Effects of Residual Solvent on Membrane Structure and Gas

ARTICLE pubs.acs.org/JPCC

Effects of Residual Solvent on Membrane Structure and Gas Permeation in a Polymer of Intrinsic Microporosity: Insight from Atomistic Simulation Liling Zhang, Weijie Fang, and Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore ABSTRACT: Microstructure and permeation in a polymer membrane are closely related to residual solvent during membrane fabrication. In this study, we conduct atomistic simulation to investigate the effects of residual solvent on free volume distribution and H2 permeation in a polymer of intrinsic microporosity (PIM-1). The interaction energies of three solvents (CHCl3, CH3OH, and H2O) with PIM-1 are predicted to be
16.3,
9.6, and
7.0 kcal/mol, respectively, which are in good agreement with available experimental data. On this basis, a structure
property relationship is proposed between interaction energy and the critical volume of solvent. The cyano and dioxane groups in PIM-1 interact preferentially with CH3OH and H2O; however, the carbon atoms interact more strongly with CHCl3. The mobility of residual solvent is found to decrease in the order of H2O > CH3OH > CHCl3. Upon comparison, the mobility of PIM-1 chains is smaller but facilitated by solvent due to the cooperative interactions between polymer and solvent. The fractional free volumes and large-size voids in PIM-1/solvent membranes are observed to decrease as CH3OH > CHCl3 > H2O, consistent with positron annihilation lifetime spectroscopy measurements. The solubility and diffusion coefficients of H2 decrease in the same hierarchy, and the predicted and experimental coefficients are in fairly good agreement. This simulation study provides atomistic insight into the microscopic properties of residual solvent in a polymer membrane and reveals the crucial role of residual solvent in tailoring membrane structure and gas permeation.

1. INTRODUCTION Gas separation is ubiquitously involved in numerous engineering processes and applications. This is particularly important for a current topical issue, CO2 capture to reduce the global warming effect. A number of techniques have been proposed for gas separation such as pressure swing adsorption, cryogenic distillation, and membrane permeation. In pressure swing adsorption, a gas mixture is separated due to different adsorption affinities, while separation in cryogenic distillation is based on different boiling points. Compared with these two energy-intensive techniques, separation using polymer membranes has advantages in high energy efficiency, low capital cost, large separation capability, and ease for scaling-up.1 In the past, extensive experimental studies have been reported for gas permeation and separation in polymer membranes.2,3 For example, Sridhar et al. prepared polyphenylene oxide (PPO) for CO2/CH4 separation. A higher selectivity was observed in sulfonated PPO, while unmodified PPO showed a larger permeability.4 Chung and co-workers reported the synthesis, cross-linking, and carbonization of copolyimides containing internal acetylene units for gas separation.5 They also proposed a novel synthetic strategy to fine-tune the cavity sizes and free volumes of polyimide membranes with homogeneous pseudointerpenetrating networks.6 Ribeiro and Freeman measured the sorption and dilation of CO2 and C2H6 in cross-linked r 2011 American Chemical Society

poly(ethylene oxide) (PEO). The dilation and sorption data were combined to calculate the partial molar volumes of gases in PEO, which were then compared against available literature data.7 Sen and Banerjee introduced
C(CF3)2
groups into polyetherimide (PEI) and found the modified PEI membrane has an exceptionally large permeability along with a higher CO2/ CH4 selectivity than unmodified counterpart.8 With ever-growing computational power, increasing molecular simulation studies have been carried out for gas permeation in polymer membranes. Theodorou and co-workers simulated the structural, conformational, and dynamic properties of amorphous poly(ethylene terephthalate) and poly(ethylene isophthalate), and predicted CO2 sorption in glassy atactic polystyrene.9,10 Heuchel et al. constructed atomistic packing models for glassy polyimides, polysulfone and poly(ether sulfone), and calculated gas solubility and diffusion coefficients.11,12 Mark and co-workers used simulation results to elucidate high permeabilities in poly(dimethylsiloxane), which were attributed to the pronounced alternation in skeletal bond angles and the relatively large value of Si
O bond length.13 These experimental and simulation studies demonstrate that gas permeation and separation in Received: March 31, 2011 Revised: May 5, 2011 Published: May 16, 2011 11233

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Figure 1. (a) Backbone of PIM-1 (the spiro carbons are denoted by “C” and the hydrogen atoms are in white). (b) Three dimensional simulation box of PIM-1 membrane (the box length is approximately 31.8 Å).

