What Determines the Location of a Small Solute in a Nanoconfined

Article pubs.acs.org/JPCB

What Determines the Location of a Small Solute in a Nanoconfined Liquid? Robert H. Wells and Ward H. Thompson* Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States S Supporting Information *

ABSTRACT: Replica exchange molecular dynamics simulations are used to investigate the position-dependent densities of three small molecules dissolved in acetonitrile confined in nanoscale hydrophilic silica pores. The solutes, methanol, acetone, and carbon dioxide, differ in polarity and hydrogenbonding properties. All three molecules are found preferentially near the pore interface at room temperature, but the surface affinity differs with the solute interactions. Methanol, in particular, exists in two distinct conformations that differ in the hydrogen-bonding state. Free energy profiles as a function of distance from the pore surface are decomposed into internal energy and entropic contributions. These reveal that entropy as well as hydrogen bonding can play important roles in determining the solute location and orientation. These and other relevant factors are examined to elucidate the origins of the solute density profiles within the pore.

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INTRODUCTION Porous materials are important in a wide variety of applications ranging from catalysis to sensing. Liquids confined within their nanoscale pores exhibit strongly modified properties that are of fundamental as well as practical interest. In particular, mesoporous materials, with pore diameters of 2−50 nm, represent a key class of such systems where the confinement effects change dramatically with pore size and surface chemistry. The location of a solute molecule, or rather the distribution of locations, can be important in many applications, e.g., catalysis or sensing, where the function depends on a molecule (reactant or analyte) reaching the surface (to react or bind). However, the distribution of solutes in nanoscale confining frameworks can be difficult to characterize experimentally1,2 and often must be inferred for specific systems. Moreover, the factors that determine the distribution are not well understood, a gap in understanding that limits the rational design and improvement of mesoporous materials for specific applications. The position distribution of a solute in a mespore must naturally be a function of the solute interactions with the pore but also depend on the solute−solvent and solvent−pore interactions. These multiple effects can play out in ways that are not obvious a priori and that can vary (even qualitatively) with the system properties, i.e., solute charge distribution,3,4 solute size,4 pore surface chemistry,3 and solvent characteristics.5 Further, both energetic and entropic contributions can shape the solute position distribution.4,5 The latter are particularly difficult to predict without explicit simulation, and more insight is needed to develop models of the entropic factors that overcome this issue. © XXXX American Chemical Society

Acetonitrile is a particularly interesting solvent for investigations. It is an organic solvent widely used as a reaction medium for chemical transformations as well as for separations. Moreover, acetonitrile in nanoscale silica pores has been characterized by multiple experimental6−17 and theoretical18−25 studies. Acetonitrile exhibits interesting structural properties as a confined liquidits combination of rodlike shape, significant dipole moment, and hydrogen-bonding properties gives rise to solvent layering and orientational ordering that vary with pore surface chemistry. It also displays useful vibrational spectroscopic features upon hydrogen bonding.6,15,17,19 In this paper, this previous work on nanoconfined acetonitrile is built upon to address the question, what determines the position distribution of a small solute? Three solutesmethanol, acetone, and carbon dioxideare examined that vary in hydrogen-bonding properties and polarity to gain insight into the effect of the solute characteristics. The remainder of this paper is organized as follows. First, the details of the replica exchange simulations of methanol, acetone, and carbon dioxide solutes dissolved in nanoconfined acetonitrile are presented, including discussions of the force fields used. Next, the results of those simulations are presented and analyzed. In particular, the role of hydrogen bonding is investigated in significant detail, and the energetic and entropic contributions to the free energy surface describing the methanol position are determined and discussed. Finally, some conclusions and perspectives for future work are offered. Received: May 19, 2015 Revised: September 3, 2015

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DOI: 10.1021/acs.jpcb.5b04770 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

