Anal. Chem. 2004, 76, 2886-2892
Simulation Studies on the Effects of Mobile-Phase Modification on Partitioning in Liquid Chromatography Collin D. Wick,† J. Ilja Siepmann,*,† and Mark R. Schure‡
Departments of Chemistry and of Chemical Engineering and Materials Science, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, and Theoretical Separation Science Laboratory, Rohm and Haas Company, 727 Norristown Road, P.O. Box 0904, Spring House, Pennsylvania 19477
Various driving forces have been suggested to explain retention and selectivity in reversed-phase liquid chromatography (RPLC). To provide molecular-level information on the retention mechanism in RPLC, configurationalbias Monte Carlo simulations in the Gibbs ensemble were carried out for model systems consisting of three phases: an n-hexadecane retentive phase, a mobile phase with varying water-methanol composition, and a helium vapor phase as reference state. Liquid n-hexadecane functions as a model of a hydrophobic stationary phase, and a wealth of experimental data exists for this system. Gibbs free energies for solute transfers from gas to retentive phase, from gas to mobile phase, and from mobile to retentive phase were determined for a series of short linear alkanes and primary alcohols. Although the magnitude of the incremental Gibbs free energy of transfer for a methylene segment is always larger for the gas- to retentive-phase transfer than the gas- to mobile-phase transfer, it is found that the partitioning of alkanes and alkyl tail groups is mostly affected by the changes in the aqueous mobile phase that occur when methanol modifiers are added. In contrast, the partitioning of the alcohol headgroup is sensitive to changes in both the n-hexadecane and the mobile phases. In particular, it is found that hydrogen-bonded aggregates of methanol are present in the n-hexadecane phase for higher methanol concentrations in the mobile phase. These aggregates strongly increase alcohol partitioning into the retentive phase. The simulation data clearly demonstrate that due to modification of the retentive-phase hydrocarbons by solvent components, neither the solvophobic theory of RPLC, advocated by Horvath and co-workers, nor the lipophilic theory of RPLC, advocated by Carr and co-workers, can adequately describe the separation mechanism of the hexadecane model system of a retentive phase studied here nor the more complex situation present in actual RPLC systems.
* Corresponding author: (e-mail)
[email protected]. † University of Minnesota. ‡ Rohm and Haas Co.
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Liquid chromatography (LC) is one of the two dominant techniques in chromatographic science, the other being gas chromatography (GC).1,2 Although both techniques function through phase equilibria of the analyte to be separated with a retentive (stationary) and a mobile phase, the two techniques differ substantially in the complexity of the physical process(es) responsible for enacting the separation. This is due to the presence of a liquid solvent in LC, which acts to preferentially solvate some analytes and can modify the retentive phase. In GC, the mobile phase is a gas that does not appreciably affect the phase equilibria of the separation process; it simply functions as a convective agent to drive the analyte through the column. Note that in this study we use the more general term “retentive phase” in place of the common term “stationary phase” because in some separation techniques, such as micellar electrokinetic chromatography3 or novel forms of chromatography with dynamically created pseudostationary phases,4 the retentive phase is not stationary. Furthermore, we refer to the “mobile phase” synonymously as the solvent because the fact that the fluid may move has little to do with the process of phase equilibrium, which is ultimately responsible for chromatographic separation.2 The retentive material most commonly utilized in LC contains octadecyl chains that are chemically bound to silica.5,6 This system is commonly referred to as reversed-phase liquid chromatography (RPLC)1,2,5,6 and is the center of interest in our inquiry into LC retention mechanisms. Although a great deal of work has been done by a variety of theoretical and experimental approaches,7-25 no consensus view has emerged on what factor(s) control the (1) Snyder, L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography; Wiley: New York, 1979. (2) Giddings, J. C. Unified Separation Science; Wiley: New York, 1991. (3) Sepaniak, M. J.; Powell, A. C.; Swaile, D. F.; Cole, R. O. In Capillary Electrophoresis Theory and Practice; Grossman, P. D., Colburn, J. C., Eds.; Academic Press: New York, 1997; pp 159-189. (4) Wells, P. J.; Zhou, S.; Parcher, J. F. Anal. Chem. 2002, 74, 2103. (5) Unger, K. K. Porous Silica; Journal of Chromatography Library 16; Elsevier: Amsterdam, 1979. (6) Retention and Selectivity in Liquid Chromatography: Prediction, Standardization, and Phase Comparisons; Smith, R. M., Ed.; Elsevier: New York, 1995. (7) Elkoshi, Z.; Grushka, E. J. Phys. Chem. 1981, 85, 2980. (8) Martire, D. E.; Boehm, R. E. J. Phys. Chem. 1983, 87, 1045. (9) Dorsey, J. G.; Dill, K. A. Chem. Rev. 1989, 89, 331. (10) Tijssen, R.; Schoenmakers, P. J.; Bo ¨hmer, M. R.; Koopal, L. K.; Billiet, H. A. H. J. Chromatogr., A 1993, 656, 135. (11) Knox, J. H.; Vasvari, G. J. Chromatogr. 1973, 83, 181. (12) Horvath, C.; Melander, W.; Molnar, I. J. Chromatogr. 1978, 158, 215. 10.1021/ac0352225 CCC: $27.50
© 2004 American Chemical Society Published on Web 04/14/2004
retention mechanism in RPLC. A first question revolves around whether the analyte can penetrate the retentive phase and resemble something like a “liquid-liquid” partitioning process or whether the analyte is retained by an adsorptive mechanism at the interface between solvent and retentive phases.6 This issue is further complicated when solvent mixtures are used where concentration gradients may exist at the interface and one or more components of the solvent mixture may preferentially partition into the retentive phase.14 One set of experiments17 demonstrated that solute retention increased with increasing surface chain density of the retentive phase and then decreased as chain density was further increased. This behavior suggests that partitioning occurred in the low-coverage region and that the solute was crowded out of the retentive phase at a critical chain density. At higher coverages, adsorption was perhaps the most dominating interaction. These observations are not universal because they are controlled by the molecular size, shape, and polarity of the solvent, solute, and retentive-phase material. Even under the assumption that partitioning processes dominate retention in RPLC, the solvent’s role in moderating retention is not clear and two conflicting schools of thinking have emerged: a view where the analyte-solvent interaction is the predominant driving force for retention18-20 and given under the guise of the so-called “solvophobic” theory21 and another view where the analyte-retentive phase interaction is the thermodynamic driving force for retention22-26 and given under the guise of “lipophilic” interactions. To allow for a meaningful comparison of the contributions arising from the two phases, a reference state is required for a thermodynamic or a molecular description of the RPLC system. An ideal gas phase with its negligible interactions is the obvious reference state that makes it possible to separate the contributions of the retentive and of the mobile phase for the overall partitioning, as also recognized by Carr and coworkers.22,23,26 Only recently has an experimental attempt been made at providing for a limited set of analytes a complete thermodynamic accounting of the various enthalpies and entropies that are pertinent to partitioning in RPLC model systems.26 In this regard, the hydrophobic molecule, n-hexadecane, was used in bulk form as a retentive phase because it is much easier to use a bulk liquid for concentration measurements performed by headspace gas chromatography, as compared to an immobilized bonded retentive phase where concentration of this phase is much more difficult to determine and control. Utilizing ethylbenzene as an analyte, the driving force for retention was shown to be the affinity (13) Colin, H.; Diez-Masa, J. C.; Guiochon, G.; Czajkowska, T.; Miedziak, I. J. Chromatogr. 1978 167, 41. (14) Riedo, F.; Kovats, E. J. Chromatogr. 1982, 239, 1. (15) Oroszlan, P.; Wicar, S.; Teshima, G.; Wu, S. L.; Hancock, W. S.; Karger, B. L. Anal. Chem. 1992, 64, 1623. (16) Bereznitski, Y.; Jaroniec, M. J. Liq. Chromatogr. 