Molecular Dynamics Study of the Relation between Analyte Retention

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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Molecular Dynamics Study of the Relation between Analyte Retention and Surface Diffusion in Reversed-Phase Liquid Chromatography Julia Rybka, Alexandra Höltzel, Andreas Steinhoff, and Ulrich Tallarek* Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany

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ABSTRACT: In reversed-phase liquid chromatography (RPLC), analyte molecules retained on the hydrophobic stationary phase can undergo fast surface diffusion within an acetonitrile (ACN)-rich border layer between the stationary phase and the water (W)−ACN mobile phase. We perform molecular dynamics simulations in an RPLC mesopore model employing an endcapped C18 phase to determine retention and diffusive mobility data for four analytes at solvent ratios between 80/20 and 10/90 (v/v) W/ACN. Simulated retention data are validated by experimental retention factors acquired over the full range of studied W/ACN ratios. Our data show that for a given analyte, the lateral mobility gain from surface diffusion increases with the retention factor because both decrease with the elution strength (ACN content) of the mobile phase. A general correlation between analyte retention and surface diffusion is, however, ruled out, as analyte properties influence retention and surface diffusion differently. Complementary simulations of bulk diffusion in W−ACN mixtures show that the lateral mobility of analyte molecules in the ACN ditch can be higher than expected from the local solvent ratio. This occurs only for W-rich mobile phases, when analyte molecules have numerous contacts with bonded-phase groups, and suggests a bonded-phase contribution to surface diffusion through lubrication of retained analytes.

1. INTRODUCTION Reversed-phase liquid chromatography (RPLC), which combines a hydrophobic stationary phase with an aqueous− organic mobile phase, remains the most important separation and purification technique for apolar to moderately polar compounds in academic and industrial settings. Typically, the stationary phase consists of a silica support bearing a chemically bonded phase, most often dimethyl octadecylsilane (C18) chains, and the mobile phase is a mixture of water (W) with methanol or acetonitrile (ACN) as the organic solvent. The silica support takes either the form of a packed bed of micrometer-sized particles with nanometer-sized pores or that of a macroporous monolith with a mesoporous skeleton, confined within a cylindrical container. Because the mesopores contain >95% of the surface area of the silica support, most of the stationary phase is located inside the mesopores.1 The mobile phase is driven by high pressure to percolate through the macropore space, but enters the mesopores through diffusion. Analyte molecules are present in the macroporous (external) and the mesoporous (internal) space. Mass transport of analytes inside the mesopores occurs through pore diffusion in the liquid mobile phase and through surface diffusion on the stationary phase, where analytes are also retained.2 Understanding analyte retention and mass transport requires a molecular-level picture of the chromatographic interface, which is the region spanning the solid−liquid transition from © XXXX American Chemical Society

the surface of the silica support to the bulk mobile phase. Important details of the chromatographic interface and the retention mechanism in RPLC have come from molecular simulation studies.3 On the basis of the solvent density profiles inside an RPLC mesopore, Siepmann and co-workers4 differentiated between three distinct regions: (I) the bondedphase region, reaching from the silica surface to the location where the total solvent density reaches 10% of its bulk value, (II) the interfacial region, over which the total solvent density increases from 10 to 90% of its bulk value, and (III) the bulk region, where the properties of the bulk solvent mixture are attained. Siepmann and co-workers also investigated the retention mechanism of RPLC, using as probe structures small solutes (alkanes and primary alcohols up to C4), polycyclic aromatic hydrocarbons containing up to four rings, and alkanes up to C14.5−11 Their results showed that small solutes and analytes are retained through a combination of partitioning into and adsorption onto the bonded-phase chains, whereby the contribution of each mechanism is influenced by solute properties (size and polarity) and stationary-phase properties (chain length, ligand density, and pore shape). Retention of larger, apolar analytes with a flat, rigid structure was found to shift toward a pure partitioning Received: December 13, 2018 Revised: January 22, 2019 Published: January 23, 2019 A

