Surface Coverages of Bonded-Phase Ligands on Silica: A

Anal. Chem. 2001, 73, 4006-4011

Surface Coverages of Bonded-Phase Ligands on Silica: A Computational Study Nikolay D. Zhuravlev† and J. Ilja Siepmann†

Departments of Chemistry and of Chemical Engineering and Materials Science, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431 Mark R. Schure*,†

Theoretical Separation Science Laboratory, Rohm & Haas Company, 727 Norristown Road, Springhouse, Pennsylvania 19477

A computational study of the packing of various bondedphase ligands bound to chromatographic silica is presented. This is done with the intention of examing the type of surface structures that are typically found in real chromatographic systems. Utilizing the surface structure of the (111) face of the β-cristobalite crystal, it is shown that the maximum surface coverages of dimethyloctylsilane, dimethyloctadecylsilane, triisopropylsilane, diisopropyloctylsilane, and diisopropyloctadecylsilane can be calculated that are in good agreement with experiment. The maximum surface coverages are also calculated for the (100) face of the β-cristobalite crystal and for a set of random silica surfaces. The coverages for the latter two surfaces types are found to be significantly lower than the experimental values for chromatographic silica surfaces. These results further suggest that chromatographic silica surfaces may resemble crystalline surface sites similar to the (111) face of β-cristobalite, as has been previously suggested in the literature. Hence, these structures can be reliably utilized in molecular simulations of bondedphase chromatography where the atomic-level detail of the silica surface has been previously lacking. The efficacy of reversed-phase liquid chromatography (RPLC) is based to a large extent on the reproducibility, efficiency, and selectivity of the retentive material.1 The most common of these materials is a chemically bonded phase composed of long-chain alkanes, typically 18 carbons in length, bound to a silica support. Numerous studies have been conducted into retention mechanisms that drive the differential phase equilibria leading to separation in RPLC.2-4 These mechanisms have been largely categorized as partitioning or adsorption. These designations are general and refer to the interaction of the solute with the retentive phase as a liquid partitioning process or as a surface adsorption † E-mail addresses: [email protected]; [email protected]; [email protected]. (1) Snyder, L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography; John Wiley and Sons: New York, 1979. (2) Vailaya, A.; Horva´th, C. J. Phys. Chem. B 1997, 101, 5875-5888. (3) Vailaya, A.; Horva´th, C. J. Chromatogr., B 1998, 829, 1-27. (4) Ranatunga, R. P. J.; Carr, P. W. Anal. Chem. 2000, 72, 5679-5692.

