On the Diffusion of Acetonitrile in Nanoscale Amorphous Silica Pores

Aug 15, 2013 - Cassandra D. Norton and Ward H. Thompson* .... Avinash Dass , Maguy Jaber , André Brack , Frédéric Foucher , Terence Kee , Thomas ...
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On the Diffusion of Acetonitrile in Nanoscale Amorphous Silica Pores. Understanding Anisotropy and the Effects of Hydrogen Bonding Cassandra D. Norton and Ward H. Thompson* Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States ABSTRACT: Molecular dynamics simulations are used to examine the diffusion of acetonitrile within ∼2.4 nm diameter amorphous silica pores with a focus on the mechanism. The role of the pore surface chemistry is examined by comparison of a hydrophilic, −OH terminated, silica pore with one that has hydrogen-bonding turned off and with an effectively hydrophobic pore obtained by setting all pore charges to zero. The anisotropy of diffusion, along and perpendicular to the pore axis, is examined through the mean-squared displacements. The origins of the anisotropy are investigated through the dependence on the acetonitrile position within the pore. The effect of hydrogen bonding of acetonitrile molecules to the hydrophilic pore surface is also probed. The simulations show that acetonitrile molecules do not diffuse axially next to the pore surface. Rather, axial diffusion is preceded by radial diffusion away from the pore surface. The same mechanism is observed for molecules independent of their hydrogen-bonding status to surface silanols though hydrogen-bonded molecules diffuse more slowly.

1. INTRODUCTION There is currently significant and growing interest in nanostructured materials that can confine liquids on molecular length scales. Nanoscale confinement can dramatically affect the fundamental properties of the liquid.1−4 These effects can be strongly dependent on the characteristics of the confining framework indicating the great potential of such materials for a variety of applications such as catalysis, separations, optical processing, and sensing. A key piece of realizing this promise is the development of a fuller understanding of the relationship between the properties of the confining framework and those of the confined liquid. In this paper, this relationship is examined for the diffusion of acetonitrile confined in nanoscale, ∼2.4 nm diameter, amorphous silica pores. A key issue for many applications of porous materials is diffusion of molecules within the pores. Mass transport can be limiting for catalysis as well as for sensing and separations. Thus, it is important to understand how, and how much, diffusion is affected by confinement along with the role of the confining framework properties. Mesoporous silica is widely studied for its potential use in a variety of applications while acetonitrile is an important organic solvent which also possesses spectral features that can be used to probe its properties in porous oxides. As such, acetonitrile in mesoporous silica has been studied both experimentally5−18 and computationally19−24 as has acetonitrile at planar silica interfaces.25,26 We have previously used molecular dynamics (MD) simulations to explore the structure, dynamics, and infrared spectra of acetonitrile confined in silica pores.20 The liquid structure was found to involve significant molecular layering next to the interface, including orientational ordering, as described briefly in section 2.3 and in detail in ref 20. This © 2013 American Chemical Society

picture for the structure of liquid acetonitrile in silica pores has since been supported by experimental measurements18 and additional simulations using a force field calibrated against electronic structure data.24 The orientational ordering had been previously posited by Farrer and Fourkas13 on the basis of the results of optical Kerr effect measurements and had been attributed to hydrogen bonding between the acetonitrile molecules and the pore hydroxyls. Our simulations found that the preferred orientation was independent of hydrogen bonding and instead was determined by the electrostatic interactions at the interface.20 Acetonitrile is of particular interest for confinement in nanoscale silica pores because of its vibrational spectroscopy. We have previously simulated the linear infrared CN stretching spectrum of acetonitrile in silica pores and have found that the spectrum is not sensitive to many changes in the liquid structure and dynamics induced by the confinement.20 However, the CN stretching mode frequency is shifted to higher frequencies upon hydrogen bonding providing a clear signature of molecules hydrogen-bonded to surface silanol groups in a pore.5,6,15,20 The localization of hydrogen-bonding sites at the surface suggests that nonlinear vibrational spectroscopy, which can probe spectral diffusion, may be sensitive to acetonitrile translational diffusion near the surface to the extent that it is related to hydrogen-bond making and breaking. It is thus interesting to examine acetonitrile diffusion and the molecular-level mechanisms involved. More broadly, diffusion to and from the surface is an important part of the Received: August 5, 2013 Revised: August 8, 2013 Published: August 15, 2013 19107

