J. Phys. Chem. 1996, 100, 5931-5934
5931
Microscopic Simulation of Solute Transfer in Reversed Phase Liquid Chromatography Steven J. Klatte and Thomas L. Beck* Department of Chemistry, UniVersity of Cincinnati, Cincinnati, Ohio 45221-0172 ReceiVed: NoVember 8, 1995; In Final Form: January 24, 1996X
Solute retention in reversed phase liquid chromatography is driven by the free energy gradient on passing from the polar mobile phase into the nonpolar stationary phase. Only a partial understanding of retention exists currently. We present large scale molecular dynamics simulations of the transfer of a simple nonpolar solute from a water/methanol solvent mixture into a C18 stationary phase at room temperature. In addition to a detailed examination of the local environment of the solute, we compute the excess chemical potential profile. The overall free energy change is consistent in magnitude with that expected for hydrophobic transfer from water rich to oil phases, but specific interfacial effects draw into question bulk partitioning models.
1. Introduction Reversed phase liquid chromatography (RPLC) constitutes perhaps the most important means of separating chemicals in solution for subsequent analysis.1,2 A central question in RPLC has been debated since it was first used as a separation method, namely, what drives the retention process?1 The two primary viewpoints are the “solvophobic” model, where the expulsion of the solute from the solvent dominates the free energy of transfer, and “partitioning,” where the stationary phase contributes in a significant way.2 In the last 10 years, a large body of experimental and theoretical work has accumulated on an increasingly detailed microscopic level directed at a moleular picture of the retention event. Progress has been made in understanding surface density,3 chain length,4 temperature, and solvent composition5,6 effects on retention. However, there does not exist a quantitatively predictive understanding of the retention process at the present time. Such an understanding is expected to be difficult due to complexities of the stationary phase (tethered alkane chains at roughly one-half close-packed density), mobile phase (typically water/alcohol or water/ acetonitrile mixtures), and the solute-mobile phase and solutestationary phase interactions. The various components consist of highly nonideal fluids in addition to the fact that the retention occurs in an inherently interfacial environment. Experimental research has focused on both the basic physical environment at the mobile phase-stationary phase interface and the motions of solutes there. Lochmu¨ller and co-workers7 carried out fluorescence experiments on chemically bound pyrene probes. They observed excimer emission implying that the stationary phase chains cluster into locally dense regions. More recently, Harris and co-workers8 observed collapse of the stationary phase upon exposure to highly aqueous solvents in fluorescence lifetime measurements.8 Montgomery et al.9 performed frequency-domain fluorescence anisotropy experiments on a very large hydrophobic probe molecule and found that this solute resides at the surface of the chains; they concluded that the interface is rough and that the alcohol in water/alcohol solvent mixtures wets the surface but does not alter the stationary phase structure. Sander et al.10 carried out IR measurements to probe the disorder in the stationary phase chains; they observed a relatively high degree of disorder (measured in terms of the number of gauche defects), even at * To whom correspondence should be addressed. E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-5931$12.00/0
low temperatures. Ziegler and Maciel11,12 used 13C NMR methods to explore the structure and dynamics of the stationary phase. They observed dynamical gradients in the chains, with increasing motions further from the tethering bond. Water-rich mobile phases attenuated the chain motions. Bliesner and Sentell13 explored the motions of solvent species in contact with stationary phases with NMR spectroscopy. They found that methanol segregates strongly to the mobile phase/stationary phase interface; yet, it is masked from the silica surface by the dense hydrophobic layer. RPLC itself has proven extremely useful in inferring the influence of the chains and solvent on retention. Berendsen and de Galan4 investigated chain length effects on retention of a range of solutes. They observed a critical chain length between C6 and C12 above which retention remained roughly constant, implying that only the outer reaches of the stationary phase participate actively in retention. Sentell and Dorsey3 measured retention Vs surface-bonding density and found a turnover in the partition coefficient with increasing density. In later work, Dorsey and co-workers5,14 examined temperature and solvent effects on retention. They concluded that retention is strongly influenced by hydrophobic processes with water/ alcohol mobile phases, but not with water/acetonitrile phases. Carr et al.15 provide an argument, based on thermodynamic measurements for partitioning between bulk phases, that the stationary phase figures prominently