Molecular Dynamics Simulations of Alkylsilane Stationary-Phase

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Anal. Chem. 2005, 77, 7852-7861

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Molecular Dynamics Simulations of Alkylsilane Stationary-Phase Order and Disorder. 1. Effects of Surface Coverage and Bonding Chemistry Katrice A. Lippa,*,† Lane C. Sander,† and Raymond D. Mountain‡

Analytical Chemistry Division and Physical and Chemical Properties Division, Chemical Sciences and Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899

“Shape-selective” polymeric alkylsilane stationary phases are routinely employed over the more common monomeric phases in reversed-phase liquid chromatography (RPLC) to improve the separation of geometric isomers of shape-constrained solutes. We have investigated the molecular dynamics of chromatographic models that represent both monomeric and polymeric stationary phases with alkylsilane surface coverages and bonding chemistries typical of actual materials in an effort to elucidate the molecular-level structural features that control shapeselective separations. The structural characterization of these models is consistent with previous experimental observations of alkyl chain order and disorder: (1) alkyl chain order increases with increased surface coverage; and (2) monomeric and polymeric phases with similar surface coverages yield similar alkyl chain order (although subtle differences exist). In addition, a significant portion of the alkyl chain proximal to the silica surface is disordered (primarily gauche conformations) and the distal end is most ordered. Models that represent shape-selective RPLC phases possess a significant region of distal end chain order with primarily trans dihedral angle conformations. This is consistent with the view that the alkyl chains comprising polymeric stationary phases contain a series of well-defined and rigid voids in which shape-constrained solutes can penetrate and hence be selectively retained. Separations of compound mixtures in reversed-phase liquid chromatography (RPLC) are often described by either solute retention through partitioning or absorption processes between stationary and mobile phases. Such models are adequate to describe a wide range of analytical solute retentive processes but are limited in accounting for the retention behavior of solutes with similar polarity and fixed conformational structures. In such cases, the use of “shape-selective” stationary phases generally yields improved separations, for which subtle differences in molecular * Corresponding author. E-mail: [email protected]. Telephone: (301) 9753116. Fax: (301) 977-0685. † Analytical Chemistry Division. ‡ Physical and Chemical Properties Division.

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shape control selectivity1,2 rather than other physical or chemical properties of the solute. The more commonly employed shapeselective alkyl-modified material for such separations is the polymeric C18 phase, which is typically prepared through silanization of microparticulate silica by solution polymerized alkylsilanes.3 These stationary phases have been characterized using 29Si nuclear magnetic resonance (NMR) and, on average, are composed of five-unit oligomers that are bound to the surface through three to four siloxane bonds.4 The use of polymeric C18 stationary phases in analytical applications has greatly improved the separations of constrained solutes, such as carotenoids,5,6 steroids,7 the geometric isomers of unsubstituted and methylated polycyclic aromatic hydrocarbons (PAH and MPAHs),2,8,9 and polychlorinated biphenyl (PCB) congeners.10 The biochemical properties and resulting toxicological effects of PCB congeners11 and PAH and MPAH isomers12 have been related to their molecular shape. Thus, the enhanced separation of individual geometric isomers of these classes of compounds will ultimately improve the characterization of PCBand PAH-contaminated materials and thus improve toxicological risk assessment. Likewise, the cis and trans isomeric forms of carotenoids are known to vary in biological activity;13 thus, separation of the individual forms is essential for the proper (1) Sander, L. C.; Pursch, M.; Wise, S. A. Anal. Chem. 1999, 71, 4821-4830. (2) Wise, S. A.; Sander, L. C. In Chromatographic Separations Based on Molecular Recognition; Jinno, K., Ed.; Wiley-VCH: New York, 1997; pp 1-64. (3) Sander, L. C.; Wise, S. A. Anal. Chem. 1995, 67, 3284-3292. (4) Fatunmbi, H. O.; Bruch, M. D.; Wirth, M. J. Anal. Chem. 1993, 65, 20482054. (5) Sander, L. C.; Sharpless, K. E.; Craft, N. E.; Wise, S. A. Anal. Chem. 1994, 66, 1667-1674. (6) Strohschein, S.; Pursch, M.; Ha¨ndel, H.; Albert, K. Fresenius J. Anal. Chem. 1997, 357, 498-502. (7) Olsson, M.; Sander, L. C.; Wise, S. A. J. Chromatogr. 1991, 537, 73-83. (8) Wise, S. A.; Sander, L. C.; Lapouyade, R.; Garrigues, P. J. Chromatogr. 1990, 514, 111-122. (9) Wise, S. A.; Bonnett, W. J.; Guenther, F. R.; May, W. E. J. Chromatogr. Sci. 1981, 19, 457-465. (10) Sander, L. C.; Parris, R. M.; Wise, S. A.; Garrigues, P. Anal. Chem. 1991, 63, 2589-2597. (11) McFarland, V. A.; Clarke, J. U. Environ. Health Perspect. 1989, 81, 225239. (12) Yang, S. K.; Silverman, B. D. Polycyclic Aromatic Hydrocarbon Carcinogenesis: Structure-Activity Relationships; CRC Press: Boca Raton, FL, 1988. (13) O’Neil, C. A.; Schwartz, S. J. J. Chromatogr. 1992, 624, 235-252. 10.1021/ac0510843 Not subject to U.S. Copyright. Publ. 2005 Am. Chem. Soc.