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process. It is presently thought4 that most small molecules of low polarity favor a partitioning process. Direct mechanistic evidence of this is extremely difficult to get because thermodynamic-based measurements that utilize retention times or other measurements of phase equilibria cannot yield a molecular picture of the retention mechanism. Clearly, thermodynamics is essentially a “bookkeeping” system which cannot directly give mechanistic details at a molecular level but can only infer mechanistic details. Spectroscopic studies that probe chain dynamics of bonded phases and solute interactions have been difficult to conduct. Because the chromatographic interaction time scale is in the picosecond to microsecond regime, NMR measurements are not able to yield a complete dynamical model of the bonded phase.5-7 However, NMR has provided invaluable information regarding the silica chemical structure and chemical structure at the silicachain bond.5,6,8,9 Both infrared10 and fluorescence techniques11 have provided a wealth of static information with regard to the alkyl chain conformation. Dynamical aspects of chain and solute-chain dynamics can be determined by fluorescence spectrometry.12,13 A recently introduced paradigm for studying the chromatographic retentive phase in RPLC is that of computer simulation.14-16 In this mode of study, atomic-detail surface models of the C18 system have been utilized to simulate the dynamical processes of the chain system typically using the molecular dynamics (5) Albert, K.; Bayer, E. J. Chromatogr. 1991, 544, 345-370. (6) Ziegler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1991, 113, 6349-6358. (7) Sentell, K. B.; Bliesner, D. M.; Shearer, S. T. In Chemically Modified Surfaces; Pesek, J. J., Leigh, I. E., Eds.; Royal Society of Chemistry: Cambridge, England, 1994; pp 190-202. (8) Sindorf, D. W.; Maciel, G. E. J. Am. Chem. Soc. 1981, 103, 4263-4265. (9) Maciel, G. E.; Sindorf, D. W.; Bartuska, V. J. J. Chromatogr. 1981, 205, 438-443. (10) Sander, L. C.; Callis, J. B.; Field, L. R. Anal. Chem. 1983, 55, 1068-1075. (11) Lochmuller, C. H.; Colborn, A. S.; Hunnicutt, M. L.; Harris, J. M Anal. Chem. 1983, 55, 1344-1348. (12) Bogar, R. C.; Thomas, J. C.; Callis, J. B. Anal. Chem. 1984, 56, 10801084. (13) Hansen, R. L.; Harris, J. M. Anal. Chem. 1996, 68, 2879-2884. (14) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford Science Publications: New York, 1987. (15) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: San Diego, CA, 1996. (16) Schure, M. R. In Advances in Chromatography; Brown, P. R., Grushka, E., Eds.; Marcel Dekker Publishing: New York, 1998; Vol. 39, pp 139-200. 10.1021/ac010298r CCC: $20.00

© 2001 American Chemical Society Published on Web 07/18/2001

simulation technique.16,17,19 In most cases the solvent is absent; however, a few studies have included the solvent.16-19 The idea of using simulation is to obtain a detailed microscopic view of the solvent and solute interactions with the retentive phase. In this way, the mechanism of separation may be elucidated in an idealized structural system. For the most part, simulation has not currently revealed striking details of the RPLC system. However, the chain orientations have been elucidated along with some other details such as the interactions of multicomponent solvents with the chains.16,17,19 The ultimate success for simulation to be viewed as reliable is for simulation to be able to compute retention factors that compare favorably with experimental data. This has not been accomplished or undertaken for the simulation of RPLC but it has been accomplished for gas-liquid chromatography where the retention indices for some linear and branched alkane and alkylbenzene solutes have been accurately computed.20-22 These types of simulations are especially needed in RPLC to establish many of the microscopic details which will be needed for further understanding and improvement of the retentive phase. One aspect that has been missing from all of the previous RPLC simulation studies is the structural detail of the silica surface and the resulting geometry of bonding at the silica surface. For example, random silica surfaces have been modeled17 using the distribution of ring sizes obtained from other simulations.23 Most of the previous simulations do not use any model of silica16,19 but rather use some restraining potential19 or just constrain the motion of the terminal silicon atom on the chain. In this paper, we go back to the basics of this issue and postulate a number of silica surface structures that may be operational in describing the atomic structure of the RPLC experiment. Few studies have examined this issue with respect to the types of surface coverages that can be expected with different surfaces. In this regard, we do not model the surfaces with molecular modeling techniques such as molecular mechanics,24 molecular dynamics,14-16 or Monte Carlo techniques.14-16 What we do here is use known bond distances and angles and perform the bonding operation of alkylsilane ligands to the silica atoms as a geometry-preserving operation. Atoms are treated as hard spheres with radii taken to be their van der Waals radii. In particular, it will be shown that the (111) face of βcristobalite, a form of crystalline silica, when used as a surface model, gives very good agreement between the experimental surface coverages of Kirkland and Henderson25 for differing bonded ligands and the distance-based calculations presented here. The use of bulkier alkyl groups, for example, isopropyl (17) Schure, M. R. In Chemically Modified Surfaces; Pesek, J. J., Leigh, I. E., Eds.; Royal Society of Chemistry: Cambridge, England, 1994; pp 181-189. (18) Klatte, S. J., Beck, T. L. J. Phys. Chem. 1995, 99, 16024-16032. (19) Slusher, J. T.; Mountain, R. D. J. Phys. Chem. B 1999, 103, 1354-1362. (20) Martin, M. G.; Siepmann, J. I.; Schure, M. R. J. Phys. Chem. B 1999, 103, 11191-11195. (21) Martin, M. G.; Siepmann, J. I.; Schure, M. R. In Unified Chromatography; Parcher, J. F., Chester, T. L., Eds.; ACS Symposium Series 748; American Chemical Society: Washington, DC, 2000; pp 82-95. (22) Wick, C. D.; Martin, M. G.; Siepmann, J. I.; Schure, M. R. Int. J. Thermophys. 2001, 22, 111-122. (23) Feuston, B. P.; Garafolini, S. H. J. Chem. Phys. 1988, 89, 5818-5824. (24) Burkert, U.; Allinger, N. L Molecular Mechanics; ACS Monograph 177; American Chemical Society: Washington, DC, 1982. (25) Kirkland, J. J.; Henderson, J. W. J. Chromatogr. Sci. 1994, 32, 473-480.