in retention. Theoretically, lattice-based mean field models have been applied to the RPLC system. Dill and co-workers predicted the turnover in the partition coefficient with increasing surface density resulting from an “entropic expulsion” of the solute due to chain-chain interactions. Bo¨hmer et al.16 computed population distributions of solutes in the mobile phase-stationary phase region. Recently, Boehm and Martire17 presented a Bethe-Guggenheim quasi-chemical extension beyond regular solution theory. While these theories have given insights into driving forces of retention, the physical assumptions inherent in them are restrictive. Molecular dynamics (MD) simulations of a realistic model of the RPLC interface can both test the assumptions of the previous theories of retention and probe in a detailed way the molecular level processes which occur during solute transfer for comparison with experiment. The goal is a microscopic picture of the driving forces for retention and local structure and dynamics at the RPLC interface. We have carried out a series of simulations of the RPLC system, starting with calculations on tethered alkane stationary phases in vacuum.18 We have examined temperature dependent phase transitions in © 1996 American Chemical Society
5932 J. Phys. Chem., Vol. 100, No. 14, 1996
Figure 1. Number density of chains, waters, and methanol Vs z. A flat 9-3 wall resides at z ) 100.
the stationary phases, surface density and chain length effects, and the influence of the various portions (attractive and repulsive) of the intermolecular and chain-surface interactions on ordering of the chains near the silica surface;19 all portions of the potentials are crucial in obtaining a realistic description of the surface. A second series of studies focused on large scale simulations of stationary phases in contact with water/methanol mobile phases.20 A distinct segregation of methanol to the interface was observed. The methanol wets the surface but does not appreciably alter the structure of the C18 stationary phase for volume ratios less than 80-90% methanol (Figure 1). In addition, the wetting layer of the methanol is highly oriented with the hydrophobic tails pointing toward the stationary phase on average. A free volume excess was observed in the interfacial region, reflecting the “repulsive” nature of the polar hydrogen-bonded/hydrophobic interface. At high bonding density (4 µmol/m2), the stationary phase chains exist in a dense, disordered, collapsed state with a clear segmental layering away from the surface. Our simulations correctly model both the stationary phase width as determined by recent neutronscattering measurements21 as well as the number of gauche bond defects determined by FTIR.10 The chain tails and interfacial solvent display anisotropic but liquid-like behavior at room temperature. The regions of the chains within 10 Å of the surface have strongly suppressed diffusion constants. Details of the simulation methods have been presented elsewhere.18,20 2. Computational Methodology In this paper, we present the first large scale MD results for the transfer of a prototypical nonpolar solute from a 50:50 water/ methanol mixture (by volume) into a C18 stationary phase at a surface bonding density of 4 µmol/m2 or 42 Å2/chain. The sets of chains were placed randomly on the surface, and the head groups were attached randomly between 2.2 and 4.2 Å from the flat 9-3 surface to mimic the roughness of amorphous silica. Periodic boundary conditions were employed in two dimensions. Chains were placed in an initial all-upright configuration on two opposing walls 100 Å apart (32 on each wall) and equilibrated for 100 ps. Then solvent was added by random placement of small particles in the empty space between the opposing stationary phases, followed by slow growth to normal
Klatte and Beck size. The process was continued until the bulk density was obtained. The final system consisted of 1496 waters and 665 methanols. A total width of 100 Å ensured bulk behavior for the solvent in the middle region. The system was then heated to 600 K for 12 ps and slowly cooled to room temperature. This process was repeated several times to ensure equilibration. The resulting z (distance from surface, Figure 1) density profiles were robust. The SPC potential22 modeled the water interactions. Solute and methanol interactions were governed by the optimized potentials for liquid simulation23 set of parameters. The intermolecular potentials were truncated, group by group, at 8.5 Å. Chain potentials were obtained from analogous simulations of alkane bulk phases and self-assembled monolayers.24 A spherical, nonpolar solute particle (methane) was inserted at a sequence of z locations by placing a small version of the molecule in an existing instantaneous cavity. Then the particle was grown to its full size over a period of 15 ps. The system temperature was raised to 600 K for 15 ps and then cooled to 298 ( 2 K and equilibrated for 50 ps. Periodic scaling of solvent velocities was necessary to prevent a temperature drift. The solute was restricted to a 3 Å z region by an umbrella potential function for each independent MD simulation. The local free energy was then obtained by computing the z dependent normalized probability function for 11 consecutive windows and then subtracting the window potential:
