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Structure and Hydrogen Bonding of Water in Polyacrylate Gels: Effects of Polymer Hydrophilicity and Water Concentration Sriramvignesh Mani, Fardin Khabaz, Rutvik V. Godbole, Ronald C. Hedden, and Rajesh Khare* Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409-3121, United States S Supporting Information *

ABSTRACT: The ability to tune the hydrophilicity of polyacrylate copolymers by altering their composition makes these materials attractive candidates for membranes used to separate alcohol−water mixtures. The separation behavior of these polyacrylate membranes is governed by a complex interplay of factors such as water and alcohol concentrations, water structure in the membrane, polymer hydrophilicity, and temperature. We use molecular dynamics simulations to investigate the effect of polymer hydrophilicity and water concentration on the structure and dynamics of water molecules in the polymer matrix. Samples of poly(n-butyl acrylate) (PBA), poly(2-hydroxyethyl acrylate) (PHEA), and a 50/50 copolymer of BA and HEA were synthesized in laboratory, and their properties were measured. Model structures of these systems were validated by comparing the simulated values of their volumetric properties with the experimental values. Molecular simulations of polyacrylate gels swollen in water and ethanol mixtures showed that water exhibits very different affinities toward the different (carbonyl, alkoxy, and hydroxyl) functional groups of the polymers. Water molecules are well dispersed in the system at low concentrations and predominantly form hydrogen bonds with the polymer. However, water forms large clusters at high concentrations along with the predominant formation of water−water hydrogen bonds and the acceleration of hydrogen bond dynamics. membranes28 concluded that unlike water molecules, ethanol molecules do not form clusters and are mostly isolated inside the network. Furthermore, water aggregation was found to affect the hydrogen bond (both water−water and water− polymer) distribution in the system.25,30−33 The dynamics of water molecules are also affected by the water content in these systems.23,27,30,32,34 Increasing water content is found to cause a reduction in both the rotational relaxation time of water molecules and the lifetime of hydrogen bonds between water molecules. A practical application of current interest where polymer membranes can be used for separations of aqueous mixtures is the purification of biofuels by pervaporation.35,36 Indeed, a main obstacle in the commercialization of biofuel technologies is the high cost of separation of the dilute alcohol−water mixture that results from the fermentation of the biomass. Polymer-membrane-based pervaporation is a promising solution to this problem. Polyacrylates constitute a class of polymers whose hydrophilicity can be systematically tuned by choosing the copolymer composition from a large library of monomers, thus making these attractive candidate materials for the membranes used to separate alcohol−water mixtures. However, little work has been done to characterize the

I. INTRODUCTION Water sorption and diffusion in polymers have a large impact on the efficiency of many practical applications such as fuel cells,1,2 controlled drug release,3 and membrane-based separation processes.4,5 Previous studies have indicated that the presence of water in the polymer matrix significantly affects its properties, such as the glass transition temperature6,7 and penetrant transport.8,9 The properties of water molecules confined in a polymer matrix are different from those of bulk water.10 The system characteristics of interest such as water mobility, clustering of water molecules, and hydrogen bond distribution show a strong dependence on the water content in the system and its interaction with the polymer matrix. The process of separating mixtures using polymeric membranes has been the subject of past experimental and simulation work.11−24 These studies showed that key characteristics of the membranes such as diffusivity, selectivity, and flux exhibit a strong dependence on the composition of the feed and the penetrant−polymer interactions. Simulation studies have indicated that the interaction between polymer and water molecules is mediated by the polar groups and that the degree of solvation of the hydrophilic groups increases with increasing water content.19−24 Several studies have also reported that increasing water concentration leads to the formation of clusters of water molecules.22,23,25−29 On the other hand, an MD simulation study of ethanol and water in poly(vinyl alcohol) (PVA) © 2015 American Chemical Society

Received: September 6, 2015 Revised: October 27, 2015 Published: October 30, 2015 15381

