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Surface Diffusion of Aromatic Hydrocarbon Analytes in Reversed-Phase Liquid Chromatography Julia Rybka, Alexandra Hoeltzel, and Ulrich Tallarek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04746 • Publication Date (Web): 28 Jul 2017 Downloaded from http://pubs.acs.org on July 31, 2017

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The Journal of Physical Chemistry

Surface Diffusion of Aromatic Hydrocarbon Analytes in Reversed-Phase Liquid Chromatography Julia Rybka, Alexandra Höltzel, and Ulrich Tallarek* Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany

* Corresponding author. E-mail: [email protected]

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ABSTRACT. In reversed-phase liquid chromatography (RPLC), retained analytes can diffuse faster along the hydrophobic surface of the stationary phase than when dissolved in the water (W) – acetonitrile (ACN) mobile phase. We investigate the surface diffusion of four typical aromatic hydrocarbon analytes in RPLC through molecular dynamics simulations in a slit-pore RPLC model consisting of a silica-supported, endcapped, C18 stationary phase and a 70/30 (v/v) W/ACN mobile phase. Our data show that the lateral (surface-parallel) diffusive mobility of the analytes goes through a maximum in the ACN ditch, an ACN-rich border layer around the terminal part of the bonded-phase chains, because the solvent composition there is more conducive to analyte mobility than the W-rich mobile phase. At their lateral mobility maximum, analytes have contacts with 12–15 bonded-phase groups, 5–6 ACN and 1–2 W molecules. The lateral mobility gain from surface diffusion decreases with analyte polarity first and size second (like and unlike retention in RPLC, respectively). The lateral diffusive mobility of analytes at the ACN density maximum in the RPLC system can be approximated by their bulk molecular diffusion coefficient in a W–ACN mixture that matches the local solvent composition at the ACN density maximum. Based on data received from analyte-free simulations of the RPLC system with mobile phases between 10/90 and 90/10 (v/v) W/ACN and from simulations of the bulk molecular diffusion coefficients of the analytes over this range of W/ACN ratios, we predict that enhanced surface diffusion persists under gradient elution conditions.


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1. INTRODUCTION Reversed-phase liquid chromatography (RPLC), which combines an apolar stationary phase with a polar mobile phase, is used for the separation and purification of a wide variety of molecules. Stationary phases for RPLC are usually silica surfaces bearing chemically bonded alkyl chains, the most popular being dimethyl octadecylsilane (C18) chains; mobile phases for RPLC are mixtures of water (W) and an organic solvent, usually acetonitrile (ACN) or methanol. RPLC separations have high resolution as well as high reproducibility, cover a wide polarity range of analytes, and are reasonably predictable, because RPLC retention follows simple principles. Due to these advantages, RPLC has been the most frequently used liquid chromatography mode for the past 30 years and its popularity will likely continue in the foreseeable future. Empirical knowledge gained from RPLC separations lead early on to questions about how RPLC works on the molecular level. Many of these questions were addressed by computer simulations, mostly by molecular dynamics (MD) and Monte Carlo (MC) methods.1 The first simulation studies focused on structure and dynamics of the stationary and mobile phase, which were investigated for different mobile phase compositions, alkyl chain bonding densities (also referred to as surface coverage), and various types of alkyl chain ligands.1 Through MC simulations of alkyl-modified silica surfaces equilibrated with W–methanol or W–ACN mixtures, Siepmann and coworkers established the presence of three different regions in the RPLC system: (I) the bonded-phase region, which is dominated by the alkyl chains, (II) the interfacial region, where the total solvent density increases from 10% to 90% of its bulk value, and (III) the bulk region, with the properties of a liquid mixture.2,3 Through adding simple solutes (low alkanes and alcohols) to their RPLC model, Siepmann and coworkers were able to provide a molecular-level perspective of the retention mechanism in RPLC.4 These simulations


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showed that small solutes are retained by a combination of partitioning into and adsorption onto the bonded-phase chains.3,4 Simulation studies including true RPLC analytes (that is, molecules that are retained under experimental conditions on a RPLC column) are limited in the literature, but have so far confirmed the mixed partitioning/adsorption mechanism, whereby the retentive contributions from partitioning and adsorption vary with the analyte, the length and surface density of the alkyl chains on the silica support, and the mobile phase composition.5–8 Contrary to solute retention, solute diffusion in the stationary phase has rarely been investigated at the molecular level.6,8,9,10 Columns for high-performance liquid chromatography contain a macro‒mesoporous solid as the chromatographic bed, either a tightly packed bed of mesoporous particles (with particle diameters between 1.5 and 5 µm) or a monolithic bed with flow-through macropores and a mesoporous skeleton.11 The macropores enable fast transport of analytes dissolved in the mobile phase through the chromatographic bed, the mesopores ensure a large surface area for stationary phase–analyte interaction. When the liquid mobile phase is pumped through the column, mass transport in the macropore space (that is, the interstitial space in a particulate bed or the flow-through pores in a monolith) is dominated by advection, but mass transport in the mesopore space (inside the particles or the monolithic skeleton) remains limited to diffusion. Analyte molecules traverse the mesopore space through a combination of pore diffusion and surface diffusion, that is, diffusion in the pore liquid and along the surface of the stationary phase, respectively.12 Surface diffusion in porous media is much discussed in the literature.13‒18 According to a widely assumed mechanism for surface diffusion, originally proposed for solid‒gas interfaces, analyte molecules move abruptly (“jump”) between specific, localized adsorption sites on the surface.17,18 For surface diffusion in RPLC, however, a jumping mechanism is difficult to reconcile with the properties of the chromatographic interface.


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Analytes adsorbed onto the bonded phase encounter the rather flexible, terminal part of the alkyl chains, analytes partitioned into the bonded phase are surrounded by the less flexible, proximal part of the alkyl chains. In the first case, the existence of specific, localized adsorption sites on a surface formed by flexible alkyl chain ends is hardly conceivable; in the second case, the presence of the surface-tethered alkyl chains hinders the lateral movement of any solute near the silica surface. Moreover, experimental studies of mass transfer in RPLC have indirectly shown that the surface diffusion of retained analytes can be faster than their diffusive movement in the mobile phase.19,20 In these studies, carried out on C18 columns, the surface diffusion coefficient was observed to increase with the retention of an analyte, suggesting a positive correlation between surface diffusion and retention. The enhanced surface diffusion in RPLC provides comparatively fast transport of retained analytes across the mesopore space. The high intraparticle diffusivity decreases the mass transfer resistance between stationary and mobile phase, which, in turn, increases the separation efficiency.19‒21 In short, surface diffusion is a distinctive, beneficial feature of RPLC separations,21 though its mechanism remains largely unknown. We have recently begun to investigate how surface diffusion in RPLC works on the molecular level through MD simulations using a simple model consisting of a plane silica slab between two solvent reservoirs containing a W‒ACN mixture.22 Due to periodic boundary conditions, the model equals a 10-nm slit pore. The silica surface is modified to bear C18 chains, endcapping groups, and residual OH groups to mimic a silica-supported, endcapped, C18 stationary phase in contact with a W‒ACN mobile phase. The model represents a simplified mesopore inside an RPLC column, eliminating the complexities introduced by curvature,23,24 roughness,25 and defects26 of the silica surface. The surface heterogeneities of the silica support provide sites for


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the heterogeneous adsorption of solute molecules, a process that causes asymmetry and widening of chromatographic peaks and thus decreases the overall separation efficiency.27 Although an inevitable complication of experimental RPLC separations, the complex features of the silica support detract from the true RPLC retention mechanism of partitioning into and adsorption onto the bonded phase. The MD simulations conducted with the RPLC slit-pore model in our first study on surface diffusion22 recovered the experimentally observed uptake of organic solvent from the aqueous–organic mobile phase by the stationary phase, which happens during column equilibration.28,29 The molecular-detail picture obtained for the equilibrated system revealed that ACN molecules accumulate around the alkyl chain ends, forming an ACN-rich border layer between the bonded phase and the mobile phase, which is why we described this layer as an “ACN ditch”. Our data showed that the diffusion of simple solute molecules (butane, 1propanol) in the direction parallel to the silica surface (lateral diffusion) was strongly hindered in the bonded-phase region, but enhanced in the interface region. The lateral mobility increase compared with the bulk region was modest for 1-propanol (8%), but spectacular (52%) for butane. The lateral mobility increase in the interface region was shown to stem mostly from the ACN-rich solvent composition in the ditch, which benefits the diffusive mobility of solutes, particularly that of apolar molecules. The solutes used in this first study were examples of simple apolar and polar molecules rather than real RPLC analytes. Butane is gaseous at room temperature and would be analyzed by gas chromatography. Propanol could be regarded as a retention-modifying co-solvent of ACN in hydrophilic interaction liquid chromatography.30,31 In this work, we want to extend our knowledge of surface diffusion in RPLC to true analytes. We selected four aromatic hydrocarbons that are frequent and typical analytes in RPLC separations (Figure 1). Benzene and ethylbenzene are apolar molecules that differ in size;


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acetophenone and benzyl alcohol are weakly to moderately polar molecules that differ in their hydrogen bond (HB) capabilities. Acetophenone is a HB acceptor, benzyl alcohol can act as HB donor and acceptor. RPLC retention increases with decreasing polarity of an analyte and, at comparable polarity, with the size or the number of C atoms of an analyte. According to these rules, the retention of the four analytes on a C18 column decreases in the order: ethylbenzene > benzene > acetophenone > benzyl alcohol.32 Each analyte species is introduced separately to our established RPLC slit-pore model.22 We use a W-rich mobile phase of 70/30 (v/v) W/ACN, which has weak elution strength on a C18 column, so that analytes are strongly retained on the stationary phase and move primarily via surface diffusion. We address the question how analyte molecules diffuse along the stationary phase surface while being retained by this surface from moving back into the liquid mobile phase, focusing on the correlation between analyte retention and surface diffusion.