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Figure 1. Mean-squared displacements (MSD) in Å2 versus time for CH3CN confined within the (a) hydrophilic and (b) hydrophobic pore. Results are shown for the total (black line), x (blue line), y (violet line), and axial or z-direction (red line) MSDs; the total bulk MSD is also shown (magenta line). The insets show the short-time behavior of the directional MSDs for the confined liquid along with the bulk directional MSD (the total bulk MSD divided by three). N

properties relevant to applications, for example, catalysis or sensing, in which a reactant (product) must reach (leave) a supported catalyst or binding site at a pore surface. Acetonitrile diffusion in nanoscale silica pores has been examined previously both experimentally7,15 and theoretically.22−24 Measurements have found a significant reduction in the diffusion coefficient for confined acetonitrile7,15 with greater slowing for smaller pores.15 While some simulations have focused on water/acetonitrile mixtures in pores,22,23 Cheng et al. have recently carried out MD simulations to examine the diffusion and reorientation of silica-confined aceotnitrile.24 They focused on axial diffusion down the length of pores of different surface functionalities and found subdiffusive mean-squared displacements that are best described by a power law. In their analysis, mean-squared displacements were calculated for molecules that continually reside in a particular layer;24 the same approach is also used in the present work. They found nearly bulk-like values for the effective axial diffusion constants for molecules near the center of the pore and significant slowing for molecules near the pore surface. In this paper, the mechanism of acetonitrile diffusion in silica pores is examined in detail with an emphasis on the anisotropy of diffusion in the pore, the effects of surface interactions including hydrogen bonding, the role of position of an acetonitrile molecule in the pore, and activation energies for diffusion. The rest of this paper is organized as follows. The results of MD simulations, the details of which are provided in section 4, are presented and discussed in section 2. Special attention is given to the anisotropy in the diffusion as well as to the effect of acetonitrile position in the pore and of hydrogen bonding to the surface hydroxyls. Finally, concluding remarks are presented in section 3.

MSD(t ) = ⟨∑ |ri(t ) − ri(0)|2 ⟩ = 6D bulk t i=1

(1)

where N is the number of molecules and ri(t) is the center-ofmass coordinates of molecule i at time t. This yields Dbulk = 4.69 × 10−9 m2/s for the bulk liquid,27 which is in good agreement with the values Dbulk = 4.04−4.7 × 10−9 m2/s reported in the literature.28−32 As pointed out by Liu et al.,33 eq 1 should not be used to determine the diffusion constant near interfaces or in confined liquids such as that considered here. This is due to the different boundary conditions as well as to the presence of free-energy barriers to diffusion, that is, the molecules are not undergoing field-free diffusion. Diffusion constants can be obtained from comparisons with Smoluchowski equation simulations with the proper boundary conditions and free-energy surfaces.33 However, unlike for the model confining frameworks that we have previously considered,34,35 for the rough, amorphous silica pores considered in this work, this would require the onerous task of computing a full three-dimensional free-energy surface. Thus, with the exception of this subsection, where we consider comparisons to reported experimental effective diffusion constants, the mechanism of acetonitrile diffusion in nanoscale silica pores is probed through the mean-squared displacements rather than through the diffusion constants. There have been two reports of measured diffusion constants of nanoconfined acetonitrile obtained using different techniques. Koone et al. used a diaphragm cell to obtain the selfdiffusion coefficient for acetonitrile (and other liquids) in sol− gel pores of 2.9 nm diameter.7 These experiments measured the permeation of the solvent through a porous sol−gel membrane and might thus be interpreted as measuring an effective diffusion coefficient for acetonitrile along the pore axis (which will be taken as the z-direction in this work). They found Deff z = 1.08 × 10−9 m2/s at T = 294 K. This is 3.7−4.4 times slower than the literature values for the bulk liquid given earlier. The present simulations give Deff z from