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Waals and electrostatic interactions, respectively. The temperature and pressure of the systems were held constant using the Nosé Hoover thermostat and barostat. 46,47 The MD simulations were carried out using the LAMMPS package48 with a time step of 1 fs, and all structural properties were evaluated at a pressure of 1 atm and a temperature of 300 K. II.A.2. Structure Preparation. Two types of model systems were studied in this work: linear acrylate polymers (formed by BA and HEA) and cross-linked acrylate networks (formed by BA, HEA, and cross-linker PETA) that are swollen in a water− ethanol mixture. In both cases, the structures were built using the simulated annealing polymerization method.49,50 All of the model structures studied in this work contained between 72 000 and 76 000 atoms. For the linear polymer systems, the reaction mixture with an appropriate stoichiometric ratio of the BA and HEA monomers was first placed in the simulation box. Five linear polyacrylate systems with HEA mole fractions of 0 (i.e., homopolymer of BA), 0.25, 0.50, 0.75, and 1.0 (i.e., homopolymer of HEA) were studied; these are denoted in the rest of the paper by PBA, P(BA75-HEA25), P(BA50-HEA50), P(BA25-HEA75), and PHEA, respectively. The optimum polymerization sequence consisting of the spatially closest potential reacting pairs was determined in the next step using the simulated annealing multivariable optimization technique. The system was then polymerized by forming bonds between the reacting pairs so identified, and the structures were relaxed using MD simulation at a temperature of 300 K for a duration 4 ns. The simulation box of the pure linear PHEA system is shown in the Supporting Information (Figure S2). The same procedure was followed for building models of cross-linked networks swollen by water and ethanol with the exception that in this case the initial reaction mixture consisted of the BA and HEA monomers, the PETA cross-linker molecules, and water and ethanol molecules. A well-relaxed and equilibrated structure was obtained by gradually cooling the system from T = 360 to 300 K at a rate of 4 K/ns. An initial temperature of T = 360 K was chosen for this purpose so as to prevent the system from separating into two phases (i.e., to prevent any possible vaporization of water). Figure 1 shows the simulation box of PHEA gel that contains water and ethanol.

performance of polyacrylate membranes for separation applications. The separation efficiency of water−1,1,2-trichloroethane mixtures using acrylate membranes was experimentally studied by Hoshi et al.,15 while Matsui and Paul16 studied the separation of toluene−isooctane mixtures using cross-linked acrylate copolymers. Our interest is the separation of dilute (10−100 g/L) ethanol−water mixtures that result from sugar fermentation during the biofuels production process. Recently, some of us demonstrated a combinatorial method for the synthesis of a large library of polyacrylate copolymers of varying composition and also demonstrated the utility of this approach for screening candidate materials for the pervaporation-based separation of alcohol−water mixtures.37 The performance characteristics of these membranes are governed by a complex interplay of factors such as feed composition, hydrogen bonding, and polymer hydrophilicity. With this motivation, we use MD simulations to investigate the local structure and hydrogen bonding characteristics of water in polyacrylate systems with varying degrees of hydrophilicity and water content. A set of experiments are also carried out to generate data that are used to support the molecular models. The specific polymer systems studied in this work consisted of the homopolymers and copolymers (in three different stoichiometric ratios) formed by monomers BA and HEA. The hydrophobic and hydrophilic natures of BA and HEA, respectively, provide the opportunity to systematically tune the hydrophilicity of these polymers and determine the effect of polymer composition on the water structure and hydrogen bonding characteristics of the system. We first built models of linear homopolymers and copolymers of these monomers and validated these against experimental data for the volumetric properties. Next, cross-linked networks of these systems containing pentaerythritol tetraacrylate (PETA) as the crosslinking agent were synthesized experimentally. Swelling experiments were carried out to determine the mass fractions of water and ethanol in the equilibrium swollen gels. Atomistically detailed model structures of swollen gels were prepared; these were used to study the effects of polymer hydrophilicity and water concentration on the local structure and hydrogen bonding in the swollen polyacrylate gel systems.

II. METHODS The work consisted of both simulations and experiments; important details of the simulation and experimental methods are described below. II.A. Simulation Procedures. II.A.1. Force Field and Simulation Details. Linear homopolymers and copolymers as well as networks formed by BA and HEA monomers were studied in this work. Of these, BA is hydrophobic and HEA is hydrophilic. Pentaerythritol tetraacrylate (PETA) was used as the cross-linking agent for creating the networks. The chemical structures of the monomers and the cross-linker are shown in Supporting Information (Figure S1). Simulations were carried out using the general AMBER force field (GAFF),38,39 while the TIP3P model40,41 was used for water. In addition, the SHAKE algorithm42 was applied to constrain the bond lengths and bond angles of the water molecules. Partial charges on the atoms were determined by the AM1-BCC method.43,44 For the polymer simulations, van der Waals and electrostatic interactions were truncated at 9 Å, while for water-containing systems, a longer cutoff of 12 Å was used. The long-range part of the interactions was handled by tail corrections and the particle−particle particle-mesh (PPPM)45 solver for van der