2. SIMULATIONS 2.1 Simulation box and force field parameters. Figure 2 shows the fully periodic, rectangular simulation box with dimensions of 12.14 nm (x) × 13.2 nm (y) × 10.93 nm (z). The box contains a central, three-layer silica slab (0.93-nm wide in z-direction) with two 5-nm wide solvent reservoirs on each side (left panel). Due to the applied periodic boundary conditions, the system is a 10-nm slit pore (right panel). The pore width suffices to recover bulk liquid behavior in ~50% of the pore volume. Following an approach of Coasne et al.,33 a surface bearing 4.5 single silanol groups/nm² (7.5 µmol/m²) was created from the (111) face of β-cristobalite SiO2, the preferred crystalline model for the amorphous structure of chromatographic silica supports.34 The surface was randomly grafted with 1.87 dimethyl octadecylsilane chains/nm2 (3.11


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µmol/m2) and 0.56 trimethylsilyl groups/nm2 (0.93 µmol/m2), which left 2.06 residual surface OH groups/nm2 (3.42 µmol/m2). The force field parameters for the Si, O, and H atoms of the silica surface were taken from Gulmen and Thompson.35 The transferable potentials for phase equilibria united-atom (TraPPE-UA) force field was used for dimethyl octadecylsilane chains and trimethylsilyl groups.36–38 The force-field choice for the solvent molecules, the simple point charge/extended (SPC/E) force field for W and the TraPPE-UA force field for ACN molecules,39,40 was informed by research of Mountain.41,42 Judging by the ability to recover experimental values for liquid density, the amount of hydrogen bonding between W and ACN molecules, and the amount of microheterogeneity, Mountain recommended this force-field combination to simulate W‒ACN mixtures. The SPC/E force field is moreover a good choice for this study because is recovers the W diffusion coefficient well. The aromatic hydrocarbon analyte molecules were treated with the explicit CHARMM general force field (CGenFF),43,44 as this force field provided parameters for all of the studied analyte structures. Our force field choices are validated by the results of our simulations for analyte retention and diffusion behavior, which agree with data from chromatographic experiments as well as estimates from empirical correlations, as pointed out at the appropriate places in the Results and Discussion section. 2.2 Molecular dynamics simulations. MD simulations were carried out with GROMACS 4.6.7.45,46 A Nosé‒Hoover thermostat with a coupling constant of 0.25 ps was used to keep the temperature at 300 K. The equations of motion were integrated with a time step of 1 fs. Productive simulations were conducted for a canonical NVT ensemble (constant number of molecules N, volume of simulation box V, and temperature T). Simulations with analyte molecules (each species separately) were carried out for a 70/30 (v/v) W/ACN mobile phase,


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with Nanalyte = 10, NW = 23970, and NACN = 4902. Simulations without analyte molecules were carried out for eleven mobile phases between 90/10 and 10/90 (v/v) W/ACN (Table S1 in the Supporting Information lists the values of NW and NACN for each W/ACN ratio). The steepest descent method was used for energy minimization. Initial velocities were randomly assigned through a Maxwell–Boltzmann distribution. After a 60-ns equilibration period, productive simulation runs were run for up to 1 µs. The output frequency for the output trajectory was set to 0.5 ps. Long-range electrostatic interactions were treated with the particle-mesh Ewald algorithm. Non-bonded 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 in earlier work,22 was used for all interactions. The necessary number of W and ACN molecules in the simulation box, NW and NACN, respectively, to recover a mobile phase of a targeted W/ACN ratio was determined in preliminary simulation runs. Preliminary simulations were carried out for an NPT ensemble (constant number of molecules, pressure P, and temperature). The values for NW and NACN were manually adjusted between simulation runs until the W and ACN densities in the center of the slit-pore (z = 3–5 nm, measured from the location of the surface Si atoms at z = 0), that is, safely away from any stationary phase influences, approached the respective solvent densities of the targeted W/ACN mixture to an accuracy of ±1%. This procedure ensured that the parallel diffusion coefficients ∥ of ACN and W in the center of the slit-pore recovered (to an accuracy of ±1.5%) the bulk molecular diffusion coefficients Dm of ACN and W, respectively, as determined from NPT ensemble simulations.


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2.3 Calculation of bonded-phase, solvent, and analyte density profiles. Density profiles were calculated from the atom 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 center-of-mass of the analyte molecules. The distance z was measured from the position of the surface Si atoms (z = 0). A bin size of 0.02 nm was used for bonded-phase groups and for solvent molecules at z < 1 nm. For analyte molecules and for solvent molecules at z > 1 nm, bin sizes of 0.05 nm and 0.1 nm were used, respectively. 2.4 Determination of analyte orientation and hydrogen bonding. The orientation of analyte molecules relative to the silica surface was determined as the probability distribution of the cosine of the angle β between the surface normal and the molecular vector for all analyte molecules within a specified z-interval. According to the definition of the molecular vector (Figure 1), cos β > 0 indicates that molecules direct their substituted group away from the surface, cos β < 0 indicates that molecules point their substituted group towards the surface, and cos β = 0 indicates a surface-parallel orientation of the benzene ring. (A graphic illustration is provided in Figure S1 in the Supporting Information.) HBs between solvent and polar analyte molecules (Table S2 in the Supporting Information lists the determined values) were assumed based on fulfillment of the following geometric criteria: (i) distance between donor O and acceptor X atom (X = N, O) < 0.35 nm, (ii) distance between donor H and acceptor X atom < 0.25 nm, and (iii) angle between the O···X vector and the OH-bond vector of the donor < 30°.47 2.5 Determination of the immediate environment of analyte molecules. The shell of solvent molecules surrounding an analyte molecule as well as the number of contacts between an analyte molecule and the bonded phase was calculated by determining the distance between an analyte


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molecule’s center-of-mass and the O atom of W, the central C atom of ACN, or the united-atom groups of the alkyl chains. A solvent molecule was counted as part of the solvation shell if the distance between solvent and analyte molecule was smaller than the first minimum in the radial distribution function of the solvent, that is, 0.49 nm for W and 0.65 nm for ACN. Likewise, a united-atom group of the alkyl chains was counted as bonded-phase contact if the distance between united-atom group and analyte molecule was smaller than 0.74 nm. The observation time was 20 ns and the number of contacts was averaged over all 0.5 ps time steps. 2.6 Calculation of the parallel diffusion coefficient of bonded-phase groups, solvent and analyte molecules. The local diffusion coefficient in the direction parallel to the silica surface, ∥ , was calculated for bonded-phase groups, solvent and analyte molecules following an approach by Liu et al.48 The mean squared displacement 〈 〉 of a bonded-phase group, solvent or analyte molecule within a specified space interval along the z-axis was repeatedly recorded for 20-ps time intervals; ∥ was then calculated from the linear slope (t = 4–16 ps) of the observation curve according to the Einstein equation: 〈 〉

∥ =

(1)

Figure S2 in the Supporting Information shows the mean squared displacement 〈 〉 of benzene molecules observed at different space intervals along the z-axis for a 20-ps time interval. The local parallel diffusion coefficient was determined with a bin size of 0.2 nm along the z-axis, allowing the molecules a shift of ±0.3 nm around their initial z-coordinate. Only molecules that remained in the specified space interval for the whole observation time were considered. The percentage of contributing molecules ranged from 76–95% in the bulk region over 79–96% in the space interval of z = 1.5–1.9 nm to 94–99% in the space interval of z = 0.3–0.7 nm. The local parallel diffusion coefficient ∥ is given as the average value with an error estimate calculated