µex(z) ) -kT ln P(z) - U(z)
(1)
A total of 11 windows were prepared ranging in z from 70 to 93 Å as shown in Figure 1. This z range covers the region from essentially bulk behavior in the mobile phase well into the stationary phase. Each prepared system was heated to 600 K for 12 ps and then slowly cooled to room temperature. An initial trajectory of 21 ps was run to allow for equilibration, and then production runs of 63 ps were carried out to generate radial distribution functions and the free energy profile of the single solute in each window. 3. Simulation Results Figure 1 presents the z number density profiles for the two solvent components and the stationary phase for an equilibrated RPLC interface. The preferential segregation of the methanol to the surface is apparent, and the chains concentrate in three disordered layers, analogous to rare gases near hard walls. The stationary phase structure here is nearly identical to that observed for chains in a vacuum, indicating that the 50:50 solvent mixture is a poor solvent for the chains. The overall interface width has an extent of nearly 10 Å. We took this distance to be that between the first bulk behavior in the density profile of the solvent and the first location where the chain density is that of the bulk octadecane. However, it is known from simulations of oil/water interfaces25 that a substantial fraction of this width results from large amplitude capillary fluctuations of the surface and not from the inherent local width of the interface. We have examined topographic maps of the chain surface which exhibit 10 Å peak to valley differences and 10-20 Å (in xy range) undulatory instantaneous chain clusters, consistent with that finding. The excess chemical potential profile as computed from eq 1 is presented in Figure 2. The profile was computed in two independent sets of simulations with nearly identical results. The computed total free energy drop is 3.6 kcal/mol upon transfer from the polar mobile phase into the stationary phase. A somewhat related free energy of transfer has been measured14
Microscopic Simulation of Solute Transfer
J. Phys. Chem., Vol. 100, No. 14, 1996 5933
Figure 2. Free energy profile of a solute transfer from aqueous methanol to the stationary phase.
for benzene in water:propanol to be 2.5 kcal/mol. We observe a free energy barrier (easily surmounted at room temperature) of 0.7 kcal/mol which occurs at z ) 75 Å. At this location, the methanol concentration begins to rise and water concentration begins to decrease. This barrier likely results from specific interfacial ordering effects at the interface; the methanols in the region around 80 Å are oriented with their tails on average pointing toward the stationary phase and their OH groups involved in hydrogen bonds to the mobile phase fluid. In the region following this small barrier, the excess chemical potential drops continuously until the solute is embedded in the stationary phase. Another barrier (1.4 kcal/mol) occurs in the region 87 < z < 91 Å. The two minima surrounding the peak are located at the two points labeled by arrows in Figure 1. These points are just prior to the outer two peak maxima in the stationary phase segment density profiles. These density peaks in the stationary phase correspond to densities well above bulk octadecane densities, so a barrier to solute penetration can be expected. The chain density peak near the surface constitutes nearly a close-packed layer of segment density and is largely impenetrable to the solute at this bonding density. This finding that the free energy minimum occurs in the outer portion of the stationary phase is consistent with the retention data of Berendsen and de Galan4 using water/methanol mobile phases and further indicates that the retention of a simple nonpolar solute occurs there for this type of system. Bo¨hmer et al.,16 in their lattice-based theory, predict solute density profiles for a range of solutes. For a methane-like solute, they found a density increase near the interface, in agreement with our results, but they predict a relatively uniform solute density profile throughout the stationary phase. Finally, we monitored the local environment of the solute by computing radial distribution functions (rdfs) from the solute to each mobile phase component and the stationary phase chains. The rdfs were normalized so that the integral generated directly the number of neighbors. The number of neighbors was computed within a sphere of radius 6 Å from the solute particle. Three sets of rdfs are presented in Figure 3, for the solute interactions with water oxygens, methanol carbons, and the chains. The average number of neighbors at several z locations is listed in Table 1. It is clear from the solute-water oxygen
Figure 3. Unnormalized rdfs of solute paired with (A) water, (B) carbon on methanol, and (C) carbon on chains in selected windows. The legend identifies each window number and its respective range of solute freedom in the z dimension.