1999, 22, 1945. (17) Sentell, K. B.; Dorsey, J. G. Anal. Chem. 1989, 61, 930. (18) Vailaya, A.; Horva´th, C. J. Chromatogr., A 1998, 829, 1. (19) Vailaya, A.; Horva´th, C. J. Phys. Chem. B 1997, 101, 5875. (20) Vailaya, A.; Horva´th, C. J. Phys. Chem. B 1998, 102, 701. (21) Sinanogˇlu, O. In Molecular Associations in Biology; Pullman, B., Ed.; Academic Press: New York, 1968; p 427. (22) Carr, P. W.; Li, J.; Dallas, A. J.; Eikens, D. I.; Tan, L. C. J. Chromatogr., A 1993, 656, 113. (23) Li., J. J.; Carr, P. W. Anal. Chem. 1993, 65, 1443. (24) Carr, P. W.; Tan, L. C.; Park, J. H. J. Chromatogr., A 1996, 724, 1. (25) Park, J. H.; Lee, Y. K.; Weon, Y. C.; Tan, L. C.; Li, J.; Li, L.; Evans, J. F.; Carr, P. W. J. Chromatogr., A 1997, 767, 1. (26) Ranatunga, R. P. J.; Carr, P. W. Anal. Chem. 2000, 72, 5679.
of analyte and retentive phase.26 Furthermore, this affinity for the retentive phase was shown to be driven by enthalpy as the entropic contribution was of minor importance. However, it was noted that the analyte-solvent interaction is larger than the analyteretentive phase interaction for various polar solutes;24 in this case, the analyte-retentive phase interaction is not the dominant driving force for retention. One route of investigation that would be useful for clarifying these retention mechanisms is that of molecular simulation, but with few exceptions,27,28 little work has been done in this area. This is because the solvation forces that control analyte-solvent and analyte-retentive phase interactions are weak and require force fields with very high accuracy when chromatographic problems are to be simulated.29 Recently, we have demonstrated the feasibility of utilizing molecular simulation for elucidating (gas-liquid) chromatographic retention mechanisms and have calculated quantitatively accurate free energies of transfer and relative retention times.30-35 In this research, we use a similar computational methodology to explore the role of different methanol-water compositions on the thermodynamics of analyte partitioning between aqueous and nonpolar hydrocarbon liquid phases and to assess the validity of the solvophobic and lipophilic theories. Guided by the experimental work of Carr and co-workers, the focus of this work is on partitioning between bulk phases without specific consideration to interfaces that would lead to additional adsorption effects. The computational study of a full RPLC system with silica-bound hydrocarbon chains and a direct interface between bonded and mobile phases will be the subject of subsequent work. Particlebased simulations are especially powerful because the origin of the thermodynamic quantities can be explained through detailed structural analysis.36-38 Using the simulation methodology described below, we can account for the number densities of all solvent and solute species and their specific local environment and, therefore, can elucidate the underlying separation mechanism for model RPLC systems. In this regard, it will be shown that neither the solvophobic nor lipophilic separation mechanisms fully explain the underlying mechanism for separation in the model system we have chosen, and consequently, it is doubtful that one of these theories can offer a comprehensive picture of the RPLC retention mechanism. (27) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1996, 100, 5931. (28) Slusher, J. T.; Mountain, R. D. J. Phys. Chem. B 1999, 103, 1354. (29) Schure, M. R. Advances in Chromatography; Marcel Dekker: New York, 1998; Vol. 39, pp 139-200. (30) (a) Martin, M. G.; Siepmann, J. I.; Schure, M. R. J. Phys. Chem. B 1999, 103, 11191. (b) Martin, M. G.; Siepmann, J. I.; Schure, M. R. In Unified Chromatography; Parcher, J. F., Chester, T. L., Eds.; ACS Symposium Series 748; American Chemiscal Society: Washington, DC, 2000; pp 82-95. (31) Wick, C. D.; Siepmann, J. I.; Schure, M. R. J. Phys. Chem. B 2001, 105, 10961. (32) Wick, C. D.; Siepmann, J. I.; Klotz, W. L.; Schure, M. R. J. Chromatogr., A 2002, 954, 181. (33) Wick, C. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2002, 74, 37. (34) Wick, C. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2002, 74, 3518. (35) Sun, L.; Wick, C. D.; Siepmann, J. I.; Schure, M. R., unpublished work. (36) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1987. (37) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: San Diego, 1996. (38) Leach, A. R. Molecular Modelling: Principles and Applications, 2nd ed.; Prentice Hall: Harlow, England, 2001.
