]acridine has comparable retention to the neutral PAHs in methanol, however is more comparable to the retention of the NPAHs in acetonitrile. On the other hand, benz[a]acridine which has an accessible nitrogen, has similar tailing behavior to its parent PAH, benz[a]anthracene in acetonitrile mobile phase. 5.3.2.1.2 XBridge Shield RP13 The retention factors for all solutes on XBridge Shield follow similar trends to those on XBridge in terms of ring number and annelation (Table 5.2). However, the retention factors for some solutes on XBridge Shield are smaller than those on XBridge. The reduced plate heights for all solutes are larger in acetonitrile (Table 5.2) than in methanol (Table 5.1). The reduced plate height is largest for 1- and 4-azapyrene, pyrene, and dibenz[a,j]acridine. However, the reduced plate height is smaller for most solutes on XBridge Shield than on XBridge, indicating that less symmetric broadening occurs on the shielded phase. This is evidenced by the value of h for dibenz[c,h]acridine on XBridge Shield (h = 13.5). Dibenz[c,h]acridine is the only solute with such a low value for the reduced plate height, however it indicates that some solutes are not as greatly affected by the symmetric sources of broadening as others. 190 Tile The skew for most solutes on XBridge Shield is similar to that on XBridge. The skew is largest for pyrene, followed by 4-azapyrene and dibenz[c,h]acridine. However, the skew is smaller on XBridge Shield than on XBridge for all solutes except 1-aminopyrene and pyrene. This behavior suggests that the shielded phase decreases the tailing for most solutes for acetonitrile mobile phase. When the two C13 phases are compared, an interesting trend is observed as a function of retention factor. An increase in retention factor between the two phases causes an increase in both reduced plate height and skew. For example, k for pyrene is larger on XBridge than on XBridge Shield with correspondingly larger values for h and skew. This behavior is observed for all solutes except benz[a]acridine, which shows only a small change in retention factor, but large changes for plate height and skew. The opposite trend was observed for methanol mobile phase, which suggests an inherent difference in the separation behavior for the two mobile phases. 5.3.2.1.3 Bridged-ethylene hybrid (BEH) The retention factors for the retained solutes are larger in acetonitrile (Table 5.2) than in methanol (Table 5.1). Several of the solutes (1-aminopyrene, benz[a]anthracene, and dibenz[c,h]acridine) are non-retained, while the other solutes are retained to some degree. Pyrene is slightly retained, which is inconsistent with its behavior in methanol. This increase in retention for pyrene in acetonitrile is consistent with the increase in broadening and skew on the C13 phases. 191 {elem than; Reduced plate heights are larger in acetonitrile than in methanol for BEH. The reduced plate height for the retained acridines are two times the magnitude of those in methanol, while those for the azapyrenes are approximately 35 times those in methanol. This indicates a large increase in broadening on the hybrid support for acetonitrile mobile phase. Of the retained solutes, only 1- and 4-azapyrene have positive skew, indicating tailing behavior. The solutes that are retained on the BEH material correspond to the same solutes that exhibit severe peak tailing on the C13 derivatized phases. This further confirms that retention on the underlying particle, not asymmetry on the underlying particle, contributes to the asymmetry on the C13 derivatized phases. The same trend was observed for methanol mobile phase. Considering the increased retention and broadening in acetonitrile, it is clear than the apparent retention mechanism is different for the two mobile phases. Hybrid supports are greatly affected by the type of mobile phase (i.e. protic vs. aprotic). The hydrogen bonding ability of methanol with surface silanols and the nitrogen-containing solutes could be the main reason for the differences in retention and shape. 5.3.2.2 With mobile phase modifier The effect of each mobile phase modifier is examined as a function of retention factor, reduced plate height, and skew. Detailed information on the change in each parameter is given in Appendix 5A.1. 192 Figure 5.4 shows the effect of mobile phase modifier on retention factor. For most solutes, triethylamine and acetic acid modifiers cause a decrease in retention factor for all phases. For acetyl acetone modifier, the retention factor increases for some solutes yet decreases for others. Pyridine causes an increase in retention factor for XBridge and BEH, the only phases where it was examined. The combination of acetic acid and triethylamine as mobile phase modifiers does not cause a change in retention factor for XBridge. However, a significant decrease in retention factor is observed for most solutes on BEH. Figure 5.5 shows the‘effect of mobile phase modifier on reduced plate height. Triethylamine causes a decrease for most solutes on most phases, however, there are several exceptions where an increase is observed. Acetic acid does not cause an overall improvement in reduced plate height. The plate height increases for some solutes, yet decreases or remains the same for others on the C13 phases. Acetic acid does not cause any noticeable change in plate height for BEH. Acetyl acetone causes an increase in plate height for some solutes and a decrease for others. Pyridine causes an increase in plate height for all solutes on the XBridge and BEH phases, the only two phases examined. The combination of acetic acid and triethylamine modifier causes an overall reduction in plate height on XBridge and BEH. Figure 5.6 shows the effect of mobile phase modifier on skew. Almost all mobile phase modifiers cause a decrease in skew for acetonitrile. The combination of acetic acid and triethylamine causes the greatest decrease in skew, with some solutes having a skew equal to zero. Triethylamine causes the 193 ...0 0000 0. 000000 00.200 ...0... 00.500500. 0..; 0.00 00000 ..... AWN. 00.0.30 ANN» 000.000 3.000 Ag. 0.00 00000 Aw”... 00.000.30.00. .AEV 0.0002000 050 000.000. 00000 0:000. .0 00000.0. 0 00 0.0009000 0. 0.0 0000mx 00 0.0.00 0000 .0. 00.00. 00.00.01 "<0... 0.50.... 