DOI: 10.1021/acs.jpcc.8b11983 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C mechanism, whereas larger, flexible analyte molecules arrange themselves to span over bonded-phase and interfacial regions and thus combine partitioning and adsorption mechanism in one molecule. More recently, the effective diffusivity of retained analytes has attracted increased interest because the separation efficiency benefits from a low resistance to mass transfer.12−17 Chromatographic studies of mass transfer have shown that small, aromatic hydrocarbon analytes can diffuse faster through mesoporous RPLC particles than in the bulk mobile phase, which points to fast surface diffusion of retained analytes,12,13 as pore diffusion can hardly be faster than bulk diffusion considering confinement and tortuosity effects in the mesoporous network.18 The experimental data showed a positive correlation between the estimated contribution of surface diffusion to the overall particle diffusivity and the retention factor.12 Considering that the number of analyte structures included in the experimental study was necessarily limited and that except for the acquisition of one data point, the elution strength of the mobile phase was not varied, the observed correlation could have been incidental or reflect a general relation between analyte retention and surface diffusion. Although the existence of fast lateral diffusion at hydrophobic surfaces has been established by chromatographic and spectroscopic experiments,12−17,19−22 the experimental evidence is indirect. Surface diffusion describes the lateral mobility within a narrow region inside the mesopore, and this spatially dependent mobility is difficult to access experimentally. Molecular dynamics (MD) simulations, on the other hand, can provide spatially resolved diffusion coefficients for solvent and solute molecules as well as bonded-phase groups in an RPLC mesopore.23−25 We therefore chose this approach to study surface diffusion in RPLC.26−28 Our RPLC mesopore model consisted of a 10 nm slit pore formed by two planar silica surfaces modified with C18 chains and trimethylsilyl endcapping groups (Figure 1). Surface modification, ligand density, endcapping, and pore size were chosen to represent a typical mesopore in an RPLC column.29 The MD simulations revealed surface diffusion in RPLC to be connected to the enrichment of ACN molecules around the ends of the bonded-phase chains. We named this ACN-rich border layer between bonded-phase and bulk region the ACN ditch because the setting is reminiscent of an irrigation ditch that separates farmland from a roadway. Formation of the ACN ditch is driven by the hydrophobic effect.30 Confronted with the hydrophobic surface formed by the alkyl chains, the microheterogeneous W−ACN mixture pushes ACN molecules toward the hydrophobic surface to conserve the hydrogen-bonding network. During column operation, fresh mobile phase constantly enters the mesopores from the external macropore space, so that ditch formation does not result in an ACN-depleted bulk region. The simulations proved that the local solvent ratio in the ACN ditch favors the diffusive mobility of organic compounds, including small solutes and analytes, ACN, and bonded-phase groups, compared to the W-rich mobile phase in the bulk region. The solvent density and lateral mobility profiles shown in Figure 1 visualize the connection between local solvent ratio and lateral mobility in the RPLC mesopore. To study surface diffusion, we chose an analyte set comprising benzene and three simple derivatives (ethylbenzene, acetophenone, and benzyl alcohol) that reflect the

Figure 1. Snapshot of the RPLC mesopore model equilibrated with a 70/30 (v/v) W/ACN mobile phase (top panel) and associated profiles for solvent density (central panel) and lateral mobility (diffusion coefficient parallel to the silica surface, D∥, bottom panel). Atoms and united-atom groups in the snapshot are colored as follows: Si, yellow; O (of silica and W molecules), red; H (of residual surface OH groups and W molecules), white; ACN molecules, green; and CH2 and CH3 united-atom groups (of C18 chains and endcapping groups), gray. Profiles are shown for the O atom of W and the central C atom of ACN molecules as a function of the distance normal to the silica surface (z). Average solvent densities in the bulk region of the pore (III) correspond to 0.712 g/cm3 (W) and 0.229 g/cm3(ACN).

polarity spectrum of the compounds separated in RPLC practice. Although all analytes achieved their maximum lateral mobility in the ACN ditch, the highest mobility gain from surface diffusion was observed for benzene, not for ethylbenzene, which in chromatographic practice is more retained than benzene. This opens the question how analyte retention and surface diffusion are related. A likely link between the two phenomena is the W/ACN ratio of the mobile phase. In chromatographic practice, analyte retention on a given RPLC B