Published on Web 11/12/2005

assessment of their biochemical properties and potential health benefits. The factors that influence shape-selective separations on alkylsilane stationary phases have been investigated through a wealth of experimental spectroscopic14-25 and chromatographic1,2,26-30 studies. A recent review31 of the progress achieved in the investigation of alkyl-modified surface architecture provides a more complete summary of such studies in the context of stationaryphase order and shape recognition properties. In the case of C18 phases, enhanced shape selectivity is observed with higher bonding density (5-6 µmol/m2) polymeric stationary phases assembled from polymerized alkylsilanes bound to a silica surface in contrast to the lower bonding density (2-3.5 µmol/m2) monomeric phases, which are prepared with monofunctional alkylsilanes through single-bond linkages with silanols at the silica surface. A growing body of evidence1,3,31 now suggests that this difference primarily results from the bonding density variation rather than the type of bonding chemistry employed. An increase in shape recognition has been observed for stationary phases with increased surface density1,3 where the overall alkyl chain proximity likely induces conformational order. The mobile-phase composition has a negligible effect on shape recognition.28 Other parameters, such as increased alkyl chain length32,33 and decreased column temperature,34-36 also increase alkyl chain conformation order and are the focus of a companion paper in this series. In general, shape selectivity is influenced by any chromatographic parameter that increases alkyl chain conformation order. The shape selectivity of an RPLC stationary phase is characterized by its ability to separate solutes based on their molecular shapes. Several chromatographic tests have been utilized based on retention differences of planar and nonplanar solutes. Standard (14) Singh, S.; Wegmann, J.; Albert, K.; Muller, K. J. Phys. Chem. B 2002, 106, 878-888. (15) Albert, K. J. Sep. Sci. 2003, 26, 215-224. (16) Pursch, M.; Strohschein, S.; Ha¨ndel, H.; Albert, K. Anal. Chem. 1996, 68, 386-393. (17) Pursch, M.; Sander, L. C.; Egelhaaf, H. J.; Raitza, M.; Wise, S. A.; Oelkrug, D.; Albert, K. J. Am. Chem. Soc. 1999, 121, 3201-3213. (18) Sander, L. C.; Glinka, C. J.; Wise, S. A. Anal. Chem. 1990, 62, 1099-1101. (19) Doyle, C. A.; Vickers, T. J.; Mann, C. K.; Dorsey, J. G. J. Chromatogr., A 2000, 877, 41-59. (20) Henry, M. C.; Wolf, L. K.; Messmer, M. C. J. Phys. Chem. B 2003, 107, 2765-2770. (21) Ducey, M. W., Jr.; Orendorff, C. J.; Pemberton, J. E.; Sander, L. C. Anal. Chem. 2002, 5576-5584. (22) Ducey, M. W., Jr.; Orendorff, C. J.; Pemberton, J. E.; Sander, L. C. Anal. Chem. 2002, 5585-5592. (23) Jinno, K.; Wu, J.; Ichikawa, M.; Takata, I. Chromatographia 1993, 37, 627634. (24) Sander, L. C.; Callis, J. B.; Field, L. R. Anal. Chem. 1983, 55, 1068-1075. (25) Singh, S.; Wegmann, J.; Albert, K.; Muller, K. J. Phys. Chem. B 2002, 106, 878-888. (26) Hesselink, W.; Schiffer, R. H. N. A.; Kootstra, P. R. J. Chromatogr., A 1995, 697, 165-174. (27) Sander, L. C.; Wise, S. A. Anal. Chem. 1984, 56, 504-510. (28) Sander, L. C.; Wise, S. A. J. Chromatogr., A 1993, 656, 335-351. (29) Wise, S. A.; May, W. E. Anal. Chem. 1983, 55, 1479-1485. (30) Wise, S. A.; Sander, L. C. J. High Resolut. Chromatogr. 1985, 8, 248-255. (31) Sander, L. C.; Lippa, K. A.; Wise, S. A. Anal. Bioanal. Chem. 2005, 382, 646-668. (32) Bell, C. M.; Sander, L. C.; Fetzer, J. C.; Wise, S. A. J. Chromatogr., A 1996, 753, 37-45. (33) Sander, L. C.; Wise, S. A. Anal. Chem. 1987, 59, 2309-2313. (34) Hesselink, W.; Schiffer, R. H. N. A.; Kootstra, P. R. J. Chromatogr., A 1995, 697, 165-174. (35) Sander, L. C.; Wise, S. A. J. Sep. Sci. 2001, 24, 910-920. (36) Sentell, K. B.; Henderson, A. N. Anal. Chim. Acta 1991, 246, 139-149.