0300.0 03.0.0 2.0.0 <.0.0 000$. 002. 055 0 5.0 ...o HOLOVd NOIlNELLEH or 194 10 —: O 0.01 1 HOlOVd NOIiNEIlEIH 195 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac P If), acetic acid (fl), acetyl acetone (7?) Solutes defined in Table 5.1. Figure 5.43: Retention factor for each solute _on XBridge Shield RP13 in acetonitrile as a function of mobile phase modifier. pure acetonitrile (I), triethylamine (:3: O0 0. 90000000099 azaaz¢zgzaazrdar /;};>OO ///// -v \D 2222 ... 000%? 10 l r 1- v- o HOiOVd NOIiNBiBH 196 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac P ), pyridine (31), acetic acid with (.9 ’7; ~), acetic acid (%), acetyl acetone (2 vv\ Retention factor for each solute on BEH in acetonitrile as a‘function of mobile phase modifier. 25:). Solutes defined in Table 5.1. pure acetonitrile, (I), triethylamine ( triethvlamine ( Figure 5.4C 'VV '7" ................................................................. b“ .0. :::x W141 .... i/x Mi [WW/W7 DOOOOOOOOQ...OOO/}/;OO (If? VVVVVVVVV::::: VVVVV VVVV VVVVV ““ “‘ AQAA‘QQ‘AAQAQLAOOA‘O‘OAAA '09000900990090...99.909000009990000ooo¢oooooo o __’(/////_//_/ Ml” /’ / 4%VA%%7‘A%%%%ZV 1 00000 [IIIII l l I IIIIII I I I IIII‘II‘T I l IIIIII I I ‘I IIIIII I l l I O O O O F T- O O \— O \— ‘— .LHEJISH BlV'ld 0300038 197 D[aj]Ac D[ch]Ac B[a]Ac B[a]A Reduced plate height for each solute on XBridge C13 in acetonitrile as a function of mobile phase 4AzaP 4), acetic acid (%), acetyl acetone (3%), pyridine (m), acetic acid I3). Solutes defined in Table 5.1. trile (I), triethylamine ( C P 1AmP 1AzaP Figure 5.5A modifier_ Pure aceton with triethylamin e (3:, WWW 10000 1 1000 g 100; 103 1 J.H‘DIEIH ale (JEIOHCEIH 198 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac p 372'), acetic acid (fl), acetyl acetone (3%). Solutes defined in Figure 5.53: Reduced plate hei ht for each solute on XBridge Shield RP13 in acetonitrile. as a function of mobile ), triethylamine (3" phase modifier. pure acetonitrile( Table 5.1. vvvvvvvvvvvvvvvvvvvvvv vvvvvvvvvvvvvv vvvvvvvvvvvvvvv .......... .................. vvvvvv VVVVVVVVVVVVVVVVVI VVVV VVVVVVVVVVVVVV AAAA AAAAAAAAl/A/AAAAA AAA AA ./////7//‘/2; Azaamzaaaaaaar Afififiéydfiydfififi/ ....... u“.- u" ------- Efiflflfifi 099000999000 1000 IIIII I I IIIIII I l I [Irtll I I I IIIIITI 1 I fir 8 o ‘- F F . ‘_ o J.H9l3H 3J.V'|d 0300038 199 D[aj]Ac D[ch]Ac B[a]Ac r each solute on BEH in acetonitrile as a function of mobile phase modifier. 1AmP 1AzaP 4AzaP B[a]A P "1), acetic acid (%), acetyl acetone 6%), pyridine (33), acetic acid with .—; In 2 .o )m é2ug,F' EVE .9813 0,.-u: .cEé 320) to?“ in!” .92 8352 53A?) 13!. 0 .c5 ‘10.. Ind-F 0E2 loo-— .q-IE Ind) 09 2m> 3 q)£§ 95.9 n. CL}: < 3:-:3t-:?:3:?:r- : “:1:1:3:3:i:’;i,~:':i:1:.’;’:.'135:3:313:3:317:11 ”0;. 09 W74. VVVVVV ‘z. VVVVVVVVVV VVVVVVVVV :DJZZZZZZZZVI’IOOZZZZZZVAZZZZAZAZ vvvvv vvv .OOOOOAQOAOOOOOOO ./>/..O ... /////////// /_///7/////4E vvvvvvvvvvvvvv vvv Hoooooooooooooo 900990000. AZZ’ 2’ AZZZV 100 10 - M3)lS 200 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac p ), pyridine (8?), acetic acid with 744% /% ), acetic acid (fl), acetyl acetone (” // acetonitrile (-),Z.triethylamine (3:13.: Figure 5.6A: Skew for each solute on XBridge C13 in acetonitrile as a function of mobile phase modifier. pure triethylamine (2:232: :53). Solutes defined in Table 5.1. V////////////Z///////////////////////////4 / 100 10" 0.1~ —” 0.01j 201 1AmP 1AzaP 4AzaP B[a]A B[a]Ac D[aj]Ac D[ch]Ac p ge Shield RP13 in acetonitrileas a function of mobile phase modifier. 1:2), acetic acid (%), acetyl acetone (2) Solutes defined in Table 5.1. Figure 5.68: Skew for each solute on XBrid pure acetonitrile (I), triethylamine (3: .mm 2%... 5 amazon m2:_ow A3 V oEEmSfiwE 53> Eom 0:08 $an 052:8 A\\\V 0:280 .308 _A3.3.........3...V Eom 058m 63. 3.Voc_Em_>£o_.a _HuV QEEQwom 95¢ ..oEuoE among 250:. v6 c0283 m mm QEEBmom E 1mm :0 928 some 5.. 33w .00. m 2:9". 9263 03.55 csgm «Em day}. chS 055 n. M3)lS #0 V V V V V V V. . o . V V . o . O, 3 Q. 3 V . o . 3 O .. .V 3 o 3 Q. 3 O. V .. V 3.3... ....V .V . V V. V V V , V V V O. V / V V V V V V V V V ‘. or 202 next greatest decrease, followed by acetic acid and acetyl acetone. On the other hand, pyridine causes an increase in skew for most solutes. It is important to note that skew decreases for most solutes, however is not completely eliminated. This phenomenon will be discussed further in Section 5.4. 5.4 Discussion As seen in Section 5.3, interesting behavior is observed as a function of solutes, mobile phase, and stationary phase. In this section, possible explanations for the behavior are discussed and hypotheses concerning the types of sites contributing to the retention and peak shape are examined. 5.4.1 Effect of bridged-ethylene hybrid (BEH) particle The BEH particle has interesting retention behavior. Only basic solutes are retained in methanol, while almost all solutes are more retained in acetonitrile. Interestingly, almost all solutes have symmetric peak shape on BEH. The symmetric peak shape suggests that the adsorption-desorption step is not rate-limiting. The peak shapes are asymmetric for solutes on the C13 phases. Thus, the asymmetry arises after derivatization of the support particle. That is, the kinetically slow step is not adsorption of the solute at silanol sites in the underlying support. This hypothesis will be discussed in more detail in Section 5.4.5. 5.4.2 Effect of polar embedded group The direct comparison of the two C13 derivatized phases provides specific information concerning the polar embedded group. Typically, the polar embedded group improves the peak asymmetry for most, if not all, basic solutes. 