Stationary-Phase Contributions to Surface Diffusion in Reversed

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Stationary-Phase Contributions to Surface Diffusion in ReversedPhase Liquid Chromatography: Chain Length vs Ligand Density Julia Rybka, Alexandra Hoeltzel, Nicole Trebel, and Ulrich Tallarek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b06160 • Publication Date (Web): 13 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

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The Journal of Physical Chemistry

Stationary-Phase Contributions to Surface Diffusion in Reversed-Phase Liquid Chromatography: Chain Length vs Ligand Density Julia Rybka, Alexandra Höltzel, Nicole Trebel, and Ulrich Tallarek* Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany

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ABSTRACT. Fast surface diffusion in reversed-phase liquid chromatography (RPLC) describes a complex phenomenon that exists in a narrow ditch region where the silica-tethered alkyl chains of the stationary phase meet the water‒acetonitrile (ACN) mobile phase. The lateral mobility of analyte molecules in the ACN-rich ditch can exceed their bulk diffusivity in the mobile phase. Through molecular dynamics simulations using an established RPLC mesopore model and analyte set we study how chain length (C18 vs C8) and ligand (C8) density of the stationary phase contribute to the lateral mobility gain from surface diffusion at low and high ACN content of the mobile phase. The simulations show that C8 chains are better solvated and more often in an upright and stretched conformation than C18 chains, which leads to a higher maximum ACN excess in the ditch. High ligand density reinforces this effect. The ACN-excess advantage of C8 phases translates not necessarily into faster surface diffusion, because the shorter chains have lower bonded-phase mobility. Surface diffusion on a C8 phase is generally slower than on a C18 phase, but surface diffusion on a high-density C8 phase can be faster than on a C18 phase when the ACN content of the mobile phase is low.


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1. INTRODUCTION Fast surface diffusion of retained analytes is a distinctive mass transport mechanism of reversedphase liquid chromatography (RPLC),1 which separates apolar to moderately polar compounds based on their distribution between a hydrophobic stationary phase and a liquid mobile phase, usually a water (W)‒methanol (MeOH) or W‒acetonitrile (ACN) mixture. The stationary phase consists of a support structure, typically porous silica, bearing the chemically bonded phase, typically unbranched alkyl chains. When chromatographers select a stationary phase, they consider type and properties of the support material (such as average particle size, average pore size, degree of metal impurities) as well as the chemical structure of the bonded-phase ligands, their density (given as amount of ligands per m2 or number of ligands per nm2 of the support structure), the number of bonds with which a ligand is tethered to the support, plus presence and type of endcapping groups.2 Surface diffusion describes the motion of analyte molecules, which are in contact with the bonded phase, in parallel (lateral) direction to the surface of the silica support. Depending on the experimental conditions, surface diffusion of analytes can be faster than their bulk diffusion in the mobile phase. In this case, analyte molecules derive a mobility gain from surface diffusion that lowers their mass transport resistance, which translates into narrower chromatographic peaks and thus an improved separation efficiency.3 Therefore, studying the parameters that determine the lateral mobility gain from surface diffusion is worthwhile to identify favorable experimental conditions.4‒6 Chromatographic experiments in this direction require for their interpretation an accurate, molecular-detail model of the chromatographic interface, particularly of the narrow region where surface diffusion takes place. Building on knowledge about the chromatographic interface established through earlier molecular simulation studies,7 we recently began a series of



molecular dynamics (MD) studies dedicated to surface diffusion.8‒11 To mimic typical conditions met in RPLC practice we employed a silica-based, monomeric, dimethyl octadecylsilane (C18) phase and a W‒ACN mobile phase. The studies linked fast surface diffusion to the presence of an ACN-rich region around the flexible ends of the C18 chains, termed the ACN ditch, and showed that the lateral mobility gain depends on the ACN content of the mobile phase and on analyte properties.10,11 Formation of the ACN ditch results from the hydrophobic effect12,13 and occurs during equilibration of the RPLC column containing the hydrophobic stationary phase with the aqueous‒organic mobile phase. To minimize the loss of hydrogen bonding at the hydrophobic surface, the W‒ACN mixture partially segregates by enriching ACN molecules towards the bonded phase, which results in an ACN-rich layer around the chain ends.14 Because the solvent reservoirs constantly deliver fresh mobile phase to the column, the local ACN enrichment does not lead to an ACN-depleted liquid phase. The ACN-enriched solvent composition in the ditch provides a lower viscosity environment and thus higher diffusive mobility for analyte molecules than the mobile phase.8 Lubrication by the flexible chain ends of the bonded phase can enhance the analyte mobility in the ACN ditch further.10 The stationary phase thus contributes twofold to surface diffusion: passively through ACN enrichment (interaction between bonded phase and mobile phase) and actively through lubrication (interaction between bonded-phase groups and analyte molecules).11 Whereas a passive contribution to surface diffusion can with reasonable certainty be predicted to exist for any RPLC phase, the same cannot necessarily be said of the active contribution, for which a certain flexibility of the bonded-phase groups in the ACN ditch seems to be required.