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SIMULATION METHODOLOGY To investigate the effects of changes in the overall watermethanol ratio on the relative contribution of the retentive and solvent phases to liquid-liquid partitioning for the hexadecane analogue of the RPLC problem, simulations were carried out for a three-phase system consisting of an n-hexadecane retentive phase, a water-methanol solvent phase, and a helium vapor phase as reference state. A combination of the configurational-bias Monte Carlo (CBMC) algorithm39-41 and the constant-pressure Gibbs ensemble Monte Carlo (GEMC) method42-46 was used for these simulations. The GEMC technique allows for the simulation of multiple phases in thermodynamic contact, each in its individual, periodically replicated simulation box without an explicit physical interface. Volume moves are performed separately for each phase to reach mechanical equilibrium with an external pressure bath, and CBMC particle-transfer moves are used to equilibrate the chemical potentials of solute and solvent species between the phases. The reference vapor phase also has the beneficial effect of facilitating the transfer of analyte and solvent molecules between the two liquid phases because the acceptance rates for liquidvapor and vapor-liquid transfers are higher than for direct liquidliquid transfers.47,48 Using the CBMC/GEMC approach, the mutual solubilities of solvents and the partition coefficients of multiple solutes can be determined at a given state point from a single simulation.48,49 The united-atom version of the transferable potentials for phase equilibria (TraPPE-UA)41,50,51 force field was used to model all alkanes, alcohols, and helium, while the TIP4P model was used for water.52 The TraPPE-UA model utilizes pseudo-atoms located at the carbon positions to represent entire methyl or methylene groups, thereby reducing the number of interaction sites and computer time needed to simulate the system. Fixed partial charges are used to model the first-order electrostatic interactions of water and alcohol headgroups by placing charges at the polar hydrogen, oxygen, and R-carbon atoms. The combination of TraPPE-UA and TIP4P force fields has already been used to successfully predict thermodynamic and structural properties of solute partitioning in water-octanol48 and helium-(squalane or glycol ether) systems.30-35 Four different methanol-water ratios were used for this investigation: neat water solvent with two methanol solutes (denoted as system W), 33% methanol (system 33M), 67% methanol (system 67M), and neat methanol solvent with two water solutes (system M). The retentive phase primarily consisted of (39) Siepmann, J. I.; Frenkel, D. Mol. Phys. 1992, 75, 59. (40) Frenkel, D.; Mooij, G. C. A. M.; Smit, B. J. Phys.: Condens. Matter 1992, 4, 3053. (41) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1999, 103, 4508. (42) Panagiotopoulos, A. Z. Mol. Phys. 1987, 61, 813. (43) Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; Tildesley, D. J. Mol. Phys. 1988, 63, 527. (44) Smit, B.; de Smedt, P.; Frenkel, D. Mol. Phys. 1989, 68, 931. (45) Mooij, G. C. A. M.; Frenkel, D.; Smit, B. J. Phys.: Condens. Matter 1992, 4, L255. (46) Siepmann, J. I.; Karaborni, S.; Smit, B. Nature 1993, 365, 330. (47) Canongia Lopes, J. N.; Tildesley, D. J. Mol. Phys. 1997, 92, 187. (48) Chen, B.; Siepmann, J. I. J. Phys. Chem. B, submitted for publication. (49) Martin, M. G.; Siepmann, J. I. Theor. Chem. Acc. 1998, 99, 347. (50) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (51) Chen, B.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2001, 105, 3093. (52) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
2888 Analytical Chemistry, Vol. 76, No. 10, May 15, 2004
Table 1. Numbers of Molecules Used for the Four Systems system
W
33M
67M
M
n-hexadecane water methanol helium other solute typesa
216 864 2 200 2
216 576 290 200 2
216 290 576 200 2
216 2 864 200 2
a Includes ethanol, 1-propanol, methane, ethane, propane, and n-butane.
