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This is to certify that the
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Thermodynamic and Kinetic Characterization of Porous
Graphitic Carbon in Reversed-Phase Liquid Chromatography

presented by

Yuening Zhang

has been accepted towards fulfillment
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6/01 c-JClRClDateDucpss-pts

___.__.__.t_._. .. —_ . --_.__ ....---

Thermodynamic and Kinetic Characterization
of Porous Graphitic Carbon
in Reversed-Phase Liquid Chromatography

By

Yuening Zhang

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of

MASTER OF SCIENCE
Department of Chemistry
2004

Abstract

THERMODYNAMIC AND KINETIC CHARACTERIZATION OF POROUS
GRAPHITIC CARBON IN REVERSED-PHASE LIQUID CHROMATOGRAPHY

By
Yuening Zhang

In this dissertation, the thermodynamics and kinetics of solute transfer for
alkylbenzenes and methylbenzenes on porous graphitic carbon were studied.

In the thermodynamic studies, the retention factor increases with an
increase in the number of methylene or methyl groups. The data indicate that
increases in the number of methylene or methyl groups result in more negative
changes in molar enthalpy (AHsm). Hence, the transition from mobile to stationary
phase is a more energetically favorable exothermic process with each methylene
or methyl group added. The data also show that the change in molar volume
(AVsm) is close to zero, which indicates that the solute molecules adsorb on the
surface of porous graphitic carbon during retention.

In the kinetic studies, the rate of solute transfer increases with increasing
number of methylene and methyl groups. The activation enthalpy from the
stationary phase to transition state (AHg) was found to increase with increasing
number of methylene and methyl groups. But the activation enthalpy from the
mobile phase to transition state (AHtm) was much smaller than AH”. The volume
barriers AV” and Avtm again are very close to zero.

These results provide a thorough and detailed characterization of the

retention mechanism for porous graphitic carbon, which is based on adsorption.

Acknowledgements

At this moment when I finished my dissertation, I am very grateful to my
advisor, Dr. Victoria L. McGuffin, for her guidance in my study and research, and
her support for me all the time.

Many thanks to my committee members, Dr. Bruening and Dr. Jackson in
the Chemistry Department of Michigan State University.

Thanks to all the group members, Sam, Carl, Xiaoping, Rashad, Melissa,
and Amber, who help me to overcome many difficulties.

Thanks to my parents, brother, Zheng and our son Dylan, whose love

supports me through all the hard times.

iii

TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
Chapter 1: Introduction and Background

1.1 Porous Graphitic Carbon (PGC)
1.1.1 Structure and Method of Preparation
1.1.2 Physical and Chemical Properties
1.1.3 Applications of PGC in Separations
1.2 Thermodynamic and Kinetic Theory
1.2.1 Thermodynamics
1.2.2 Kinetics
1.3 Previous Investigations of Thermodynamics and Kinetics in
Reversed-Phase Liquid Chromatography
1.3.1 Thermodynamics
1.3.2 Kinetics
1.4 Conclusions
1.5 References

Chapter 2: Retention of Aromatic Hydrocarbons on Porous Graphitic
Carbon

2.1 Introduction
2.2 Experimental Methods
2.2.1 Solutes
2.2.2 Chromatographic system
2.2.3 Data Treatment and Analysis
2.4 Results and Discussion
2.4.1 Thermodynamic Behavior
2.4.1 .1 Retention Factor
2.4.1.2 Molar Enthalpy
2.4.1.3 Molar Volume
2.4.2 Kinetic Behavior
2.4.2.1 Rate Constant
2.4.2.1 Activation Enthalpy
2.4.2.1 Activation Volume
2.5 Conclusions
2.6 References

Chapter 3: Conclusions and Future Directions
3.1 Results
3.2 Future Directions
3.3 References

iv

25

25
28
28
29
32
35
35
35
39
46
51
51
55
62
66
67

68
68
70
72

Table 2.1:

Table 2.2:

Table 2.3:

Table 2.4:
Table 2.5:
Table 2.6:
Table 2.7:

Table 2.8:

Table 2.9:

Table 2.10: Activation enthalpy for alkylbenzenes on porous graphitic carbon

LIST OF TABLES
Corresponding pressure and length of restrictor in the
chromatographic system

Retention factors (k) for alkylbenzenes on porous graphitic
carbon

Retention factors (k) for methylbenzenes on porous graphitic
carbon

Molar enthalpy for alkylbenzenes on porous graphitic carbon
Molar enthalpy for methylbenzenes on porous graphitic carbon
Molar volume for alkylbenzenes on porous graphitic carbon
Molar volume for methylbenzenes on porous graphitic carbon

Kinetic rate constants for alkylbenzenes on porous graphitic
carbon

Kinetic rate constants for methylbenzenes on porous graphitic
carbon

Table 2.1 1: Activation enthalpy for methylbenzenes on porous graphitic

carbon

Table 2.12: Activation volume for alkylbenzenes on porous graphitic

carbon

Table 2.13: Activation volume for methylbenzenes on porous graphitic

carbon

31

36

37
42
43
49

50

52

53

57

58

65

LIST OF FIGURES

Figure 1 .1: Atomic structure of graphite: Bemal structure of perfect three-

dimensional graphite with ABAB... layer registration 3
Figure 1.2: Atomic structure of graphite: Warren structure of two-dimensional

turbostratic graphite with no layer registration 3
Figure 1.3: Scanning electron micrograph: spherical particle of PGC

(black band represents 2 pm) 5
Figure 1.4: Scanning electron micrograph: High magnification of surface

(white horizontal line represents 400 nm) 5
Figure 1.5: Transmission electron micrograph: Spherical particle of PGC 6
Figure 1.6: High-resolution electron micrograph of PGC after heating

to 2340 °C 6
Figure 1.7: Energy coordinate diagram 11
Figure 2.1: Structure of alkylbenzenes used to study retention on PGC 26

Figure 2.2: Structure of methylbenzenes used to study retention on PGC 27
Figure 2.3: Schematic diagram for the chromatographic system 30

Figure 2.4: Regression results with the Gaussian equation (A) and the EMG
equation (B). Experimental data: (—), regression: ( - - - ).
34

Figure 2.5: Representative graph of the retention factor (k) versus inverse
temperature (K'I) used to calculate the change in molar enthalpy
according to Equation 1.8. Column: porous graphitic carbon. Mobile
phase: methanol, 1.21X107 Pa (1760 psi), 0.955 mL/min. Solutes:
toluene (o), m-xylene (I), 1,3,5-trimethylbenzene (A),
pentamethylbenzene (A), hexamethylbenzene (a) 40

Figure 2.6: Differential change in molar enthalpy (AAH) (lemol) versus carbon
number for alkylbenzenes at P = 5.24%106 Pa (760 psi) and T = 295
to 327 K 44

Figure 2.7: Differential change in molar enthalpy (AAH) (kJ/mol) versus carbon
number for methylbenzenes at P = 5.24X10 Pa (760 psi) and T =
295 to 327 K 45

vi

Figure 2.8: Representative graph of the retention factor versus pressure used to

Figure 2.9:

calculate the change in molar volume according to Equation 1.10.
Column: porous graphitic carbon. Mobile phase: methanol, 327 K,
1.38 mUmin. Solutes: toluene (o), m-xylene (I), 1,3,5-
trimethylbenzene (A), pentamethylbenzene (A),
hexamethylbenzene (a) 47

Representative graph of the rate constant (ks...) versus inverse
temperature (K‘) used to calculate the change in activation
enthalpy according to Equation 1.14. Column: porous graphitic
carbon. Mobile phase: methanol, 2760 psi, 0.956 mUmin. Solutes:
toluene (o), m-xylene (I), 1,3,5—trimethylbenzene (A),
pentamethylbenzene (A), hexamethylbenzene (a) 56

Figure 2.10: Differential change in activation energy from the stationary phase to
transition state AAHts (kJ/mol) versus carbon number for
alkylbenzene at 5.24x1o‘5 Pa (760 psi) 59

Figure 2.1 1: Differential change in activation energy from the stationary phase to

transition state AAHn (kJ/mol) versus carbon number for
methylbenzene at 5.24x1o6 Pa (760 psi) 61

Figure 2.12: Representative graph of the rate constant versus pressure used to

calculate the change in activation volume according to Equation
1.16. Column: porous graphitic carbon. Mobile phase: methanol,
327 K, 1.38 mUmin. Solutes: toluene (o), m-xylene (I), 1,3,5-
trimethylbenzene (A), pentamethylbenzene (A),
hexamethylbenzene (c1) 63

vii

Chapter 1: Introduction and Background

High-perfonnance liquid chromatography (HPLC) is one of the most widely
used techniques in the analytical sciences. By relying on the subtle interplay of
solute interactions with mobile and stationary phases, HPLC is capable of
separating a variety of complex mixtures, including neutrals, charged species,
enantiomers, and biological materials. However, to separate a wide range of
sample types, different stationary phases are often required. During the past few
years, there has been an intense search for new adsorbents because of the rapid
proliferation of HPLC and the realization of the disadvantages of most commonly
used silica-based materials.