TABLE 1: Number of Neighbors within 6 Å of the Solutea
a
regiona (Å)
Owater
Cmethanol
Cchain
70-73 72-75 74-77 76-79 78-81 80-83 82-85 84-87 86-89 88-91 90-93
9.4 14.5 9.4 9.4 5.0 5.6 3.8 4.8 1.1 0.0 0.0
7.9 5.6 8.0 7.5 6.6 6.1 5.8 4.9 2.9 0.6 0.0
0.0 0.0 0.1 0.6 5.8 7.3 10 12 20 36 34
The Å scale of each region is the same as in Figure 1.
rdfs that the density of water around the solute decreases in accord with the decreasing z density profile for water apparent in Figure 1. The number of water nearest neighbors drops from nine near z ) 76 Å to five at z ) 81 Å to zero at z ) 90 Å. The methanol density around the solute remains large somewhat further along the path from mobile phase to stationary phase. The average number of methanol neighbors decreases monotonically from six at 81 Å to three at 88 Å, to finally disappear around z ) 90 Å. The number of methanol neighbors is not simply proportional to the methanol mole fraction, which reaches a maximum at 82 Å. It is also clear from examination of the rdfs for solute-methanol carbon Vs solute-methanol oxygen that the methyl is selectively located near the solute preferentially over the oxygen. This frees the oxygen for subsequent hydrogen bonding. Substantial solute-chain interactions begin at roughly z ) 82 Å. However, it is clear from the rdfs that the solute is not completely solvated by the chains until z ) 90 Å. This location corresponds to the portion of the free energy profile where a double minimum was observed separated by a barrier, due to specific chain-ordering effects in the interfacial region.
5934 J. Phys. Chem., Vol. 100, No. 14, 1996 4. Discussion The MD results lead to a detailed physical picture of the retention event which cannot be unambiguously classified as “solvophobic” or “partitioning.” The overall free energy drop is consistent with that for the hydrophobic transfer from water/ alcohol mixtures to oil. However, a significant portion of the free energy decrease occurs in the region where the solute is still significantly solvated by mobile phase molecules. In particular, the primary drop occurs in the z region in which the segregated methanol is located. In this region, the solute is partially solvated by chains, but it is not completely surrounded by chains until the minimum of the free energy has been reached. In this z region, detailed ordering effects (layering of chains) lead to free energy features which could not be expected for bulk isotropic fluids. Therefore, we propose that the solute transfer process for this prototypical but experimentally relevant system should be considered largely an interfacial process and not bulk partitioning. However, the stationary phase does clearly participate importantly in the transfer process. The simulations suggest that idealized models of hard sphere chains, flat interfaces, and regular solution theory are not entirely adequate for this complex molecular interfacial system; these models cannot be expected to incorporate the specific ordering effects which are apparent in the simulations. Our results are consistent with a range of experimental probes of the interfacial region, including fluorescence spectroscopic, IR, NMR, neutron-scattering, and chromatographic data. The simulations lead to a more detailed microscopic understanding of the complex solute transfer process, and these studies show that experimentally relevant quantities in chromatography can be computed with current computer capabilities. Recent research by Martire and co-workers6,26 has shown conclusively that there exist substantial qualitative differences between thermodynamics of retention in water/alcohol Vs water/ acetonitrile mobile phase mixtures. They ascribe the differences to particular microstructures in the two solvents. The water/ alcohol cases are dominated by hydrogen-bonding effects, while the water/acetonitrile mixtures are influenced by clustering of the acetonitrile molecules around nonpolar solutes. Our results are