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velocities were randomly assigned through a Maxwell− Boltzmann distribution. After a 60 ns equilibration period, productive simulations were run for up to 1.5 μs. The output frequency for the trajectory was set to 0.5 ps. Long-range electrostatic interactions were treated with the particle-mesh Ewald algorithm, and nonbonded interactions were modeled with a 12−6 Lennard−Jones potential. Lennard−Jones parameters for unlike interactions were calculated using Lorentz−Berthelot combination rules. A cutoff radius of 1.4 nm, validated earlier,26 was used. 2.1.3. Calculation of Density Profiles, Distribution Coefficients, and the Number of Bonded-Phase Contacts. Density profiles were calculated from the atom number density of the O atom of W, the central C atom of ACN, the CH2 and CH3 united-atom groups of the bonded phase, and the centerof-mass (cms) of the analyte molecules. The distance z was measured starting from the position of the surface Si atoms (z = 0). For bonded-phase groups and for solvent molecules at z < 1 nm, a bin size of 0.02 nm was used. For analyte molecules and for solvent molecules at z > 1 nm, bin sizes of 0.05 and 0.1 nm were used, respectively. Distribution coefficients for the analytes were calculated as the ratio between the average analyte concentrations in the stationary phase and the mobile phase, taken directly from the analyte density profiles by averaging the analyte density from z = 0 nm (silica surface) to the stationary-phase limit and from the stationary-phase limit to z = 5 nm (pore center), respectively. The number of bonded-phase contacts for analytes was calculated by determining the distance between an analyte molecule’s cms and the united-atom groups of the alkyl chains. If the distance was smaller than 0.74 nm, which corresponds to the location of the first minimum in the respective radial distribution function, a bonded-phase contact was counted. The number of contacts was averaged over all 0.5 ps time steps during a 20 ns observation time. 2.1.4. Calculation of Spatially Resolved Parallel Diffusion Coefficients in the Slit-Pore Model. As in our previous studies of transport in liquid chromatography mesopores,26−28,46,47 the local diffusion coefficient of solvent or analyte molecules and bonded-phase groups in the parallel direction to the silica surface, D∥(z), was calculated following an approach by Liu et al.48 The mean squared displacement r2(t) of a bonded-phase group, solvent, or analyte molecule parallel to the silica surface within a specified space interval along the z-axis was repeatedly recorded for 20 ps time intervals. D∥(z) was then calculated from the linear slope of the observation curve (t = 4−16 ps) according to the Einstein equation

column is controlled by the elution strength of the mobile phase, which increases with its organic solvent content. From our previous work,26 we know that the W/ACN ratio of the mobile phase also determines the local solvent ratio in the ACN ditch and is thus expected to influence the lateral mobility gain of the analytes from surface diffusion. In this study, we combine MD simulations and chromatographic experiments to investigate the relation between analyte retention and surface diffusion. Relying on our established RPLC mesopore model and analyte set, retention and mobility data are simulated for mobile phases between 80/20 and 10/ 90 (v/v) W/ACN. The simulated data are complemented by experimental retention factors determined for the analytes on an RPLC column with an endcapped C18 stationary phase over the same W/ACN range as used in the simulations.

2. METHODS 2.1. Simulations. 2.1.1. Slit-Pore Model and Force-Field Parameters. A rectangular simulation box with dimensions of xyz = 12.14 × 13.2 × 10.93 nm3 contained a three-layer silica slab (0.93 nm wide in z-direction) between two 5 nm wide solvent reservoirs. Owing to periodic boundary conditions applied in all directions, the system mimics a 10 nm slit pore (top panel of Figure 1). Following an approach of Coasne et al.,31 a surface bearing 4.5 single silanol groups/nm2 (7.5 μmol/m2) was created from the (111) face of β-cristobalite, the preferred crystalline model for the amorphous structure of chromatographic silica supports.32 The surface was randomly grafted with 1.87 C18 chains/nm2 (3.11 μmol/m2) and 0.56 trimethylsilyl groups/nm2 (0.93 μmol/m2), which left 2.06 residual OH groups/nm2 (3.42 μmol/m2). Force-field parameters for silica surface atoms (Si, O, and H) were taken from Gulmen and Thompson.33,34 The transferable potentials for phase equilibria united-atom (TraPPE-UA) force field was used for C18 chains and trimethylsilyl groups.35−37 The choice of the simple point charge/extended (SPC/E) force field for W molecules38 and the TraPPE-UA force field for ACN molecules39 was informed by research of Mountain.40,41 Analytes were treated with the explicit CHARMM general force field (CGenFF)42,43 because it provided parameters for the entire set. A detailed validation of the chosen force fields can be found in an earlier publication.28 2.1.2. Simulations in the Slit-Pore Model. MD simulations were carried out with GROMACS 5.1.1.44,45 A Nosé−Hoover thermostat with a 0.25 ps coupling constant was used to hold the temperature at 300 K. Equations of motion were integrated with a 1 fs time step. Productive simulations conducted for a canonical NVT ensemble (constant number of molecules N, simulation box volume V, and temperature T) were carried out for 80/20, 70/30, 60/40, 50/50, 40/60, 30/70, 20/80, and 10/ 90 (v/v) W/ACN; each analyte species was simulated separately (with Nanalyte = 10), yielding 32 simulation systems. In chromatographic practice, the ACN ditch forms during column equilibration (before sample injection), when the mobile phase is pumped through the column until the effluent composition matches the influent composition. Our simulation protocol mimics this process to ensure that ACN-ditch formation is complete and the solvent ratio in the bulk region meets the targeted W/ACN ratio of the mobile phase with an accuracy of ±1%. The necessary number of ACN and W molecules in the simulation box for each W/ACN ratio (Table S1) was determined in preliminary simulations.28 The steepest descent method was used for energy minimization. Initial