2. NANOCONFINED ACETONITRILE DIFFUSION 2.1. Effective Diffusion Constants and Comparisons with Measurements. The diffusion of acetonitrile molecules in a ∼2.4 nm amorphous silica pore was examined using MD simulations. The details of the system and simulations are provided in section 4. In the bulk liquid, the diffusion constant, Dbulk, for CH3CN is calculated from the mean-squared displacement (MSD) as

N

MSDz (t ) = ⟨∑ |zi(t ) − zi(0)|2 ⟩ = 2Dzeff t i=1

(2)

as 1.46 × 10−9 m2/s, in the 2.4 nm pores and, combined with the calculated Dbulk value, and are in general agreement with these experimental measurements. While the measurements did 19108

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divided into layers on the basis of the probability density P(d) shown in Figure 2. We have verified that the results are not

not include hydrophobic pores, the present simulations predict −9 m2/s for that case. a slightly higher value of Deff z = 1.82 × 10 Kittaka et al. obtained diffusion coefficients for acetonitrile in the bulk liquid and in capillary condensed MCM-41 pores of diameters 2.04 and 3.61 nm by fitting quasi-elastic neutron scattering data.15 In contrast to the diaphragm cell approach, these measurements are sensitive to motions over only a few molecular diameters. They obtained Dbulk = 3.3 × 10−9 m2/s at T = 297 K for the bulk liquid, lower than the other values reported in the literature,28−32 and they obtained Deff = 0.99 × 10−9 and 0.27 × 10−9 m2/s for the 3.6 and 2.0 nm pores, respectively. These results indicate significant slowdown of acetonitrile diffusion upon confinement, factors of 3.3 and 12.2 for the larger and smaller pores, respectively, but implicitly contain the effect of free-energy barriers particularly in the radial direction in the pores. 2.2. Anisotropy. Confinement of acetonitrile in a roughly cylindrical pore would naturally be expected to lead to significant anisotropy in the diffusion. This is indeed the case as illustrated in Figure 1 where the mean-squared displacement along the pore axis, MSDz(t) in eq 2, is compared to MSDs in the other two Cartesian coordinates and to the total MSD. The results for the MSD in x and y are essentially identical, which indicates that the pore model, while lacking cylindrical symmetry, has no average asymmetry. As anticipated, for both the hydrophilic and hydrophobic pore, Figure 1 shows that the diffusion in the axial (z, ∥) direction parallel to the pore axis is faster than in the radial (x and y, ⊥) direction perpendicular to the pore axis. At long times, the MSDs in the perpendicular coordinates naturally plateau because of the finite space available in the pore cross section. However, the inset in Figure 1 shows that, even at the shortest times, the acetonitrile molecules exhibit greater mobility in the axial direction independent of the pore surface chemistry. This is not necessarily a reflection of a difference in diffusion constants (which can vary with position) but represents the collective effects of such effects along with free-energy barriers (because of layering of the liquid20) and the presence of the pore boundary. In the remainder of the paper, the anisotropy is examined in more detail along with some of the factors leading to its existence. Other workers have examined the anisotropy in diffusion constants for nanoconfined liquids. A recent study by Milischuk and Ladanyi on water confined in similar silica pores found the radial and axial diffusion constants, obtained by fitting the corresponding MSDs, to be nearly equal.36 Mittal et al. obtained a similar result for hard spheres confined in slit pores.37 They found that D∥ and D⊥, obtained by the method of Liu et al.,33 exhibited the same dependence on the slit pore width and concluded that diffusion parallel and perpendicular to the pore walls are affected similarly by the confinement. 2.3. Axial Diffusion versus Pore Position. To better understand how the acetonitrile molecules diffuse and the origins of the anisotropy represented in Figure 1, it is useful to consider the effect of position in the pore. The pore roughness means that the radial distance from the pore axis has limited utility for characterizing the molecular position. The distance from the pore surface, d, can provide a clearer approach for distinguishing molecules adjacent to or far from the pore surface.20 Here, d is calculated as the distance from the CH3CN center-of-mass to the closest oxygen atom in the pore structure. We have calculated the MSD in the z-direction for acetonitrile molecules in different positions in the pore as defined by d and

