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Composition, Structure, and Mobility of Water-Acetonitrile Mixtures in a Silica Nanopore Studied by Molecular Dynamics Simulations Sergey M. Melnikov,† Alexandra H€oltzel,‡ Andreas Seidel-Morgenstern,† and Ulrich Tallarek*,‡ † ‡
Max-Planck-Institut f€ur Dynamik komplexer technischer Systeme, Sandtorstrasse 1, 39106 Magdeburg, Germany Department of Chemistry, Philipps-Universit€at Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany ABSTRACT: To investigate the effect of the nanoscale confinement on the properties of a binary aqueous-organic solvent mixture, we performed molecular dynamics simulations of the equilibration of water-acetonitrile (W/ACN) mixtures between a cylindrical silica pore of 3 nm diameter and two bulk reservoirs. Water is enriched, and acetonitrile is depleted inside the pore with respect to the bulk reservoirs: for nominal molar (∼volumetric) ratios of 1/3 (10/90), 1/1 (25/75), and 3/1 (50/50), the molar W/ACN ratio in the pore equilibrates to 1.5, 3.2, and 7.0. Thus, the relative accumulation of water in the pore increases with decreasing water fraction in the nominal solvent composition. The pore exhibits local as well as average solvent compositions, structural features, and diffusive mobilities that differ decidedly from the bulk. Water molecules form hydrogen bonds with the hydrophilic silica surface, resulting in a 0.45 nm thick interfacial layer, where solvent density, coordination, and orientation are independent of the nominal W/ACN ratio and the diffusive mobility goes toward zero. Our data suggest that solute transport along and across the nanopore, from the inner volume to the interfacial water layer and the potential adsorption sites at the silica surface, will be substantially different from transport in the bulk.
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eparation of analytes in chromatography is based on their retention, which takes places in a thin layer at the surface of the stationary phase. This chromatographic interphase is only a few nanometers thick, so that a thorough understanding of the processes in this layer requires a molecular-scale description.1 In reversed-phase (RP) HPLC, the interphase comprises the surface of the porous silica support, the hydrocarbon layer of the bonded phase, and all solvent molecules that are near the silica surface or intercalated between or adsorbed on the alkyl chains.2 Over the last decades, several groups have focused on a development of adequate molecular models of the retention mechanism in RP-HPLC.3-23 The influence of temperature, alkyl chain length, surface density of the ligands, dissociation of residual silanol groups, and mobile phase composition on the conformation and mobility of the bonded phase were investigated, and free energy profiles for the transfer of simple solute molecules from mobile to stationary phase were presented. Siepmann and coworkers have provided an excellent summary of previous simulations of RP-HPLC systems,13,23 as well as a novel, molecularlevel insight into the different retention of polar and nonpolar solutes.15 Compared with RP-HPLC, retention in hydrophilic interaction chromatography (HILIC), which uses a polar (often bare silica) stationary phase and a mobile phase of water and a high fraction (g60%) of organic solvent (usually acetonitrile), is far less understood.24 Although HILIC does not cover such a wide range of analytes as RP-HPLC, it has the same potential for separation of polar analytes as RP-HPLC has for nonpolar analytes.25 Separation in HILIC involves (among other possible r 2011 American Chemical Society
interactions) the differential partitioning of solutes between the organic-solvent rich mobile phase and a water-rich layer at the surface of the polar stationary phase that retains polar analytes.24-29 Mass transport in a chromatographic column packed with porous particles occurs in the relatively large (flow-through) interparticle macropores as well as the much smaller intraparticle meso- or nanopores, where solutes travel only by diffusion. The largest surface area and consequently the main location for enrichment of water molecules is inside the nanopores. Equilibration of a binary mobile phase between the high-surface-area nanopores and the macropores of the chromatographic support could, therefore, be a key feature of the HILIC retention mechanism. Additionally, the nanoscale confinement may alter the properties of the solvent inside a pore. The static and dynamic properties of water in the pores of nanostructured materials differ strongly from those of bulk water.30-32 Molecular simulation studies33 (and references therein) have contributed to an understanding of this effect, which has also recently been investigated for binary solvent mixtures.34,35 The knowledge of how a solvent mixture behaves inside a high-surface-area pore is highly relevant to understand the transport of solutes in a porous network such as a chromatographic silica support. In this work, we use molecular dynamics simulations to study the equilibration of water-acetonitrile (W/ACN) mixtures Received: October 30, 2010 Accepted: February 14, 2011 Published: March 02, 2011 2569
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Figure 1. Simulation box has a quadratic 6 6 nm2 cross-section (Lx = Ly = 6 nm) and a length of Lz = 16 nm and consists of a central silica block of 4 nm length and two adjoining reservoirs of 6 nm length on each side. (A) Front view onto the nearly cylindrical silica pore of 3 nm diameter carved into the silica block. (B) Side view of the studied model, shown as a ball-and-stick representation. Shown is solvent partitioning for a nominal solvent composition of 50/50 (v/v) water-acetonitrile with a simulation snapshot of the instant conformation after 80 ns. Atoms are color-coded as follows: silicon, yellow; oxygen, red; hydrogen of water and silanol, white; central carbon and methyl group of acetonitrile, cyan; nitrogen, blue.