Porous graphitic carbon (PGC) is a two-dimensional graphite with a
unique sponge-like structure, which gives it good mechanical strength while
maintaining an adequate surface area (around 150 mzlg) and porosity (around
80%) [1]. Porous graphitic carbon has unique chromatographic properties, being
the only truly hydrophobic adsorbent. It shows strong retention of non-polar,
polar, and ionic organic compounds as well as novel stereoselectivity. It gives
chromatograms of high efficiency.

This chapter presents a description of the PGC stationary phase that was

used in this study, as well as the relevant thermodynamic and kinetic theory.
1.1 Porous Graphitic Carbon (PGC)

1.1.1 Structure and Method of Preparation
There are, in fact, three distinct forms of carbon to which the term

“graphitic" can reasonably be applied and which have well-defined crystal

structures. Two of these forms are shown in Figures 1.1 and 1.2. The Bemal
structure of perfect three-dimensional graphite consists of layers of carbon atoms,
organized in a hexagonal array and ordered ABABAB.... This form of graphite is
termed hexagonal graphite. A second, rarer form of three-dimensional graphite,
the Lipson and Stokes form, also exists, but here the layers are ordered
ABCABC.... This is termed rhombohedral graphite. In both crystalline forms, the
layer spacing is 3.354 A and the atomic spacing within the layer is 1.42 A.

Most synthetic carbons, when heated to about 3000 °C, assume the
second structure shown in Figure 1.2. This is two-dimensional graphite in which
graphitic sheets are randomly oriented relative to one another. In two-
dimensional graphites, the layer spacing is slightly greater than in three-
dimensional graphites at 3.40-3.43 A, and the atomic spacing within the layers is
slightly less.

The template required for the production of PGC should be a well-bonded
silica gel of high porosity. The spherical silica is specially prepared and has a
pore volume of 1.4 cm3/g with a specific surface area of 50 mzlg. The mean
particle size diameter is 7 pm. This template is impregnated with a melt of phenol
and hexylamine in a 6:1 weight ratio. The impregnated material is heated
gradually to 150 °C to form phenol-formaldehyde resin within the pores of the

silica gel.

am 2-13A
Figure 1.1: Atomic structure of graphite: Bemal structure of perfect three-

dimensional graphite with ABAB. .. layer registration [1]

ii
I

 

I

\

am 2-10A

Figure 1.2: Atomic structure of graphite: Warren structure of two-dimensional

turbostratic graphite with no layer registration [1]

This silica-polymer is then heated slowly to 900 °C in a stream of oxygen-
free nitrogen in a specially designed rotary furnace. Approximately 50% of the
weight of the polymer is thereby lost, and the density of what remains is
increased to about 2 g/cm3. The silica-carbon particles are then treated with hot
aqueous potassium hydroxide to dissolve the silica template. The remaining
porous glassy carbon has a BET (Brunauer-Emmet-Teller) surface area of 450-
600 mzlg and a pore volume of 2.0 cm3lg, corresponding to a particle porosity of
about 80%. This carbon is then heated to 2500 °C in oxygen-free argon. The final

carbon has a surface area of about 150 mzlg and a pore volume similar to that of
the carbon before high-temperature treatment. The carbon retains the spherical
form and the particle size of the original silica template [1].

1.1.2 Physical and Chemical Properties

The structure of the porous carbon has been studied in detail by X-ray
diffraction, electron diffraction, scanning electron microscopy, and high-resolution
electron microscopy. These techniques provide a self-consistent picture.

The scanning electron micrograph in Figure 1.3 clearly shows the
spherical shape of the particles and their sponge-like structure [1]. The strong
sponge—like structure is capable of withstanding considerable shearing forces,
such as those met with in high-performance liquid chromatography. Figure 1.4 is
the high magnification of the surface [1]. The porous two-dimensional graphite
(PGC) consists of 3-10 pm spherical particles.

Figure 1.5 is the transmission electron micrograph of a spherical particle of

PGC. Figure 1.6 shows the high-resolution electron micrograph (HREM) of PGC

 

Figure 1.3: Scanning electron micrograph: Spherical particle of PGC

(black band represents 2 pm) [1]

 

Figure 1.4: Scanning electron micrograph: High magnification of surface

(white horizontal line represents 400 nm) [1]

 

Figure 1.5: Transmission electron micrograph: Spherical particle of PGC

 

Figure1.6: High-resolution electron micrograph of PGC after heating to 2340 °C

[1]

after heating to 2500 °C [1]. Particularly notable are the straight, parallel lines,
indicating ordered graphitic sheets. Also seen are a number of rounded corners
and several groups of curved or bent sheets. There is also some evidence of
surface defects.

The high-resolution electron micrograph (HREM) indicates that PGC
consists of intertwined ribbons of carbon, where each ribbon consists of some 30
discrete layers or sheets about 3.4 A apart. It is this ribbon form that accounts for
the high mechanical strength of PGC. The crystallites comprise tens of layers of
graphitic sheets, thus giving stack heights of 30-60 A, in agreement with the X-
ray evidence.

Carbon in the form of graphite is one of the most attractive packing
materials for HPLC, as it should be free from the disadvantages peculiar to silica
gels, such as the limited pH of the mobile phase and the strongly adsorptive
silanol groups. The reason is the following. Pure graphite is a crystalline material
made up of sheets containing hexagonally arranged carbon atoms linked by the
same conjugated 1.5-order bonds that are present in any large polynuclear
aromatic hydrocarbon. There are, in principle, no adventitious functional groups
on the surface because the aromatic carbon atoms have all valencies satisfied
within the graphitic sheets. Perfect graphite is therefore an intrinsically
reproducible material with a completely uniform surface, free from any functional
groups.

Furthermore, graphite is one of the most unreactive substances known and

can withstand any mobile phase that will not attack the HPLC equipment itself.

Problems, however, may arise when a material of high specific surface
area is required. Surface defects must therefore be present at the edges of such
crystallites and the ideality of bulk graphite is lost to some extent. However, it is
still possible to provide high-surface-area graphites with minimal adventitious
surface groups. As an example, a square array of graphitic carbon atoms with a
side of 10 nm will contain 40,000 C atoms, of which 160 will be at the edge of the
sheet. The edge atoms will thus comprise about 0.4% of the total C atoms.

In fact, characterization using X-ray photoelectronic spectroscopy (XPS) of
the graphitic carbon spheres detected only the C(1s) band, pointing to a surface
devoid of any appreciable oxygen-containing functionalities (estimated detection
limit, 0.2 atomic %) [2]. If these oxyen-containing functionalities are present, they
will produce much stronger retention for the solutes than graphitic carbon.

1.1.3 Applications of PGC in Separations
There are several main factors that influence retention by graphite in HPLC

[31-
1. Mobile phase-solute attraction

These attractive interactions include dispersion, dipole-dipole, dipole-induced
dipole, ion-ion, ion-dipole, ion-induced dipole, and hydrogen bonding forces.
These interactions discourage retention by keeping the solute in the mobile
phase.
2. Mobile phase-solute repulsion

These repulsive interactions arise from disruption of the structure of the

hydrogen-bonded mobile phase by non-hydrogen-bonding solutes. These

hydrophobic interactions occur between an aqueous or aqueous-organic mobile
phase and any nonpolar segments of the solute. These interactions encourage
retention by expelling the solute from the mobile phase.

3. Stationary phase-solute interaction

These interactions arise from dispersion forces of the London type
between the graphite surface and the solute. These interactions are balanced to
a greater or lesser extent by similar interactions between the graphite surface
and the mobile phase. The net effect may either encourage or discourage
retention, but may have an important effect on selectivity.

In addition, charge-induced interactions between the stationary phase and
solute can promote the retention of polar compounds. These charge-induced
interactions are strongest when the polar groups of the solute are forced into
direct contact with the graphite surface by the stereochemistry of the solute
molecule. In such cases, the additional interactions resulting from a polar group
can be so strong that they more than compensate for the increased solute-mobile
phase interactions. When stereochemistry does not force direct contact of the
polar groups with the surface, the effect is less strong but still significant.

The overall effect of these competing interactions is that an increase in the
hydrophobicity of the solute, say by adding alkyl groups, always increases
retention, as expected in a typical reversed-phase mode. However, an increase
in the polarity of the solute by adding groups that can either donate or accept

electrons or can polarize the graphite surface may also increase retention,

particularly if these groups are constrained to be in close contact with the
graphite surface.

Porous graphitic carbon shows separations of nonpolar organic compounds
[4], highly polar organic compounds [5], geometric isomers [6], and ionized
organic compounds [7]. Porous graphitic carbon has proven to have a number of
unsuspected properties that have substantially enlarged its area of applications

and opened up entirely new possibilities.

1.2 Thermodynamic and Kinetic Theory

In order to characterize the solutes undergoing adsorption on the PGC
stationary phase, it is necessary to utilize a mathematical system by which they
can be compared. The relationships of chemical thermodynamics and kinetics
provide such a system. For this purpose, traditional thermodynamic and
transition state theories need to be synthesized first.