203 Several authors have discussed the reason for this improvement. First, the carbamate polar embedded group could directly interact with surface silanols, decreasing the interaction of those silanols with the solutes. O’Gara et al. [23] studied the effect of carbamate surface concentration on tailing behavior using aqueous mobile phases. They determined that peak shape improvement did not result from the direct interaction of the carbamate with silanols. They suggested that, instead, the surface layer contains a higher concentration of the aqueous mobile phase component due to the presence of the polar carbamate group. Thus, the strength of the interaction between a basic solute and residual silanols is reduced. A similar argument was made by Neue et al. that, in aqueous mobile phases, the polar embedded group attracts water molecules from the bulk mobile phase to form a tightly bound water layer [24]. The water layer effectively blocks the accessible silanols in the underlying material, yet does not interfere with the C13 region, resulting in symmetric peak shapes. in the present research, however, aqueous mobile phases are not employed, thus eliminating water from playing a role in peak symmetry. Instead, the polar embedded group is free to interact with the solute, the mobile phase, and residual silanols in the support. The difference in peak shape as a function of solute, mobile phase, and stationary phase suggests that each of these variables play a role in the separation process. In methanol mobile phase, the peak tailing worsens for four solutes and remains constant for the others, while in acetonitrile, the peak tailing improves for six of the eight solutes for the phase containing a polar embedded group. In methanol, the solvent can hydrogen 204 bond to the residual silanols in the support and, in addition, hydrogen bond to the carbamate polar embedded group. In acetonitrile, hydrogen bonding cannot occur between the solvent and the silanols, leaving the silanols free to hydrogen bond with the polar embedded group. The polar embedded group — silanol site interaction masks the silanols, reducing the interaction of solute and silanol, and in turn, decreases peak tailing. However, many of the C18 chains would remain unbent (unbound to silanols) so that the carbamate polar group is accessible. This hypothesis explains the greater tailing in acetonitrile than methanol, as the same interactions of the solutes with the carbamate could occur, yet without hydrogen bonding from solvent. For XBridge, the tailing worsens by as much as 15 times for methanol compared to acetonitrile, while for XBridge Shield, the tailing worsens only by as much as 4 times. However, the benefit of the polar embedded group is not as apparent using pure organic mobile phase as it is using aqueous mobile phases. 5.4.3 Effect of mobile phase The differences in retention behavior and peak shape that occur for methanol (Table 5.1) compared to acetonitrile mobile phase (Table 5.2) are apparent. The difference in peak tailing is due to the difference in the chemical properties of the solvent. In silica-based materials, it has been hypothesized that methanol hydrogen bonds to accessible silanols. Methanol can also hydrogen bond to residual silanols in the hybrid support, as discussed in Chapter 4. For this reason, tailing in methanol is less severe than that in acetonitrile. Relative to a methanol mobile phase, increased tailing is observed for acetonitrile on the 205 hybrid C18 materials used in the current study. Differences in mobile phase properties also manifest themselves on the underlying BEH support, where increased retention occurs in acetonitrile compared to methanol. This behavior suggests that the bulk mobile phase not only plays a role in retention, but also plays a significant role in the peak shape for a given solute. 5.4.4 Effect of mobile phase modifiers 5.4.4.1 Triethylamine Triethylamine blocks residual silanol sites in silica supports, which reduces or eliminates the interaction of silanols with other amines to decrease the tailing for such solutes [7]. This process occurs because triethylamine acts as a proton acceptor, and can effectively bind to silanols in the underlying support. In this study, peak shape sometimes improves in the presence of triethylamine, but a universal improvement is not seen. On XBridge with methanol mobile phase, an improvement in peak shape is observed. This behavior suggests that many of the slow sites are blocked, however, they are not completely eliminated. However, on XBridge Shield, an increase in plate height and skew is observed. This behavior suggests that the slow sites are not blocked, and perhaps additional slow sites are created. The retention and symmetry of solutes on BEH does not change with addition of triethylamine, which suggests limited interaction of the modifier with the support material. Thus, in XBridge Shield, triethylamine may interact with the carbamate embedded group in the C13 chain in such a way to cause an increase in the broadening and asymmetry. The change is not universal, suggesting that solute structure plays a significant role. 206 On the other hand, triethylamine is beneficial for both C18 stationary phases in acetonitrile, where tailing is more pronounced. The reduced plate height and skew decrease on all phases including BEH. In fact, the reduced plate height and skew are comparable to those in pure methanol for XBridge Shield. This reduction is due to the ability of triethylamine to hydrogen bond to silanols. The effect is greater in acetonitrile as no hydrogen bonding of the solvent with residual silanols can occur. The concentration of triethylamine in each mobile phase is similar to concentrations reported in the literature [7,9,13]. This concentration is chosen because the number of molecules of triethylamine should be sufficient to cover the number of accessible silanols. This point suggests that broadening and asymmetry may come from another set of sites in the stationary phase. Therefore, triethylamine improves peak shape under some conditions, yet does not provide a clear indication as to the type of slow site. 5.4.4.2 Acetic acid The change in retention and skew associated with acetic acid modifier can be ascribed to the acid dissociation constant for each solute. ln acidic media, the NPAHs could become protonated. The protonation could change the mechanism of interaction with the slow site to yield lower retention factors and a change in peak asymmetry. This behavior is also observed on BEH, where many solutes elute before the non-retained marker. When solutes become protonated they are excluded from the pores of the solute and thus elute prior to the non-retained marker. The degree of protonation is indicated by the retention factor. For 207 example, 1-azapyrene elutes before the non-retained marker and is likely fully protonated. Benz[a]acridine