groups at the base of the alkyl chains, for shielding unreacted silanols is discussed in detail. COMPUTATIONAL METHODOLOGY To build a model of the retentive phase, we follow a series of steps similar to the experimental method for synthesis of chemically modified silica phases. First, the unbonded silica substrate is created through an idealized model of bond distances and bond angles. Alkylsilane chains are then bound to the surface silanol oxygen groups with certain bond angles preserved for this bonding operation. This is similar to previous work from this laboratory.17 Although silica is thought to be amorphous, it has been shown to have some amount of short-range structural order.26-28 Thus, the (111) and (100) surfaces of the β-cristobalite crystal structure have been suggested to be useful as models of small silica segments.28-30 Another reason for choosing crystalline β-cristobalite is that it has a density and refractive index similar to that of silica.30 A surface model based on the β-cristobalite crystal structure can also account for the hydroxyl density on the silica surface. Specifically, the (111) surface fully covered with single silanol groups provides ∼4.6 silanol groups/nm2(7.6 µmol/m2). As reported by Sander and Wise,31 an unbonded chromatographic silica substrate has ∼4.8 silanols/nm2. The difference may be because silica has some amount of geminal groups. Geminal groups are two hydroxyl groups (i.e., silanols) bound to the same silicon atom. Vicinal silanols are the more common single hydroxyl group bound to the silicon atom. Furthermore, surface defects would be expected to be present in such a structure. Other experimental studies26,27 report 5 ( 1 silanols/nm2(8.3 (1.7 µmol/ m2). Some recent reviews and papers concerned with these aspects of silica and phase loadings are given in refs 32-36. Three surface structures are utilized for the study in this paper. These include the (111) and (100) faces of the β-cristobalite crystal structure and a set of random silica surfaces. These structures are built with a Fortran computer program. The bond lengths and angles employed in these structures are given in Table 1. The remaining angles and the structure of the all-trans alkyl chains are obtained from the Macromodel modeling program.37 The chains are energy minimized using the MM3 force field38 and the Polak-Ribiere conjugate gradient energy minimization algorithm contained in Macromodel. (26) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979; Chapter 6. (27) Unger, K. K. Porous Silica; Elsevier Scientific Publishing: New York, 1979. (28) Chuang, I.-S.; Maciel, G. E. J. Phys. Chem. B 1997, 101, 3052-3064. (29) Sander, L. C.; Wise, S. A. In Retention and Selectivity in Liquid Chromatography; Smith, R. M., Ed.; Elsevier Science B. V.: Amsterdam, The Netherlands, 1995; J. Chromatogr. Lib. 1995, 57, 337-369. (30) Sander, L. C.; Wise, S. A. J. Chromatogr., A 1993, 656, 335-351. (31) Sander, L. C.; Wise, S. A. In Advances in Chromatography; Giddings, J. C., Grushka, E., Cazes, J., Brown, P. R., Ed.; Marcel Dekker Publishing: New York, 1986; Vol. 25, pp 139-218. (32) Zhuravlev, L. T. Colloids Surf. A 2000 173 1-38. (33) Berthod, A. J. Chromatogr. 1991 549, 1-28. (34) Nawrocki, J. Chromatographia 1991 31, 177-192. (35) Nawrocki, J. Chromatographia 1991 31, 193-205. (36) Rustamov, I.; Farcas, T.; Ahmed, F.; Chan, P.; LoBrutto, R.; McNair, H. M.; Kazakevich, Y. V. J. Chromatogr., A 2001 913 49-63. (37) Mohamadi, F.; Richards, N. G. J.; Guida, W. C.; Liskamp, R.; Lipton, M.; Caufield, C.; Chang, G.; Hendrickson, T.; Still, W. C. J. Comput. Chem. 1990, 11, 440-467. (38) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 85518566.