Reference Material (SRM) 869a Column Selectivity Test Mixture for Liquid Chromatography37 evaluates the RPLC retentive behavior of three PAHs, (phenanthro[3,4-c]phenanthrene (PhPh), tetrabenzonaphthalene (TBN). and benzo[a]pyrene (BaP)), two of which are nonplanar (PhPh and TBN). The elution order for these PAHs changes depending on the phase type; for monomeric phases, BaP elutes before the nonplanar PAHs (PhPh and TBN), whereas for polymeric phases, the planar BaP elutes last. The elution order ratio (k′) for the nonplanar (TBN) and planar (BaP) solutes (i.e., RTBN/BaP ) k′TBN/k′BaP) therefore provides a numerical assessment of the phase’s shape selectivity. Values of RTBN/BaP < 1 are typical of highly shape selective phases (e.g., polymeric C18 columns), values between 1 < RTBN/BaP < 1.7 are considered intermediate, and values of RTBN/BaP > 1.7 are more typical of monomeric C18 columns with reduced shape recognition.1 Thus, this shape selectivity factor RTBN/BaP is used to predict how effectively a particular RPLC phase will separate isomer mixtures and solutes with constrained molecular shape. As described herein, a considerable amount of experimental effort has been exerted to characterize the conformational structure of alkyl-modified surfaces used in RPLC. A number of theoretical approaches through molecular simulation techniques have also been employed to elucidate the specific structural features that may control such solute retention processes.38-51 Klatte and Beck described molecular dynamic (MD) simulations for chromatographically relevant models consisting of C8-, C12-, and C18-modified surfaces over a range of alkyl chain densities in a vacuum40,41 and within water/methanol solvent mixtures.42 The surface topography of the C18 phases in a vacuum was characterized as rough and disordered at lower densities, and ∼25% gauche defects were overall present in the chains at room temperature.40,41 Yarovsky et al. studied n-alkyldimethylsilyl (C4, C8, and C18) modified amorphous silica at surface densities of 1.6-3.7 µmol/ m2.48 It was observed that both alkyl chain gauche fractions and overall chain mobility were reduced for higher density phases. Mountain and co-workers have examined a system of selfassembled octadecylthiol chains in a vacuum43 as well as an RPLC model consisting a slab of aqueous solvent (methanol, acetonitrile) surrounded by C8 chains at 5.1 µmol/m2 density.46 The C8 alkyl (37) Certificate of Analysis, Standard Reference Material 869a, Column Selectivity Test Mixture; National Institute of Standards and Technology, Gaithersburg, MD, 1998. (38) Ban, K.; Saito, Y.; Jinno, K. Anal. Sci. 2004, 20, 1403-1408. (39) Beck, T. L.; Klatte, S. J. In Unified Chromatography; Parcher, J. F., Chester, T. L., Eds.; American Chemical Society: Washington, DC, 2000; pp 67-81. (40) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1993, 97, 5727-5734. (41) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1995, 99, 16024-16032. (42) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1996, 100, 5931-5934. (43) Mountain, R. D.; Hubbard, J. B.; Meuse, C. W.; Simmons, V. J. Phys. Chem. B 2001, 105, 9503-9508. (44) Schure, M. R. In Chemically Modified Surfaces; Pesek, J. J., Leigh, I. E., Eds.; The Royal Society of Chemistry: Cambridge, U.K., 1994; pp 181-189. (45) Schure, M. R. Adv. Chromatogr. 1998, 39, 139-200. (46) Slusher, J. T.; Mountain, R. D. J. Phys. Chem. B 1999, 103, 1354-1362. (47) Wick, C. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2004, 76, 28862892. (48) Yarovsky, I.; Aguilar, M. L.; Hearn, M. T. W. Anal. Chem. 1995, 67, 21452153. (49) Zhang, L.; Sun, L.; Siepmann, J. I.; Schure, M. R. J. Chromatogr., A 2005, 1079, 127-135. (50) Zhuravlev, N. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2001, 73, 4006-4011. (51) Ashbaugh, H. S.; Pratt, L. R.; Paulaitis, M. E.; Clohecy, J.; Beck, T. L. J. Am. Chem. Soc. 2005, 127, 2808-2809.