D (z ) =

1 dr 2(t ) 4 dt

(1)

D∥(z) was determined with a bin size of 0.2 nm along the zaxis, allowing molecules or bonded-phase groups a shift of ±0.3 nm around their initial z-coordinate. Only molecules or bonded-phase groups that remained in the specified space interval for the whole observation time were considered. The percentage of contributing molecules ranged from 79 to 92% in the bulk region, over 77−97% in the interfacial region, to 96− 98% in the bonded-phase region. D∥(z) is given as the average value with an error estimate calculated from the difference between the values obtained from the slope of the mean C


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The Journal of Physical Chemistry C squared displacement curve over the two halves of the fit interval (i.e., t = 4−10 ps and t = 10−16 ps). 2.1.5. Simulations of Bulk Diffusion in W−ACN Mixtures. Bulk molecular diffusion coefficients of analyte molecules, Dm, were determined through NPT ensemble simulations with Nanalyte = 2 and Nsolvent = 10 000 for 40/60 (v/v) W/ACN (NW = 6588 and NACN = 3412) and for 29/71 (v/v) W/ACN (NW = 5419 and NACN = 4581). Each analyte species was simulated separately, yielding eight NPT simulations. Trajectories were run over 10 ns of which the final 5 ns were used for data analysis, and 501 time origins were used to estimate the mean squared displacement of analyte molecules. The diffusion coefficient was calculated directly in GROMACS from the mean squared displacement, using the time interval of t = 4− 16 ps as described above. Simulated Dm values are given as the average value ± the standard deviation determined from three individual simulation runs. Dm values for 53/47, 35/65, 28/72, 24/76, 16/84, and 9/91 (v/v) W/ACN were extrapolated from the previously simulated Dm curves of the analytes covering the range between 10/90 and 100/0 (v/v) W/ACN (cf. Figure 7 in Rybka et al.28) and are thus given without an error estimate. 2.2. Chromatography. 2.2.1. Chemicals. High-performance liquid chromatography (HPLC)-grade water was obtained from a Milli-Q gradient water purification system (Millipore, Bedford, MA). HPLC-grade ACN was purchased from Fisher Scientific (Loughborough, Leics., U.K.). Uracil, ethylbenzene, and acetophenone were bought from SigmaAldrich (Steinheim, Germany), benzene from Merck (Darmstadt, Germany), and benzyl alcohol from Grüssing GmbH (Filsum, Germany). All chemicals had a minimum purity of 99%. 2.2.2. Apparatus. Chromatographic experiments were run on a 1220 Infinity HPLC system (Agilent Technologies, Waldbronn, Germany) equipped with a binary solvent pump, an autosampler with a 20 μL injection loop, a column thermostat, and an UV−vis detector. The system was controlled via ChemStation software. The RPLC column (150 mm length × 4.6 mm i.d.), generously offered by Waters (Milford, MA), was packed with fully porous, high-strength silica particles (average particle size: 5 μm and average pore diameter: 10.2 nm), modified with C18 chains at a ligand density of 2.7 μmol/m2 and endcapped with trimethylchlorosilane to a final C load of 13.9%. 2.2.3. Experiments. Chromatograms were acquired with mobile phases of 80/20, 70/30, 60/40, 50/50, 40/60, 30/70, 20/80, and 10/90 (v/v) W/ACN at a flow rate of 1 mL/min, a temperature of 300 K, and a detection wavelength of 250 nm. Each analyte was analyzed separately. For this, 5 μL of a sample containing the analyte and uracil dissolved either in the current mobile phase (if the latter contained ≥50 vol % ACN) or in 50/50 (v/v) W/ACN (to ensure solubility of the apolar analytes) was injected. Retention factors k′ were determined through ChemStation software from the retention time of the respective analyte, tR, and the elution time of the nonretained compound uracil, t0, as k′ = (tR − t0)/t0, and reflect the average of 2−4 measurements.

