TVRFS": Lr.:::.:3.3: 3” :2 Michigan » ”"1“ * QMVGI‘STZW . ““1”“ - This is to certify that the thesis entitled MULTINUCLEAR MAGNETIC RESONANCE, ELECTROCHEMICAL, AND CALORIMETRIC STUDIES OF SOME MACROCYCLIC COMPLEXES presented by ATfred J. Smetana has been accepted towards fulfillment of the requirements for Ph . D . deg“. in Chemistry figmehvflfil 7,. / Major profes r Alexander I. Popov Date August 10, 1979 0-7 639 OVLhDUE FINES. 25¢ per day per iten. RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records :‘l- MU! MULTINUCLEAR MAGNETIC RESONANCE, ELECTROCHEMICAL, AND CALORIMETRIC STUDIES OF SOME MACROCYCLIC COMPLEXES Alfred J. Smetana A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry l979 I.» Since of formin: this fiel. ferent ph; dynamic a Li thi out on 11' and l8-cn tion form. variation: The Stabi‘ SOIVent_ versely w the Stabi‘ “from Since Separatiol ABSTRACT MULTINUCLEAR MAGNETIC RESONANCE, ELECTROCHEMICAL, AND CALORIMETRIC STUDIES OF SOME MACROCYCLIC COMPLEXES By Alfred J. Smetana Since the introduction of synthetic macrocyclic ligands capable of forming stable complexes with the alkali ions, the popularity of this field of research has grown very rapidly. A large number of dif- ferent physicochemical techniques has been used to study the thermo- dynamic and kinetic aspects of macrocyclic complexation. Lithium-7 nuclear magnetic resonance studies have been carried out on lithium ion complexes of crown ethers l2-crown-4, lS—crown-S, and lB-crown-6 in water and in several nonaqueous solvents. Concentra- tion formation constants of these complexes were determined from the variations of the 7Li chemical shifts with the ligand/Li+ mole ratios. The stability of the complexes varied very significantly with the solvent. With the exception of pyridine, the stability varies in- versely with the Gutmann donor number of the solvent. In general, the stability order of the complexes was found to be l5-crown-5-Li+ > l2-crown-4-Li+ > l8-crown-6-Li+. Since in this case the complexation reaction does not involve a separation or combination of charges, it has been generally assumed that at lc essentiall ity of thi l8-crown-E potentiome The concer thermodyne strengths, The tl three crov of 136°, Al complexes cases, thi destabili: bond strel Oxygen have also atoms in - to be qua' by a ma t0 be mlo Alfred J. Smetana that at low ionic strength the concentration equilibrium constant is essentially equal to the thermodynamic value. To determine the valid— ity of this assumption, concentration formation constants for the l8-crown-6iNa+ complex in anhydrous methanol solutions were measured potentiometrically as a function of ionic strength of the solution. The concentration constant values remained reasonably close to the thermodynamic value at ionic strengths g_0.05 M, At higher ionic strengths, the concentration value decreased significantly. The thermodynamics of the complexation of the lithium ion by the three crown ethers was studied calorimetrically. Experimental values of AG°, AH°, and AS° indicate that in most cases, the lithium-crown complexes are both enthalpy and entropy stabilized. However, in few cases, the complexes were found to be either enthalpy or entropy destabilized. The results are explained in terms of electrostatic bond strengths, ligand configurational entropy, and solvent effects. Oxygen-l7 nuclear magnetic resonance studies in natural abundance have also been used to probe the chemical environment of the oxygen atoms in free and complexed crown ethers. This method has been shown to be qualitatively sensitive to the complexation of the crown ether by a metal cation. The 170 resonance of the complexes was found to be mlO ppm upfield from the resonance of the free crown ethers. The a guidance, He al helpful 5 fulness. Grati State Uni aid. Deep their pra' would lik tion of it her deep Studies 1’ tion. ACKNOWLEDGMENTS The author wishes to thank Professor Alexander I. Popov for his guidance, encouragement, and friendship throughout this study. He also wishes to thank Professor Andrew Timnick for his numerous helpful suggestions as second reader and especially for his resource- fulness. Gratitude is extended to the Department of Chemistry, Michigan State University and the National Science Foundation for financial aid. Deep appreciation is extended to my Mom, Dad, and sister for their prayers, encouragement, and constant support. Finally, I would like to thank my wife, Dianne, for her assistance in the prepara— tion of this manuscript, her love, her patience, and especially for her deep understanding of the trials and tribulations of graduate studies in Chemistry. It is to Dianne that I dedicate this disserta- tion. Chapter LIST OF Tl LIST OF F] CHAPTER T. A. I B. T T TABLE OF CONTENTS Chapter LIST OF TABLES ........................ LIST OF FIGURES ........................ CHAPTER l. HISTORICAL REVIEW ................. A. Introduction ..................... B. Cation Selectivity and Macrocyclic Complex Stability .................. l. Size of Cation and Ligand Cavity ......... 2. Number, Type, and Arrangement of Donor Atoms ................... a. Number of donor atoms ............ b. Type of donor atoms ............. c. Arrangement of donor atoms .......... 3. Type and Charge of Cation .- ........... 4. Substitution on Macrocyclic Ring ......... 5. Solvent Properties ................ C. Thermodynamics of Metal-Ligand Interactions ..................... l. Stepwise Complex Formation ............ 2. Chelate Effect .................. 3. Macrocyclic Effect ................ 4. Cryptate Effect ................. D. Lithium—Macrocyclic Complexes ............ CHAPTER 2. EXPERIMENTAL PART ................. A. Materials ...................... l. Solvents ..................... iv , , - ,_.,.. _.-. .... . .. __.—._~__________-___ -._, u. Page viii x l TS T6 T7 18 25 27 35 36 36 Chapter CHAPTER 3. CHAPTER 4. Chapter 2. 3. 8. Techniques and Instrumentation l. CHAPTER 3. A. Introduction ..................... 8. Results and Discussion ................ l. Lithium—7 NMR .................. 2. Electrochemistry ................ CHAPTER 4. THE INFLUENCE OF IONIC STRENGTH ON THE CONCENTRATION FORMATION CONSTANT 0F ION—MOLECULE COMPLEXES ............. A. Introduction ..................... B. Results and Discussion ................ Spectroscopy .................. a. Multinuclear magnetic resonance ....... b. Infrared .................. a. Instrumentation ............... b. Experimental procedure ........... c. Testing of calorimeter ........... Other Techniques ................ a. Data analysis ................ b. Solution preparation ............ STABILITIES OF LITHIUM COMPLEXES WITH SOME MACROCYCLIC POLYETHERS. . ........ ooooooooooo Page 37 37 38 38 38 4T 4T 4T 43 43 43 44 48 49 49 so 51 52 52 52 74 80 81 84 Chapter CHAPTER 5 A. B. l CHAPTER E A. i B. T CHAPTER ] APPENDICI APPENDIX Chapter Page CHAPTER 5. ENTHALPY AND ENTROPY OF THE LITHIUM— CRONN COMPLEXES .................. 94 A. Introduction ..................... 95 B. Results and Discussion ................ 97 CHAPTER 6. NATURAL ABUNDANCE OXYGEN-l7 NMR STUDY OF SOME MACROCYCLIC COMPLEXES ........... l05 A. Introduction ..................... l06 B. Results and Discussion ................ 107 CHAPTER 7. SUGGESTIONS FOR FUTURE STUDIES .......... ll4 A. Strong Lithium-Macrocyclic Complexes ......... ll5 B. The 12C4-l8C6 Interaction ............... ll5 C. Microprocessor Control Solution Calorimeter ...................... ll6 APPENDICES APPENDIX A. THE CRYSTAL AND MOLECULAR STRUCTURES OF THREE CYCLOPOLYMETHYLENE TETRAZOLE COMPOUNDS A. Introduction ..................... ll8 B. Experimental Part ................... 119 C. Structure Solution and Refinement ........... 120 D. Discussion ...................... lZl APPENDIX B. APPLICATION OF COMPUTER PROGRAM KINFIT4 TO THE CALCULATION OF FORMATION CONSTANTS FROM NMR DATA AND THE CALIBRATION 0F ION—SELECTIVE ELECTRODES A. Calculation of Formation Constants from NMR 134 Data ......................... l34 1. Program Function ................. vi Chapter APPENDIX Chapter Page 2. SUBROUTINE EQN .................. T35 3. Sample Data Listing ................ T36 8. Calibration of Ion-Selective Electrodes ........ T36 1. Program Function ................. 136 2. SUBROUTINE EQN . ................. T37 3. Sample Data Listing ................ 137 APPENDIX C. APPLICATION OF COMPUTER PROGRAM MINIQUAD76A TO THE DETERMINATION OF EQUILIBRIUM CONSTANTS FROM POTENTIOMETRIC DATA A. Program Function ................... l38 B. Data Input Instructions ................ 139 C. Sample Data Listing .................. T44 LIST OF REFERENCES ...................... T45 Table LIST OF TABLES Table Page l Thermodynamics of Some Tetraamine-Niz+ Complexes in Aqueous Solution ........... l9 2 Thermodynamics of Some Tetraamine-Cu2+ Complexes in Aqueous Solution ........... 21 3 Reported Formation Constants for Lithium-Macrocyclic Complexes ........... 30 4 Reported Thermodynamics of Lithium—Macrocyclic Complexes ........... 33 5 Some Solvent Properties and Diamag— netic Susceptibility Corrections .......... 40 6 Lithium-7 NMR Chemical Shift-Mole Ratio Data at 27 i T°C ............... 54 7 Formation Constants for Some Lithium— Crown Complexes in Various Solvents ........ 63 8 Limiting Chemical Shifts of Some Lithium- Crown Complexes in Various Solvents ........ 72 9 Ionic Diameters of Alkali Ions and Ring Sizes of Some Crown Ethers ............. 73 T0 Concentration Formation Constants Kc’ for the Reaction Na+ + l8C6 I l8C6iNa+ in Anhydrous Methanol at Various Ionic Strengths, I ....... 9T viii Table 12 13 M IS Table 13 T4 Thermodynamic Quantities for Some Lithium- Crown Complexes in Various Solvents ........ Calculation of Formation Constants from Calorimetric Data ................. Some Properties of the Oxygen-l7 Nucleus ...... Oxygen-l7 NMR Study of Macrocyclic Poly- ether 12c4 and Its Li+ Complex ........... Oxygen-l7 NMR Studies of Crown Ethers lSCS and l8C6 and Their lzl Complexes ....... Cyclopolymethylenetetrazole Crystallographic Data ........................ Cyclopolymethylenetetrazole Inter- atomic Distances (A) and Angles (°) ........ Page 98 T03 T07 T08 TlT T25 T26 Figure Figure LIST OF FIGURES Synthetic macrocyclic polyether ligands ...................... Calorimeter calibration response Calorimeter response curve for a fast exothermic reaction ................ Lithium-7 chemical shifts 1/3. l2C4/Li+ mole ratio in various solvents. The solutions were 0.02 M.in LiClO4 .......... Observed chemical shift vs, mole fraction free lithium ion for l2C4-Li+ in acetone and pyridine solutions ......... Lithium-7 chemical shifts 33. iSCS/Li+ mole ratio in various solvents. The solu— tions were 0.02 M_in LiClO4 ............ Lithium-7 chemical shifts vs: l8C6/Li+ mole ratio in various solvents. The solutions were 0.02 M_in LiClO4 except in nitromethane where the concentration was 0.01 M ..................... Page 46 46 53 65 67 68 Figure Figure TO TT T2 T3 T4 T5 T6 T7 T8 Calibration curve for the sodium-ion electrode in anhydrous methanol measured at I = 0.40M ................... Titration curve of sodium perchlorate with l8C6 in anhydrous methanol measured at I = 0.40 M, The arrow indicates the equivalence point ............... A plot of KC for the l8C6-Na+ complex in anhydrous methanol against the ionic strength of the solution .............. Molecular structure of TNT ............. Molecular structure of PMT ............. Molecular structure of 8-t-butyl PMT ........ Packing diagram for TNT .............. Packing diagram for PMT .............. Packing diagram for 8-t—butyl PMT ......... Overlap of molecules in TMT ............ Overlap of molecules in PMT ............ xi Page 87 89 92 T22 T23 T24 T28 T29 T30 T3T T32 CHAPTER T HISTORICAL REVIEW A. Intro: Unti' in solutir that thesr Consequen' "high and the studir Since the type reaC‘ pate in tl alkali ior ethylened‘ of which I these com] T-trans-l of EDTA, r TePOT‘ted 4 Stud' PT the all When Peder called m fPC these PTTTTy bar PEdersen | and kind i “Pills 1' n . A. Introduction ___ Until l967, the coordination chemistry of the alkali metal ions in solutions was virtually unexplored by chemists. It was believed that these ions were inert, unreactive, and therefore uninteresting. Consequently, it was a common practice to use alkali salts to maintain "high and constant" ionic strength of the solution, particularly for the studies of complexation reactions involving transition metal ions. Since the alkali ions are unreactive to most solvolysis and redox type reactions, workers assumed that the alkali salt did not partici- pate in the complexation reaction. However, it has been shown that alkali ions do indeed form complexes in solution with ligands such as ethylenediaminetetraacetic acid (EDTA),(l) the transition metal complexes of which have received a considerable amount of attention. Some of these complexes, namely the sodium and lithium ion complexes with t-trans-l,2-diaminocyclohexane N,N,N',N'-tetraacetic acid, an analog of EDTA, were very stable in aqueous solution, with stability constants reported as log K == 4.7 and 6.l, respectively.(2,3) Studies directed toward the solution and coordination chemistry of the alkali ions became a particularly exciting field of research when Pedersen discovered a new type of synthetic ligands which he called crowns or macrocyclic polyethers.(4,5) The IUPAC nomenclature for these compounds is quite cumbersome, and these ligands have gen- erally been discussed using their trivial names shown in Figure l. Pedersen pr0posed that these ligands be identified by (a) the number and kind of substituent groups on the ring, (b) the total number of atoms in the ring, (c) the name crown (for the compound class), and (fl) ' (“flop C) C) c) C) \\___// l\\//(3\\s/J l2-crown—4 (l2C4) (l 2-l.5 A) l5-crown-5 (TSCS) (1.7-2.2 A) l8-crown-6 (l8C6) (2.6-3.2 A) {3"\\(jTr—I‘\(3)S~‘\\ a = b = 0, c = l c211 rd”7l;»C){’7L/eCDTKJZIPFT a = b = T, c = 0 C22l k/QLJO\)\/l a = b = c = l c222 C CRYPTAND Figure l. Synthetic macrocyclic polyether ligands. (d) the num the molecul sizes of th dissertatio of syntheti cussed shor Macrocy stable comp other ions plexes are plexes. Nh parable, cr solution, w form the cc tion that t observatior crowns, all Pedersen ot in benzene Shortl) TTCST Crowr by Lehn am A cUptand COHtaining The 99hera7 ligands an (CWT) Tates (d) the number of oxygen donor atoms in the ring. Figure l presents the molecular structures, trivial names, and approximate cavity sizes of the three crown ethers used in the study discussed in this dissertation. The structure of a cryptand is included in the family of synthetic macrocyclic ligands for completeness, and will be dis- cussed shortly. Macrocyclic polyether ligands have been shown to form remarkably stable complexes with alkali and alkaline earth ions, as well as some other ions (and molecules) in various solvents. Some of these com- plexes are of comparable stability to the EDTA-transition metal com— plexes. When the size of the cation and the ligand cavity are com- parable, crown ether ligands form two-dimensional complexes in solution, where the metal ion "sits" in the center of the cavity to form the complex. This model of the complex utilizes the naive assump- tion that the ligand is a rigid ring. One particularly interesting observation made in the early days was that in the presence of some crowns, alkali salts can be solubilized in non-polar organic solvents; Pedersen observed that potassium permanganate could be solubilized in benzene by the crown ether dicyclohexyl-T8C6.(5) Shortly after Pedersen's publication on the synthesis of the first crown ethers, a logical extension to these ligands was introduced by Lehn and coworkers with the first reported syntheses of cryptands.(6,7) A cryptand (the name suggested by Lehn) is a macrobicyclic polyether containing three polyether strands joined at two nitrogen bridgeheads. The general formula for a cryptand is shown in Figure l. These ligands are capable of forming three dimensional inclusive complexes (cryptates) with an ion of suitable size, where the ion is usually e i It: found in the outside or b by increasin strands. Th 222 (a=b=c=l and "222" ir The cryptanc cryptand. I and [4]—cryr It shut synthesized replaced by effect on tl Numeror and at this chemistry 0. intended to were selectr assess the , Severa‘ the detemi: stability. “UP" to b. and arrange found in the center of the cavity, more or less insulated from the outside or bulk solution environment. The cavity size can be varied by increasing the number of ether oxygen groups in the bridging strands. The cryptand compound shown in Figure l is named cryptand- 222 (a=b=c=l) or more simply C222 where the "C" stands for cryptand and "222" indicates that there are two oxygens in each of the strands. The cryptand C222 is a bicyclic ligand, hence it is called a [2]- cryptand. Ligands containing three and four macrocycles (called [3]- and [4]-cryptands) have also be synthesized.(8,9) It should also be noted that macrocyclic ligands have also been synthesized in which some or all of the oxygen donor atoms have been replaced by sulfur or nitrogen. Such substitution has a dramatic effect on the stabilities of the complexes. Numerous review articles have been published in recent years,(lO-l5) and at this time there exist also three books (l6-l8) on the chemistry of macrocyclic ligands. This historical review is not intended to be a comprehensive literature review. Specific references were selected to provide the necessary background information and to assess the significance of this study. B. Cation Selectivity and Macrocyclic Complex Stability Several factors have been shown to be of paramount importance in the determination of cation selectivity and macrocyclic complex stability. These include (a) the size relationship between the cation to be complexed and the ligand cavity, (b) the number, type, and arrangement of donor atoms in the ligand, (c) the type and charge of the cation these complex: solvent must . 1. Size ,— From the complexes bet match is opti matches the l strongest her be formed whi bonding. If and therefor. cases 2:l (l metal ion is atoms is too that other c and tetratwi Thus fa the method ( merits some t0 d‘eterminr m°TeCuTar m: Than the H is better a Obtained by of the cation, (d) substitution on the macrocyclic ring, and (e) since these complexes are formed in solution, the properties of the solvent must also be considered. 1. Size of Cation and Ligand Cavity From the early days, Pedersen recognized that the strongest complexes between metal ions and crown ethers result when the size match is optimum. That is, when the crystal radius of the ion closely matches the radius of the crown cavity.(5) Workers reasoned that the I strongest bonds between the metal ion and ligand donor atoms could I be formed when all of the donors could participate equally in the bonding. If the cation is too large, it cannot fit inside the cavity, and therefore, the bonding interactions are weakened. Also, in some cases 2:1 (ligand to metal) sandwich complexes can be formed. If the metal ion is too small, the distance between the ion and the donor atoms is too large for effective bonding. It should be pointed out that other classes of macrocycles, namely cyclic tetraamine (19,20) and tetrathia (21) ligands also follow this general rule. Thus far, the word "size" has been used rather arbitrarily, but the method of precise size determinations (particularly in solution) merits some discussion at this time. Molecular models have been used to determine ligand cavity sizes.(5) Corey-Pauling-Koltun (CPK) molecular models yield cavity diameters which are substantially smaller than the Fisher-Hirschfelder-Taylor (FHT) models. In general, there is better agreement between the CPK model measurements and the results obtained by X-ray crystallographic determinations of the structures I“ of the complv consideratiov the well aco used to accu ionic sizes it is expect solution wit cavity of be strongest 5: which folds The results correlate mv density mea: ions are cm The ab with cavity the ligand fairly rigi ethers like and/or mm the macrocy c"T’Stdi st} folds on iv ten OXYgen diameter m.