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In this study we explore the stationary-phase contribution further by investigating how chain length and ligand density of the bonded phase affect the lateral mobility gain of retained analytes from surface diffusion. In addition to their relevance for stationary-phase selection in RPLC practice, chain length and ligand density can be expected to affect the flexibility of the chain ends as well as the extent of the ACN enrichment. In selecting a model phase, we looked for the following properties: i) highly similar retention to the formerly investigated C18 phase; ii) available with comparable as well as higher ligand density as the formerly investigated C18 phase; and iii) relevant to current chromatographic practice. Each of these conditions is met by dimethyl octylsilane (C8) phases, which are next-in-popularity to C18 phases and offered by every major column manufacturer. All other column parameters that affect retention being equal, C8 phases are less retentive than C18 phases, which is useful to shorten the analysis time of wellseparated analytes and reduce the amount of organic solvent for elution. Another aspect is that C8 phases can be prepared with higher ligand density than C18 phases.15 (For example, Phenomenex (Torrance, CA) offers two silica-based, monomeric C8 phases with ligand densities of 4.0 and 5.5 µmol/m2. The typical ligand density of C8 and C18 phases is 3‒3.5 µmol/m2.)2 Higher ligand density increases the shape selectivity of a column, which is important for the separation of isomeric/isobaric compounds.16 C8 phases have been included in molecular simulation studies that investigated the conformation of the bonded phase, solvent penetration into the bonded phase, and the retention of n-alkanes and primary alcohols.7,17‒21 These earlier works established some key differences between a C8 and a C18 phase (at identical ligand density) relevant to this study: i) C8 chains have a higher preference to align orthogonally to the silica surface than C18 chains, which have a tendency to fold back towards the surface; ii) organic solvent is present along the length of the C8 chains, whereas the middle segment of the C18 chains is nearly solvent-



depleted. Judging by the results of former molecular simulation studies, which compared silicabased, monomeric, trimethyl silane (C1), C8, C18, and dimethyl triacontyl silane (C30) phases, some details of the chromatographic interface can be highly specific to a particular chain length and organic solvent (MeOH or ACN) in the mobile phase.17‒21 It is thus impossible to predict a general influence of chain length on surface diffusion that applies to all RPLC phases without studying them first. Here, the effect of chain length expressly refers to C18 vs C8, the most important RPLC phases, when equilibrated with a W‒ACN mobile phase. The study is conducted using our established RPLC mesopore model8‒11 with three monomeric bonded phases: i) a moderate-density C18 phase (3.11 µmol/m2) with endcapping, as used in our previous studies; ii) a moderate-density C8 phase (3.11 µmol/m2) with endcapping; and iii) a high-density (hd) C8 phase (4.04 µmol/m2) without endcapping (high ligand density is achieved by substituting C8 chains for endcapping groups). Each stationary phase is equilibrated with 70/30 and 20/80 (v/v) W/ACN to realize conditions where a high or low lateral mobility gain from surface diffusion can be expected, respectively.11 MD simulations are performed for each bonded phase and W/ACN ratio with an analyte set consisting of two apolar compounds of different size, benzene and ethylbenzene, and two moderately polar compounds of different hydrogen-bonding capability, acetophenone and benzyl alcohol. At low to moderate ACN content of the mobile phase, the lateral mobility gain from surface diffusion on a C18 phase increases from benzyl alcohol to acetophenone to ethylbenzene to benzene, that is, with decreasing analyte polarity and size. From moderate to high ACN content of the mobile phase, analyte-specific behavior is progressively lost.10,11 The analyte set allows us to monitor whether differences in surface diffusion between the three bonded phases depend on analyte properties. In particular, we intend to answer the following questions: 1. Do shorter (C8) chains reduce the


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lateral mobility gain that analytes can derive from surface diffusion? 2. Does higher (C8) ligand density increase the lateral mobility gain? 3. Can shorter (C8) chains provide an active stationaryphase contribution to surface diffusion?