between a cylindrical silica pore of 3 nm diameter and two sufficiently large reservoirs for molar (approximate volumetric) ratios of 1/3 (10/90), 1/1 (25/75), and 3/1 (50/50) W/ACN. The silica surface and nominal solvent compositions used in our model approximate typical conditions of HILIC separations.24,25 We analyze the solvent composition and distribution in the nanopore, at the external surfaces of the pore (toward the reservoirs), and in the reservoirs, and investigate structural arrangement, coordination, and diffusive mobility of the solvent molecules inside the nanopore.
’ SIMULATION DETAILS The simulation box had a quadratic cross-section of 6 6 nm2 and a length of 16 nm and was divided into a central silica block of 4 nm length and two adjoining reservoirs of 6 nm length on each side. The center of the silica block contained a nearly cylindrical silica pore of 3 nm diameter and 4 nm length. The volumetric ratio of ∼15 between the two reservoirs and the silica nanopore is sufficient to minimize finite-size effects on the equilibration of solvent mixtures between (ideally infinite) reservoirs and the nanopore. The chemical structure of the silica pore was prepared analogous to Coasne et al.36 The central silica block was carved from a β-cristobalite body such that the axis of the pore formed an angle of 35° with the (100) vector, an angle of ∼121° with the (010) vector, and an angle of ∼104° with the (001) vector of the β-cristobalite crystal. This procedure was preferred over pursuing a geometry with a 90° angle between pore axis and the (111) vector of the crystal, because it yielded a pore with a more circular cross-section and corresponding distribution of inner surface silanol groups (Figure 1A). After carving, under-coordinated silicon atoms and unconnected oxygen atoms in the pore and at the external surfaces of the silica block were removed, and dangling oxygen bonds were saturated with hydrogen atoms. Geminal silanol groups resulting from this procedure were converted into single silanol groups by building siloxane bridges to the nearest available silicon atoms. Final surface silanol densities were 5.4 nm-2 (8.95 μmol/m2) inside the pore and 5.2 nm-2 (8.50 μmol/m2) at the two external surfaces exposed to the reservoirs. These are typical values for bare-silica stationary phases.37 Molecular dynamics simulations were carried out for a canonical NVT-ensemble with Gromacs 4.5.2,38 using 8 nodes with
32 processors each on an IBM Power6 supercomputer at RZG (Rechenzentrum Garching, Germany). Periodic boundary conditions were used in all directions. An adequate representation of the polar silica surface is important in a study of electrostatic interactions with aqueous-organic mobile phases, which is why we took the silica force field parameters of Gulmen and Thompson.39 This force field uses point charges on every atom of the silica structure, i.e., it considers the silanol groups as well as the siloxane backbone. The point charges used were as follows: þ1.28e0 on silicon atoms, -0.64e0 on siloxane oxygen atoms, -0.74e0 on silanol oxygen atoms, and þ0.42e0 on silanol hydrogen atoms (where e0 is the elementary charge of the electron). For nonbonded interaction potentials, a cutoff radius of 1 nm was used. The silicon and oxygen atoms of the silica structure as well as the silicon and oxygen atoms of surface silanol groups were frozen during simulations. Parameters for unlike interactions were calculated using the conventional combination rule, and the particle-mesh Ewald algorithm was used for Coulomb interactions. The equations of molecular motion were integrated with a time step of 1.5 fs. Water-acetonitrile (W/ACN) mixtures of three nominal molar (approximate volumetric, v/v) compositions, 1/3 (10/ 90), 1/1 (25/75), and 3/1 (50/50), were studied; the corresponding numbers of solvent molecules in the productive simulation runs are given in Table 1. Water was modeled with the so-called SPC/E model, a rigid three-site model.40 Similarly, acetonitrile was considered a rigid three-site (but linear) molecule, for which we employed the united-atom version of the transferable potentials for phase equilibria force field (TraPPEUA).41 Mountain42 recently recommended the TraPPE-UA model to simulate W/ACN mixtures using three-site models, because it reproduces both the liquid density and the experimental estimates of hydrogen bonding derived from Raman scattering of the CN stretching band or from NMR quadrupole relaxation measurements. Furthermore, Rafferty et al.43 have shown that this force field enables very accurate predictions of the transfer free energies for alkane and alcohol solutes. Solvent molecules were initially placed in the simulation box in random positions on the basis of nonoverlapping van der Waals radii. For biased starting configurations, where the pore is filled initially with either acetonitrile or water molecules, water or acetonitrile molecules, respectively, were manually removed from the pore volume. Next, energy minimization of the system 2570
