Molecular Origins of Dynamic Coupling between Water and Hydrated

Sep 21, 2016 - Fardin Khabaz , Yong Zhang , Lianjie Xue , Edward L. Quitevis ... Rutvik V. Godbole , Fardin Khabaz , Rajesh Khare , and Ronald C. Hedd...
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Molecular Origins of Dynamic Coupling between Water and Hydrated Polyacrylate Gels Fardin Khabaz, Sriramvignesh Mani, and Rajesh Khare* Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409-3121, United States S Supporting Information *

ABSTRACT: Energy efficient separation of dilute alcohol−water mixtures is a critical consideration in commercialization of biofuels; pervaporation is an attractive separation technique for this purpose. Knowledge of the mechanism of solvent mobility inside polymeric membranes is of great interest for designing pervaporation-based separation processes. Recently, we employed molecular simulations to study water structure in three polyacrylate gels composed of homopolymers and copolymers of n-butyl acrylate (P(BA)) and 2-hydroxyethyl acrylate (P(HEA)). In this work, water and ethanol dynamics were studied using simulations in two systems: polyacrylate gels swollen to equilibrium and gels with low water content. Solvent dynamics show a concentration-dependent behavior in the gels. For gels swollen to equilibrium, both water and ethanol exhibit the highest mobility in the P(HEA) gel due to the larger degree of swelling of the system, while for gels with a low solvent content, they show the lowest mobility in the P(HEA) gel due to hydrogen bonding between solvent and polymer. Solvent dynamics in gels with low solvent content was characterized by determining solvent diffusivity, rotational relaxation time, and Van Hove autocorrelation function. The dynamics of water molecules is strongly coupled with polymer dynamics due to hydrogen-bonding interactions, while ethanol does not show such strong coupling due to a smaller degree of interaction with the polymer. Ethanol mobility instead follows the trend in the density and glass transition temperature of the polymer. Our results suggest that dynamic coupling between solvent and polymer can be exploited as a mechanism for separating dilute alcohol−water mixtures.

1. INTRODUCTION

potential candidates for energy efficient separation of alcohol− water mixtures of different compositions. Recently, Godbole et al.21 have shown that a combinatorial method can be used to screen polyacrylate copolymers for pervaporation-based separation of alcohol−water mixtures. Acrylate monomers with varying degree of hydrophilicity were used to build test gel networks for this purpose. In our recent simulation study,22 it was observed that at low concentration water molecules predominantly formed hydrogen bonds with the polymer in polyacrylate gels, while at high concentration they mainly formed hydrogen bonds with other water molecules. For the gels with low water content, the lifetime of water−polymer hydrogen bonds increased with an increase in polymer hydrophilicity.

Polymeric membranes are increasingly used in applications such as separation of mixtures of water and organic solvents1−8 and direct methanol fuel cells.9−19 In recent years, the problem of efficient separation of dilute alcohol−water mixtures has achieved prominence due to renewed emphasis on bioalcohol as an alternative fuel. In previous experimental studies, polydimethylsiloxane (PDMS) and poly(vinyl alcohol) (PVA) membranes have been used to enhance the alcohol concentration in the permeate.2,5,7,8,20 Biomass variability results in a large variation of the composition of bioalcohol− water mixture produced. Thus, it is important to design membranes whose separation ability can be rapidly tuned based on the composition of the alcohol−water mixture to be separated. In this regard, availability of monomers of varying hydrophilicity allows for a fine control over the separation characteristics of polyacrylate copolymers, in turn making them © XXXX American Chemical Society

Received: May 4, 2016 Revised: August 3, 2016

A

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were studied. The chemical structure of the monomers and the cross−linker are shown in Figure S1 (see Supporting Information). The general AMBER force field (GAFF)38,39 was used to determine the intra- and interatomic interactions with water being treated by the TIP3P model.40,41 The SHAKE algorithm42 was employed to constrain the bond lengths of the water molecules. The AM1−BCC method43,44 was applied to determine the partial charges on the atoms. A cutoff distance of 12 Å was utilized to calculate the van der Waals and electrostatic interactions in the systems. The tail correction approximation and particle−particle particle−mesh (PPPM) algorithm45 were used to handle the long-range part of the potential energy. In addition, temperature and pressure of the systems were held constant with the Nosé−Hoover thermostat and barostat, respectively.46,47 All MD simulations were performed using the LAMMPS48 package with a time step of 1 fs. The model structures used here are from our recent study,22 and the reader is referred to that paper for the details of the system preparation methods and the validation of the structures. Briefly, network structures were prepared by the simulated annealing polymerization method,49,50 and force field parameters were validated by comparing the density and glass transition temperature (Tg) with experimental data for linear polyacrylates.22 For the sake of completeness, the details of system composition are given in Tables 1 and 2.

Mobility of water and ethanol molecules is an important consideration in designing the alcohol−water separation applications. In the fuel cell applications, the interest is in minimizing the diffusive flux of methanol through the polymer (mostly Nafion),19,23 while for pervaporation, the interest is in maximizing the diffusive flux of alcohol (ethanol or butanol) through the polymer. The effect of solvent concentration on the dynamics of the penetrant molecules inside polymeric gels, such as Nafion, copolymer of ether/ester, poly(ethylene glycol), poly(N,N-dimethylacrylamide), and copolymer of stearyl itaconamide/N,N-dimethylacrylamide, has also been investigated experimentally.24−28 These studies showed that at low solvent concentration the penetrant molecules exhibit slower mobility due to their interaction with the gel network. On the other hand, the molecules show enhanced dynamics in gels with a larger degree of swelling.26−28 Similar observations have also been reported from molecular dynamics (MD) simulations of water diffusion in polymeric systems including Nafion, sulfonated poly(ether ether ketone), perfluorinated ionomer, polydimethylsiloxane, poly(vinyl alcohol), and poly(ethylene oxide).9−12,29−37 The effect of solvent concentration (or the degree of swelling of the gel) on the mobility of solvent molecules has been established in the literature.9−12,24−32,34−37 But the relationship between dynamics of penetrant molecules and polymer atoms and the underlying molecular mechanism are not well understood. In this work, our focus is on using atomistic simulations to study solvent dynamics in polyacrylate pervaporation membranes that are being evaluated as candidate materials for separating dilute alcohol−water mixtures. The thickness of the actual pervaporation membranes used in practice is of the order of a few micrometers (with a concentration gradient across the membranes from the feed side to the vapor side), while our atomistic simulation systems are of the size ≈10 nm. The simulation models thus represent snapshots of the system at “local” values of concentration along the membrane. Our specific goal in this work is to elucidate the molecular mechanisms underlying the solvent molecule mobilities in these systems. With this goal in mind, we have investigated the relationship between the dynamics of solvent molecules and polymer atoms in polyacrylate gels under two conditions: gels swollen to equilibrium and gels with a low amount of solvent (that was the same in all gel systems). Our results demonstrate that the dynamics of water molecules is strongly coupled with dynamics of the polymer atoms due to hydrogen-bonding interactions; this behavior is not exhibited by ethanol molecules. These results suggest that in addition to polymer hydrophilicity, dynamic coupling between polymer and water provides an additional mechanism for separating alcohol−water mixtures. We begin by describing the simulation details and methods. We then present our findings on the dynamic coupling between the solvent molecules and polymer in different gels. We close the paper with a discussion of our results and conclusions.