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from the difference between the values obtained from the slope of the mean squared displacement curve over the two halves of the fit interval (i.e., t = 4–10 and t = 10–16 ps). For solvent molecules and bonded-phase groups 40 ns of the trajectory were analyzed, for analyte molecules the whole trajectory (1 µs) was analyzed. Complementary, a 50 ns trajectory was collected for solvent and analyte molecules after equilibration of the respective system. During this additional interval, the bonded-phase chains were frozen in place, that is, they could not move any longer and so mimicked a hard (but still permeable) wall. 2.7 Calculation of the bulk molecular diffusion coefficient of solvent and analyte molecules. The bulk molecular diffusion coefficients of solvent and analyte molecules in 90/10, 80/20, 75/25, 70/30, 60/40, 50/50, 42/58, 40/60, 31/69, 30/70, 29/71, 26/74, 25/75, 22/78, 20/80, 15/85, 13/87, 10/90, 8/92, and 0/100 (v/v) W/ACN were determined with an NPT ensemble consisting of Nsolvent = 10000 (i.e., NW = 9000 and NACN = 1000 for 90/10 (v/v) W/ACN, etc.) and Nanalyte = 2 of a certain species. Trajectories were run over 10 ns of which the final 1 ns (solvent molecules) or 5 ns (analyte molecules) were used for data analysis. 101 and 501 time origins were used to estimate the mean squared displacement of solvent and analyte molecules, respectively. 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. The bulk molecular diffusion coefficient is given as the average value ± standard deviation determined from 3–5 individual simulation runs.

3. RESULTS AND DISCUSSION 3.1 Distribution of bonded-phase chains, solvent molecules, and analyte molecules in the RPLC system. Figure 3 shows the density profiles of the bonded-phase chains, the solvent


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molecules, and the analyte molecules at a mobile phase of 70/30 (v/v) W/ACN in the bulk region of the reservoirs. We start with a short description of the bonded-phase and solvent density in the RPLC system as background for the analyte distribution. The bonded phase shows well-defined density peaks close to the silica support and broader peaks toward the bulk region, which reflect the increasing flexibility of the alkyl chains with increasing distance from the surface. W molecules are mostly confined to the bulk region, except for some surface-adsorbed W molecules (peak at z = 0.25 nm), that is, W molecules that form HBs with residual surface OH groups. ACN molecules are also present in the surface-near region: the peaks at z = 0.37 nm and 0.57 nm stem from ACN molecules that accept HBs from residual surface OH groups and surface-adsorbed W molecules, respectively, and are thus oriented with their N atoms to the silica surface. W and ACN molecules of the first two density peaks constitute solvent spots between the alkyl groups of the bonded-phase rather than solvent layers. The same solvent structure was observed previously for W‒ACN mixtures at a silica surface modified with 3-(2,3dihydroxypropoxy)-propyldimethylsilyl chains.49 In the latter case the chain ends bore polar functionalities as opposed to the fully hydrophobic C18 chains studied here, but the stationary phase structure at and near the hard surface was similar, namely, isolated, hydrophilic spots formed by residual surface OH groups in an otherwise hydrophobic environment formed by the alkyl groups of the bonded phase. The presence of the bonded-phase chains prevents the formation of a laterally coherent solvent layer close to the hard surface and thus the organization of ACN molecules into a lipid-bilayer-like structure, such as exists at the unmodified silica surface in the presence or absence of W.50,51 The most distinctive as well as relevant feature of the ACN density profile is the broad peak in the interface region, where the ACN density (6.81 ± 0.01 atoms/nm3) is twice as high as in the


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bulk region (3.34 ± 0.03 atoms/nm3). The ACN ditch is easily recognized in a snapshot of the equilibrated system (Figure 2), resembling a protective layer that guards the hydrophobic alkyl chains against the W-rich mobile phase. The ACN ditch forms during column equilibration with the mobile phase, when the W‒ACN mixture segregates upon contact with the hydrophobic surface formed by the bonded-phase chains. The hydrophobic interaction between the bonded phase and ACN molecules is driven by W molecules who prefer W‒W HBs over W‒ACN HBs.52 Although the physicochemical mechanism of hydrophobic attraction is driven by W, the chromatographic literature refers to the selectivity of the column towards the components of the mobile phase,28,29,31 because in chromatography the column is the central concept to which everything else relates. The hydrophobic bonded phase takes up ACN from the W‒ACN mobile phase so that ACN density is increased and W density decreased in the interface region. As a result, the W/ACN ratio is tipped towards the organic component. The local solvent ratio at the ACN density maximum (z = 1.75 ± 0.1 nm) is 28/72 (v/v) W/ACN, roughly the opposite of the W/ACN ratio in the bulk reservoirs. All analyte density profiles contain a peak in the bonded-phase region (peak 1) and a peak in the interface region (peak 2), reflecting retention through partitioning and adsorption, respectively. Analyte density in the bulk region is generally low, in accordance with the weak elution strength of the W-rich mobile phase. The analyte density profiles in Figure 3 allow an easy differentiation between apolar and polar molecules. The apolar analytes, benzene and ethylbenzene, have nearly equal-sized partitioning and adsorption peaks, so that analyte density is well distributed over the length of the alkyl chains. The polar analytes, acetophenone and benzyl alcohol, strongly favor the adsorption over the partitioning peak, so that analyte density is concentrated on the mid-to-end segments of the alkyl chains. Also, the location of the adsorption


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peak shifts toward the bulk region at increasing analyte polarity (from z = 1.28 nm for benzene and ethylbenzene to z = 1.58 for acetophenone and z = 1.63 for benzyl alcohol), whereas the partitioning peak location is not influenced by analyte polarity. The experimentally observed retention order of the four analytes on a C18 stationary phase (ethylbenzene > benzene > acetophenone > benzyl alcohol) is reflected in the density of the analytes in the bulk region and in the relative weight of partitioning and adsorption peak. Analyte density in the bulk region increases from ethylbenzene (0.38 ± 0.06 × 10–4 nm–3) to benzene (1.92 ± 0.08 × 10–4 nm–3) to acetophenone (5.3 ± 0.5 × 10–4 nm–3) to benzyl alcohol (11.7 ± 0.6 × 10–4 nm–3), that is, analyte density in the bulk region increases with decreasing retention on the stationary phase. The partitioning peak area reaches 53.1% (ethylbenzene), 46.4% (benzene), 14.9% (acetophenone), and 3.4% (benzyl alcohol) of the adsorption peak area, that is, the relative weight of the partitioning peak decreases with decreasing retention on the stationary phase. Taken together, the analyte density profiles of Figure 3 reflect the intricacies of RPLC retention, while agreeing very well with the empirical knowledge garnered from RPLC practice. For a quantitative comparison with experimental data, we calculated the retention factor of the analytes. The retention factor is defined as the ratio between the number of molecules residing (at any time) in the stationary phase and the number of molecules in the mobile phase. In the literature, the Gibbs dividing surface is used to define the border between stationary and mobile phase.1 In our system, the Gibbs dividing surface (i.e., the surface where the excess number of solvent molecules is zero) is located at z = 1.75 nm. Using this definition, we determined retention factors of 27.9 (ethylbenzene), 9.9 (benzene), 3.2 (acetophenone), and 2.2 (benzyl alcohol) for the analytes. These values reflect experimental retention factors of 20.68 (ethylbenzene), 5.45 (benzene), and 2.05 (acetophenone), which were obtained on a C18 column


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with a mobile phase of 60/40 (v/v) W/ACN,53 rather well. The good agreement between simulated and experimental retention factors validates our force field choices with respect to analyte retention. 3.2 Orientation of analyte molecules in the RPLC system. To investigate how analyte molecules orient themselves at the retention-relevant locations in the system (Figure 4), we calculated the probability distributions of the cosine of the angle β between surface normal and the molecular vector of an analyte molecule at z-intervals of ±0.05 nm around the maxima of the partitioning peak (peak 1), the adsorption peak (peak 2), and the ACN density (ACN ditch). Benzene molecules have random orientation in the interface region (adsorption peak and ACN ditch). In the bonded-phase region (partitioning peak), benzene molecules show a slight preference for an orientation where the molecular plane forms an angle of either 63° or 117° with the surface normal. The snapshot shows that a partitioned benzene molecule has contacts with dimethylsilyl and trimethylsilyl groups of C18 chains and endcapping groups, respectively. Partitioned ethylbenzene molecules preferentially intercalate between the alkyl chains, whereby the ethyl side chain may point to or away from the surface. In the interface region, ethylbenzene molecules have a slight preference to point the ethyl chain to the surface, whereby the probability for this orientation is higher in the ACN ditch than in the adsorption peak. According to Figure 4, maximum contact between analyte molecules and bonded-phase chains, which allows maximizing van der Waals attractions between analytes and the bonded phase, as well as minimal space consumption in the surface-near region are the guiding principles for the orientation of apolar analytes in the RPLC system. Because of their HB capabilities, the polar analytes show a far stronger orientational preference than the apolar analytes in the RPLC system. In the bonded-phase region, polar