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Table 1. Bond Lengths and Angles bond

length, Å

angle type

angle, deg

Si-O Si-C C-C C-H O-H

1.61 1.90 1.54 1.11 0.94

Si-O-Si O-Si-O Si-O-H

147.0 109.5 114.9

The average angles from energy minimization yield C-C-C, C-Si-C, H-C-H, and C-Si-O angles of approximately 112°, 110°, 110°, and 109°, respectively. Unwanted edge effects on the planar silica surface edges are avoided by employing periodic boundary conditions14-16 in the planar coordinates which make up the surface. A typical periodic box size is approximately 3 nm by 3 nm. The β-cristobalite structures are computed using the known atom connectivities and geometries which are coded in the Fortran program. The random silica structure is constructed as follows. Silicon atoms are placed on a 3 nm by 3 nm flat surface in a purely random fashion. The distance between two neighboring silicon atoms is constrained to be >5 Å. This limit is imposed by the structure of β-cristobalite. The program keeps putting silanols on the surface until it cannot find a free location. The search for a free location stops after 10 000 consecutive unsuccessful placement attempts. After building a silica substrate, alkyl chain ligands terminated with a silane group are attached to the surface as follows. First, a surface silanol site for binding with the ligand is randomly chosen. Then the ligand is bonded to the oxygen atom in the silanol group at the silane atom forming a Si-O-Si-alkane linkage. The Si-alkane bond is rotated while the surface silicon and oxygen atoms are kept fixed. A certain number of random rotations are done until the chain finds a position where it does not collide with other chains already on the surface. The ligands used for bonding in this study are trimethylsilane, dimethyloctylsilane, dimethyloctadecylsilane, triisopropylsilane, diisopropyloctylsilane, and diisopropyloctadecylsilane. Standard van der Waals parameters39 are utilized to check for atom collisions as the atoms are treated as hard spheres. For the sake of simplicity and speed, the alkyl chains are not allowed to undergo any conformational changes. The algorithm keeps searching for available silanol groups to bond the alkyl chains to until an exhaustive search has taken place. We use two sets of units in this paper to express surface coverages. These are micromoles per meter squared and molecules per nanometer squared. The two units are used simultaneously because experimental data are typically reported with the first set of units but theoretical studies usually use the second. These are related through Avogadro’s number so that the coverage in micromoles per meter squared when multiplied by 0.6022 gives the coverage in molecules per nanometer squared. All molecular visualizations use Raster3D V2.5f software40 to render the images. (39) Bondi, A. J. Phys. Chem. 1964, 68, 441-451. (40) Merritt, E. A.; Bacon, D. J. Raster3D V2.5f software. Methods Enzymol. 1997, 277, 505-524.