2. METHODS 2.1. Slit-Pore Model and Force-Field Parameters. A 10 nm slit pore (left panel of Figure 1) was constructed by placing a central silica slab (xyz = 12.14 × 13.2 × 0.93 nm3) between two solvent reservoirs (xyz = 12.14 × 13.2 × 5 nm3) and applying periodic boundary conditions in all directions. The three-layer slab was cut from -cristobalite silica parallel to the (111) face, whose hydroxylation closely approximates the surface hydroxylation of chromatographic silica.22 The cut silica surface bearing dangling bonds was turned into a fully hydroxylated silica surface,23 from which then three different stationary phases, each of them containing 2.06 residual OH groups/nm2 (3.42 µmol/m2), were prepared. The C18 phase was created by randomly grafting 1.87 C18 chains/nm2 (3.11 µmol/m2) and 0.56 C1 groups/nm2 (0.93 µmol/m2) onto the surface. The C8 phase was created from the C18 phase by shortening C18 to C8 chains through removal of the redundant united-atom groups. The hd-C8 phase with 2.43 C8 chains/nm2 (4.04 µmol/m2) was generated from the C8 phase by replacing all C1 groups with additional C8 chains. Figure 1, which shows a snapshot of the slit-pore model featuring the hd-C8 phase equilibrated with 70/30 (v/v) W/ACN (left panel) alongside a top view onto the silica-supported hd-C8 phase (right panel), illustrates the “picket fence” structure14,24 as well as the surface coverage of the hd-C8 phase.



The force-field parameters for the Si, O, and H atoms of the silica surface,25,26 the C1 groups, C8 and C18 chains of the bonded-phase,27–29 the solvent molecules of the W‒ACN mixture,30,31 and the analyte molecules32,33 were as used and validated in earlier work.10,11,34,35 2.2. Simulations. MD simulations were carried out at 300 K with GROMACS 2016.5.36,37 Simulations in the slit-pore model were conducted as NVT ensemble simulations (that is, the number of molecules in the simulation box N, the volume of the simulation box V, and the temperature T were held constant). Simulations were run for each of the three bonded phases with 70/30 and 20/80 (v/v) W/ACN, whereby each analyte species (with Nanalyte = 10) was simulated separately, yielding a total of 3 × 2 × 4 = 24 simulation systems. The number of each solvent species in the simulation box varied with the W/ACN ratio and bonded phase (Table S1) and was determined in preparatory simulations without analyte molecules.10 The system was equilibrated for 60 ns prior to simulation runs of ≤1.0 µs. Simulation details regarding the thermostat, integration time step, trajectory output frequency, energy minimization and initial velocity assignment, as well as the modeling of long-range electrostatic and non-bonded interactions were as described previously.11 Simulations of bulk diffusion were conducted as NPT ensemble simulations (constant N, pressure P, and T) with Nanalyte = 3 and Nsolvent = 10000 for 48/52, 40/60, 39/61, 16/84, 11/89, and 10/90 (v/v) W/ACN (Table S2). Each analyte species was simulated separately, yielding a total of 6 × 4 = 24 NPT simulations. 30 ns trajectories were run of which the final 20 ns were used for data analysis. 2.3. Calculation of Bonded-Phase Conformations, Density Profiles, and Bonded-Phase Contacts. The positions of the united-atom groups in an alkyl chain are given as a function of the vertical distance z from the silica surface and horizontal distance rxy from the grafting point


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of the respective C8 or C18 chain on the silica surface. Probability distributions of the positions of the united-atom groups reflect the average of a 40 ns trajectory and are normalized, that is, integration over the whole contour plot yields the number of alkyl groups in a chain (8 or 18). A gauche defect along an alkyl chain was detected if the dihedral angle was less than 120°. The average number of gauche defects per chain, Ngauche, reflects the average of a 40 ns trajectory. Bonded-phase, solvent, and analyte number density profiles were determined as described previously11 and refer to CH2 and CH3 united-atom groups of C1 groups, C8 and C18 chains, the O atom of W, the central C atom of ACN, and the center-of-mass of analyte molecules. The surface Si atoms mark the starting point for distance measurements (z = 0). The average number of bonded-phase contacts for analytes, Nbp, was determined over a 40 ns observation period as previously described.11 2.4. Determination of Diffusion Coefficients. As in our previous studies,8‒11,38,39 the distancedependent diffusion coefficient in parallel direction to the silica surface, D||(z), was determined from simulations in the slit-pore model following an approach by Liu et al.40 For the observed species, the mean squared displacement 〈𝑟2(𝑡)〉 in parallel direction to the silica surface was recorded in 20 ps observation intervals, which were shifted consecutively in 0.5 ps time steps throughout the whole trajectory. The observation intervals were kept short to prevent molecules from sampling several z-regions at once, leading to loss of spatial resolution. Each unit of the observed species (alkyl group of the bonded-phase, solvent or analyte molecule) was indexed according to its initial distance z from the surface. If a unit of the observed species changed its initial z-value by more than ±0.3 nm during an observation interval, the displacement of this unit was discarded from the data. At maximum, 24% of units left their allowed z-interval in the bulk region, 18% in the interfacial region, and 4% in the bonded-phase region. The linear slope of the