In Figure 1.7, the retention behavior is depicted by using an energy
coordinate diagram when the solute moves from mobile (X...) to stationary phase
(X3). The thermodynamic changes in molar enthalpy (AH...) and molar volume
(AVsm) represent the difference between the final and initial states. If the molar
enthalpy (AHsm) is positive, it means the solute gains enthalpy when it transfers
from mobile to stationary phase. The chromatographic process is thus
unfavorable. Conversely, if the molar enthalpy is negative, the chromatographic
process is energetically favorable. If the change in molar volume (AV...) is
positive, it implies the solute occupies a larger volume when it is adsorbed on the

stationary phase than in the mobile phase. The reverse is true too.

10

Energy

 

 

 

 

Reaction Coordinate

Figure 1.7: Energy coordinate diagram depicting the transfer of solute from
mobile phase (X...) to stationary phase (X3) via a high-energy transition state (xi).

Other thermodynamic and kinetic parameters as described in the text.

11

The kinetic aspects of the retention behavior are characterized by a fast
equilibrium between the mobile phase (X...) and transition state (X;) with
equilibrium constant Km, followed by a rate-limiting step between the transition
state and the stationary phase with rate constant k3,... The corresponding
changes in activation enthalpy and activation volume are represented by 13th
and Avg", respectively.

A similar diagram can be drawn to illustrate the transition from stationary
to mobile phase, in which the rate constant km... activation enthalpy AH]... and
activation volume Avg are used.

1.2.1 Thermodynamics

The equilibrium distribution of the solute (X) between mobile (m) and

stationary phases (5) can be characterized by

X... <—> Xs
This process can be mathematically defined by using the equilibrium constant
expression

=a_s~_[Xi_ (1.1)

a... “' [X]...
where a... and a. are the activities, and [X]... and [X]s are the molar concentrations
of the solute in the mobile and stationary phases, respectively.
The physical characteristics of the system in which molecules enter
equilibrium is characterized by the phase ratio ([3), which is the ratio of the

surface area of the stationary phase (As) and volume of the mobile phase (Vm):

A8
l3=7 (1.2)

m

12

The equilibrium constant and phase ratio are important because they are utilized
in the calculation of thermodynamic parameters that characterize solutes as they
undergo adsorption.

The retention factor (k) is a function of the retention times of a solute (t.)

as well as an unretained compound (to):

t —to
to

k=5
I3

r

k:

 

(1.3)

(1.4)

The change in Gibbs free energy (AG) can describe whether or not an
equilibrium transfer is spontaneous. When applied to the chromatographic
process, the Gibbs free energy is an indicator of how favorable is a transition
from the mobile to the stationary phase. Traditionally defined as

G = H - TS (1.5)
this equation describes the inherent energy of a molecule in some defined state
where H is the enthalpy, T the absolute temperature, and S the entropy. Given
that a single molecule in a chromatographic system can exist in one of two
mutually exclusive phases, it is necessary to define each phase with its own
energy (G... or 6.). As the molecule equilibrates between these two states, the

change in energy (AGsm) can be measured. This change is defined by
AGsm = AH,,,, -A(TS)sm (1.6)
This energy can be directly related to the equilibrium constant described in

Equation 1.1 through the van’t Hoff equation:

13

mK=1§§1-UJ)
RT

The importance of this equation is that it directly links the equilibrium constant to
the Gibbs free energy, thus correlating a molecule’s affinity for a given phase to a
thermodynamic value that describes how energetically favorable is a transition
into that phase.

Instead of K, AHS... is used as a quantitative measure of the equilibrium
event. A relationship between the retention factor (k) and phase ratio ([3) allows
for the calculation of AH... By substituting Equation 1.4 into Equations 1.6 and

1.7, the resulting equation is

AH AS
5m 3m -| 1.8
RT + R "B( )

 

mk=‘

Equation 1.8 allows for the calculation of AH... from the slope of a graph of In k vs.
1/T at constant pressure. The assumption within this calculation is that neither
AH... nor ASS... are temperature dependent. The intercept contains information
about the change in molar entropy as well as the phase ratio. Because it is not
known how the phase ratio [3 changes with temperature and pressure, the
change in molar entropy ASS... cannot be reliably calculated.

In addition to the energetic parameters that describe a system, the change
in molar volume (Avg...) can also be calculated. When applied to the
chromatographic system, AV... is the physical change a molecule undergoes as it
tranfers from mobile to stationary phase. This transition can be described
through a model of solvation. In the mobile phase, a solute molecule is

surrounded by a given number of solvent molecules. As the solute transfers into

14

the stationary phase, these solvent molecules may be stripped away. When the
transition is complete, the molecule is solvated by the stationary phase
molecules if it has partitioned, or has lost some of its hydration shell if adsorbed.
As a result, AV... is an indicator of physical change as the molecule moves
between the mobile and stationary phases.

In order for Avg... to be calculated, enthalpy must be further defined as a
function of the internal energy (AE), pressure (P), and volume (V). When using
these three fundamental variables of a system, the change in enthalpy (AH...) is
defined as

AHsm = AEsm +A(PV)3m (1.9)
By substituting Equation (1.9) into Equations (1.6) and (1.7), under constant

temperature, the retention factor k can be related to the pressure:

A5,,“ +TASsm - PAVsm)
RT

mk=(

 

-In[3 (1.10)

Equation (1.10) allows for the change in molar volume to be extracted from the
slope of a graph of In k vs. P at constant temperature by assuming that neither
AEs... nor ASS... are pressure dependent. Using these graphical methods of
analysis, it is possible to quantify the physical change of a solute as it transfers
between phases.

Thermodynamics provide a simple method by which physical and
energetic properties can be calculated. While the parameters defined above
allow for the comparison of solutes, they do not provide insight into the rate at

which a given transition may occur. As a result, transitions that may be

15

energetically favorable (i.e. large negative AG...) may be either slow or fast.
Since thermodynamics is incapable of describing the rate at which a transfer
between mobile and stationary phases will occur, kinetic studies need to be
conducted.
1.2.2 Kinetics

Kinetic theory requires an initial definition of the transitions a molecule
undergoes, where kms is the rate constant for transfer from stationary to mobile
phase and K...“ is the rate constant from mobile to stationary phase. The first step
in elucidating kinetic data is the determination of the rate constants. By using the

retention factor (Equation 1.3), the rate constants are defined by

_ 2kto

ms 2
T

_ 2k2to

k =kkm, 12

 

 

(1.11) . k (1.12)

am

where ‘t is the exponential component. These rate constants quantitatively define
the transfer, thereby allowing for comparison between solutes, mobile phases,
and stationary phases. However, a more in depth treatment of kinetics using
transition state theory allows for other rate parameters to be calculated.
Transition state theory is an expansion on the kinetic process shown
above. The crux of the theory is based upon the existence of a transition state: a
short-lived, high-energy state on the reaction coordinate diagram (Figure 1.7),
where K]... is an equilibrium constant for the solute from mobile phase to
transition state reaction, k3... is a rate constant, and X; is the transition state. This
conformation can be defined more clearly by relating the rate constants km and

k... to transition state energy (AEp... AEp), enthalpy (AHm, AH”), and volume

16

 

(AV... AV”). To demonstrate the mathematical relationships, k... will be used as
an example.

In order to calculate the three kinetic parameters, the Arrhenius equation
is first used. Defined by the form

ksm = Atmexp(—AEtm IRT) (1.13)

this equation relates the rate constant to the internal energy necessary to cross
the barrier on the reaction coordinate, where A... is the pre-exponential factor
and AE... is the activation energy. By algebraic rearrangement, the Arrhenius

equation becomes

AE
lnksm=lnAtm- R?“ (1.14)

 

Thus, AEt... can be calculated from the slope of a plot of In k... vs. 1/T at constant

pressure under the assumption that A... and AE;.. are temperature independent.

In order for activation enthalpy to be calculated, a relationship between the

energy and the enthalpy must be defined. Given the form
A5,", = AH.“ + RT- A(Pv,m) (1.15)

Equation (1.15) directly relates the activation energy to the activation enthalpy at
a given temperature and pressure. As illustrated, though, the change in
activation volume (AV...) as a molecule moves between the mobile phase and
the transition state must first be calculated.

Using a similar method to the thermodynamic equations,

A5,", + TAStm -PAvm)

Ink5m =(
RT

 

(1.16)

17

AV.. is calculated from the slope of a plot of In k... vs. P at constant temperature.
Once again an implicit assumption is that AE... and AS... are pressure
independent. As a result, it is possible to calculate the activation enthalpy (AH...)
by using the activation volume and activation energy by means of Equation 1.15.
By using the above method, the thermodynamic and kinetic parameters
that characterize the adsorption events in reversed-phase liquid chromatography

can be determined in the following chapter.