Table 1. Mole Fractions of Components in Gels Swollen to Equilibriuma component

P(BA)

P(BA50−HEA50)

P(HEA)

nBA HEA PETA ethanol water

0.9600 0.0000 0.0030 0.0200 0.0170

0.2550 0.2610 0.0010 0.0500 0.4330

0.0000 0.0973 0.0003 0.0378 0.8646

a

The model systems are the same as those used in our previous work,22 the compositions of which, in turn, were based on experimental measurements.

Table 2. Mole Fractions of Components in Gels with Low Water Contenta component

P(BA)

P(BA50−HEA50)

P(HEA)

nBA HEA PETA ethanol water

0.9600 0.0000 0.0030 0.0200 0.0170

0.4800 0.4800 0.0030 0.0200 0.0170

0.0000 0.9600 0.0030 0.0200 0.0170

a

The model systems are the same as those used in our previous work.22

The translational mobility of various components was characterized by measuring the mean-squared displacement (MSD) of the relevant molecules or atoms, while the rotational mobility of water and ethanol molecules was studied by using the orientational order parameter (P2) function. For this purpose, the model structures were subjected to constant NPT (constant number of atoms, pressure, and temperature) MD simulations, and coordinates of relevant atoms were stored at regular intervals. Specific details for each individual property calculation are given in the Results section.

2. SIMULATION DETAILS AND METHODS Networks formed by the monomers n-butyl acrylate (nBA) and 2-hydroxyethyl acrylate (HEA), which are hydrophobic and hydrophilic, respectively, were studied in this work. Pentaerythritol tetraacrylate (PETA) was the cross-linking agent in the systems. Specifically, networks formed by nBA (denoted as P(BA)), by HEA (denoted as P(HEA)), and by 50−50 random copolymer of nBA and HEA (denoted as P(BA50−HEA50)) B

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3. RESULTS AND DISCUSSION Two aspects of solvent dynamics were studied in this work. First, the dynamics of water and ethanol molecules in gels swollen to equilibrium (see Table 1) were studied to determine the effect of solvent concentration on the mobility of the penetrant molecules. Second, the mobility of these molecules in the gels with a low water content (water content was the same in all gels; see Table 2) was studied, and the relationship between solvent mobility, polymer mobility, structure of the systems, and polymer hydrophilicity was elucidated by determining hydrogen bond probability, Van Hove autocorrelation function, and the incoherent intermediate scattering function. 3.1. Gels Swollen to Equilibrium: Solvent Mobility Increases with an Increase in Solvent Content. Translational Mobility. In order to characterize the translational mobility of the solvent molecules and the gel, mean-squared displacement (MSD) of the center of mass of the water and ethanol molecules and MSD of backbone atoms of the polyacrylate gels were determined at T = 300 K in the systems swollen to equilibrium. The MSD of water and ethanol molecules are shown in Figures 1a and 1b, respectively. As can be seen, the values of MSD in the P(BA) and the copolymer systems are significantly smaller than those in the P(HEA) system. These results can be explained by considering the effect of water concentration on the local structure of solvent molecules and the polymer chain. The mole fraction of water (see Table 1) increases significantly with an increase in the hydrophilicity of the gel. A snapshot of simulation box (see Figure 2) shows that water molecules create a large cluster in the P(HEA) gel due to the high water content. Thus, water and ethanol molecules diffuse primarily inside the solvent cluster and subsequently show a high mobility. Snapshots also show a small cluster of water molecules in the copolymer gel and the presence of welldispersed water molecules in the P(BA) gel. As a result, in the P(BA) and the P(BA50−HEA50) systems, water and ethanol molecules interact with the polymer network and hence have a lower mobility. We note that although there are clusters of water in the P(BA50−HEA50) gel, these clusters cannot enhance the translational mobility of the molecules due to their smaller size. On the other hand, the size of water clusters is significantly large in the P(HEA) gel which allows solvent molecules to travel a long distance without encountering the polymer matrix. This phenomenon (i.e., the segregation of hydrophilic and hydrophobic domains) has also been reported in Nafion membranes.18,51 The segregation of these domains helps the formation of water channels to transport the hydronium ions in the Nafion membranes. In our case, such a long-range nanoscale segregation is only observed in the highly hydrophilic P(HEA) gel when swollen to equilibrium; this behavior is not exhibited by other systems studied here. A consequence of lower solvent mobility in the P(BA) and the P(BA50−HEA50) gels is that at T = 300 K, both water and ethanol show subdiffusive behavior over the simulation time scale in these two gels. On the other hand, using the Einstein relation, diffusion coefficients of water and ethanol molecules in the P(HEA) gel are obtained to be 2.04 × 10−9 and 0.429 × 10−9 m2/s, respectively. These diffusivity values are close to the experimentally measured self-diffusion coefficients of these molecules in pure solvent systems52,53 (Dwater = 2.299 × 10−9 m2/s and Dethanol = 1.05 × 10−9 m2/s). These results support

Figure 1. Mean-squared displacement (MSD) of (a) water molecules, (b) ethanol molecules, and (c) polymer backbone atoms in gels swollen to equilibrium at T = 300 K. Results for different gels are shown using the following symbols: P(BA) (black square), P(BA50− HEA50) (green circle), and P(HEA) (red circle).

the assertion that water molecules predominantly move within the large solvent clusters in the P(HEA) gel. Our results are also consistent with MD simulation and NMR experiment results of diffusion of water molecules inside PVA36 and Nafion11,54 membranes at high concentration of solvent which yielded a value of ∼10−9 m2/s for water diffusivity. C

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order Legendre polynomial (P2) of the angle of rotation of the specific bond vectors associated with each type of the solvent molecules. In particular, to determine this P2 function, we tracked the angle of rotation of O−H and C−C bonds of water and ethanol, respectively, over the simulation time and calculated the P2 function as follows: P2(t ) =

3⟨cos2(θ )⟩ − 1 2

(1)

where cos(θ) = u(t)·u(0), and u(t) is the unit vector at time t along the O−H and C−C bonds in water and ethanol molecules, respectively. From Figures 3a and 3b, it is observed that the P2 function for water and ethanol molecules decays faster in the P(HEA) gel compared to the other gels, while the P2 function of water in the P(BA) system exhibits the slowest decay. As was the case for translational mobility, these results show that rotational mobility is enhanced in the presence of a large water cluster in the P(HEA) gel which leads to solvent

Figure 2. Snapshots of simulation box of the gels swollen to equilibrium: (a) P(BA), (b) P(BA50−HEA50), and (c) P(HEA). Water, ethanol, and polymer backbone atoms are shown using red, blue, and cyan colors, respectively.