- but, howev of the complexed (with metal ions) ligands. The other size under consideration, of course, is that of the metal ion. Traditionally, the well accepted Pauling's radii for the alkali metal ions have been used to accurately describe their size. 0n the basis of Pauling's ionic sizes and the CPK molecular model measurements (see page 73), it is expected that the sodium ion forms the strongest complexes in solution with 15C5, but it has been experimentally determined that the cavity of benzo-15C5 is too small for the sodium ion,(22,23) and the strongest sodium crown complexes are formed consistently with l8C6,(24) whith folds itself slightly to accommodate the sodium ion.(25) The results presented above as well as those presented in Chapter 3 correlate much better with the ionic sizes obtained from electron density measurements, from which the ionic diameters for the alkali ions are considerably larger than Pauling's values. The above discussion applies strictly to crown ether ligands with cavity sizes as large as 18C6 (or perhaps even 21C7) where, although the ligand has many degrees of freedom, it may be conceptualized as a fairly rigid ring. The strongest complexes formed with larger crown ethers like dibenzo-27C9 and dibenzo-30C10 are with potassium ion and/or rubidium ion, the sizes of which are considerably smaller than the macrocyclic cavity (assuming a planar ligand configuration). The crystal structure of dibenzo-30ClO-KI (26) shows that this large ligand folds on itself and forms a "wrap around“ complex with K+ so that all ten oxygen atoms participate in the bonding, and the ligand cavity diameter may not really be defined as previously. It has been pointed OUt. however, that crystal structures may differ significantly from the structur similarities of cation or The cor cavity is nc of complex 5 for each of is better W‘ flexibility 2. Nu a. 0r influence ( and coworki found that ion. For complex st increased. Stability We of dc "POD There is Probab‘ iTTUstrat. from the . the structures in solution, although it is likely that there will be similarities between the two conformations, particularly in the case of cation ordered complexes.(27,28) The consonance between the size of the metal ion and macrobicyclic cavity is not unexpectedly of extreme importance in the determination of complex stability. Lehn and Sauvage (29) report cryptands selective for each of the alkali metal ions. As with the crowns, the selectivity is better with the smaller cryptands (mC222) due to the increased flexibility of the larger cryptands. 2. Number, Type, and Arrangement of Donor Atoms a. Number of donor atoms Only a small amount of data is currently available on the influence of the number of donor atoms on complex stability. Cram and coworkers,(30) the originators of the so-called host-guest chemistry, found that 18C5 is a much poorer host than 18C6 for the t-butylammonium ion. For thia-substituted crown complexes with silver ion, increased complex stability is found as the number of sulfur atoms in the ring is increased.(3l) However, it must be pointed out that this increased stability is due to the combination of two factors, the number and the type of donor atom, because the type of donor atom has also been changed upon increased substitution. In this case, the type of donor atom is probably the more important factor (see below). An excellent illustration of the effect of the number of donor atoms may be cited from the studies of Lehn and coworkers with cryptands C222 and C22C8. In the latter substituted t in size, but due to the it L. Con systems stud tuted for ti gen for oxyg and alkaline silver ion 1 same decrea and n” and complexes a explained b bases.(32) Strongly w' and “92+ av and sulfur T0" intera the Stabi °<3 4) are fbrmed with these two cryptands. Mei gt_al, (47) studied cesium ion complexes with crowns and cryptands in various solvents and found that in general, the solvating ability as defined by Gutmann (48) agrees quite well with the behavior of these cesium ion complexes in nonaqueous solvents. Along these same lines, Shchori and Jagur—Grodzinski (43) found that with dibenzo-T8C6 in dimethoxymethane and dimethylformamide solutions the complex stabilities h, were more similar than expected on the basis of polarity considerations alone, and may be attributed to the bidendate character of the less polar dimethoxymethane. Similar solvent effects have been observed by Dechter and Zink.(49) From these selected references, it is seen that the solvent has a very significant effect on the stability of the complex. Likewise changes in selectivity patterns can also be induced by different solvents. Agostino et_al, (50) studied alkali metal ion complexes with dicyclo- hexyl-T8C6 in methanol, ethanol, and n-propanol. The dicyclohexyl— 18C6 ligand is specific for K+, but while the Cs+ complex was more stable than the Na+ complex in these alcohols, the Na+ complex was found to be more stable in aqueous solution.(31) Similar reversals have been observed for the complexes of Ba2+ and KT with dibenzo-18C6 in methanol and water.(12,51) Solvent effects were also studied by Arnett and Moriarity.(52) They reported that the stabilities of the complexes of larger cations with dicyclohexyl-18C6 are less affected by changes i pointed out complexation totally negl complexatior LEM The pr the thermod only briefl complexes t effect has ring closuv constant,il enhancemen' connecting HSand or two compoh to determi and the cy effect" it With a cor with the . depends o l5 by changes in the solvent than those of smaller ions. It should be pointed out that these workers measured indirectly the enthalpy of complexation and discuss the stabilities in terms of enthalpy while totally neglecting the contribution of entrapy to the free energy of complexation. C. Thermodynamics of Macrocyclic Complexes The previous section discussed the major factors which influence the thermodynamic stability of macrocyclic complexes. It was mentioned, only briefly however, that the cyclic polyethers form much more stable complexes than do their corresponding open chain analogs. The same effect has been observed for cyclic tetraamine ligands. It seems that ring closure is responsible for the increase in the complex stability constant,in some cases by several orders of magnitude. An even larger enhancement of complex stability is obtained by the addition of another connecting bridge onto the macrocyclic ring to form a macrobicyclic ligand or cryptand. Since the thermodynamic stability is comprised of two components (enthalpy and entropy) it was of considerable interest to determine the origin of this “macrocyclic effect" for the crowns and the cyclic tetraamines and the "cryptate effect" or "macrobicyclic effect" in the cases of the cryptands. The enthalpy changes associated with a complexation reaction are due to the energy changes associated with the formation/destruction of bonds, while the entropy change depends on the changes in the order of the system. l. Ste The thi plexes with reviewed by and hard do of the firs is due almc soft intera change is 4 to the com line hard/ contribute In a on the the Cd2+,(59) dimethyl 1 entrepy 9. formation than in t cules lea bulk Soly Wthh are €358. thi than 0M3. between 1985 sta 16 l. Stepwise Complex Formation The thermodynamics of the stepwise formation of metal ion com- plexes with halides and other anions in aqueous solution has been reviewed by Ahrland.(53) In general, reactions between hard acceptors and hard donors are most often endothermic particularly in the case of the first step.(53-56) In this case the stability of the complex is due almost exclusively to a large favorable entropy change. Soft/ soft interactions are usually strongly exothermic while the entropy change is often negative or, if positive, it contributes only slightly to the complex stability.(53-55) For complexes formed between border- line hard/soft donors and acceptors, the entropy and enthalpy often contribute equally to the complex stability.(53) In a later publication, Ahrland (57) examined the effect of solvent on the thermodynamic quantities by comparing complexes of Zn2+,(58) Cd2+,(59) and Hg2+ (60) with halides and thiocyanates in water and dimethyl sulfoxide (DMSO) solutions. He summarizes that the total entropy gain due to the desolvation of cations and anions upon complex formation is much larger in a relatively unstructured solvent, DMSO, than in the more highly structured water. In DMSO, the solvent mole— cules leave the well ordered solvates and enter into a fairly unordered bulk solvent upon complex formation. In water, they leave solvates which are either more or less ordered than in DMSO, but in either case, they enter a bulk solvent which is definitely much more ordered than DMSO. By enhancing the structure of the solvent via H-bonding between solvent molecules, the complexes in protic solvents become less stable. This view, of course,neglects consideration of any possible H-b 2. Che Based o itis genera stability it almost entii been named 1 increase in For example is six, the in the rele complexatio strongly tc In adc empirical a solution ca There is a1 factors ar coincidenc turns out the theore l7 possible H-bonding between the solvent molecules and the ligand. 2. Chelate Effect Based on the work of Schwarzenbach (54,6l) and others,(62,63) it is generally agreed that the dramatic increase in metal ion complex stability for multidendate over unidendate ligand complexes is due almost entirely to favorable entropy changes, and this enhancement has been named the "chelate effect." Schwarzenbach (61) relates the increase in the entropy upon complex formation to the desolvation effect. For example, assuming that the solvation number of a given metal ion is six, the formation of a complex with a (hexadendate) ligand results in the release of six solvent molecules or five new particles in the complexation process. Thus, the overall entropy change contributes strongly to the complex stability. In addition, Rasmussen (64) has shown that the use of some empirical equations for the entropy of dissolved species in aqueous solution can be used to calculate the magnitude of the chelate effect. There is at least one recent report (65) in which many more possible factors are considered. The author concludes that it is probably a coincidence that the standard enthalpy change for a chelation reaction turns out to be near zero and the entropy change is positive and near the theoretical value. 3. Macro Both ther elucidate the gerum (66) we' describe the with cyclic t structure. l for the chela figuration W! and Margerum tetraamines stability of substituted counterpart destabilize: Hinz a desolvation considered cIslic lig; cyclic Hg; tion step. ligand am Preformed l5 undoubi Stability colltl‘lbut 3. Macrocyclic Effect Both thermodynamic and kinetic approaches have been proposed to elucidate the origin of the macrocyclic effect. Cabiness and Mar— gerum (66) were the first to use the term ”macrocyclic effect" to describe the greater stability observed for the complexes of Cu2+ with cyclic tetraamines over those of open—chain ligands of similar structure. However, their data do not support the same argument made for the chelate effect. They proposed that ligand solvation and con— figuration were more important than the entropy change. Later, Hinz and Margerum (67) reported data (Table l) on the Ni2+ complexes with tetraamines in water and reached the same conclusion. The increased stability of the Ni2+ complex of cyclam (which is l4C4 with nitrogens substituted for all oxygens, also called 4N—l4C4) over its linear counterpart was of enthalpic origin while the entropy change actually destabilized the cyclic complex. Hinz and Margerum explained their results by assuming that the desolvation step of Ni2+ is the same in both reactions, and therefore considered the solvation of the ligand. They reasoned that since the cyclic ligand is much more compact, it is less solvated than the non— cyclic ligand, and therefore, less energy is expended in the desolva— tion step. Also, more entropy is expended to wrap the open—chain ligand around the metal ion, than to simply insert the ion into a preformed ligand cavity. They proposed that while this entropy tenn is undoubtedly the most important one toward the enhancement of the stability of macrocyclic complexes, it is outweighed by the enthalpy contribution in H-bonding solvents due to ligand solvation. In J phone. \UOELmtk O MU+EME F2.®:$EMML¢MF mEOW L Jomzc< Cw mwxmeEOU +N. FUJPOW m :3 :o. cow—iz¢ z 2 o.N C w.o_- A_-mwu.pim_os._muv om< 3.28.65 22 V. 9: Akov :owuzpom mzowzc< c? mwwaQEoo +Nwz.w:?Emmprp mEom mo mowsmczvoscmch ._ wFDmH solvents tional e ! the same studies Pm thennod the mac ‘ thalpy cluded results i i studied ‘ actuall I confin 4N~l2C assumi what m I tl‘adic Microc 4N-l2( 20 solvents where H-bonding is weak or absent, the changes in configura- tional entrOpy should be more dominant. Dei and Gori (68) also used the same ligand solvation enthalpy stabilization explanation in their studies of Cu2+ complexes with these same ligands in aqueous solution. Paoletti gt a1, (69) presented some preliminary results on the thermodynamics of 4N-l2C4~Cu2+ complexes in water and proposed that the macrocyclic effect results from a combination of favorable en- thalpy and entr0py changes. Later, after further studies, they con- cluded that only entropy contributions are important.(20) Their results (Table 2) as well as those of Kodama and Kimura (70-7l) who studied the same systems, showed that the closed ring complexes are actually enthalpy destabilized and highly entropy stabilized. The results of Hinz and Margerum (4N-l4C4oCu2+ in water) and Paoletti 2+ £3.31, and Kodama and Kimura (4N-l2C4-Cu in water) are directly opposite. However, it really doesn't seem that the apparently small differences in ligand sizes and metal ions should produce such dras- tically different results. Space filling models show that w12+ or Cuz+ can fit into the cavity of the larger 4N-l4C4, which has been confirmed by crystal studies,(72-74) but molecular models show that 4N-l2C4 is too small to accommodate either of these ions. Therefore, assuming that the experimental results are correct, it is not clear what makes the results of these two systems so different. In a more recent paper, Paoletti gt_al, (75) examined this con- tradiction in detail. They measured the enthalpy of complexation 2+ 2+ and Zn with the ligands microcalorimetrically for complexes of Cu 4N-l2C4, 4N-l3C4, 4N-l4C4, 4N-15C4, and the corresponding linear NJU.m:wEMMLumH mEom $0 mUmEMCXUOELQSH .N mKQMH AONV :Owuzpom m30m30< cw mmxwanOU + 2l ilillllllllllllllll llllllllll 82-2.6 Z Z m.Fm m.w—u w.¢m Z Z Z. Z m.m_ ©._Nu _.om szz N.m N.mmu RA: m 2 Z APIGmu.pnmPoE._muv om< A—iwpoE._muxv oz< x mofi ill Aomv cowp:_om mzomsc< cw mwwaQEou +m:u.mcwsmmcpmp msom we mqumczuoELwch .N m_omh counterpa calculate other mee due to a term. Tl match be enthalpy the entr increasi They ind the resu because other gr temperai less ac constan action Fr He dete magnitu Cyclic Stabili h‘gand repuis. Entropy S counterparts in aqueous solution. The value of the entropy term was calculated by difference since the formation constants were known from other measurements. They summarized the macrocyclic effect as being due to a favorable entropy term and to a normally favorable enthalpy term. The magnitude of the latter critically depends on the size match between the cation and the ligand. They found that while the enthalpy went through a maximum with the best size match, (4N-l4C4-Cu2+) the entropy of the macrocyclic complexes decreased steadily with increasing size and decreasing rigidity of the macrocyclic ligands. They indicated that their enthalpy results are more trustworthy than the results of Hinz and Margerum (67) and Kodama and Kimura,(70,7l) because the enthalpies were measured directly. In the work of the other groups, the thermodynamic quantities were determined from the temperature dependence of the formation constants, which is generally less accurate than the calorimetric method. A small error in equilibrium constants can result in a large error in AH°, particularly if the re- action is studied over a narrow temperature range. Frensdorff (3l) noted similar behavior with cyclic polyethers. He determined stability enhancements of three to four orders of magnitude for Na+ and K+ complexes with l8C6 over those with the non- cyclic pentaglyme in methanol. He suggested that the decreased stability of the open chain ligands is due to the inability of the ligand to completely envelop the cation, due to the electrostatic repulsion between the terminal oxygens and the unfavorable change in entropy as a result of wrapping the ligand around the cation. Since that time, the enthalpy and entropy of complexation have been dete Unfortuna Ba2+ sysi As° to e) very mucl lized anc and entri results 1 systems : ferent s contradi Lig macrocyc diaza-l8 aqueous same lig l" aquec It must and its Cyclic ' Ize effect ' Contain' aqueouS both 1; flrSt S been determined for some of the systems studied by Frensdorff.