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The simulation cell was 44 Å × 44 Å × 30 Å; the interactions were evaluated with a cutoff of 15.0 Å, and long-range electrostatic interactions were included using three-dimensional periodic boundary conditions with an Ewald summation with a tolerance of 10−4. For each pore, 25 ns REMD simulations were run with a time step of 1 fs and configurations saved every 100 fs using ten temperatures: 298.15, 319, 341, 364, 388, 413, 439, 466, 494, and 523 K. The temperatures were maintained using a Berendsen thermostat34 with a time constant of 100 fs. The temperatures were chosen using the procedure of Rathore et al.,35 which is based on an assumption of a Gaussian distribution of energies. The temperatures are chosen to satisfy

SIMULATION METHODOLOGY Replica exchange molecular dynamics (REMD) simulations of each solute dissolved in nanoconfined liquid acetonitrile were carried out using the LAMMPS package.26,27 The linear, threesite ANL model,28 with Lennard-Jones and Coulombic interactions, was used for acetonitrile. The force field parameters for the solutes, solvent, and pore are given in Tables 1 and 2. Table 1. Intermolecular Potential Parameters for the Acetonitrile Solvent, Methanol, Acetone, and Carbon Dioxide Solutes, and Silica Pore Atoms atom type

σ (Å)

ϵ (kcal/mol)

q (e)

m (amu)

3.48 3.287 3.190

0.319 31 0.083 65 0.083 65

0.287 0.1376 −0.4246

15.035 12.011 14.007

3.775 3.07 0.0

0.207 0.170 0.0

0.265 −0.7 0.435

15.035 16.000 1.0079

3.91 3.75 2.96

0.160 0.105 0.210

0.062 0.3 −0.424

15.035 12.011 16.000

2.757 3.033

0.0559 0.159 98

0.6512 −0.3256

12.011 16.000

2.5 2.7 3.07 1.295

0.000 10 0.456 86 0.169 95 0.000 37

1.28 −0.64 −0.74 0.42

28.000 16.000 16.000 1.000

ΔE(Ti ) ⎡ ΔE ⎤ =⎢ ⎥ σE(Ti ) ⎣ σE ⎦target

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acetonitrile CH3 C N methanol29 CH3 O H acetone30 CH3 C O carbon dioxide31 C O silica pore32 Si Ob Onb H

where ΔE(Ti) = ⟨E ⟩(Ti) − ⟨E ⟩(Ti−1) is the difference in average energies at adjacent temperatures and σE (Ti) = [σE(Ti) + σE(Ti−1)]/2 is the average width of the energy distributions at the two adjacent temperatures with σE(Ti) = ⟨(E−⟨E ⟩)2⟩Ti. The target ratio is taken to be that estimated by Rathore et al. to achieve an acceptance ratio between temperatures of 20%.35 Error bars were calculated using block-averaging with 10 blocks and reported at a 95% confidence level using the Student t distribution.36

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METHANOL SOLUTE We first examine a single methanol molecule dissolved in nanoconfined acetonitrile. Methanol differs from the other two molecules considered in this work in that it can act as both a hydrogen-bond (H-bond) donor and acceptor. Density Profiles. The distribution of positions of the methanol molecule in the nanoscale silica pore can be quantified in terms of an effective density. We have previously shown that the distance, d, of a site from the nearest pore oxygen atom presents a clearer picture of the liquid structure than, for example, the radial position.37 Thus, we define the density of a molecular site, x, where for example, x = CH3, as

Table 2. Molecular Geometries Used for Acetonitrile, Methanol, Acetone, and Carbon Dioxide bond acetonitrile28 CH3−C CN methanol29 CH3−O O−H acetone30 CH3−C CO carbon dioxide31 CO

r0 (Å)

angle

θ0 (deg)

1.460 1.170

CH3−C≡N

1.430 0.945

CH3−O−H

108.5

1.51 1.22

CH3−CO CH3−C−CH3

121.4 117.2

1.149

OCO

180

(1)

180.0

ρx (d) =

Nx(d) Vx(d)

(2)