To further elucidate these results, the MSD values of the backbone atoms of polymer were calculated and are shown in Figure 1c. It is clear that backbone atoms in the P(HEA) gel have the highest mobility. In addition, translational mobilities of the P(BA) and the P(BA50−HEA50) polymer atoms are comparable to each other and are much lower than that in the P(HEA) system. The comparative behavior of polymer atom mobility is very similar to that of water mobility in these gels and suggests a correlation between dynamics of water molecules and polymer atoms in these systems. Rotational Mobility. The rotational mobility of the solvent molecules was characterized in these systems using the second-

Figure 3. P2 function of O−H and C−C bond vectors of (a) water and (b) ethanol molecules in gel systems swollen to equilibrium at temperature T = 300 K. Results for different gels are shown using the following symbols: P(BA) (black square), P(BA50−HEA50) (green circle), and P(HEA) (red circle). D

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Macromolecules molecule rotation within the water cluster, while it is reduced in the P(BA) and the copolymer gels that contain smaller amounts of water. The rotational dynamics of the solvent molecules can be quantified by fitting the P2 function values to the Kohlrausch− Williams−Watts (KWW) stretched exponential relationship:55 P2(t) = exp(−(t/τ)β), where β is the stretching exponent. The average rotational relaxation time can then be determined as56,57 τave =

∫0

∞

P2(t ) dt =

τ ⎛1⎞ Γ⎜ ⎟ β ⎝β⎠

(2)

where Γ is the gamma function. The P2 function values were fitted to the KWW equation, and the corresponding τ and β values were determined for water and ethanol molecules in the three gels swollen to equilibrium (τ values are shown in Figure S2 in the Supporting Information). As expected from the time dependence of P2 function seen in Figure 3a, the values of τave obtained using eq 2 (see Figures 4a and 4b) show that the rotational relaxation time of water is the smallest in the P(HEA) gel while it is the largest in the P(BA) gel. These results quantitatively demonstrate that the existence of water clusters enhances the rotational mobility of the solvent molecules in these gels. The width of the relaxation spectrum is represented by the value of the exponent β in the KWW equation such that it increases as β decreases. The values of the exponent β for both water and ethanol molecules increase (see inset in Figures 4a and 4b) with an increase in the degree of swelling of the gel, indicating that the relaxation spectrum is narrow at high solvent concentration. We attribute this observation to the presence of a large water cluster in the highly hydrophilic P(HEA) gel which leads to an increased similarity between water dynamics in the swollen gel and in bulk water, thus leading to a narrow relaxation spectrum. On the other hand, the increased interaction between water and polymer in the P(BA) gel leads to inhomogeneities in water dynamics and hence results in a broad spectrum. In summary, both translational and rotational mobility exhibit similar trends with the degree of swelling of the gel, which, in turn, is governed by the polymer hydrophilicity. 3.2. Gels with a Low Amount of Solvent. In the gel systems swollen to equilibrium that were described so far, the degree of swelling (i.e., solvent concentration) changed with a change in polymer hydrophilicity. To separate the effects of gel hydrophilicity and solvent concentration on the mobility of the water and ethanol molecules, dynamic properties were compared in three gel systems that contained the same amount of water (Xwater = 0.017; see Table 2). These are the same gel systems as the ones used in our previous work for studying structural properties.22 3.2.1. Solvent Molecules Interact with the Gel via Hydrogen Bonding. The hydrogen bond distributions in the three gels with low water content were determined using the geometric criteria58,59 at T = 400 K. As seen in Figure S3, for the systems with low water content, the probability of hydrogen bonding between water and polymer is significantly higher than that between two water molecules. Furthermore, as the degree of gel hydrophilicity increases, the number of hydrogen bonds formed by water with polymer increases. Similar results were also observed for ethanol molecules with the hydrogen bond probability between ethanol and polymer being smaller than that between water and polymer (see Figure S4). These results

Figure 4. Values of the average relaxation time τave (filled green diamond) as a function of the mole fraction of HEA in the polymer at temperature T = 300 K for (a) water and (b) ethanol molecules. Inset: stretching exponent β (open blue diamonds) obtained from the KWW equation.

are consistent with those previously reported by us22 for the same systems at a lower temperature value of T = 300 K. 3.2.2. Water Dynamics Is Strongly Coupled to Polymer Dynamics but Ethanol Dynamics Is Not. As noted earlier, solvent dynamics calculations were performed at temperature T = 400 K. This high value of temperature was chosen to capture the diffusive behavior of water. The solvent molecules had a very low mobility at 300 K in these systems due to a combination of two effects: lack of water clusters and glass transition. In particular, due to the high cooling rates used in simulations, Tg of the P(HEA) model system is shifted to 372 K,22 while it is 339 and 290 K for P(BA50−HEA50) and P(BA), respectively. Thus, water molecules have very low mobility in the P(HEA) system at T ≤ 372 K. Since our goal is to compare the effect of polymer hydrophilicity, all systems were studied at the high temperature of T = 400 K, at which E

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Macromolecules water shows diffusive behavior in the P(HEA) system as well. This temperature is higher than the boiling point of pure water; nevertheless, a gel network is expected to contain some water at this temperature. A very small amount of water is used (Xwater = 0.017), which is the same as that used in our recent work.22 Translational Mobility of Polymer Atoms. We begin by focusing on the translational mobility of the polymer atoms. Similar to the gels swollen to equilibrium, we determined the MSD of the backbone atoms of the gel. As can be seen in Figure 5, the P(BA50−HEA50) chains show slightly higher

Figure 5. MSD of polymer backbone atoms in gels with low water content at T = 400 K. Results for different gels are shown using the following symbols: P(BA) (black square), P(BA50−HEA50) (green circle), and P(HEA) (red circle). Figure 6. MSD of (a) water molecules and (b) oxygen atoms of polymer in gels with low water content at T = 400 K. Results for different gels are shown using the following symbols: P(BA) (black square), P(BA50−HEA50) (green circle), and P(HEA) (red circle).