(24) Unfortunately, the thermodynamic values for the l8C6°Na+, K+, and Ba2+ systems in methanol do not yield reproducible trends in AH° or AS° to explain the macrocyclic effect. While the sodium complex is very much entropy stabilized, the potassium complex is enthalpy stabi- lized and entropy destabilized, and the barium complex is both enthalpy and entropy stabilized, but the enthalpy term is dominant. These results show that the macrocyclic effect depends very much on the systems studied and that different systems may be responding to dif- ferent stabilizing factors. This may be the reason for the apparently 2+ and Ni2+ complexes discussed earlier. contradictory results for the Cu Ligands with mixed types of donor atoms do not seem to show a macrocyclic effect. Frensdorff (31) studied Ag+ complexes with l,l0- diaza-l8C6 and a similar linear analog with fewer donor atoms in aqueous solution and found no indication of a macrocyclic effect. The same ligands were studied by Anderegg (76) with Cd2+ and Hg2+ ions in aqueous solution, and again, no macrocyclic effect was observed. It must be pointed out however, that in these cases, the cyclic ligand and its linear counterpart are not strictly comparable as the non- cyclic ligand has fewer total atoms as well as fewer donor atoms. Izatt gt_al, (24) also determined the absence of the macrocyclic effect for mixed donor crowns. They studied linear sulfur and oxygen containing crowns and their cyclic analogs with HgZ+ and Ag+ in aqueous solution. These systems are complicated by the formation of both lzl and 2:l (ligand to metal) complexes. The enthalpies for the first step in the complexation reaction with ZS-TSCS were nearly identical plexes wer As indicai inclusive' and l,4-d' ally. If surprisin the ring The from a ki complexes Cabbiness Cu2+ Cyc. analog. Slow ion reSponsi figurati Stabilii themseli Size thi tion St the fre 24 identical for the cyclic and noncyclic ligands. The 2:l cyclic com- plexes were found to be l§§§_stable than the 2:l linear complexes. As indicated previously, there is some doubt that the metal ions bind inclusively. In the crystal structures of both l,lO-dithia-l8C6-PdCl2 (77) and l,4-dithia-l8€6-HgCl2 (24) the metal ions were bound extern- ally. If similar structures exist in solution, then it is not at all surprising that the macrocyclic effect is absent, since only part of the ring participates in the complexation reaction. The origin of the macrocyclic effect has also been examined from a kinetic viewpoint. The intriguing stabilities of macrocyclic complexes are due to the slow rate of the decomplexation reaction. Cabbiness and Margerum (78) found that the decomplexation rate of the Cu2+ cyclic tetraamine complex is much slower than that of its linear analog. The decomplexation rate was so slow that it overshadowed the slow formation rate of the cyclic complex. The kinetic approach has also been supported by the data of Jones _t_al, (2T) which illustrate that the slow decomplexation rate of the 4S—l4C4oCu2+ complex in 80% methanol compared to the linear ligand is responsible for the extra stability. The authors conclude that con— figurational effects in the dissociation step are responsible for the stability of the cyclic complex and that these effects should manifest themselves primarily in the entropy term. Furthermore, they hypothe- size that solvation effects must be important only in the decomplexa- tion step, and therefore, only for the complexed species and not for the free ligand. a... Lehn in comple another 5 ligand. "macrobic stability orders of added arm ties for Kauf and dicyc cryptate cannot be Anderegg somewhat with mete addition: Plexes w‘ seems to entropy : origin(sj Kau' $de of mEthanol they alsl 25 4. Cryptate Effect Lehn and coworkers (29) have observed an even greater enhancement in complex stability over the macrocyclic effect by the addition of another strand onto the macrocyclic ring to fOrm a macrobicyclic ligand. This enhancement has been named the "cryptate effect" or "macrobicyclic effect." When the added bridge is fully connected, the stability of the €222°K+ complex in 95% methanol increases by five orders of magnitude compared with the ligand in which one end of the added arm remains unattached. Unfortunately, the thermodynamic quanti- ties for these complexes have not been elucidated. Kauffmann gt_al:(79) compared the thermodynamics of the CZZZ-K+ and dicyclohexyl-l8C6'K+ complexes in water and concluded that the cryptate effect is of enthalpic origin. However, these macrocycles cannot be compared directly due to the substitution on the crown. Anderegg (76) reached the same conclusion, but with ligands which are somewhat more comparable. He studied the 2N-l8C6 and £222 complexes with metal ions. It should be noted, however, that C222 has two additional donor atoms. Anderegg's data for the Hg2+ and Cd2+ com— plexes with these ligands are contradictory, because the Hg2+ ion seems to show no cryptate effect while the Cd2+ bicyclic complex is entropy stabilized. Obviously, more data are needed to elucidate the origin(s) of the cryptate effect. Kauffmann et_al, (79) also report the results of a calorimetric study of alkali metal and alkaline earth cryptates in aqueous and 95% methanol solutions. From stability constants published previously, they also present the calculated entropies of complexation. The thermodyn classes ( AS < 0, ( and (e) A Kauffmann above cas in the er the free larger (n stabilize frequent' vent molt favors tl andmono The solvatio ligand i tional c translat entropy the rigi ment of 6“(filing because but the maker 5‘ 26 thermodynamics of complexation (for AG < 0) may be divided into five classes (a) AH < 0 and dominant, AS > 0, (b) AH < 0 and dominant, AS < 0, (c) AH < 0, AS > 0 and dominant, (d) AH > 0, AS > 0 and dominant, and (e) AH < 0, AS > 0, and of equal importance. The results of Kauffmann §t_al, (79) are difficult to summarize, because each of the above cases has been observed for the various complexes. The trends in the enthalpies of complexation follow the same trends exhibited by the free energies of complexation, but the enthalpies are generally larger (more negative). Therefore, these complexes are mostly enthalpy stabilized. The entropies of complexation are much less positive (and frequently quite negative) than expected based on the release of sol- vent molecules upon complex formation. In general, the entropy term favors the complexes of small and bivalent cations over those of large and monovalent ones. The many contributions to the overall entropy changes include solvation entropies of the metal cation and ligand, the changes in ligand internal entrOpy (due to orientation, rigidity, and conforma- tional changes), the change in the total number of particles, and translational entropy. The two best explanations for the negative entropy changes (complex destabilization) seem to be the increase in the rigidity of the ligand upon complex formation, and the rearrange— ment of solvent (water) structure on cryptate formation. An alkali/ alkaline earth ion in aqueous solution acts as a structure breaker, because solvation effects disturb the organization of the bulk solvent, but the complexed ion (inside an organic coat) acts as a structure maker since it is much less solvated. Therefore the overall effect of comple: Lasz noncyclic -l7 kcal- particula pected wt have repc dine (8lf complexe: cases by aqueous negative of the l It macrocyc effect ' stabili conside SVstems 27 of complexation leads to a loss in the entropy. Laszlo gt_al, (80) report a study of the Na+ ion complex with a noncyclic heptadendate ligand in pyridine. They report AH° = 1 -l7 kcalrmole’ and AS° = -48 calcmole'l.deg'l. These results are not particularly surprising since unfavorable entropy changes are ex- pected when the ligand is wrapped around the sodium ion. Mei gt_al, have reported a 133Cs NMR study of cesium complexes with l8C6 in pyri- dine (BT) and with C222 in various solvents.(82) In all cases, the complexes were enthalpy stabilized, but entropy destabilized, in some cases by nearly 20 entropy units. Since pyridine and the other non- aqueous solvents studied are relatively unstructured, these large negative changes in entropy must be attributed to increasing rigidity of the ligand upon complex formation. It is clear that there is no one answer to the question of the macrocyclic/cryptate effect. Systems have been studied in which the effect is either a result of enthalpic stabilization, entropic stabilization, or a combination of both. At this time, despite the considerable amount of data available, more data on carefully selected systems must be obtained in a variety of solvents. D. Lithium-Macrocyglic Complexes Among the macrocyclic complexes of the alkali metal ions, the complexes of the Li+ and Rb+ ions have been neglected, especially in the case of the lithium crown complexes. Very few data exist on the stabilities of lithium crown complexes, and there appear to be no data l on the the The l the highes vated. Ir ion is pre ing solver expected i due to so‘ drying any of water Base strong li for the a informati The of view. disorders recePtor pSYChOtl( interest HErVOUS : cation ( “lay be a A l used to comPlexa 28 on the thermodynamics of the lithium ion-crown interactions. The lithium ion is the smallest of the alkali metal ions, has the highest charge density, and therefore, is the most strongly sol- vated. In nonaqueous solvents of low solvating ability, the lithium ion is preferentially solvated even by traces of water or other solvat- ing solvents. Therefore, the lithium ion macrocyclic complexes are expected to be weaker than other alkali metal-macrocyclic complexes due to solVation effects alone, and extreme care must be taken in the drying and purification of nonaqueous solvents since small amounts of water can cause misleading results. Based on the few data which are available, it is doubtful that strong lithium-crown complexes can exist in aqueous solution. It is for the above reasons, perhaps, that there is only a small amount of information on lithium-macrocyclic complexes. The lithium ion is certainly an important one from several points of view. Lithium salts are used in the treatment of some nervous disorders,(83) and studies of lithium ion complexes with carrier/ receptor type molecules may be of some help in understanding the anti- psychotic effect of the lithium ion, which is a subject of current interest.(84) The lithium ion may interact with a modified central nervous system receptor which would normally function with a biological cation (Na+, K+, MgZ+, or Ca2+). In addition, nonaqueous solvents may be applied to mimic nonpolar membrane-type environments. A large number of different physicochemical techniques have been used to study the thermodynamic and kinetic aspects of macrocyclic complexation.(85) Several years ago it was demonstrated that the nuclear me very sens‘ have used ion,(86) and C222, reaction the Cle~ in this c solvent t cryptands studied l Lehn and Very literatu extremel hexyl~l8 and cycl Matsuure COmplexe and rep respect The Plexes thermod It is e Constar nuclear magnetic resonance of alkali nuclei in solution offers a very sensitive probe for such studies. For example, Cahen _t__l, have used the 7Li NMR technique to study the solvation of lithium ion,(86) the complexation of lithium ion by cryptands C2ll, C221, and C222,(46) and the kinetics of the CZIl'Li+ decomplexation reaction (87) in various solvents. The limiting chemical shift of the C2llrLi+ complex was found to be solvent independent, indicating in this case, that the lithium ion is completely insulated from the solvent by this three-dimensional ligand. Lithium cryptates (with cryptands C2ll, C22l, 0222, C322, C332, and C333) have also been studied potentiometrically in water and in 95% methanol solutions by Lehn and Sauvage.(29) Very little quantitative data are currently available in the literature on lithium complexes with crown ethers. Studies of extremely weak lithium ion complexes with dibenzo—l8C6,(5l) dicyclo— hexyl-l8C6,(3l) cyclohexyl-l8C6,(31) di-(tert-butyl)dicyclohexyl-l8C6,(88) and cyclohexyl-lSCS (31) have been reported in aqueous solutions. Matsuura §t_al, (89) studied conductiometrically dibenzo-l8C6°Li+ complexes in dimethylformamide and propylene carbonate solutions, and reported the formation constants of 3.04 and 3.27 (log K), respectively. However, these results have been questioned.(90,9l) The quantitative data currently available on lithium crown com- plexes and lithium cryptates are presented in Table 3. All of the thermodynamic data which seem to be available are shown in Table 4. It is extremely difficult to draw any conclusions from the stability constant data, but it appears that the complex stability varies Hlttlllllllllllllllt mwmeQEOU UwFUXUOLUmZIEDTSHTJ LOL mucmumcov :OwmeLOl UmeOQmm -M mhnmi. 30 we Umzz mm.o cmpmz mmmu mm go; 0.0 A Focmgpmz mm boa w_.e Axmmv _oee;eez mm pom om.m memz meu mm pom m.m A Focmgpwz om boa mm.e Aemmv _oce;eez mm pom m.m smug: __No mm coo mm.m um mm coo vo.m use —m uomam o v Lopez oum_-0Ncmneo mm accu 0.0 v cape: ©Qw_-_»xeeo_eseee-fl_»ese-ev-eo _m sea e.o ease: euw_-_»xeeo_eseea Fm pee e.o V cape: ouw_-_>xeeo_uxu _m eboe o._ v eeeez mum_-~sxeeo_e>u wucmcmemm cospmz x mo_ pcm>_om ucwmwA mmwaQEou ow_uxoocumz-E:wcuw4 Low mpcwpmcou :owumscom umpcogwm .m mFQmH ~.p.p:oov .m pence mm pom N.N Focusumz wommu PF #0; m.m Focmcuwz mmmmmu __ eoe m.N _oee;eez NNmmu FF pom o.m Focmgumz _Nmmu —_ pom QR.N Foamspmz w_meu mm mzz e©.N eeeeeexe mm mzz N_.m LIP mm mzz mm.m e_eeeeeoeee< n“ ma mzZ a A mcmgpmsocpmz mommmu mm pom m.m Focmgpmz mmmu am can N v Lopez mmmu .Nmmo .mmmu ow mzz em.m mcecwcxa mm pom mm.m Focmgpmz mm pom o.N v Loam: NNNQ mucocwmmm vocpmz x mo_ pcm>Fom ccmmvg A.e.eeoev .m meeee ttlllllllllllllt «.UKZLOU» .m, mhnmg. 32 .cocov campzm mwpmuwccw em: pawcomnsm; .Locou :mmxxo mmpmowucw :o: parcumnsmm .ONcmn mmpmuwncv em: pawcumazmw .NNNU we Empom_wu any we ammmuw mocmcommc uwpmcmme campus: NissvngJ u xcmeOpozaocpomamu mocmpozvcoun xcpwsovpcmgoam F_ pee m.N _oeeebez mmmomomu _F boa N.N _oee;bez e.mmmomomo wucwcmemm negumz mo_ p:m>_om canoe; A.e.o=oev .m 8—3e» mmwaQEoo UwPUXUOLUQZIEavxuwu n+0 mUwEGCXUOEL®SF DmHLoqmm .v mfinmfi porn ewe: p_:m> museCOMmL ovacmwe campus: Rigswcpwg a % acquCoEum mm mzz mm _.o mcmspmeocpvz mm nmzz mm m._ wrecprcopwu< QNNNU ox ~00 q.__ o.o cape: _Nmu mu mfiwu mo.w _.m- cwpmz __Nu mucmcwewm vocpmz A_-mmv._-m_oe._muv om< A_-w_oe.emuxv oI< pcw>Fom ucwme4 mwxm_qsou uw_u>uocomz-E:wcpw4 mo mqumczuoEmeh umpcoamm .v wFDMF inversely ' dynamic da entropy st The s lithium cr consideral 34 inversely with the solvating ability of the solvent. From the thermo- dynamic data in Table 4, it is seen that the lithium cryptates are entropy stabilized. The stabilities, thermodynamics, and influence of solvent on lithium crown complexes remains virtually unexplored. Therefore, a considerable part of this dissertation addresses such a study. CHAPTER 2 EXPERIMENTAL PART 35 A. Mater‘ 1 Acet and metha hydride ( tillatior sieves (I hours,an< distille under a foxide ( lPY, Fis operatic that the methanol Therefon Hammond lngs an refluxe fied by mEthods determi The sol llltl‘og( A. Materials 1. Solvents Acetonitrile (Matheson, Coleman, and Bell), acetone (Mallinckrodt), and methanol (Fisher or Mallinckrodt) were refluxed over calcium hydride (Fisher) for N48 hours, then transferred by fractional dis- tillation to another vessel containing freshly activated molecular sieves (Davison, 3 A pore size, 8-l2 mesh), allowed to stand for ~12 hours,and then redistilled. Molecular sieves were first washed with distilled water, oven dried at 200°C, and then activated at 500°C under a flow of dry nitrogen. Nitromethane (Aldrich), dimethyl sul- foxide (DMSO, Fisher), propylene carbonate (PC, Aldrich), and pyridine (PY, Fisher) were dried and purified in the same manner, except all operations were performed under reduced pressure. It was determined that the calcium hydride drying method was inadequate for acetone and methanol due to a reaction of calcium hydride with these solvents. Therefore, acetone was subsequently dried over calcium sulfate (N. A. Hammond Drierite, 8 mesh), and methanol was dried over magnesium turn- ings and then distilled. Tetramethylguanidine (TMG, Eastman) was refluxed over granular barium oxide (Fisher) for oI48 hours and puri- fied by fractional distillation under reduced pressure. These drying methods produce solvents with water contents of less than l00 ppm determined (except for acetone) by an automatic Karl Fischer titration. The solvents were stored in brown glass bottles in a glove box under nitrogen atmosphere. 36 A. Lit! were ove perchlorz over P20 was recr atamMe from dis perature crystall vacuum. cipitate and then the prod Tetra-n; was obta as recei Weswi L- Twe Aldrich] Sure ant Parish) c°leex. 37 2. Salts Lithium perchlorate (K & K) and sodium perchlorate (G. F. Smith) were oven dried for several days at l80 and l50°C respectively. Silver perchlorate (Matheson, Coleman, and Bell) was dried for several days over P205 under vacuum at ambient temperature. Lithium iodide (K & K) was recrystallized from acetone and dried under vacuum over P205 at ambient temperature. Thallium perchlorate (K & K) was recrystallized from distilled water and dried under vacuum over P205 at ambient tem- perature. Potassium hexafluorophosphate (Pflaltz and Bauer) was re- crystallized from water and dried for several days at ll0°C under vacuum. Tetra-n7butylammonium perchlorate (TBAP, Eastman) was pre- cipitated from acetone and then from methanol by the addition of water, and then precipitated from methanol by the addition of diethyl ether; the product was dried further under vacuum at ambient temperature. Tetra-g;butylammonium hydroxide (TBAH, Matheson, Coleman, and Bell) was obtained as a 25 mass percent solution in methanol and was used as received. Flame emission analysis showed that the concentration of the sodium and potassium ions in the TBAH solution was < 10‘6 molar. 3. Ligands Twelve-crown-four (l2C4, Aldrich) and fifteen-crown-five (l5C5, Aldrich) were purified by fractional distillation under reduced pres- sure and dried under vacuum. Eighteen-crown-six (l8C6, Aldrich or Parish) was purified by first forming the solid acetonitrile-l8C6 complex.(94) The adduct was precipitated from an l8C6 solution in acetonitr filtered vacuum. satisfac LIL“ l_. field 0 was loc Varian holds t ppm at cited a l083 m data. 8l92 d Precis 0f men Parame order artif the f USlng acetonitrile by cooling it in an ice-acetone bath. The solution was filtered rapidly and the weakly bound acetonitrile was removed under vacuum. The purified product had a melting point of 37-38°C in satisfactory agreement with the literature value of 39°C.(94) 8. Techniques and Instrumentation l. Spectroscopy a. Multinuclear magnetic resonance Lithium-7 NMR measurements were made at 23.3l80 MHz and at a field of 14.1 kgauss in the pulsed Fourier transform mode. The field was locked externally with a home—built probe (95) which used the Varian DP-60 console to lock on a proton resonance. This lock system holds the field within :l Hz which corresponds to less than 10.05 ppm at this frequency. Therefore the errors on the chemical shifts are cited as :0.05 ppm. The NMR spectrometer is interfaced to a Nicolet 1083 computer for time averaging and on-line Fourier transformation of data. The maximum computer memory available for data acquisition is 8l92 data points. In order to obtain a relatively high degree of precision, a sweepwidth of l000 Hz was selected, and all of the 8 K of memory was used for data acquisition. With these acquisition parameters, the optimum flip angle was determined to be m7U°. In order to increase the signal to noise ratio (S/N), the lines were artificially broadened by 0.l-0.4 Hz by exponential multiplication of the free induction decay before Fourier transformation of the data. Using these acquisition and data manipulation parameters, and a lithium obtainec measurer correcti of the : these c where E respeci ceptib' some pi numeri' study. lower sample which I MHz al mode 1 broad for d detec iicia loduc lithium ion concentration of 0.02 M, a good signal (S/N NS) could be obtained with less than 50.scans (< 3.5 min). All 7Li chemical shift measurements are referred externally to 4 M_LiCl04 in water, and are corrected for differences in bulk volume diamagnetic susceptibility of the solvents.(96,97) Equation l shows the relationship used to make these corrections. _ 2n r S 5corr " Robs + 7?'(Xv ' Xv ) (1) where 5 and Sobs are the corrected and observed chemical shifts, corr respectively, and er and XVS are the bulk volume diamagnetic sus- ceptibilities of the reference and sample solvents. Table 5 presents some properties of the solvents used in this investigation and the numerical values of the susceptibility corrections applied in this study. A positive value of the chemical shift indicates a shift to lower field. All 7Li NMR measurements were made at 27 i l°C. The samples (2 ml) were contained in precision l0 mm o.d. Wilmad NMR tubes which were not spun. Natural abundance oxygen-l7 NMR measurements were made at 24.399 MHz and at a field of 42.3 kgauss in the pulsed Fourier transform mode on a Bruker WH-l80 superconducting spectrometer. Due to the broadness of the resonances, only l K or l024 data points were used for data acquisition with a sweep width of 20,000 Hz in the quadrature detection mode. In order to increase the S/N, the lines were arti- ficially broadened by 50 Hz by exponential multiplication of the free induction decay before Fourier transformation of the data. A 50 psec mcoquwLLOU Aflwpwnw#uwom:m UwumzmmEva Ucm mm+uLmQ0Ll u:w>~0m mEow .m mpnmk 0000 umpo00mcan 00 mocwcwkwmw Ill ll: 'llt ll' 000.0 000.0- 00m 8 0.00 cwumz 000.0- 000.0- -- 0.00 mcwvwcmzmpzzpmsmcpw0 000.0- 000.0- 0.00 0.00 muvxo0_:m cmpmew0 000.0- 000.0- 0.00 0.00 0:000000 000.0- 000.0- 0.00 0.00 Focwspmz mw 000.0- 000.0- 0.00 0.00 mcopmo< 000.0- 000.0- 0.00 0.00 mpwconcmo wcwfixaoga 000.0- 000.0- 0.00 0.00 mpwspwcopwu< 000.0- 000.0- 0.0 0.00 mcmgmeocuwz 05000 00_ x 00000000006030 Longsz 0:000:00 pcm>Fom :o0pomcgo0 00002005000 Loco0 ccmspzw uwcpum_mv0 wE: _.O> v— _.:m m mcovpumgeou 00000000000020 00002005000 0cm mmwugmaogm u:m>_om 0500 .0 00000 radio f order t manipul (contai molecul with m5 l5 mm 0 which c a lock chemica chemica were ma not spu and 237 0f soli length bands. I!" SodiUm. 4T radio frequency pulse was used with a pre-delay time of 500 usec in order to avoid pulse feed through. Using these acquisition and data manipulation parameters, and a sample concentration of 0.5-l.0 M, (containing between four and six equivalent oxygen atoms per sample molecule) a good signal (signal to noise ratio m5) could be obtained with m500,000 pulses (m4.3 hr.). The samples (5 ml) were contained in l5 mm o.d. NMR tubes which were fitted inside 20 mm o.d. NMR tubes which contained acetone-d6 (Stohler). The acetone-d6 served as both a lock compound and a secondary external reference. All 170 NMR chemical shifts are referred to pure distilled water. A positive chemical shift indicates a shift to lower field. All measurements were made at ambient temperature (m25°C). The sample NMR tubes were not spun. b. Infrared Infrared spectra were obtained using Perkin Elmer models 457 and 2378 grating infrared spectrometers. Solutions and Nujol mulls of solid samples were placed between sodium chloride plates. Wave- length calibration was performed by using the standard polystyrene bands. 