polymer membranes are governed by several crucial factors such as polymer structure, backbone functionalization, and chain rigidity. A handful of experiments have revealed that the fabrication protocol of polymer membranes also affects performance. Joly et al. prepared 6FDA-mPDS polyimide films by spreading solutions from different solvents (CH2Cl2, dioxane, tetrahydrofurane, N-methyl-2-pyrrolidone and N-N-dimethylacetamide) and found the solubilities, diffusivities, and permeabilities of N2 and CO2 in the films were dependent on residual solvents.14 Kostina et al. showed CHCl3 resident in PEI could preferentially bind with oxygen atoms in membrane and lead to the conformational change of polymer chains.15 Budd et al. observed a very strong sensitivity of gas permeability to casting method for a novel polymer of intrinsic microporosity (PIM-1). In particular, PIM-1 membrane with residual H2O exhibits a substantially low permeability.16 Currently, it remains elusive how residual solvent specifically interacts with a membrane and affects membrane microstructure and performance. In this regard, fundamental understanding at a molecular level is desirable. In this work, an atomistic simulation study is reported for the effects of residual solvent on PIM-1 membrane structure and H2 permeation. Three residual solvents (CH3OH, CHCl3, and H2O) are considered and the simulation results are compared with the experimentally data by Budd et al.16 The microscopic insight from simulation can facilitate the design of new membranes for gas purification. In a previous study, we have constructed an atomistic model for PIM-1 membrane and calculated gas sorption/diffusion by Monte Carlo (MC)/molecular dynamics (MD) simulations.17 It was found that the voids in PIM-1 have diameter up to 9 Å and are largely interconnected. The simulated solubility and diffusivity of H2, O2, CO2, and CH4 are consistent with experimentally measured results. As attributed to its intrinsic microporous structure, PIM-1 appears to outperform most glassy polymer membranes in sorption and diffusion. Following this section, the models and methods are described in Section 2 including how to construct PIM-1 membranes with residual solvents and to calculate H2 sorption and diffusion. In Section 3, the membranes are characterized in terms of fractional free volume and void distribution. The interaction and mobility of solvent and polymer are discussed. The simulated solubility and diffusion coefficients of H2 are presented and compared with experimental data. Finally, the concluding remarks are summarized in Section 4.

Table 1. Physical Properties of Residue Solvents22 molecular

van der Waals

weight

volume (Å3)

CH3OH

32.04

36.82

118

CHCl3

119.38

70.55

239

18.01

19.24

solvent

H2O

critical volume (cm3/mol)

55.9

2. MODELS AND METHODS 2.1. Membrane Construction. PIMs are amorphous and thermally stable glassy polymers. Remarkably, they have ultrahigh interconnected voids and are potentially useful for gas storage and separation.18 The prototype PIM-1 was experimentally synthesized from 5,50 ,6,60 -tetrahydroxy-3,3,30 ,30 -tetramethyl-1,10 -spirobisindane by polycondensation reaction.19 As illustrated in Figure 1a, the backbone of PIM-1 contains aromatic rings connected by spiro carbon atoms that are shared by two five-membered rings with a torsional angle of 90
. The rigid ladderlike polymer chains cannot pack efficiently, thus leading to a three-dimensional microporous structure. The atomistic model of PIM-1 membrane was constructed by Amorphous Cell module in Materials Studio 4.3 (Accelrys Inc., San Diego, CA, U.S.A.) using Theodorou and Suter’s scheme.20,21 The model membrane was composed of three polymer chains in a periodic cubic simulation box (with a length of approximately 31.8 Å as shown in Figure 1b) and each polymer chain consisted of 15 repeat units. To prevent ring catenation during model construction, 200 CH4 molecules were inserted into the simulation box and removed after the model was built. Ten configurations were generated and three of them were selected for equilibration by the following subsequent procedures: (1) energy minimization; (2) 500 ps NVT-MD simulation at 600 K; (3) 500 ps NPT-MD simulation at 600 K at 1 bar; (4) thermal annealing at 1 bar from 600 to 300 K with a temperature interval of 50 K; (5) 100 ps NPT-MD simulation at 10 bar with a time step of 0.1 fs; and (6) 2000 ps NPT-MD simulation with a time step of 1 fs at 300 K and 1 bar. As in the experimental study,16 three residual solvents are considered here including CH3OH, CHCl3, and H2O. Table 1 lists the physical properties of the three solvents.22 Experimental thermogravimetric analysis revealed that there were 0.5, 2.2, and 2.3% of CH3OH, CHCl3, and H2O, respectively, in PIM-1 membrane.16 Approximately, 4 CH3OH, 4 CHCl3, and 27 H2O molecules existed in the simulation box shown in Figure 1b. The 11234

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Table 2. Predicted Densities and Fractional Free Volumes of PIM-1/Solvent Membranes membrane

density (g/cm3)

FFV (%)

PIM-1/CH3OH

1.07

44.88

PIM-1/CHCl3 PIM-1/H2O

1.09 1.09

44.27 43.67

Figure 2. Void distributions in PIM-1/solvent membranes.