1.3 Previous Investigations of Thermodynamics and Kinetics
in Reversed-Phase High-Performance Liquid

Chromatography

A number of very unusual separations can be successfully performed with
PGC as stationary phase. These separations are difficult or impossible with more
conventional reversed-phase materials, such as octadecylsilica (ODS) or
polymeric materials. Porous graphitic carbon is thus a totally unique
chromatographic material which will, no doubt, be the subject of much further
research. At this stage, the retention mechanism on PGC is not well understood.
A detailed thermodynamic and kinetic study of the solutes on PGC will help to
understand the retention better. Before this, a brief summary of thermodynamic
and kinetic studies on conventional reversed-phase materials will be summarized
for comparison with PGC.
1.3.1 Thermodynamics

A number of homologous series have been used to study the effect of

repeating structural units on chromatographic retention behavior. Such series

18

have included fatty acids, alkylbenzenes, and polycyclic aromatic hydrocarbons
(PAHs). These series can offer a simple relationship between the retention factor
(k) and the number of units, such as the methylene (CH2) groups. Early studies
showed that an increase in methylene unit number results in a logarithmic
increase in the retention factor [8].

The effect of stationary phase chain length was studied by Berendsen and
de Galan for a number of solutes with varying methylene unit numbers [9]. The
data from their study indicated that there is a critical chain length, beyond which
retention does not change. According to the authors, the limiting chain length lies
between 6 and 14 carbons for the alkylsilica materials. The critical chain length is
independent of mobile phase composition, but increases with increasing length of
the solute alkyl chain.

Similarly, Tchapla et al. investigated seven series of alkyl-substituted
solutes including alkylbenzenes, alkylchlorides, and carboxylic acids on different
stationary phases. They concluded that the solute alkyl chains intercalate into the
alkylsilica stationary phase [10].

In addition to studies of retention, the molar enthalpy and molar entropy
have also been studied for homologous series. lssaq and Jaroniec calculated the
molar enthalpy using Equation 1.8 for alkylbenzenes using binary mobile phases
and alkylsilica stationary phases (C1, C4, C3, C18) [11]. They concluded that the
change in molar enthalpy and molar entropy depend linearly on the number of
methylene units in the alkyl chains of the homologous series, not the bonded

stationary phases. McGuffin and Chen studied the retention of a series of even-

19

numbered fatty acids (C10 through 022) not only as a function of temperature, but
also pressure [12]. From their experiments, they quantitated the changes in
molar enthalpy (AAH) and molar volume (AAV) of —3.5 kcal/mol and —14.1
mL/mol, respectively, for methylene units.

In addition to the studies of retention as a function of methylene unit
number, series containing phenyl units have also been investigated. Most notably,
PAHs have been used since they have repeating phenyl units in different
configurations. Whereas alkylated solutes can be characterized as a function of
the number of methylene units, PAHs have been studied as a function of ring
number, annelation structure (i.e. degree of ring fusion), and planarity [13-16].
Studies have shown that an increase in the ring number leads to a logarithmic
increase in the retention factor. An increase in temperature results in a decrease
in the retention of PAHs. By contrast, the effect of pressure is much smaller.

McGuffin and Howerton studied the thermodynamics of solute transfer for
a series of PAHs as a function of ring number, annelation structure, planarity,
temperature, pressure, and bonding density using octadecylsilica (ODS) [17,18].
The data from their study indicated that an increase in ring number results in
more negative changes in molar enthalpy (AH...) and molar volume (AV...) For a
series of isomers, solutes with condensed annelation structure exhibited less
negative changes in molar enthalpy and molar volume than the more linear
solutes. Nonplanar solutes demonstrated changes in molar enthalpy and molar
volume that are less negative than would be expected based upon ring number

alone. These data indicated that the condensed PAHs, as well as the nonplanar

20

PAHs, interacted with the first few carbons near the distal terminus of the ODS
phase. But the more linear solutes as well as those with more rings interacted
with the more ordered regions of the ODS closer to the proximal terminus.

1.3.2 Kinetics

Although the thermodynamics of retention have been extensively probed,
less work has been conducted into the kinetics of retention. Work on kinetics has
generally fallen into two classes based on the techniques employed: non-
chromatographic and chromatographic.

Nonchromatographic experiments have utilized pressure, temperature,
and dipole jump methods [19-24], as well as fluorescence correlation
spectroscopy [25,26] to investigate chromatographic materials. However, the
inherent difference between these systems and a packed chromatography bed
provide limited information about the kinetics of an actual separation. A greater
problem is that the temperature or pressure jump actually changes the kinetics of
the system, according to Equations 1.14 and 1.16.

To circumvent these difficulties, several chromatographic techniques have
been used, including frontal analysis and pulse methods [27-29]. Frontal analysis
involves injecting a large concentration of the solute onto the chromatography
column, and then analyzing the resultant curve. Also know as a breakthrough
curve, this curve provides information about the kinetics of sorption. However, it
does not represent the most common type of chromatography, which involves

injecting smaller concentrations of material onto the column.

21

Pulse methods better approximate a typical chromatographic separation
since they involve the injection of smaller volumes/concentrations. However, the
current method to elucidate the kinetics is also questionable. Thus the current
chromatographic methods are not ideal for characterizing the kinetics of retention
since these methods rely upon a number of assumptions and approximations.

Using the exponentially modified Gaussian model (EMG), McGuffin and
Howerton have studied the kinetics of PAHs in ODS [17,18]. The rate constants
decreased with increasing ring number and less condensed annelation structure.
The enthalpic and volume barriers were found to be very large. These barriers
increased as a function of ring number, but decreased with more condensed

annelation structure.

1.4 Conclusions

Although significant efforts have been invested in the applications of PGC
in both chromatography and extraction, the retention mechanism is far from
being understood. Limitations in both theory and experimental design have
hindered definitive quantitative analysis.

In this dissertation, the thermodynamic and kinetic contributions to
retention of two series of aromatic compounds on PGC will be explored using the
EMG model. These studies will help to understand the retention mechanism on

PGC.

22

1.5 References

[1] J. H. Knox, B. Kaur, G. R. Millward, J. Chromatogr., 352 (1986) 3-25.
[2] R. S. Deinhammer, E. Ting, M. D. Porter, Anal. Chem., 67 (1995) 237-246.

[3] J. H. Knox, P. Ross, in Advances in Chromatography, P. R. Brown, E.
Grushka, Marcel Dekker, New York, NY, vol. 37, pp 73-119 (1997).

[4] M. C. Hennion, V. Coquart, S. Guenu, C. Sella, J. Chromatogr. A, 712
(1995) 287-301 .

[5] G. Machtalere, V. Pichon, M. C. Hennion, J. High Resol. Chromatogr., 23
(2000) 437-444.

[6] M. C. Pietrogrande, A. Benvenuti, S. Previato, F. Dondi, Chromatographia,
52 (2000) 425-432.

[7] M. C. Hennion, ESPCI (Ecole Supérieure de Physique et de Chimie
Industrielles), private communication, 2003.

[8] E. Grushka, H. Colin, G. Guiochon, J. Chromatogr., 248 (1982) 325-339.
[9] G. E. Berendsen, L. de Galan, J. Chromatogr., 196 (1980) 21-37.

[10] A. Tchapla, S. Heron, H. Colin, G. Guiochon, Anal. Chem., 60 (1988) 1443-
1448.

[11] H. J. Issaq, M. Jaroniec, J. Liq. Chromatogr., 12 (1989) 2067-2082.

[12] V. L. McGuffin, S. H. Chen, J. Chromatogr. A, 762 (1997) 35-46.

[13] L. A. Cole, J. G. Dorsey, Anal. Chem., 64 (1992) 1317-1323.

[14] K. B. Sentell, J. G. Dorsey, J. Chromatogr., 461 (1989) 193-207.

[15] M. Olsson, L. C. Sander, S. A. Wise, J. Chromatogr., 477 (1989) 277-290.
[16] L. C. Sander, M. Pursch, S. A. Wise, Anal. Chem., 71 (1999) 4821-4830.
[17] S. B. Howerton, V. L. McGuffin, J. Chromatogr. A, 1030 (2004) 3-12.

[18] S. B. Howerton, V. L. McGuffin, Anal. Chem., 75 (2003) 3539-3548.

[19] D. B. Marshall, J. W. Burns, D. E. Connolly, J. Chromatogr., 360 (1986) 13-
24.

23

[20] S. W. Waite, J. M. Harris, E. H. Ellison, D. B. Marshall, Anal. Chem, 63
(1991) 2365-2370.

[21] S. W. Waite, D. B. Marshall, J. M. Harris, Anal. Chem, 66 (1994) 2052-2061.
[22] F. Y. Ren, J. M. Harris, Anal. Chem, 68 (1996) 1651-1657.

[23] J. M. Harris, D. B. Marshall, J. Microcolumn Sep., 9 (1997) 185-191.

[24] S. R. Shield, J. M. Harris, Anal. Chem, 74 (2002) 2248-2256.

[25] R. L. Hansen, J. M. Harris, Anal. Chem, 70 (1998) 2565-2575.

[26] R. L. Hansen, J. M. Harris, Anal. Chem, 70 (1998) 4247-4256.

 

[27] K. Miyabe, G. Guiochon, Anal. Chem, 72 (2000) 5162-5171.
[28] K. Miyabe, S. Sotoura, G. Guiochon, J. Chromatogr. A., 919 (2001) 231-244.
[29] K. Miyabe, G. Guiochon, Anal. Chem, 74 (2002) 5754-5765.