entirely consistent with this view of the water/alcohol mobile phases but say nothing about the water/acetonitrile mixtures. In another study, Alvarez-Zepeda and Martire27 have examined sorption behavior of water/acetonitrile mixtures at the chromatographic interface. Our simulations do not lead to a picture of the interface which appears consistent with recent slot models of retention.28 However, we note here that for our particular system, the shape selectivity factor is not good for water/methanol mixtures unless the methanol concentration is very high, where partial solubilization of the stationary phase chains is possible.28 The chains in our simulated system are largely collapsed on the silica surface due to interaction with a poor solvent. Chain extension can be expected for high methanol concentrations20 and for
Klatte and Beck water/acetonitrile mixtures, where substantial association of the acetonitrile with the chains has been experimentally observed.13 More work needs to be done to further explore at the molecular level the roles of surface chain density, temperature, solvent composition, and solute type and shape in retention. Future research will focus on these issues and on extracting the particular enthalpic and entropic contributions along the chemical potential profiles.29 Acknowledgment. We would like to thank John Dorsey, Ken Dill, Lane Sander, and Daniel Martire for helpful and informative discussions. We acknowledge the support of the donors of the Petroleum Research Fund of the American Chemical Society and NSF Grant CHE-9225123. We thank the Ohio Supercomputing Center for a generous grant of computing resources. References and Notes (1) Dorsey, J. G.; Cooper, W. T. Anal. Chem. 1994, 66, 857A. (2) Dorsey, J. G.; Dill, K. A. Chem. ReV. 1989, 89, 331. (3) Sentell, K. B.; Dorsey, J. G. J. Chromatogr. 1989, 461, 193. (4) Berendsen, G. E.; de Galan, L. J. Chromatogr. 1980, 196, 21. (5) Cole, D. A.; Dorsey, J. G. Anal. Chem. 1992, 64, 1317. (6) Alvarez-Zepeda, A.; Barman, B. N.; Martire, D. E. Anal. Chem. 1992, 64, 1978. (7) Lochmu¨ller, C. H.; Colburn, A. S.; Hunnicutt, M. L.; Harris, J. M. Anal. Chem. 1983, 55, 1344. (8) Wong, A. L.; Hunnicutt, M. L.; Harris, J. M. Anal. Chem. 1991, 63, 1076. (9) Montgomery, M. E.; M. A. Green, J.; Wirth, M. J. Anal. Chem. 1992, 64, 1170. (10) Sander, L. C.; Callis, J. B.; Field, L. R. Anal. Chem. 1983, 55, 1068. (11) Zeigler, R. C.; Maciel, G. E. J. Phys. Chem. 1991, 95, 7345. (12) Zeigler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1991, 113, 6349. (13) Bliesner, D. M.; Sentell, K. B. Anal. Chem. 1993, 65, 1819. (14) Cole, L. A.; Dorsey, J. G.; Dill, K. A. Anal. Chem. 1992, 64, 1324. (15) Carr, P. W.; Li, J.; Dallas, A. J.; Eikens, D. I.; Tan, L. C. J. Chromatogr. A 1993, 656, 113. (16) Bohmer, M. R.; Koopal, L. K.; Tijssen, R. J. Phys. Chem. 1991, 95, 6285. (17) Boehm, R. E.; Martire, D. E. J. Phys. Chem. 1994, 98, 1317. (18) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1993, 97, 5727. (19) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1995, 99, 16024. (20) Klatte, S. J.; Beck, T. L. To be submitted for publication in J. Phys. Chem. (21) Sander, L. C.; Glinka, C. J.; Wise, S. A. Anal. Chem. 1990, 62, 1099. (22) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; Reidel Publishing Company: New York, 1981; p 331. (23) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (24) Bareman, J. P.; Klein, M. L. J. Phys. Chem. 1990, 94, 5202. (25) Pohorille, A.; Wilson, M. A. J. Mol. Struct. 1993, 284, 271. (26) Stalcup, A. M.; Martire, D. E.; Wise, S. A. J. Chromatogr. 1988, 442, 1. (27) Alvarez-Zepeda, A.; Martire, D. E. J. Chromatogr. 1991, 550, 285. (28) Sander, L. C.; Wise, S. A. In Retention and SelectiVity in Liquid Chromatography; Smith, R. M., Ed.; Journal of Chromatography Library; Elsevier Science: New York, 1995; Vol. 57, p 337. (29) Guillot, B.; Guissani, Y. J. Chem. Phys. 1993, 99, 8075.
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