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observation curve (t = 4–16 ps) was used to calculate D||(z) for the observed species according to the Einstein equation 𝐷 ∥ (𝑧) =

1d〈𝑟2(𝑡)〉 4 d𝑡

(1)

The value of D||(z) was determined from the whole linear interval (t = 4–16 ps). The difference between two additional D||(z)-values calculated from each half of the linear interval (t = 4–10 and 10–16 ps) was used as error estimate. Molecular diffusion coefficients, Dm, for analytes were determined from bulk diffusion simulations. Dm-values and their error estimates were calculated directly in GROMACS from the mean squared displacement of analyte molecules (in any direction) as described above.

3. RESULTS AND DISCUSSION 3.1. Conformation of the Bonded Phase. Our starting point for investigating the stationaryphase contribution to surface diffusion is to evaluate the sensitivity of the bonded-phase conformation to chain length, ligand density, and ACN content of the mobile phase. The conformations of the three phases are compared through probability distributions (Figure 2) and accompanying chain statistics (Table 1). Based on the angle between the vector pointing from the chain grafting position on the silica surface to the first alkyl group, CH2(1), in the chain and the surface normal, chains can be categorized as upright or tilted (angle of 9.6° ± 0.2 or 32.8° ± 0.3°, respectively). Upright chains have a slightly higher number of gauche defects than tilted chains. All phases favor upright chains (69%‒76%) over tilted chains, whereby the fraction of upright chains increases from C18 to C8, from C8 to hd-C8, and from 70/30 to 20/80 (v/v) W/ACN (Table 1).


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Based on the number of gauche defects per chain (Table S3), all alkyl chains (upright as well as tilted) can be divided into three groups: bent, stretched, and backfolded. (Snapshots of typical examples of each category for C8 and C18 chains are shown in Figure S1.) Most chains (70‒79%) are bent, which is reflected in the spatial distribution of the chain ends (Figure 2). The contour plots give the probability for the terminal methyl group to be found at a certain horizontal distance rxy from the chain grafting point and vertical distance z from the silica surface. (Contour plots showing the spatial distribution of all alkyl groups in a chain are shown in Figure S2.) Bent C8 chains (Ngauche = 1.6) have their terminal methyl groups at z = 0.64‒1.25 nm; bent C18 chains (Ngauche = 3.9) have their terminal methyl groups at z = 0.96‒2.40 nm. The majority of C8 chain ends is thus confined within a narrower z-interval than the majority of C18 chain ends. The contour lines at rxy > 0.5 nm and z < 1 nm in the plots for the C18 phase reflect a considerable degree of backfolding (21‒24% of C18 chains). Backfolded C18 chains have three conformations, whereby the dominant one (88% of backfolded chains) has the lowest number of gauche defects among the backfolded C18 chains (Ngauche = 3.8) and places the terminal methyl groups at rxy ≥ 1.2 nm. From 70/30 to 20/80 (v/v) W/ACN, the number of backfolded C18 chains decreases in favor of bent chains. The contour plots reveal that C8 chains can also fold back (lines at z < 0.64 nm), but do so rarely (≤3%). Instead, the secondary conformation of C8 phases are stretched chains (18‒28%). The terminal methyl group of stretched C8 chains (Ngauche = 0.4) is found at two locations; the first one, at rxy ≤ 0.45 nm and z ≥ 1.25 nm, is associated mostly with upright chains, the second one, at rxy ≥ 0.65 nm and z ≥ 0.85 nm, with tilted chains. The fraction of stretched C8 chains increases from C8 to hd-C8 and from 70/30 to 20/80 (v/v) W/ACN. Stretched C18 chains (Ngauche = 1.4) are rare ( 1.05 nm, which to >80% consist of groups beyond CH2(12). In contrast, C8 chains are solvated along their full extension. (C8 chains are so open to solvent penetration that at 20/80 (v/v) W/ACN, the total solvent density does not fall below 10% of its bulk value before the surface-coordinating peaks are reached, so that bonded-phase and interfacial region merge.) Ditch and surfacecoordinating ACN molecules are connected, reflecting an accumulation of ACN molecules that relies on all bonded-phase groups along the chain, the endcapping groups (if present), and surface-coordinating ACN molecules. Thus, shorter chain length translates to increased bondedphase solvation and ultimately a higher maximum ACN excess in the ditch. That higher ligand density returns higher maximum ACN excess is expected. Higher ligand density forces more C8 chains into an upright and stretched conformation (cf. Table 1), which leads to a narrower interfacial region with higher bonded-phase density (cf. Figure 3) and a more focused chain ends distribution in z-direction (cf. Figure 2). Higher bonded-phase density in the ACN ditch (3.5 vs 2.5 united-atom groups/nm3 for the hd-C8 and the C8 phase at 70/30 (v/v) W/ACN) yields, in turn, a higher maximum ACN excess. Overall, the analysis of solvent and bonded-phase density profiles has revealed that the shorter chain length (C8 vs C18) allows for full solvent penetration of the bonded phase, which, in turn, leads to a higher maximum ACN excess in the ditch. Additionally, the ACN ditch at the C8 phase is shifted closer to the bulk region and thus the chain ends. Higher ligand density (C8 vs hd-C8) reinforces these effects through increased bonded-phase density and conformational order in the interfacial region. 3.3. Distribution of Analyte Density. Preparatory to discussing the lateral mobility of retained analytes, Figure 4 shows the density profiles of the four analytes in relation to the bonded-phase