2. Electrochemistry a. Potentiometry Potentiometric titrations were done using the Corning NAS ll-l8 sodium-ion electrode which was preconditioned to methanol as described by Frens< electrodl this ele ing Vyco lower tr junction high-iml greater Potenti Ti 25.0 i In ord- airtig enclos An air BlECtl elect solut strer This perc cali asc tot 42 by Frensdorff.(3l) A methanolic silver-silver chloride reference electrode was used with saturated KCl as the supporting electrolyte; this electrode was constructed with a "thirsty quartz” junction (Corn— ing Vycor brand 7930 acid—leached quartz) which seems to show a much lower transfer of potassium ion into the test solution than any other junction. The output from the electrodes was measured by means of a high-impedance operational amplifier voltage follower (input impedance greater than TO12 0) connected to an Analogic 2546 digital voltmeter. Potentials could be read in a range i2.00 V with :0.l mV accuracy. Titrations were carried out in an all-glass cell thermostated at 25.0 i 0.l°C. The titrant was delivered from two or five ml microburets. In order to avoid solvent losses, the titration cell, while essentially airtight, was not purged with nitrogen. The titration assembly was enclosed in a grounded Faraday cage so as to reduce electrical noise. An air-driven magnetic stirrer was used for solution mixing since electrical stirrers introduced noise into the titration assembly. The titrations were performed in the following manner. The electrodes were inserted into the cell and 20 ml of a methanolic TBAH solution (the supporting electrolyte and the solvent at a given ionic strength) was introduced and temperature equilibrated for 30 min. This solution was then titrated with a methanolic solution of sodium perchlorate (at the same ionic strength) to generate the electrode calibration curve. The resulting solution was then back titrated with a solution of the ligand, which was also of the same ionic strength, to generate the titration curve. Applie Hewlet with r suppor electr Tetra- suppor flow - two f the s degas Guil C00! 43 b. Cyclic voltammetry Cyclic voltammograms were obtained by using a Princeton Applied Research Model l74A polarographic analyzer and recorded on a Hewlett Packard 7040A x-y recorder. Voltage measurements were made with respect to an aqueous calomel electrode with 0.l M_NaCl as the supporting electrolyte; a platinum wire was used as the auxiliary electrode, and a hanging mercury drop as the working electrode. Tetra-nybutylammonium or tetraethylammonium perchlorate served as the supporting electrolyte. The solutions were degassed by passing a slow flow of pure dry nitrogen through them after first passing it through two fritted pre-saturators, one containing sulfuric acid and the other the solvent under study. The solution volumes were readjusted with degassed solvent after bubbling. Both direct and indirect methods were used to study the complexa- tion equilibria. In the direct method, the half-wave potential of Tl(I) ion was observed for various ligand concentrations while the metal concentration was held constant. In the indirect method, a competing metal salt was then added, and the Tl(I) half-wave potential was remeasured. 3. Calorimetry_ a. Instrumentation Enthalpies of complexation reactions were determined with a Guild Model 401-ll5 isoperibol solution calorimeter.(99) This system consists of a calorimeter cell, calorimeter insert (including thermist cooling calibrai purged v offset‘ were fa which h either was use circuit with at fabric coeffi $2.00 record 44 thermistor, calibration heater, stirrer, and internal stainless steel cooling coil), stand, stirrer motor, temperature measurement and calibration control unit, stop clock, and an external cooling coil purged with a flow of nitrogen which is inserted in an ice bath to offset the heat of stirring. Two sizes of silvered glass dewar cells were fabricated in the Michigan State University glass shop,(100) which have an inner wall glass thickness of 0.4-0.6 mm and require either m35 or ~55 ml of solution. A millivolt strip chart recorder was used to record the output of the thermistor-Wheatstone bridge circuit. The voltage applied to the calibration heater was measured with an Analogic 2546 digital voltmeter and an 8.5:l voltage divider fabricated with l% precision metal film resistors with temperature coefficients of l00 ppm. Potentials could be read in a range of i2.00 V with i0.l mV accuracy. The entire system (control unit, recorder, and instrument stand) was grounded to a cold water pipe. b. Experimental procedure The actual experiment is performed in the following manner. A solution of one of the reaction components (the metal salt, in the case of complexation reactions) in the given solvent is allowed to equilibrate in the calorimeter cell for ml.5 hours while the flow rate of the cooling gas is carefully adjusted to maintain a horizontally straight baseline as close as possible to the initial temperature of the above mentioned solution. The system is then calibrated by electrically delivering a known quantity of heat into the calorimeter cell and ohms) of bration are all using E( in whic is tra< per aw It fectly dewar requir calibi eousr The c avera used the for Droc Droc 45 cell and measuring the recorder response. Since the resistance (R, ohms) of the calibration heater, the voltage (V, volts) across the cali- bration heater, and the time (t, sec) during which current flows are all known, the heat generated (0, calories) may be easily calculated using Equation 2 (101) 2 v t 0 = 4‘_.184 R (2) in which the factor 4.l84 converts joules to calories. The response is traced by the recorder which is then calibrated in units of calories per division on the chart paper. It is extremely difficult, if not impossible, to obtain per— fectly adiabatic conditions even with a well designed/fabricated dewar cell. Therefore, some heat losses are observed. Also, since it requires a finite time period to generate electrically the heat of calibration, the final solution temperature is not reached instantan— eously. A typical calibration response curve is shown in Figure 2. The curve is analyzed using a temperature extrapolation and time averaging procedure (Figure 2), in which the solid vertical line is used to represent the heat delivered by the calibration heater. After this first calibration run, the system is brought back to the initial temperature by increasing the flow rate of the cooling gas for several seconds and re-equilibrating. Then the entire calibration procedure is repeated. In general, the precision of the calibration procedure has been determined to be better than il%. Since the temperature of the solution inside the calorimeter heat of calibration --) Figure 2. Calorimeter calibration response curve. -/F---nh. heat of reactionfi TIME Figure 3. Calorimeter response curve for fast exothermic reaction. cell is temperat experime pure so' ing the ference solutio ture as other r by a s has ta re-equ A Figure decay (Figm the r is an I recte expe- The- reco brat reac Any 47 cell is not exactly equal to the initial temperature (the inside temperature is usually lower than the ambient temperature), a "blank“ experiment is performed by adding a known volume (I ml or less) of pure solvent to the calorimeter cell by means of a syringe and measur— ing the recorder response. This corrects for both temperature dif- ferences and any heat of dilution of the salt solution when the ligand solution is added. The system is brought back to the initial tempera- ture as previously described, and the same volume of a solution of the other reaction component (the ligand) is added to the calorimeter cell by a syringe and the response is measured. After the chemical reaction has taken place, the system is brought back to the initial temperature, re-equilibrated, and re-calibrated twice. A typical response curve for an exothermic reaction is shown in Figure 3. For fast reactions, the linear portion of the temperature decay is extrapolated back to the initial time of the reaction (Figure 3) to determine the heat involved. For slower reactions, the response curve looks more like a calibration response curve and \ is analyzed similarly. The recorder deflection observed for the reaction is then cor- rected for any differences in temperature determined in the "blank" experiment by adding or subtracting the latter deflection as necessary. The enthalpy of reaction is calculated by comparing the corrected recorder deflection with the post-reaction calibration data. The cali- bration data obtained aftgr_the reaction are used, because the heat of reaction is released into/absorbed from the final resulting solution. Any differences in the calibration data obtained before 3;, after the reaction a resul Sin on the be omit ing the This m. tion, known, be pre right. menta Percl begu Vari hydr rem The -l3 the to 48 reaction are due to any change in the specific heat of the solution as a result of the reaction. Since the system is calibrated directly in calories per division on the recorder chart paper, solution heat capacity measurements may be omitted. The standard enthalpy of reaction is calculated by divid- ing the heat of reaction by the number of moles of product formed. This may be done directly for reactions which go virtually to comple- tion, but for incomplete reactions, the equilibrium constant must be known, or a large enough excess of one of the reaction components must be present in solution so as to drive the reaction completely to the right. c. Testing of calorimeter The accuracy and the precision of the calorimeter and experi- mental procedure were determined by using the standard reaction between perchloric acid and sodium hydroxide in aqueous solution. The experimental procedure described previously was used and was begun with exactly 55 ml of 0.0l405 M_HClO4 in the calorimeter cell. Various volumes of 0.6406 M_Na0H (standardized against potassium hydrogen phthalate) were added during separate experiments to cover reaction conditions which ranged from excess base to excess acid. The results of six determinations were: ~l3.33, -l3.75, -l2.92, ~13.34, -l3.48, and -l3.5l kcalemole'l which average to -l3.4 i 0.3 kcal-mole’l. If the high and low values are omitted, the average would be -l3.4 i 0.l kcal°mole'l. The literature value for the heat of this reaction is -l3.33 kcal°mole'l.(l02-l04) It the hea' was obt tilled mental a comp' tion 0‘ -8.38 -8.36 A nor to f‘ SElEe C005 fit. know wet be dat cal 49 It should be noted that these results have been corrected for the heat of dilution of the added sodium hydroxide solution. This heat was obtained separately by adding some of the NaOH solution to dis- tilled water and determined to be 0.75 kcal-mole"1 under these experi- mental conditions. The calorimeter and experimental procedure were also tested for a complexation reaction. The enthalpy of reaction for the complexa- tion of sodium ion by l8C6 in anhydrous methanol was determined to be -8.38 kcalemole'l, in excellent agreement with the value of -8.36 kcal-mole'l reported by Izatt §t_al,(24) 4. Other Techniques a. Data analysis Use of a CDC 6500 computer system was made for data analysis. A nonlinear least squares curve fitting program KINFIT4 (l05) was used to fit experimental data to mathematical equations to linearize ion- selective electrode calibration curve data and to calculate formation constants from NMR data. The KINFIT4 program provides three checks on the “goodness of fit." A small standard deviation on the calculated value of an un- known is not in itself an indication of a good data fitting. The weights on the data points calculated and applied by the program should be all nearly equal, or this may indicate a systematic error in the data analysis. Lastly, in the case when two or more unknowns are calculated, the output contains a matrix of correlation coefficients. If the u in adjus results small ce Foi culated Details analyt for nc one se conce vent. molar 50 If the unknowns are coupled, the program experiences some difficulties in adjusting each unknown for its "best" value. The best data fitting results when one obtains small standard deviations, equal weights, and small correlation coefficients. Formation constants from potentiometric titration data were cal- culated using a general equilibrium-solving program MINIQUAD76A.(l06,l07) Details on the use of these programs are given in the appendices. b. Solution preparation All samples were weighed out into volumetric flasks using an analytical balance and transferred to a nitrogen atmosphere glovebox for nonaqueous solution preparation. Solutions containing more than one solute were usually prepared by mixing apprOpriate volumes of more concentrated solutions followed by dilution to the mark with pure sol- vent. Unless otherwise noted, all concentrations are reported in molar units. CHAPTER 3 STABILITIES OF LITHIUM COMPLEXES WITH SOME MACROCYCLIC POLYETHERS 5l A. Intr ____.-——-—' As complexe the lit of comp the con l2C4, I this c comple W 70 an new new It i in t fie fol val cle sh A. Introduction As indicated previously in the historical review, lithium ion complexes with crown ethers have received a minimum of attention in the literature. The first part of this chapter reports the effects of complex formation on the 7Li NMR spectra and the determination of the complex concentration formation constants with crown ethers 12C4, l5C5, and l8C6 in several solvents. In the second part of this chapter, the results of electrochemical studies on the same complexes are discussed. 8. Results and Discussion l. Lithium—7 NMR The variation of the 7Li chemical shifts as a function of the l2C4/Li+ mole ratio in various solvents is shown in Figure 4. The lithium-7 NMR chemical shift — mole ratio data are shown in Table 6. It is immediately obvious that the solvent plays an important role in the complexation reaction. For example, the addition of l2C4 to a solution of lithium perchlorate in nitromethane results in a down- field shift with a sharp break at the l:l ligand/cation mole ratio followed by an upfield shift which gradually approaches a limiting value as the concentration of the ligand is increased. This behavior clearly indicates a two-step complexation reaction, jpgp, the succes- sive formation of a l:l and a 2:l "sandwich" complex. TWO complexes are also formed with l204 in propylene carbonate solution, but the exact location of the break is not certain due to the small change 52 ~3.0C *2.5( Bippl 53 - 3.00 —2.50 l2C4 '— 2.00- - LSO— W “W2 - s A . 1 - A 1 <5 4? CH3CN 00130 ' ’Y L/L’ 0% MeOH 0.00— Mez CO 0.50— LOO— PY 50/ 2.00 J l I l I l l I I 2"50.0 |.O 2.0 3.0 4.0 5.0 6.0 70 8.0 Ce2c4 Cui- Figure 4. Lithium-7 chemical shifts vs. l264/Li+ mole ratio in various solvents. The solutions were 0.02 M in LiClO4. 54 Table 6. Lithium—7 NMR Chemical Shift-Mole Ratio Data at 27 :_l°C NITROMETHANE CLi+a 64(ppm) CLi+ 6 (ppm) CLi+b 6 (ppm) 0.00 ~0.57 0.00 —0.54 0.00 -0.57 0.25 -0.53 0.l0 -0.56 0.l0 -0.63 0.5l -0.42 0.20 -0.68 0.l9 -0.64 0.76 -0.33 0.30 -0.70 0.29 -0.69 l.02 -0.28 0.40 -0.80 0.39 -0.7l l.22 -0.42 0.5l -0.77 0.48 -0.72 l.53 -0.52 0.6l -0.89 0.57 -0.75 l.78 -0.62 0.7l -O.99 0.67 -O.76 2.03 -0.70 0.8l -l.l0 0.77 -0.76 2.54 —0.85 l.0l -l.l3 0.96 -0.77 3.05 -0.9l l.2l -l.l9 l.l6 -0.77 4.07 -l.07 l.62 -l.l9 l.54 —0.82 5.09 -l.l9 2.02 -l.23 l.93 -0.83 6.l0 -l.22 2.43 -l.2l 2.3T -0.79 7.63 -l.27 3.04 -l.23 2.89 -0.80 ACETONITRILE 0.00 —2.58 0.00 -2.64 0.00 -2.67 0.25 ~2.l6 0.25 -2.35 0.26 -2.43 0.50 -l.70 0.49 -2.22 0.75 -l.99 0.76 -l.34 0.74 -l.97 0.93 -l.90 55 Table 6. (cont'd.) £1299. ClSCS C18C6 CLi”a 6 (ppm) CLi+ 5 (ppm) 6171—. 6 (ppm) 1.01 -1.17 0.98 -l.8l l.O6 -l.83 1.26 -1.03 1.23 —l.8l 1.44 -1.70 1.51 -1.05 1.47 -1.79 l.86 -1.59 1.76 -1.01 1.72 -l.8O l.88 -1.59 2.02 -1.03 1.97 -1 78 2.14 -l.48 2.62 -1.02 2.21 -1.75 2.59 -1.43 3.02 -1.01 2.46 -1.77 3.60 -l.38 4.03 -1.09 2.70 -1 79 4.32 -1.32 5.04 -1.07 2.95 —l.80 5.22 -1.27 6.05 —1 05 3.93 -1.73 5.52 -1.40 7.56 -1.07 4.92 -l.8l 7.94 -l.36 PROPYLENE CARBONATE 0.00 -0.62 0.00 -0.64 0.00 I -0.66 0.25 -O.6O 0.24 -O.85 0.25 -0 72 0.50 -0.53 0.49 -0 99 0.50 -O.80 0.75 -0.52 0.73 -1.23 0.75 -O.85 1.00 -0.54 0.97 -1.39 1.00 -0.90 1.25 -0.51 1.22 —1.39 1.25 -O.89 1.50 -0 47 1.46 -1.44 1.50 -0.94 1.75 -O.48 1.70 -1 40 1.75 -0.97 2.00 -0.52 l.95 -l.4l 2.00 -0.99 56 Table 6. (cont'd.) _l_2fl _15_cp 18C6 CL1+al 6 (ppm) CLi+ <3 (ppm) fL—i—T— 6 (ppm) 2 49 -0.52 2 l9 -l.43 2.50 -0.98 2.99 -0.55 2.43 -l.38 3.00 -0.97 3.99 -0.59 2.68 -l.43 4.00 -0.99 4.99 -0.63 2.92 -l.4l 5.00 -0.99 5 99 -0.67 3 89 -l.39 6.00 -l.00 7 48 -0.63 4 87 -l.4l 7.49 —l.04 PYRIDINE 0 00 2.33 0 00 2.37 0.00 2.38 0 25 2.25 0 24 l.73 0.25 2.32 0.5l 2.l9 0.48 l.04 0.5l 2.25 0.76 2.l7 0.72 0.46 0.76 2.l9 l.02 2.09 0.96 0.06 l.02 2.l7 l.27 2.0T l.20 -0.24 l.27 2.l3 l.53 l.99 l.44 -0.45 l.53 2.09 l.78 l.89 l.68 -0.59 l.78 2.03 2.03 l.84 l.92 -O.70 2.03 2.04 2.54 l.70 2.40 -0.84 2.54 l.89 3.05 l.58 2.88 —0.89 3.05 l.86 4.07 l.49 3.83 —0.95 4.07 l.70 5.09 l.3l 4.79 -l.0l 5.09 l.52 6 l0 l.2l 5 75 -l.07 6.l0 l.48 7 63 l.03 7 l9 —l.05 7.63 l.32 57 Table 6. (cont'd.) METHANOL Ejgggg C1505 C1806 CLi+a 6 (ppm) CLi+ 6 (ppm) 5T377_ 6 (ppm) 0.00 -0.49 0.00 -0.49 0.00 -0.53 0.99 -0.53 0.26 -0.53 1.00 -0 51 1.97 -0.50 0.51 -0.57 1.99 -0.53 3.95 -O.48 0.77 -O.6O 3.98 -0.53 7.40 -0.49 1.02 -0.64 7.47 -0.59 1.28 -0.72 1.53 -0 72 1.79 -0.73 2.05 -0.75 2.56 -O.84 3.07 —0.84 4.09 -0.90 5.11 -0.99 6.14 -O.98 7.67 -1.01 DIMETHYL SULFOXIDE 0.00 -1.04 0.00 -1.04 0.00 -1.04 0.98 -1.02 1.49 -1 01 0.95 -O.96 6.56 -1.07 7.46 -1.04 6.30 -0 97 9.84 -l.00 9.47 —l.07 58 Table 6. (cont'd.) TETRAMETHYLGUANIDINE flzfl 9151:; C1806 CLi+a 6 (ppm) CLi+ 6 (ppm) CLi+ (ppm) 0.00 0.44 0.00 0.36 0.00 0.44 l0.65 0.42 0.99 0.40 8.73 0.46 l.97 0.36 3.95 0.36 7.40 0.33 WATER 0.00 0.06 0.00 0.03 0.00 0.06 9.80 0.05 0.87 0.05 9.67 0.0l l.74 0.00 2.6T 0.0T 4.36 -0.02 8.7l -0.02 ACETONE 0.00 l.47 0.00 l.43 0.00 l.46 0.25 l.26 0.25 0.90 0.24 l.3l 0.49 l.09 0.50 0.33 0.48 l.ll 0.74 0.97 0.75 -0.l2 0.7l 0.96 0.98 0.83 l.00 -0.5l 0.95 0.82 l.23 0.69 l.25 —0.7l l.l9 0.74 l.47 0.59 l.50 -0.74 l.43 0.66 Table 6. (cont'd.) C1204 C1505 Elppp Cu” 6 (ppm) Cw 5 (ppm) Cm (ppm) 1.72 0.57 1.75 -0.77 1.67 0.59 1.96 0.47 2.00 -O.78 1.90 0.48 2.46 0.42 2.50 -O.83 2.38 0.37 2.95 0.26 3.00 -o.80 2.86 0.28 3.93 0.16 4.00 -0.78 3.81 0.11 4.91 0.12 5.00 -O.82 4.76 0.03 5.89 0.00 6.00 -0.79 5.71 -0.04 7.37 -0.05 7.50 -0.83 7.14 -O.l6 Elppp CLPL GAMM) 0.00 1.25 0.25 1.09 0.50 0.92 0.74 0.83 0.99 0.75 1.24 0.65 1.49 0.59 1.74 0.51 1.98 0.44 2.58 0.34 2.98 0.23 Table 6. (cont'd.) C l8C6 W 6 (ppm) 3.97 0.l0 4.96 0.06 5.95 -0.04 7.44 -0.07 aThe samples were 0.02 M_in LiClO4 unless otherwise noted. bThese samples were 0.01 M in 1.10104. CIn this case only, the salt was LiI. 6T in the chemical shift. Similar behavior was observed by Mei gt_al, (47) with the lace-Cs+ system in a number of nonaqueous solvents. Evidently, in both the cases the ligand cavity is too small to com- fortably accommodate the metal ion. On the other hand, the variation of the 7Li chemical shift in pyridine, acetone, and acetonitrile solutions is monotonic. No varia- tion in the chemical shift could be detected upon addition of l2C4 to LiClO4 solutions in methanol, DMSO, TMG, and water. In the last four cases the solvation of the lithium ion must be strong enough to pre- clude the complexation reaction. It should be noted that in all cases reported in this chapter the 7Li linewidth at peak half-height remained reasonably narrow (l-4 Hz) and independent of ligand concentration. Although the natural linewidth is less than T Hz, the lines observed in this study were somewhat broader due to the inhomogeneity created by the use of fairly wide bore (lO mm) sample tubes which were not spun. The variation of the chemical shift with the ligand/Li+ mole ratio was used as previously described (l08) to obtain complex forma- tion constants by means of a nonlinear least squares curve-fitting program, KINFIT4.