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Table 1. Studied Nominal Water-Acetonitrile (W/ACN) Compositions nominal molar composition
nominal volumetric composition
number of water molecules
number of acetonitrile molecules
1/3
10/90
2462
4434
1/1
25/75
4851
3693
3/1
50/50
8496
2445
was performed, and initial velocities were randomly assigned according to a Maxwell-Boltzmann distribution. Simulations were carried out at 300 K. A Berendsen thermostat with a coupling constant of 0.1 ps was used for temperature control.44 To enforce that the solvent composition in the bulk reservoirs does not deviate from the nominal composition by more than 0.5%, we performed preliminary simulations. After ca. 30 ns simulation time, when an equilibrium state was observed, the number of water and acetonitrile molecules in the simulation box was readjusted; i.e., acetonitrile molecules were removed and water molecules were added to the nominal solvent composition. This procedure was repeated once, before the productive simulation run over 90 ns was carried out.
’ RESULTS AND DISCUSSION Figure 1 illustrates our simulation model and visualizes equilibrium partitioning of a W/ACN mixture between two bulk reservoirs and a silica nanopore. The simulation box has a crosssection of 6 6 nm2 and comprises a β-cristobalite-based silica block of 4 nm length sandwiched between two reservoirs of 6 nm length each (overall dimensions: cross-section, Lx = Ly = 6 nm; length, Lz = 16 nm). A nearly cylindrical pore of 3 nm diameter drilled through the silica block connects the two reservoirs. The pore was carved into the β-cristobalite crystal such that its crosssection is nearly circular. Figure 1A provides a view onto the silica block cross-section with the empty pore and the silanol groups lining the inner pore surface. Figure 1B is a simulation snapshot of the instant conformation at t = 80 ns for a nominal solvent ratio of 50/50 (v/v) W/ACN. The bulk solvent displays microheterogeneity,45-53 i.e., the two solvent species are not evenly distributed at the microscopic scale. This does not imply a specific local order, only that deviations from uniformity have dimensions larger than a few molecular diameters. According to Mountain,42 the structure of such W/ACN mixtures chiefly results from the preference of water molecules for hydrogen bonding to other water molecules, not from a clustering tendency of acetonitrile molecules. Figure 2 describes the time evolution of the equilibration of W/ACN mixtures between the silica nanopore and the two reservoirs by recording the number of water molecules (top panel) and acetonitrile molecules (bottom panel) inside the pore as a function of simulation time. The simulations start from a biased configuration, where the pore is initially filled with acetonitrile molecules only (red, green, and blue curves in Figure 2). During the simulation, water molecules move from the bulk reservoirs into the pore, while the number of acetonitrile molecules in the pore decreases. After a simulation time of t ≈ 25 ns (dashed line in Figure 2), an equilibrium state is achieved; this demonstrates that the employed simulation time span of 90 ns is more than adequate to observe equilibrium solvent distributions with our model. For a nominal W/ACN ratio of 50/50 (v/v), we additionally performed a simulation that started from a completely water-filled pore (black curves in Figure 2). The two extremely biased starting configurations yielded identical
Figure 2. Equilibration of solvent molecules between the silica nanopore and the bulk reservoirs for nominal solvent compositions of 10/90 (blue), 25/75 (green), and 50/50 (red, black) water-acetonitrile (v/v). The simulation starts from a completely acetonitrile-filled (red, green, blue) or a completely water-filled pore (black). The number of water (top panel) and acetonitrile (bottom panel) molecules in the pore was calculated from the solvent molecules’ trajectories over 90 ns. The dashed line marks the beginning of equilibrium.