Figure 2. Bonded-phase and solvent density profiles in the RPLC mesopore model for mobile phases between 80/20 and 10/90 (v/v) W/ACN. Bonded-phase density maxima at low z-values were truncated for better visibility of the ACN ditch. Dashed black lines separate bonded-phase (I), interfacial (II), and bulk regions (III); dashed green lines indicate the ACN density maximum.

phase and solvent density profiles for the whole range of studied W/ACN ratios. With increasing ACN content of the mobile phase (from top to bottom in Figure 2), the extension of the bonded-phase chains increases from z = 1.89 to 2.15 nm (at high ACN content, the bonded-phase density reaches into the bulk region.) Concomitantly, the location of the border between bonded-phase (I) and interfacial region (II), zI/II, or the location where the total solvent density drops to 10% of its bulk value shifts toward the silica surface because more ACN molecules enter the bonded-phase region. The border between interfacial and bulk region, zII/III, or the location where the total solvent density drops to 90% of its bulk value, however, goes through a maximum at 40/60 (v/v) W/ACN. This evolution results from two countercurrent effects: elongation of the bonded-phase chains, which shifts the border outward

3. RESULTS AND DISCUSSION 3.1. Properties of the Chromatographic Interface. Before presenting analyte-related results, we consider the subtle changes in the chromatographic interface at increasing elution strength of the mobile phase. Figure 2 shows bondedD


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The Journal of Physical Chemistry C (to the bulk region), and increased ACN solvation of the bonded-phase chains, which shifts the border inward (to the silica surface). As the net result of the shifts in zI/II and zII/III, the width of the interfacial region increases from wII = 0.84 to 1.2 nm (Table S2) and the ACN density peak in the interfacial region flattens out. The ACN density maximum moves from the middle of the interfacial region toward zII/III, and the maximum ACN excess decreases from 48 to 2 vol % ACN (Table S3). At 10/90 (v/v) W/ACN, the ACN density maximum is located in the bulk region and cannot be visually discerned in the density profile. Overall, Figure 2 shows three properties of the chromatographic interface that are particularly relevant to this study: first, the presence of an ACN ditch for most of the W/ACN range; second, the decrease in interfacial ACN excess with increasing elution strength of the mobile phase; third, the dependence of the bonded-phase extension on the elution strength of the mobile phase. The first property allows the prediction that a lateral mobility gain from surface diffusion in the ACN ditch can be expected for most W/ACN ratios. The second property allows the prediction that the lateral mobility gain from surface diffusion decreases (as retention does) with the ACN content of the mobile phase. The third property predicts that the stationary-phase limit, zSP, required for the calculation of the retention data is sensitive to the W/ACN ratio in the bulk region. 3.2. Analyte Retention. Analyte retention on a chromatographic column is quantified through the retention factor k′, which relates the amount of analyte molecules in the stationary phase compared to the mobile phase. The retention factor is related to the distribution coefficient K, which gives the analyte concentration in the stationary phase compared with the mobile phase, through k′ = Kβ, where β is the phase ratio that relates the volume of the stationary phase to that of the mobile phase in a given column. Our slit-pore model allows the determination of K from the analyte density profiles (Figure 3) through calculation of the respective analyte concentrations in the stationary and mobile phase. The distribution and orientation of retained analyte molecules was discussed in breadth in our previous study,28 which is why only the salient points are mentioned here. All analyte density profiles contain peaks in the bonded-phase region and in the interfacial region, assigned to partitioning and adsorption, respectively. Judging by peak area, which reflects the amount of analyte molecules within the peak limits, adsorption is the dominant retention mechanism for all studied analytes. This observation agrees with results from a recently developed technique, surface bubble-modulated liquid chromatography.49,50 The relative contributions from partitioning and adsorption to retention (Table S4) show only little variation with the W/ACN ratio of the mobile phase, but they reflect analyte properties. Partitioning contributes (averaged over all W/ACN ratios) 31% to ethylbenzene retention, 27% to benzene retention, 14% to acetophenone retention, and 6% to benzyl alcohol retention in the RPLC mesopore model. To calculate distribution coefficients from the analyte density profiles, the border between stationary and mobile phase needs to be defined. This cannot be done solely from the properties of the chromatographic interface (Figure 2), as the extension of the analyte molecules must be taken into account. An analyte molecule with its cms in the bulk region can be in contact with bonded-phase groups, which is why zII/III, for example, is unsuitable as stationary-phase limit. Instead of a