24

Chapter 2: Retention of Aromatic Hydrocarbons on
Porous Graphitic Carbon

2.1 Introduction

As depicted in Figures 2.1 and 2.2, eighteen aromatic hydrocarbons have
been chosen to investigate the effect of length of alkyl chain and number of
methyl substituents on the thermodynamics and kinetics of retention on porous
graphitic carbon (PGC). Alkyl-substituted benzenes were chosen as the solutes
for two reasons. First, they make a good homologous series in establishing
retention trends. Second, for environmental and toxicity concerns, BTEX levels in
oil are a very important parameter. BTEX is the collective name of benzene,
toluene, ethylbenzene, and the xylene isomers (o-, m-, and p-xylenes). BTEX
compounds are the most common aromatic compounds in petroleum, comprising
up to a few percent of the total weight for some crude oils. BTEX constitutes the
most soluble, most mobile fraction of crude oil and many petroleum products.
BTEX compounds have many chemical applications and are widely used in the
manufacture of paints, synthetic rubber, agricultural chemicals, and chemical
intermediates. The concentration of BTEX in petroleum can directly affect the
physical and chemical properties of petroleum such as density, viscosity, flash
points, dispersibility, emulsion stability, solubility, and weathering processes. On
the other hand, BTEX compounds frequently enter soil, sediments, and
groundwater because of accidental oil spill, leakage of gasoline and other
petroleum fuels from underground storage tanks and pipelines, and improper

waste disposal practices.

25

I

F‘fi

 

Figure 2.1: Structure of alkylbenzenes used to study retention on

porous graphitic carbon.

26

Figure 2.2: Structure of methylbenzenes used to study retention on

porous graphitic carbon.

27

In these cases, BTEX compounds can also be used as markers in
identifying the presence and determining the composition of these weathered
fuels originating from leaking underground fuel tanks or pipelines. BTEX are
hazardous carcinogenic and neurotoxic compounds and are classified as priority
pollutants regulated by the US. Environment Protection Agency (EPA) [1],
especially benzene, which has a very low tolerance standard in drinking water of

5 pg/L.
2.2 Experimental Methods

2.2.1 Salutes

The alkylbenzenes (Figure 2.1) were chosen as a homologous series to
study the effects of methylene addition on retention. Benzene, ethylbenzene,
propylbenzene, butylbenzene, pentylbenzene and hexylbenzene were obtained
from Aldrich.

The methylbenzenes (Figure 2.2) were chosen as a homologous series to
study the effects of methyl substituent addition on retention. Toluene, o-xylene,
m-xylene, p-xylene, 1,2,3-trimethylbenzene, 1,2,4-trimethylbenzene 1,3,5-
trimethylbenzene, 1,2,3,5-tetramethylbenzene, 1,2,4,5-tetramethylbenzene,
pentamethylbenzene, and hexamethylbenzene were obtained from Aldrich.
Mixed standard solutions were prepared around 10‘3 M in high-purity methanol
(Burdick and Jackson, Baxter Healthcare) such that there was no overlap of
solute zones at any temperature and pressure. A nonretained marker, acetonitrile,

was added to each solution at a concentration of 1 M.

28

2.2.2 Chromatographic System

The chromatographic system is shown schematically in Figure 2.3. It
includes a single-piston reciprocating pump (Model 114 M, Beckman Instruments)
operating in constant pressure mode (:t 15 psi) over the range of 6.90 x 106 Pa
(1000 psi) to 3.45 x 107 Pa (5000 psi). The pump allows for the mobile phase to
be supplied continuously without the need for depressurization during the refill
cycle. At all pressures, the flowrate was maintained at approximately 1 mUmin at
room temperature.

Samples are introduced via a manual injection valve (20 pL, Model 7125,
Rheodyne Instruments). Once the sample is introduced, it is carried by the
methanol mobile phase to the column. The Hypercarb column is supplied by
Shandon HPLC (100 x 4.6 mm id, mean particle diameter 7 pm).

At the end of the column, a 100 pm i.d. fused-silica capillary (Polymicro
Technologies) is attached to serve as a restrictor. The length of the restrictor is
reduced as the inlet pressure is decreased in order to maintain a constant
pressure drop along the column (3.31x 105 Pa (48 psi)/cm). The length of the
restrictor and corresponding pressures and flow rate are listed in Table 2.1.

The injector, column, and restrictor are all housed within an oven (Model
SM900, Anspec Instruments) that maintains a constant temperature (10.1 K)
through the use of resistive heating coils. The oven was operated through the

temperature range of 296 to 326 K.

29

 

 

 

Pump

 

®

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

UV-Visible
@— Column Absorbance
Detector
Oven
Computer

 

 

Figure 2.3: Schematic diagram for the chromatographic system.

I: injection valve, R: restrictor.

30

 

 

 

 

Table 2.1: Corresponding pressure, flow rate, and length of restrictor in the

chromatographic system.

 

 

 

 

 

Pressure (psi) Length of restrictor (m) Flow rate (mL/min)"
1000 1.450 0.965
2000 3.777 0.955
3000 5.982 0.956
4000 8.194 0.949
5000 10.345 0.993

 

 

 

 

 

A at room temperature

31

 

The spectroscopic technique used for detection is ultraviolet-visible
absorbance. As shown in Figure 2.3, a commercially available unit (Model
UVlDEC-100—V, JASCO) is directly coupled to the column such that the effluent
is directed to a capillary flow cell. The flow cell is a transparent fused-silica

capillary with a 180-pm i.d., able to hold high pressure in the chromatographic

system. The wavelength for detection (210 nm) is chosen based upon the
absorption maximum of the solutes. The output from the detector is directed to a
data acquisition board (National Instruments) and computer for further data
analysis. The data collecting program was written in Labview (National
Instruments, v3.1).
2.2.3 Data Treatment and Analysis

Since the desired data are zone profiles contained within a
multicomponent chromatogram, the first challenge for the data analysis is the
reproducible extraction of the individual profiles. The integration limits will affect
the accuracy of the analysis results [2]. Once removed, the zone profiles are
iteratively fit using a commercially available program (Peakfit v3.18, SYSTAT
Software). Since there are many functions available for the analysis of zone
profiles, the second obstacle to the analysis is choice of an appropriate function.

The accurate description of asymmetrical peaks usually requires a large
number of statistical moments and a large number of data points [3]. In addition,
noise can affect the values for the moments [4]. As a result of these limitations,

alternative equations such as the exponentially modified Gaussian (EMG) [5], the

32

nonlinear chromatography (NLC) [6], and the Haarhoff-Van der Linde function [7]
have been developed for evaluating non-Gaussian zone profiles. The EMG and
NLC models provide variables that can be directly related to experimental
parameters. As a result, these two functions were initially chosen to study
chromatographic zones. The results of nonlinear regression of a typical
experimental zone profile with the Gaussian function and the EMG equation are
shown in Figure 2.4. The Gaussian equation (Figure 2.4A) produces nonrandom
residuals with a relatively small value for the square of the correlation coefficient
(R2 = 0.987). The EMG equation (Figure 248) provides significantly better fit with
only small residuals around the maximum of the zone profile (R2 = 0.998).
Moreover, the EMG equation yields better statistical results than the NLC and
other models mentioned above. On the basis on these results, the EMG model
was used throughout the studies in this dissertation. The EMG is a convolution of

a Gaussian and an exponential function. The form of the equation is

_A i tG—t t—tG_ o
C(t)—21exp|:212+-——t :l[erf[ J‘z‘. JEJHI (2.1)

where A is the area, ts is the mean of the Gaussian component, a is the standard

 

deviation of the Gaussian component, and 17 is the exponential component.

Over the past thirty years, several authors have sought to characterize the
use of the EMG function for chromatographic analysis. While Grushka [8,9] and
Yau [10] presented some early work, Foley and Dorsey have published two

seminal papers reviewing the EMG function in the intervening years [11,12].

33

Figure 2.4

 

 

 

 

 

140 145 150 155 160 165 170 175 180
Time (s)

Figure 2.4: Regression results with the Gaussian equation (A) and the EMG

equation (8). Experimental data: (—), regression: ( - - - ).

These reviews have demonstrated the use of the EMG function for a variety of
chromatographic applications. More recent studies have compared the EMG to
other equations for the analysis of zone profiles [13,14]. The studies have
concluded that high-order polynomials that exceed the four parameters used in
the EMG function can describe asymmetrical peaks very well. However, the
complex nature of such functions makes them impractical for common use. In
addition, the parameters for these high-order polynomials may not have any
physical significance as do those calculated using the EMG function.

Within this thesis, the EMG is employed predominantly to calculate the
thermodynamics and kinetics of retention. The thermodynamic and kinetic
parameters can be calculated by substituting the measured values of t6 and 1
into Equations 1.3, 1.11, and 1.12 of Chapter 1, where

t. = ta + T (2.2)
2.4 Results and Discussion

2.4.1 Thermodynamic Behavior
2.4.1.1 Retention Factor
The retention factor (k) is the simplest of the measurable parameters that
allow for the comparison of the relative strength of interaction. A larger retention
factor indicates that the solute has greater affinity for the stationary phase. This
comparison is useful to evaluate the effect of different solute structural features.
Using Equation 1.3, the retention factor for each solute on PGC was
calculated. The results of these calculations are summarized in Tables 2.2 and

2.3. For the homologous series of alkylbenzenes, the retention factor increases

35

Table 2.2: Retention factors (k) for alkylbenzenes on porous graphitic carbon.