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chain end-to-end distance profile was bimodal in nature, with a small portion of fully extended chains with an all-trans configuration and the majority of chains containing a mixture of gauche defects (reduced end-to-end distance). The presence of solvents did not significantly influence the end-to-end distance or tilt angle of the alkyl chains. Ban et al.38 described a monomeric phase model constructed of low-density (1.9 µmol/m2) octadecyldimethylsilyl ligands on amorphous silica subjected to various solvent environments (water, methanol, n-hexane). The distribution of solvent molecules within the alkyl phase changed with solvent composition; however, a distinct solvent layer between the alkyl chains was observed in the case of pure water. More recently, Ashbaugh et al.51 described a system of n-C18 alkyl chains tethered to a solid surface (at 50% surface coverage) in contact with a water layer at 300 K. In this model, the water molecules sufficiently permeate into the interfacial region of the alkyl chains; this effect was attributed, in part, to the inherent roughness of the alkyl layer at the surface coverage investigated. Wick et al.47 also applied Monte Carlo simulations to RPLC models composed of a n-hexadecane retentive phase with a varying water/methanol composition mobile phase. The partition coefficients of alkane and alcohol solute probes were quantified in an effort to characterize RPLC retention thermodynamics. Zhang et al.49 has recently investigated the conformation of an intermediate density (2.9 µmol/m2) dimethyl octadecyl/silica model in the presence of pure water through Monte Carlo simulations; a broad distribution of alkyl chain conformational states was observed, rather than any significant phase collapse due to presence of 100% aqueous solvent. Further details of these studies are also provided in several reviews.31,39,45 These prior simulation studies of monomeric-type RPLC phases under variable solvent conditions are directly relevant to the application of chromatography phases commonly used in analytical separations. However, the lessons learned from these investigations are limited in clarifying the potential factors that may control shape recognition processes on shape-selective polymeric C18 alkylsilane stationary phases. In this paper, we describe the application of molecular dynamic simulation techniques to investigate the structural features of various C18 alkylsilane chromatographic models as part of our ongoing experimental1,31 and computational52 efforts to understand the specific mechanism of the shape-selective retention process that has been observed with polymeric C18 stationary phases. Specifically, we have simulated both monomeric- and polymerictype C18 stationary phases (Figure 1) over a range of densities (1.6-5.9 µmol/m2) to compare alkyl chain order and overall phase thickness and topography between the two phase types. Additional models with polymeric alkylsilane ligands of varying polysiloxane chemistry were also simulated (see Supporting Information, Figure S-1). Structural features such as end-to-end chain length, phase thickness, chain tilt angle, gauche dihedral angle profile along the alkyl chain, and carbon density profile throughout the alkyl phase were examined. The structural details of chromatography models that represent RPLC chromatographic phases for which shape-selectivity numerical descriptors (RTBN/BaP) have been measured were compared in an effort to identify key structural (52) Lippa, K. A.; Sander, L. C.; Wise, S. A. Anal. Bioanal. Chem. 2004, 378, 365-377.

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Figure 1. Structure representation of (a) monomeric C18 and (b) polymeric C18 chromatography models illustrating the different ligand types.

features that may be responsible for controlling such shapeselectivity processes. Complimentary simulations of alkylsilane models of various chain length (C8, C18, C30) subject to various temperature conditions (-5 to 59 °C) are the focus of part 2 of this series;53 these monomeric and polymeric models were constructed to closely resemble RPLC phases for which their shape-selective behavior has been well characterized over a range of temperatures. The study described herein and in part 2 of this series53 together represent the initial, nonsolvated component of our shapeselectivity modeling efforts to investigate constrained solute retention processes. Fully solvated computational models of shapeselective RPLC systems will be the subjects of subsequent work. COMPUTATIONAL METHODS Chromatography Model Description. A silica model was constructed by slicing a 7.5-Å-thick segment of the (101) face of a quartz crystalline lattice with width dimensions of 41 × 59 Å. (53) Lippa, K. A.; Sander, L. C.; Mountain, R. D. Anal. Chem. 2005, 77, 78627871 (ac051085v).