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density profile of the respective stationary phase at low and high ACN content of the mobile phase. Also indicated are the limits of bonded-phase and interfacial region (Table S4) and the stationary-phase limits (Table S5) as introduced in our recent MD study.11 The stationary-phase limit (zsp) considers the interaction between the bonded phase and analyte molecules. Analyte molecules whose center-of-mass is at z < zsp count as retained by the stationary phase, because averaged-over-time they have at least one contact with bonded-phase groups. zsp is sensitive to the extension and orientation of analyte molecules in the interfacial region and thus to the analyte species. To focus on the role of the stationary phase for surface diffusion, we look for generic changes in the analyte density profiles caused by shorter chain length or higher ligand density. The analyte-specific properties of the profiles, discussed in-depth in earlier work,10,11 are of minor relevance here. (Recent studies focusing on mechanistic details of analyte retention can be found here.42‒45) Apart from the expected overall decrease in analyte density at z < zsp due to the increased elution strength of the mobile phase, changes in the analyte density profiles between 70/30 and 20/80 (v/v) W/ACN are related to changes in interfacial width. Compared with the C18 phase, the analyte density distribution at the C8 phase is necessarily narrower due to the reduced bonded-phase depth. The distribution is narrowed by increasing the analyte density towards the silica surface, which results in density peaks that tail towards the bulk region. This is, for example, easily visible in the ethylbenzene profile: two density peaks of similar height at the C18 phase merge into a larger peak that tails towards the bulk region at the C8 phase (light blue lines in Figure 4). The benzyl alcohol profile (yellow lines), which at the C18 phase has a very small peak near the silica surface and a larger, broad peak closer to the limit of the interfacial region, becomes two closely spaced peaks of similar height at the C8 phase. Higher ligand density has a much smaller effect on the analyte density distribution than shorter



chain length. Compared with the C8 phase, the analyte density distribution on the hd-C8 phase is barely wider, but some of the analyte density is increased towards the bulk region, that is, towards the higher numbered bonded-phase groups. This redistribution of analyte density is in line with the higher bonded-phase density of the hd-C8 phase in the bonded-phase and interfacial region and becomes particularly apparent in the benzyl alcohol profile. Recent simulations of multiscale diffusion in a physically reconstructed, macro‒mesoporous chromatographic bed have shown that pushing analyte density towards the chain ends, where surface diffusion takes place, increases the bed diffusivity.46 3.4. Lateral Mobility Gain From Surface Diffusion. Figure 5 displays the D|| profiles of the four analytes for each stationary phase at 70/30 and 20/80 (v/v) W/ACN. Bonded-phase and ACN density profiles in the background of Figure 5 visualize the location of the lateral mobility maximum of the analytes, z(D||,max), relative to the extension of the bonded phase and z(ACN,max). The stationary-phase limits indicated in Figure 5 prove that analyte molecules with increased lateral mobility are in contact with and thus retained by the stationary phase. Generally (for all analytes, stationary phases, and W/ACN ratios), D|| in the bulk and interfacial region increases from low to high ACN content of the mobile phase due to the accompanying viscosity decrease, but the lateral mobility in the ACN ditch compared with the bulk region decreases from low to high ACN content of the mobile phase due to the loss in ACN enrichment. At each phase, z(D||,max) > z(ACN,max), that is, analytes at z(D||,max) do not experience the maximum ACN excess, but also have fewer contacts with lower-numbered, less mobile bonded-phase groups. z(D||,max) is a compromise between ACN content and bonded-phase mobility in the analyte environment. The ACN excess in the analyte environment is determined by z(D||,max) and the shape of the ACN ditch. Because the ditch at the C18 phase is slightly wider than at the C8 phase, the C18