Figure 2. Probability density, P(d), as a function of the center-of-mass distance, d, to the nearest pore oxygen atom for a hydrophilic (black line) and hydrophobic (red line) pore. Layers used in the analysis are indicated by dashed blue lines.

highly sensitive to the precise definition of the layers. However, while our use of d to define the layers is motivated by the structure of the confined CH3CN (see Figure 2), it means that the layers are not defined perpendicular to z and, thus, purely axial diffusion can result in movement from one layer to another. As found previously20 and as shown in Figure 2, P(d) is barely changed when the pore charges are set to zero. This indicates that the structure in P(d) is due primarily to packing effects. This structure consists of clear layers located at d ≃ 3.3 and 6.5 Å with sublayers evident as shoulders in the peaks present at ∼4.5 and 9 Å.20 However, the insensitivity of P(d) to the surface chemistry should not be taken as an indication that the liquid is unaffected. Rather, the orientational ordering of the acetonitrile molecules is changed quite substantially when the pore is changed from hydrophilic to hydrophobic even while P(d) is nearly unaffected.20 In brief, the layers in the hydrophilic pore involve the CH 3 CN molecules lying perpendicular to the pore surface in the layers with the nitrogen atom closer to the surface with the sublayers representing anti-parallel orientations with the methyl group pointing toward the interface. These structural features are preserved even when the hydrogen-bonding of surface silanols is turned off as described in section 4. However, in the hydrophobic pore, the molecules lie parallel to the pore surface in the layers and perpendicular to the surface in the sublayers without preference for the nitrogen or methyl end.20 The z-direction (axial) MSDs for acetonitrile molecules initially in a particular layer, S , with the layers defined in Figure 2, are plotted for hydrophilic and hydrophobic pores in Figure 3a and b, respectively. Specifically, the MSD is calculated according to N

⟨Δz 2(t )⟩d(0) ∈ S = ⟨∑ |zi(t ) − zi(0)|2 ΘS[di(0)]⟩ i=1

(3)

where ΘS (d) =1 for d within layer S and 0 otherwise. Note that no condition is placed on which layer the molecules are in after t = 0. As would be expected, the interactions of the CH3CN molecules with the pore surface lead to slower axial diffusion for molecules in layers nearer the interface. This is true for both the 19109

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Figure 3. (a) MSD in z (in Å2) versus time for CH3CN molecules in a hydrophilic pore in a particular layer, defined in Figure 2 at t = 0 (solid lines), eq 3, and continuously within a layer (dot−dashed lines), eq 4; layer 1 (black), layer 2 (red), layer 3 (blue), and layer 4 (violet). (b) Same as a but for a hydrophobic pore.

Figure 4. (a) Same as Figure 3, but results are shown only for layer 1 for a hydrophilic (black lines) and hydrophobic (green lines) pore. MSDs for molecules initially (solid lines) and continuously (dot−dashed lines) in layer 1 are shown. (b) Survival probabilities versus time for molecules in layer 1 (black line), 2 (red line), 3 (blue line), and 4 (violet line) in the hydrophilic pore. Inset shows results for layer 1 in the hydrophilic (black line) and hydrophobic (green line) pores for long times.

In the hydrophilic pore, MSDs ⟨Δz 2(t )⟩d(t ) ∈ S for layers S = 1 and 2 deviate at relatively early times from those constrained only by the initial position, ⟨Δz 2(t )⟩d(0) ∈ S . In particular, the MSDs for molecules residing continuously in layers 1 and 2 are significantly smaller than those calculated for all molecules that simply begin in the same layer. This indicates that axial diffusion is substantially enhanced by radial diffusion out of layers 1 and 2. The effect of radial diffusion is significantly less pronounced for layer 3. For layer 4, furthest from the pore surface, ⟨Δz 2(t )⟩d(t ) ∈ S approaches ⟨Δz 2(t )⟩d(0) ∈ S so that movement out of this layer does not greatly enhance the axial diffusion. A closer look at ⟨Δz 2(t )⟩d(t ) ∈ S for layer S = 1 is provided in Figure 4a, where results are plotted for the hydrophilic and hydrophobic pores out to 500 ps. The fraction of molecules that remain in a layer after a time t, that is, the survival probability, is shown in Figure 4b. In both pores, ⟨Δz2(t)⟩d(t)∈1 reaches a maximum around t ∼ 25−30 ps. The decrease at longer times reflects the removal from the average of more mobile CH3CN molecules as they exit the layer; the decreased number of molecules included in the average also increases the statistical errors particularly in the hydrophobic pore where the radial diffusion is faster. In the hydrophilic pore, some molecules remain in layer 1 for more than 2 ns (Figure 4b), and ⟨Δz2(t)⟩d(t)∈1 can be calculated out to times that long. The fact that ⟨Δz2(t)⟩d(t)∈1 never exceeds 1.2 Å2 for the hydrophilic