This resulted in a surface with a vicinal silanol density of 9.8 µmol/ m2. Although this value is higher than the commonly reported (8.0 ( 1.0 µmol/m2)54 silanol concentration of silica, this surface with its extensive array of vicinal silanols facilitates the placement of ligands randomly over a wide range of densities. Chromatography models were created by covalently tethering alkylsilane ligands (with the alkyl chains in an initial all-trans conformation) to the silanol oxygen atoms of the quartz surface and at an orthogonal (⊥) position to the bulk quartz (Figure 1). A 15-Å vacuum layer was fixed above the ligands, resulting in a unit cell with dimensions of 41 × 59 × 50 Å. Ligands were evenly distributed over the surface silanols in a randomized fashion to result in a specific surface coverage. Duplicate models at selected densities were constructed to determine any biases in the manual ligand placement on the surface; similar results were obtained for these replicate models. Monomeric- and polymeric-type alkylsilane ligands of carbon length 18 were employed in these simulation models. The monomeric phases, for example, would have a dimethyloctadecyl ligand that was tethered to a silica surface via a single silanol (Figure 1a). Polymeric alkylsilane ligands of varying bond chemistry types were also constructed. Here, idealized polymeric C18 ligands were constructed in four ways: (1) trifunctional, triC18 (originating from the solution reaction of trichlorooctadecylsilane in water forming a polymer of three alkylsilane units, Figure 1b); (2) difunctional (originating from the solution reaction of dichloromonomethyl-octadecylsilane in water forming a polymer of three alkylsilane unit (Figure 1b); (3) trifunctional, branched 12-mer-C18 (originating from the solution reaction of trichlorooctadecylsilane in water forming a linearly branched polymer of 12 alkylsilane units; see Supporting Information, Figure S-1a); and (4) trifunctional, cyclic 12-mer-C18 (originating from the solution reaction of trichlorooctadecylsilane in water forming a six-member cyclic polymer with a total of 12 alkylsilane units; see Figure S-1b). These polymer ligands were also tethered to the quartz surface via one silanol. To test the influence of the silanol concentration and surface arrangement on the resulting alkylsilane ligand conformation, additional silica models were constructed by slicing a 8.8-Å-thick segment of the (101) face of a β-cristoballite crystal resulting in a 51 × 53 Å silica model with a vicinal silanol density of 7.6 µmol/ m2. A monomeric C18 and trifunctional tri-C18 polymeric model was created with surface coverages of 2.43 and 4.86 µmol/m2, respectively. Similar results were obtained to the quartz models at comparable surface coverages. The influence of the type of silica surface structures and silanol groups on the molecular simulations of monomeric-type chromatography models with various alkyl ligands has been previously described by Zhuravlev et al.50 Molecular Dynamics. The molecular systems were subject to a constant-volume, constant-temperature MD simulation method using the Discover molecular dynamics module employing the COMPASS force field55,56 within Cerius2 (v. 4.6) and Materials Studio (v. 2.2) software (Accelrys, Inc., San Diego CA). An atombased summation method was utilized with the nonbonded interactions cutoff set to a distance of 11.0 Å, accompanied by a spline width of 1.0 Å and a buffer width of 0.5 Å. A group-based (54) Nawrocki, J. J. Chromatogr., A 1997, 779, 29-71. (55) Sun, H.; Rigby, D. Spectrochim. Acta, Part A 1997, 53, 1301-1323. (56) Sun, H. J. Phys. Chem. B 1998, 102, 7338-7364.

Figure 2. Structural descriptors used to measure alkyl chain and phase order.

summation method and various cutoff distances (up to 20 Å) and spline widths for both summation methods were also tested. More rigorous methods, such as cell multipole and Ewald sums, were too computationally expensive to apply to the relatively large molecular systems described here. The initial models with 3D periodic boundary conditions were first minimized using the steepest descent convergence method, followed by a conjugate gradient method until the convergence reached 0.1 kcal/mol‚Å. The constant-volume, constant-temperature systems were then subject to equilibration for 100 ps with a time step of 1 fs. Temperature control was maintained by the Nose´-Hoover thermostat57 at the appropriate temperature (298 K). MD simulation was then allowed to progress with the same operational conditions for up to 2500 ps. The atomic positions of the bulk quartz surface (with the exception of the exposed surface silanols) were held constant during both equilibration and simulation steps. The atomic coordinates of the MD simulation models were recorded at 1-ps intervals for analysis. Structural Analysis. Following MD simulation, selected structural parameters that describe the order of alkylsilane chains of the model were determined for each picosecond over a total of 100 ps. These included the alkylsilane chain spacing and length, phase thickness, chain tilt angle, and dihedral angles (Figure 2) as well as the carbon density profiles in the direction orthogonal to the quartz surface (z). The phase thickness was determined as the magnitude of the alkylsilane chain length vector in the z direction. The tilt angle (θ) was determined from the cosine ratio between the phase length and the chain length (Figure 2). Dihedral angles were measured along the alkylsilane chain beginning with the tethering point to the quartz surface (Si atom) (ω1) and through the terminal carbon atom of the chain (ω16); these angles were classified as a gauche defect for magnitudes (57) Hoover, W. G. Phys. Rev. A 1985, 31, 1695-1697.