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phase loses less ACN density between z(ACN,max) and z(D||,max). Although at 70/30 (v/v) W/ACN, the C8 phase holds more ACN excess at z(ACN,max) than the C18 phase (44 vs 41 vol %, respectively, cf. Table 2), the advantage is lost at z(D||,max), where the C8 phase holds only 22 vol % ACN excess compared with 30 vol % held by the C18 phase. The hd-C8 phase, where z(ACN,max) is closer to the bulk region and thus to z(D||,max), loses less ACN excess (from 47 to 31 vol % ACN) between z(ACN,max) and z(D||,max) than the C8 phase. The hd-C8 phase maintains the highest ACN excess at z(D||,max) among the three phases at low and high ACN content of the mobile phase. Figure 6, which compares the three phases with respect to the maximum lateral mobility gain that analytes can derive from surface diffusion, reflects the influence of the local ACN excess in the analyte environment. At 70/30 (v/v) ACN, all analytes experience the lowest mobility gain on the phase with the lowest ACN excess at z(D||,max), the C8 phase. The apolar analytes, benzene and ethylbenzene, have the highest mobility gain on the phase with the highest ACN excess at z(D||,max), the hd-C8 phase, whereas the polar analytes, acetophenone and benzyl alcohol, have a comparable mobility gain on the C18 and the hd-C8 phase, indicating a comparable response to the higher ACN excess provided by the hd-C8 phase and the higher flexibility of the C18 chains. Overall, the same analyte-specific behavior is observed on all three phases. At 70/30 (v/v) W/ACN, the lateral mobility gain decreases with increasing analyte polarity and size, whereas differences between the analytes have largely vanished at 20/80 (v/v) W/ACN, along with differences between the phases in the local ACN excess at z(D||,max). At only 4‒7 vol % ACN excess in their environment, analytes at 20/80 (v/v) W/ACN experience a correspondingly small mobility gain, which is highest on the C18 phase.



In summary, a shorter chain length (C18 to C8) decreases the lateral mobility gain of analytes from surface diffusion, whereas a higher (C8) ligand density can push the lateral mobility gain of apolar analytes over the values reached by the C18 chains. Under conditions that favor the ACN enrichment in the interfacial region, higher ligand density can more than compensate for shorter chain length. Under conditions that produce only low ACN excess, the bonded-phase flexibility becomes the decisive factor for the mobility gain. 3.5. Active Stationary-Phase Contribution to Surface Diffusion. In past MD studies,8,10,11 we observed an active contribution of the C18 phase to the analyte mobility with mobile phases of 87% at 70/30 and 100% at 20/80 (v/v) W/ACN) with the segment CH2(6) to CH3(8), which has a minimum mobility of D|| ≈ 0.5 × 10‒9 m2s‒1 (Figure 7 and Table S6). The active stationary-phase contribution to surface diffusion can be deduced from comparison of the D||,max-values with bulk molecular diffusion coefficients (Dm,analyte_max) simulated for the local W/ACN ratio at z(D||,max). Dm,analyte_max represents the hypothetical analyte mobility at z(D||,max) without bonded-phase contact. Thus, the step from D||,bulk to Dm,analyte_max quantifies the response of an analyte to the ACN increase in its environment, and the step from D||,max to Dm,analyte_max quantifies the response to contact with the bonded-phase groups. Figure 8 shows the values of D||,max, Dm,analyte_max, and D||,bulk for each analyte and stationary phase at low and high ACN content of the mobile phase (all values are also listed in Tables S7‒S10). First, we observe Dm,analyte_max > D||,max for all analytes, phases, and W/ACN ratios, that is, all analytes respond with a mobility gain to the increased ACN content in their environment. The response to the increased ACN content is phase-specific as well as analyte-specific, because the phases differ in the ACN excess they provide and the apolar analytes are more receptive to the changing environment than the polar analytes. At 70/30 (v/v) W/ACN, D||,max > Dm,analyte_max is valid for all analytes and phases, that is, all analytes respond with a mobility gain to bonded-phase contact, confirming an active stationary-phase contribution also for the two C8 phases. Differences in the response to