hydrophilic and the hydrophobic (uncharged) pores. However, the axial diffusion is more strongly slowed in the hydrophilic pore. In comparison, diffusion in the hydrophobic pore is faster compared to the hydrophilic pore near the pore surface but slower near the pore interior. As seen in Figure 1, the net effect is slightly faster diffusion in the hydrophobic environment. Additional insight into the mechanism of axial diffusion can be obtained by comparing these results to the MSDs obtained by counting only molecules that remain continuously in a given layer over the time interval examined, that is, N

⟨Δz 2(t )⟩d(t ) ∈ S = ⟨∑ |zi(t ) − zi(0)|2 Θ̃S[di(t )]⟩ i=1

(4)

where Θ̃S [d(t)] = 1 for d(t) within the layer S for all times from 0 to t and zero otherwise. Note that this means a molecule that at time t′ leaves the layer it began in at t = 0 will only contribute to ⟨Δz 2(t )⟩d(t ) ∈ S for times t < t′. The results for ⟨Δz 2(t )⟩d(t ) ∈ S are shown in Figure 3a and b for a hydrophilic and hydrophobic pore, respectively. Cheng et al. recently calculated MSDs in a similar way for acetonitrile in silica pores.24 They used the radius to define two layers, that is, core and shell, and found subdiffusive dynamics in the MSDs that could be fit to a power law for t > 1 ps. Our MSDs for molecules continuously in a layer have similar qualitative behavior. 19110

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molecules. It is clear from this figure that, as would be expected, molecules that are hydrogen bonded diffuse more slowly than those that are not. However, non-hydrogen-bonded molecules initially in layer 1 also exhibit significantly slowed diffusion relative to molecules in the layers further from the pore surface. Indeed, the axial MSD of non-hydrogen-bonded molecules initially in layer 1 is closer to that for hydrogen-bonded molecules than it is for molecules outside the first layer. These results should also be viewed in the context of the average number of hydrogen bonds: 20.1 molecules or 13% of the total are hydrogen bonded compared to 39% that are in layer 1 but are not hydrogen bonded and to 48% lying outside of layer 1. Also shown in Figure 5 is the axial MSD for acetonitrile molecules initially in layer 1 in a pore with hydrogen bonding turned off by setting the hydrogen charge to zero (see section 4). The MSD in that case is the same, within statistical errors, as that for non-hydrogen-bonded molecules in layer 1 in the normal hydrophilic pore. This indicates that the presence of hydrogen-bonded molecules in the hydrophilic pore does not significantly affect those interfacial molecules that are not hydrogen bonded. This further indicates that axial diffusion from layer 1 is modulated by the exchange time into the center of the pore. This exchange dynamics, shown in Figure 4 for the hydrophilic pore, is essentially unchanged for the pore with no hydrogen-bond donors (not shown). This is consistent with the insensitivity of the distribution of acetonitrile molecules in the pore to the surface chemistry, Figure 2, which largely determines the free-energy barrier to exchange. 2.5. Estimated Activation Energies. The activation energies associated with diffusion can provide further insight into the effects of confinement. However, while obtaining these from a diffusion constant is straightforward according to an Arrhenius-like expression, D(T) = D0 exp(−Ea/RT), it is not as clear how to obtain Ea from the MSDs here, which are not linear for all times. However, an effective activation energy can be obtained by analogy with the diffusion constant