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Table 1. Structural Details of Simulated C18 Alkylsilane Chromatographic Phase Models

ligand type

chain density (µmol/m2)

average chain spacinga,b(Å)

monofunctional C18 monofunctional C18 monofunctional C18 monofunctional C18 monofunctional C18 monofunctional C18

1.71 2.46 3.28 3.28h 4.91 4.91h

9.5 ( 1.4 7.6 ( 0.6 7.2 ( 0.7 5.3 ( 1.0 5.2 ( 0.8 4.1 ( 0.4

trifunctional, tri-C18 trifunctional, tri-C18 trifunctional, tri-C18 difunctional, tri-C18 trifunctional, tri-C18 trifunctional, tri-C18 difunctional, tri-C18 trifunctional, tri-C18 trifunctional, branched12-mer-C18 trifunctional, cyclic 12-mer-C18 trifunctional, tri-C18

1.64 2.46 3.28 3.89 4.09 4.30 4.91 4.91 4.91

average end-to-end chain lengthb,c(Å)

average phase thicknessb,d(Å)

average tilt angleb,e (θ)

average % of gauche dihedrals

Monomeric 14.9 ( 2.3 15.4 ( 3.0 16.8 ( 2.9 19.6 ( 2.6 21.5 ( 1.2 21.9 ( 1.8

9.0 ( 4.6 12.5 ( 3.9 15.7 ( 3.3 19.0 ( 3.1 21.3 ( 1.3 21.6 ( 2.1

50.3 ( 22.4 34.8 ( 15.1 19.7 ( 10.3 13.4 ( 9.7 7.8 ( 3.9 8.5 ( 5.1

38.2 39.1 38.4 26.3 16.0 13.0

3.1 ( 0.2 3.1 ( 0.1 3.1 ( 0.1 3.1 ( 0.1 3.1 ( 0.2 3.1 ( 0.2 3.1 ( 0.2 3.1 ( 0.1 3.1 ( 0.2

Polymeric 14.0 ( 3.6 17.1 ( 3.5 20.9 ( 1.6 21.2 ( 1.9 21.4 ( 1.4 21.3 ( 1.9 21.9 ( 0.9 21.3 ( 1.3 21.6 ( 1.2

9.7 ( 4.2 14.3 ( 5.0 19.4 ( 2.3 20.2 ( 5.0 21.1 ( 1.6 21.1 ( 2.5 21.7 ( 1.1 20.9 ( 1.6 21.1 ( 1.5

44.6 ( 18.4 30.5 ( 18.4 19.7 ( 10.2 13.7 ( 20.4 8.7 ( 4.3 9.3 ( 7.4 7.6 ( 4.2 8.5 ( 5.0 8.8 ( 5.8

34.2 32.4 20.4 18.7 19.6 18.2 14.1 19.2 15.7

4.91

3.1 ( 0.2

22.1 ( 1.1

21.8 ( 1.2

9.9 ( 4.7

12.6

5.94

3.0 ( 0.2

22.2 ( 0.9

22.1 ( 1.0

6.1 ( 2.7

10.4

phase selectivity RTBN/BaPf and categoryg

1.72 (L)

1.61 (I) 1.11 (I) 0.71 (H)

0.49 (H)

a Distance between Si atoms of the alkylsilane chains. b Uncertainty represents standard deviation of 100 measurements. c Distance between Si atom and end C atom of the alkylsilane chain. d Magnitude of the distance vector between Si and end C of the alkylsilane chain perpendicular to the quartz surface. e Relative to the axis perpendicular to the quartz surface. f Experimentally determined selectivity coefficients for C18 RPLC phases at room temperature that are represented by simulation models (see ref 33 for more details). g Shape selectivity of stationary phases categorized as high (H; RTBN/BaP < 1), intermediate (I; 1 < RTBN/BaP < 1.7), and low (L; RTBN/BaP > 1.7). h Ligands placed in a clustered formations to minimize interchain spacing.