residual solvent molecules were randomly inserted into the equilibrated PIM-1 model membrane, then equilibrated by 8000 ps NPT-MD simulation at 300 K and 1 bar, and finally by 2000 ps NVT-MD simulation. The energy minimization and MD simulations were conducted in DL_POLY.23 To do this, the files created by Materials Studio were converted to DL_POLY using an in-house code. In such a way, computational time was reduced by 1
2 orders of magnitude. The polymers were mimicked by polymer consistent force field (PCFF), which has been found to be fairly accurate for PIM membranes.17 The Lennard-Jones interactions were calculated with a cutoff of 13 Å and the Coulombic interactions were treated by the Ewald summation with a precision of 10
6. The velocity Verlet algorithm was used to integrate the equations of motion. Temperature and pressure were controlled by the Berendsen method with a decay constant of 0.6 ps. The equilibrated model membranes were characterized by fractional free volume (FFV) and void distribution. These quantities play a key role in governing gas permeation in a polymer membrane, and they were estimated here on the basis of geometric consideration using an in-house MC code. Specifically, a probe was randomly inserted into the simulation box and the insertion was considered to be successful if the probe did not overlap with any polymer atom. The ratio of successful insertions over the total number of insertions gave the FFV.24 The probe size used in this study was set to be zero, that is, the maximum FFV was estimated. A total number of 200 000 insertions were found to be sufficient for the accurate estimation of FFV. The void size distribution was calculated by a method previously used for microporous materials.25,26 In brief, the simulation box was divided into three-dimensional fine grids with a width of 0.12 Å. At a given grid, the void size was determined as the diameter of maximum cavity that enclosed the grid and had no overlap with any polymer atom. The percentage of a void size was normalized by the total number of grids each with a nonzero void.

2.2. Sorption and Diffusion of H2. On the basis of solutiondiffusion mechanism, gas permeability P in a polymeric membrane is equal to SD in which S is solubility coefficient and D is diffusion coefficient. In this work, S and D of H2 in the PIM-1/ solvent membranes were calculated at room temperature and infinite dilution. The sorption was simulated by NVT MC method with a single H2 molecule added into the membrane. The number of trial moves in the MC simulation was 2  107 with the first 107 moves for equilibration and the subsequent 107 moves for ensemble averages. Two types of trial moves were randomly attempted, namely, translation and rotation. In translation, H2 molecule was translated with a random displacement in x, y, or z dimension; and the maximum displacement was adjusted to an overall acceptance ratio of 50%. In rotation, H2 molecule was rotated around x, y, or z dimension with a random angle, and the maximum angle was adjusted to an overall acceptance ratio of 50%. The solubility coefficient was estimated from Z S ¼ β exp½
βua ðr, ϖÞdr dϖ ð1Þ

where β = 1/kBT is the reciprocal temperature, ua(r,ϖ) is the interaction energy between the membrane and H2 molecule at position r and orientation ϖ. The diffusion was simulated by NVT MD method. To improve statistical accuracy, three H2 molecules were inserted into the membrane. At least half of the box length existed between the H2 molecules to minimize their interactions. The MD simulation was performed for 13 ns, in which the first 2 ns was used for equilibration and the subsequent 11 ns for production. Similar to the MD simulation used for model construction, the LJ and Coulombic interactions were also calculated with a cutoff of 13 Å and the Ewald summation with a precision of 10
6. Temperature was controlled by the Berendsen method with a decay constant of 0.6 ps. The mobility was estimated by meansquared displacement (MSD) MSDðtÞ ¼

1 N Æjrk ðtÞ
rk ð0Þj2 æ N k¼1

∑

ð2Þ

where N is the number of gas molecules, rk(t) is position of the molecule k at time t. MSD was calculated from the ensemble average Æ...æ of the trajectory. In this study, multiple-origin method was used to calculate the MSD.

3. RESULTS AND DISCUSSION 3.1. Membrane Characterization. Table 2 lists the densities and FFVs of PIM-1/solvent membranes predicted from simulation. Compared with dry PIM-1 in the absence of solvent,17 the density increases from 1.03 to 1.07
1.09 g/cm3 and the FFV decreases from 47.7 to 44
45%. This is because the volume of membrane remains almost a constant in the absence/presence of solvent molecules and solvent molecules tend to occupy the voids in membrane; consequently, the density increases slightly. The increasing effect on density by residual solvent was also observed in PEI membranes.27 It is worthwhile to note the FFVs in PIM-1 membranes are substantially larger than in common polyimide membranes (30
38%),11 thus leading to a faster diffusion in PIM-1 membranes as discussed below. Figure 2 shows the void distributions in PIM-1/solvent membranes. Because of the presence of solvent molecules, the 11235

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Figure 3. Simulation snapshots of PIM-1 with 27 residual water molecules. (a) Initial structure with water molecules randomly inserted in the simulation box. (b) Equilibrated structure after 5 ns simulation.