and dibenz[a,j]acridine are more retained than the non-retained marker, yet have decrease retention compared to pure mobile phase and are likely only partially protonated. The neutral solutes, pyrene and benz[a]anthracene, are least affected by the acetic acid because of the lack of nitrogen in the structure. The difference in retention and skew for similar solutes can be explained by their ability to accept a hydrogen atom. For example, 4- azapyrene does not exhibit the same behavior as 1-azapyrene, which suggests that the two isomers have different pKa values. While information regarding the pKa for the azapyrenes is not currently available, it is available for isomers of benz[a]acridine. The pKa of benz[a]acridine is 4.70, while the pKa of benz[c]acridine is 3.45 in water at 298 K. In addition, the pKa values explain some of the trends observed in this study. For example, benz[a]acridine contains one fewer ring than dibenz[a,j]acridine, while benz[c]acridine contains one fewer ring that dibenz[c,h]acridine. If the pKas of the dibenzacridines are similar to their benzacridine counterparts, then dibenz[a,j]acridine would have a higher pKa value and become neutral at a higher pH value. The difference in protonation of dibenz[a,j]acridine and dibenz[c,h]acridine would explain the retention and asymmetry observed on XBridge. On XBridge Shield, however, acetic acid only causes a negative retention factor for one solute and none of the solutes exhibit fronting behavior. All NPAHs are less retained when acetic acid is present. However, the increase in skew 208 indicates an increased interaction with the slow site or the addition of a new slow site. In this case, the protonated solute may be attracted to the carboxyl group of the carbamate due to the positive charge, which causes an increase in the skew for any protonated solute. Therefore, acetic acid is not beneficial for improvement of peak shape for NPAHs in methanol mobile phase. Retention and skew decrease relative to pure acetonitrile for most solutes on the C18 phases when acetic acid is present in the mobile phase. In addition, k and skew on BEH are similar with and without acetic acid modifier, indicating protonation does not occur to the same extent as it did with methanol mobile phase. The difference in protonation in methanol versus acetonitrile is expected as the pKa for simple amines is known to differ as a function of solvent. The pKas of both simple and complex amines are larger in acetonitrile than in methanol, indicating a difference in protonation with solvent [30,31]. In this case, acetic acid can hydrogen bond with residual silanols (in XBridge and XBridge Shield) and to both the carboxyl and amine groups of the carbamate (in XBridge Shield) to block both types of sites. When these sites are blocked, the solute cannot interact with the slow site and, thus, tailing decreases. This also explains the slight decrease in retention on both phases. Thus, acetic acid is an adequate mobile phase modifier for an acetonitrile mobile phase, yet does not improve the peak shape to the same extent as triethylamine. 5.4.4.3 Acetyl acetone Acetyl acetone is chosen for its ability to selectively bind to metals in the support material. If the cause of the tailing is due to solute interaction with 209 metals, then a decrease in tailing behavior would be observed. However, acetyl acetone is detrimental to the peak shape for the C13 phases when using a methanol mobile phase. No change in the retention or peak shape is observed on BEH. In acetonitrile, the peak shape is improved for most solutes on all phases. If metal chelation is occurring with the acetyl acetone, it seems that it is only occurring in acetonitrile mobile phase. In addition, acetyl acetone could hydrogen bond with silanols or with the carbamate embedded group. However, these effects would cause an improvement in tailing, which is not seen in methanol mobile phase. While it is unclear what role acetyl acetone is playing in the separation, this role is solvent dependent. That is, acetyl acetone is detrimental in methanol, but beneficial in acetonitrile. 5.4.4.4 Pyridine Pyridine is a basic amine with similar chemical structure to the solutes of interest and, for this reason, was chosen as a possible displacing agent. Overall, the tailing behavior worsens with the addition of pyridine for XBridge C13 and BEH phases. Clearly, pyridine does not act as a displacing agent for either phase. While the mechanism of interaction is unclear, it is clear that pyridine is not an ideal choice for a mobile phase modifier under the current conditions. 5.4.4.5 Acetic acid and triethylamine Overall, the combination of triethylamine and acetic acid modifiers is most influential in improving the peak shape. This combination could cause the change in two types of sites simultaneously. Values for retention factor for the solutes are between the retention factors for the two modifiers separately. 210 However, the values for reduced plate height and skew are dramatically reduced. This observation provides evidence for at least two types of sites that can be modified simultaneously when two distinctly different types of modifiers are added to the mobile phase. While it is unclear exactly how this acid — base combination interacts with the solutes or stationary phases, it is an obvious improvement over each of the other modifiers. 5.4.5 Additional arguments It is clear that one type of modifier does not completely eliminate the broadening and tailing behavior. These results indicate that a solutes affinity for silanol sites may be the initial source of the problem, however, it alone is not the slow step. Only when the support is derivatized with C13 is peak asymmetry observed. Thus, solutes that have an affinity for the silanol sites will be attracted to them, but must migrate through the C13 layer to interact. Diffusion through this C13 layer is slow compared to the actual adsorption-desorption step. Thus, diffusion dominates the kinetic behavior and is the kinetically slow step. The attraction of the solutes to the residual silanols is greater is acetonitrile. This attraction causes a greater number of solute molecules to migrate through the C13, thus creating a greater degree of peak asymmetry. The polar embedded group did not improve peak asymmetry. In fact, the polar embedded group may deleteriously effect the diffusion through the C13 layer, creating an additional site that solutes must navigate. The addition of mobile phase modifiers somewhat improves the asymmetry for some solutes under some conditions. This slight improvement is due to competition at the 211 silanol site from the modifier. However, the solutes continue to have affinity for the silanol sites and diffuse through the C18. Since diffusion is the slow step, it continues to dominate the kinetic behavior even when mobile phase modifiers are included. 