mobility than the P(BA) gel chains, while P(HEA) gel atoms exhibit significantly lower translational mobility than the atoms in the other two systems. We attribute the lowest mobility of the P(HEA) gel to its proximity to Tg; at 400 K, it is only about 25 K above its Tg whereas the other two systems are significantly above their Tg.22 The origin of the higher mobility of the copolymer gel atoms (higher than either homopolymer gel) is more subtle. Interestingly, investigation of mobility of backbone atoms of linear polyacrylates (see Figure S5) indicates that for linear polymers the mobility trend is the same as the Tg trend; i.e., copolymer atom mobility is between that of the two linear homopolymers. Thus, the origin of the higher mobility of backbone atoms of the copolymer gels is in cross-linking and swelling. We note that addition of solvent to the system and cross-linking of the network increase the density of gels compared to the linear polymers. The values of the relative change in the density ρr (ρr = (ρgel − ρpolymer)/ρpolymer) are 0.087, 0.055, and 0.07 for P(BA), P(BA50−HEA50), and P(HEA) gels, respectively. Thus, the relative change in the density is smaller in the P(BA50−HEA50) copolymer system, and we believe that this aspect contributes to its backbone atoms showing slightly higher mobility than those of P(BA) gel. In summary, the proximity to the glass transition and densification due to the addition of solvent and cross-linking are the main governing factors in determining the dynamics of the polymer atoms. Translational Mobility of Water and Ethanol. The MSD of the water molecules in all three systems showed a true dif f usive behavior at T = 400 K (see Figure 6a). Similar results were obtained for the ethanol molecules which are not shown here (see Figure S6). The MSD values of water molecules (at long

time) are close to each other in the P(BA) and the P(BA50− HEA50) gels with the MSD in the copolymer gel being slightly higher than that in P(BA) gel, while MSD is the lowest in the P(HEA) gel, especially at long times. The values of diffusion coefficients of water and ethanol were determined using the Einstein relation in the diffusive regime and are shown in Figure 7. The diffusion coefficient values obtained for water in the P(BA) and the P(BA50−HEA50) systems are close to each other and are about ∼5 × 10−11 m2/s, while diffusivity is lower by a factor of 5 in the P(HEA) gel. For ethanol molecules, a weak dependence of diffusivity on polymer hydrophilicity, specifically, a small decrease in diffusivity with an increase in polymer hydrophilicity, was observed. The trend in water mobility, i.e. (water mobility)copolymer > (water mobility)P(BA) > (water mobility)P(HEA)

is the same as the trend in polymer backbone atom mobility that was described above. On the other hand, ethanol mobility shows the trend: (ethanol mobility)P(BA) > (ethanol mobility)copolymer > (ethanol mobility)P(HEA) F

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Figure 7. Diffusion coefficient of water (red circles) and ethanol (blue diamonds) molecules obtained in different gels with a low water content as a function of the HEA mole fraction.

These observations suggest a strong dynamic coupling between water molecules and polymer atoms but not between ethanol molecules and polymer atoms. At low concentration, water molecules were present in a dispersed state in the gel systems and formed a significant number of hydrogen bonds with the polymer hydrophilic groups (Figure S3). To test if this structural coupling between water and polymer atoms leads to dynamic coupling, we calculated the MSD of oxygen atoms of the polymer, which strongly interact with solvent molecules via hydrogen bonding. As seen in Figure 6b, as was also the case for the backbone atoms, the oxygen atoms in the P(BA50− HEA50) gel are the most mobile, while oxygen atoms in the P(HEA) system are the least mobile. This trend for polymer oxygen atom mobility is qualitatively similar to the trend for water mobility as seen in Figure 6a. In order to gain further insight into the higher water mobility in the copolymer system, the MSD values of different types of oxygen atoms of the polymer were calculated and are shown in Figures 8a, 8b, and 8c for all three gels. As shown in Figure 8a, the mobility of the carbonyl oxygen atoms is higher than that of the alkoxy oxygen atoms in the P(BA) system. Similar behavior is seen for the BA segment of the copolymer gel, and the mobility of these oxygen atoms is similar to that in the P(BA) system. On the other hand, the mobility of hydroxyl oxygen atoms is significantly higher in the P(BA50−HEA50) gel, which, in turn, increases the mobility of water molecules that are hydrogen bonded with hydroxyl group. The mobilities of the oxygen atoms of the P(HEA) gel show the same trend as seen for oxygen atoms in the other two systems. In summary, the following order holds for the mobility of different oxygen atoms in the polyacrylate gels studied here: in P(BA)gel:

Figure 8. MSD of polymer oxygen atoms in (a) P(BA), (b) P(BA50− HEA50), and (c) P(HEA) gels at T = 400 K. Results for different oxygen atoms are shown using the following symbols: BA carbonyl (red circle), BA alkoxy (hollow green circle), HEA carbonyl (blue diamond), HEA alkoxy (hollow brown diamond), and HEA hydroxyl (hollow blue square).

Ocarbonyl > Oalkoxy

in copolymer gel:

different functional groups in polyacrylate gels as reported in our previous paper.22 This observation suggests that the origin of dynamic coupling between water and polymer atoms is hydrogen bonding. In summary, our results demonstrate that water mobility is strongly coupled to polymer oxygen mobility due to formation of substantial number of hydrogen bonds with polymer, while ethanol does not show significant hydrogen bonding with the

Ohydroxyl > Ocarbonyl,BA ≈ Ocarbonyl,HEA

> Oalkoxy,BA ≈ Oalkoxy,HEA in P(HEA) gel:

Ohydroxyl > Ocarbonyl,HEA > Oalkoxy,HEA

This order of oxygen mobility is exactly the same as the order of the relative strength of interaction of water molecules with G

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polymer atom mobility is the highest in the copolymer system, these results for rotational relaxation of solvent molecules once again suggest that water dynamics is strongly coupled with polymer dynamics but ethanol dynamics is not. 3.2.3. Bimodal Translational Relaxation of Solvent Molecules in Gels with Low Water Content. In the previous section, we found that for the gels with low water content, the dynamics of water molecules are coupled with polymer dynamics due to strong hydrogen-bonding interactions in the gel network. In order to further investigate the mechanism of the dynamic coupling between the solvent molecules and polymer atoms in these gels, dynamic heterogeneity analysis was carried out. The self-part of the Van Hove autocorrelation function (Gs(r,t)), which captures the distribution of translational mobilities of particles in a given system, was used for this purpose. Gs(r,t) is defined as follows:60−63

gels, and subsequently its motion is not strongly coupled with that of polymer oxygen atoms. Rotational Mobility of Water and Ethanol. Similar to the gels swollen to equilibrium, the rotational mobility of solvent molecules was studied by means of the P2 function of O−H and C−C bonds in water and ethanol molecules, respectively. As shown in Figures S7a and S7b, the P2 function values of water in all gels are close to each other, while ethanol clearly shows a longer rotational relaxation time in the P(HEA) gel system. To further analyze the results, the P2 functions were fitted to the KWW equation, and the values of the parameters τ (see Figure S8), β, and τave were determined. We note that the error bars on the values of τ and β obtained from KWW fit are large which lead to a large uncertainty in the values of τave. The average rotational relaxation times (τave) for water and ethanol molecules show the smallest value in the copolymer and the P(BA) gel, respectively (see Figures 9a and 9b). Recalling that