 

 

 

Solute k“ k3 Aklk k° k° Aklk
(%) (%)

Benzene 0.16 0.16 49 0.16 0.16 1.90
Toluene 0.36 0.31 -16.2 0.34 0.33 -119

 

Ethylbenzene 0.37 0.30 -17.2 0.34 0.33 -0.89

 

Propylbenzene 0.53 0.43 -18.4 0.49 0.49 -0.41

 

Butylbenzene 0.80 0.62 -23.1 0.71 0.71 -0.14

 

Pentylbenzene 1.43 1.04 -27.8 1.23 1.24 1.30

 

 

 

 

 

 

 

 

Hexylbenzene 2.34 1.56 -33.3 1.90 1.93 1.53

 

A Retention factor calculated at 3.28 x 107 Pa (4760 psi) and 298 K
B Retention factor calculated at 3.28 x 107 Pa (4760 psi) and 326 K
C Retention factor calculated at 5.24 x 106 Pa (760 psi) and 309 K

D Retention factor calculated at 3.28 x 107 Pa (4760 psi) and 309 K

36

 

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with alkyl chain length at all temperatures and pressures. Solutes with longer
alkyl chains are more retained due to increased dispersion forces from
methylene groups with stationary phase. The only exception is toluene and
ethylbenzene, which produce very similar retention factors. This might be due to
the greater effect on retention that a methyl group produces, which is discussed
below.

The effect of temperature on the retention factor is very pronounced on
porous graphitic carbon. For all alkylbenzenes, an increase in temperature
results in a decrease in the retention factor. Solutes with longer alkyl chain
demonstrate a greater change in retention factor.

In contrast, the effect of pressure is much smaller on PGC. The retention
factors for all alkylbenzenes nearly do not change with pressure considering the
error in measurement. The reason is that the robust stationary phase does not
change with pressure.

For the homologous series of methylbenzenes, the retention factor
increases with the number of methyl substituents at all temperatures and
pressures. Solutes with more methyl substituents are more retained due to the
increased interactions with the stationary phase that result from the increased
dispersion forces and the increased electron density of the phenyl ring from
electron-donating methyl groups.

The effect of temperature on the retention factor again is very pronounced.

For all methylbenzenes, an increase in temperature results in a decrease in the

38

retention factor. Solutes with more methyl substituents demonstrate a greater
change of retention factor.

In contrast, the effect of pressure is again much smaller on PGC. The
retention factors for all methylbenzenes change very little with pressure, due to
the robust stationary phase.

For the methylbenzenes, each group of positional isomers produces
similar retention factors. For example, the o-, m-, and p-xylenes have similar
retention factors at the same temperature and pressure. But m-xylene is least
retained because it has the lowest electron density of the phenyl ring among the
isomers. Again, 1,2,3-trimethylbenzene, 1,2,4-trimethylbenzene, and 1,3,5-
trimethylbenzene have similar retention factors. But 1,3,5-trimethylbenzene is
least retained for the same reasons. 1,2,3,5-Tetramethylbenzene and 1,2,4,5-
tetramethylbenzene also have similar retention factors.

Comparing the retention factors between the alkylbenzene and
methylbenzene series, it can be concluded that the addition of a methyl group
produces a greater effect on retention than a methylene group. This is because
the methyl group can change the electron density of the phenyl ring to a greater
extent than the methylene group.
2.4.1.2 Molar Enthalpy

Using Equation 1.8 and the methods described in Section 1.2.1, the
change in molar enthalpy was calculated. A representative graph used in the
calculation of the change in molar enthalpy is shown in Figure 2.5. For all solutes

at all pressures, the data are linear (R2 = 0.9730999) and the slope of the line is

39

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positive. A linear graph indicates that the change in molar enthalpy is constant
with temperature. A positive slope is demonstrative of a negative change in molar
enthalpy, which indicates that the transition from the mobile to stationary phase is
an energetically favorable exothermic process. Molar enthalpies for
alkylbenzenes and methylbenzenes at different pressures are summarized in
Tables 2.4 and 2.5.

For the alkylbenzenes (Table 2.4), the change in molar enthalpy with
pressure is very small. At constant pressure, the homologous series illustrates a
trend of decreasing molar enthalpy, where retention becomes more exothermic
as the number of methylene groups increases. The differential change in molar
enthalpy (AAH...) versus carbon number for alkylbenzenes is shown in Figure 2.6.
From benzene to toluene, AH... changes about -3 kJ/mol. But from toluene to
propylbenzene, the change in AH... is very small (—0.5 kJ/mol). This small
change indicates the addition of one methylene group at this stage does not
significantly affect the retention. Thereafter, the change in AH... becomes
relatively constant at approximately -2 kJ/mol.

The methylbenzenes (Table 2.5) also illustrate decreasing molar enthalpy
as the number of methyl groups increases. Solutes with the same number of
methyl substituents have similar molar enthalpies. For example, o-, m-, and p-
xylenes have comparable molar enthalpies of -8 kJ/mol. The same is true for
1,2,3-trimethylbenzene, 1,2,4-trimethylbenzene, and 1,3,5-trimethylbenzene with
molar enthalpies of —11 kJ/mol. The differential change in molar enthalpy versus

carbon number for methylbenzenes, shown in Figure 2.7, is relatively constant at

41

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around —2.5 kJ/mol. This value is slightly larger than that for the alkylbenzenes
when the carbon number is greater than three. The constant change suggests
that the addition of each methyl group produces a similar effect on retention. The
methylbenzenes also demonstrate very small differences in molar enthalpies at
different pressures.

For the high-density octadecylsilica stationary phase, the change in molar

enthalpy (AH-m.) ranges from —44 kJ/mol to —128 kJ/mol for fatty acids ranging
from C10 to C22, respectively, at 303 K and 1.01 x 107 Pa (1470 psi) [15]. The

differential change in molar enthalpy per ethylene group remains constant for
solutes C10 to C13 with an average value of -15 kJ/mol [15]. Thus, when PGC is
compared with octadecylsilica, the addition of each methylene group has less
effect on retention.
2.4.1.3 Molar Volume

Similar to the molar enthalpy, the molar volume also provides insight into
the effects that arise from structure. Using Equation 1.10 and the methods
described in Section 1.2.1, the change in molar volume was calculated. A
representative graph used in the calculation of the change in molar volume is
depicted in Figure 2.8. For all solutes at all temperatures, the data are relatively
linear. However, because of the small change in retention factor with pressure,
the square of the correlation coefficient is small (R2 = 0.549-0.889). A linear
graph indicates that the molar volume is constant with pressure. The slope of the
line is slightly positive or negative. A negative slope results in a positive change

in molar volume, which indicates that the molecule occupies more space in the

46

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stationary phase than in the mobile phase. Conversely, a positive slope indicates
that the transition from the mobile to stationary phase results in a smaller volume.
Representative data are contained in Tables 2.6 and 2.7

Overall, the change in molar volume is very small on PGC, compared with
that of polycyclic aromatic hydrocarbons (PAHs) on octadecylsilica, which is
around -2 cm3/mol [16]. The change in molar volume for methylene homologues
on high—density octadecylsilica ranges from -40 to -110 cm3lmol [15], which is
much greater than that on PGC. Considering the uncertainty in measurement,
the change in molar volume on PGC is very close to zero. This is consistent with
the retention mechanism on PGC, which is based on adsorption and desorption
of the solute molecules from the solid surface, rather than partition of the solute

molecules into the stationary phase as on octadecylsilica.

48

Table 2.6: Molar volume for alkylbenzenes on porous graphitic carbon.