5.5 Conclusions The effect of the underlying particle, the polar embedded group, and mobile phase modifiers on retention and peak shape provides interesting results. Basic NPAH solutes are slightly retained in methanol, yet are more retained in acetonitrile on the underlying particle. However, the peak shapes are symmetric, indicating that adsorption and desorption at residual silanols is not a kinetically slow process. The polar embedded group does improve the overall peak shape in acetonitrile mobile phase. However, asymmetry is still observed. Therefore the polar embedded group in the C13 phase only partially helps shield the solute from the support material. Peak tailing in methanol is substantially better than that in acetonitrile. This is due to the hydrogen bonding ability of methanol as discussed in Chapter 4. The additional tailing in acetonitrile can be reduced using mobile phase modifiers, but does not compare to pure methanol mobile phase. The effect of each modifier is both solute and phase dependent. Many of the mobile phase modifiers improve peak shape for several solutes on one or both C18 phases, but do not cause an overall improvement. The combination of triethylamine and acetic acid substantially improves the overall peak shape. Triethylamine 212 provides comparable improvement on the XBridge phase. However, no modifier or pair of modifiers completely removes the tailing from all peaks. The combination of these results indicates that a solutes affinity for silanol sites may be the initial source of the problem, however, it alone is not the slow step. Only when the support is derivatized with C18 is peak asymmetry observed. Thus, solutes can partition into and out of the C18 chain and can adsorb and desorb from silanol sites. These steps, taken individually, have relatively rapid mass transfer and adsorption-desorption kinetics. However, when the steps are combined sequentially, as is the case in a chromatographic separation, they are kinetically slow. That is, the solutes that have an affinity for the silanol sites will be attracted to them, but must migrate through the C13 layer to interact. Diffusion through this C13 layer is slow compared to the actual adsorption-desorption step. Thus, diffusion dominates the kinetic behavior and is the kinetically slow step. 213 References [1 ] [2] [3] [4] [5] [5] [7] [8] [9] [10] [111 [121 [13] [14] [151 [16] [17] [18] [19] J. Nawrocki, Chromatographia 31 (1991) 177-192. J. Nawrocki, Chromatographia 31 (1991) 193-205. Y.K. Ye, R.W. Stringham, J. Chromatogr. A 927 (2001) 47-52. R.K. Gilpin, S.S. Yang, G. Werner, J. Chromatogr. Sci. 26 (1988) 388-400. J.J. Naleway, N.E. Hoffman, J. Liq. Chromatogr. 4 (1981) 1323-1338. A. Wehrli, J.C. Hildenbrand, H.P. Keller, R. Stampfli, R.W. Frei, J. Chromatogr. A 149 (1978) 199-210. K.E. Bij, C. Horvath, W.R. Melander, A. Nahum, J. Chromatogr. 203 (1981) 65-84. R. Gill, S.P. Alexander, A.C. Moffat, J. Chromatogr. A 247 (1982) 39-45. J.S. Kiel, S.L. Morgan, R.K. Abramson, J. Chromatogr. A 320 (1985) 313- 323. R.W. Roos, C.A. Lau-Cam, J. Chromatogr. A 370 (1986) 403-418. G. Stoev, D. Uzunov, J. Liq. Chromatogr. 15 (1992) 3097-3114. A.I. Gasco-Lopez, A. Santos-Montes, R. Izquierdo-Hornillos, J. Chromatogr. Sci. 35 (1997) 525-535. M. Reta, P.W. Carr, J. Chromatogr. A 855 (1999) 121-127. Y.K. Ye, R. Stringham, J. Chromatogr. A 927 (2001) 53-60. X. Li, V.L. McGuffin, J. Liq. Chromatogr. Relat. Technol. 30 (2007) 937- 964. Y.K. Ye, R.W. Stringham, M.J. Wirth, J. Chromatogr. A 1057 (2004) 75-82. P.C. Sadek, C.J. Koester, L.D. Bowers, J. Chromatogr. Sci. 25 (1987) 489-493. P.C. Sadek, P.W. Carr, L.D. Bowers, J. Liq. Chromatogr. 8 (1985) 2369- 2386. RC. Watson, P.N. Shaw, H.J. Ritchie, P. Ross, D.A. Barrett, J. Liq. Chromatogr. Relat. Technol. 24 (2001) 1253-1273. 214 [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [311 T. Cecchi, F. Pucciarelli, P. Passamonti, S. Ferraro, J. Liq. Chromatogr. Relat. Technol. 22 (1999) 429-440. A.E. Martell, Determination and Use of Stability Constants, VCH Publishers, New York, 1992. T.L. Ascah, B. Feibush, J. Chromatogr. 506 (1990) 357-369. J.E. O'Gara, D.P. Walsh, B.A. Alden, P. Casellini, T.H. Walter, Anal. Chem. 71 (1999) 2992-2997. U.D. Neue, Y.-F. Cheng, Z. Lu, B.A. Alden, P.C. Iraneta, C.H. Phoebe, K. Van Tran, Chromatographia 54 (2001) 169-177. K.D. Wyndham, T.H. Walter, P.C. Iraneta, U.D. Neue, P.D. McDonald, D. Morrison, M. Baynham, Waters White Paper 720001159EN (2006) 8 pp. J.E. O'Gara, K.D. Wyndham, J. Liq. Chromatogr. Relat. Technol. 29 (2006) 1025-1045. 8.8. Howerton, C. Lee, V.L. McGuffin, Anal. Chim. Acta 478 (2003) 99. SB. Howerton, V.L. McGuffin, J. Chromatogr. 1030 (2004) 3-12. V.L. McGuffin, S.B. Howerton, X. Li, J. Chromatogr. A 1073 (2005) 63-73. R. Carabias-Martinez, E. Rodriguez-Gonzalo, J. Dominguez-Alvarez, E. Miranda-Cruz, Anal. Chim. Acta 584 (2007) 410-418. M.D. Cantu, S. Hillebrand, E. Carrilho, J. Chromatogr. A 1068 (2005) 99- 105. 215 APPENDIX 5A.1 DETAILED AFFECTS OF THE MOBILE PHASE MODIFIERS 5A.1. Introduction As discussed in Chapter 5, the addition of mobile phase modifiers affects solute retention and peak shape. This appendix provides a detailed examination of the effect of each mobile phase modifier in methanol and acetonitrile mobile phases. 5A.2. Methanol mobile phase with modifiers 5A.2.1. XBridge C13 Table 5A.1 provides the retention factor, reduced plate height, and skew for solutes on XBridge C18. Compared with pure methanol mobile phase (Table 5.1), triethylamine modifier causes a decrease in retention factor (2 to 10 %), as well as smaller plate heights for each solute (by as much as 92 %). The skew decreases for solutes with asymmetric peak shape, but the asymmetry is not completely removed. Acetic acid modifier causes a decrease in retention. The most notable decreases occur for 1-azapyrene, benz[a]acridine, and dibenz[a,j]acridine. 