n-hexadecane, and helium is the major component of the bridging gas phase. The total numbers for each type of molecule used for the four systems are listed in Table 1. All simulations were carried out at a temperature of 323.15 K and at a pressure of 101.5 kPa (1 atm). Whereas water, methanol, helium, and all solutes were allowed to transfer between all three phases, n-hexadecane was confined to remain in the retentive phase because its solubility in the aqueous phase is extremely low. In addition, the saturated vapor pressure of hexadecane is very low and almost none would be expected in the gas phase under these conditions. Ten independent simulations were carried out for each of the four systems. The number of Monte Carlo (MC) cycles (one MC cycle equals N moves, where N is the total number of particles) used for equilibration varied depending on the system being simulated, but each was equilibrated for at least 104 MC cycles. Equilibration was monitored via the amount of water or methanol in the n-hexadecane phase and the pressure of the vapor phase. Following upon the initial equilibration period, 104 MC cycles of production were used for each of the 10 independent simulations. Therefore, a total of 105 MC cycles was available to calculate averages for each system. Statistical uncertainties were estimated from the results of the independent simulations. RESULTS AND DISCUSSION Since the volumes of the mobile and retentive phases were of similar magnitude, as is often the case in RPLC,1 and methanol and water have different solubilities in the retentive phase and different vapor pressures, the equilibrated compositions of the mobile phase do not exactly coincide with the overall methanolwater ratios used in the simulated systems. The average amounts of methanol and water in the three phases, along with the actual mole fractions of methanol or water in the mobile phase are given in Table 2. As can be seen, more methanol molecules than water leave the mobile phase for systems 33M and 67M, resulting in an actual mobile-phase methanol mole fraction ∼0.05 lower than its overall mole fraction for the system. This is expected, since the vapor pressure of methanol and its solubility in an organic phase is greater than those of water.53,54 Moreover, it can be observed that there is very little methanol present in the nhexadecane retentive phase for system 33M, whereas large increases of the methanol mole fraction are found in the retentive phase for systems 67M and M. It should be emphasized that the methanol mole fraction found in the retentive phase of system M (53) Ambrose, D.; Sprake, C. H. S. J. Chem. Thermodyn. 1970, 2 631. (54) Bridgeman, O. C.; Aldrich, E. W. J. Heat Transfer 1964, 86, 279.