Figure 3. Analyte density profiles in the RPLC mesopore model at different elution strengths (ACN content) of the mobile phase. Profiles are shown for the cms of analyte molecules. The shaded area indicates the stationary-phase limit (zSP), which varies with the analyte and the ACN content of the mobile phase (cf. Table S5).

universal border, we therefore introduced a universal definition of the stationary-phase limit based on the interaction between analyte molecules and bonded-phase groups. For each analyte and W/ACN ratio, we determined the stationary-phase limit, zSP, as the distance from the surface where an analyte molecule residing with its cms at this location has averaged over time less than one contact with bonded-phase groups (Table S5). The calculated distribution coefficients (Table S6) show an exponential decrease with the elution strength of the mobile phase, as expected from chromatographic theory, whereby the K-values of the apolar analytes are more sensitive to the W/ACN ratio than those of the polar analytes (Figure 4). At each W/ACN ratio, the retention order K(ethyl-

Figure 4. Distribution coefficients K calculated from the analyte density profiles in the RPLC mesopore model at different elution strengths (ACN content) of the mobile phase.

benzene) > K(benzene) > K(acetophenone) > K(benzyl alcohol) is conserved and parallels the order observed for the relative contribution from partitioning to analyte retention (Table S4). Among the analyte set, higher retention thus equals a higher partitioning contribution. Simulated retention data have been compared with experimental data in the past,5−11,51,52 validating molecular E


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discrepancy between simulated and experimental data is, however, very minor, particularly considering that the pore space in a chromatographic column is much more complex than in a single-pore model.18,55 Overall, the experimental retention factors provide an excellent validation of the simulated distribution coefficients. 3.3. Surface Diffusion. The parallel diffusion coefficient profiles of the analytes (Figure 6) resemble the D∥ profile of

simulations as a method to investigate solute retention in RPLC, but a validation of simulated retention data over a wide range of W/ACN ratios has not been done before. Capturing the experimentally observed dependence of the retention data on the W/ACN ratio in our simulations is of central importance to our study, which is why we determined for each simulated distribution coefficient an experimental retention factor on a silica-based C18 column with similar ligand density, endcapping, and pore size as in our RPLC mesopore model. The acquired set of experimental retention factors (Figure 5 and Table S7) would not have been available

Figure 5. Retention factors k′ of the analytes determined on an endcapped C18 column at different elution strengths (ACN content) of the mobile phase.

from the literature because of the wide range of k′ values involved (to keep analysis times reasonable, a range of k′ = 1− 5 is targeted in chromatographic practice). The comparison of the simulated and experimental retention data (Figures 4 and 5, respectively) shows that our RPLC mesopore model represents analyte retention on an RPLC column very well, which, in turn, also validates the force fields chosen for the simulations. Because the retention factor and distribution coefficient are related through the phase ratio β = k′/K, we calculated β-values as the ratio between experimental retention factor and simulated distribution coefficient (Table S8). The received values were β = 0.18−0.32 for ethylbenzene, β = 0.22−0.30 for benzene, β = 0.27−0.41 for acetophenone, and β = 0.14−0.28 for benzyl alcohol, yielding a total average (over all analytes and W/ACN ratios) of β = 0.27. Chromatographers understand that the border between stationary and mobile phase is sensitive to the W/ACN ratio of the mobile phase (e.g., as seen in Figure 3 with the stationary-phase limit, zSP) and that β therefore depends on the W/ACN ratio (as reflected by the range of β-values received for each analyte). This knowledge cannot be turned into accurate data, however, because the volume of the stationary phase (as distinct from the volume occupied by the porous silica particles that support the stationary phase) cannot be directly accessed. Phase ratios are thus rarely given for columns and should be regarded as estimates. For C18 columns, phase ratios as low as β = 0.146 and as high as β = 0.665 have been reported,53 but β = 0.2−0.4 is a more representative range for the column used in this study.54 Judging on this basis, the simulations approach chromatographic experiments quite closely. Because the ligand density of the stationary phase is lower in the column than in our RPLC mesopore model (2.7 vs 3.1 μmol/m2), the calculated β-values are on the lower side of the experimental range. From the comparison of Figures 4 and 5, acetophenone retention appears slightly underestimated and benzyl alcohol retention slightly overestimated by the simulations. This