 

 

AVsm AVsm
Solute (cm3lmol)A (cm3lmol)8
Benzene -0.24 :1: 0.22 0.23 :l: 0.20

 

Toluene 0.25 1 0.19 0.16 1 0.09
Ethylbenzene 0.18 1 0.17 -0.25 1 0.21
Propylbenzene -0.35 1 0.21 0.25 1 0.19
Butylbenzene 0.23 1 0.20 0.29 1 0.15
Pentylbenzene -0.29 1 0.15 0.36 1 0.26
Hexylbenzene 0.33 1 0.26 -0.24 1 0.20

 

 

 

 

 

 

 

 

 

 

A Molar volume (AV...) calculated at T = 296 K and P = 5.24 x 10° Pa (760 psi) to
3.28 x 107 Pa (4760 psi)

'3 Molar volume (Av...) calculated at T = 327 K and P = 5.24 x 106 Pa (760 psi) to
3.23 x 107 Pa (4760 psi)

49

Table 2.7: Molar volume for methylbenzenes on porous graphitic carbon.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AVsm Avsm
Solute (cm3/mol)A (cm3/mol)B
Benzene -0.24 1 0.22 0.23 1 0.20
Toluene 0.25 1 0.19 0.16 1 0.09
o-Xylene 0.28 1 0.19 -0.22 1 0.21
m-Xylene -0.35 1 0.21 0.23 1 0.19
p-Xylene 0.24 1 0.20 0.21 1 0.15
1,2,3-Trimethylbenzene 0.29 1 0.15 -0.36 1 0.26
1,2,4-Trimethylbenzene 0.33 1 0.26 0.24 1 0.20
1,3,5—Trimethylbenzene -0.34 1 0.23 0.29 1 0.20
1,2,3,5-Tetramethylbenzene 0.36 1 0.26 -0.46 1 0.39
1,2,4,5-Tetramethylbenzene 0.34 1 0.17 0.37 1 0.21
Pentamethylbenzene -0.55 1 0.21 0.61 1 0.36
Hexamethylbenzene 0.63 1 0.28 0.69 1 0.34

 

A Molar volume (AV-m.) calculated at T = 296 K and P = 5.24 x 106 Pa (760 psi) to

3.23 x 107 Pa (4760 psi)

'3 Molar volume (Av...) calculated at T = 327 K and P = 5.24 x 106 Pa (760 psi) to

3.28 x 107 Pa (4760 psi)

50

 

2.4.2 Kinetic Behavior
2.4.2.1 Rate Constants

Although the thermodynamic data demonstrate the steady-state aspects,
they do not fully explain the mechanism of retention. Using Equations 1.11, 1.12,
1.14, and 1.16 and the method described in Section 1.2.2, the pseudo-first-order
rate constants, activation enthalpies, and activation volumes were calculated.
These values help to quantify the kinetic aspects of solute transfer between the
mobile and stationary phases.

Representative values of the rate constants are summarized in Tables 2.8
and 2.9. For the alkylbenzenes (Table 2.8), the structures with longer alkyl chains
result in larger rate constants for the mobile to stationary phase (km), and
stationary to mobile phase (km) transitions. From benzene to butylbenzene, the

rate-limiting step is the transfer from mobile to stationary phase (i.e., kms > ksm)

because the retention factor, which is the ratio of km and kms, is less than 1.

51

Table 2.8: Kinetic rate constants for alkylbenzenes on porous graphitic carbon.

 

 

 

 

 

 

 

 

Solute kms (s“)A ksm (s")B

Benzene 5.9 1.0

Toluene 13.1 4.9
Ethylbenzene 1 1.8 4.5
Propylbenzene 1 5.0 8.4
Butylbenzene 16.7 14.0
Pentylbenzene 16.3 24.5
Hexylbenzene 1 5.4 37.4

 

 

 

 

 

A Rate constants for the stationary to mobile phase transition at 5.24 x 106 Pa
(760 psi) and 295 K.

3 Rate constants for the mobile to stationary phase transition at 5.24 x 106 Pa
(760 psi) and 295 K.

52

Table 2.9: Kinetic rate constants for methylbenzenes on porous graphitic carbon.

 

 

 

 

 

 

 

 

 

 

 

 

 

Solute kms (5'1)A ksm (8-1)8

Benzene 5-9 1'0

Toluene 13.1 4.9

o-Xylene 13.9 14.2
m-Xylene 16.3 14,0
prlene 15.0 14.9
1,2,3-Trimethylbenzene 14.5 44.9

1 ,2,4-Tnmethylbenzene 145 33.1

1 ,3,5-Trlmethylbenzene 20.4 38.4
1,2,3,5-Tetramethylbenzene 3 5 25 5
1,2,4,5-Tetramethylbenzene 16 0 120 6
Pentamethylbenzene 3 5 99 o
Hexamethylbenzene 2 6 292 o

 

 

 

 

 

A Rate constants for the stationary to mobile phase transition at 5.24 x 10'5 Pa
(760 psi) and 295 K

'3 Rate constants for the mobile to stationary phase transition at 5.24 x 106 Pa
(760 psi) and 295 K

53

However, for pentylbenzene and hexylbenzene, the rate-limiting step is the
transfer from stationary to mobile phase (i.e., kms < k3...) because the retention
factor is greater than 1.

For the methylbenzenes (I' able 2.9), generally the molecules with more
methyl substituents produce larger rate constants for the mobile to stationary
phase (km), and stationary to mobile phase (km) transitions. For benzene,
toluene, and the xylenes, the rate-limiting step is the transfer from mobile to
stationary phase (i.e., kms > ksm) because the retention factor is less than 1. But
for the trimethylbenzenes, tetramethylbenzenes, pentamethylbenzene, and
hexamethylbenzene, the rate-limiting step is the transfer from stationary to
mobile phase (i.e., kms < ksm) because the retention factor is greater than 1.

In addition, an increase in temperature yields an increase in the rate
constants for all molecules. For example, the rate constant (km) for
hexylbenzene ranges from 15.4 to 32.8 s'1 for temperatures from 295 to 327 K,
respectively, at 5.24 x 106 Pa (760 psi). In contrast, an increase in pressure
yields only slight changes. The rate constant (km) for hexylbenzene ranges from
23.6 to 20.4 s'1 for pressures from 5.24 x 106 to 3.28 x 107 Pa (760 to 4760 psi),
respectively, at 309 K.

Overall, the data indicate that the rate constants (km and ksm) increase as
the retention factor increases, which is the reverse order of the rate constants on

octadecylsilica for PAHs [16].

54

2.4.2.2 Activation Enthalpy

Using Equation 1.14 and 1.15 and the methods described in Section 1.2.2,
the activation enthalpies were calculated. Figure 2.9 illustrates a typical graph of
the natural logarithm of the rate constant versus inverse temperature used in the
calculation of the activation enthalpy. For all solutes at all pressures, the data are
linear (R2 = 0443-0869) and the slope of the line is negative. A linear graph
indicates that the change in activation enthalpy is constant with temperature. A
negative slope is demonstrative of a positive change in activation enthalpy, which
is the energy barrier for the transfer from mobile or stationary phase to the
transition state. Tables 2.10 and 2.11 contain the activation enthalpies for
alkylbenzenes and methylbenzenes.

As demonstrated for the alkylbenzenes (Table 2.10), an increase in the
number of methylene groups results in an increase in the activation enthalpy.
The data indicate that the energy barrier from the stationary phase to the
transition state AH;s increases with the addition of every methylene group. The
differential change in AH” versus carbon number for the alkylbenzenes is shown
in Figure 2.10. From benzene to toluene, AAHts is about 3 lemol. But from
toluene to propylbenzene, AAHts increases only slightly at 0.5 kJ/mol. When the
carbon number is greater than three, AAH¢3 is relatively constant at around 2 kJ
lmol, indicating that the effect of each methylene group on activation enthalpy is

relatively constant.

55

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For the methylbenzenes (Table 2.11), the activation enthalpy from the
stationary phase to the transition state AH” increases with increasing number of
methyl substituents. This result suggests that with the addition of each methyl
group, the energy barrier from the stationary phase to the transition state
increases. Figure 2.11 shows the differential change in AHp versus carbon
number for the methylbenzenes. From benzene to tetramethylbenzenes, the
differential change in activation enthalpy AAHts is relatively constant at around 3
kJ lmol. But for pentamethylbenzene and hexamethylbenzene, AAHt. is much
greater.

For both alkylbenzenes and methylbenzenes, the change in activation
enthalpy from the mobile phase to transition state AH;m is nearly constant,
considering the uncertainty in the kinetic data. But AH;m for pentamethylbenzene
and hexamethylbenzene is greater than that of other solutes in the same
homologous series. Comparison between AHB and AH;m indicates that the
retention on PGC is controlled by desorption, which is decided by the molecular
structures of the solutes. Thus, the structure of the molecules affects the energy
needed to transfer between mobile and stationary phases. Comparing the
activation enthalpy with the absolute value of molar enthalpy, the trend is AH” >
AHsm > AHtm. As expected, AH,"m is nearly equal to the difference between AH”
and AHtm.

Comparing with the activation enthalpy for PAHs on octadecylsilica [16],
the activation enthalpy for PGC is much smaller. This indicates that the energy

barrier for retention on PGC is much smaller than that on octadecylsilica.

60

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61

2.4.2.3 Activation Volume

Using Equation 1.16 and the methods described in Section 1.2.2, the
activation volumes were calculated. A representative graph of the natural
logarithm of the rate constant versus pressure is depicted in Figure 2.12 and
resulting values for the activation volume are presented in Tables 2.12 and 2.13.
The slope of the line is either slightly positive or slightly negative. The activation
volumes for the stationary phase to transition state (Av...) and the mobile phase
to transition state (Av...) appear to be larger than the change in molar volume
(Avg...) because of greater uncertainty of the kinetic data. However, these values
are also nearly zero. They are much smaller than the activation volumes reported
for methylene and benzene homologues on octadecylsilica [15]. This suggests
that the volume barrier on PGC is much smaller than that on octadecylsilica

stationary phase.

62

 

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Table 2.12: Activation volume for alkylbenzenes on porous graphitic carbon.