Figure 1. Simulation box of PHEA that is swollen to equilibrium with water and ethanol. Carbon, oxygen, and hydrogen atoms are shown in cyan, red, and white colors, respectively. 15382

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polymer. The resulting polymer likely contains some degree of long-chain branching, based on the fact that bulk HEA polymerization forms gels in the absence of any cross-linking agents as reported by Bian and Cunningham. 53 The concentration of Irgacure 2959 was 1.0% w/w based on the total mass of water and monomer. Polymerization was started at ambient temperature (22 °C) and allowed to proceed in a fluoropolymer dish without stirring. The thickness of the polymerized layer was 3 to 5 mm. Water was removed by placing the solution under vacuum at ambient temperature (22 °C) overnight in a desiccator with excess anhydrous Ca(SO4). Residual monomer and oligomers were removed by dissolving the polymer in DMF and precipitating using toluene−hexane mixtures; this procedure was repeated three times. The remaining polymer (yield 50%) was then dried under vacuum until the mass of the sample stabilized. The product structure was confirmed by 1H NMR in DMSO-d6 (Figure S3a in Supporting Information), and the spectrum closely matched that reported by Coca et al.52 The details of the 1H NMR spectroscopy are given in the Supporting Information. II.B.3. Synthesis of 50/50 HEA/BA Copolymer. A similar procedure was employed to polymerize a 50/50 mol % HEA/ BA mixture in DMF (total concentration of monomers 50% w/ w). Polymerization was conducted under an N2 atmosphere with 1.0% w/w Irgacure 2959. The polymerization was terminated after 4 h, and the polymer was precipitated by the addition of excess water. Residual HEA monomer and oligomers were removed by redissolving the polymer in DMF and precipitating using water; this procedure was repeated three times. The polymer was vacuum dried and washed three additional times with hexane to remove any hydrophobic extractable components and then dried again under vacuum (yield 70%). II.B.4. Synthesis of BA Homopolymer. Thermal polymerization of BA was conducted in toluene solution with a 1:2 v/v ratio of BA to toluene. The initial concentration of thermal initiator 2,2′-azobis(isobutyronitrile) (AIBN) was 1% of the total mass of the solution. Polymerization was carried out under N2 at 70 °C. The reaction was terminated after 4 h, and the polymer was precipitated using excess methanol. The polymer was redissolved in toluene and precipitated using methanol three times. The poly(n-butyl acrylate) was then dried under vacuum (yield 45%). The product structure was confirmed by 1 H NMR in CDCl3 (Figure S3b in Supporting Information), and the spectrum closely matched that reported by Farcet et al.54 Part of the polymer was dissolved in tetrahydrofuran (THF) to determine the molar mass using gel permeation chromatography (GPC). The details of the GPC are given in Supporting Information. II.B.5. Synthesis of Gel Networks. Homopolymer and copolymer networks were synthesized by thermally initiated, bulk free-radical polymerization of 2-hydroxyethyl acrylate (96%, Aldrich) and n-butyl acrylate (≥99%, Aldrich) using pentaerythritol tetraacrylate (PETA, 10−40% triester, Aldrich) as the cross-linker and 2,2′-azobis(isobutyronitrile) (AIBN, 98%, Aldrich) as the initiator. The same procedure as described in the recent work by two of us37 was followed to purify the acrylate monomers and to mix AIBN with the components. Networks were prepared by pipetting calculated masses of monomers and cross-linker into a 1.8 mL sealed glass vial. For copolymer, the mole fraction of acrylates belonging to both monomers was taken to be 0.5, while the mole fraction of

For the purposes of studying the effect of water concentration on the system properties, two sets of model structures were prepared: (1) In the first set, the model structures contained the same mass fractions of water and ethanol as that measured in experiments on the equilibrium swollen gels (section II.B); thus each gel had a different amount of solvent, with PHEA gel containing the highest amount (Table 1). (2) In the second set, Table 1. Component Mole Fractions (Converted from Experimentally Measured Mass Fractions) in Cross-Linked Gels That Are Swollen to Equilibrium with Water and Ethanol system

BA

HEA

PETA

water

ethanol

PBA gel P(BA50-HEA50) gel PHEA gel

0.96 0.255 0.0

0.0 0.261 0.0973

0.003 0.001 0.0003

0.017 0.433 0.8646

0.02 0.05 0.0378

all of the polyacrylate gel structures contained the same mole fraction of water (0.017) as that contained in the PBA gel swollen to equilibrium (Table 2); thus the only difference in Table 2. Component Mole Fractions in Cross-Linked Gels That Have the Same Water Mole Fraction as the PBA Gel That Is Swollen to Equilibrium system