pore indicates that those molecules remaining in the first layer do not significantly diffuse in the axial direction even on a 2 ns time scale. Rather, the axial diffusion occurs by acetonitrile molecules diffusing first radially away from the pore interface where they then diffuse in the axial direction. This is reinforced by the comparison to ⟨Δz2(t)⟩d(t)∈1, which passes 4 Å2 around t ≃ 25 ps. Clearly, the anisotropy in diffusion for acetonitrile molecules next to the pore surface is extreme since effectively there is no axial diffusion for this first layer (S = 1). This indicates that the local diffusion anisotropy can be quite different than the global average anisotropy. It further suggests that the radial diffusion is a key component of the axial diffusion mechanism for molecules starting near the surface. Since the S = 1 layer comprises ∼52% of the CH3CN molecules in the pore, this is a significant part of the overall axial diffusion. This differs from the observation by Mittal et al. that hard-sphere diffusion perpendicular and parallel to the surface of a slit pore are similarly affected by confinement.37 We also note that the survival probabilities, Figure 4b, are not monoexponential so that a single exchange time, such as that appearing in two-state models with exchange,11−13,24,38 is not readily identified; this feature in the survival probabilities is insensitive to the definition of the dividing surfaces. In the hydrophobic pore case, the picture is somewhat less stark. Axial diffusion within layer 1 is markedly faster than in the hydrophilic pore case rising to a maximum of 2 Å2 at t ≃ 25 ps before falling off at longer times. After this time, as shown in the inset of Figure 4b, only 5% of the acetonitrile molecules initially in layer 1 still remain in the layer; in comparison, in the hydrophilic pore roughly 22% of the molecules remain after this time interval. Thus, it is clear that acetonitrile molecules leave the interfacial region before diffusing significantly in the axial direction as radial diffusion is more facile. 2.4. Hydrogen Bonding. It is interesting to examine the role of hydrogen bonding in the acetonitrile axial diffusion. This is illustrated in Figure 5 which shows the z-direction (axial) MSD for CH3CN molecules initially hydrogen bonded to surface silanols using a geometric definition of a hydrogen bond (RON ≤ 3.5 Å, RHN ≤ 2.45 Å, θHON ≤ 30°). This is compared to the axial MSDs for non-hydrogen-bonded molecules that are initially in layer 1 and that for all other non-hydrogen-bonded

⎛ −E eff ⎞ MSD(t ; T ) = MSD0(t )exp⎜⎜ a ⎟⎟ ⎝ RT ⎠

(5)

Eeff a

In the case of normal diffusive motion, reduces to the activation energy for diffusion since MSD(t; T) = 6D(T)t for motion in three dimensions. It is not obvious a priori that eq 5 will hold in general for the MSDs considered here. However, that it does so for the MSDs on the basis of initial layer location, that is, the ⟨Δz 2(t )⟩d(0) ∈ S plotted in Figure 3, is shown in Figure 6. There, the MSDs for T = 298.15, 315, and 330 K are scaled to T = 285 K according to eq 5 and are compared to the MSD at that temperature. It is clear that the MSDs for each layer follow well this Arrhenius-type expression for the 500 ps time range shown. The same is true for molecules in layer 1 divided by initial hydrogen bonding status (not shown). Effective activation energies can then be obtained by fitting the scaling factors used to match the MSDs in Figure 6 to eq 5. An Arrhenius-type plot for these scaling factors is presented in Figure 7a for the four layers and molecules initially in layer 1 with different hydrogen-bonding statuses. The linear fits shown give Eeff a for these cases, which are compared to each other and to the bulk liquid activation energy in Figure 7b. These data show that the effective activation energy decreases with the distance from the pore wall dropping from ∼8.5 kJ/mol in layer 1 to ∼4.8 kJ/mol in layers 3 and 4. These are activation energies for diffusion on the basis of only the starting location

Figure 5. The axial MSD (in Å2) versus time for CH3CN molecules initially hydrogen-bonded to the pore silanols (black line) is compared to that for molecules not hydrogen-bonded but in layer 1 (red line) and all other non-hydrogen-bonded molecules (blue line). For comparison, results are also shown for molecules starting in layer 1 in the pore with hydrogen-bonding turned off (brown line). 19111