Here Nx(d) is the probability of finding a site x at distance d weighted by the number of such sites in the system. This weighting means that for a site x on the single methanol solvent, Nx(d) is simply the probability distribution while for an acetonitrile site it is a probability distribution normalized to the total number of molecules, i.e., 152. Also, Vx(d) is the volume available for a site x at the same distance. While Nx(d) is obtained from the molecular dynamics simulation, Vx(d) is calculated from a Monte Carlo simulation where each step attempts an insertion of a Lennard-Jones particle corresponding to the site x into the pore. A successful attempt occurs if there is no overlap between the inserted site and a pore atom and the probability of a successful insertion is collected as a function of d; this is then multiplied by the total volume into which insertions are attempted to give Vx(d). The calculated ρx(d) and Nx(d) for the acetonitrile solvent (x = N, C, and CH3) and the methanol solute (x = H, O, and CH3) are shown in Figure 1. The acetonitrile density profiles are consistent with those previously reported in the absence of a solute.37 They show a substantially enhanced density, by a

A previously developed32,33 amorphous silica pore model with pore diameter ∼2.4 nm was used in the simulations. The pore has a rigid silica (SiO2) framework with surface silanol groups, SiOH and Si(OH)2, that have flexible bonds, angles, and dihedrals; the pore has 42 SiOH and 7 Si(OH)2 groups giving an approximate surface density of ∼2.5 OH/nm2. The pore atoms also interact with Lennard-Jones and Coulombic interactions19 (see Table 1). The number of acetonitrile molecules in each pore was determined in previous grand canonical Monte Carlo (GCMC) simulations,18 152 for the pore considered here. A single solute was inserted in the pore, replacing an acetonitrile molecule (two in the case of acetone). B


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Figure 1. Left: density profiles, ρx(d), for top: the acetonitrile solvent sites x = N (blue dashed line), C (red dashed line), and CH3 (black dashed line) and bottom: the methanol solute sites x = H (blue solid line), O (red solid line), and CH3 (black solid line). Right: the corresponding probability distributions, Nx(d), for the same acetonitrile and methanol sites.

factor of ∼3, of the liquid near the pore surface due to the favorable CH3CN···silica interactions. From previous studies, the dominant interactions are electrostatic with only a minor contribution from H-bonding.19,37 The nitrogen atom lies closest to the surface, indicative of a more perpendicular arrangement of the acetonitrile molecules, and all three sites show structure in the density profile as a function of the distance from the pore surface. Thus, these density profiles indicate both solvent layering and orientational ordering of the molecules; this has been discussed extensively elsewhere by us19 and others.24,38 One effect of pore curvature is illustrated by the comparison of ρx(d) and Nx(d) in Figure 1, where the probability distribution decays at larger d due to the reduced volume available in the center of the pore; however, no other significant differences appear. The methanol site densities differ from those of acetonitrile in that the density is dramatically higher at the pore surface; the probability of finding the methanol molecule within d ⩽5 Å is ∼86%. Note that this number includes the effects of both free energy, discussed in detail below, and the greater volume available near the pore interface. The main peaks for the methanol O and CH3 sites at d = 2.7 and 3.3 Å are similarly positioned to those for the acetonitrile N and CH3 sites at d = 2.85 and 3.15 Å, respectively. However, the H density is qualitatively different as it exhibits a bimodal character with peaks at both d = 1.86 and 3.0 Å. The origin of these two peaks can be investigated by decomposing the density according to the H-bonding status of the molecule as ρx (d) = ρxdon (d) + ρxacc (d) + ρxnoHB (d)

Figure 2. Decomposition of the methanol site densities CH3, O, and H (top to bottom) in terms of the H-bonding status of the molecule with the silica pore. Densities for molecules donating an H-bond (blue lines), accepting an H-bond (red lines), and not H-bonding with the pore (violet lines) are compared to the total density (black lines).

(3)

Figure 3. Snapshots of the two hydrogen-bonding configurations of the methanol solute with the pore surface. Left: accepting an H-bond from a silanol group. Right: donating an H-bond to a pore oxygen atom. Silicon (yellow), oxygen (red), hydrogen (white), and methyl (cyan) are shown.