equilibrium pore solvent compositions, proving that the equilibrium pore solvent composition is not influenced by the initial pore solvent composition. Figure 3 presents laterally averaged (i.e., along x- and ydirections, cf. Figure 1A) number density profiles of the solvent molecules (water: top panel; acetonitrile: bottom panel) along the z-axis (length) of the simulation box (cf. Figure 1B). The profiles quantify the equilibrium solvent distribution inside the pore, at the external surfaces of the silica block, and in the bulk reservoirs. Distinct peaks in the water density profiles at each side of the pore (z ≈ 5.8 nm and z ≈ 10.2 nm) reflect the accumulation of water molecules at the external surfaces of the silica block. The acetonitrile density at the surface is concomitantly decreased. The interfacial water layer is also recognizable in the simulation snapshot of Figure 1B. It takes a distance of ∼1 nm from the surface, before water and acetonitrile reach their respective bulk solvent number densities. The flat number density profiles in the bulk region (z e 5 nm and z g 11 nm) agree well with experimental densities for the respective W/ACN mixtures indicated by the dashed horizontal lines.54,55 Inside the pore, water is enriched and acetonitrile is depleted with respect to the bulk solvent composition. The enrichment of water in the pore holds for all investigated W/ACN mixtures; the nominal W/ACN ratio determines only the relative differences between bulk and pore solvent composition. For a nominal solvent composition of 1/3 or 10/90 (v/v) W/ACN, the W/ ACN ratio is 0.318 in the bulk reservoirs but 1.526 in the pore, i.e., a factor of 4.8 higher (Table 2). At a nominal composition of 1/1 or 25/75 (v/v) W/ACN, the W/ACN ratio in the pore is a 2571
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Figure 3. Laterally averaged number density profiles of water molecules (oxygen atoms, top panel) and acetonitrile molecules (central carbon atoms, bottom panel) along the z-axis in the model (z = 0-16 nm, cf. Figure 1B), calculated from the time interval between t = 45 ns and t = 90 ns (cf. Figure 2) for nominal solvent compositions of 10/90 (blue), 25/ 75 (green), and 50/50 (red) water-acetonitrile (v/v). The dashed area indicates the pore (z = 6-10 nm). The dashed gray lines mark the number density values according to the nominal solvent composition.
Figure 4. Radial density profiles of atoms inside the silica nanopore. Top panel: oxygen (black) and hydrogen (gray) of surface silanol groups. Middle and bottom panels: oxygen of water and central carbon of acetonitrile for nominal solvent compositions of 10/90 (blue), 25/75 (green), and 50/50 (red) water-acetonitrile (v/v).