Table 2. Average Numbers, 〈N〉, and Mole Fractions, 〈x〉, of Water and Methanol phase retentive
gas 〈Nigas〉
〈Nimob〉
〈ximob〉
46.0 ( 1.3 72 ( 3 94.1 ( 0.8 66.9 ( 0.9 210.7 ( 1.4 416.3 ( 0.6
817.9 ( 1.3 504 ( 3 194.0 ( 0.8 222.6 ( 0.9 348.4 ( 0.5 417.8 ( 0.5
1 0.72 0.28 0.39 0.61 1
system
molecule
〈Niret〉
W 33M 33M 67M 67M M
water water methanol water methanol methanol
0.087 ( 0.003 0.16 ( 0.06 1.9 ( 0.2 0.53 ( 0.07 16.9 ( 1.3 29.9 ( 0.2
mobile
is ∼2 orders of magnitude larger than the water mole fraction for system W. However, the calculated solubility limit of 12% methanol in n-hexadecane agrees well with the experimental value of 13% at 323 K.55 A strong advantage of the GEMC methodology is that the Gibbs free energy of transfer of an analyte from phase R to phase β can be easily calculated, without approximations, from the ratio of its average number densities:49
∆GRfβ ) - RT ln(〈Fβ〉/〈FR〉)eq where R and T are the molar gas constant and the absolute temperature, respectively. The quantities 〈FR〉 and 〈Fβ〉 are the ensemble-averaged number densities of the analyte for phases R and β, respectively. The values for the gas-retentive phase Gibbs free energies of transfer, ∆Gvapfret, are given in Figure 1.56 It can be seen that the addition of methanol has little effect on the partitioning of the n-alkane solutes into n-hexadecane. For water and the alcohol solutes, though, the ∆Gvapfret for systems W and 33M are similar but differ from those for systems 67M and M, which again are relatively close to each other. This can be attributed to the fact that there are very few methanol molecules in the n-hexadecane phase for systems W and 33M, but significant amounts are present in both systems 67M and M. While the sorption of methanol in n-hexadecane has a strong effect on polar groups, the incremental ∆Gvapfret(CH2) per methylene group for both n-alkane and alcohol solutes does not vary significantly between the four systems, ranging from -2.2 to -2.7 kJ/mol for alcohols and from -3.0 to -3.1 kJ/mol for alkanes (see Figure 2). Figure 3 shows snapshots of the n-hexadecane phase for systems 67M and M. It is clearly evident that methanol aggregates are formed in both cases, but medium-sized cyclic clusters seem to be preferred for system 67M, while the aggregate sizes and architectures are more varied for system M. The size distributions for hydrogen-bonded aggregates in the n-hexadecane phases were determined from analyzing periodically recorded configurations of the systems. The criteria for the formation of a hydrogen bond consisted of an oxygen-oxygen distance less than 3.3 Å, an oxygen-hydrogen distance less than 2.5 Å, and an interaction energy of the hydrogen, oxygen, and R-carbon (alcohol) or other hydrogen (water) between the two molecules being less than -13 (55) Arai, Y.; Higashiuchi, H., Sakuragi, Y. Fluid Phase Equilib. 1993, 89, 187. (56) The values of ∆Gtrans for water are only shown for systems W, 33M, and 67M, since for system M (i.e., at infinite dilution) sampling problems lead to large statistical uncertainties.
Figure 1. Gibbs free energies for the analyte transfer from gas to n-hexadecane retentive phase, ∆Gvapfret, for systems W (circles and solid lines), 33M (squares/dashed), 67M (diamonds/dotted), and M (triangles/dash-dotted). The results for n-alkane solutes (black symbols) and for polar solutes (red symbols), consisting of water and the primary alcohols, are depicted as a function of the number of carbon and oxygen atoms (e.g., the data for water and methanol are shown at values of 1 and 2, respectively, on the abscissa).
kJ/mol.48,57 The cluster distributions for systems 67M and M are shown in Figure 4. For the system 67M, about half of the polar molecules are found in clusters of size four and five, whereas for system M, the cluster size distribution is much broader. As is often the case with micellar formations,58 it appears that, at low methanol concentrations, the aggregates form compact structures similar to spherical micelles, while as the concentration increases, the aggregates change their shape to accommodate more molecules. A larger fraction of smaller aggregates is found for system M, which arises from clusters of molecules in close contact with another aggregate, but not satisfying the conditions used here for hydrogen-bond formation. The gas-mobile phase Gibbs free energies of transfer, ∆Gvapfmob, are depicted in Figure 5. In contrast to the gashexadecane Gibbs free energies (see Figure 1), the addition of methanol has a large effect on the gas-aqueous partitioning for the n-alkane analytes. For all four alkanes, the addition of methanol (57) Stubbs, J. M.; Siepmann, J. I. J. Phys. Chem. B 2002, 106, 3968. (58) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; WileyInterscience: New York, 1989.