1- Azapyrene has a negative retention factor, indicating it has an elution time less than that of the non-retained marker. In a strictly partition-like mechanism, this behavior could indicate that 1-azapyrene becomes charged (via protonation) in the presence of acetic acid. The reduced plate height remains unchanged for most solutes, yet decreases by 95 % for 1-azapyrene and benz[a]acridine. The skew decreases for all solutes that exhibit asymmetric peak shapes. 216 on: we 83 m: ed 83 m: mm mm? 2.55 mom 8... 30o and. em Boo cod mod mend céca m3 owe o 5d mad. 3 83 Ed we Ewe 9&ch m3. 5 $3 cod Hm «8.0 cod 3 Rod <3ch :3 com memo 3N 8e 23 e3 8 3.3 may; «3 8e memo Ed- 3 Bad. mod F. c Ed dcfi: 8.0 we Bod 8.0 Nu mood 8d 5 god dES com 8 «mod 9.0 E 80o 8.0 3 20o d e c e. a e e. e. c 0. so cmctmx ecoaoo< _boo< _u_o< u=oo< oEEmSfieth .2 came 2 ccécc 856.0. .983 259: .8255 5E .20 cmccmx 5. AmV 396 new 6.: Ech 66.6 8038.. .QV 290$ cancer“: :0 ..mEnoE owmca 6.59: .0 8th u...>0xw 0:0 .ALV 390: 00.0 000300.. .AxV L003 £03590; CO c0509.: 000£Q 0:00p: LO ~00tw ..N.5o_:. emptmx ...m each s cccecc $.28 .88.. 239: 6:855 £3, 2%. 222m 825x 5. .mV 396 ago .5 .299. 9m... 8038.. ..xV .689. 53:88 :0 5500:. $ch 0.306 .0 8th "win win... 219 reduc sduu swnn oppos XBrEdg excep reduce 5AL2£ kw sol tmfihyl hmght Chang! moret sohne dibew fora“ becon SYmm. Chang reduced plate height increases for all solutes. The skew increases for most solutes, decreases for dibenz[a,j]acridine, yet remains unchanged for the symmetric solutes. The increase in broadening and skew on XBridge Shield is opposite that on XBridge. In contrast, fronting peak shapes do not arise on XBridge Shield. Acetyl acetone causes an increase in retention factor for all solutes, except benz[a]anthracene and dibenz[c,h]acridine, which remain constant. The reduced plate height and skew increase for all solutes. 5A.2.3. Bridged-ethylene hybrid (BEH) particle Table 5A.3 tabulates the retention factor, reduced plate height, and skew for solutes on BEH. Compared to pure methanol mobile phase (Table 5.1), triethylamine modifier produces no change in retention factor. The reduced plate height increases (6 to 43 %) for each retained solute. The skew does not change. That is, the majority of the peaks are wider, but not more retained or more tailing when triethylamine is present. Acetic acid modifier causes a decrease in retention factor for all retained solutes. Several solutes (pyrene, 1-azapyrene, benz[a]acridine, and dibenz[a,j]acridine) exhibit negative retention factors. The reduced plate height for all solutes slightly increases. Two solutes (1-azapyrene and benz[a]acridine) become fronting with negative values for the skew, while all others remain symmetric (skew = 0). Acetyl acetone modifier brings about no significant change in retention factor. An overall increase in the reduced plate height occurs. There is no change in the skew, with all solutes remaining symmetric. 220 ...J an? .. l—llln .V‘ .11.!(“HL Io 520... 1mm .3 20$ 5 08000 $8.0m 60ch 0.50.: 6:2on 5:5 toaaam Iwm .8 E 39% van .EV £92 230 among. .0; 0903 c0356. :0 .mEnoE @0ch 0.506 ho Hootm ”m.50_0._. 002090 ._..m 0.00... E “50:00 wmuaom 00000 0.59.0 0.0009000 53> 0&1 20:5 magmx 00.. Amv 30x0 000 .30 3900 0003 0000000 .3 09000 00000000 00 00.000000 00000 0:090 v6 605. 64m 030... 226 increase occurs for 4-azapyrene, benz[a]acridine, and dibenz[a,j]acridine. The skew decreases for all solutes except benz[a]acridine. Values for h and skew are lower for XBridge Shield than for XBridge, indicating more symmetric and less tailing peak shapes, however, some degree of tailing remains for all solutes except benz[a]anthracene. Acetic acid modifier causes only small changes (less than 15 %) in the retention factor with some increasing and some decreasing. There are no discernable trends in the data. The reduced plate height decreases drastically for most solutes, yet increases for 4-azapyrene, benz[a]acridine, and dibenz[a,j]acridine. The skew decreases for most solutes, except 1-azapyrene, benz[a]acridine, and dibenz[a,j]acridine, which remain unchanged. Acetyl acetone causes an increase in retention factor for most solutes, yet a decrease for 1-aminopyrene, 4—azapyrene, and benz[a]anthracene. The reduced plate height increases for most solutes (27 to 56 %), yet decreases for the same three solutes (64 to 96 %). The skew increases for half of the solutes and decreases for the others (1-aminopyrene, pyrene, 4-azapyrene, benz[a]anthracene). Acetyl acetone seems to improve peak shape for several solutes, however is deleterious for others. 5A.3.3. Bridged-ethylene hybrid (BEH) particle Tables 5A.? and 5A8 display the retention factor, reduced plate height, and skew for solutes on BEH. Relative to pure acetonitrile mobile phase (Table 5.2), triethylamine modifier causes a decrease in retention factors for all retained solutes except for pyrene. 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"min 0.00... 229 azapyrene, but increases for the other retained solutes. The skew decreases substantially for 1- and 4-azapyrene (skew = 0). That is, the peak shapes for all solutes are symmetric, however, several solutes continue to be retained on BEH (Table 5A.7). Acetic acid causes an increase in retention factor for pyrene and 1- azapyrene, a decrease for 4-azapyrene, and no change for benz[a]acridine and dibenz[a,j]acridine. The reduced plate heights remain constant or increase. The skew remains constant for the symmetric solutes, increases for 1-azapyrene, and decreases for 4-azapyrene. Acetyl acetone modifier causes an increase in retention factor for all retained solutes (5 to 16 %). The reduced plate height decreases for 1- and 4- azapyrene, but increases for the other retained solutes. The skew remains unchanged for the symmetric solutes, but decreases for 1- and 4-azapyrene. Pyridine causes an increase in retention factor for all retained solutes (12 to 25 %), a substantial increase in reduced plate height, and an increase in skew. Thus, the broadening and skew worsen when pyridine is added to the mobile phase. The acetic acid and triethylamine pair cause a decrease in retention factor for 4-azapyrene, benz[a]acridine and dibenz[a,j]acridine. However, the retention factor increases for 1-aminopyrene, benz[a]anthracene, and dibenz[c,h]acridine, which were not previously retained. The reduced plate height decreases for all solutes except for pyrene. Again, several solutes have reduced plate heights near 2. The skew is also dramatically reduced for 1- and 4-azapyrene. 