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slower dynamics as the axial MSD for the hydrophilic pore is a factor of ∼3.3 slower than the one-dimensional diffusion in the bulk liquid; for the hydrophobic pore, this factor is ∼2.6. The present results are in general agreement with experimental measurements reported in the literature7,15 though direct comparisons are made difficult by uncertainties in the molecular-level meaning of the measured diffusion constants. There is significant anisotropy in the acetonitrile diffusion in the silica pores as observed in the MSDs in the axial (z) and radial (x and y) directions. In the present analysis, we cannot separate the effects of changes in the axial and radial diffusion constants, the boundary conditions imposed by the pore wall, or the free-energy barriers to diffusion because of layering of the liquid. However, the diffusion mechanism was examined to better understand this anisotropy. It was found that the axial diffusion is strongly dependent on the position of the acetonitrile molecule position in the pore. In fact, molecules at the pore surface do not significantly diffuse along the pore axis without first leaving the interface. Thus, the mechanism of diffusion along the pore for an interfacial molecule is radial diffusion followed by axial diffusion indicating that the diffusion anisotropy is strong at the pore surface. The relatively modest overall anisotropy is then a consequence of the coupling of axial and radial diffusion at the interface as well as the averaging over all the acetonitrile molecule positions. The effect of acetonitrile hydrogen bonding with the surface silanols in a hydrophilic pore is to slow down diffusion but perhaps not as dramatically as one might expect. The activation energy for axial diffusion only increases by 2.0 kJ/mol for interfacial acetonitrile molecules when they are initially engaged in a hydrogen bond. This suggests strong contributions to the slowdown in interfacial diffusion from other factors such as liquid layering, electrostatic interactions with the surface, and steric effects. Hydrogen bonding does not appear to be the dominant effect leading to slower diffusion in hydrophilic pores. This is consistent with the behavior of the liquid structure observed in simulations20,24 but is at odds with a recent analysis of the confined acetonitrile dynamics.24 However, the frequency shift in the CN stretching mode upon hydrogen bonding may provide a route to monitor diffusion of molecules from the pore surface with nonlinear infrared or Raman spectroscopy.20

Figure 6. Axial MSDs (in Å2) are shown for layers 1−4 (solid, dashed, dot−dashed, and dash−dash−dotted lines, respectively) for T = 285 K (black lines) along with scaled results for T = 298.15 K (red lines), 315 K (blue lines), and 330 K (purple lines).

of the molecule and so represent both axial and radial motion as illustrated in section 2.3. By comparison, the activation energy for CH3CN diffusion in the bulk liquid is 4.8 kJ/mol indicating that while axial diffusion is restricted near the pore interface it is actually just as facile as the bulk in the pore interior. The resulting overall axial diffusion, represented by MSDz(t) in eq 2, has an effective activation energy of 6.6 kJ/mol, 37% higher than that for the bulk liquid. The effective activation energy for axial diffusion from layer 1 is naturally an average of those interfacial molecules that are hydrogen-bonded to surface hydroxyls and those that are not hydrogen-bonded. The Eeff a values for these two subpopulations are shown for comparison in Figure 7b. Hydrogen bonding increases the activation energy, but by only 2.0 kJ/mol, which is significantly less than the typical energy of a hydrogen bond. Recalling that axial diffusion for molecules initially in layer 1 is due to initial radial diffusion, this suggests that hydrogen bonding to surface silanols only moderately restricts acetonitrile diffusion from near the interface toward the pore interior.

3. CONCLUDING REMARKS Molecular dynamics simulations have been used to investigate the diffusion of acetonitrile confined within ∼2.4 nm amorphous silica pores. This confinement leads to significantly

Figure 7. (a) Arrhenius-type plot for the scaling factors used in Figure 6 to match MSDs at different temperatures; this scaling factor is 1 by definition at T = 285 K in all cases. Results are shown for layers 1−4 (black, red, blue, and purple circles, respectively) as well as for molecules in layer 1 initially hydrogen bonded (magenta squares) and not initially hydrogen bonded (maroon squares). Linear fits are shown as dashed lines of the same color for each case. (b) Effective activation energies obtained from Arrhenius fits to the scaling factors used in a are shown as a function of layer index (black circles), the dashed black line is intended only as a guide to the eye, and of the bulk liquid (red line). The layer 1 results are further divided into Ea for molecules that are initially hydrogen bonded (blue square) and that are not initially hydrogen bonded (blue diamond). 19112