BA

HEA

PETA

water

ethanol

PBA gel P(BA50-HEA50) gel PHEA gel

0.96 0.48 0.0

0.0 0.48 0.96

0.003 0.003 0.003

0.017 0.017 0.017

0.02 0.02 0.02

the structures in this set was the chemical structure of the polymer and hence its hydrophilicity. For the first set (gels swollen to equilibrium), structural properties were calculated by running MD simulations for a period of 10 ns and recording the trajectory at a 400 ps interval, while for the second set (gels with water mole fraction = 0.017), MD simulations were carried out for at least 20 ns with the trajectory being saved at a 1 ns interval to evaluate the structural properties. II.B. Experimental Procedures. II.B.1. Synthesis of UnCross-Linked Polymers. n-Butyl acrylate (BA) (≥99%, Aldrich) was purified by single-stage vacuum distillation to remove the inhibitor hydroquinone monomethyl ether prior to use. 2Hydroxyethyl acrylate (HEA) (96%, Aldrich) was expected to contain impurities51 such as acrylic acid and ethylene glycol diacrylate (EGDA) that could affect the Tg of the polymers produced; the HEA was therefore washed via the extraction procedure reported by Coca et al.52 After treatment, HEA was further purified by single-stage vacuum distillation in a custombuilt apparatus with a cryogenic condenser cooled by acetone to approximately −60 °C. Solvents tetrahydrofuran (THF) (99.9%, Fisher Scientific), N,N-dimethylformamide (DMF) (99.8%, Macron), deuterated chloroform (99.8 atom % D, Aldrich), methanol (≥99.5%, Macron), toluene (≥99.5%, Aldrich), hexanes (≥99%, Macron), and diethyl ether (≥99%, Aldrich) were used as received. II.B.2. Synthesis of HEA Homopolymer. Photoinitiator Irgacure 2959 (Ciba) was used to photopolymerize HEA monomer in solution using a 100 W, broadband UV bulb (peak wavelength 365 nm) at a distance of 20 cm with a UV exposure time of 4 h. Polymerization of HEA was conducted in aqueous solution with a 1:5 v/v ratio of HEA in water to discourage the formation of a cross-linked network via chain transfer to 15383

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resulted in gelation via branching due to chain transfer to polymer.53 Glass-transition temperatures were measured by differential scanning calorimetry (DSC) using identical heating and cooling rates of 10 °C/min. The details of DSC are given in the Supporting Information. Glass-transition temperatures (Tg) obtained by Analysis 2000 software (TA Instruments) are reported. Three heating cycles were conducted for each sample to verify reproducibility, and the second and third cycles always produced the same value of Tg within 0.1 °C. Following literature practice,55 we use the fictive temperature (Tfg) measured with the identical heating and cooling rates as an approximation to Tg. We note that because negligible relaxation occurs upon reheating at the same rate, Tfg is taken as a reasonable approximation for T′f, the limiting fictive temperature; additionally, Badrinarayanan et al. have noted that T′f measured on heating approximates the value of Tg measured on cooling.56 The measured values of Tg for PBA, PHEA, and the P(BA50-HEA50) copolymer were 228, 266, and 252 K, respectively. For the simulations, the same protocol as employed by one of us in previous work57,58 was followed to determine the volume−temperature behavior. In particular, the model structures were cooled in a stepwise fashion from a high temperature of T = 600 K to T = 20 K in steps of 20 K. At each temperature, the system was subjected to constant NPT (constant number of molecules, pressure, and temperature) MD simulation for 2 ns, and the specific volume was obtained by averaging the data over the second half of the runs. Tg is obtained as the point of intersection of linear fits to specific volume data over rubbery and glassy regions. Figure 2 shows the specific volume of the model linear polyacrylate systems as a function of temperature. As expected,

reactive groups belonging to cross-linker (XC) was kept at 0.0105 for all samples. All of the samples were cured at 47 °C in a temperature-controlled water bath overnight. Care was taken to prevent water from entering the sample containers. II.B.6. Swelling in Mixed Solvents: Extraction of Sol Fraction. As described in our recent work,37 the soluble fraction was extracted by swelling the samples in ethanol. At the end of the procedure, the samples were dried under vacuum until the sample mass reached an equilibrium value Mex. II.B.7. Swelling in Mixed Solvents: Calculation of Mass Fractions. The mass fractions of water and alcohol were determined using gravimetric swelling measurements and high performance liquid chromatography (HPLC) as described in detail in recent work by two of us.37 The sum of masses of water (Mwm) and alcohol (Mam) in the network phase can be expressed in terms of the swollen mass of the network in the mixture (Mm) as M wm + Mam = M m − Mex