230 5A.3.4. Conclusions This appendix provides a detailed examination of the effect of mobile phase modifiers in methanol and acetonitrile mobile phases. This description supplements the prior discussion held in Chapter 5 concerning the effect of mobile phase modifiers on retention and peak shape. 231 CHAPTER 6 CONCLUSIONS AND FUTURE DIRECTIONS 6.1 Introduction Liquid chromatography is used in more than 75 "/0 of all analytical methods, with reversed-phase chromatography (RPLC) leading the way [1,2]. The separation of a series of solutes is governed by the retention mechanism of the phase. For this reason, a deep understanding of the retention mechanism is necessary in order to maximize the beneficial contributions and minimize the detrimental contributions to the separation. Hybrid stationary phases, comprised of both organic and inorganic components, are among the newest advancements in the field of liquid chromatography. Thus, a thorough investigation of these phases is essential to understand their retention behavior. Thermodynamic and kinetic investigations provide insight into the retention mechanism and illustrate solute interaction with the stationary phase at the molecular level. In this dissertation, the effect of the analysis method (Chapter 3), temperature (Chapter 4), and mobile phase composition (Chapter 5) on retention and peak shape were examined. 6.2 Study of theoretical analysis methods Chapter 3 details the comparison and validation of theoretical methods to extract thermodynamic and kinetic information from liquid chromatographic data. The effect of column length, linear velocity, and solute carbon number are evaluated. Overall, values for the retention factor are similar for each model. Retention factors are constant with distance, decrease with velocity, and 232 increase with chain length of the solute. However, the values for the kinetic rate constants differ for each model. The statistical moment and EMG models show the largest variation in rate constant as a function of distance. However, the variation decreases substantially when the rate constants are calculated by difference between two detectors. The moment and EMG methods by difference are more reliable than the Thomas model at one detector. As a function of velocity and chain length, the moment and EMG models show the most consistent and reliable trends, as compared with the Thomas method. Problems with the Thomas model could be related to the inherent assumptions of the model, as it assumes that broadening arises due to nonlinear isotherms and slow kinetics, and that all column and extra-column effects are negligible. However, due to the nature of the model, extra-column effects cannot be eliminated using the difference approach. Based on these results, the statistical moment and EMG models yield reasonable values for retention factors and rate constants in an experimental liquid chromatographic system. While this work validates the use of several methods under experimental conditions, additional information could be obtained using simulation studies. Earlier work in this lab used stochastic simulation to validate different mathematical models for extracting thermodynamic and kinetic information. However, only the partition mechanism was employed. A further understanding could be obtained by examining methods to validate different mathematical methods for the adsorption mechanism, as well as for a mixed-mode partition- adsorption mechanism, as is commonly seen in experimental investigations. 233 6.3 Study of hybrid stationary phases Chapters 4 and 5 detail the thermodynamic and kinetic investigation of hybrid stationary phases. The statistical moment model is used for all data analysis. The effect of temperature and mobile phase (Chapter 4) and mobile phase modifiers (Chapter 5) are evaluated. Temperature effects are typically neglected in liquid chromatographic separations. However, the effect of temperature is substantial for the separation of polycyclic aromatic hydrocarbons (PAHs) and nitrogen-containing polycyclic aromatic hydrocarbons (NPAHs). Detailed thermodynamic and kinetic information is obtained as a function of temperature. The parent PAHs are separated primarily by the partition mechanism with the octadecyl groups, but some minor interaction with the silanol groups can occur through the aromatic system. In methanol mobile phase, the retention factors for the NPAHs are less than those for the parent PAHs, which is consistent with a partition mechanism. In addition, the trends of retention with ring number and annelation structure are consistent with the partition mechanism. The changes in molar enthalpy are very similar for all solutes indicating similarity in their retention mechanism. However, the kinetic rate constants indicate that adsorption at silanol sites could play a role, as they are significantly smaller for the NPAHs than for the parent PAHs. The different thermodynamic and kinetic behavior in the presence of the aprotic solvent acetonitrile provides an interesting picture of the retention process. Methanol is able to hydrogen bond with both the NPAH solutes and the underlying silanols, which causes a reduction in the number of available silanols. 