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analytes orient their side chain to the silica surface to form HBs with surface-adsorbed solvent molecules; in the interface region, polar analytes orient their side chain to the bulk region to form HBs with solvent molecules of the mobile phase. Throughout the system, benzyl alcohol forms more HBs than acetophenone. For both species the average number of HBs per analyte molecule (HBanalyte) decreases by ~50% from the bulk region to the bonded-phase region (Table S2 in the Supporting Information). In the bonded-phase region, acetophenone orientation is more strongly enforced than benzyl alcohol orientation (the probability maximum is 2.65 for acetophenone and 2.05 for benzyl alcohol, both at an angle of 130.5°). Acetophenone forms less HBs (HBanalyte = 0.6) than benzyl alcohol (HBanalyte = 1.0) in the bonded-phase region, but the stiff acetophenone molecule requires a specific orientation to act as HB acceptor to the surface-bound W molecules. (The carbonyl group of acetophenone lies in plane with the ring C atoms, because carbonyl group and benzene ring are part of the same π-electron system.) In the interface region, benzyl alcohol orientation is more strongly enforced than acetophenone orientation, because benzyl alcohol forms more HBs (HBanalyte = 1.5–1.6) with the mobile phase than acetophenone (HBanalyte = 0.8–0.9). Acetophenone molecules reach their probability maximum of 0.86 at an angle of 49°, that is, the side chain is nearly diagonal to the surface normal. Benzyl alcohol molecules have their probability maximum of 1.02 (adsorption peak) and 1.07 (ACN ditch) at 18°, that is, the side chain is nearly parallel to the surface normal. Overall, the polar analytes orient themselves so that their hydrophobic part is immersed in the bonded phase and their polar side chain is well positioned for HB formation with solvent molecules. 3.3 Immediate environment of analyte molecules in the RPLC system. To complete the molecularly detailed picture of the studied RPLC system, we analyzed how the immediate environment of an analyte molecule changes as it moves from the bulk into the bonded-phase


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region (Table 1). In the bulk region, analyte molecules are surrounded by 5–6 ACN and 3–5 W molecules of the mobile phase. Expressed in volumetric ratios, the solvation shell of an analyte molecule in the bulk region equals 23/77 (v/v) W/ACN for benzene, 22/78 (v/v) W/ACN for acetophenone and benzyl alcohol, and 17/83 (v/v) W/ACN for ethylbenzene. These numbers show that the four analytes have quite similar solvation shells in the bulk region and that all of them prefer an environment significantly richer in ACN than the mobile phase of 70/30 (v/v) W/ACN. At the border between the bulk and interface regions, that is, at the outer edge of the ACN ditch, analyte molecules enter a more hydrophobic environment. An analyte molecule at this location has contacts with 4–5 bonded-phase groups. One ACN molecule is added to the solvation shell, while 1–2 W molecules are lost. In the middle of the ACN ditch, at the ACN density maximum, analyte molecules are in contact with 18–19 (apolar analytes) or 16 (polar analytes) bonded-phase groups. The ACN molecule that was added to the solvation shell at the outer edge of the ACN ditch is lost here, along with another 1–2 W molecules. The differentiation between apolar and polar analytes that started in the ACN ditch with the number of bonded-phase contacts reaches its maximum in the adsorption peak. Adsorbed apolar analytes have contacts with 32 bonded-phase groups, adsorbed polar analytes only with 19–20 bondedphase groups, that is, adsorption of polar analytes involves less interaction with the bonded phase than adsorption of apolar analytes. This finding corresponds to the slightly different location of the adsorption peaks of polar and apolar analytes (Figure 3), that is, with the shift of the adsorption peaks of the polar analytes towards the bulk region. Consequently, adsorbed polar analytes hold more solvent molecules in their environment than adsorbed apolar analytes. Apolar analytes have lost practically all W molecules from their environment and reduced the number of ACN molecules to 3–4. Adsorbed polar analytes still hold a W molecule in addition to 4–5 ACN


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molecules in their environment. In the partitioning peak, the difference between apolar and polar analytes has largely vanished. Apart from a slightly lower number of bonded-phase contacts (40– 41 for polar vs. 43 for apolar analytes), polar analytes retain 0.5 W molecules in their immediate environment. These are the surface-attached W molecules with which the polar analytes form HBs. Polar as well as apolar partitioned analytes have one ACN molecule left in their environment, owing to the presence of ACN molecules near the silica surface as coordinators of residual surface OH groups or of surface-attached W molecules. The snapshots in Figure 5 illustrate the changing environment of an ethylbenzene molecule at increasing distance from the silica surface. A fully partitioned ethylbenzene molecule (Figure 5A) is surrounded by bonded-phase groups first and ACN molecules second. The same applies to an adsorbed ethylbenzene molecule (Figure 5B), though the bonded-phase contacts now involve the mid-to-end rather than the more surface-near segments of the alkyl chains. In the ACN ditch (Figure 5C), the number of bonded-phase contacts decreases in favor of more ACN molecules in the immediate environment. In the bulk region (Figure 5D), the number of W and ACN molecules in the solvation shell does not reflect the W/ACN ratio of the mobile phase, but the W-driven hydrophobic attraction between ethylbenzene and the organic solvent. The data in Table 1 reflect that for all analyte species, the number of W molecules in the immediate analyte environment decreases monotonically from mobile phase to silica surface, while the number of ACN molecules goes through a maximum in the interface region. The analyte environment contains the maximum number of ACN molecules at the outer edge of the ACN ditch, where bonded-phase contacts are still few. At the ACN density maximum, the analyte environment is already dominated by bonded-phase contacts, but analytes nevertheless


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cling to their ACN neighbors. The analyte environment at the ACN density maximum contains practically as many ACN molecules as the solvation shell of the analyte in the bulk region. 3.4 Lateral mobility of solvent and analyte molecules in the RPLC system. After setting the stage by describing distribution, orientation, and immediate environment of the analyte molecules at different locations in the RPLC system, we return to the question of surface diffusion. Figure 6 shows the diffusion coefficient profiles of solvent and analyte molecules for motion parallel to the silica surface. In addition, Table 2 gives explicit values of the parallel diffusion coefficient ∥ for analytes at specific locations in the system (the corresponding ∥ values for solvent molecules are listed in Table S3). The lateral mobility of W molecules decreases, as expected, monotonically from the bulk region (∥ = 2.20–2.23 × 10–5 cm2/s) to practically zero in the bonded-phase region (∥ = 0.003‒0.005 × 10–5 cm2/s). In contrast, the ∥ values of ACN and the analytes go through a maximum in the interface region, that is, the lateral movement of ACN and the analytes is faster in the ACN ditch, where alkyl chains of the bonded phase are present, than their diffusive movement in the purely liquid bulk region. The ∥ maximum of ACN (z = 1.75 nm) coincides with the ACN density maximum; the ∥ maximum of the analytes (z = 1.90 nm) is shifted by 0.15 nm from the ACN density maximum to the bulk region. ACN has the highest lateral mobility of all organic components in the ACN ditch (∥, = 2.32–2.35 × 10–5 cm2/s), followed by benzene ( ∥, = 2.10 ± 0.10 × 10–5 cm2/s), ethylbenzene (∥, = 1.67 ± 0.08 × 10–5 cm2/s), then acetophenone (∥, = 1.34 ± 0.03 × 10– 5

cm2/s), and finally benzyl alcohol (∥, = 1.29 ± 0.03 × 10–5 cm2/s). Interestingly, the lateral

mobility of ethylbenzene is comparable with that of the terminal bonded-phase group, CH3(18), for which a parallel diffusion coefficient of ∥ = 1.64 × 10–5 cm2/s was estimated at the analyte ∥ maximum (Table 3), and the lateral mobility of the polar analytes is comparable with that of