(1)

A simple mass balance on the system permits the calculation of the masses of water and ethanol inside the network when the initial mass of the ethanol−water mixture (Ml), initial mass fractions of alcohol and water (ωa0 and ωw0, respectively), and final mass fractions of alcohol and water in the external solution (ωas and ωws) are known. Masses of water and ethanol inside the network are given by eqs 2a and 2b. Mam = ωa0(Ml) − ωas(Ml − (M m − Mex ))

(2a)

M wm = ωw0(Ml) − ωws(Ml − (M m − Mex ))

(2b)

III. RESULTS AND DISCUSSION III.A. Volumetric Properties of Linear Polyacrylate Model Structures Are in Good Agreement with the Experimental Data. The linear (i.e., uncross-linked) polymer model structures without any solvent molecules were validated by determining their volumetric properties, namely, the density and glass-transition temperature (Tg), and comparing these against experimental data. For the experimental part, samples of linear polymers (PBA, P(BA50-HEA50) copolymer, and PHEA) were prepared by free radical polymerization as described above. The precipitation and vacuum drying procedures applied to the raw polymers were designed to remove oligomers that might plasticize the materials and lower their measured Tg values. GPC analysis of the PBA revealed that it was essentially free of oligomers with a molar mass Oalkoxy P(BA50‐HEA50) gel: Ohydroxyl > Ocarbonyl,BA ≈ Ocarbonyl,HEA > Oalkoxy,BA ≈ Oalkoxy,HEA

PHEA gel: Ohydroxyl > Ocarbonyl > Oalkoxy

where symbols Ox and Ox,y in the relations denote the oxygen atom belonging to the x functional group and the oxygen atom belonging to the x functional group in the y monomer, respectively. We attribute the observed differences in water affinity to three factors: (1) The hydroxyl group offers two possibilities for hydrogen bonding since both oxygen and hydrogen atoms of the group can form a hydrogen bond with a water molecule (while carbonyl and alkoxy groups offer only one possibility), (2) higher electron density around the carbonyl oxygen than around the alkoxy oxygen, and (3) steric environment of these groups, specifically, that the alkoxy group is in a relatively crowded environment compared to the carbonyl and the hydroxyl groups. III.C. Clustering and Hydrogen Bonding of Water. At low concentrations, water is well dispersed in the polyacrylate systems and predominantly forms hydrogen bonds with the polymer, while at high concentrations, water forms clusters with a predominance of water−water hydrogen bonding. III.C.1. Water−Water RDF. To study the distribution of water molecules in the system, we first focus on the water− water RDF (Figure S7 in Supporting Information) for polyacrylate gel systems containing identical amounts of water (water mole fraction = 0.017 in all systems, which is the same as that measured experimentally for the PBA gel swollen to equilibrium). The water−water RDF shows only one peak for all systems, with the peak height being the highest for PBA and the lowest for PHEA. This observation can be explained as follows: Because of the presence of the hydroxyl group (in addition to the carbonyl and alkoxy that are also present on BA), HEA monomer offers more sites for hydrogen bonding than for the BA monomer. Thus, water is more likely to be hydrogen bonded to a polymer oxygen than to itself in PHEA gel. The effect also occurs to a smaller extent in the P(BA50-HEA50) copolymer gel. III.C.2. Water Clustering at Low Water Concentration. Information about the distribution of water molecules in the system can be obtained by quantifying the probability of water molecule cluster formation. In this analysis, two water molecules were considered to be in the same cluster if the distance between their oxygen atoms was less than the cluster cutoff distance value of 3.5 Å. This value of the cluster cutoff distance corresponds to the location of the first minimum in the water−water RDF. Following the approach used in the literature,22,26 the algorithm employed for this purpose consisted of picking a water molecule at random and searching for another water molecule lying within the specified cluster cutoff distance from it. If a molecule was found, then it was added to the cluster. The process was continued until all water molecules that reside within the cluster cutoff distance of any of the molecules in the cluster were found. Figure 6 displays the cluster size probability distribution (the ordinate is the probability that a randomly chosen water molecule will belong to a cluster of a given size) for the three polymer gel systems containing the same amount of water (i.e., same mole fraction of water as that in the PBA gel swollen to equilibrium). As seen