Gs(r , t ) =

1 n

n

∑ ⟨δ(r + ri(t ) − ri(t0))⟩ i=1

(3)

where ri(t) is the position vector of a tagged particle at time t and n is total number of particles in the system. This function determines the normalized probability of finding a particle with displacement r at time t. In eq 3, at t = t0, Gs(r,t0) = δ(r)|r=0, since the position of the particle has not changed. Consequently, ∫ Gs(r,t) dr = 1, implying that the total number of particles is conserved in the system at any time. The calculated values of Gs(r,t) for water, ethanol, and polymer oxygen atoms are shown in Figures 10a, 10b, and 10c, respectively, in different gels at T = 400 K and at t = 20 ns. The first thing to note is the large difference in the magnitude of the displacement (x-axis range) in the three cases: over a time scale of 20 ns, some water molecules have displacements of 60−70 Å and ethanol molecules show displacements up to 30−35 Å, while polymer atoms only move up to 6−7 Å. Another important observation from the Gs(r,t) of solvent is that both water and ethanol molecules exhibit a bimodal distribution of the displacements. For water in P(BA) and P(BA50−HEA50) gels, the first peak is distinct and occurs at a short length scale (r ≃ 2 Å), and it is followed by a second peak that occurs at a longer distance (r ∼ 20 Å). The same phenomenon can be observed in the P(BA) and the P(BA50− HEA50) gels for ethanol molecules. Gs(r,t) of solvent molecules in the P(HEA) system exhibits a narrower distribution, and rather than observing a distinct second peak, a shoulder is observed in that case due to the merging of the first and second peaks. This merging occurs because the second peak of water and ethanol molecules in the P(HEA) gel is at a shorter distance than the second peak in the other two gels due to the lower mobility resulting from the stronger interaction between solvent molecules and the gel network. The magnitude of the first peak for water is the highest in the P(HEA) gel and is the lowest in the copolymer gel. These observations are consistent with the values of MSD of water (see Figure 6a) in these systems in that water MSD is the highest in the copolymer system and is the lowest in the P(HEA) gel. For ethanol, the first peak is very strong in the P(HEA) system; we attribute this to the higher density of P(HEA) system (density of P(HEA) gel is 14% higher than that of copolymer and 27% higher than that of the P(BA) gel) which effectively leads to the spatial confinement of the ethanol molecules which are larger in size than the water molecules. The self-part of the Van Hove function of the gel network oxygen atoms is also determined

Figure 9. Values of the average rotational relaxation time τave (filled green diamond) as a function of the mole fraction of HEA in the polymers at temperature T = 400 K for (a) water and (b) ethanol molecules. Inset: stretching exponent β (open blue diamonds) obtained from the KWW equation. H

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These observations for the correspondence of the peak positions of the water molecules and the polymer oxygen atoms along with our previously reported22 result that the lifetime of water-polymer hydrogen bonds in these systems is less than 60 ps leads us to the following conclusions: There are two populations of water molecules in these hydrated gel systems. One set of water molecules break and (repeatedly) re-form hydrogen bonds with the polymer atoms. These water molecules get “effectively locked” into the hydrogen-bonding sites, thus leading to dynamic coupling between water and polymer as exhibited by very similar locations of peaks in Gs(r,t) for these molecules. The other set of water molecules “effectively escape” from the polymer hydrogen-bonding sites; these show diffusive motion in the matrix, thus leading to a second peak in Gs(r,t) at a larger distance. These observations are further confirmed by the inspection of the Gs(r,t) of water at different times. As seen in Figure 11, the position of the first

Figure 11. Comparison of the Van Hove autocorrelation function of water molecules in the P(BA) gel with a low water content at t = 1 ns (magenta circle), t = 10 ns (dashed blue line), and t = 20 ns (black solid line) at temperature T = 400 K. The inset shows an enlarged view of the short length scale behavior.

peak does not change with simulation time. But the position of the second peak slowly shifts to right (i.e., increasing distance) with time. In summary, the motion of the water molecules is hampered due to significant hydrogen-bonding interactions with the polymer. This coupling of motion between the polymer and the water molecules leads to a bimodal distribution of the displacements for the solvent molecules inside the gel. The dynamic heterogeneity in the system can be further elucidated by comparing the observed motion (MSD) with the Gaussian approximation to the MSD. For this purpose, the Van Hove autocorrelation function corresponding to the Gaussian approximation to MSD can be evaluated as follows:64

Figure 10. Van Hove autocorrelation function of (a) water molecules, (b) ethanol molecules, and (c) polymer oxygen atoms in different gels with a low water content at T = 400 K and t = 20 ns. Results for different gels are shown using the following symbols: P(BA) (black square), P(BA50−HEA50) (green circle), and P(HEA) (red circle). The insets in (a) and (b) show an enlarged view of the short length scale behavior.

⎛ 3 ⎞3/2 ⎛ 3r 2 ⎞ G0(r , t ) = ⎜ exp ⎟ ⎜− 2 ⎟ ⎝ 2π ⟨r 2⟩ ⎠ ⎝ 2⟨r ⟩ ⎠

(4)

where ⟨r ⟩ is the mean-squared displacement of the tagged particle at time t. The normalized Van Hove function which shows the deviation from the Gaussian distribution is defined as Gn(r,t) = [Gs(r,t) − G0(r,t)]/G0(r,t).64 For the purpose of determining the mobile fraction of the different components in the systems, following prior simulations studies,65,66 we can 2

and is shown in Figure 10c. Gs(r,t) for the polymer shows the typical single peak distribution of the displacements. Interestingly, positions of the peaks for the polymer systems are very close to the positions of the first peak for water and ethanol molecules in the same systems. I

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Within statistical uncertainties, Fs(k,t) of ethanol is the same in P(BA) and the copolymer gels.

define a threshold value of the displacement r* at which Gn(r*,t) is zero, i.e., Gs(r*,t) = G0(r*,t). The normalized Van Hove functions for the gel systems are shown in the Supporting Information (Figure S9a−c). The values of r* are greater than 4.5 Å in all systems for water and ethanol; on the other hand, this value for the polymer is ∼0.6 Å. As can be seen in Figure S9c, the Gn of the polymer exhibits Gaussian behavior at very short length scales (r < 2 Å). The value of the Gn(r,t) increases significantly at larger length scales, which is in agreement with prior MD simulations.64 Because of a strong peak in Gs(r,t) of the solvent molecules that is caused by the dynamic coupling with the polymer, both water and ethanol molecules show significant deviations from the Gaussian approximation at short length scales (r ≤ 5 Å). This is followed by a plateau region of low magnitude at an intermediate length scale, suggesting that the distribution is close to the Gaussian prediction. Gn(r,t) of solvent molecules increases significantly at longer distances, indicating that some fraction of the molecules are more mobile than suggested by the Gaussian approximation. The mobile fraction of each component was calculated as ∫∞ r* Gs(r,t) dr = XM. As shown in Table 3, the fractions of