greater than 66°. Average chain spacing was determined as the distance between the silicon atoms of the alkylsilane ligands, whether directly bound to the quartz surface (as in the case of the monomeric phases) or within the polysiloxane network of the ligands (as in the case of the polymeric phases). The molecularlevel features within each model (i.e., chain length, tilt angle (θ)) were averaged for each alkyl chain over a 100-ps interval; the model was deemed stable when the 100-ps interval averages of these parameters were constant over four successive intervals (400 ps total). In most cases, these parameters remained constant by 1000 ps. Only in the lower density models (e.g., 1.7 µmol/m2) was stability delayed until >1800 ps. RESULTS AND DISCUSSION A group of C18 alkylsilane chromatography models of both monomeric and polymeric types was constructed over a range of densities (1.64-5.94 µmol/m2) to discern the influence of ligand density and type on the overall order of the alkyl phase. The structural details (Figure 2) of the models following molecular dynamics simulations are presented in Table 1. These values represent an average of the parameters measured over a 100-ps time frame (100 measurements) and for each alkyl chain present in the model with the corresponding standard deviations. Also included in this table for comparative purposes are the shapeselectivity descriptors (RTBN/BaP) of similar density RPLC phases. Side- and top-view snapshots of selected monomeric and polymeric chromatographic phase models at comparable ligand densities are provided in Figure 3 and represent the atomic positions of the last measurement within the 100-ps time frame used to collect the structural data. These snapshots are primarily used to illustrate 7856 Analytical Chemistry, Vol. 77, No. 24, December 15, 2005

the structural trends within the computational models and are not intended to substitute for quantitative results. Chain Gauche Defects. Generalized trends of the effect of ligand density on overall chain order can be made through an examination of the average percentage of gauche dihedrals (Table 1). An overall reduction in chain gauche dihedrals is observed as the ligand density increases for both the monomeric and polymeric models. This is consistent with the review31 of spectroscopic (Fourier transform infrared (FT-IR), Raman, NMR) evidence for increase alkyl chain order for higher bonding densities as well as with the results observed from previous simulation studies for monomeric-type systems over various surface densities.41,48 The proximity of the neighboring alkyl chains restricts the flexibility of the chains, and thus, an increase in chain order (reduction in gauche defects) is observed. However, to fully characterize the overall conformation of the alkyl chains relative to the quartz surface, an examination of the individual dihedral angles (1-16) along the alkylsilane chain is necessary to determine the extent and location of disorder along the chain. The fraction of gauche dihedral angle defects (defined as a magnitude greater than 66°) for each dihedral along the chain (1-16) for both the monomeric and polymeric phase models at various densities is illustrated in Figure 4. Dihedral 1 describes the conformation of the Si-C1-C2-C3 bond proximal to the quartz surface whereas dihedral 16 describes the conformation of the C15-C16-C17-C18 bond, including the terminal methyl carbon at the distal end of the chain. For the monomeric C18 models, a significant alternation of the dihedral angle profile between relatively high and low gauche

Figure 3. Side- and top-view snapshots of simulated (a) monomeric C18 and (b) polymeric C18 chromatography models at various surface coverages. The atoms are color-coded according to the legend; H atoms are not displayed in the interest of clarity.

fractions exists in the proximal portion of the chain over the wide range of ligand densities examined (Figure 4a). It is likely that alignment of the alkylsilane chain through rotation about the tethering point (OquartzsSialkylsilane) is hindered by the steric constraints imposed by the bulky CH3 groups of dimethyloctadecylsilane ligand. The extensive gauche state in the proximal carbons may be necessary to redirect the alkyl chain conformation

to maximize the association of alkyl segments toward the distal end of the chain. This is exemplified in the proximal portion of the chain for the monomeric C18 model at a relatively high density (4.91 µmol/m2). It is also important to highlight that this highdensity monomeric C18 model was created in this study to directly compare with polymeric C18 models and does not reflect a laboratory-relevant stationary phase. Typically, monomeric phases Analytical Chemistry, Vol. 77, No. 24, December 15, 2005

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Figure 4. Dihedral angle profiles for (a) monomeric C18 and (b) polymeric, trifunctional tri-C18 chromatography models.