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the CH2(17) group of the alkyl chains at this location (∥ = 1.33 × 10–5 cm2/s, Table 3). That the last two bonded-phase groups of the alkyl chains have comparable lateral mobility as the analyte molecules with which they are in contact reinforces the concept of the ACN ditch as a region of increased lateral mobility for all organic components. From the bulk region to their maximum mobility in the ACN ditch, ∥ increases by 25% for ACN, by 53% for benzene, by 37% for ethylbenzene, by 25% for acetophenone, and by 16% for benzyl alcohol. The apolar analytes, benzene and ethylbenzene, experience a larger mobility increase than ACN, whereby the effect is stronger for the smaller molecule. Acetophenone shows the same mobility increase as ACN (both are polar, aprotic molecules), whereas benzyl alcohol (a polar, protic molecule) has a lower mobility increase than ACN. The absolute lateral mobility in the ACN ditch as well as the relative gain in lateral mobility from the bulk region to the ACN ditch decreases in the order: benzene > ethylbenzene > acetophenone > benzyl alcohol, that is, surface diffusion depends, like retention in RPLC, on analyte polarity first and size second. Like retention, surface diffusion increases with decreasing analyte polarity, but unlike retention, surface diffusion increases with decreasing analyte size. 3.5 Influence of local solvent composition and the bonded phase on lateral mobility. In our first publication on surface diffusion,22 we had shown that the lateral mobility of small solutes in the interface region between a C18 stationary phase and a W–ACN mobile phase was nearly equal to their diffusive mobility in a bulk liquid of the same W/ACN ratio as present in the interface region. Based on this observation, we proposed the ACN-rich solvent composition in the interface region as the origin of the enhanced surface diffusion in RPLC. To verify this hypothesis for retained compounds such as the studied aromatic hydrocarbon analytes, we first determined the average local solvent compositions felt by analytes at the ACN density maximum


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and at the ∥ maximum. For this, we took the z-extension of the analytes, that is, their size and orientation at these locations, into account. Benzene molecules at their maximum lateral mobility (that is, with their center of mass at z = 1.90±0.01 nm) extend over z = 1.72–2.08 nm, ethylbenzene molecules over z = 1.68–2.12 nm, acetophenone over z = 1.67–2.11 nm, and benzyl alcohol over z = 1.69–2.11 nm; in each case, the average local solvent composition over the zextension of the analyte is 40/60 (v/v) W/ACN. Analytes at the ACN density maximum (that is, with their center of mass at z = 1.75 ± 0.01 nm) experience an average local solvent composition of 29/71 (v/v) W/ACN. Next, the bulk molecular diffusion coefficients Dm of the analytes were simulated for W–ACN mixtures containing between 10 and 100 vol % ACN, that is, over the practical range used in RPLC separations, and including explicitly the local solvent compositions experienced by the analytes at the ACN density maximum and the ∥ maximum. Figure 7 shows that Dm of ACN and all analyte species increases considerably at high ACN volume fractions. The Dm curves of the polar analytes are close together and have a similar dependence on the ACN volume fraction as the Dm curve for ACN. An appreciable increase in Dm of ACN and the polar analytes starts at ~60 vol % ACN, whereas the Dm values of the apolar analytes show a higher sensitivity to the ACN volume fraction and begin their increase already at ~30 vol % ACN. Calculating the bulk diffusion coefficients of the analytes provided another opportunity to validate our force field choices with respect to diffusion behavior. The simulated Dm values were compared with experimental data (if available) and with Dm values estimated according to the empirical correlations approach of Li and Carr.54,55 The comparison with experimental data, where possible, gave excellent agreement. Experimental Dm values were available for benzene in 80, 90, and 100 vol % ACN and for acetophenone in 30 vol % ACN for a temperature of 303.15


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K,54 so that for comparison purposes we simulated the corresponding Dm values at this temperature. We obtained values of Dm = 2.48 ± 0.12 × 10–5 cm2/s, 2.89 ± 0.03 × 10–5 cm2/s, and 3.46 ± 0.14 × 10–5 cm2/s for benzene in 80, 90, and 100 vol % ACN, respectively. The experimental values were Dm = 2.32 × 10–5 cm2/s, 2.82 × 10–5 cm2/s, and 3.73 × 10–5 cm2/s in 80, 90, and 100 vol % ACN, respectively, which amounts to a deviation of less than 10% of the simulated from the experimental values. For acetophenone in 30 vol % ACN, the simulated value of Dm = 1.03 ± 0.09 × 10–5 cm2/s showed less than 20% deviation from the experimental value of Dm = 0.86 × 10–5 cm2/s.54 Comparison of simulated Dm data for all analytes over a wide range of W/ACN ratios was possible through the approach of Li and Carr.55 The simulated data deviated at maximum by 15–20% from the estimated Dm values, which is excellent agreement considering that Li and Carr give an error of 10% for their approach. Table 4 compares the ∥ values obtained for ACN and the analytes in the bulk region, at the analyte ∥ maximum, and at the ACN density maximum with the Dm values at the W/ACN ratios experienced by ACN and the analytes at these locations. The ∥ values of ACN and all analyte species in the bulk region agree (within the statistical limits) with the respective Dm values at 70/30 (v/v) W/ACN, fulfilling another validation criterion for our simulations. The ∥ values of ACN and all analyte species at the analyte ∥ maximum are higher than the respective Dm values at 40/60 (v/v) W/ACN, whereas at the ACN density maximum, only the ∥ value of ACN remains above its Dm value at 29/71 (v/v) W/ACN. The ∥ values of the analytes at the ACN density maximum are either equal to (benzene and benzyl alcohol) or slightly lower (ethylbenzene and acetophenone) than their Dm values at 29/71 (v/v) W/ACN. In short, for all analytes species, ∥ = Dm in the bulk region, ∥ > Dm at the analyte ∥ maximum, and ∥ ≈ Dm at the ACN density maximum.


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The comparison of ∥ and Dm values in Table 4 confirms the local solvent composition as the main influence on the lateral mobility of ACN and the analyte molecules and thus establishes the ACN-rich solvent composition in the interface region as the origin of the enhanced surface diffusion of retained analytes in RPLC. The data in Table 4 also reflect a moderating influence of the bonded phase on the lateral mobility of retained analytes. Observing ∥ > Dm at the analyte ∥ maximum (z = 1.90 nm) suggests a beneficial influence of the bonded phase on the lateral mobility of analytes at this location, which has vanished at the ACN density maximum (z = 1.75 nm). From z = 1.90 to 1.75 nm, the number of bonded-phase contacts grows from 13.0 to 18.3 for benzene, from 14.7 to 19.0 for ethylbenzene, from 12.3 to 16.4 for acetophenone, and from 11.5 to 15.9 for benzyl alcohol (Table 1), which corresponds to a 29–40% increase in bondedphase contacts for the analytes. Further, the ∥ values of the bonded-phase groups forming the terminal third of the alkyl chains, CH2(13) to CH3(18), which account for >95% of the bondedphase presence in the interface region, decrease by 9‒13% from z = 1.90 to 1.75 nm (Table 3). And last, the contribution to the bonded-phase presence from the most flexible, last two groups of the alkyl chains, CH2(17) and CH3(18), decreases from 71% at z = 1.90 nm to 53% at z = 1.75 nm in favor of increased contributions from less mobile, lower numbered groups (Table 3). Apparently, bonded-phase contacts are conducive to the lateral mobility as long as their number remains moderate and focused on the most flexible groups at the alkyl chain ends. Thus, these flexible bonded-phase groups, whose lateral mobility is comparable to that of the analytes in this region, may be viewed as lubricants.25,56 The lateral mobility enhancement from contact with the bonded phase, that is, the increase from the expected value at the local solvent composition, Dm at 40/60 (v/v) W/ACN, to the actual ∥ value observed at z = 1.90 nm (Table 4), is larger for benzene (21%) than for ethylbenzene (14%) and the polar analytes (12%). Contrary to the


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randomly oriented benzene molecules, ethylbenzene and the polar analytes have orientational preferences at z = 1.90 nm (Figure 4). Maintaining a preferred orientation may detract something from the lateral mobility enhancement provided by the flexible end groups of the bonded phase. It is also conceivable that benzene benefits more from bonded-phase lubrication because of its smaller size. The contribution of chain flexibility to the overall mobility increase of ACN and analyte molecules in the ACN ditch was evaluated through additional simulations, during which the bonded phase was frozen in place after equilibration. In these simulations, where the bondedphase chains mimicked a hard (but still permeable) wall, ACN mobility at z = 1.75 nm decreased by 31% and analyte mobility at z = 1.90 nm by 39–46%. The resulting D|| values at the former mobility maxima were even lower (by 7% for ACN and by 13–32% for the analytes) than the corresponding bulk values. Thus, alkyl chain flexibility is a key factor for the high lateral mobility of ACN and analytes in the ACN ditch. 3.6 Dependence of enhanced surface diffusion on the W/ACN ratio of the mobile phase. We have shown that the enhanced surface diffusion of retained analytes in RPLC originates mainly from the difference between the ACN-rich solvent composition in the interface region and the W-rich bulk region, which suggests that enhanced surface diffusion is susceptible to the W/ACN ratio of the mobile phase. The W/ACN ratio of the mobile phase is the most easily and most frequently changed experimental parameter in RPLC practice. Gradient elution conditions, where the ACN volume fraction in the mobile phase is continually increased over the course of the separation, are the norm in RPLC practice. To estimate the W/ACN range over which enhanced surface diffusion of analytes can be expected to occur without performing a large number of explicit, analyte-including simulations, we took advantage of the observation that the ∥ value of analytes at the ACN density maximum can be approximated by their Dm value at the