4. SUMMARY AND CONCLUSIONS Molecular dynamics simulations were used to elucidate the mechanism of solvent molecule dynamics in polyacrylate gels. In the gels swollen to equilibrium, both translational and rotational dynamics of the solvent molecules show a significant solvent concentration dependence. Diffusivity values of water and ethanol molecules in the P(HEA) gel (which is the most hydrophilic system) are similar to values of the self-diffusion coefficient of water and ethanol in their pure states; this is attributed to creation of the large clusters of water in the gel that is swollen to equilibrium.22 Water and ethanol have lower mobility in the P(BA) and copolymer systems due to the absence of large water clusters which leads to increased interaction with the polymer matrix. A similar trend is observed for the mobility of the backbone atoms of polymer; i.e., the backbone atoms of P(HEA) show significantly higher mobility than the backbone atoms in the other two gels that were swollen to equilibrium. To distinguish between the effects of polymer hydrophilicity and solvent concentration, a set of systems was studied in which the mole fraction of the water and ethanol molecules was low and was the same in all polyacrylate gels. The water molecules in these systems predominantly formed hydrogen bonds with the polymer atoms rather than with other water molecules. These strong hydrogen-bonding interactions between water and polymer led to dynamic coupling between the two; this behavior was not exhibited by ethanol molecules whose mobility follows the trend of Tg and density instead. As a result, across the polyacrylate systems studied, water molecules followed the same nonmonotonous trend of mobility with polymer hydrophilicity as that shown by the polymer atoms. The order of mobility of the various oxygen atoms in the gels was the same as the order of the strength of hydrogen bonding of these oxygen atoms with water molecules that was established in our previous work.22 Finally, dynamic heterogeneity analysis indicated presence of two populations of solvent molecules: an immobile fraction and a mobile fraction. In summary, the mobility of solvent molecules in gels depends on several factors: solvent concentration, polymer hydrophilicity, proximity to polymer glass transition temperature, polymer density, and dynamic coupling between solvent molecules and polymer atoms. In gels swollen to equilibrium, the amount of solvent in the gel is related to the polymer hydrophilicity. If solvent content in the swollen gel is high enough such that the solvent molecules can form large clusters, their mobility will be significantly enhanced. On the other hand, at low solvent content, solvent molecules disperse in the system and form hydrogen bonds with the polymer. The resulting interaction with the polymer leads to strong dynamic coupling between water and polymer; such coupling was not observed for ethanol. These results suggest that dynamic coupling between solvent molecules and polymer atoms provides an additional mechanism for tuning the separation characteristics of polymer membranes. Thus, polymer mobility can be selectively altered by tailoring the chain topology and chemistry to optimize performance characteristics of the membranes for separation of a given mixture.

Table 3. Fractions of Mobile Atoms/Molecules (XM) of Each Component in the Three Gels with a Low Content of Water at t = 20 ns component

P(BA)

P(BA50−HEA50)

P(HEA)

water ethanol polymer

0.76 0.54 0.93

0.82 0.48 0.97

0.52 0.41 0.73

mobile molecules of water and ethanol show the same trend as was seen in the diffusion coefficient results; i.e., water and ethanol molecules are more mobile in the P(BA) and P(BA50− HEA50) gels (Figure 7). The fraction of the mobile polymer atoms is large due to the smaller value of r*, and the values of XM of the polymer also show behavior consistent with the MSD results. Finally, to compare the dynamic heterogeneity over the simulation time at short length scales, the Van Hove function at different times can be converted to the incoherent intermediate scattering function (Fs(k,t)) by taking the spatial Fourier transform using the relation Fs(k , t ) =

∫ Gs(r , t ) exp(ir·k) dr

(5)

We have determined the function Fs(k,t) at different values of t and wave vectors (k). Results are shown in the Supporting Information (Figure S10a−c) for Fs(k,t) at k = 1.8 Å−1 for water and ethanol molecules and polymer chain atoms at T = 400 K. This chosen value of the wave vector approximately corresponds to the location of the first minimum in the Van Hove function. As expected, the results are consistent with those presented for the Van Hove function earlier in the text. Specifically, dynamics of water molecules and polymer atoms at short length scales at all times show a nonmonotonic behavior with respect to the degree of gel hydrophilicity as was previously seen in the Van Hove function results at t = 20 ns. At short times, fast motion of the atoms contributes to a sharp drop in the values of Fs in all cases. At intermediate times (1 ns ≤ t ≤ 10 ns), water molecules in P(BA) and P(HEA) gels and ethanol molecules in P(HEA) gels show caging behavior, while they exhibit higher mobility in the P(BA50−HEA50) gel. J