prepared from the relatively bulky and less reactive dimethylmonomchlorosilanes result in surface coverages of 3.9 µmol/m2 or less.58 Such a variable pattern in the dihedral angle profile near the quartz surface is not observed for the polymeric C18 models (Figure 4b). Overall, the change in dihedral angles along the chains is more modest, with the greatest change in the fraction of gauche defects occurring between the first two dihedrals for only the lower densities models (1.64 and 2.46 µmol/m2) and near the midpoint of the chains for the lowest density model (1.64 µmol/m2). For the more moderate to high ligand densities (3.285.94 µmol/m2), a consistent decrease in gauche defects is observed toward the distal end of the chains. A more conservative trend is observed with the FT-IR studies of Singh et al.14 in which the quantity of gauche conformers was characterized for n-alkylmodified silicas with selective deuteration along the alkyl chain. Three C18-modified surfaces at ∼4 µmol/m2 were deuterated (CD2) at chain positions C4, C6, and C12; at room temperature, the gauche conformers were 40, 20, and 25%, respectively, and reflect a general trend of conformational order toward the distal end of the alkyl chain. The effect of bonding chemistry on the overall structure of the alkyl phase can be examined by comparing the dihedral angle profiles for both monomeric and polymeric models at comparable densities. Profiles for the monomeric and polymeric models at 2.46, 3.28, and 4.91 µmol/m2 surface coverages are provided in the Supporting Information (Figure S-2a,b,c). At the lowest comparable surface coverage (2.46 µmol/m2), the dihedral angle distribution is generally similar between monomeric- and polymerictype ligands, with the exception of the relatively high fraction of gauche defects at dihedrals 1 and 6 for the monomeric model. Toward the distal end of the C18 chain, however, both ligand types result in a similar fraction of gauche defects (∼0.25). A similar trend is observed for the models with high surface coverage (4.91 µmol/m2). Both the polymeric models constructed from difunc(58) Sander, L. C.; Wise, S. A. Crit. Rev. Anal. Chem. 1987, 18, 299-415.

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tional and trifunctional tri-C18 ligands illustrated a steady reduction in gauche defects from 15 Å; this alternatively can be described as broad interface between the alkyl stationary phase layer and the vacuum layer above the chains. In the case of the polymeric model at comparable density (1.64 µmol/m2), significant chain “kinking” was also observed midpoint along the chain (Figure 4b), together with overall chain tilting (θ ) 45° ( 18°). A visual inspection of the simulation snapshots (Figure 3b), however, illustrates the tendency of the polymeric ligands to aggregate and form clusters and cavities with considerable amount of exposed quartz surface. The trifunctional polymeric ligands were observed to rotate about their tethering point (OquartzsSialkylsilane) during the simulation to maximum contact of the alkylsilane chains with those of the neighboring polymeric ligand. This results in a surface topography that is disordered but also isolated into distinct alkyl sections. An overall increase in phase thickness is observed for an increase in surface coverage for both the monomeric and polymeric stationary-phase models. This is illustrated by the steady increase in both the average phase thickness (Table 1) and extension of the carbon density profiles along the z axis (Figure 5) for the models over a density range of 1.6-3.28 µmol/m2. For the monomeric phase models, however, the average percentage of gauche dihedrals does not change appreciably over this density range; the increase in phase thickness is a likely a result of a reduction in tilt angle (θ) from 50° to 20°. Notably, the calculated phase thickness value of 16 ( 3 Å for the 3.28 µmol/m2 C18 monomeric model is well within the range of experimentally determined values (17 ( 3 Å) from small-angle neutron scattering 7860 Analytical Chemistry, Vol. 77, No. 24, December 15, 2005

(SANS) experiments18 on a common-employed C18 monomeric stationary phase at 3.7 µmol/m2. The resulting topography of these models is still rough and disordered, with peak-to-valley distances of up to 8 Å (Figures 3a and 6a) and significant densities of carbon well into the middle of the alkyl phase. Such irregular surfaces are comparable to those observed by Klatte and Beck41 for alkane stationary-phase chain systems at 2.5 and 3.25 µmol/m2 at 300 K. For the polymeric models, a significant decrease in the average percentage of gauche dihedrals is observed for the surface coverage range of 1.6-3.28 µmol/m2 (Table 1). This change is most prominent in the upper region of the chains (dihedrals 8-16) for the 3.28 µmol/m2 model (Figure 4b). A reduction in both gauche defects and tilt angle results in a significant increase in phase thickness. Furthermore, a comparison of the carbon density profiles (Figure 5) for the monomeric and polymeric models at moderate surface coverage (3.28 µmol/m2) illustrates subtle differences between the monomeric and polymeric ligand types. Here, the polymeric model profile is more similar to the higher density (4.09 and 4.91 µmol/m2) profiles, in contrast to the monomeric models at comparable densities. This difference is also highlighted by the snapshots of the 3.28 µmol/m2 density monomeric and polymeric models in Figure 3a and b, respectively. The top-view projection of the polymeric model clearly illustrates the formation of cavities within the alkyl chains; such a structural change may indicate a critical density for polymeric RPLC phases at which chain aggregation and extension is enhanced by the initial, ordered placement of the alkyl chains of the silane polymer. At higher surface densities (>4 µmol/m2), the chains exhibit a significant reduction in overall gauche defects (