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Figure 2. Incremental Gibbs free energies of transfer for the methylene group, ∆Gtrans(CH2), in normal alkanes (black symbols) and primary alcohols (red symbols) as a function of overall methanol concentration. Circles, squares, and diamonds depict the results for ∆Gvapfret(CH2), ∆Gvapfmob(CH2), and ∆Gmobfret(CH2).
increases the partitioning into the polar mobile phase and modifies the slope for the homologue series from positive methylene increments for system W to negative methylene increments for system M (see Figure 2); that is, the mobile-phase affinity of alkane analytes increases with increasing chain length for aqueous phases with large content of organic modifier, whereas it decreases for a neat aqueous phase. For the alcohols, the addition of methanol also significantly alters their gas-mobile phase partitioning, changing the slope of the homologue series from positive for system W to negative for
system M. While the changes for the methylene increments show similar trends for the alkane and alcohol analytes, the addition of methanol has different effects on the affinity of the alcohols for the mobile phase: methanol’s affinity is strongest for the neat water phase (system W), whereas 1-propanol least favors partitioning into the neat water phase. For methanol, unlike for methane, systems W, 33M, and 67M systems yield similar values for ∆Gvapfmob and only system M shows a large difference compared to the aqueous systems. For the ethanol analyte, the ∆Gvapfmob for all four systems fall within 2 kJ/mol; i.e., this transfer is rather insensitive to the methanol concentration of the mobile phase. These trends for alcohol analytes can be explained by the compensation of two factors. The loss of hydrogen bond donors in the mobile phase with increasing methanol concentration (water has two donor sites, while methanol has only one) allows for fewer hydrogen bonds for the solvated hydroxyl groups of the analytes, accounting for an increase in ∆Gvapfmob (i.e., less partitioning into the mobile phase). A favorable contribution for methylene groups arises from the increase of nonpolar contact area in the mobile phase with increasing methanol concentration. For system M, it appears that the complete loss of water and its extra hydrogen bond donor sites dominates over the increase in nonpolar contact area from the increased amount of methanol. The gas-mobile phase partitioning of water changes quite regularly with the addition of methanol (i.e., an increase in ∆Gvapfmob with higher methanol concentration), which is expected because water is only affected by the loss of hydrogen bond donors but does not benefit from the increase in nonpolar contact area. The values for ∆Gmobfret for the complete thermodynamic cycle (i.e., the transfer from the mobile to the retentive phase, ∆Gmobfret ) ∆Gvapfret - ∆Gvapfmob) are shown in Figure 6. The addition of methanol affects ∆Gmobfret for the alkane analytes inversely related to ∆Gvapfmob, which is expected, since their ∆Gvapfret, are relatively
Figure 3. Snapshots of the n-hexadecane phase for systems 67M (left) and M (right). 2890 Analytical Chemistry, Vol. 76, No. 10, May 15, 2004
Figure 4. Size distributions for hydrogen-bonded aggregates consisting of primarily methanol, water, and the other alcohol analytes in systems 67M (circles and solid line) and M (diamonds and dotted line).