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(7) Peng, P.; Shi, B.; Lan, Y. A Review of Membrane Materials for Ethanol Recovery by Pervaporation. Sep. Sci. Technol. 2010, 46, 234− 246. (8) Xiangli, F.; Chen, Y.; Jin, W.; Xu, N. Polydimethylsiloxane (PDMS)/Ceramic Composite Membrane with High Flux for Pervaporation of Ethanol-Water Mixtures. Ind. Eng. Chem. Res. 2007, 46, 2224−2230. (9) Mahajan, C. V.; Ganesan, V. Atomistic Simulations of Structure of Solvated Sulfonated Poly(ether ether ketone) Membranes and Their Comparisons to Nafion: II. Structure and Transport Properties of Water, Hydronium Ions, and Methanol. J. Phys. Chem. B 2010, 114, 8367−8373. (10) Devanathan, R.; Venkatnathan, A.; Dupuis, M. Atomistic Simulation of Nafion Membrane. 2. Dynamics of Water Molecules and Hydronium Ions. J. Phys. Chem. B 2007, 111, 13006−13013. (11) Blake, N. P.; Mills, G.; Metiu, H. Dynamics of H2O and Na+ in Nafion Membranes. J. Phys. Chem. B 2007, 111, 2490−2494. (12) Urata, S.; Irisawa, J.; Takada, A.; Shinoda, W.; Tsuzuki, S.; Mikami, M. Molecular Dynamics Simulation of Swollen Membrane of Perfluorinated Ionomer. J. Phys. Chem. B 2005, 109, 4269−4278. (13) Mahajan, C. V.; Ganesan, V. Atomistic Simulations of Structure of Solvated Sulfonated Poly(ether ether ketone) Membranes and Their Comparisons to Nafion: I. Nanophase Segregation and Hydrophilic Domains. J. Phys. Chem. B 2010, 114, 8357−8366. (14) Daly, K. B.; Benziger, J. B.; Debenedetti, P. G.; Panagiotopoulos, A. Z. Molecular Dynamics Simulations of Water Sorption in a Perfluorosulfonic Acid Membrane. J. Phys. Chem. B 2013, 117, 12649− 12660. (15) Park, C. H.; Lee, C. H.; Sohn, J.-Y.; Park, H. B.; Guiver, M. D.; Lee, Y. M. Phase Separation and Water Channel Formation in Sulfonated Block Copolyimide. J. Phys. Chem. B 2010, 114, 12036− 12045. (16) Vishnyakov, A.; Neimark, A. V. Self-Assembly in Nafion Membranes upon Hydration: Water Mobility and Adsorption Isotherms. J. Phys. Chem. B 2014, 118, 11353−11364. (17) Tse, Y.-L. S.; Herring, A. M.; Kim, K.; Voth, G. A. Molecular Dynamics Simulations of Proton Transport in 3M and Nafion Perfluorosulfonic Acid Membranes. J. Phys. Chem. C 2013, 117, 8079− 8091. (18) Jang, S. S.; Molinero, V.; Cagin, T.; Goddard, W. A. NanophaseSegregation and Transport in Nafion 117 from Molecular Dynamics Simulations: Effect of Monomeric Sequence. J. Phys. Chem. B 2004, 108, 3149−3157. (19) Neburchilov, V.; Martin, J.; Wang, H.; Zhang, J. A Review of Polymer Electrolyte Membranes for Direct Methanol Fuel Cells. J. Power Sources 2007, 169, 221−238. (20) Bolto, B.; Hoang, M.; Xie, Z. A Review of Membrane Selection for the Dehydration of Aqueous Ethanol by Pervaporation. Chem. Eng. Process. 2011, 50, 227−235. (21) Godbole, R. V.; Ma, L.; Doerfert, M. D.; Williams, P.; Hedden, R. C. Combinatorial Methodology for Screening Selectivity in Polymeric Pervaporation Membranes. ACS Comb. Sci. 2015, 17, 663−670. (22) Mani, S.; Khabaz, F.; Godbole, R. V.; Hedden, R. C.; Khare, R. Structure and Hydrogen Bonding of Water in Polyacrylate Gels: Effects of Polymer Hydrophilicity and Water Concentration. J. Phys. Chem. B 2015, 119, 15381−15393. (23) Heinzel, A.; Barragán, V. A Review of the State-of-the-art of the Methanol Crossover in Direct Methanol Fuel Cells. J. Power Sources 1999, 84, 70−74. (24) Hallinan, D. T.; De Angelis, M. G.; Giacinti Baschetti, M.; Sarti, G. C.; Elabd, Y. A. Non-Fickian Diffusion of Water in Nafion. Macromolecules 2010, 43, 4667−4678. (25) Horstmann, M.; Urbani, M.; Veeman, W. S. Self-Diffusion of Water in Block Copoly(ether-ester) Polymers: An NMR Study. Macromolecules 2003, 36, 6797−6806. (26) Masaro, L.; Ousalem, M.; Baille, W. E.; Lessard, D.; Zhu, X. X. Self-Diffusion Studies of Water and Poly(ethylene glycol) in Solutions

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00938. Chemical structure of the monomers and the crosslinker, values of τ for water and ethanol molecules in gels swollen to equilibrium at T = 300 K, hydrogen bond probability between water−polymer and water−water in gels with low water content at T = 400 K, hydrogen bond probability between ethanol−polymer and ethanol− ethanol in gels with low water content at T = 400 K, MSD of backbone atoms of linear polymers at T = 400 K, MSD of ethanol molecules in the gels with low water content at T = 400 K, P2 of water and ethanol molecules in the gels with low water content at T = 400 K, values of τ for water and ethanol molecules in gels with low water content at T = 400 K, normalized Van Hove function of water, ethanol, and polymer oxygen atoms in gels with low water content at T = 400 K, incoherent intermediate scattering function of water, ethanol, and polymer oxygen atoms in gels with low water content at T = 400 K (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph (806) 834-0449 (R.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Rutvik V. Godbole and Ronald C. Hedden for insightful discussions on the topic of pervaporation-based separation of water−ethanol mixtures. This material is based on work supported by the National Science Foundation under Grant NSF CMMI-1335082. We also acknowledge the computational resources provided by the Texas Advanced Computing Center (TACC) at The University of Texas at Austin that were used in performing the molecular simulations.

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REFERENCES

(1) Vankelecom, I. F. J.; De Beukelaer, S.; Uytterhoeven, J. B. Sorption and Pervaporation of Aroma Compounds Using ZeoliteFilled PDMS Membranes. J. Phys. Chem. B 1997, 101, 5186−5190. (2) Miyata, T.; Nakanishi, Y.; Uragami, T. Ethanol Permselectivity of Poly(dimethylsiloxane) Membranes Controlled by Simple Surface Modifications Using Polymer Additives. Macromolecules 1997, 30, 5563−5565. (3) Uragami, T.; Okazaki, K.; Matsugi, H.; Miyata, T. Structure and Permeation Characteristics of an Aqueous Ethanol Solution of Organic-Inorganic Hybrid Membranes Composed of Poly(vinyl alcohol) and Tetraethoxysilane. Macromolecules 2002, 35, 9156−9163. (4) Ozcam, A. E.; Petzetakis, N.; Silverman, S.; Jha, A. K.; Balsara, N. P. Relationship between Segregation Strength and Permeability of Ethanol/Water Mixtures through Block Copolymer Membranes. Macromolecules 2013, 46, 9652−9658. (5) Uragami, T.; Matsugi, H.; Miyata, T. Pervaporation Characteristics of Organic-Inorganic Hybrid Membranes Composed of Poly(vinyl alcohol-co-acrylic acid) and Tetraethoxysilane for Water/ Ethanol Separation. Macromolecules 2005, 38, 8440−8446. (6) Sun, L.; Baker, G. L.; Bruening, M. L. Polymer Brush Membranes for Pervaporation of Organic Solvents from Water. Macromolecules 2005, 38, 2307−2314. K