bonded-phase contact are analyte-specific (apolar analytes being more receptive than polar analytes) rather than phase-specific. At 20/80 (v/v) W/ACN, however, the C8 phases differ clearly from the C18 phase: D||,max ≈ Dm,analyte_max on the C18 phase, but D||,max < Dm,analyte_max on the C8 phases, that is, analyte mobility is barely influenced by contact with the C18 chains, but hindered by contact with the C8 chains. According to Figure 8, the analyte mobility profits from bonded-phase contact at low ACN content of the mobile phase, but not at high ACN content of the mobile phase, regardless of the mobility of a particular phase. Bonded-phase groups increase the organic fraction in the analyte environment, which is favorable for the diffusion coefficient. At 70/30 (v/v) W/ACN, analytes at z(D||,max) have a high number of bonded-phase contacts (11.5‒14.7, 4.5‒5.6, and 6.5‒7.4 for the C18, C8, and hd-C8 phase, respectively, depending on the analyte), which makes a difference to an analyte environment containing between 52 and 61 vol % ACN (depending on the phase, cf. Table 2). At 20/80 (v/v) W/ACN, the number of bonded-phase contacts has dropped to 2.0‒3.8, 1.2‒1.3, and 1.8‒2.3 for the C18, C8, and hd-C8 phase, respectively. The bonded-phase presence at z(D||,max) is now too low to have a beneficial effect on an analyte environment that already contains 84‒87 vol % ACN. When additionally the contacting bonded-phase groups have low mobility, they detract from the analyte mobility. To visualize the difference between the C18 phase and the two C8 phases in this respect, Figure 9 shows the average number of bonded-phase contacts for a benzene molecule at z(D||,max) in dependence of the lateral mobility of the bondedphase groups (i.e., bonded-phase groups are not represented by their position along the chain, but by their D||-values, cf. Figure 7). Because the bonded-phase D||-values are rather insensitive to the ACN content of the mobile phase, switching from 70/30 to 20/80 (v/v) W/ACN results mostly in an overall drop in bonded-phase contacts. Most contacts (73‒100%) at 20/80 (v/v) W/ACN are


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with the last three alkyl groups, which have much higher mobility in a C18 chain than in a C8 chain. The lower mobility of C8 chains is thus a disadvantage at high ACN content of the mobile phase, but does not affect the active stationary-phase contribution to surface diffusion at low ACN content of the mobile phase.

CONCLUSIONS In this MD simulations study we investigated how shortening the chain length (from C18 to C8) or increasing the ligand (C8) density of the bonded phase (by 30%), both criteria for stationaryphase selection in RPLC practice, affects the lateral mobility gain that retained analytes can derive from surface diffusion. In particular, we asked whether shorter chains reduce the mobility gain, whether a higher ligand density increases the mobility gain, and whether shorter chains provide an active stationary-phase contribution. Each question has been answered in the affirmative. Shortening the chain length has a favorable effect on conformation and solvation of the bonded phase, leading to a more focused chain ends distribution in z-direction and a narrower ACN ditch with higher maximum ACN excess compared with the C18 phase. On the other hand, the shorter chain length comes with a reduced bonded-phase mobility, which prevents analytes from profiting from the high maximum ACN excess. Increasing the ligand density of the C8 phase raises the bonded-phase density and thus the ACN excess in the interfacial region and shifts the ditch closer to the bulk region and the higher-numbered, more mobile bonded-phase groups. At low ACN content of the mobile phase, the lateral mobility gain from surface diffusion at the hdC8 phase is higher than or comparable with that at the C18 phase. At high ACN content of the mobile phase, when the ACN excess is low, analyte mobility is limited by the bonded-phase



mobility, where C18 chains are superior to C8 chains. The lower chain mobility does not affect the active stationary-phase contribution to surface diffusion, which exists only at low ACN content of the mobile phase. Overall, the results suggest the existence of an optimal chain length and ligand density in view of the mobility gain from surface diffusion. Identifying these parameters falls within the realm of molecular simulation studies, but whether the ideal stationary phase can be realized is decided in the laboratory. Considering that chromatographers seek to improve the mass transport properties of RPLC columns, a stationary phase for enhanced surface diffusion could be a promising goal of column design.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website in the PDF file format. Number of W and ACN molecules for simulations in the slit-pore model (Table S1). Number of W and ACN molecules for simulations of bulk diffusion (Table S2). Average number of gauche defects per chain (Table S3). Locations of the limits of bonded-phase and interfacial region (Table S4). Locations of the stationary-phase limit (Table S5). Diffusive mobility data for bonded-phase groups, benzene, ethylbenzene, acetophenone, and benzyl alcohol (Tables S6‒S10). Snapshots of typical chain conformations (Figure S1). Spatial distribution of the alkyl groups in a chain (Figure S2).

AUTHOR INFORMATION Corresponding Author


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*Phone: +49-(0)6421-28-25727. Fax: +49-(0)-6421-28-27065. E-mail: [email protected]. ORCID Ulrich Tallarek: 0000-0002-2826-2833 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the Deutsche Forschungsgemeinschaft DFG (Bonn, Germany) under grant TA 268/11-1. Simulations were carried out on the ForHLR1 cluster at the Steinbuch Center for Computing (SCC) of the Karlsruhe Institute of Technology (Karlsruhe, Germany) under the project acronym RPLCMD.