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respective local solvent composition (Figure 7). To determine the local solvent composition at the ACN density maximum for different W/ACN ratios of the mobile phase, we performed simulations without analytes for mobile phases between 90/10 and 10/90 (v/v) W/ACN. From the resulting solvent density profiles, the average solvent composition over a range of ±0.22 nm around the ACN density maximum was calculated. This range approximates the z-extension of analytes in the ACN ditch, as observed in simulations with the 70/30 (v/v) W/ACN mobile phase. The underlying assumption that analytes in the ACN ditch maintain a similar z-extension over the investigated range of W/ACN ratios was reasonable considering that the bonded-phase conformation is rather insensitive to the mobile phase composition.1–3 Figure 8A shows the ACN excess in the ditch (calculated as the difference in ACN volume fraction between the ditch and the bulk region) for mobile phases between 10/90 and 90/10 (v/v) W/ACN. The ACN excess in the ditch decreases with increasing ACN content of the mobile phase; the curve has a faintly sigmoidal shape with an inflection point at 50 vol % ACN. Next, the Dm values of the analytes at the W/ACN ratios calculated for the ACN ditch were simulated and compared with the corresponding Dm values simulated at the W/ACN ratios for the bulk region. (Tables S4 and S5 in the Supporting Information list the explicit values for apolar and polar analytes, respectively.) The relative lateral mobility increase that analytes experience between bulk region and ACN ditch was estimated as the increase in Dm from the solvent composition of the bulk region to the solvent composition in the ACN ditch. Figure 8B shows the expected diffusive mobility increase for each analyte species as a function of the ACN content of the mobile phase. Generally, large gains in diffusive mobility are expected for a pronounced ACN excess in the ditch, that is, for mobile phases with lower ACN content. But the individual Dm dependence on ACN volume fraction of each analyte species (Figure 7) must also


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be taken into account. Accordingly, the data in Figure 8b display the individuality of the four analytes. Benzene, ethylbenzene, and acetophenone have their largest mobility gains at 20–25 vol % ACN in the mobile phase, whereas the curve for benzyl alcohol does not take off before 40 vol % ACN, but then stays up until 80 vol % ACN in the mobile phase, where the ACN excess in the ditch is already low. Overall, the mobility gain decreases in the order benzene > ethylbenzene > acetophenone > benzyl alcohol, the same order as observed in the simulations with a mobile phase of 70/30 (v/v) W/ACN. Benzene and ethylbenzene show mobility gains of up to 46% and 41%, respectively, and acetophenone and benzyl alcohol of 34% and 24%, respectively. For benzyl alcohol, the whole effect is not only weaker, but also confined to a narrower range of favorable W/ACN ratios. To observe a lateral mobility gain of at least 20% simultaneously for benzene, ethylbenzene, and acetophenone, the mobile phase may contain between 20 and 70 vol % ACN. To observe a lateral mobility gain of at least 20% simultaneously for all four analytes, the mobile phase must contain between 40 and 70 vol % ACN. On the other hand, Figure 8 shows that Dm is always larger at the solvent composition of the ACN ditch than at the solvent composition of the bulk region, which means that a lateral mobility gain per se is expected for all analyte species at all considered W/ACN ratios. Taken together, the data reflect that, although the extent of the lateral mobility increase is sensitive to the ACN content of the mobile phase, analytes show enhanced surface diffusion over a wide range of W/ACN ratios.

4. CONCLUSIONS Through MD simulations in a slit-pore model, we have elucidated origin and details of the surface diffusion of four typical analytes (benzene, ethylbenzene, acetophenone, and benzyl


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alcohol) in RPLC separations with a C18 stationary phase and a W–ACN mobile phase. Our simulations have shown that the aromatic hydrocarbon analytes have higher lateral mobility in the interface region, where they are already in contact with bonded-phase groups, than in the purely liquid environment of the 70/30 (v/v) W/ACN mobile phase. The enhanced lateral mobility originates mainly from the ACN-rich solvent composition in the interface region, that is, the lateral mobility of analytes benefits from the presence of the ACN ditch, the ACN-rich border layer surrounding the terminal part of the alkyl chains. Analytes reach their maximum lateral mobility 0.15 nm short of the ACN density maximum (i.e., short of experiencing the optimal W/ACN ratio in the system), because at the ACN density maximum increased contacts with bonded-phase groups exert a dampening effect on the mobility. At their lateral mobility maximum, analytes are surrounded by 12–15 bonded-phase groups, 5–6 ACN and 1–2 W molecules. This moderate degree of bonded-phase contacts involves mainly the last two groups of the alkyl chains, CH2(17) and CH3(18), whose lateral mobility is comparable with that of the analytes they are in contact with. The maximum parallel diffusion coefficients of the analytes are larger than their bulk molecular diffusion coefficients at the respective local W/ACN ratio, because the flexible chain ends contribute to the lateral mobility of the analytes. The extent to which the lateral mobility in the ACN ditch is enhanced compared with the bulk region decreases in the order benzene > ethylbenzene > acetophenone > benzyl alcohol, that is, with increasing polarity of the analytes (like their retention) and, at comparable polarity, with increasing size of the analytes (unlike their retention). For the studied system, enhanced surface diffusion of all analyte species is expected for mobile phases between 90/10 and 10/90 (v/v) W/ACN, whereby the magnitude of the lateral mobility gain depends on the W/ACN ratio as well as the analyte species.


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Apart from the conclusions pertaining to the specifics of our study, the presented data support the general conclusion that enhanced surface diffusion in RPLC hinges on the difference in solvent composition between the bulk region and the ACN ditch, which develops upon equilibration of the stationary phase with the mobile phase. The preference of the hydrophobic bonded phase for ACN over W (that is, the W-driven hydrophobic attraction between the bonded-phase chains and ACN molecules) ensures that the ditch holds more ACN than the bulk region over a range of W/ACN ratios in the mobile phase, predicting that enhanced surface diffusion of analytes persists under gradient elution conditions. System variables that are expected to determine the extent of enhanced surface diffusion include the length, chemistry, and surface density of the bonded-phase chains, but also geometry and diameter of the pore. These issues will be addressed and investigated in future work.


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ASSOCIATED CONTENT Supporting Information. Number of W and ACN molecules used in productive simulations of the RPLC system (Table S1). Number of polar analyte–solvent HBs in the RPLC system (Table S2). Parallel diffusion coefficients of solvent molecules at different locations in the RPLC system (Table S3). Bulk molecular diffusion coefficients of apolar analytes at the local solvent compositions of bulk region and ACN ditch (Table S4). Bulk molecular diffusion coefficients of polar analytes at the local solvent compositions of bulk region and ACN ditch (Table S5). Calculation of analyte orientation in the RPLC system (Figure S1). Calculation of the parallel diffusion coefficient of analyte molecules at different locations in the RPLC system (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * Corresponding author. Phone: +49-(0)6421-28-25727; Fax: +49-(0)6421-28-27065; E-mail: [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT We thank the Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften (Garching, Germany) for the allocation of a CPU-time grant (Project ID: pr48su).


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(17) Yang, K.; Sun, Y. Structured Parallel Diffusion Model for Intraparticle Mass Transport of Proteins to Porous Adsorbent. Biochem. Eng. J. 2007, 37, 298–310. (18) Medved, I.; Černý, R. Surface Diffusion in Porous Media: A Critical Review. Microporous Mesoporous Mater. 2011, 142, 405–442. (19) Gritti, F.; Guiochon, G. New Insights on Mass Transfer Kinetics in Chromatography. AIChE J. 2011, 57, 333–345. (20) Gritti, F.; Guiochon, G. Importance of Sample Intraparticle Diffusivity in Investigations of the Mass Transfer Mechanism in Liquid Chromatography. AIChE J. 2011, 57, 346–358. (21) Gritti, F.; Guiochon, G. Comparison between the Intra-Particle Diffusivity in the Hydrophilic Interaction Chromatography and Reversed Phase Liquid Chromatography Modes. Impact on the Column Efficiency. J. Chromatogr. A 2013, 1297, 85–95. (22) Rybka, J.; Höltzel, A.; Melnikov, S. M.; Seidel-Morgenstern, A.; Tallarek. U. A New View on Surface Diffusion from Molecular Dynamics Simulations of Solute Mobility at Chromatographic Interfaces. Fluid Phase Equilib. 2016, 407, 177–187. (23) Rafferty, J. L.; Siepmann, J. I.; Schure, M. R. The Effects of Chain Length, Embedded Polar Groups, Pressure, and Pore Shape on Structure and Retention in Reversed-Phase Liquid Chromatography: Molecular-Level Insights from Monte Carlo Simulations. J. Chromatogr. A 2009, 1216, 2320–2331. (24) Wells, R. H.; Thompson, W. H. What Determines the Location of a Small Solute in a Nanoconfined Liquid? J. Phys. Chem. B 2015, 119, 12446–12454.