Table 2. Equilibrium Water-Acetonitrile (W/ACN) Compositions in the Pore (z = 6-10 nm) and the Bulk Solvent (z e 5 nm and z g 11 nm, cf. Figure 3) nominal molar (volumetric) W/ACN composition 1/3 (10/90)
1/1 (25/75)
3/1 (50/50)
nanopore
1.526
3.201
7.014
reservoirs
0.318
0.975
2.908
factor of 3.3 higher, and at a nominal composition of 3/1 or 50/ 50 (v/v) W/ACN, it is a factor of 2.4 higher than in the reservoirs. Increasing the acetonitrile fraction in the nominal solvent composition from 50/50 via 25/75 to 10/90 (v/v) W/ACN decreases the W/ACN ratio at each step by a factor of ∼3 in the bulk reservoirs but only by a factor of ∼2 inside the pore. In other words, the effect of an increasing acetonitrile fraction in the bulk is attenuated in the pore, where water is retained. Figure 4 provides an in-depth analysis of the radial solvent distribution inside the pore from the inner silica surface to the pore center. The top panel contains the radial density profile for oxygen (black) and hydrogen atoms (gray) of the surface silanol groups. The silanol groups yield two radial distribution peaks (with maxima at R ≈ 0.17 nm and R ≈ 0.32 nm), because our structural model considers that the silica surface is not flat on the atomic level (“microscopic roughness”), so silanol groups may be situated on “hills” or “valleys” (cf. Figure 1A). The radial density profiles for the pore water (middle panel) contain two peaks that correspond to the two surface silanol peaks and represent water molecules located near surface silanol groups. The first water peak at R ≈ 0.13 nm is much smaller than the main peak at R ≈ 0.37 nm, because of the limited spatial accessibility of the “valley” silanol groups. Acetonitrile molecules (bottom panel) are excluded from the immediate surface region (R < 0.45 nm), which constitutes ∼30% of the total nanopore volume. Beyond the immediate surface region, the density profiles depend on the nominal W/ACN ratio. At R > 1.2 nm, the number densities of
Figure 5. Radial projection of the hydrogen bond network of water (top panel) and acetonitrile (bottom panel) molecules inside the pore for nominal solvent compositions of 10/90 (blue), 25/75 (green), and 50/ 50 (red) water-acetonitrile (v/v). Thick curves denote water-water hydrogen bonds (HBs), dashed thick curves display water-acetonitrile hydrogen bonds, and thin curves with circles show hydrogen bonds with silanol groups.
the two solvents approach (but never fully attain) their respective bulk values according to the nominal W/ACN ratio. Coordination of the solvent molecules inside the pore was analyzed from the radial distribution of their hydrogen bonds (according to geometric hydrogen bonding criteria56). Figure 5 distinguishes between hydrogen bonds of water molecules to surface silanol groups, hydrogen bonds between water molecules, and hydrogen bonds between acetonitrile and water molecules. Additionally, hydrogen bonding between acetonitrile molecules and silanol groups was considered, but as acetonitrile molecules are excluded from the immediate surface region and silanol groups prefer water as the hydrogen bonding partner, silanol-acetonitrile hydrogen bonds are scarce. Water molecules are coordinated throughout the pore. In the immediate surface region (R < 0.45 nm), water molecules prefer hydrogen bonds to silanol groups over water-water hydrogen bonds, with an average of ∼1.5 2572
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Figure 6. Orientation of water (top panel) and acetonitrile (bottom panel) molecules along the radial position in the pore for nominal solvent compositions of 10/90 (blue), 25/75 (green), and 50/50 (red) water-acetonitrile (v/v). Radial distribution of cos(χ), where χ is defined as the angle between a solvent molecule’s dipole vector and the vector pointing from the pore center to the surface.