ρdon x

where is the density for site x in methanol molecules donating an H-bond to a pore oxygen atom, ρacc x is that for molecules accepting an H-bond from a pore silanol group, and ρnoHB corresponds to molecules with no H-bond to the pore x surface. We note that methanol molecules that are not donating an H-bond to the pore surface instead donate an H-bond to an acetonitrile molecule. These results are presented in Figure 2 for d ⩽4.5 Å for all three methanol sites. It is immediately clear from this decomposition that the bimodal character of ρH(d) is due to the different H-bonding states for the methanol molecule, which is illustrated in Figure 3. In particular, the peak at d = 1.86 Å is due almost completely to methanol donating an H-bond to a pore oxygen atom. The peak at larger distances representsin roughly equal measuremolecules

that are either accepting an H-bond from a pore silanol group and molecules not engaged in H-bonding with the pore. Interestingly, these two H-bonding states of methanol do not yield different peaks for the O and CH3 sites as those sites peak at nearly the same d whether the molecule is donating an Hbond with the pore or accepting one. Thus, the H-bonding state of the molecule primarily affects only the O−H bond direction. C


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represents methanol accepting an H-bond from the pore surface or lying near the surface and donating an H-bond to an acetonitrile molecule. In addition, the free energy required for the molecule to move to the pore interior decreases with increasing T and is only ∼0.5 kcal/mol at T = 523 K. This strong dependence on temperature indicates that entropy must be playing a key role in shaping the free energy curves. These entropic contributions can be straightforwardly calculated from ΔAx(d) = ΔUx(d) − TΔSx(d) if it is assumed that ΔUx(d) and ΔSx(d) are independent of temperature. Then, ΔSx(d) is obtained as the negative of the slope of a linear fit of ΔAx(d) versus temperature (see the Supporting Information). The internal energy can then be calculated from

Effects of curvature and pore roughness are evident in the comparison of ρH(d) and NH(d) in Figure 1. Specifically, in ρH(d) the peak at smaller d corresponding to methanol donating an H-bond is larger than that at larger d due to methanol accepting an H-bond or donating an H-bond to acetonitrile, but this trend is reversed in NH(d). From eq 2 we can see that this is a consequence of the available volume for the methanol H atom, which increases near the interface both because of the increasing space available at larger radii in the approximately cylindrical pore and the atomic roughness of the pore interface which is accessible to the H atom. The small size of an H atom means that it is more sensitive to atomic scale roughness than the larger O and CH3 moieties while its capacity for H-bonding increases this effect through favorable interactions with the surface. Free Energy, Internal Energy, and Entropy. The bimodal character of ρH(d) must naturally correspond to a double well in the free energy profile along the same

ΔUx(d) = ΔAx (d) + T ΔSx(d)

These results are shown along with the free energy curves for the three methanol sites, H, O, and CH3, in Figure 5. As would

Figure 4. Free energy, ΔAH(d), for the methanol hydrogen as a function of distance from the pore surface, d, is plotted for T = 298 K (black line), 341 K (violet line), 439 K (magenta line), and 523 K (red line). The higher T curves are shifted by 1, 2, and 3 kcal/mol for clarity.

Figure 5. Free energy, ΔAx(d), for the methanol CH3, O, and H (top to bottom) sites as a function of distance from the pore surface, d, is plotted for T = 298 K (black lines) along with the internal energy, ΔUx(d) (red lines), and entropic contribution to the free energy, −TΔSx(d) (blue lines, shifted for clarity).

coordinate. This is shown in Figure 4 where the relative free energy ΔAH(d) = −kBT ln

ρH (d) ρH (d0)

(5)

(4)

be expected from the densities, ρx(d), shown in Figure 1, the free energies for O and CH3 have a clear single minimum located near the surface with a flat free energy profile in the pore interior that is ∼1.8 kcal/mol higher. For CH3 there is an additional ∼0.5 kcal/mol barrier to leave the pore surface that is not present for the other sites, presumably attributable to the steric packing of these hydrophobic moieties in the pore. As anticipated from Figure 4, the entropic contribution to ΔAH(d) is notable. In particular, −TΔSH(d) decreases from its maximum near the pore wall (i.e., where the entropy is minimized) until plateauing around d ∼ 4 Å. There appears to be some minor structure near the barrier between the double minima in the free energy, but it is small and not resolvable outside the statistical errors. The consequence of this entropic effect is that the internal energy differs significantly from the free energy. Specifically, the global minimum for ΔUH(d) is at d = 1.74 Å. This corresponds to methanol donating an H-bond to a pore oxygen atom, indicating that this H-bonding arrangement is favored energetically but disfavored entropically. The