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(25) Black, J. E.; Iacovella, C. R.; Cummings, P. T.; McCabe, C. Molecular Dynamics Study of Alkylsilane Monolayers on Realistic Amorphous Silica Surfaces. Langmuir 2015, 31, 3086– 3093. (26) Pfeiffer-Laplaud, M.; Costa, D.; Tielens, F.; Gaigeot, M.-P.; Sulpizi, M. Bimodal Acidity at the Amorphous Silica/Water Interface. J. Phys. Chem. C 2015, 119, 27354–27362. (27) Mabry, J. N.; Skaug, M. J.; Schwartz, D. K. Single-Molecule Insights into Retention at a Reversed-Phase Chromatographic Interface. Anal. Chem. 2014, 86, 9451–9458. (28) Gritti, F.; Kazakevich, Y. V.; Guiochon, G. Effect of the Surface Coverage of Endcapped C18-Silica on the Excess Adsorption Isotherms of Commonly Used Organic Solvents from Water in Reversed Phase Liquid Chromatography. J. Chromatogr. A 2007, 1169, 111–124. (29) Gritti, F. Determination of the Solvent Density Profiles Across Mesopores of Silica-C18 bonded phases in Contact with Acetonitrile/Water Mixtures: A Semi-Empirical Approach. J. Chromatogr. A 2015, 1410, 90–98. (30) Melnikov, S. M.; Höltzel, A.; Seidel-Morgenstern, A.; Tallarek, U. How Ternary Mobile Phases Allow Tuning of Analyte Retention in Hydrophilic Interaction Liquid Chromatography. Anal. Chem. 2013, 85, 8850–8856. (31) Gritti, F.; Höltzel, A.; Tallarek, U.; Guiochon, G. The Relative Importance of the Adsorption and Partitioning Mechanisms in Hydrophilic Interaction Liquid Chromatography. J. Chromatogr. A 2015, 1376, 112–125. (32) Meyer, V. R. Practical High-Performance Liquid Chromatography, 4th ed.; John Wiley & Sons, Ltd, 2004, p. 160.


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(33) Coasne, B.; Di Renzo, F.; Galarneau, A.; Pellenq, R. J.-M. Adsorption of Simple Fluid on Silica Surface and Nanopore: Effect of Surface Chemistry and Pore Shape. Langmuir 2008, 24, 7285–7293. (34) Zhuravlev, N. D.; Siepmann, I. J.; Schure, M. R. Surface Coverages of Bonded-Phase Ligands on Silica: A Computational Study. Anal. Chem. 2001, 73, 4006–4011. (35) Gulmen, T. S.; Thompson, W. H. Testing a Two-State Model of Nanoconfined Liquids: Conformational Equilibrium of Ethylene Glycol in Amorphous Silica Pores. Langmuir 2006, 22, 10919–10923. (36) Martin, M. G.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 1. UnitedAtom Description of n-Alkanes. J. Phys. Chem. B 1998, 102, 2569–2577. (37) Stubbs, J. M.; Potoff, J. J.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 6. United-Atom Description for Ethers, Glycols, Ketones, and Aldehydes. J. Phys. Chem. B 2004, 108, 17596–17605. (38) Martin, M. G.; Siepmann, J. I. Novel Configurational-Bias Monte Carlo Method for Branched Molecules. Transferable Potentials for Phase Equilibria. 2. United-Atom Description of Branched Alkanes. J. Phys. Chem. B 1999, 103, 4508–4517. (39) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269–6271. (40) Wick, C. D.; Stubbs, J. M.; Rai, N.; Siepmann, J. I. Transferable Potentials for Phase Equilibria. 7. Primary, Secondary, and Tertiary Amines, Nitroalkanes and Nitrobenzene, Nitriles, Amides, Pyridine, and Pyrimidine. J. Phys. Chem. B 2005, 109, 18974–18982.


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(41) Mountain, R. D. Microstructure and Hydrogen Bonding in Water–Acetonitrile Mixtures. J. Phys. Chem. B 2010, 114, 16460–16464. (42) Mountain, R. D. Molecular Dynamics Simulation of Water–Acetonitrile Mixtures in a Silica Slit. J. Phys. Chem. C 2013, 117, 3923–3929. (43) Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; et al. CHARMM General Force Field: A Force Field for Drug-Like Molecules Compatible with the CHARMM All-Atom Additive Biological Force Fields. J. Comput. Chem. 2010, 31, 671–690. (44) Fischer, N. M.; van Maaren, P. J.; Ditz, J. C.; Yildirim, A.; van der Spoel, D. Properties of Organic Liquids when Simulated with Long-Range Lennard-Jones Interactions. J. Chem. Theory Comput. 2015, 11, 2938–2944. (45) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free. J. Comput. Chem. 2005, 26, 1701–1718. (46) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. (47) Marti, J. Analysis of the Hydrogen Bonding and Vibrational Spectra of Supercritical Model Water by Molecular Dynamics Simulations. J. Chem. Phys. 1999, 110, 6876–6886. (48) Liu, P.; Harder, E.; Berne, B. J. On the Calculation of Diffusion Coefficients in Confined Fluids and Interfaces with an Application to the Liquid–Vapor Interface of Water. J. Phys. Chem. B 2004, 108, 6595–6602.


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(49) Melnikov, S. M.; Höltzel, A.; Seidel-Morgenstern, A.; Tallarek, U. A Molecular Dynamics View on Hydrophilic Interaction Chromatography with Polar-Bonded Phases: Properties of the Water-Rich Layer at a Silica Surface Modified with Diol-Functionalized Alkyl Chains. J. Phys. Chem. C 2016, 120, 13126–13138. (50) Melnikov, S. M.; Höltzel, A.; Seidel-Morgenstern, A.; Tallarek, U. Evaluation of Aqueous and Nonaqueous Binary Solvent Mixtures as Mobile Phase Alternatives to Water–Acetonitrile Mixtures for Hydrophilic Interaction Liquid Chromatography by Molecular Dynamics Simulations. J. Phys. Chem. C 2015, 119, 512–523. (51) Berne, B. J.; Fourkas, J. T.; Walker, R. A.; Weeks, J. D. Nitriles at Silica Interfaces Resemble Supported Lipid Bilayers. Acc. Chem. Res. 2016, 49, 1605–1613. (52) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640‒647. (53) Long, W. J.; Mack, A. E. Comparison of Selectivity Differences Among Different Agilent ZORBAX Phenyl Columns using Acetonitrile or Methanol, Application Note, Pharmaceutical, Agilent Technologies, Inc., Wilmington, DE, 2009. (54) Li, J.; Carr, P. W. Accuracy of Empirical Correlations for Estimating Diffusion Coefficients in Aqueous Organic Mixtures. Anal. Chem. 1997, 69, 2530–2536. (55) Li, J.; Carr, P. W. Estimating Diffusion Coefficients for Alkylbenzenes and Alkylphenones in Aqueous Mixtures with Acetonitrile and Methanol. Anal. Chem. 1997, 69, 2550–2553.


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(56) Summers, A. Z.; Iacovella, C. R.; Billingsley, M. R.; Arnold, S. T.; Cummings, P. T.; McCabe, C. Influence of Surface Morphology on the Shear-Induced Wear of Alkylsilane Monolayers: Molecular Dynamics Study. Langmuir 2016, 32, 2348–2539.