 

 

 

 

 

 

 

 

 

Av... Av...n Av... AV¢m
Solute (cm3/mol)A (cm3lmol) (cm3/mol)l3 (cm3lmol)
Benzene -0.94 :l: 0.92 0.93 1: 0.70 -1.24 :h 0.92 1.23 :I: 1.20
Toluene 1.15 :l: 0.69 0.76 :l: 0.89 1.25 :l: 1.19 -1.16 :l: 0.99
Ethylbenzene 1.18 :l: 0.97 -1.05 :l: 0.91 -0.98 :l: 0.87 -0.95 :l: 0.91
Propylbenzene 1.35 :t: 1.21 0.95 :l: 0.69 -1.15 1 1.21 1.25 :l: 0.89
Butylbenzene 1.33 :1: 0.90 -1.29 :l: 0.85 0.99 :1: 0.80 0.73 :l: 1.15
Pentylbenzene -1.29 :t 0.85 0.96 :1: 0.76 -1.36 :l: 1.25 0.99 :l: 0.76
Hexylbenzene 1.33 :l: 0.76 -0.84 :l: 0.70 1.33 :l: 0.96 -1.24 :l: 0.90

 

 

 

 

 

A Activation volumes for the stationary phase to transition state (Ava), and
mobile phase to transition state (Av...) were calculated at T = 296 K and P = 5.24
x 106 Pa (760 psi) to 3.28 x 107 Pa (4760 psi)
3 Activation volumes for the stationary phase to transition state (AV;), and
mobile phase to transition state (AVm) were calculated at T = 327 K and P = 5.24
x 10‘5 Pa (760 psi) to 3.28 x 107 Pa (4760 psi)

 

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65

2.5 Conclusions

To illustrate the full implications of the data presented above, it is helpful
to describe the entire retention event for a single solute. For example, as
hexylbenzene transfers from the mobile to stationary phase, it passes through a
high-energy transition state. The creation of this transition state requires an
enthalpy change of 2 lemol and a volume change of -0.84 cm3lmol. This transfer
occurs with a rate constant of 37 s". As hexylbenzene transfers from the
stationary to mobile phase, it passes through another high-energy transition state.
This transition state requires an enthalpy change of 14 kJ/mol and a volume
change of 1.33 cm3/mol. This transfer occurs with a rate constant of 15 s", which
is only half of the rate constant for mobile to stationary phase transfer. Hence,
the rate-limiting step is the transfer from stationary to mobile phase.

This description illustrates that both the thermodynamics and kinetics are
necessary to fully describe the retention event. By using the necessary
theoretical foundation and instrumentation, this dissertation demonstrates a
comprehensive study of retention for two series of known pollutants on porous

graphitic carbon.

66

2.6 References

[1] List of lists, U.S. Environmental Protection Agency, July 1987.
[2] S. B. Howerton, C. Lee, V. L. McGuffin, Anal. Chim. Acta, 478 (2003) 99-110.
[3] S. N. Chesler, S. P. Cram, Anal. Chem., 43 (1971) 1922-1929.

[4] J. V. H. Schudel, G. Guiochon, J. Chromatogr., 457 (1988) 1-12.

[5] W. E. Barber, P. W. Carr, Anal. Chem., 53 (1981) 1939-1942.

[6] J. L. Wade, A. F. Bergold, P. W. Carr, Anal. Chem., 59 (1987) 1286-1295.
[7] P. C. Haarhoff, H. J. Van der Linde, Anal. Chem., 38 (1966) 573-582.

[8] E. Grushka, Anal. Chem., 44 (1972) 1733-1738.

[9] E. Grushka, J. Phys. Chem., 76 (1972) 2586-2593.

[10] W. W. Yau, Anal. Chem., 49 (1977) 395-398.

[11] J. P. Foley, J. G. Dorsey, J. Chromatogr. Sci., 22 (1984) 40-46.

[12] M. S. Jeansonne, J. P. Foley, J. Chromatogr. Sci., 29 (1991) 258-266.
[13] M. L. Phillips, R. L. White, J. Chromatogr. Sci., (1997) 75-81.

[14] J. R. Torres-Lapasio, J. J. Baeza-Baeza, M. C. Garcia-Alvarez-Coque, Anal.
Chem., 69 (1997) 3822-3831.

[15] V. L. McGuffin, S.-H. Chen, J. Chromatogr. A, 762 (1997) 35-46.
[16] S. B. Howerton, V. L. McGuffln, Anal. Chem., 75 (2003) 3207-3216.

67

Chapter 3: Conclusions and Future Directions

Porous graphitic carbon (PGC) is a nonpolar reversed-phase adsorbent.
Wrth aqueous or aqueous-organic mobile phases, porous graphitic carbon has
stronger retention for the same solutes than the alkyl-bonded silica gels.
Increasing the hydrophobicity of a solute by the addition of a methylene group or
other nonpolar groups increases retention. In addition, by virtue of its great
adsorptive strength, PGC can be used with nonpolar mobile phases for the
retention of polar analytes.

Porous graphitic carbon has proven to have a number of unsuspected
properties, which have substantially enlarged its area of applications and opened
up entirely new possibilities. However, the investigations of molecular
contributions to retention on PGC have been limited primarily to selectivity factor

[1,2]. Virtually no experimentation has sought to characterize the change in molar

enthalpy and molar volume, which provide insight into how molecules interact

with the stationary phase. In addition to thermodynamic information, the kinetics
of retention have also been largely overlooked. The kinetics of retention are
important because they provide insight into the rate at which transitions occur, as
well as the energy barriers that exist for a molecule to move from one phase to

another.

3.1 Results

In the research presented in this dissertation, solute transfer of two series
of aromatic hydrocarbons (alkylbenzenes and methylbenzenes) has been studied

as a function of molecular structure. By quantitating the thermodynamics and

68

kinetics together, a better description of retention on PGC is made, providing a
more accurate comparison of different solutes and stationary phases.

In the thermodynamic studies, the retention factor of alkylbenzenes
increases with increasing number of methylene groups, and the retention factor
of methylbenzenes increases with increasing number of methyl substituents. For
the same solute, the retention factor (k) decreases with an increase in
temperature, but does not change significantly with pressure. The data from this
study indicate that increases in the number of methylene and methyl groups
result in more negative changes in molar enthalpy (AHsm). The more negative
change in AH8m suggests that the transition from the mobile to stationary phase is
a more energetically favorable exothermic process with a methylene or methyl
group added. The data also show that the change in molar volume (AV...) is
close to zero on PGC, which indicates that during the retention, the solute
molecules adsorb on the surface of PGC instead of penetrating further into the
stationary phase, as in octadecylsilica.

In the kinetic studies, the rate constants of alkylbenzenes and
methylbenzenes increase with increasing number of methylene and methyl
groups. The enthalpic barriers between the stationary phase and transition state
(AH...) were found to increase with increasing number of methylene and methyl
groups as well. But the enthalpic barriers between the mobile phase and
transition state (AHm) were much smaller than AH;s and, at the same time, very
similar for all the solutes. The values of enthalpic barriers suggest that the

retention on PGC is controlled by the adsorption and desorption of the solutes on

69

the stationary phase. The volume barriers AV... and AV,m again are very close to
zero due to the adsorption mechanism on porous graphitic carbon.

3.2 Future Directions

In order for a complete and quantitative description of retention to be
presented, a series of experiments beyond those presented herein can be done.
The first series of experiments that could lead to a more comprehensive
explanation of retention would be a systematic study of the effect of mobile
phase composition, such as methanol/water or acetonitrile/water, on the derived
values.

Similar to varying the mobile phase, a series of stationary phases, such as
phenylsilica, octadecylsilica, and polystyrene divinylbenzene, could be used to
compare the effect of solute structure on retention.

Porous graphitic carbon exhibits unexpected and largely unexplained
retentive properties for molecules containing polar groups. This property makes
PGC particularly useful for the separation of highly polar compounds that would
be difficult to retain on octadecylsilica phases. To help understand the retention
of polar solutes on PGC better, a number of environmentally important polar
solutes, such as atrazine and its polar metabolites can be used [3].

Porous graphitic carbon also shows unusual discrimination of closely
related stereoisomers [4]. Chiral separations can be achieved when the molecule
is very flexible and can adapt to the flat surface of PGC. The study of the

retention of some stereoisomers on PGC can help to better understand the

70

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retention mechanism. These position isomers can be the o-, m-, p- substituted
benzene derivatives.

In conclusion, the adsorption retention mechanism on PGC is totally
different from that of octadecylsilica, the most widely used stationary phase in
liquid chromatography. A better understanding of the retention mechanism on

PGC will advance its applications in separation.

71

 

3.3 References

[1] J. Kriz, E. Adamcova, J. H. Knox, J. Hora, J. Chromatogr. A, 663 (1994) 151-
161.

[2] Q. H. Wan, P. N. Shaw, M. C. Davies, D. A. Barrett, J. Chromatogr. A, 697
(1995) 219-227.

[3] M. C. Hennion, V. Coquart, S. Guenu, C. Sella, J. Chromatogr. A, 712
(1995) 287-301 .

[4] M. Josefsson, B. Carlsson, B. Norlander, Chromatographia, 37 (1993) 129-
138.

72

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