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RESULTS AND DISCUSSION The visualization of the (111) and (100) faces of β-cristobalite are shown in parts A and B of Figure 1, respectively, and a typical random silica surface phase is shown in Figure 1C. Note that all of these structures employ periodic boundaries so that connectivity through an edge to the opposite edge occurs. The silanol concentration for the (111) face model is ∼4.6 silanol groups/ nm2 (7.6 µmol/m2). In the case of the (100) face of β-cristobalite, all silanol groups are geminal, as shown in Figure 1B. This type of crystalline surface structure provides a silanol surface concentration of ∼8 silanol groups/nm2 (13.3 µmol/m2). This is much larger than the 4.8 silanols/nm2 (8.0 µmol/m2) given by Sander and Wise31 for a typical silica surface. In an early modeling effort of the silica surface, Peri and Hensley41 theorized that some silanols would be randomly removed in pairs. This would bring the silanol concentration to a more realistic value of 4.6 groups/nm2 (7.6 µmol/m2) for the (100) face of β-cristobalite, but this would require additional local changes to the underlying Si-O network. Overall, the resulting structure would be similar to that of an all-vicinal model. The random surface silanol concentration is lower than those present in a real silica substrate. Apparently the relatively high silanol concentration found in a real silica system can only be reached when silanol groups are arranged in a closely packed, highly regular (crystalline) manner. For example, the random surface model, under the distance constraint discussed above, typically gives a silanol concentration of 3.0 silanols/nm2 (5.0 µmol/m2). However, 4.0 silanols/nm2(6.6 µmol/m2) appears to be higher than a purely random surface assembly can obtain. On average, these surfaces have 80% ( 10% of vicinal silanols. This compares with the experimental observation that 15-30% of the silanols in a fully hydroxylated amorphous silica are of the geminal type.42 Although silanol concentration is a constant for the (111) and (100) faces of β-cristobalite, dictated by the geometry of the crystal lattice, the randomly build phase has a distribution of silanol concentrations, which will be discussed below. The calculated maximum surface coverages of different ligands bonded to β-cristobalite silica surfaces are given in Table 2. In addition, data from the experimental study of Kirkland and Henderson25 are also given in Table 2. The data are not given for the random surfaces in Table 2 because the values found were significantly lower. This will be discussed below. The agreement with the (111)-face model is very good and further suggests that the (111) face of β-cristobalite makes a reasonably good model for the silica surface. Although these calculations agree with experiment, this is circumstantial proof that the proposed structure is a good representation of the real silica surface. However, the logical alternatives of the (100) face and the random surface show poorer agreement. These results suggest that the (111) face of β-cristobalite is good for the purpose of giving a quantitative model of these bonded phase concentrations. Other models of the silica surface are possible and others have been postulated. For example, Chuang and Maciel28 suggested a combination of the (111) and (100) surface of β-cristobalite. These (41) Peri, J. B.; Hensley, A. L. J. Phys. Chem. 1968, 72, 2926-2933. (42) Wise, S. A.; Sander, L. C.; May, W. E. J. Liq. Chromatogr. 1983, 6, 27092721.

Figure 1. Silica substrates and bonded phases. The (111) face (A) and the (100) face (B) of β-cristobalite, and a random phase (C). Trimethyl ligands as a limiting case for dimethyl-substituted silanes on the (111) face (D) and on the (100) face (E) of β-cristobalite. Triisopropyl ligands as a limiting case for diisopropyl-substituted silanes on the (111) surface (F). Hydrogen, oxygen, silicon, and carbon atoms are depicted in white, red, blue, and green, respectively.