is plotted for different temperatures based on the replica exchange simulations; here, kB is Boltzmann’s constant, T is the temperature, and d0 is a reference distance. Note that the choice of reference distance, d0 = 3.3 Å for the methanol data shown here, only serves to define the zero of energy but does not change the shape of ΔA(d). The double-well structure of ΔAH(d) is clearly present for T = 298 K. The two minima at d = 1.86 and 3.0 Å are separated by only 0.35 kcal/mol. This small difference in free energy means it is not possible to determine the global minimum outside of the statistical errors. The methanol hydrogen has a free energy penalty of ∼1 kcal/mol to move from the surface to the pore interior. However, Figure 4 also shows that ΔA(d) has a strong temperature dependence. The local minimum at d ≃ 1.9 Å corresponding to methanol donating an H-bond to the pore surface is increasingly disfavored as the temperature increases. As a consequence, the well at d ≃ 3 Å becomes the clear global minimum at higher temperatures. Recall that this D


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significant cancellation between the internal energy and entropy contributions to the free energy profiles in Figure 5 and implicates H-bonding of methanol to the pore as a key factor. In particular, it indicates that H-bonds with the pore surface are favorable energetically but not entropically with a net effect that they are slightly preferred overall; note that the free energy for H-bonding to the surface is relative to methanol H-bonding to acetonitrile solvent molecules. The H-bond donors on the pore surface are naturally only the silanol and geminal groups, so that increased OH surface density should make more favorable the entropy for surface Hbonding where methanol is the acceptor. The H-bond acceptor when methanol acts as a donor is also predominantly (∼64% of the time) a silanol or geminal group with bridging oxygens in the silica framework representing the remainder, indicating that the OH surface density should have the same effect for this Hbond arrangement. The smaller contribution of the more numerous bridging oxygens is presumably due to their smaller partial charges in the model (see Table 1) and the fact that many are less accessible than the protruding silanol oxygens.

net result, as discussed above, is that methanol donating an Hbond to the pore is not the dominant arrangement. It comprises approximately 41% of methanol configurations compared to 24% for methanol accepting an H-bond from a pore silanol group and 35% for methanol having no H-bond with the pore at all (uncertainties are ±4%). Entropy also impacts the oxygen atom free energy profile, ΔAO(d), though less dramatically, as is evident in Figure 5. As in the case of the hydrogen atom, the entropic contribution, −TΔSO(d), decreases from a maximum at the pore surface. Thus, the internal energy exhibits a deeper well for the oxygen to move from the surface to the pore interior than the free energy, ∼2.6 kcal/mol compared to ∼1.8 kcal/mol. However, for the methyl group, the free energy and internal energy are effectively the same, indicating a minimal role for entropy. This is consistent with the result discussed above that the entropy associated with the H-bonding state of the methanol molecule, e.g., donating or accepting, affects primarily the O−H bond orientation, such that the methyl position distribution is not strongly affected by entropic contributions. Pore Hydrogen Bonding. The overall contribution of hydrogen bonding to the free energy minimum of the methanol molecule near the pore surface can be examined by defining the equilibrium constant PHB − pore KHB − pore(T ) = Pno‐HB − pore (6)

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ACETONE SOLUTE We next consider a different solute, acetone, dissolved in nanoconfined acetonitrile. Like methanol, it is a polar molecule with methyl groups and can act as an H-bond acceptor. However, it cannot act as an H-bond donor, a quality that clearly influences the distribution of methanol in the silica pore. Density Profiles. The density profiles for the acetone sites (x = C, O, and CH3) are shown in Figure 7; note that the two

where PHB−pore is the integrated probability of finding the solute with an H-bond to the pore surface and Pno‑HB−pore = 1 − PHB−pore is the probability of not having an H-bond with the pore. Note that both H-bonds donated to and accepted from the pore are included in PHB−pore. This equilibrium constant is shown in a van’t Hoff plot, ln KHB−pore(T) versus 1/T in Figure 6. From the slope of the linear fits to the data shown in this