Figure 6. Cluster size distribution of water molecules in polyacrylate gels with a water mole fraction of 0.017. Results are shown using the following symbols: PBA (black ●), P(BA50-HEA50) (red ▲), and PHEA (blue ◆).

for this case, the cluster size probability distribution is the same for all three polymers with most of the water molecules existing as single molecules in the system and only about 15% existing in the form of pairs. We also note that ethanol is present at a low concentration in all of the systems (as seen from Tables 1 and 2) and the clustering behavior of ethanol is very similar to that of water (Figure S8 in Supporting Information) in systems with low water contents. Figure 4 (see earlier text) and Figure 7a,b show the probabilities of water−water and water−polymer hydrogen bond formation for a water molecule in the PBA, P(BA50HEA50), and PHEA gel systems (all with a water mole fraction of 0.017), respectively. As seen from these figures, when the water concentration in the system is low, the water molecules predominantly form hydrogen bonds with polymer with the probability of forming a hydrogen bond with another water molecule being very small. III.C.3. Effect of Water Concentration on the Clustering Behavior. The effect of water concentration on cluster formation behavior can be determined by studying the cluster size distribution in the three gels (PBA, P(BA50-HEA50) copolymer, and PHEA) that are swollen to equilibrium. As was seen in Table 1, there is a large difference in the water content in the three systems, which could affect the clustering behavior of water in these systems. Figure 8 presents a comparison of the water cluster size distribution in the three gels that are swollen to equilibrium. The main observation from this figure is that water forms very large clusters in the P(BA50-HEA50) copolymer and PHEA gel systems. In fact, even though PHEA is highly hydrophilic, still almost all of the water molecules in the PHEA gel reside within a single cluster rather than being distributed throughout the polymer matrix. This observation of the formation of large water clusters for increasing water concentration in the system is consistent with a similar observation reported in the literature22,23,26 for water clustering in polymers containing sulfonic acid side groups that are important for fuel cell applications. The effect of water concentration on the probability of water−water and water−polymer hydrogen bond formation can be seen by comparing the results presented in Figure S9 (for (P(BA50-HEA50) gel) in the Supporting Information and Figure 9 (for PHEA gel) with those presented earlier in Figure 15387

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Figure 7. (a) Hydrogen bond probability distribution in a P(BA50-HEA50) gel with a water mole fraction of 0.017. (b) Hydrogen bond probability distribution in PHEA gel with a water mole fraction of 0.017.

7a,b. A key observation from these figures is that unlike the behavior at low water concentration (seen earlier in Figure 7a,b), when the water concentration is high, water predominantly forms hydrogen bonds with other water molecules rather than forming hydrogen bonds with the polymer. In summary, the following conclusions can be drawn for the effects of water concentration on the distribution of water molecules in the swollen gel systems. If there is a scarcity of water, in all polymers studied, a majority of water molecules are

in an unassociated state with only a small fraction (∼15%) forming pairs. Also, water predominantly forms hydrogen bonds with the polymer functional groups rather than with other water molecules at this low concentration. As the water concentration increases, water begins to form clusters, accompanied by the formation of a larger number of water− water hydrogen bonds rather than water−polymer hydrogen bonds. For the system with the highest water concentration (PHEA gel swollen to equilibrium), water predominantly forms 15388

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The Journal of Physical Chemistry B C(t ) =

⟨h(0) h(t )⟩ ⟨h2(t )⟩

(3)