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were modeled by removing the charges on the pore atoms to give a neutral pore. Additionally, non-hydrogen-bonding pores were generated by setting the silanol and geminal hydrogen charges to zero (compensated by a change in the charge on the bonded oxygen); this yielded a pore with no hydrogen bond donor groups but left the remaining liquid-pore electrostatic interactions intact. These models allowed the effects of surface chemistry to be studied independent of the effective radius or of the number of CH3CN molecules. Error bars were calculated using block-averaging with five blocks and were reported at a 95% confidence level using the Student t distribution.45

Effective activation energies for axial diffusion in hydrophilic pores are somewhat, ∼40%, higher than those for bulk acetonitrile. However, the similarity obscures the averaging over molecular positions in the pore: the activation energy is roughly that of the bulk liquid for molecules away from the interface but is significantly greater for those at the pore surface. In summary, the mechanism of acetonitrile diffusion in nanoscale silica pores involves exchange between the pore surface and the interior as a key component. Molecules at the pore interface exhibit significantly limited mobility, particularly in the axial direction, and this effect falls off smoothly with the distance from the surface. While this has features reminiscent of a two-state model with exchange,11−13,24,38 the diffusion is not clearly described in terms of two states, and exchange between the pore interface and the interior cannot be characterized by a single time constant. The degree to which these properties of acetonitrile diffusion are general is not yet clear and requires further study; protic and nonpolar liquids will have different interactions with the pore surface and may show different dynamics.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (Grant CHE-1012661).

4. SIMULATION METHODOLOGY Classical molecular dynamics (MD) simulations of bulk and nanoconfined liquid acetonitrile were carried out using the DL_POLY_2 package.39 Bulk simulations involved 500 acetonitrile molecules at a density of 0.764 g/cm3 in the NVT ensemble using a Nosé-Hoover thermostat40,41 (1 ps time constant) and cubic periodic boundary conditions. The linear, three-site ANL model,42 with Lennard-Jones and Coulombic interactions, was used for acetonitrile. Interactions were evaluated with a cutoff of 10.0 Å, and long-range electrostatic interactions were included using three-dimensional periodic boundary conditions with an Ewald summation using an Ewald parameter of α = 0.243 and a 6 × 6 × 6 k-point grid. Data were collected from a 2 ns simulation preceded by a 1 ns equilibration with a time step of 2 fs. Previously developed43,44 amorphous silica pore models were used to simulate confined acetonitrile. The pores have a rigid silica (SiO2) framework with surface silanol groups, SiOH and Si(OH)2, with fixed bond lengths but variable bond angles; ten pore models, prepared with the same procedure and a nominal diameter of ∼2.4 nm but with different amorphous structure, were examined. Only quite modest variations between pores were observed in preliminary calculations so that the results presented here are obtained from a single pore. The pore atoms also interact via Lennard-Jones and Coulombic interactions as described in detail elsewhere.20 The number of acetonitrile molecules in each pore was determined in previous grand canonical Monte Carlo (GCMC) simulations,19 152 for the pore considered here. The simulation procedure was the same as for the bulk except that the simulation cell was 44 × 44 × 30 Å and the k-point grid was 10 × 10 × 8. For each pore, simulations were initiated with a 1 ns equilibration (starting from the results of GCMC simulations19), and data was collected every 0.1 ps over a subsequent 20 ns simulation. Two trajectories were propagated at a temperature of 298.15 K while one was run at 285, 315, and 330 K. In addition to the hydrophilic pores, two modified pore surfaces were studied. The hydrophilic pores were terminated with hydroxyl groups present as silanol, SiOH, or geminal, Si(OH)2 groups;43,44 the pore considered here contained 42 silanols and 7 geminals (though not all were sterically accessible to an acetonitrile molecule in the pore). Hydrophobic pores

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