authors proposed a generalized model of silica where fragments of these two surfaces, perhaps hundreds of atoms of each type of face, are present on a silica surface. This model may be correct but is difficult to implement in a simple model that can explain the surface coverages given in Table 2. Figure 1 shows the bonding of trimethylsilane ligands as a limiting case for the dimethyl-substituted silanes bonded to the (111) surface (Figure 1D) and the (100) surface of β-cristobalite (Figure 1E). Triisopropyl ligands bound to the (111) surface are shown in Figure 1F. In all figures shown here, periodic boundaries are utilized not only for the silica substrate but also for the loading of the bonded phase. From experiment25 it is suggested that the phases with bulky side chains show better retention characteristics and stability,

especially at high temperatures and elevated pH values. This may be due to better steric protection of surface silanol groups provided by the bulky side chains. This is suggested by the visualization shown in Figure 1F where only a few accessible silanols are revealed from the surface normal view and a large number of silanols appear to be shielded by the triisopropyl groups and are not accessible. The phases with bulky side chains have smaller maximum coverages than the phases with methyl side groups, as given in Table 2. It becomes increasingly difficult to build the simulated alkyl-modified surface once the surface concentration approaches 3.3 µmol/m2 (2.0 chains/nm2). A close examination of the interligand distances in these model structures using Macromodel reveals that these limitations exist due to the bulky side groups, Analytical Chemistry, Vol. 73, No. 16, August 15, 2001

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Table 2. Maximum Surface Coverage Values experimenta ligand trimethyl dimethyl-C8 dimethyl-C18 triisopropyl diisopropyl-C8 diisopropyl-C18 a

(111) face

(100) face

µmol/ groups/ µmol/ groups/ µmol/ groups/ m2 nm2 m2 nm2 m2 nm2 3.65 3.30 2.22 2.00 2.14

2.20 1.98 1.34 1.20 1.29

3.83 3.83 3.83 2.13 2.13 2.13

2.31 2.31 2.31 1.28 1.28 1.28

3.32 3.32 3.32 1.66 1.66 1.66

2.00 2.00 2.00 1.00 1.00 1.00

Data from ref 25.

Figure 2. Distributions of silanols on the unbonded random phase (open histograms) and of the coverage of trimethyl groups (filled histrograms). The distributions are based on 20 000 random surfaces.

which sterically block some of the surface silanols. The surfaceprojected surface area of the side ligands is the limiting factor in determining the overall surface coverage of the bonded group. To provide maximal surface coverages, bonded-phase ligands have to be tightly packed in a very specific way, as shown in Figure 1D and E. Due to the tighter hexagonal packing of the surface silanols, the (111) surface yields higher coverages than the (100) surface. At maximum surface coverage, side groups lock each other in place. Note that when one of the geminal silanol groups in the (100) surface is occupied by a bonding ligand, the neighboring silanol group is shielded. Due to the square arrangement of geminal pairs, it is impossible to reach the maximum coverage values characteristic of hexagonally packed vicinal groups of the (111) substrate. When trimethylsilane ligands are bonded to a random surface, much lower coverages are found. The distribution of surface coverages calculated from 20 000 random surfaces is shown in Figure 2 (lower values). The maximum coverage of trimethylsilane ligands was found to be 2.00 groups/nm2 (3.32 µmol/m2), but only 4 out of the 20 000 random surfaces reached this coverage. The distribution of silanols on unmodified random surfaces is shown as the right-most distribution in Figure 2. From this distribution it is evident that the random surfaces have much smaller silanol concentrations than the β-cristobalite phases. The correlation between these two surface distributions is moderate because they use the same surfaces; i.e., a surface that is covered 4010