In this expression, ⟨···⟩ represents the ensemble average over all hydrogen bonding pairs in the system. The function h(t) takes a value of either 1 or 0 as follows. If a particular tagged (i.e., hydrogen bonded at time t = 0) pair of molecules is hydrogen bonded at time t, then h(t) = 1; otherwise, h(t) = 0. On the basis of this expression, the ACF can be calculated in two ways:70 (1) For a continuous time ACF, h(t) takes a value of 1 only if the same tagged molecules remain hydrogen bonded continuously from time t = 0 to time t. (2) For an intermediate time autocorrelation function, h(t) takes a value of 1 if the same tagged molecules that were hydrogen bonded at time t = 0 are also hydrogen bonded at time t (irrespective of the hydrogen bonding state at intermediate times). In what follows, we report only results for the continuous time autocorrelation function; the results for the intermediate time autocorrelation function are qualitatively similar, although the decay of the ACF is slow for that case. We note that any motion of the water molecule by translation, rotation, or vibrationthat can break an existing hydrogen bond will lead to a decay of the continuous-time ACF. Since hydrogen bond dynamics occur on a fast time scale, the simulation trajectory was saved at intervals of 5 ps to calculate these ACFs. Figure 10 shows the continuous-time ACF of water−water hydrogen bonds in polyacrylate gels that are swollen to equilibrium. The correlation function decays rapidly for PHEA and the P(BA50-HEA50) copolymer systems, while it decays slowly for the PBA system. To quantify this effect, the ACFs were fitted to the Kohlrausch−Williams−Watts (KWW) functional form,75 C(t) = exp[−(t/τ)β] (where τ and β are the relaxation time and stretching exponent, respectively), yielding relaxation times of 44, 6, and 3 ps for the PBA,

Figure 8. Cluster size distribution of water molecules in gels swollen to equilibrium. Results are shown using the following symbols: PBA (in inset, black ●), P(BA50-HEA50) (red ▲), and PHEA (blue ◆).

hydrogen bonds with other water molecules, and most of the water molecules associate into a single, very large cluster. III.D. Increase in Water Concentration Accelerates the Hydrogen Bond Dynamics of Water Molecules. In addition to static properties such as the probability of hydrogen bond formation and water clustering, the hydrogen bond dynamics of water molecules are also of interest from the point of view of pervaporation-based separation using polymer membranes. As water molecules move, the hydrogen bond network is continuously broken and reformed over time. The dynamics of the hydrogen bonds were quantified by calculating the time autocorrelation function (ACF) defined as follows:30,70,72−74

Figure 9. Hydrogen bond probability distribution in a PHEA gel swollen to equilibrium. 15389

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Figure 11. Continuous ACF for water−polymer hydrogen bonds in the gels with a water mole fraction of 0.017. The following symbols are used: PBA gel (black ●), P(BA50-HEA50) copolymer gel (red ▲), and PHEA gel (blue ◆).

Figure 10. Dynamics of water−water hydrogen bonds as captured by the continuous ACF. Results are shown for the gels that are swollen to equilibrium. Symbols are PBA gel (black ●), P(BA50-HEA50) copolymer gel (red ▲), and PHEA gel (blue ◆). Inset: Comparison of continuous ACF of water−water hydrogen bonds in PHEA gels containing different amounts of water. Results are shown for the PHEA gel with a water mole fraction of 0.017 (low water content, dashed line) and PHEA gel swollen to equilibrium (high water content, solid line).

mobility of water molecules is much lower near the highly hydrophilic hydroxyl group, which is present only in the PHEA and the P(BA50-HEA50) copolymer gel systems. We note that this observation is consistent with a previous literature report in which water molecules have smaller density fluctuations near hydrophilic surfaces than near hydrophobic surfaces.76 Finally, an inspection of the ACF for the water−polymer hydrogen bonds in the gel systems swollen to equilibrium (Figure S10 in Supporting Information) indicates that there are relatively small differences in the dynamics of water−polymer hydrogen bonds in these systems. It appears that this behavior is a result of the interplay of two opposing factors. Comparing PBA, P(BA50-HEA50) copolymer, and PHEA gels, the water content in the swollen systems increases as the HEA content in the polymer increases, thus accelerating hydrogen bond dynamics. At the same time, polymer hydrophilicity also increases, which slows down hydrogen bond dynamics.