(105) Equation 3 represents the equilibrium for the formation of a l:l complex, + 0 + 14+L._ML (3) where MT, L, and ML+ represent the metal ion, ligand, and complex, respectively. The concentration equilibrium constant (K) is given 62 by Equation 4, K = M. (4) [Mine] where the brackets represent the molar concentrations of each specie. Using the mass balance equations, it can be shown that, _ 2 2 2 2 2 1/2 6 — 6 f c I:“‘2“"'100 0000:000 00000000000 0:» 0L0 00:0u0cou :00005000 0 .00Emp L000: .0000 000 00 #:0500000 0000 .0000 00:0 :0 0000 003 000000 5000000 0 .000: x 00_ 0.0.H :00 #0000 000:00 :0 :0 000200 0:00 0 .00 00:0000000 -1- 0 e 0 a 0 a 00 a 0.00 mmm 0 a 0 e 0 a --- 0.__ 020 0 a 0 a 0 a 0.00 0.00 0020 00.0.0 00.0 00.0.0 00.0 00.0.0 00.0 _.00 0.0_ 00 0 a 00.0.0 00._ 0 e 0.00 0.00 10010 23 000.0.“ _0._ ....... .M-- 0.0_ 0.00 00000100 .6 00.0.“ 00.0 00.0.0 00.0 00.0 + 00.0 0.0_ 0.00 00000000 __.0 H 00.0 0 A ..... 0.0_ 0.00 00 00.0.0 00.0 0 A U00.0.0 00.0 _.0_ 0.00 20000 0 A 0 A 0.0 00 00_ 0 A _x 000 0.0 0.00 N020:0 0000 0000 0000 000502 9:000:00 p:0>000 x 00F x 000 x 000 000:00 000000—000 mpcw>rom msowLm> 2.0 00083500 530.00.003.02pr mEom .0000 002000500 cowmeLom .N @700.— 64 The behavior of the 7Li resonance as a function of 12C4/Li+ mole ratio in pyridine and acetone solutions does not give an immediate indication of a step-wise complexation reaction. The monotonic change of the chemical shifts, however, does not preclude the possibility of formation of a l:l and a 2:l complex in these solutions. In fact, similar monotonic curves were observed for the l8C6°Cs+ system in dimethyl sulfoxide and acetonitrile solutions, but an analysis of the data showed the presence of two complexes.(47) If only one complex is formed and the exchange between the two ' cationic sites is fast on the NMR time scale, then the resonance ; frequency of the cation is given by dobs = Gfxf + 5cxc (6) where of and 6C are the 7Li chemical shifts corresponding to the free and the complexed cation, and Xf and Xc are the populations of the lithium ion at each of the two sites. Since Xf + Xc = l, Equation 6 can be rearranged to give aobs = (6f - ac)xf + ac (7) A value of Kf, assuming a l:l reaction was obtained, the mole frac- tion of free Li+ ion, Xf, was calculated, and 5obs was plotted vs, Xf. The plots are shown in Figure 5. The data points fail on two very respectable straight lines with the predicted slopes and intercepts, indicating that the experimental data accurately fit the l:l complex —o.ao —— —oeo— —o.40 — —o.2o — ooo— - o.2o-— ’ 0.40 >- \. 0.60 — ° 0 0.80 — 8 (ppm) . ACETONE LOO —— ' O l.20 — L40 ~— l.60 —— ° PYRIDINE l.80 — 2.0 L 2.20 ~— 240 '— l J I .0J, .1 .1 0J_0 J .L000J 0.0 0.l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 LO XLr‘ Figure 5. Observed0chemical shift vs. mole fraction free lithium ion for l2C4-L1+ in acetone and pyridine. 66 model. If a 2:l complex is also formed, its concentration is negli- gible vis-a-vis the concentration of other species in solution. No evidence for 2:l complex formation is obtained when the lithium ion can comfortably fit inside the crown cavity. Figure 6 shows the mole ratio plots for the lSCS-Li+ complex in various solvents. Sharp breaks in these plots at a l:l mole ratio in nitromethane, acetonitrile, and propylene carbonate solutions indicate the formation of a very stable (log K > 4) l:l complex. 0n the other hand, such sharp breaks are not observed in the pyridine, acetone, and methanol solutions indicating that in these solvents the complex is much less stable. The addition of the ligand to a Li+ salt in dimethyl sulfoxide, tetramethylguanidine, and water did not change the 7Li chemical shift indicating, at best, only a very weak interaction between the ligand and the Li+ ion. A much weaker lithium complex is formed with a larger crown, l8C6. The mole ratio plots shown in Figure 7 indicate the formation of a stable complex only in nitromethane solutions where ion-solvent interactions are extremely weak. It is particularly interesting to note that the lithium ion does form a complex with a crown ether which is substantially larger than the ion. In fact, the cavity of 18C6 is substantially larger than the sodium ion.(25) No complexation reaction is observed in methanol, dimethyl sulfoxide, tetramethylguanidine or aqueous solutions. Various scales of the solvating ability of solvents have been pr0posed. The scale proposed by Gutmann (48) seems to agree quite well with the behavior of alkali complexes in nonaqueous solvents. 67 -3.00—' l5C5 l —2.50 —2.00— — l.50— ——uoo' abpml _. " c. — 0.50" 0.00- 050— LCD J l.50— 2.00 4 250 .i J_ I .J_ La aJ l J 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 CISCS CLi* Figure 6. Lithium-7 chemical shifts vs. iscsm+ mole ratio in various solvents. The solutions were 0.02 M_in LiCl04. -—aoo—— l8C6 -—2L50 —e00— —l.50L- CH CN 4 * J. 3 * DMSO 1h ——L0CW* t? it i37$v~ ijr—fPC T CHBNCE L MGOH 4 _.1 -—050 ’T ,7 T a(ppm) MeZCO 000—- (150—— Loo—- PY isol— 200- I 2150 l l .J l L 4J I l 00 IO 20 30 40 50 80 7o 80 Chece (:Lfi Figure 7. Lithium-7 chemical shifts vs. l8C6/Li+ mole ratio in various solvents. The solutions were 0.02 fl_in LiCl04 except in nitromethane where the concentration was 0.0l M. The Gutmann donor number is defined as the negative enthalpy (in kcal-mole'T) of the reaction between a solvent molecule and antimony pentachloride in dilute l,2-dichloroethane solution to form a l:l adduct. 3 + SbCl5 1,2-oce_% S-SbCl5 (8) dilute soln DONOR NUMBER 2 "AHS-SbClS It is seen from Table 7 that, in general, the stability of the complexes varies inversely with the Gutmann donor number of the sol- vent. Since the latter expresses the solvating ability of the solvent, this relationship is not unexpected. An obvious exception, however, is found in the case of pyridine solutions, where stable complexes are formed despite the very high donicity of this solvent. Similar behavior for pyridine solutions has been observed previously by Mei .gt_al,(47) A possible reason for such an exception may be the rela- tively poor solvating ability of pyridine (a nitrogen donor, soft base) towards alkali cations (hard acids). Another anamaly found in Table 7is the stability reversal for the l8C6'Li+ complex in acetonitrile and propylene carbonate solutions. 0n the basis of both the donor numbers and the dielectric constants, it would be expected that this complex would be more stable in aceto- nitrile. However, ligand—solvent interactions should likewise affect the extent of the complexation reaction. Unfortunately, very little seems to be known about such interactions. It has been shown previously 70 that the crown ether l8C6 forms a relatively stable complex with acetonitrile which can be isolated in the solid state.(94) It is reason- able to assume that there is a considerable interaction between aceto- nitrile and lBC6 (and probably other crown ethers) in solution, which would obviously destabilize the iacs-Li+ complex. In a given solvent the stabilities of the lZC4°Li+ and l8C6-Li+ complexes are nearly the same. It has already been shown that the l2C4 ligand is too small to accommodate the lithium ion, while the l8C6 ligand is too large for a tight fit inside the cavity. Both of these effects have been shown to destabilize the complex. Another considera— tion is the fact that the 12C4 ligand has only four donor atoms which would also tend to destabilize the resulting complexes compared to ligands with more donors. The method used for the calculation of the formation constants does not take into account possible ionic association into solvent- separated, solvent-shared, or contact ion pairs. The literature indi- cates that in propylene carbonate (109) lithium perchlorate is es- sentially completely dissociated, while in acetonitrile and methanol solutions, ionic association is small since the ion pair formation constants have been reported to be K = 4 (llO) or 68.4 (lll) in aceto- nitrile, and K = 13.7 (llZ,ll3) in methanol. It is reasonable to expect that the same conditions will prevail in nitromethane which has a dielectric constant of 35.9. Therefore, in these four solvents, the competition from ion pairing should be negligible. The situation is somewhat more complicated in the case of acetone solutions since it appears that the lithium salts undergo a considerable 71 amount of ion pairing in this solvent. The ion pair formation con- stants have been reported to be 5300 for LiCl04 (ll4) and l45 for LiI.(ll5) As seen from Table 7 however, the same complexation constant for the isco-Li+ complex is obtained with the perchlorate and iodide counterions. Also, the calculated limiting chemical shift of the complex is independent of the counterion (Table 8). It seems that if the ion pairing constants truely differ by more than one order of magnitude, the value of the "apparent" complexation constant should not be the same. In the case of pyridine solutions it seems that the data on the ionic association in this solvent are not available. However, it would be expected that the low dielectric constant will favor ionic association and that in this case the complexation reaction competes with the ion pair formation. Therefore the values given in Table 7 represent relative complexing abilities of the three ligands in this solvent. It is seen in Figures 4, 6, and 7 and Table 8 that the limiting chemical shifts of the lithium crown complexes approach the same general area, but the mole ratio plots do not converge to the same limiting value as was observed in the case of the Cle-Li+ complex in various solvents.(46) The limiting chemical shifts are somewhat solvent dependent, because the solvent molecules may still approach the complexed lithium ion from the open faces of the crown ethers. It is well known, of course, that one of the main factors affect- ing the stability of macrocyclic complexes is the consonance between the size of the macrocyclic cavity and the ionic diameters. As seen 72 .fiO—QwA mm: Pram wcw .mwmmo Lmzpo _—m CH .wmmu mwcp Cw wa: mm; waUOF EDPLHPJ . . . U .Eaa mo.o.H op mumszuom mew mw:_w> mmmzp .Fmswcmm :H .mcwppvt mpmu mmsmsom ummw— Laws? Fcoc esp soot mcpp_:mms meowpow>mu usmucapm _mueumwpopm 050 meg mpeecm _mowEm;0 umpm_30_80 one cw um» .pu mLOLLw wcho .saa mo.o.H do opossuom men one mac—Q owpms w_oE mcp Eosm >Fuumswn uw:TEmemv mew; mvacemwsmocz “secpez copwu wm:_m>m om.o + ee.o- _o.o H m_._- 8N.o.w ek.o- >a ..... mo.o.H mm._- .1... :omzu omo.o.H mm.o- ..... ----- oumfimzov No.0.“ mm.o- ow.o- mo.o.u Om.o- oomflmzuv 88.0- _e._- ----- 0a Nm._- mm._- eo.F- zumzu 08.8- _N._- A_ NV emo.o.fl _m._- M_upv emN.o- Nozmzo oow_ mum_ ¢QN_ pcm>pom Agaav oawsm _eoeso;u messaged mpcw>_om msowsm> :w mwxw_QEou czosu-53wcuw4 meow $0 mpmwcm _80eEm:u mcwpwEWA .w w_nm» 73 in Table 9, if the well accepted Pauling's ionic size of the lithium ion is assumed, the stability of the lithium complexes should be in Table 9. Ionic Diameters of Alkali Ions and Ring Sizes of Some Crown Ethers O Cationic Diameters (A) Rihg SizegAiE 8 Fisher- Electron Crown Corey-Pauling- Hirschfelder- Cation Pauling Density Ether Koltun Taylor Li+ 1.20 l.86 i2c4 1.2 1.5 Na+ 1.90 2.34 lSCS l.7 2.2 K+ 2.66 2.98 l806 2.6 3.2 Rb+ 2.96 3.28 Cs+ 3.38 3.66 aReference ll6. bReference ll7. the order 1204 > 1505 > l806. Since the order is experimentally determined to be lSCS > lZC4 m 1806, it seems that the ionic sizes obtained from the electron density measurements give better agreement with our results. It should also be noted that in all cases reported thus far, the sodium ion forms stronger complexes with l806 than with lSCS;(24) again, these results correlate better with the ionic sizes l_— 74 obtained from electron density measurements. The formation constants given in Table 7 were calculated in concentration units. Since in these cases, the complexation reaction does not result in a separation or combination of charges, we can assume that as long as the total ionic strength of a solution remains low, the values of the concentration constant will closely approximate the thermodynamic value. The validity of this assumption is investi- gated in Chapter 4. 2. Electrochemistry Several strong lithium crown complexes (log K > 4) were encountered during this study. Due to the overall small range of lithium-7 chemical shifts and the method used to treat the NMR data, formation constants > l04 for l:l complexes could not be accurately determined. However, electrochemical techniques lend themselves quite well to the determination of very stable complexes. It should be noted that the intensity of a spectrometric signal (including NMR) is proportional to the concentration of the chemical species observed, while in poten- tiometric and polarographic studies, the signal is proportional to the logarithm of the concentration. A considerable amount of time was spent trying to obtain a lithium ion-selective electrode, but without any success. Furthermore, the monovalent cation electrodes tested (Beckman 39l37 and Corning 476220) yielded neither Nernstian nor reproducible response curves for the lithium ion. A competition method using a glass silver ion-selective electrode (Corning NAS ll—18) in methanol was successfully applied. 75 In this case, the ligandsAg+ equilibrium constants were determined, and then the system was titrated with a lithium salt solution. Since some ligand~Li+ complex is formed, there is an increase in the Ag+ ion con- centration. With these data, the ligand-Li+ formation constant can be calculated. Only very weak lithium crown complexes were observed in methanol. For studies in aprotic nonaqueous solvents, silver wire electrodes (Sargent, Catalog #S-305150) were used to perform similar competitive experiments, but the silver wire electrode responses were neither Nernstian nor reproducible. Cyclic voltammetry was then used to determine these large forma- tion constants. The method used by Lingane (ll8) may be applied to the study of labile complexes provided the following assumptions are met. First, the electrode reaction must be reversible. The hetero- geneous electron transfer at the electrode surface must be able to keep up with the potential sweep rate. Second, a large excess of ligand must be used so that the concentration of free ligand at the electrode surface may be assumed to be equal to that in the bulk solution, and also so that the change in the free ligand concentration upon com- plexation is small compared to its analytical concentration, and the free and analytical concentrations may be assumed to be equal. Lastly, it is assumed that the diffusion current constants for the free and complexed metal ions are nearly the same. Also, the experiment is performed at constant ionic strength. With these assumptions applied to reaction 9 M + jL : MLj (9) where 76 [MLJ-J B = ---mr (10) ”Li [MiniJ Lingane's equation is AE1/2 = (El/2)free ' (El/2)complex (‘1) . 3 T . . = ———-—-—Z 39“, R log BMLj + ——.————Z 32,? RT J log cL (12) where CL is the analytical ligand concentration. This equation pre- dicts that the measured half-wave potential of an electroactive cation should shift to a more negative potential in the presence of the ligand. A plot of AE1/2 y§,log CL should yield a straight line from which the combining ratio, j, and the formation constant BMLj can be determined. In many solvents, it is difficult to observe directly the reduc- tion of the lithium ion, because it is too close to or beyond the solvent reduction wave. However, in acetonitrile, the lithium ion behaves fairly reversibly, but the addition of 1506 resulted in ir— reversible behavior. Therefore, this direct method would not be applicable. Since the ligands used in this study have small cavity sizes, it is desirable to use a small electroactive cation to avoid higher order complexes in solution. Cadmium(II) perchlorate was then used to perform this experiment in an indirect manner. The Cd2+-Cd0 couple behaved reversibly, but this behavior became irreversible when 1505 was added. While the Cd(C104)2 behaved irreversibly in the 77 presence of 1505, the 0d12 behaved partially reversibly, perhaps due to some specific adsorption of the iodide ion at the electrode sur- face. Reversible behavior has been found for Tl(I) with cryptand 0222 in dimethylformamide and dimethyl sulfoxide.(119) This reversibility may be due to the partially covalent character of the T1+-0 bonds. Thallium(I) perchlorate behaves fairly reversibly in acetonitrile and propylene carbonate solutions in the absence and presence of 1505 as is apparent in the forward to backward peak separation ofni80 mV (theoretical 57 mV) with potential sweep rates of 20 mV/sec or less. However, Tl+ ion is much larger than Li+ ion, and both 1:1 and 2:1 complexes can be formed with ligands 1204 and 1505. Therefore, many more solutions must be studied to define the plot of AE1/Z gs, CL, because it would not be linear due to 1:1 and 2:1 complex formation. In principle, this does not present a problem, but practically, some difficulties were encountered. First of all, the aqueous SCE reference electrode with K01 as the supporting electrolyte could not be used due to the formation of a precipitate on the tip of the reference electrode. This was due to the low solubility of K0104 in non— aqueous solvents, where the 0104' comes from the supporting electrolyte in the sample solution. Then saturated NaCl in H20 was used as the fill solution, but NaCl is not soluble enough in certain nonaqueous solvents, and the above problem reappeared.~ Finally a 0.1 M_NaCl in H20 fill solution was used more successfully. The problem comes when many solutions are analyzed. It is preferable to leave the reference electrode in the solution so that the liquid junction potential remains fairly constant. However, as the reference electrode remained in the solution over a period of time, a preci- pitate formed on the fiber at the tip of the reference electrode, which changed the reference potential. Furthermore, as this aqueous reference electrode is allowed to remain in the solution, water dif- fuses into the specifically dried and purified nonaqueous solvent. It should be possible to overcome these difficulties by the use of a reference electrode in the same solvent under study. This is more easily said than done, however. Since two complexes exist between T1+ and 1204 and 1505, the equations of DeFord and Hume (120) must be applied for step-wise reactions _ 2.303 RT 3 AE1/2 - nF 109 BMLjCL (13) _ 2.303 RT 2 ' nF 109(BMLCL + BMLZCL + "°) (14) The data may then be analyzed using the Fronaeous equations.(121) Should the ligand-Tl+ equilibrium constant be quantitatively determined, a modification of the Ringbom and Eriksson (122,123) method can be applied to determine the ligand°Li+ equilibrium constant. It was observed in this study that the addition of 1505 to a solution of T1+ results in a shift of the half-wave potential to more negative values as the free ligand concentration is increased. The addition of another complexable metal ion should decrease the concentration 79 of free ligand, and the half-wave potential of Tl(I) reduction should revert to more positive values. From the equations given previously, the formation constants of the strong lithium crown complexes can then be evaluated. CHAPTER 4 THE INFLUENCE OF IONIC STRENGTH ON THE CONCENTRATION FORMATION CONSTANT OF ION-MOLECULE COMPLEXES 80 A. Introduction Experimental measurements of equilibrium constants of ionic reactions in solutions involve the vexing problem of activity cor- rections. A very common practice is to make the measurements at a l‘high and constant" ionic strength. It should be noted, however, that if alkali salts are used to maintain high ionic strength, they can sometimes participate in the reactions (particularly in complexation reactions) and, in addition, at high concentrations even in aqueous solution some ionic association can occur. It is preferable (although more difficult) to measure the concen- tration constant at several ionic strengths and to extrapolate the results to an ionic strength of zero. Another procedure, although not as effective as the extrapolation method, is to calculate the activity coefficients using an appropriate form of the Debye-HUckel equation. 