Figure 6. Parallel diffusion coefficient profiles for analytes in the RPLC mesopore model at different elution strengths (ACN content) of the mobile phase. The shaded area indicates the stationary-phase limit (zSP) to visualize the location of increased analyte lateral mobility in relation to the border between stationary and mobile phase.

ACN (cf. bottom panel of Figure 1). Except for 10/90 (v/v) W/ACN, where no ACN ditch forms, the D∥ profiles go through a maximum in the interfacial region, before decreasing steadily over the bonded-phase region to zero at the silica surface. The W/ACN ratio influences the lateral mobility of all analytes in identical fashion; in bulk and interfacial regions, that is, before the bonded phase enforces a general mobility descent, the lateral mobility increases with the ACN content of the mobile phase because the viscosity of the W−ACN mixture decreases. Additionally, as the C18 chains elongate with increasing ACN fraction (cf. Figure 2), the location of D∥,max, the maximum analyte lateral mobility, shifts outward, from z = 1.9 nm at 80/20 (v/v) W/ACN to z = 2.3 nm at 20/80 (v/v) W/ACN (Table S5). Whereas the lateral mobility maximum of ACN is located at the ACN density maximum (cf. bottom and middle panels of Figure 1), the lateral mobility maximum of the analytes is located closer to the bulk region, but still within the stationary-phase limit (Table S5). The gray shaded area in Figure 6 indicates the zsp-range to emphasize that analyte molecules undergoing fast surface diffusion are at the same time retained by the stationary phase. At the analyte lateral mobility maximum, the local solvent ratio is not as ACN-rich as at the ACN density maximum (Table S3), but the bondedphase presence involves mainly the flexible chain ends. The parallel diffusion coefficients calculated for the bonded-phase groups CH2(17) and CH3(18), which make up most of the F


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analyte retention (Figures 4 and 5). The main difference between Figures 4 and 5 on the one hand (please note the logarithmic scale of the y-axis here) and Figure 8 on the other hand is found in the behavior of the apolar analytes; at every W/ACN ratio, ethylbenzene is more strongly retained than benzene, but benzene gains more lateral mobility from surface diffusion than ethylbenzene. Ethylbenzene retention is also much more sensitive to the ACN content of the mobile phase, particularly at low elution strength, than benzene retention, whereas both apolar analytes show a similar sensitivity of the lateral mobility gain to the ACN content of the mobile phase. From these observations, we deduce that analyte retention and surface diffusion depend differently on analyte properties. Analyte molecules at the outer edge of the adsorption peak, where surface diffusion takes place, show orientational preferences in accordance with their respective molecular structures; acetophenone and benzyl alcohol molecules orient their polar side chain toward the bulk region and retain the hydrogen bond contact with W molecules of the mobile phase; ethylbenzene molecules point their apolar side chain to the silica surface, whereas benzene molecules have no preferred orientation (cf. Figure 4 in Rybka et al.28). The large lateral mobility gain of benzene could be related to its smaller size and/or the absence of a side chain. An apolar side chain buried in the bonded phase could detract from the lateral mobility of an ethylbenzene molecule in the ACN ditch similar to how the hydrogen bond connection with the mobile phase detracts from the lateral mobility of the polar analytes in the ACN ditch. Retention is a quantity calculated over the whole pore, whereas the lateral mobility gain from surface diffusion is calculated from a locally resolved quantity. Figure 9, which

bonded-phase presence at the analyte lateral mobility maximum (Table S9), reveal the chain ends to be as laterally mobile as the analytes themselves. Figure 7, which shows the