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TABLES Table 1. Number and type of immediate neighbors of an analyte molecule at different distances z from the silica surface (cf. Figure 3). Nneighbors Analyte

Location

z (nm)

Benzene

partitioning peak max (I)

Ethylbenzene

Acetophenone

Benzyl alcohol

bonded phase

ACN

W

0.73

42.8

0.7

0.1

adsorption peak max (II)

1.28

32.0

3.8

0.4

ACN density max (II)

1.75

18.2

5.4

1.2

analyte ∥ max (II)

1.90

13.0

5.8

1.7

edge of ACN ditch (II/III)

2.19

5.3

6.5

2.8

bulk (III)

>2.21

0

5.6

5.0


0.78

43.3

1.0

0.03


1.28

32.0

3.4

0.2


1.75

19.0

5.1

0.7


1.90

14.7

5.7

0.9


2.19

5.2

6.4

1.8

bulk (III)

>2.21

0

5.1

3.1


0.73

40.7

0.7

0.5


1.58

20.2

4.3

1.3


1.75

16.4

4.7

1.6


1.90

12.3

5.2

1.9


2.19

4.6

5.9

2.6

bulk (III)

>2.21

0

4.9

4.2


0.73

40.0

0.8

0.5


1.63

19.4

4.8

1.4


1.75

15.9

5.3

1.7


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1.90

11.5

5.5

2.1


2.19

3.9

6.4

2.9

bulk (III)

>2.21

0

5.4

4.6


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Table 2. Parallel diffusion coefficients ∥ of analyte molecules at different distances z from the silica surface (cf. Figures 3 and 6). ∥ (10‒5 cm2 s‒1)

Analyte

Location

z (nm)

Benzene


0.73

0.27 ± 0.02


1.28

1.29 ± 0.04


1.75

1.98 ± 0.05


1.90

2.10 ± 0.10

bulk (III)

>2.5

1.37 ± 0.05


0.78

0.27 ± 0.03


1.28

1.01 ± 0.03


1.75

1.55 ± 0.04


1.90

1.67 ± 0.08

bulk (III)

>2.5

1.22 ± 0.08


0.73

0.12 ± 0.03


1.58

1.11 ± 0.02


1.75

1.26 ± 0.02


1.90

1.34 ± 0.03

bulk (III)

>2.5

1.07 ± 0.03


0.73

0.21 ± 0.04


1.63

1.09 ± 0.01


1.75

1.24 ± 0.02


1.90

1.29 ± 0.03

bulk (III)

>2.5

1.11 ± 0.02

Ethylbenzene

Acetophenone

Benzyl alcohol


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Table 3. Contribution to overall bonded-phase presence and parallel diffusion coefficients ∥ of individual bonded-phase groups at different distances z from the silica surface (cf. Figure 6). analyte ∥ maximum

ACN density maximum

z = 1.90 nm

z = 1.75 nm

contribution

∥ (10‒5 cm2 s‒1)

contribution

∥ (10‒5 cm2 s‒1)

CH2(11)

–

n.a.

0.1%

0.61 ± 0.09

CH2(12)

0.1%

0.82 ± 0.14

1.0%

0.66 ± 0.11

CH2(13)

0.5%

0.77 ± 0.12

4.1%

0.68 ± 0.11

CH2(14)

3.2%

0.85 ± 0.12

8.5%

0.74 ± 0.10

CH2(15)

8.4%

0.94 ± 0.13

13.8%

0.82 ± 0.10

CH2(16)

17.1%

1.09 ± 0.17

19.1%

0.96 ± 0.12

CH2(17)

29.3%

1.33 ± 0.17

24.6%

1.18 ± 0.15

CH3(18)

41.4%

1.64 ± 0.23

28.8%

1.49 ± 0.21

Bonded-phase group


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Table 4. Comparison of parallel diffusion coefficients ∥ at different distances z from the silica surface (cf. Figure 6) with bulk molecular diffusion coefficients Dm at the corresponding local solvent compositions (cf. Figure 7).

Compound

bulk region

analyte ∥ maximum

ACN density maximum

z > 2.5 nm, 70/30 (v/v) W/ACN

z = 1.90 nm, 40/60 (v/v) W/ACN

z = 1.75 nm, 29/71 (v/v) W/ACN

∥

Dm

(10‒5 cm2 s‒1)

∥

Dm

(10‒5 cm2 s‒1)

∥

Dm

(10‒5 cm2 s‒1)

ACN

1.87 ± 0.04

1.84 ± 0.02

2.29 ± 0.02

1.96 ± 0.02

2.34 ± 0.03

2.21 ± 0.02

Benzene

1.37 ± 0.05

1.42 ± 0.12

2.10 ± 0.10

1.74 ± 0.08

1.98 ± 0.05

2.00 ± 0.10

Ethylbenzene

1.22 ± 0.08

1.24 ± 0.04

1.67 ± 0.08

1.46 ± 0.10

1.55 ± 0.04

1.65 ± 0.10

Acetophenone

1.07 ± 0.03

1.03 ± 0.08

1.34 ± 0.03

1.20 ± 0.06

1.26 ± 0.02

1.36 ± 0.05

Benzyl alcohol

1.11 ± 0.02

1.09 ± 0.03

1.29 ± 0.03

1.15 ± 0.08

1.24 ± 0.02

1.24 ± 0.07


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Page 44 of 53

FIGURES

Figure 1. Chemical structure and size of the aromatic hydrocarbon analytes. The maximum distance between two atoms in a molecule (the length of the molecular vector, red arrow) was taken as the analyte size.


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Figure 2. The slit-pore RPLC model (snapshot of the equilibrated system). The simulation box (with dimensions as shown) contains the stationary phase, a planar silica surface modified with 1.87 C18 chains/nm2 and 0.56 endcapping groups/nm, which leaves 2.06 residual OH groups/nm2 on the surface, and the mobile phase of 70/30 (v/v) W/ACN. Atoms and united-atom groups are colored as follows. Si: yellow, O (of silica and W molecules): red, H (of residual OH groups and W molecules): white, ACN molecules: green, CH2 and CH3 united-atom groups (of C18 chains and endcapping groups): gray.


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Figure 3. Distribution of bonded-phase chains, solvent and analyte molecules in the RPLC system. Shown are the number density profiles for the bonded phase (C atoms, black), W (O atom, blue), ACN (central C atom, green), and the four analytes (center of mass; red, cyan, lime, and yellow for benzene, ethylbenzene, acetophenone, and benzyl alcohol, respectively). Dashed vertical lines indicate the limits of bonded-phase (I), interface (II), and bulk region (III). Analyte density maxima (1 – partitioning peak, 2 – adsorption peak) are indexed for reference in the text.


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Figure 4. Analyte orientation at the retention-relevant locations in the RPLC system. Shown is the probability distribution of the cosine of the angle β between the surface normal and the molecular vector of an analyte molecule in a z-interval of ±0.05 nm around the maxima of the partitioning peak (purple), the adsorption peak (red), and the ACN density (green). The orientation in the bulk region (grey) is given as reference. Snapshots (with color-coded frames) visualize the preferred analyte orientation at a particular location.


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Page 48 of 53

Figure 5. Snapshots showing the immediate environment of an ethylbenzene molecule at different locations in the RPLC system: the partitioning peak (A), the adsorption peak (B), the ACN ditch (C), and the bulk region (D). Atoms and united-atom groups are colored as follows. Si: yellow, O: red, H (of ethylbenzene and W molecules): white, ACN molecules: green, CH2 and CH3 united-atom groups (of the bonded phase): gray, C (of ethylbenzene): cyan.


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Figure 6. Parallel diffusion coefficient profiles for solvent and analyte molecules in the RPLC system. Shown are the diffusion coefficients for motion parallel to the silica surface of W (O atom, blue), ACN (central C atom, green), and the four analytes (center of mass; red, cyan, lime, and yellow for benzene, ethylbenzene, acetophenone, and benzyl alcohol, respectively). Dashed vertical lines indicate the limits of bonded-phase (I), interface (II), and bulk region (III).


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Figure 7. Bulk molecular diffusion coefficients of ACN (central C atom, green) and the four analytes (center of mass; red, cyan, lime, and yellow for benzene, ethylbenzene, acetophenone, and benzyl alcohol, respectively) simulated for W/ACN ratios between 90/10 and 0/100 (v/v).


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Figure 8. (A) ACN excess in the ditch (calculated as the difference in ACN volume fraction between ACN ditch and bulk region) for mobile phases between 10/90 and 90/10 (v/v) W/ACN. The ditch solvent composition was determined over a range of ±0.22 nm around the ACN density maximum to approximate the z-extension of the analytes there. (B) Lateral mobility increase from bulk region to ACN ditch expected for the four analytes (red, cyan, lime, and yellow for benzene, ethylbenzene, acetophenone, and benzyl alcohol, respectively) for mobile phases between 10/90 and 90/10 (v/v) W/ACN. The expected lateral mobility increase was


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calculated as the increase in Dm from the solvent composition of the bulk region to that of the ACN ditch, taken from the simulated Dm curves of the analytes (cf. Figure 7).


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TOC Graphic


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Surface Diffusion of Aromatic Hydrocarbon ... - ACS Publications

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