0n the other hand, for ion molecule reactions of the type M+ + L : ML+ (3) where M+ represents a metal ion and L some neutral ligand, the thermo- dynamic equilibrium constant is given by aML+ YML+ (15) Kt = = Kc aM+aL YM+YL where Kt’ Kc’ 8'5, and v's represent the thermodynamic value, 81 5'." g 82 concentration value, activities, and activity coefficients, respec- tively. It is generally assumed that YML+ = YM+ and that YL = 1. Thus the concentration equilibrium constant, Kc’ is assumed to be essentially equal to the thermodynamic constant, Kt' However, it is obvious that the first approximation is valid only within the validity of the Debye-Hiickel limiting law, _i_._e_._, for I < 10"3 M in aqueous solutions and at much lower ionic strength in nonaqueous solvents with an intermediate or low value of the dielectric constant. At ionic strengths where the exact form of the Debye-HUckel equation, 10 =—————AZ"2E <16) - 9 Y1 l + Bai/I is valid, the activity coefficients of the free and complexed metal ions will not be equal since the size parameters (a1) will be different, presumably with aML+ > aM+. This relationship predicts that yML+ > YM+ and therefore, Kc < Kt at appreciable ionic strengths. In addition, at higher ionic strengths the activity coefficient of the neutral ligand YL will not be equal to unity. In a saturated solution of the ligand, L, the chemical potential of dissolved L, is necessarily equal to that of solid L. L _ 0,L L usolid ' usoln + RT z” asoln (17) The addition of an electrolyte to the above solution may change the solubility of L, but not the chemical potential of the solid. As long as the solution remains saturated, the activity of L, 3:01", 83 will also remain constant. Let m = solubility (molal) of L in pure solvent v0 = activity coefficient of L in saturated solution m1 = solubility (molal) of L in a solution of ionic strength I y1 = activity coefficient of L in the above solution Then, m0Y0 = mIYI (18) which may be rearranged to 21.- (.9. Yo I It has been found experimentally (124) that log :l-m kI (20) Yo which is of the exact same form as the well known empirical Setschenow equation,(125,126) where k is a constant which depends on the nature of L and of the electrolyte, and presumably on the solvent as well. For most electrolytes, 0 < k < 0.1 so that the addition of an electro- lyte decreases the solubility of the nonelectrolyte (salting out effect). Therefore, yL varies directly, but slightly with the ionic strength of the solution and tends to counteract the action of the ion size parameter. However, Mohilner, gt_al, (127) have shown in aqueous solutions that for concentrations of a neutral molecule (2-butanol) up to 0.7 M, the activity coefficient of 2-butanol re- mained equal to unity in the presence of an electrolyte (sodium sul- fate) whose concentration was 0.1 M, which corresponds to an ionic strength ofh.0.3 M, It is seen therefore, that in this work we assume that yL = unity. For complexation reactions of the type shown in Equation 3, it is a common practice to report the thermodynamic formation constants YML+ YM+Y L interest to us to test the validity of the above practice. Since the in concentration units, which assumes that = unity. It was of values of aM+ and aML+ are generally unknown and since it is not pos- sible at the present time to calculate precisely the variation of the activity coefficient of a neutral molecule as a function of the ionic strength of the solution, concentration formation constants were determined potentiometrically for the reaction 11,-." + 1806 : 18C6-Na+ (21) in anhydrous methanol solutions at (25.0 i 0.l)°C at various ionic strengths using tetra-M:butylammonium hydroxide as the supporting electrolyte. 8. Results and Discussion The cell used in the potentiometric titrations was as follows: Ag/AgCl/lsalt solution/glass electrode sensitive to Na+ 85 where the cell potential is given by _ 0 RT E ' Eglass + nFmaNa+ ' EAg/AgCl + Ej (22) _ 0 RT ' cell + 61'2" aNa+ + Ej (23) _ 0 RT RT + - Ecell + Ej + 61'9”" YNa+ '1' fiFSLn[Na :1 (24) At constant ionic strength, y~a+ should remain constant. In the course of the titration, since the electrodes are not removed from the solu- tion, and the solution composition changes very little, the liquid junction potential E. should also remain constant. Therefore the J expression for the cell potential may be rewritten as o. + E = lace” + granule] (25) where E°' is the sum of the standard, liquid junction, and glass asym- metry potentials, and the activity coefficient term. Concentration electrode calibration removes the uncertainty involved in relating potentials of buffer solutions of known activity to measurements made at different ionic strengths. This electrode calibration procedure gave calibration curves which deviated from linearity at 6.10"5 M, Midgley and co- workers (128) discussed the factors affecting the linearity of glass ion-selective electrode calibration curves and concluded that the major contributions to nonideal calibrations fall in three classes: interfering contaminants, reagent blank, and dissolution of alkali metal ions from the glass membranes at or near the limit of detection. In this work, the contribution from the dissolution of the glass is considered to be negligible. Therefore, the calibration curves were linearized by fitting the experimental data to Equation 26 E = E°' + mlog ([Na+] + R) (26) where E°', m (the Nernst slope) and R (the effective residual cation concentration contributed by the impurities in the solvent) are per- mitted to vary using a non-linear least-squares curve fitting pro- cedure until the difference between the calculated and observed po- tentials is sufficiently small. Usually, the residual, R, was cal- culated to be 6:10"6 M_which is in agreement with the concentration of sodium ions which may be experimentally realized in the reagent blank. A typical titration calibration curve is shown in Figure 8. The solid curve is the calculated calibration curve, and the solid circles are the experimental points. After the calibration solution is back-titrated with the ligand, the value of the concentration complex formation constant can be calculated. Since the residual cation concentration is negligible compared to the total metal concentration, the amount of ligand used to complex this residual cation is also negligible. The concentration of the free sodium ion can be determined from Equation 27. 87 POTENTIAL (mV) 0'1 0 1 J. l l 12 -4.5 -4.0 -3.5 -3.0 log [NOT] Calibration curve for the sodium-ion electrode in anhydrous methanol measured at I = 0.40 M, 88 [1121*] = 10(E—2‘111‘E1) (27) The mass balance equations are [1806-Na+] = CNa+ - [Na+] (28) [1806] = 018C6 - [1806-Na+] (29) where CNa+ and C1806 are the analytical concentrations of the sodium ion and the 1806 ligand, respectively. Before the equivalence point, the condition that [1806.Na+] % C1806’ leads to large errors in the calculation of [1806] by Equa— tion 29. Therefore, only data after the equivalence point were used as input to the MINIQUAD76A general equilibrium solving program. A typical titration curve is shown in Figure 9. The agreement between the experimental and the calculated results was quite good, and the residuals on the calculated concentrations also showed little syste- matic error. Concentration equilibrium constants for reaction 21 were obtained at various ionic strengths using TBAH as the supporting electrolyte. We assumed that TBAH was indeed an "inert" supporting electrolyte since the logarithms of the formation constants of 1806 complexes with dimethylammonium and diethylammonium cations in methanol solu- tions are 1.76 and 0.85 respectively (129) and, therefore, one would not expect any complexation of the TBA ion by the 1806 ligand. In addition, precise electrical conductance studies of ionic association 89 .ucwoa mono—m>w:cm mzu mmpmuwucw gossm 0:8 .2 08.0 n H pm umszmmws Focmgums msocvzscm cw mow_ spwz mwmgopsusmg 53wu0m we m>s=u cowumspvh .m wczmwd ES omooq 54th m230> om m._ 0.. S N. o._ 0.0 0.0 6.0 No 0.0 7 _ _ H W A _ _ A A AVN.1 nvvi. A>EV J<_._.Zm:.On_ 90 in anhydrous methanol solutions by Kay gt_al, (130) could not detect ion-pair formation in tetrabutylamnonium chloride solutions. Data on the TBAH do not seem to be available in the literature, but it seems reasonable to conclude that in this case, the amount of ion pairing at best would be very small. The results are shown in Table 10 and Figure 10. It is seen that for the ionic strength of 0.005 M_to 0.05 M, the value of the concentration formation constant remains reasonably close to the extrapolated value at zero ionic strength (Kt)° At higher ionic strengths however, the Kc value is somewhat further from the thermo- dynamic value. Since YL increases with increasing ionic strength (tending to increase the value of Kc)’ the decrease in KC indicates that the variation in the ion-size parameter is the more important factor than the variation in YL‘ Extrapolation of these results to infinite dilution yields a value of log Kt = 4.34 which is in good agreement with the value of 4.32 obtained by Frensdorff (31) also from potentiometric measurements, and a value of 4.36 obtained by Izatt, gt_al, (131) from calorimetric measurements. The results plotted in Figure 10 illustrate that the influence of ionic strength on the concentration formation constant is measur- able by our technique. However, the effect of the ionic strength on the ion-molecule reaction is rather small. The data given in Table 10 were used to fit the distance of closest approach for the com- plexed metal ion, aML+’ to the Debye—HUckel equation. Values of 4.0, 4.5, and 5.0 A were assumed for the distance parameter of the 91 Table 10. Concentration Formation Constants, Kc, for the Reaction Na+ + 1806 2 18C6-Na+ in Anhydrous Methanol at Various Ionic Strengths, I. I (M) 109 KCa 0.005 4.33 0.01 4.32 0.03 4.30 0.05 4.29 0.08 4.27 0.10 4.28 0.20 4.22 0.30 4.17 0.40 4.13 0.50 4.09 aThe uncertainty in log KC is :_0.02. ; .— 92 .cowpapom 0:9 we gumcmgum owcow 05p umcwmmw _o:mcpme mzosvxccm 2w xmpnsoo +mz.muw_ 05p :00 0x mo_ 00 HOFQ < .o_ wszmwu Auwav nJXU 31$ Ihwzmmkm UHZOH Auwdu Auwfiv oenv _ nxvv AUfiv Aumd. ox 8. anv ,3; .1: 93 solvated sodium ion, and the KINFIT4 program was used to fit the data. The corresponding values of aML+ were calculated to be (8.01:0.9), (9.2 i 0.5), and (10.4 i 0.7) A respectively. Since the "small a" parameter in the Debye-Hfickel equation is related to the distance of closest approach, these values are quite reasonable for the size of the solvated complex ion. Furthermore, these values should be considered to be at best only approximate, because the Debye-Hfickel equation was used at ionic strengths where its usefulness is, at best, rather limited. CHAPTER 5 ENTHALPY AND ENTROPY OF THE LITHIUM-CROWN COMPLEXES 94 A. Introduction The thermodynamic stability (AG°) of a complex is comprised of two components, the enthalpy (AH°) and the entropy (AS°) of com— plexation. The enthalpy changes are associated with the formation/ destruction of bonds among the metal ion, ligand, and solvent mole- cules. The entropy changes depend on the overall changes in the order of the system. Although it is nearly impossible to separate the enthalpy and the entropy into their microscopic components, the macroscopic or overall quantities can be determined experimentally. TWo methods exist for the determination of these thermodynamic quantities. The temperature dependence of the stability constant can be determined, and the van't Hoff isotherm can be applied AG° = —RT in K + RT 2 v tn 0 (30) in which 0 is the concentration of the reactant/product and u < 0 for reactants and v > 0 for products. The abbreviated form of the van't Hoff isotherm is obtained by selecting the standard state as the hypothetical ideal l M solution of each specie. AG° = -RT In K (31) Since AG° = AH° - TAS° (32) 95 96 then -RT 8n K = AH° - 168° (33) which may be arranged to _ AH° 1 65° QnK“-T(T)+—'R— (34) A plot of In K gs, +-should yield a straight line (provided AH° is independent of the temperature) from which AH° and AS° can be obtained. This method has been criticized because it assumes that AH° is temperature independent. Furthermore, the determination of the thermodynamic quantities from the temperature dependence of the formation constant is generally less accurate than the calorimetric method, because a small error in the equilibrium constants can result in a large error in AH°, particularly if the reaction is studied over a narrow temperature range. Also, this method was ineffective when the lithium-7 NMR technique was used, because the change in the resonance as a function of the temperature was ex- tremely small. The more accurate and direct method is to obtain AH° calorimetric- ally and calculate AS° by difference using the value of the equilib- rium constant determined by a complementary technique. It should be noted that formation constants for l:l complexes up to ~104 can also be determined calorimetrically,(l32) provided that AH° 97 is measurable. This chapter presents the results of a calorimetric study in which the enthalpies of complexation for the lithium-crown com- plexes have been determined. The entropies of complexation are also discussed. 8. Results and Discussion Table 11 shows the results of this calorimetric study. In general, the lithium-crown complexes are both enthalpy and entropy stabilized, but sometimes slightly entropy destabilized. It is im- mediately obvious that the enthalpy of complexation is strongly sol- vent dependent. As the solvating ability of the solvent increases, the complexation reaction becomes less exothermic for the formation of the 1204-Li+ and the 1505-Li+ complexes. For these two complexes, the favorable enthalpy term follows the same trend as the overall complex stability. This trend does not seem to be followed in the case of the 1806tLi+ complex in these solvents. In fact, just the opposite trend is observed. However, in all cases, the enthalpy term is the most negative (the most stabilizing) for the 1505-Li+ complex, in which the cation-ligand cavity size consonance is the closest. In the case of the 1806-Li+ complex, as the donicity of the solvent increases, the entropy term becomes increasingly negative (destabilizing). In propylene carbonate and acetone solutions the entropy term generally becomes increasingly negative (less positive) with increasing ligand cavity size. This observation may be 0 n x nor Low cmpm_:u_00 p050_ smzoqn Am smuamsuv pcmpmcou cowpmseo0 mcvm: 0000_:0_muw ¢o_004 :0 m.om.00 czocx 000000000 po: 00 x mo_ 0030000 czocxczu 000_ 00 000_000_0m 000_00_ 00 000 0_0e._0ox _ 00 _-000._-0000._0oo N . . 1. .000 _-0_00 _000 N 0 +0 N 0 i. . 3:00 0_000 00 2 N0 00 --- . - . - . - --- . - 0 0 00 N 00 0 00 N 0 00 0 :0 :0 00.0 00.0 - . - . - --- . - . - . - N 0 00 0 00 0 00 0 00 0 0N 0 00 A :00 m” 00.0 - 00.0 - 00.0 A 0.0 - 0 .0_x 00.N - 00 0N.0_ 0 e 00., A _.0 - 00.0 00.0 - Z0010 mammow I Uhnwoov I --- . - --- . - N 0 0 x 0 0 a 0 0 0_ 0 0 0 0z :0 om< oI< om< o:< oomq noz< p:0>_om 000. 000_ 00N_ 0.mpcm>_om msowem> :0 mmxmpgsou 2300015005004 050m 000 0000002030 0050000050010 .__ 00000 99 explained by the consideration of the ligand configurational entropy. The free uncomplexed crown ether in solution is flexible, but when it is complexed by the lithium ion, it becomes more ordered. The larger free ligands are more flexible than the smaller ones, and consequently have more degrees of freedom to lose in the complexa- tion process. With respect to the ligand configurational entropy alone, it is expected to be the most negative for the 1806-Li+ complex, because the ligand must contract and/or fold to bring the donor ether oxygen atoms within bonding distance of the lithium ion. Consequently, in acetone solutions, the entropies of complexation fall in the order 1806'Li+ < 1505.Li+ < 1204°Li+. In propylene carbonate solutions the order is 18C6-Li+ < 1204-Li+ < 15050Li+. While the entropies of complexation in propylene carbonate and acetone solutions are the most negative for 1806~Li+, the enthalpies for the formation of this complex are consistently more stabilizing than in the case of 1204-Li+. Even though the 1866-Li+ complex is less stable than 1204'Li+ in these two solvents, there is more heat associated with the participation of six ligand donor atoms (1806) than with the formation of four bonds (1204). Since several of the lithium-crown complexes have stability constants greater than 104 which could not be determined quanti- tatively in this study, some of the calculated entropies of complexa- tion in acetonitrile and propylene carbonate solutions are reported in Table 11 as the lower limits of 63° for log K = 4. In nitromethane the 1204-Li+, (12c4)2-Li+, and iscs-Li+ complexes are enthalpy stabilized, while 1806°Li+ is enthalpy destabilized. 100 The stability of the 1806'Li+ complex in nitromethane is due totally to favorable entropy changes. This complexation reaction is endo- thermic, but in the actual experiment, a heat change of only 0.2 calories was obtained due to the low solubility of 1806 in nitro- methane (<0.05 M) and the small amount of the complex which is formed in the solution. Therefore, this enthalpy is the least certain of all of the values reported in Table 11. Even though the bonding interactions in the 1806-Li+ complex occur at larger distances than in the cases of the two smaller ligands, it is difficult to explain the enthalpy destabilization of 1806°Li+ in nitromethane. In acetonitrile, there is a substantial interaction between the solvent molecules and the 1806 molecules which causes the heat of ligand-cation bond formation to be very small. Similar en- thalpy destabilization of a lithium macrocyclic complex (0222-di- lactamoLi+) has been reported (93) in acetonitrile and nitromethane solutions. Both 12c4-Li+ and 1505-Li+ are both enthalpy and entropy stabilized in acetonitrile solutions. In propylene carbonate solutions, the three lithium-crown com- plexes are both enthalpy and entropy stabilized except for the 1806-Li+ complex which is very slightly entropy destabilized. In the acetone solutions, the use of the formation constants determined by the 7Li NMR mole ratio method and the calorimetric data for the 1204-Li+ and 1806~Li+ complexes (incomplete reactions) led to unreasonably large negative enthalpies and large negative en- tropies of complexation. This indicates that the formation constants are probably too small, which is probably due to the ion pair forma- tion in this solvent. Therefore, the enthalpies of complexation 101 in acetone solutions were determined under two sets of experimental con- ditions. The heats of reaction were determined at high ionic strength (0.5 M_in Li0104) to provide a sufficiently large excess of the lithium ion to complex essentially all of the ligand. This was done because the lithium-crown complexes in acetone solutions are relatively un— stable. Since only a small fraction of the ligand is complexed, small heat changes result. These same determinations were also carried out at low ionic strength (0.02 M_in Li0104) under conditions of an incomplete complexation reaction. The standard enthalpy of reaction, AH° (obtained under conditions of a large excess of the lithium ion), can be used with the heat associated with partial complexation, q (obtained at low ionic strength), to calculate the value of the complex formation constant. The number of moles of the complex, ML+, formed in the solution at low ionic strength can be calculated by Equation 35 + = 1 . # moles ML AHO q (35) The concentration of the complex is obtained by dividing by the volume of the solution. The value of the concentration formation constant is then calculated according to Equation 4 [ML+] = 11191 (4) [M+l[L] (cM - [11minsL - [ML*11 102 where 0M and CL are the analytical concentrations of the metal ion and the ligand respectively. This provides a complementary method and a check on the formation constants obtained by the lithium-7 NMR mole ratio method. It should be noted that in the actual experiment, a concentrated solution of the ligand (No.5 M) in the given solvent was added to the salt solution. It was determined that the heat of dilution of the ligand solution was negligible, but at high ionic strength, the enthalpy of complexation values had to be corrected fer the heat of dilution of the salt solution when the ligand in pure solvent was added. The formation constants for the 1204~Li+, iscs-Li+ and 1806°Li+ complexes in acetone were determined calorimetrically (Table 12) to be log K = 2.1, 3.3, and 2.2 respectively, compared with the values reported in Chapter 3, log K = 1.62, 3.59, and 1.50 respectively. The agreement between the two methods is satisfactory considering that data from only two calorimetric experiments were used in each calculation. The results in methanol are similar to those observed in acetone solutions. However, within experimental error, the enthalpies for the formation of lscsoLi+ and 1806°Li+ in methanol are identical. The formation constants for the 1505-Li+ and 1806-Li+ complexes in methanol were also determined calorimetrically, and were found to be equal. In both cases log K is equal to 1.1 (Table 12). While the 1806tLi+ complex is expected to be weaker than the 1505-Li+ complex (the NMR method could not detect any complex formation), these 00205005 o e . P F . . mom 0 0m _ 0mo.o om.o w.N . +04.oomp mmé ~.F . . 