Figure 6. Gibbs free energies for the analyte transfer from mobile phase to n-hexadecane retentive phase, ∆Gmobfret. Symbol types and line styles are the same as in Figure 1.
have the strongest affinity for the mobile phase without organic modifier (system W), whereas 1-propanol is least retained in system 33 M. The free energy analysis indicates that the partitioning of alcohol solutes is governed by both mobile and retentive phase effects as the organic modifier concentration is changed. A decrease in the free energy for the mobile to retentive phase transfer for a given solute, ∆Gmobfret, will drive the chromatographic system toward longer retention times for this solute. Overall, relative retention times of the alcohols are governed by a combination of factors arising from both phases. As the amount of organic modifier is increased, the hydrogen bond acceptor and donor ability of the retentive phase increases, the hydrogen bond donor ability of the mobile phase decreases, and the nonpolar contact area of the mobile phase increases. Figure 5. Gibbs free energies for the analyte transfer from gas to mobile phase, ∆Gvapfmob. Symbol types and line styles are the same as in Figure 1.
insensitive to the addition of methanol. It should be emphasized (see Figure 2) that although ∆Gvapfret(CH2) is larger in magnitude than ∆Gvapfmob(CH2) and ∆Gmobfret(CH2) is negative regardless of composition (in accord with the “lipophilic” view), changes in retention order caused by the composition of the mobile phase (i.e., relative values of ∆Gmobfret) are driven by changes in ∆Gvapfmob in accord with the “solvophobic” theory. For the alcohol analytes, the mobile to retentive phase partitioning shows the effects of both legs of the thermodynamic cycle. The slope of the homologue series for the alcohols follows similarly with the n-alkanes, which is driven by the aqueous phase. Addition of methanol affects methanol analytes in both phases. Specifically, the large change in ∆Gmobfret observed between systems 33M and 67M is the result of the aggregation of methanol in the n-hexadecane retentive phase for high modifier content (e.g., systems 67M and M). The difference in ∆Gmobfret between systems 67M and M originates from the mobile phase and its change in hydrogen bond donor ability. Again, water and methanol
CONCLUSIONS Configurational-bias Monte Carlo simulations in the Gibbs ensemble using the TraPPE-UA and TIP4P force fields were used to investigate the effects of mobile-phase modification on partitioning and retentive-phase structure for a model RPLC system without explicit treatment of interfaces. Changes in the retentive behavior of alkane solutes and of alkyl tail groups are governed by the mobile phase (“solvophobic effect”), despite the magnitude of ∆Gvapfret being larger than ∆Gvapfmob (in agreement with the “lipophilic” view). The transfer from mobile to retentive phase for water and the hydroxyl groups of the primary alcohols shows effects of changes in both the mobile and the retentive phases. In particular, it needs to be emphasized that addition of organic modifier not only changes the properties of the mobile phase (i.e., decrease in hydrogen bond donor ability and increase in nonpolar contact area) but also leads to changes in the retentive phase, where the formation of methanol aggregates at higher overall methanol mole fraction leads to a dramatic increase in the hydrogen bond donor and acceptor ability of the n-hexadecane retentive phase. In conclusion, neither the solvophobic theory nor the lipophilic model alone is sufficient to explain the changes in partition Analytical Chemistry, Vol. 76, No. 10, May 15, 2004
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behavior observed for different classes of analytes in reversedphase liquid chromatography. Furthermore, a distinction needs to be made between the net contribution of a phase to retention (i.e., the magnitude of the Gibbs free energy of transfer into this phase) and whether the retentive properties for a particular phase-analyte combination are altered by addition of organic modifier. Currently, this computational approach is applied to more complex models of the RPLC system including an explicit treatment of the hydrocarbon chains tethered to a silica substrate and of the interface between retentive and mobile phases to investigate the concomitant partition and adsorption effects that most likely govern retention in RPLC. However, the present study establishes the quantitative nature of this approach and explains,
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on a molecular scale, retention mechanisms that elude an experimental thermodynamic investigation. ACKNOWLEDGMENT We thank Peter Carr for many stimulating discussions. Financial support from the National Science Foundation (CHE0213387) and through a Department of Energy Computational Science Graduate Fellowship (C.D.W.) is gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute. Received for review October 15, 2003. Accepted March 5, 2004. AC0352225