Figure 7. Density profiles, ρx(d), for the acetone solute sites x = C (blue solid line), O (red solid line), and CH3 (black solid line). Contribution to the density from molecules accepting an H-bond from a pore silanol is also shown (dashed lines).

methyl groups are equivalent. The acetonitrile density in the silica pore is the same as that for the methanol solute case, shown in Figure 1. The results in Figure 7 show that acetone, like methanol, is predominantly located at the pore interface. The oxygen is found nearest the surface, peaking at d = 2.85 Å, while the carbon and methyl sites are located further away, near 3.4 and 3.3 Å, respectively. This indicates that the acetone CO bond is directed generally toward the surface but not perpendicular to it. The contributions to the density from Hbonded acetone molecules show that this orientational preference is not due solely to hydrogen bonding. Indeed, only 8.5% (±0.5%) of the acetone molecules are accepting an H-bond on average (compared to 24% for methanol). This suggests that the electrostatic interactions at the surface are an important factor, as was previously found in an examination of

Figure 6. van’t Hoff plot of ln KHB−pore(T) versus 1000/T for the methanol (top, black), acetone (middle, red), and carbon dioxide (bottom, blue) solutes. Data (circles) and fits to the van’t Hoff equation, eq 7 (lines), are shown.

figure the internal energy of an H-bond to the pore surface can be obtained from ln KHB − pore(T ) = −

ΔUHB − pore 1 ΔSHB − pore + R T R

(7)

where R is the gas constant. The data for methanol are well described by eq 7 and yield ΔUHB−pore = −1.99 ± 0.13 kcal/mol along with −TΔSHB−pore = 1.68 ± 0.10 kcal/mol (assuming that ΔUHB−pore and ΔSHB−pore are independent of temperature). This is consistent with the E


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The Journal of Physical Chemistry B the orientational ordering of the acetonitrile solvent itself.19 After the initial peak, the O atom density has a small peak around d = 5−6 Å where the C and CH3 site densities exhibit a minimum before they rise to a local maximum around 7.3 Å; the distance between maxima is roughly the same as the Lennard-Jones diameters of the sites, σC = 3.75 Å and σCH3 = 3.91 Å, indicating that this structure is related to steric effects. The surface affinity of acetone is reduced somewhat compared to methanol. This can be seen from comparison of the density profiles in Figures 1 and 7, where the methanol densities are more sharply peaked while the acetone density is greater at larger d. It can also be quantified by calculating the probability of finding the O atom within 5 Å of the surface, which gives ∼71% for acetone compared to 86% for the methanol O atom. The lower overall propensity of acetone for sitting at the pore surface along with the smaller H-bonding contribution may be attributable to the partial charges within the two molecular models. In particular, within the force fields used in this work, the acetone oxygen would be expected to be a weaker H-bond acceptor due to its smaller negative charge compared to the methanol O atom (qacetone = −0.424e; qmethanol O O = −0.7e). These charges also affect the other solute electrostatic interactions with the pore surface. Free Energy, Internal Energy, and Entropy. The free energy as a function of site distance from the pore wall, ΔA(d), is shown for each acetone site in Figure 8. The corresponding

modest for acetone than for methanol. These differences again indicate that the origin of the entropic effect for methanol is the H-bond donation by the methanol to a pore oxygen atom. Pore Hydrogen Bonding. A van’t Hoff plot for the hydrogen bonding equilibrium of acetone with the pore surface is given in Figure 6. The data for acetone follow the van’t Hoff relationship given in eq 7 with ΔUHB−pore = −0.32 ± 0.18 kcal/ mol along with −TΔSHB−pore = 1.65 ± 0.13 kcal/mol. These results suggest that H-bonding to the pore surface is only weakly preferred energetically and is entropically unfavorable, resulting in a overall endergonicity relative to no H-bonding. As such, it indicates that the surface affinity of the acetone molecule is not attributable to H-bonding but rather to more nonspecific electrostatic interactions with the pore surface that are stronger than acetonitrile solvation.