ABBREVIATIONS ACN, acetonitrile; C1, trimethyl silane; C8, dimethyl octylsilane; C18, dimethyl octadecylsilane; C30, dimethyl triacontylsilane; MD, molecular dynamics; MeOH, methanol; RPLC, reversedphase liquid chromatography; W, water.

REFERENCES 23 ACS Paragon Plus Environment


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Table 1. Distribution of chain conformations. bonded phase

C18

C8

hd-C8

uprighta

tilteda

bentb

stretchedb

backfoldedb

(v/v)

(%)

(%)

(%)

(%)

(%)

70/30

68.6

31.4

75.4

1.1

23.5

20/80

70.7

29.3

77.4

1.8

20.8

70/30

70.0

30.0

79.4

17.5

3.1

20/80

75.8

24.2

76.1

21.3

2.6

70/30

72.9

27.1

73.8

23.2

3.0

20/80

75.2

24.8

70.0

27.8

2.2

W/ACN

a According to the angle between the surface normal and the vector pointing from the chain’s grafting position to CH2(1). b

According to the position of the terminal methyl group in a chain.



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Table 2. Location of and local ACN excess at the ACN density maximum and the analyte lateral mobility maximum in the interfacial region of the pore. bonded phase

C18

C8

hd-C8

z(ACN,max)

z(D||,max)

(v/v)

(nm)

(nm)

at z(ACN,max)

at z(D||,max)

70/30

1.75

1.9

+41

+30

20/80

2.15

2.3

+6

+4

70/30

1.25

1.5

+44

+22

20/80

1.45

1.73

+9

+5

70/30

1.35

1.5

+47

+31

20/80

1.55

1.73

+10

+7

W/ACN


excess vol % ACN

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Figure 1. Snapshot of the RPLC mesopore model featuring the hd-C8 phase equilibrated with 70/30 (v/v) W/ACN (left panel) and top view onto the silica surface bearing the hd-C8 phase (right panel). Atoms and united-atom groups 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, gray. The snapshots are represented with VMD using the drawing methods “Licorice” (left panel) and “VDW” (right panel).



Figure 2. Spatial distribution of chain ends. Shown is the probability for the terminal methyl group in a chain to be found at a certain horizontal distance rxy from the chain grafting position and vertical distance z from the silica surface.


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Figure 3. Distribution of bonded-phase and solvent density in the mesopore. Bonded-phase, ACN, and W density profiles are colored black, dark green, and dark blue, respectively. Dashed vertical lines divide bonded-phase (I), interfacial (II), and bulk region (III) of the pore.



Figure 4. Distribution of analyte density in the mesopore. Analyte density profiles (thick lines) are colored red, light blue, light green, and yellow for benzene, ethylbenzene, acetophenone, and benzyl alcohol, respectively. Bonded-phase density profiles (thin lines) are shown in grey. Vertical grey bars indicate analyte-specific stationary-phase limits. Dashed vertical lines divide bonded-phase (I), interfacial (II), and bulk region (III) of the pore.


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Figure 5. Distribution of analyte lateral mobility in the mesopore. Parallel diffusion coefficient profiles (thick lines) for benzene, ethylbenzene, acetophenone, and benzyl alcohol are colored red, light blue, light green, and yellow, respectively. ACN and bonded-phase density profiles (thin lines) are shown in dark green and grey, respectively. Vertical grey bars indicate analyte-specific stationary-phase limits. Dashed vertical lines divide bonded-phase (I), interfacial (II), and bulk region (III) of the pore. 37 ACS Paragon Plus Environment


Figure 6. Lateral mobility gain of analytes from surface diffusion. Lines between data points belonging to a particular stationary phase and W/ACN ratio serve as a guide to the eye.


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Figure 7. Lateral mobility of bonded-phase groups. Lines between data points serve as a guide to the eye. For error bars see Table S6.



Figure 8. Comparison of D||,max, the maximum parallel diffusion coefficient in the pore (black), with D||,bulk, the diffusion coefficient in the bulk region of the pore (dark blue), and Dm,analyte_max, the bulk molecular diffusion coefficient for the local W/ACN ratio at the analyte lateral mobility maximum in the pore (red). Lines between data points serve as a guide to the eye.


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Figure 9. Average number of bonded-phase contacts for a benzene molecule at its lateral mobility maximum in the pore as a function of the lateral mobility of the contacting bonded-phase groups. Each point represents an alkyl group along the chain up to the terminal methyl group (last point of curve). Lines between data points serve as a guide to the eye.



TOC Graphic


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Stationary-Phase Contributions to Surface Diffusion in Reversed

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