DOI: 10.1021/acs.macromol.6b00938 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules and Gels of Selected Hydrophilic Polymers. Macromolecules 1999, 32, 4375−4382. (27) Matsukawa, S.; Ando, I. A Study of Self-Diffusion of Molecules in Polymer Gel by Pulsed-Gradient Spin-Echo 1H NMR. Macromolecules 1996, 29, 7136−7140. (28) Matsukawa, S.; Ando, I. Study of Self-Diffusion of Molecules in Polymer Gel by Pulsed-Gradient Spin-Echo 1H NMR. 3. Stearyl Itaconamide/N,N-Dimethylacrylamide Copolymer Gels. Macromolecules 1999, 32, 1865−1871. (29) Tamai, Y.; Tanaka, H.; Nakanishi, K. Molecular Simulation of Permeation of Small Penetrants through Membranes. 1. Diffusion Coefficients. Macromolecules 1994, 27, 4498−4508. (30) Sun, D.; Zhou, J. Effect of Water Content on Microstructures and Oxygen Permeation in PSiMA-IPN-PMPC Hydrogel: a Molecular Simulation Study. Chem. Eng. Sci. 2012, 78, 236−245. (31) Demontis, P.; Jobic, H.; Gonzalez, M. A.; Suffritti, G. B. Diffusion of Water in Zeolites NaX and NaY Studied by Quasi-Elastic Neutron Scattering and Computer Simulation. J. Phys. Chem. C 2009, 113, 12373−12379. (32) Muller-Plathe, F. Diffusion of Water in Swollen Poly(vinyl alcohol) Membranes Studied by Molecular Dynamics Simulation. J. Membr. Sci. 1998, 141, 147−154. (33) Muller-Plathe, F. Microscopic Dynamics in Water-swollen Poly(vinyl alcohol). J. Chem. Phys. 1998, 108, 8252−8263. (34) Xiang, T.-X.; Anderson, B. Distribution and Effect of Water Content on Molecular Mobility in Poly(vinylpyrrolidone) Glasses: A Molecular Dynamics Simulation. Pharm. Res. 2005, 22, 1205−1214. (35) Borodin, O.; Bedrov, D.; Smith, G. D. Concentration Dependence of Water Dynamics in Poly(Ethylene Oxide)/Water Solutions from Molecular Dynamics Simulations. J. Phys. Chem. B 2002, 106, 5194−5199. (36) Zhang, Q. G.; Liu, Q. L.; Chen, Y.; Yang, J. Microstructure Dependent Diffusion of Water-ethanol in Swollen Poly(vinyl alcohol): A Molecular Dynamics Simulation Study. Chem. Eng. Sci. 2009, 64, 334−340. (37) Wu, Y.; Joseph, S.; Aluru, N. R. Effect of Cross-Linking on the Diffusion of Water, Ions, and Small Molecules in Hydrogels. J. Phys. Chem. B 2009, 113, 3512−3520. (38) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General AMBER Force Field. J. Comput. Chem. 2004, 25, 1157−1174. (39) Wang, J.; Wang, W.; Kollman, P. A.; Case, D. A. Automatic Atom Type and Bond Type Perception in Molecular Mechanical Calculations. J. Mol. Graphics Modell. 2006, 25, 247−260. (40) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926−935. (41) Price, D. J.; Brooks, C. L. A Modified TIP3P Water Potential for Simulation with Ewald Summation. J. Chem. Phys. 2004, 121, 10096− 10103. (42) Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-alkanes. J. Comput. Phys. 1977, 23, 327−341. (43) Jakalian, A.; Bush, B. L.; Jack, D. B.; Bayly, C. I. Fast, Efficient Generation of High-quality Atomic Charges. AM1-BCC model: I. Method. J. Comput. Chem. 2000, 21, 132−146. (44) Jakalian, A.; Jack, D. B.; Bayly, C. I. Fast, Efficient Generation of High-quality Atomic Charges. AM1-BCC model: II. Parameterization and Validation. J. Comput. Chem. 2002, 23, 1623−1641. (45) Hockney, R. W.; Eastwood, J. W. Computer Simulation Using Particles; Taylor & Francis, Inc.: Bristol, PA, 1988. (46) Shinoda, W.; Shiga, M.; Mikami, M. Rapid Estimation of Elastic Constants by Molecular Dynamics Simulation under Constant Stress. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 134103. (47) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182−7190.

(48) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (49) Khare, R.; Paulaitis, M. E.; Lustig, S. R. Generation of Glass Structures for Molecular Simulations of Polymers Containing Large Monomer Units: Application to Polystyrene. Macromolecules 1993, 26, 7203−7209. (50) Lin, P.-H.; Khare, R. Molecular Simulation of Cross-Linked Epoxy and Epoxy-POSS Nanocomposite. Macromolecules 2009, 42, 4319−4327. (51) Cui, S.; Liu, J.; Selvan, M. E.; Keffer, D. J.; Edwards, B. J.; Steele, W. V. A Molecular Dynamics Study of a Nafion Polyelectrolyte Membrane and the Aqueous Phase Structure for Proton Transport. J. Phys. Chem. B 2007, 111, 2208−2218. (52) Holz, M.; Heil, S. R.; Sacco, A. Temperature-dependent Selfdiffusion Coefficients of Water and Six Selected Molecular Liquids for Calibration in Accurate 1H NMR PFG Measurements. Phys. Chem. Chem. Phys. 2000, 2, 4740−4742. (53) Price, W. S.; Ide, H.; Arata, Y. Solution Dynamics in Aqueous Monohydric Alcohol Systems. J. Phys. Chem. A 2003, 107, 4784−4789. (54) Kreuer, K.-D.; Paddison, S. J.; Spohr, E.; Schuster, M. Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology. Chem. Rev. 2004, 104, 4637−4678. (55) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1998. (56) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids, 3rd ed.; Academic Press: New York, 2006. (57) Muntean, S. A.; Gerasimov, R. A.; Lyulin, A. V. Dynamics of Water Near Oxidized Polystyrene Films. Macromol. Theory Simul. 2012, 21, 544−552. (58) Luzar, A.; Chandler, D. Effect of Environment on Hydrogen Bond Dynamics in Liquid Water. Phys. Rev. Lett. 1996, 76, 928−931. (59) Luzar, A.; Chandler, D. Structure and Hydrogen Bond Dynamics of Water-dimethyl sulfoxide mixtures by computer simulations. J. Chem. Phys. 1993, 98, 8160−8173. (60) Van Hove, L. Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles. Phys. Rev. 1954, 95, 249−262. (61) Kob, W.; Andersen, H. C. Testing Mode-coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1995, 51, 4626−4641. (62) Boon, J. P.; Yip, S. Molecular Hydrodynamics; Dover Publications: New York, 1980. (63) Toepperwein, G. N.; Schweizer, K. S.; Riggleman, R. A.; de Pablo, J. J. Heterogeneous Segmental Dynamics during Creep and Constant Strain Rate Deformations of Rod-Containing Polymer Nanocomposites. Macromolecules 2012, 45, 8467−8481. (64) Kob, W.; Donati, C.; Plimpton, S. J.; Poole, P. H.; Glotzer, S. C. Dynamical Heterogeneities in a Supercooled Lennard-Jones Liquid. Phys. Rev. Lett. 1997, 79, 2827−2830. (65) Gebremichael, Y.; Schrøder, T. B.; Starr, F. W.; Glotzer, S. C. Spatially Correlated Dynamics in a Simulated Glass-forming Polymer Melt: Analysis of Clustering Phenomena. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2001, 64, 051503. (66) Donati, C.; Glotzer, S. C.; Poole, P. H.; Kob, W.; Plimpton, S. J. Spatial Correlations of Mobility and Immobility in a Glass-forming Lennard-Jones Liquid. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1999, 60, 3107−3119.

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