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CARBON DIOXIDE SOLUTE Finally, we examine a CO2 solute dissolved in nanoconfined acetonitrile. This nonpolar molecule represents the solute with the weakest interactions with the pore and solvent. Density Profiles. The density for the C and O sites of carbon dioxide are shown in Figure 9 as a function of the

Figure 9. Density profiles, ρx(d), for the carbon dioxide solute sites x = C (blue solid line) and O (red solid line). Contribution to the density from molecules accepting an H-bond from a pore silanol is also shown (dashed lines).

distance from the nearest pore oxygen atom; the two O sites are equivalent. As for acetone, the acetonitrile density is not perturbed by the solute and is the same as shown in Figure 1. The C and O densities are relatively aligned, both peaking at d ≃ 2.85 Å and ∼7 Å. This suggests a relatively parallel arrangement with respect to the pore wall, in contrast to the methanol and acetone cases. The surface affinity of CO2 is the smallest of the three solutes considered in this work. The density is less highly peaked, and the tail to increasing d is larger. This is reflected in the ∼64% probability of finding the CO2 within 5 Å of the pore surface. This is nearly the same as the probability of finding an acetonitrile molecule near the pore interface, suggesting that the CO2 density reasonably tracks that of the CH3CN solvent, in contrast to methanol and acetone. In addition, the Hbonding contribution to the carbon dioxide density is almost negligible as the CO2 molecule is H-bonded to the pore surface only 3.6% (±0.3%) of the time. Free Energy, Internal Energy, and Entropy. The free energy profiles for the carbon dioxide C and O sites are shown in Figure 10 along with the internal energy and entropic contributions. The free energy curves, ΔA(d), show a weak

Figure 8. Same as Figure 5 except for acetone, with results for the acetone CH3, O, and C (top to bottom) sites.

energetic, ΔU(d), and entropic, −TΔS(d), contributions are also presented. As with methanol, the most favorable location of the acetone molecule is next to the pore surface, where the free energy is ∼1 kcal/mol lower than in the pore interior, with no additional barrier to move from the interface to the pore center above this endergonicity. The origin of this attraction of acetone to the pore surface is different than that for methanol, however. In particular, the global minimum in the internal energy near the pore is not as deep as that of the free energy. The entropic contribution thus stabilizes the acetone near the pore wall, contributing to the deeper free energy well. Thus, this entropic contribution has the opposite effect of that for the H and O sites of methanol where entropy disfavored the molecule near the surface. However, the size of the entropic contribution is also more F


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dioxide. The electrostatic effects in hydrophilic pores have been previously shown to drive the orientation of the acetonitrile molecules to a relatively perpendicular arrangement, with the nitrogen pointing toward the pore surface.14,17,19,24,38 Thus, not surprisingly, these non-H-bonding electrostatic interactions play a key role in determining the distribution of acetone, which is a polar molecule and an H-bond acceptor of comparable strength to acetonitrile but poorer than methanol. A key feature is observed in the methanol H atom distribution, which is bimodal with one peak associated with methanol donating a hydrogen bond to a silica oxygen atom and the other arising from methanol accepting a hydrogen bond from a surface silanol group. The relative free energies of these two hydrogen-bonding conformations changes with temperature, implicating a significant role for entropy. In particular, entropy disfavors hydrogen bonding of methanol to the surface in general (relative to hydrogen bonding with the acetonitrile solvent). It is most unfavorable for arrangements in which methanol donates a hydrogen bond to the pore, presumably due to the more constrained solute (and solvent) arrangements associated with that structure. It is important to note that the entropic effect is a global one, involving both the possible conformations of the solute and solvent within the nanoscale pore. Thus, it should depend not only on the solute properties but also on the characteristics of the solvent and pore. Entropy also influences the acetone and carbon dioxide distributions, favoring solute positions near the pore interface in both cases. In the case of methanol, these entropic effects compete with the energetic preference of methanol to donate a hydrogen bond to a pore oxygen atom. Using a van’t Hoff analysis, this competition was quantified showing that the internal energy associated with a methanol−pore hydrogen bond is nearly, but not completely, canceled by the unfavorable entropy associated with the hydrogen bond. This fine balance shows that the location of solutes can certainly be tuned directly by temperature. However, it also indicates that it can be readily influenced by relatively small changes to the solute, solvent, and pore properties and thus, for example, that the surface affinity observed for methanol may be reversed for other solvents or pore chemistries. The internal energy for forming a H-bond with the pore surface, ΔUHB−pore, is less favorable for acetone compared to methanol and least favorable for carbon dioxide, while the entropic contribution, −TΔSHB−pore, is nearly independent of the solute. Interestingly, ΔUHB−pore changes linearly with the oxygen charge involved in the H-bond (even though methanol is the only H-bond donor). These trends suggest potential avenues for simple predictive models of solute partitioning in silica mesopores that deserve further study. These predictions of the distribution of small solutes in acetonitrile-filled silica pores are difficult to confirm directly via experiment. One approach might take advantage of the difference in hydrogen-bonding states by using vibrational (IR or Raman) spectroscopy to distinguish different solute locations. It is not yet clear that such an approach would work for the systems studied here, but a solute−solvent system can be designed for which it would be feasible, e.g., by taking advantage of the blue-shift in the CN stretching frequency in an acetonitrile solute upon hydrogen bonding to surface silanols in an aprotic solvent.