water-silanol hydrogen bonds per water molecule. Beyond the immediate surface region water-water hydrogen bonding is preferred, with an average of 2.5-3 hydrogen bonds per molecule, but hydrogen bonding between acetonitrile and water also contributes to the solvent structure in the pore (dashed lines). The maximum coordination for water-water (Figure 5, top panel) and acetonitrile-water (bottom panel) hydrogen bonds occurs just beyond the extended surface region (R ≈ 0.6 nm) and then decreases to approach bulk behavior toward the pore center. The orientational arrangement of the pore solvent molecules was probed by the angle χ between the dipole vector of a solvent molecule and the vector pointing from the pore center to the surface. Figure 6 shows the radial distribution of cos(χ) for water and acetonitrile molecules in the pore. The first peak in the water profile (R < 0.25 nm, cos(χ) > 0) refers to water molecules pointing with at least one of their hydrogen atoms toward the surface. Such an orientation has also been observed in recent molecular dynamics simulations of SPC/E water adsorbed on crystalline silica with various surface silanol densities.33 At R ≈ 0.3 nm, cos(χ) ≈ 0, i.e., χ ≈ 90°, reflecting an orientation of the water molecules’ molecular plane nearly parallel to the surface. These water molecules are in-plane with the oxygen atoms of the surface silanols at R ≈ 0.3 nm (see maximum peak for the silanol oxygen atoms in the top panel of Figure 4), an orientation that allows for two hydrogen bonds with the surface silanols (cf. Figure 5, R ≈ 0.3 nm). The second peak in the water orientation profile (with its maximum at R ≈ 0.5 nm) represents water molecules pointing with their dipole vector toward the surface, similar to the first peak, but the second peak is smaller and broader because hydrogen bonds between water molecules become the dominating coordination, as seen in the top panel of Figure 5. In fact, the second peak corresponds to the location of maximum coordination between pore water molecules (2 to 3 hydrogen bonds per molecule). Beyond the second peak in the water orientation profile, water molecules tend to adopt bulklike behavior and show no preferred orientation. The orientational arrangement of the acetonitrile molecules inside the pore (Figure 6, bottom panel) has two features. The first one characterizes the small fraction of acetonitrile molecules (R ≈ 0.45-0.5 nm) that form hydrogen bonds with the surface silanol groups (cf. Figure 5, bottom panel); these point with their nitrogen toward the surface, resulting in negative cos(χ) values.
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Figure 7. Diffusion coefficients parallel to the pore axis of water (top panel) and acetonitrile (bottom panel) molecules for nominal solvent compositions of 10/90 (blue), 25/75 (green), and 50/50 (red) wateracetonitrile (v/v). Dashed lines indicate the corresponding bulk values in the reservoirs.
The second feature is the oscillating behavior in cos(χ) toward the pore center. It resembles the layering of neat acetonitrile at an anastase surface, which was shown to enable dipole pairing and thus contribute to structural order and stability.57 The alternating orientation of acetonitrile molecules in successive solvent layers, although disturbed compared with neat acetonitrile, is still apparent in the wavy cos(χ) distributions. Each peak in the radial density profile of acetonitrile (bottom panel of Figure 4) roughly corresponds to nearly two peaks in the orientational profile (bottom panel of Figure 6). As observed for water, ordering decreases toward the pore center. Figure 7 visualizes how the solvent diffusion coefficients inside the pore (solid lines) depend on the radial position. The pore diffusion coefficients for water (top panel) and acetonitrile (bottom panel) molecules are based on the molecules’ mean square displacements parallel to the pore axis monitored over a time interval of 12 ps, following the approach of Liu et al.58 for calculating anisotropic diffusion constants near an interface. Bulk diffusion coefficients for the respective W/ACN compositions are included as dashed horizontal lines for comparison. Figure 7 shows that solvent mobility inside the pore is significantly reduced compared with the respective bulk mobile phase for all investigated W/ACN ratios. In neither case is the bulk diffusivity attained in the pore center. The slight decrease of the water diffusion coefficient toward the pore center for the water-richest 50/50 (v/v) W/ACN mixture (red curve, R > 1.2 nm) can be explained by a local increase of viscosity with the acetonitrile content (cf. Figure 4). This behavior, not seen for the acetonitrile-richer compositions, is related to the well-known maximum in the mole fraction-dependent viscosity of W/ACN mixtures.59,60 Toward the silica surface, the solvent mobility decreases drastically and for water even approaches zero (R < 0.45 nm), reflecting water molecules nearly immobilized by hydrogen bonding to surface silanol groups. In the immediate surface region (R < 0.45 nm), the dependence of the diffusive mobility is, therefore, also unaffected by the actual W/ACN composition, in agreement with the radial number density distributions (Figure 4), hydrogen-bonding characteristics (Figure 5), and orientational arrangement (Figure 6).
’ SUMMARY AND OUTLOOK Molecular dynamics simulation studies of the equilibration of W/ACN mixtures between a 3 nm-diameter silica pore and two 2573
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’ AUTHOR INFORMATION Corresponding Author
*Phone: þ49-(0)6421-28-25727. Fax: þ49-(0)6421-28-27065. E-mail: tallarek@staff.uni-marburg.de.
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