00205002 Nam o om _ wmo.o mm.o 0.N . 04.mum_ m . +. i. om _ N.N oo._ . 0200000 mo N mmo.o mm.0 m.m i +04.mom_ mm.m m.m mo.0 . 0:00000 mm _ 0mo.o ¢©.m 0.0 1 +04.mump mm.F _.N No._ . mcopmom mm P mmo.o ©0._ N.m . +04.¢um— mzZ 00005000 0. m . F 0 i. 1. x o— x 00_ Amop x 2v 00 Amo_ x 2v 20 02%NW A0000 0 A0-0_oe._0uxv .wmwwvwm > xm EO H11 003300 0:0 _ 0 .N_ 00000 .mpme owspmewso_0u Eosm mucmpmcoo :o0pmesom mo 20000030000 104 results are in good agreement with the 1505-Li+ stability constant determined by NMR (log K = 1.23). The small quantity of heat re- leased upon the formation of 1204°Li+ in methanol, prevented the calculation of the formation constant. This small enthalpy is in agreement with the NMR results, in which complex formation could not be detected. The many contributions to overall entropy changes include the solvation entropies of the metal ion and the ligand, the changes in the ligand internal entropy (due to orientation, rigidity, and con- formational changes), and the change in the total number of particles and the translational entropy. The negative entropy change for the formation of 1505°Li+ in methanol can certainly be attributed to pos— sible increased ligand rigidity upon complex formation, but since methanol is a structured solvent, the rearrangement of the solvent structure during the complexation process should also be considered. The lithium ion which is strongly solvated in methanol acts as a structure breaker, because solvation effects disturb the organization of the bulk solvent, but the complexed ion (inside of the crown ether organic coat) acts as a structure maker, because it is much less solvated. The overall effect is a loss in entropy. CHAPTER 6 NATURAL ABUNDANCE OXYGEN-17 NMR STUDY OF SOME MACROCYCLIC COMPLEXES 105 A. Introduction Cation—ligand interactions in macrocyclic complexes can be examined by observing the magnetic resonance of the nuclei of the ligand and/or of the cation. In the first case, 1H and 13C NMR measurements were widely used since the "early" days of macrocyclic complexes. While the resonance frequency of both nuclei are usually sensitive to the ( complexation reaction, these nuclei do not participate directly in the formation of the complex. The immediate chemical environment of the lithium ion in the lithium—crown complexes was probed directly ( by observing the lithium-7 NMR resonance (Chapter 3). Obviously, it would be interesting to examine the influence of complexation on the NMR spectra of the ligand atoms which directly form the ligand-cation bond(s). Evidently, oxygen—l7 NMR would be a good candidate for such a study. The pr0perties of the oxygen-l7 nucleus are given in Table 13. It has a large range of chemical shifts (~1000 ppm), and despite the low natural abundance and low sensitivity, a number of NMR studies have been carried out on reactions involving oxygen compounds, albeit of enriched samples.(l33,l34) The resonance of the 170 nucleus seems to be a very sensitive probe of chemical environment and structure. For example, the two ether oxygens of propylene carbonate (propane- diol-l,2-carbonate) show two separate 170 resonances, while the dif- ferences in the corresponding chemical environments are quite subtle. There appears to be only one report of an oxygen-l7 NMR study involving metal complexes with acetate and citrate ions (135) where the car- boxylate groups were enriched to'y5% 170. The addition of calcium(II) 106 _+ 107 Table 13. Some Properties of the Oxygen-l7 Nucleus Spin 5/2 Electrical Quadrupole Moment -2.6 x 10'26 (e x cm2) Natural Abundance 0.037% NMR Sensitivity vs. 1H _2 (at constant field) 2.91 x 10 Resonance Frequency (at 42.3 kgauss) 24.399 MHz Magnetic Moment -l.8930 Nuclear magnetons to a solution of these anions did not induce any changes in the 170 resonance. However, large shifts were induced by the addition of dysprosium(III) ion which was used as a (paramagnetic) model for the calcium(II) ion. It was of interest to us, therefore, to investigate the possible use of oxygen-l7 NMR as a probe of the complexation reaction of macro- cyclic polyethers with alkali metal cations. 8. Results and Discussion The 170 NMR chemical shifts for the free and complexed 1204 in various solvents are shown in Table 14. Neat 1204 is a viscous liquid which produces a very broad resonance with a linewidth of ~1200 Hz. Introduction of this compound into a solvent of lower viscosity drastically decreases the linewidth. The chemical shifts of the free 108 .000002 00 0000 0:0 .0000 0000 00:0 2H0 .N: 0 .000>0000000s 00,0,0mm 0mm 000 00 0000_z000_ :00; 000 0- 000 0- 00 000000 _00_s0:0 00 000_0000 00N_ 00 000000_00 . . U wCMLHwEOwa: OH mquOF£ULmQ ESwEOEEmPXHZDMLHwfi $0 HCSOEQ LGPOEPSUw cm $0 COwflwUUw QLPQ 0N all I I mm + 00 0:000:000_ 0:0 Eng m + 00 mumssuom 0:0 mumw:m 000050:0 .00000 0:0 00 0000000L: 0:0 ca 0:00 1.1-11111111111 mum up 1 uo._ 000 00 1 0.0 000 m 1 020000< 0N0 0. 1 0; 0N0 m 1 0:02:00 000 up 1 0._ 0mm 0 1 0_000000000< 000 0_ 1 00.0 000 mp 1 0.0 mmc _m 1 0.0 000 w_ 1 o.m 00m w 1 0:0:u050Lumz --- -- -- 00N_ e 0 a 000000 0002 A010 m\~>< A5000 0 00m_\+00 0ANIV m\—>< mfisaav 0 pc0>pom 00_000 + 03000 02000 0000 : x0_0000 +00 000 000 00N_ 000000_00 0000000000: 00 00000 0:2 N_-0000x0 .0_ 00000 109 crown in the four solvents investigated (Table 14) are several ppm upfield from the resonance of the neat ligand. The addition of an equimolar amount of Li0104 to the solution of the crown shifts the 170 resonance upfield by'wlO ppm. A complexable cation decreases the electron density from the oxygen atoms via ion-dipole and ion-induced dipole interactions so that the population average signal shifts upfield. Since the addition of a salt with a large uncomplexable cation, tetrabutylammonium perchlorate, does not change the chemical shift of the ligand, the observed shift must be due to the complexa- tion reaction. The overall effect of the complexation on the 170 chemical shift is disappointingly small. It seems that with the present state of the art only a qualitative indication of the ligand-cation interaction can be obtained by this technique. The lithium-7 NMR study discussed in Chapter 3 showed that the 1204-Li+ complex is quite stable (log K > 4) in nitromethane and acetonitrile solutions and weak in acetone and pyridine solutions. It is seen that this distinction cannot be ob- served by the 170 NMR. In nitromethane solutions, lithium-7 NMR showed the existence of 1204-Li+ and (1204)2-Li+ complexes. A similar conclusion can be ob- tained from the 170 NMR measurements. The addition of the Li+ ion to a solution of 1204 in nitromethane results in an upfield shift of the 170 signal, but after the 1:1 mole ratio of Li+/1204 is reached, further addition of the lithium ion reverses the direction of the chemical shift. The chemical shift of the 1204-Na+ complex in acetone was found 110 to be -14 ppm (Table 14). The chemical shift of (1204)2oNa+ could not be obtained, because the preparation of 2:1 solutions in these solvents always resulted in the formation of a precipitate. Similar studies were carried out on crown ethers 1505 and 1806 (Table 15). In general, the results are similar to those observed for 1204. Here again, the complexation produces a 010-16 ppm upfield shift. A somewhat different behavior is observed for the 1806°K+ and the 1806-Ag+ complexes in acetonitrile. In these cases, the addition of the metal ion to the ligand solution resulted in a much smaller change in the 170 resonance frequency. In the case of the silver ion, the complex may be quite unstable in acetonitrile solu— tions due to the strong 0H3CNoAg+ interaction.(l36) 0n the other hand, it seems difficult to explain the insensitivity of the 170 chemical shift of 1806 towards the formation of a potassium complex since it is quite stable in both acetone and acetonitrile solutions.(l37) The chemical shifts of the oxygen atoms of the solvent molecules remain constant and independent of the solution composition. The resonance of the perchlorate anion is split into a quadruplet by the 35Cl nucleus. The center of the quadruplet is at 291 ppm, in excel- lent agreement with the literature value of 290 ppm.(l38) Such con- stancy is not at all surprising, because the solvent molecules are in large excess, and the perchlorate anion is known to be quite inert. It was of obvious interest to us to extend this investigation to several other common solvents such as alcohols, ethers, sulfoxides, and water. However, in these cases the crown ether 170 resonance was totally masked by the solvent oxygen resonance. In pyridine 111 0mm 0 + +0< 000_ N + +¥ 000 - 0 +02 0N0 - 0. +_0 -- -1- -- 000 0 + 0_00000000o< 0000 00 - 0 m_ +02 mmm 001 +00 mfim m 1 000000< 0N0 00- +00 000 N - 00000000 000 0_- +00 000 0 - 000000000000 000 00- +00 0N0 0 1 000000000002 -- -- -- 00N_ e 0_+e 000000 0002 0000 ANIV N\_>0 A0000 0 +2 ANIV N\_>0 A0000 0 000>000 000000 x0_0200 :30:0 0000 00x000000 _n_ 00000 000 0000 000 000_ 000000 03000 00 0000000 022 0_-0000x0 .m— 00000 112 omm . mp +m< mkm m + +¥ mmm - NP +mz o . ow or +w4 -l- -a- I-» mmm o m:owmu< muw_ ANIV m\_>< AEQQV @ +2 ANIV m\_>< AEQQV @ pcw>_om vcmmwg meQEou cZogu mmgu A.u.pcouv .m_ m_nwh 113 soiutions the 17O resonance of the comp1exed 18C6 was so broad so as to prec1ude the observation of the 170 resonances of even 0.5 [v1 so1utions of the 1igand (3 M'in equiva1ent oxygens) with very 1on9 scanning periods (more than 106 scans). The so1ubi1ity of 18C6 in nitromethane was so 1ow that its signa1 cou1d not be detected under our experimenta1 conditions. Since the overa11 range of 170 chemical shifts is so large it was anticipated that the shifts upon comp1exation wou1d be more sig- nificant. However, the interaction between the oxygens of a crown ether and a meta1 ion is predominant1y e1ectrostatic,(40,41) conse- quently the change in the environment of a sing1e oxygen atom upon comp1exation shou1d be sma11. It shou1d be noted that the 1arge 17O chemica1 shifts are usua11y observed when a change occurs in the cova1ent bonding of an oxygen atom. Therefore, it seems the 170 NMR is not a sensitive probe of the immediate chemica1 environment of a macrocyc1ic po1yether. Simi1ar resu1ts were obtained by Foster and Roberts with a 15N NMR study of cryptates (139) where the 15N resonance a1so seems to be quite insensitive to comp1exation. CHAPTER 7 SUGGESTIONS FOR FUTURE STUDIES 114 115 A. Strong Lithium-Macrocyclic Complexes The stability constants for the very stable lithium-crown com- plexes (log K > 4) could not be quantitatively determined due to the reasons described in Chapter 3. The preliminary data indicate that the cyclic voltammetric method is applicable, and the necessary quantita- tive data are obtainable by utilizing the thallium(I) competition method. The main problem remaining deals with the reference electrode in nonaqueous solvents (see Chapter 3). The applicability of this tech- nique should also be examined for the strong lithium cryptate complexes observed by Cahen gt_al,(46) These data can then be used with comple— mentary calorimetric data to obtain the thermodynamic quantities for the complexation reactions. B. The 12C4-18C6 Interaction Crown ether l8C6 is a solid at 25°C with a melting point of 39°C, while 12C4 is a liquid with a boiling point of m70°C at mo.05 mm Hg. Eighteen-crown-six and lZC4 were dried separately under vacuum, but when they were placed together under a common vacuum, l8C6 absorbed l2C4. Similar behavior was not observed with 1505, which is also a liquid at 25°C. This is a particularly interesting observation from both kinetic and thermodynamic view points. Twelve-crown-four was absorbed in a more than l:l but less than 2:l mole ratio. Examination of infrared spectra was inconclusive as no new bands were observed. The vapor pressure of l2C4 in and of itself is not large enough for 12C4 to distill over into the container of 18C6 under vacuum. ii 116 Therefore, there must be some "complex" formation. This complex would be interesting to study, but the method of instrumental analysis is not obvious at this time as the two compounds are very similar in structure. C. Microprocessor Control Solution Calorimeter The calorimeter used for the determination of enthalpies of reac- tion in Chapter 5 and described in Chapter 2 is of the adiabatic (more correctly isoperibol) design. The experience of this author with this particular system has indicated the necessity of equilibra- tion periods consisting of several hours in some cases. In addition, the temperature of the calorimeter contents cannot be precisely measured with the present apparatus. This equilibration time could be shortened considerably by electronic modification of the instrument so that the temperature of the calorimeter contents is automatically held constant (isothermal) by intelligent instrument control. This modification is also attractive from another point of view, because, since the temperature is held constant, heat capacity measurements may be totally omitted. Several types of isothermal calorimeter designs have been de- scribed (l40—l44) 'Hnarecent advances in applications of microprocessor control of analytical instrumentation makes this problem particularly amenable to such control. It is out of the scope of this discussion to treat this project in any detail, but rather to mention the im— portance of its implementation. The calorimeter cell, insert, and stirrer assembly would remain unchanged. In the actual experiment, 117 the flow rate of cooling gas would be increased so that the heat of stirring is more than offset, and the heater would cycle for very well defined short periods of on time (heat pulses) to maintain constant temperature. With well defined heating periods, it is then necessary to count the heat pulses. The rest of the experiment may be performed in virtually the same manner. It should be pointed out however, that this method requires constant cooling throughout the entire experiment which may present some difficulty with the present apparatus. Com- monly, Peltier thermoelectric coolers with constant current sources have been employed for constant cooling.(l4l-l44) APPENDICES APPENDIX A THE CRYSTAL AND MOLECULAR STRUCTURES OF THREE CYCLOPOLYMETHYLENE TETRAZOLE COMPOUNDS A. Introduction Cyclopolymethylenetetrazoles are known for their strong stimulat- ing effect on the central nervous system. In sufficient doses, they ‘ are capable of inducing epileptic convulsions. The formula for tetrazole (I), a l,5-disubstituted tetrazole (II), and a cyclopoly- methylenetetrazole (III) are shown below. The activity increases H H (CH )n \Nl—C’S §;__C’R2 («j-c 5 2N/ \\N4 N/ \\N 2 N/ \\N 4 \\N/ \N/ \N/ 3 3 I II 111 with the length of the hydrocarbon chain and varies from 1000 mg/kg for trimethylenetetrazole (TMT, n=3) to 30 mg/kg for heptamethylene- tetrazole (n=7).(l45) As expected, the aqueous solubility decreases with increasing length of the hydrocarbon chain. Trimethylenetetrazole is soluble to the extent of l.4 molal, while the solubility of heptamethylene- tetrazole is 0.18 molal. A glaring exception is pentamethylenetetra- zole (PMT, n=5) which is soluble to the extent of 5.0 molal.(l46) Crystallographic studies of the PMT complex of iodine mono- chloride (147) showed that PMT acts as a monodendate ligand and 118 "I"?! I .‘ 119 coordinates through N(4) of the tetrazole ring. In the silver complex AgN03-(PMT)2,(148) monodendate tetrazoles are coordinated to the silver atom via N(4) and bridging tetrazoles are linked to silver atoms via N(3) and N(4). It was of interest to determine the crystal struc- ture of the free ligand to see if there were any changes in the con- figuration of the molecule upon complexation. Previous studies have indicated that TMT (146) and PMT (149) form dimers in aqueous solution which may be related to the high solu— bility of these two compounds. When a tert-butyl group is substituted for a hydrogen in the 8-position of PMT (Figure 13, page 124), the solubility in water decreases tremendously to N3 x 10’3 molal.(146) Solvation of these compounds is expected to be due primarily to dipole-dipole interactions of the tetrazole with the solvent molecules, but the dipole moments of substituted tetrazole compounds are found to be near 6D,(150) and reside in the tetrazole ring itself. Therefore, one would expect similar solvation effects for substituted tetrazoles. Therefore, it was of interest to us to examine the crystal structures of these compounds for features which can help to explain the unusual solubility characteristics of these compounds. 8. Experimental Part Trimethylenetetrazole (Aldrich) was recrystallized from a 5:1 mixture of carbon tetrachloride and ethanol, m.p. 110°C, lit. 110°C;(151) PMT (Aldrich) was recrystallized from diethyl ether and dried under vacuum, m.p. 60°C, lit. 59°C;(152) and 8-tert-buty1pentamethylene- tetrazole (8-t-butyl PMT) was prepared (146) according to the method 120 of D'Itri,(153,154) m.p. 133°C, lit. 132.5—133.0°C.(155) Crystals of these three compounds were grown from covered dilute solutions of the tetrazoles (~0.05 molal) in ether (TMT and PMT) or in acetone (8-t-butyl PMT) from which the solvent was permitted to evaporate slowly to dryness. Single crystals were mounted for each compound. Both PMT and 8—t-butyl PMT were mounted on glass fibers, and TMT was mounted in a glass capillary under vacuum to minimize the apparent air decomposition. The diffraction data were measured with a Picker FACS—I automatic diffractometer using zirconium-filtered (PMT) or graphite-monochrom- atized (TMT and 8-t-butyl PMT) Mo Ka radiation. C. Structure Solution and Refinement The three crystal structures were determined by Wei and Ward.(156) The structures were refined to convergence by full-matrix least- squares calculation. The molecules are symmetrical except for N(l) and C(5) of the tetrazole ring. Since the thermal parameters for these atoms were unusual, and since the final difference maps showed the largest positive densities to be near C(5) and the largest negative densities near N(l), the refinements were continued after reversing the identities of atoms (1) and (5). The results of these "reversed" refinements corresponded closely to the earlier refinements indicating that atoms (1) and (5) refine equally well as C and N or as N and C, and therefore these two atoms are disordered by approximately 50% occupancy of each atom-type at each location. Further refinements, using composite "NC" atoms (1/2 N+-1/2 C in their scattering factors) 121 for (l) and (5), gave much better agreement without increasing the number of refined parameters. 