P(BA50-HEA50), and PHEA systems, respectively. Noting that there is a significant difference in the water content of these systems (Table 1), we conclude that the higher water content in PHEA and the P(BA50-HEA50) copolymer systems provides greater opportunities for hydrogen bond formation with other water molecules, thus leading to the frequent breakup and formation of water−water hydrogen bonds. This effect is more clearly seen in the inset of Figure 10, which presents a comparison of the water−water hydrogen bond ACF in PHEA gel systems with different water contents: the PHEA gel swollen to equilibrium (high water content) and the PHEA gel containing the same mole fraction of water as the PBA gel that was swollen to equilibrium (low water content). The inset of Figure 10 clearly shows that the ACF decays very rapidly for the PHEA gel with a high water content, whereas the decay is much slower for the PHEA gel with a lower water content. The presence of a large number of water molecules in the high-water-content systems allows the water molecules to break existing water−water hydrogen bonds and readily form new ones with other water molecules, thus accelerating hydrogen bond dynamics in this system. III.E. Increase in Polymer Hydrophilicity Slows Down the Hydrogen Bond Dynamics. The effect of polymer hydrophilicity on the dynamics of hydrogen bonds is also of interest. For this purpose, we focus on hydrogen bond dynamics in three polyacrylate gels that have the same water mole fraction as that in the PBA gel swollen to equilibrium. We focus only on the dynamics of the water−polymer hydrogen bonds because as seen from Figures 4 and 7a,b almost all of the hydrogen bonds in these systems are those between water and polymer. The rate of decay of the ACFs for the PHEA and the P(BA50-HEA50) copolymer gels (Figure 11) is about the same and is smaller than that for the PBA gel. Fitting these ACFs to the KWW functional form75 yields relaxation time values of 27, 58, and 59 ps for the PBA, P(BA50-HEA50), and PHEA systems, respectively. This observation suggests that the local

IV. SUMMARY AND CONCLUSIONS We carried out MD simulations to study the effects of water concentration and polymer hydrophilicity on the structure and hydrogen bonding of water in a set of polyacrylate gel structures. The model structures of linear polyacrylates were first prepared and validated by comparing their thermal and volumetric properties (glass-transition temperature and density) with experimental values; good quantitative agreement was found for these properties. Subsequently, model structures of polyacrylate gels swollen by a dilute ethanol mixture were prepared; these were used to study the water structure and hydrogen bonding in the polymers. Large differences were observed between the affinities of water molecules for the hydrophilic functional groups in the polyacrylates: water had the highest affinity for the hydroxyl groups due to their ability to form two hydrogen bonds, while its affinity was the lowest for the alkoxy group, presumably due to a combination of lower electron density around this group and the steric effects. The water concentration was found to have a significant influence on the structure of water in the polyacrylate gels. In particular, at low concentrations, water molecules were well-dispersed in these gels and predominantly formed hydrogen bonds with the polymer. On the other hand, 15390

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The Journal of Physical Chemistry B at high concentrations, water formed clusters with a predominance of water−water hydrogen bonding accompanied by the acceleration of hydrogen bond dynamics of water molecules. This dependence of system properties on water concentration is coupled with the dependence on polymer hydrophilicity because the gels formed by hydrophilic polymers have a larger water content when swollen to equilibrium. For the gels with the same water concentration, an increase in polymer hydrophilicity was found to retard hydrogen bond dynamics of the water molecules near the polymer functional groups. The local mobility of water molecules was inferred from hydrogen bond dynamics. The local mobility influences the long length scale translational mobility that is quantified by diffusivity, which is a topic of current interest. Finally, the distribution of alcohol molecules in the swollen gels is also of interest from the point of view of separation processes. Alcohol is typically present at very low concentrations in the product formed by the enzymatic hydrolysis of cellulosic biomass. At these low concentrations, ethanol did not form clusters in the polyacrylate gel systems. The interplay between water concentration and polymer hydrophilicity in determining the structure and local dynamics of water molecules that is elucidated here is useful for interpreting the results from the laboratory experiments. For example, experimentally, diffusion coefficient values are measured either by monitoring the initial water uptake in a dry gel or the initial mass loss from a swollen gel. There is a large difference in the water content of these dry gel and swollen gel experimental systems. Our simulation results suggest that the clustering of water molecules in the highwater-content systems will lead to a higher diffusion coefficient (since water will predominantly diffuse through the water cluster rather than through the polymer matrix) than that measured from the low-water-content systems. Further quantitative investigation of this phenomenon is currently underway. This work shows that, in general, molecular simulations can be used to decipher the mechanisms underlying the concentration dependence of the penetrant diffusion coefficient that is commonly observed in systems containing strongly interacting components.

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ACKNOWLEDGMENTS

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REFERENCES

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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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b08700. Chemical structures of monomers, picture of a simulation box of the PHEA system, 1H NMR spectra of polymer samples, description of methodologies used for the experimental characterization of polymer samples (1H NMR, GPC, HPLC, and DSC), simulation results for Tg, CVTE, radial distribution functions for water, cluster size distribution of ethanol molecules, hydrogen bond probability distribution in P(BA50-HEA50) gel, and hydrogen bond dynamics in the gels swollen to equilibrium (PDF)

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Corresponding Author

*E-mail: [email protected]. Tel: (806) 834-0449. Notes

The authors declare no competing financial interest. 15391

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