Figure 7. Maximum parallel diffusion coefficients of analyte molecules and bonded-phase groups in the ACN ditch at different elution strengths (ACN content) of the mobile phase.

maximum parallel diffusion coefficients of bonded-phase groups and analytes in the ACN ditch, visualizes that over the studied W/ACN range, CH3(18) compares in lateral mobility with ethylbenzene and CH2(17) with the polar analytes. Surface diffusion on a C18 phase is thus characterized by a comparable lateral mobility of analyte molecules and the end groups of the retaining alkyl chains. 3.4. Surface Diffusion and Analyte Retention. Like retention, which depends on the excess of analyte molecules in the stationary phase compared to the mobile phase, fast surface diffusion is a differential effect, relying on increased lateral diffusivity in the ACN ditch compared to the bulk region. To quantify this mobility increase, we calculated the ratio between D∥,max and D∥,bulk (Tables S10−S13). Figure 8 shows the

Figure 9. Maximum lateral mobility of analyte molecules in the ACN ditch relative to their mobility in the bulk region vs the simulated distribution coefficient K (left panel) and the experimental retention factor k′ (right panel).

Figure 8. Maximum lateral mobility of analyte molecules in the ACN ditch relative to their mobility in the bulk region at different elution strengths (ACN content) of the mobile phase.

shows the lateral mobility increase from surface diffusion (D∥,max/D∥,bulk) versus the simulated distribution coefficient K (left panel) or the experimental retention factor k′ (right panel), directly relates (locally resolved) surface diffusion and (pore-scale) retention data. For each individual analyte, both panels show a positive correlation between retention and surface diffusion, confirming an earlier experimental observation.12 For benzyl alcohol, the positive correlation is restricted to low K- or k′-values (corresponding to ≥60 vol % ACN content of the mobile phase), before the plateau reflecting the upper limit in lateral mobility increase (cf. Figure 8) is reached. A general correlation between retention and surface diffusion is ruled out, as the retention factor and the lateral mobility gain from surface diffusion respond differently to analyte properties. The studied analyte set does not include a sufficient variety of

D∥,max/D∥,bulk values of the analytes as a function of the ACN content of the mobile phase. The D∥,max/D∥,bulk values of the apolar analytes are generally higher and also more sensitive to the ACN volume fraction than the D∥,max/D∥,bulk values of the polar analytes. The plateau observed between 20 and 60 vol % ACN in the D∥,max/D∥,bulk curve of benzyl alcohol suggests an upper limit to the lateral mobility increase for the most polar compound of the analyte set. Except for this plateau, the lateral mobility increase that all analytes experience in the ACN ditch decreases with the ACN content of the mobile phase. Concomitantly, mobility gain differences between the analytes are largest at low ACN content and level out with increasing ACN volume fraction. These observations apply as well to G


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The Journal of Physical Chemistry C molecular structures to draw definite conclusions about the influence of analyte properties on surface diffusion, but the present data indicate that the absence of a polar group benefits analyte retention and surface diffusion, whereas the presence of an apolar side chain benefits only retention. 3.5. Bonded-Phase Contribution to Surface Diffusion. So far, the system property considered relevant to surface diffusion has been the local solvent ratio in the ACN ditch, which results from the interaction of the bonded-phase chains with the W−ACN mobile phase. Apart from this, our earlier work26,28 has suggested an active role of the bonded-phase chains for surface diffusion, that is, that the lateral mobility of analyte molecules in the ACN ditch benefits not only from the favorable solvent ratio but also from contact with bondedphase groups. Figure 10 shows the number of contacts

Figure 11. Maximum parallel diffusion coefficient of analyte molecules in the ACN ditch (D∥,max) and their corresponding bulk molecular diffusion coefficient (Dm,analyte_max) as a function of the local W/ACN ratio at the analyte lateral mobility maximum.

ACN, for example, the local solvent ratio at the analyte lateral mobility maximum contains 60 vol % ACN (Table S3), but the D∥,max values of the analytes are comparable with Dm values for bulk mixtures containing ≥70 vol % ACN (Figure 11). D∥,max > Dm,analyte_max, which can be interpreted as a lubrication of retained analytes by the bonded phase, is observed for all analytes with mobile phases of Dm,analyte_max for local solvent ratios containing

Molecular Dynamics Study of the Relation between Analyte Retention

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