0. Discussion As shown in Figures 11-13, the cyclopolymethylenetetratetrazole molecules each contain a planar tetrazole ring. Table 16 presents some of the crystallographic data. The polymethylene ring in TMT is planar to within :0.02 A and lies 0.5° from the plane of the tetrazole ring. The polymethylene rings in PMT and 8-t-buty1 PMT are planar only to within :0.36 A (seven-membered rings in chair form) and lie approxi- mately 24° from the planes of the tetrazole rings. The bond distances in the tetrazole rings range from 1.307 to 1,340 3 (Table 17). The digit in parentheses following the bond length is the estimated standard deviation as it applies to the least significant digit. The relative average lengths of these bonds are in agreement with the disordered model in which all bonds, except NC(1)-NC(5), are averages of single and double bonds. The average angles (Table 17) indicate that N(3) is displaced towards the NC(l)-NC(5) bond thereby increasing the bond angle at N(3) and decreasing the bond angles at N(2) and N(4) from the overall average of 108°. The bond angles differ significantly from those in the unsubstituted tetrazole (157) in which the angles at N(2), N(3), N(4) are all approximately 108°. Except for the N(2)-N(3) bond length (reported at l.30(l) A), the tetrazole ring average bond lengths in TMT, PMT, and 8-t-butyl PMT agree with those in tetrazole. The bond lengths in the polymethylene rings appear to be normal 122 \ NC(5)' . '/NC(1) / ‘ \N(4) “N(2) @\’ 1 ‘“n {—7 N(3) Figure 11. Molecular structure of TMT. 123 . // . \§%._,1 \ \\ ”I,” x"\\ /. \“ C 8 . NW) c(9)\/ J \ ’ ) Figure 12. 124 ‘ ‘ ~ 1 ====: .iééz%7 r ‘ ,nzay N(4) TEEEél T=s . -—' Figure 13. Molecular structure of 8-t-butyl PMT. 125 Nm_._ Q\_Na o.ON~_ Amvmm.e__ Amvmm_.¢_ Amve_o.w A¢v_ww.m_ wN.qm_ ezw_Io_Q Hza Pagan-p-w mvm._ mwm.— AmEU\mV xpwmcwo :\_Nm :\_m¢ azocw macaw o.mmk m.©mm Ammv > Amvmfi.¢m Aevmo.wo_ on m Amvammw.© Amvemo.w a Amvmoe.w Amvkom.o_ a Amvo_m.m_ Amvwme.k Amv a N_.wm2 N_.o__ Seawaz La_:aa_oz qzo_zmu qzmzqu aF=ELoa H22 HEP mama owsgmcmo__mumxcu wFOngpwpwcmcmme>FOQoFuxQ .m_ mfinah 126 O Table 17. Cyclopolymethylenetetrazole Interatomic Distances (A) and Angles (°) 8-t—butyl TMT PMT PMT NC( l)-N(2) 1-329 (3) 1.340 (3) 1-337 (2) NC(I )—NC(5) 1-307 (3) 1-326 (2) 1.322 (2) NC(l)-C(8) 1-473 (4) — — NC(I) C(10) - 1415(3) 1-469 (3) N(2)—N(3) 1-332 (3) 1-322 (3) 1-325 (2) N(3)-N(4) 1-324 (3) 1-309 (3) 1-324 (3) N(4)-NC(5) 1-335 (3) 1-336 (3) 1-338 (2) NC(5)——C(6) («173(3) 1-471 (3) 1-462 (3) C(6)-C(7) 1.517 (5) 1-511 (4) 1-524 (3) C(7)—C(8) 1-600 (5) 1-516 (4) 1-527 (3) C(s)-C(9) - 1-503 (4) 1-323 (3) con—cu 1) - — 1-558 (3) C(9)—C( 10) - 1-514 (5) 1-525 (3) C(1 l)—C(12) — - 1-531 (3) cum—C(13) - - 1-526 (3) CU 1)-C(14) - - 1-530 (3) N(2)—NC( 1)—NC(5) 109.4 (2) 103-3 (2) 103-9 (2) N(2)-NC( l)-—C(8) 137-2 (3) — — N(2)—NC( 1)—C(10) - 125-0 (2) 124-7 (2) NC(5)—NC(l)-C(8) 113-4 (2) - — NC(S)—NC(I)—C(10) - 126-6 (2) 126-3 (2) NC(l)—N(2)—N(3) 104-6 (3) 105-7 (2) 106-0 (2) N(2)—N(3)—N(4) 111-6 (3) 111-3 (2) 110-5 (2) N(3)-N(4)—NC(5) 104-5 (3) 106-1 (2) 106-3 (2) NC(l)—NC(5)—N(4) 109-7 (2) 108-6 (2) 108-3 (2) NC(l)—NC(5)—C(6) 113-5 (2) 127-2 (2) 121-4 (2) N(4)—NC(5)-C(6) 136-9 (3) 124-2 (2) 124-3 (2) NC(S)—C(6)—-C(7) 101-0(3) 1120(2) 113-9 (2) C(6)—~C(7)—-C(8) 110-6 (3) 115-2 (3) 115-3 (2) C(7)—C(8)-—NC(1) 101-4 (3) - — C(7)—C(8)—C(9) - 115-5 (3) 111-6 (2) C(7)—C(8)-—C(l 1) — - 113-3 (2) C(9)—C(8)—C(l 1) — - 112-5121 C(8)—C(9)—C(10) - 114-9 (3) 113-8 (2) C(9)—C(10)-NC(1) - 112-7 (2) 113-5 (2) C(8)—-C(l 1)—C(12) — — 110-0 (2) C(8)—C(l 1)—C(13) — — 110-3 (2) C(8)—C(l 1)—C(14) — — 111-4 (2) C(12)—-C(l I)-—C(13) — - 106-5 (2) C(12)-C(l 1)—C(14) — - 109-3 (3) C(lJ)-C(ll)—-C(l4) - — 108-8(3) 127 with average NC-NC distances of 1.335 A, average NC-C distances of 1.471 A, and average C-C distances of 1.516 A. The angles in the polymethylene ring of TMT are quite different from those in PMT and 8-t-butyl PMT and reflect the differences between a planar five- membered ring (TMT) and the chair form seven—membered rings (PMT and 8-t-butyl PMT). The only major angular difference between PMT and 8-t-butyl PMT is C(7)-C(8)-C(9) which in 8-t-buty1 PMT is de- creased by the substitution of the t-butyl group at C(8). The major differences in the molecular structures of the free ligand (PMT) and the AgNO3 (148) and ICl (147) complexes are due to the disorder of atoms (1) and (5) in the tetrazole ring of PMT. The tetrazole ring bond-lengths in PMT relative to those in the two complexes show the averaging of double and single bonds by the dis— ordered structure. The bond angles are essentially the same in the three determinations. The pentamethylene rings are all in the chair form, the average C-C bond lengths are shorter by 0.030 A in PMT, and the bond angles agree rather well except for those at NC(l), NC(5), and C(7) which average 3.1° larger in PMT. The cyclopolymethylenetetrazole molecules pack together without hydrogen bonding as shown in Figures 14—16. The tetrazole rings of TMT and PMT, in adjacent molecules related by a center of symmetry, overlap significantly to produce "dimers," presumably by dipole- dipole interactions. The distances between the least-squares planes of the tetrazole rings are 3.408 A for TMT and 3.705 A for PMT com- pared with 3.226 A for tetrazole.(157) The overlaps are illustrated in Figures 17 and 18. The 8—t-buty1 PMT does not crystallize with Figure 16. 130 Packing diagram for 8-t—buty1 PMT. 131 .42» cw mmrzow—oe mo ampgm>o .N_ 62:02; 132 .HZQ cw mmpzuwpos mo ampcm>o .mp masmwu 133 the tetrazole rings of adjacent molecules parallel to each other. It appears that adjacent molecules, related by twofold screw axes, form "chains" in which N(3) of one molecule is directed towards the center of the tetrazole ring of the next molecule. The distances between the centers of the tetrazole rings of the two molecules forming "dimers" are 3.481 A for TMT and 3.741 A for PMT, which indicate fairly strong dipole-dipole interactions. The "dimers“ themselves do not interact strongly with each other as indicated by the distances between tetrazole ring centers of 5.401, 5.902, and 6.694 A for TMT and 5.863, 6.589, and 8.072 A for PMT. Thus, the forces between "dimers" are weak and this may account for the large solubilities of TMT and PMT. The distances between the centers of the tetrazole rings of in- dividual molecules of 8-t-buty1 PMT are 4.390 A along the "chains" and 6.132, 6.614, and 7.557 A to other adjacent molecules. It would be expected that the lattice energy of 8-t-buty1 PMT would be higher (interactions at 4.390 A between individual molecules) than those of TMT or PMT (interactions at 5.4 A minimum between "dimers"), and consequently, the solubility of 8-t-butyl PMT would be less than that of TMT or PMT. APPENDIX B APPLICATION OF COMPUTER PROGRAM KINFIT4 TO THE CALCULATION OF FORMATION CONSTANTS FROM NMR DATA AND THE CALIBRATION OF ION—SELECTIVE ELECTRODES A. Calculation of Formation Constants from NMR Data 1. Program Function The KINFIT4 computer program is a nonlinear least squares curve fitting routine. The equation to which the data are fitted is inserted by the user into the SUBROUTINE EQN. This program was used to fit the lithium-7 NMR chemical shift vs, mole ratio data to Equa- tion 5. In many cases, the limiting chemical shift of the complex, _ 2 2 2 2_ 2 1/2 dobs - [(KCM-KCL-l) + (K CL+K CM 2K CLCM+2KCL+2KCM+1) 1 [—163] + 6. <5) 0C, was obtained directly from the mole ratio plot. However, when the complex is relatively unstable (K < 100), the value of 5c cannot be determined directly from the mole ratio plot, and Equation 5 has two unknowns, 6c and K, designated U(1) and U(2) respectively, in the FORTRAN CODE. The input variables are the analytical concentra- tion (M) of the ligand (XX(1)) and the observed chemical shift (XX(2)-ppm). The data input includes the usual control cards and the NMR data. The first control card gives the number of data points, the maximum number of iterations to be performed, the number of constants to be read, and the convergence tolerance. The subsequent cards include a title card, a card containing the values for the constants (if any). 134 135 a card containing the initial estimates for the unknown parameters, and data cards. Each data entry is followed by its estimated variance. The SUBROUTINE EQN and a sample data listing are given for the case when two unknowns are calculated. If the value of 0c is already known, U(1) is replaced by its value. 2. SUBROUTINE EQN SUBROUTINE EON COunDN KOUNIvlTAPt'JIAPCOIdToLAPoTlNEE.NOPT.NOVAR.uouuK,x.U,]tngx, 191xalE$T.1.Av65ESlD.IAE.LPs.1Tyr.xn.a)1yp,0x13,rop.:o,ru,p.7L.10.f 216VAL.:$1,1.o1.L.n.JJJ.v.01.VEc1.uc51.co~51.Nboi.3061.noP1.LoPT. BYYTqCUNSTS CCIHDN/FREDTIIHETH CDHuON/PDJHT/KGPTOJDDTQXXX DIMENSION “(“0330)0U(2019311(~.300).XXTQ)QFOPTBOOIoFDTSOOIqFU(300) 162120.?11.v€CT(20.211.ZLTSOG).TCT2014EIGVALTZO).x51(son).y(1o), 2031101.c0~615158.161.Nr51(501.1SMIN(50).Rx1yp(sc).ozlx(so),lg;(50, 3-"0PTTSC16LDPTTSO)oiYYTSD).CONST(16)6111(15) 50 10 (2650“9501979999OIOol1'12) ITYP 1 CONTINUE ITAszbo c METAL nun EOUATION FOR R). F)! KI AND DELTL HL. no lo" paznxuc. NOUNK:2 Novqszz CDNSTTI)=HETAL CONCENTRATION. n CCNSTT21=CHEHICAL SHIFT OF FREE NETAL. PPM IxTI):LIGtND CONCENTRATION. n 7x(2)=C8$ERvEC CHEMICAL SHIFT. P9P U(1’=LIHITIN5 CHEuICAL SHIFT 0F :cn;;€x, ppn 0121=FORHATIc~ CONSTANT FOR 1 To 1 COMPLEx JTAPE=EI fiETufiN 7 CONTINUE RETURN B CONTINUE RETURN 2 C3\TINUE IFTIWETdoNE.-l) 60 TC 3: PETU?% 35 CONTINUE A=(U(2)--ZTOTXX(l)0-2) B:(U(2)°-2)0(CONST(11’22) C=-2.0-(U(2)00Z)0(xx(1))-C0NST(1) 0:2.C-(u(2))o(xxtli) E=2.0-(0(2)1-(CCNST(111 AA:(U(2))0(CONST(1)) BB=-(U(2))-xx(1) C=TCONST(2)-U(1))/(2.-(CDNST(I))0(U(2))) 53“C‘A’Ee'lo)9SCRT(‘BS‘A’E‘C°D*£91c)))°CC)‘U(1A RESID=S-xx¢2) . RETURN 3 CONTINUE RETURN 4 CONTINUE RETURN 5 CONTINUE l‘tlHETH.NE.-l) 68 T0 20 RETURN 20 CONTINUE .RETURN 9 CONTINUE RETURN 10 CONTINUE RETURN 11 CONTINUE RETURN 12 CONTINUE RETURN ENO rint1(1r3n 136 3. Sample Data Listing 15 100' 1.0001 LI'7 N"? RF 0: 15C5L1CLD‘ IN A: TOY " = . 0.02073 -1.‘3 E E AT 2‘ 050 C I 0.02 N DAT! III 19. 0080 10°C. 000 Iauf-dé-Iofli ZOSE‘DECOODSIBS 560E°06'0o90 ZQSE‘OE 0.01337 Luann-3.35 ZoSE-DSOoDISSS SoOE-OSDoIZ 2.5E'03 0.32:7“ 500"D‘COSI 305E'030002591 500i‘0‘0071 ZOSE'OS 0.33.111 SoOE-06€.TQ loss-030.03‘29 5oCE'C60o77 ZoSE‘OS O-Chl‘ut 5.D£°Cfi‘.‘.7$ 1.5C-030.091‘35 SoOE'063o83 2.5E-Cl 0.10:7 SOOE‘C‘OOE: 105E’030012‘O? S-Ui-Ofioo79 ZOSE‘OD 301.33.; 50°C'06003} 2.55-93 8. Calibration of Ion-Selective Electrodes 1. Program Function The KINFIT4 program was also used to linearize the sodium ion- selective electrode calibration data by fitting these data to Equa- tion 26. E = E°' + m log ([Na+] + R) (26) Initially, the unknowns used were m, E°', and R. Although the cal- culated value of m, the Nernst slope, was always in excellent agree- ment with the theoretical value, it was coupled to the intercept, and a statistically superior data fitting resulted when the value of the slope was inserted as a constant. The input variables are the logarithm of the sodium ion concentration (XX(1)) and the observed potential (XX(2), mV). 137 2. SUBROUTINE EQN SUBROUTINE EON couuoh Koyu1,11APL.JTAP{,1:1,LAP.ITNCR.NOPT.NOVLR.NOUNK.X.UoIlHAX. 1‘1'0113‘01GAVI‘ESIOQJ‘£Ol'sOl1YFQX'QRx‘Y'QD‘IIOFOPO;0"”.P‘ZL.1°.[ 2ICVAL6X$1.T.DT.LQH.JJJ6YoOT.VECT.NESquDNSTcNDchJDATohDPToLOPTo 57116CDNSTS EDPHDN/FREDl/IHETH CD"“ON/POINTIKDPT~JD°16XIX DINENSIDN x14.:co).0120).a1114.3001.xxzu).Fov¢3001.rot3003oFUTSOOT 16PT20621)qVECT(20621)oZLTSDOT.TOTZDToEIBVALT2016351(300)6Y¢10)6 2UYTIO).CONSTSTSC.I6).NCST(501.ISHINTbD).RxTYPISO).OXIIT50).IRRTSO) 3.“DPT(SCTvLOPTTSO)6771(5016CONSTT16)6111(152 GO TO (2030‘05910799090100'1912’ ’1'? 1 CONTINUE ITAPErsc NDJNK=3 NCttkzz U(I)=VDLTAEE - FNA INTEPCEPT U(2):RESIDUAL CATIDL CONCENTRATION CENSTilizREACTIDN TEHP. IN EEG. C. JTLPE=51 RETURN 7 CONTINUE RETU‘h P CONTINUE RETUFN P CLNTINUE IF(1hETN.NE.-1) SC TL 35 RETURN :5 CONTINUE . SODIUM:IC°-1rx¢12100421 S=LLOGIFTSDDIUMT P01:C.I9FA'(?71.150CCNST(I)1-53UTI) RESIDzPOT-XXTZT RETURN CONTINus RETURN A CDNTTNUE EETURN CONTINUE IFTIHETH.N£.-I) 6: To 20 RETURN 20 CONTINUE RETURN S CONTINUE RETURN IC CONTINUE RETURN 11 CONTINLE RETURN 12 CCNTTNCE RETURN END (Th?) '1‘ Ll" 3. Sample Data Listing 12 100 1.0001 STANDARDIZATION OF NAS 11-15 HITH NRCLO. 1N HEDH ‘1 25.L DEG C. l=3o10 11-34. 25.0 2000 1005-05 ‘9.5575 1.05'96 -‘90.40 “.OE-OZ "o6638 loDE-Ob ‘81.SD 9.05.0? -.o“221 IOCE-OE -7OQ‘O ‘0'E’D? -‘0209‘ IOCE-06 -590.c “ODE‘OZ -:09325 1.0E-C6 ~47.IC b.0E-C2 ~3o7£51 loCE-Ob ~35.?D floDE-C2 -3.55~6 1601-06 -23.10 ~.CE-C2 '3o3‘78 loOE-Db '11010 QoOE’O? -501987 1005-56 002063 BoOE-CZ '209‘3] 1.0E-06 100700 ‘003‘02 than. APPENDIX C APPLICATION OF COMPUTER PROGRAM MINIQUAD76A TO THE DETERMINATION OF EQUILIBRIUM CONSTANTS FROM POTENTIOMETRIC DATA A. Program Function The MINIQUAD76A program is a general equilibrium solving routine for the calculation of equilibrium constants from potentiometric data. Up to 20 equilibria involving five reactants can be considered, and a maximum of three electrodes can be used to determine the concentra- tions of free species. The equilibrium constant for reaction 21 Na++18C6 I 1806-Na+ (21) was calculated as _ [18C6 Na+] ’ + (36) [Na ][1806] As indicated in the data input instructions which follow, the user specifies the number of formation constants to be used in the calculation. The formation constants can be either held constant or refined in the calculation. The stoichiometries, initial solution volume, reaction temperature, initial number of millimoles of each reactant, and the titrant concentration and temperature are specified by the user. The electrode calibration parameters are entered as the slope and intercept of the calibration plots. The titration data are entered as the measured electrode potentials as a function of the volume of the titrant added. The data input instructions and a sample data listing are presented in the following sections. 138 139 B. Data Input Instructions 1. 1 card /20A4/ : descriptive title 2. 1 card /815/ : LARS, NK, N, MAXIT, IPRIN, NMBEO, NCO, ICOM. LARS is an indicator for the data points to be considered in the refinement: with LARS=l all the data points are used, with LARS=2 alternate points, with LARS=3 every third point, egg, (last points on all titration curves are always used). NK is the total number of formation constants. N is the number of formation constants to be refined. MAXIT is the maximum number of iteration cycles to be performed: with MAXIT=0 and according to the values of JPRIN and JP (see below) the residuals on mass balance equations and/or the species distribu- tion are evaluated for the given formation constants and conditions. IPRIN=0 is normal; IPRIN=1 monitors the progress of the refine- ment at each cycle; IPRIN=2 produces an additional listing of the experimental data at each titration point. NMBEO is the total number of reactants (mass balance equations) in the system under consideration. NCO is the maximum number of unknown concentrations of free reactants; if NCO=0 the whole job is abandoned before refinement. ICOM=0 is normal; with ICOM=1 data points are eliminated before the refinement if the corresponding block of the normal equation matrix is found to be not positive-definite. 140 3. 1 card /3F10.6, 8X,12/ : TEMP, ADDTEMP, ALPHA, NOTAPE TEMP is the reaction temperature in °C. ADDTEMP is the titrant temperature in °C. ALPHA is the coefficient of cubical expansion for the solvent used, °c'1. NOTAPE=O is normal; NOTAPE=1 reads values for EZERO and SLOPE (see below) from device TAPE3. This allows calibration curve data to be calculated and used in the same computer run. 4. NK cards /F10.6,7IS/ : BETA(I), JPOT(I), JQRO(J,I) (NMBEO values), KEY(I) The formation constants are expressed in exponential notation 8, = BETA(I) - ToJP°T(I) . JQRO(J,I) (J=l, NMBEO) are the NMBEO stoichiometric coefficients of the 1th species with formation constant Bi‘ The order of coef- ficients is arbitrary, except that those referring to reactants, of which the free concentration is determined potentiometrically, must come last. Such a choice implies that a progressive integer number (from 1 to NMBEO) is assigned to each reactant. KEY(I) is the refinement key of the 1th formation constant: with KEY=0 the formation constant is not refined and with KEY=1 the formation constant is refined. 141 5. The following set of cards for each titration curve: 1 card /1215/ : NMBE, JNMB(I) (NMBE values), NC, JP(I) NMBE is the number of reactants (mass balance equations) involved in the titration curve. JNMB holds the integer numbers previously assigned to the NMBE reactants involved. NC is the number of unknown free concentrations at each point of the titration curve; the number of concentrations experimentally determined (i;g;, the number of electrodes) is NEMF=NMBE~NC. JP contains integer numbers corresponding to selected reactants: in the subroutine STATS the formation percentages relative to these reactants will be calculated, depending on the value of JPRIN. 1 card /5A10/ : REACT(I) (NMBE values) REACT contains the names of the reactants, listed in the same order as JNMB. 1 card /415/ : JEL(I) (NEMF values), JCOUL JEL holds the number of electrons transferred at each electrode. If the decimal cologarithm of concentration (§;g;) pH) is to be read in, put JEL(I)=O. JCOUL=0 is normal; JCOUL=1 if the total volume of the solution does not change during the titration (e.g., coulometric experiments). 142 S l (or 2) card(s) /8F10.6/ : TOTC(I) (NMBE values , EZERO(I) (NEMF values ADDC(I) NMBE values VINIT 9 TOTC contains the initial number of millimoles of reactants in solution; the order of reactants is the same as in JNMB. EZERO(I) holds the standard potential of the 1th electrode (mV); the value is ignored if JEL(I)=0. ADDC contains the molar concentrations of titrant solutions (there is one for each reactant); the order of the reactants is the same as in JNMB. VINIT is the initial volume of the solutions (cm3), and should correspond to the volume expected at the temperature of the TITRANT. 1 card /8F10.6/ : SLOPE (NEMF values). SLOPE contains the slopes of the calibration curves for the species measured, in units of mV per decade of concentration, the value is ignored if JEL(I)=0. cards /15,8F8.3/ one for each point of the titration curve: LUIGI, TITRE(I) (NMBE values), EMF(I) (NEMF values) LUIGI=O is normal, LUIGI=1 indicates the end of a titration curve, LUIGI < 0 indicates the end of all titration curves, LUIGI=2 indicates that, for coulometric titration, current (mA) and fractional 143 current efficiency are read instead of a data point. TITRE contains the volumes of titrant solutions (cm3) added in volumetric titrations or time of current passage (sec) in coulometric experiments. EMF contains the potentials (mV) measured on each electrode with non-zero JEL value (otherwise the decimal cologarithms of concentra- tion). 6. 1 card /15/ : JPRIN JPRIN controls the amount and type of output produced by STATS: Statistical JERIN_ Analysis Tables Graphs 0 no no no 1 yes no no 2 yes yes no 3 yes no yes 4 yes yes yes If JPRIN > 1, the amount and type of tables and/or graphs is determined by the values contained in JP for each titration curve. 7. 1 card /IS/ : NSET NSET=1 for another set of formation constants - items 1-4, 6, and 7, only -; NSET=0 for another complete set of data, NSET=-l for the termination of the run. Sample Data Listing any»:rjrerDI‘Tr‘Ivjtgnnqvjr161323g~nwv11fiul 3 1 1 25 15 l 9.1 '7 char. 6“?“ '1' () 2J1. H .‘OJNHOdh-Ob. I—PCDC‘Dfi'J'fi (h '5 K r. o a O o O o O O f.‘ O \1' f‘ 'T‘ 3" N ~l 'J‘ ".3 on C) U" 1") U" 0 r3 r3 r1 (3 r‘ r3 (3 "i D H C) 3 I ("6” D.PCI C.COC C.Cu. 0.033 0.00? C.CCL C.OOO C.COO O.DCC C.CDC C.CCC C.CDL 0.533 .CCC 0.003 C.CLC 0.003 C.COC 155.37 I c .- U1 0 I f-I‘lnl O T v I n ._n In H: ~3- mo~uF3