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with more silanol groups will also allow with greater probability for a higher chain coverage. Indeed one might note that the relative spread of the two distributions is similar. According to Sander and Wise,31 if dimethyloctadecylchlorosilane is used in bonded-phase synthesis, the maximum number of chains that can be attached to the surface is ∼2.0 chains/nm2 (3.3 µmol/m2). Due to steric hindrance created by the side methyl groups, more than half of the silanol groups on the surface remain unoccupied.31 It is interesting to note that we have seen a similar limit in our calculations: 58% of silanols remain unoccupied when a maximum coverage is reached for dimethyl-C18 ligands. We have assumed a flat surface in these calculations. Obviously there must be curvature in real chromatographic silica and this may contribute to additional surface coverage and less entropic repulsion of alkyl tails for thermal systems. In our study, however, the maximum coverages are limited by the headgroup packing, which would be relatively insensitive to curvature effects. Other methods of binding C18 chains to surfaces have produced bonding densities of ∼4.0 µmol/m2.43-46 In these cases, techniques such as ultrasonic energy or novel chemistry were used to achieve this density. Kirkland25 reported lower coverages for longer alkyl chains, because chains in a real system have some amount of conformational disorder. These chains have a higher chance of “sticking out” and hitting neighboring chains, lowering the possibility of very dense phase formation. In our calculations, chain flexibility effects cannot take place because the alkyl chains are fixed in the all-trans conformation. However, molecular dynamics simulations,17 when viewed temporally in movie format, reveal that bonded-phase C8 and C18 chains are highly flexible and highly disordered and show a high degree of excluded volume effects in their disordered conformation. To illustrate this effect, a simulation of diisopropyloctylsilane on the (111) substrate is conducted where a conformational defect is introduced into the next to last dihedral angle of the C8 chain. This dihedral angle is set to 6°, i.e., an almost fully eclipsed conformation. Gauche dihedral angles are located at (60°, and all-trans dihedral angles are 180°. The choice of 6° in this case was arbitrary. The maximum concentration value for this phase was 2.04 µmol/m2 (1.23 chains/nm2). This is ∼5% less than the all-trans conformation concentration on the same substrate given in Table 2, further illustrating that flexibility can cause a change in the surface coverage. Clearly, we have shown that the (111) face of β-cristobalite provides a structure reasonably close to that typically found for chromatographic silica when these structures are used as bonding models for the chemically bound phase. In that regard, the distribution of ligands on the surface, while reproduced in the maximum coverages given in this paper, lack a number of important details which are now discussed. There is undoubtedly a contribution of geminal groups that is not considered in the (111) face model but is known to occur in nature. The more advanced models of the silica surface, for (43) Kovats, E. sz.; Szabo, K.; Ha Le, N.; Schneider, Ph.; Zeltner, P.; Helv. Chim. Acta 1984 67, 2126-2127. (44) Sentell, K. B.: Dorsey, J. G. Anal. Chem. 1989, 61, 930-934. (45) Buswewski, B.; Sienko, D.; Suprynowicz, Z. J. Chromatogr. 1989 464, 7381. (46) Sentell, K. B.; Henderson, A. N. Anal. Chim. Acta 1991 246, 139-149.

example, the mixture model of (111) and (100) faces proposed by Chuang and Maciel,28 is difficult to balance on a small atomic scale; i.e., the proportions and locations of any random, pseudorandom, or correlated structure are difficult to model. The real interest in this paper is to be able to provide a model that can give a good quantification of the grafted layer, and the accuracy of the unbound silanol locations is of secondary importance once the bonded phase has been attached. We have reported the maximum concentrations of these types of bonded ligands whereby chain flexibility due to thermal effects was not considered. Because all of the chain structures are bonded in the all-trans conformation, these models cannot distinguish between the C1, C8, and C18 surface coverages, where entropic (steric) effects lead to to small differences in the (47) Fenter, P., Eisenberger, P., Liang, K. S. Phys. Rev. Lett. 1993, 70, 24472450. (48) Siepmann, J. I., McDonald, I. R. Thin Films 1998, 24, 205-226.

experimental data. However, it is well documented47,48 that entropic effects do not prevent the formation of ordered self-assembled monolayers, such as the high-coverage structures found for alkanethiols on the (111) face of gold. The results given in this paper provide a good starting point for estimating the maximum coverage with satisfactory accuracy, and the incorporation of flexibility effects will be investigated in the future. ACKNOWLEDGMENT Financial support from the National Science Foundation under Grant CHE-9816328 is gratefully acknowledged. Part of the computational resources were provided by the Minnesota Supercomputing Institute. Received for review March 13, 2001. Accepted June 11, 2001. AC010298R

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