Figure 10. Same as Figure 5 except for carbon dioxide, with results for the C (bottom) and O (top) sites.

global minimum near the surface that is ∼0.9−1.0 kcal/mol lower than at the pore interior. Both sites exhibit a small barrier of ∼0.4 kcal/mol to approaching the surface from the interior. The same general features are observed in the internal energy profile, ΔU(d), but the minimum near the interface is raised to the point that there is not a statistically significant internal energy difference between the surface and the pore interior. This can be attributed to the smaller partial charges on the carbon dioxide (qC = +0.6512e and qO = −0.3256e). This naturally indicates that the entropy favors CO2 locations near the interface, which is clearly seen from the −TΔS(d) shown in Figure 10. For both C and O, the entropic contribution to the free energy has a minimum near the pore interface that is lower than in the interior by ∼0.8 kcal/mol. The entropy thus is the larger factor in determining the free energy curve for carbon dioxide. This behavior contrasts with that of methanol, where the entropy and internal energy compete to determine the shape of the free energy profile, and acetone, where the internal energy dominates but is reinforced by the entropic contributions. Pore Hydrogen Bonding. The minor role of hydrogen bonding with the pore in the distribution of carbon dioxide in the pore is further illustrated in Figure 6, where the van’t Hoff plot for the hydrogen bonding equilibrium of CO2 with the pore surface is shown. The results are qualitatively different than that for methanol and acetone as the fraction of time CO2 is H-bonded to the pore increases with temperature. The data is roughly fit by the van’t Hoff relationship, eq 7, with ΔUHB−pore = 0.43 ± 0.15 kcal/mol along with −TΔSHB−pore = 1.42 ± 0.11 kcal/mol, indicating that H-bonding is not favored either energetically or entropically.

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CONCLUSIONS The results presented here show that the position distribution for a small solute is localized near the silica pore surface, with a position distribution that is strongly modulated by the acetonitrile layering in the pore.19 For methanol the hydrogen is located closest to the hydrophilic pore surface while the methanol oxygen and methyl group are found to be in good registry with the acetonitrile nitrogen and methyl group, respectively. The coincidence of the heavy atom distributions suggests a role for both steric packing, governing the methyl group distributions, and electrostatic interactions with the pore that drive the nitrogen and oxygen atoms closer to the surface. Similar registry of the solute and acetonitrile densities is observed for acetone and even more strongly for carbon G


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b04770. Data for ΔAx(d) versus temperature and corresponding fits from which the entropic contributions are obtained (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.H.T.). 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). R.H.W. acknowledges support from the National Science Foundation Research Experience for Undergraduates program (Grant CHE-1263259). W.H.T. thanks Dr. Jacob A. Harvey for useful discussions.

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