234 However, acetonitrile cannot hydrogen bond in this way to shield interactions of the solute with the underlying particle. Therefore, the retention factors for the NPAHs are larger in acetonitrile than those in methanol. In addition, the retention factors for the NPAHs are more similar to those for their parent PAHs, indicating the adsorption mechanism is likely dominant for the NPAH solutes. The changes in molar enthalpy are slightly more negative and are sufficient to account for the small changes in retention factor. In this case, there does not seem to be a significant change in the entropy of the phase when acetonitrile is used. The kinetic behavior also reflects the increased role of adsorption, as the rate constants are one to four orders of magnitude smaller than those in methanol. The thermodynamic and kinetic behavior of the solutes on this hybrid phase is similar in nature to that on silica supports [3]. The retention factors in both mobile phases are smaller for the same set of solutes under similar conditions than on the silica phases. The rate constants in methanol are faster, while those in acetonitrile are slower on the hybrid phase compared to the silica phase. The change in molar enthalpy is less negative for the hybrid phases compared to the silica phases for the same solutes. However, the bonding density of the hybrid phase is more similar to the bonding density of the monomeric phase used for the separation of fatty acids [4,5]. When this silica phase is considered, the changes in molar enthalpy are more consistent. The thermodynamic and kinetic information provides a clearer description of the retention mechanism of NPAHs on hybrid supports in reversed-phase liquid chromatography. 235 The addition of mobile phase modifiers is a common and important practice towards the improvement of chromatographic peak shapes. In this work, the mobile phase itself shows remarkable differences in solute retention and peak shape (also shown in Chapter 4). However, mobile phase modifiers change the peak shape in both protic and aprotic solvents. Mobile phase modifiers used for silanol blockage, such as triethylamine and pyridine, and those for metal chelation, such as acetic acid and acetyl acetone, are investigated. The effect of each modifier is both solute and phase dependent. Many of the mobile phase modifiers improve peak shape for several solutes on one or both C18 phases, but do not cause an overall improvement to symmetric and asymmetric peak shape. Using the combination of triethylamine and acetic acid provides the best results for overall peak shape improvement. The only other modifier that provides comparable improvement is triethylamine on XBridge. However, no modifier or pair of modifiers completely removed the tailing from all peaks. The contribution of the underlying support, BEH, and the polar embedded group in XBridge Shield RP13 are also investigated. Based on the observed retention factors, the underlying support does not contribute to the retention and peak shape that is observed on the C13 phases. The BEH seems to contribute more to the overall retention and asymmetry when acetonitrile is the mobile phase. The additional tailing caused from acetonitrile can be reduced using mobile phase modifiers, but does not compare to using methanol alone. The XBridge Shield material contains a polar embedded group in the C18 phase, 236 which has been known to shield the solute from the support material. However, in these studies, asymmetric peak shapes are observed for several solutes. The combination of these results indicates that a solutes affinity for silanol sites may be the initial source of the problem, however, it alone is not the slow step. Only when the support is derivatized with C18 is peak asymmetry observed. Thus, solutes can partition into and out of the C13 chain and can adsorb and desorb from silanol sites. These steps, taken individually, have relatively rapid mass transfer and adsorption-desorption kinetics. However, when the steps are combined sequentially, as is the case in a chromatographic separation, they are kinetically slow. That is, the solutes that have an affinity for the silanol sites will be attracted to them, but must migrate through the C13 layer to interact. Diffusion through this C13 layer is slow compared to the actual adsorption-desorption step. Thus, diffusion dominates the kinetic behavior and is the kinetically slow step. The interesting behavior of the hybrid phases provides detailed information concerning the retention mechanism in protic and aprotic solvents. However, additional information could be learned from these phases. The hybrid phases are designed to operate well under pH controlled conditions, specifically at high pH. Thus, it would be beneficial to characterize the retention mechanism at several carefully controlled pH values in the acidic, neutral, and basic pH ranges. The retention and peak shape for the NPAHs could be evaluated as a function of pH. In addition, temperature studies would allow for calculation and comparison of the change in molar enthalpy at each pH. 237 The cause of the severe asymmetry is not yet completely understood for these materials. Several analytical measurements could be made on the support particle to provide a more detailed description of its chemical nature. For example, inductively coupled plasma atomic emission spectrometry could be used to identify the concentration of various metals in the underlying support. Values for Al, Fe, and Na are reported in the 1 — 2 ppm range, however, these and other metals effect the acidity of nearby silanols [6]. Knowing the type and concentration of each metal would permit accurate calculation of the amount of chelating mobile phase modifier needed. 6.4 Conclusions The characterization of stationary phase retention behavior is an important practice in liquid chromatography. Many parameters can affect the quality of the separation including mobile phase modifiers, temperature, and pressure. In addition, the theoretical method used for characterization is important to the overall quality of the data. Thus, chromatographic parameters and theoretical methods for characterizing retention behavior should be carefully selected for a given separation. 238 6.5 References [1] LR. Snyder, J.J. Kirkland, Introduction to Modern Liquid Chromatography, John Wiley & Sons, New York, NY, 1974. [2] High Performance Liquid Chromatography Fundamental Principles & Practice, Blackie Academic & Professional, Glasgow, United Kingdom, 1996. [3] V.L. McGuffin, S.B. Howerton, X. Li, J. Chromatogr. A 1073 (2005) 63-73. [4] V.L. McGuffin, S.-H. Chen, J. Chromatogr. A 762 (1997) 35-46. [5] SB. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-35448. [6] J. Nawrocki, Chromatographia 31 (1991) 193-205. 239 M'llllilllljllllfillljlllllllllllllllilss