Figure 4. Distributions of interaction energy E between a single solvent molecule and PIM-1. The inset is the ensemble averaged energy ÆEæ versus the critical volume of solvent.

largest voids (8 Å) in the three membranes are smaller than that (9 Å) in dry PIM-1.17 The percentage of large-size voids (>6 Å) decreases following the order of PIM-1/CH3OH > PIM-1/ CHCl3 > PIM-1/H2O, which is in accord with positron annihilation lifetime spectroscopy measurements.16 As listed in Table 1, CHCl3 has a van der Waals (vdW) volume larger than that of CH3OH; therefore, CHCl3 occupies a greater void space and PIM-1/CHCl3 has a smaller percentage of large-size voids. Although H2O has the smallest vdW volume among the three solvents, 27 H2O molecules (vs 4 CH3OH or CHCl3 molecules) exist in PIM-1/H2O membrane and occupy a greater number of voids. Consequently, PIM-1/H2O contains fewer large-size voids compared with PIM-1/CH3OH and PIM-1/CHCl3. Gas diffusion in a polymer membrane is largely governed by large-size voids. As we shall see, the diffusion coefficient of H2 in PIM-1/ H2O is lower than in the other two membranes. It is observed from simulation that 4 CH3OH molecules in PIM-1/CH3OH or 4 CHCl3 molecules in PIM-1/CHCl3 remain essentially separated during the entire simulation. Nevertheless, H2O molecules in PIM-1/H2O behave differently. As shown in Figure 3, initially 27 H2O molecules are randomly distributed in the membrane, but they form into clusters after 5 ns. It was indeed observed experimentally by IR spectroscopy that alcohol in PIM-1 exists as monomers but H2O as associates.27 We therefore infer PIM-1 is a hydrophobic membrane in which

highly polar H2O interacts weakly with the polymer and tends to aggregate. As a result of the formation of large clusters occupying large-size voids, PIM-1/H2O membrane possesses the lowest percentage of large-size voids among the three PIM-1/solvent membranes. 3.2. Polymer
Solvent Interaction and Mobility. To quantify polymer
solvent interaction, Figure 4 shows the distributions of interaction energy between a single solvent molecule and PIM-1. A sharp peak is seen in the distribution for CHCl3 and CH3OH but not for H2O. The probability and energy value decrease in the order of CHCl3 > CH3OH > H2O, which is consistent with the decreasing order in solvent hydrophobicity. Among the three solvents, CHCl3 is the most hydrophobic, then CH3OH, and finally H2O. Therefore, the interaction between CHCl3 and hydrophobic PIM-1 is the strongest and the weakest interaction is seen for H2O. This implies that the primary interaction between solvent and PIM-1 is hydrophobic. On the basis of the energy distribution, ensemble averaged energy ÆEæ was evaluated from Z Eðr, ϖÞexp½
βEðr, ϖÞdr dϖ Z ð3Þ hEi ¼ exp½
βEðr, ϖÞdr dϖ For CHCl3, CH3OH, and H2O, ÆEæ are approximately
16.3,
9.6, and
7.0 kcal/mol, respectively. The experimentally measured values are
14.4 and
10.2 kcal/mol for CHCl3 and CH3OH (not available for H2O).16 Fairly good agreement is found between the predicted and experimental ÆEæ. It is recognized that hydrophobic interaction is largely proportional to molecular size.28 Therefore, we plot ÆEæ as a function of the critical volume of solvent Vc. As shown in the inset, ÆEæ increases when Vc becomes larger and a good correlation is found between ÆEæ and Vc hEi ¼
3:89
0:051V c

ð4Þ

This molecular-based structure
property relationship can be used to predict the interaction energies for other solvents in PIM-1. A polymer chain contains various groups that experience different interactions with residual solvent. To elucidate this, 11236

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Figure 5. Radial distribution functions g(r) between solvent molecules and (a) nitrogen atoms in cyano groups, (b) oxygen atoms in dioxanes, (c) carbon atoms in phenyl rings, and (d) spiro carbon atoms.

radial distribution functions g(r) were calculated by gij ðrÞ ¼

ΔNij ðr, r þ ΔrÞV 4πr 2 ΔrNi Nj

ð5Þ

where r is the distance between species i and j, ΔNij(r,r þ Δr) is the number of species j around i within a shell from r to r þ Δr, V is the system volume, Ni and Nj are the numbers of species i and j. Figure 5 illustrates g(r) between solvent molecules and (a) nitrogen atoms in cyano groups, (b) oxygen atoms in dioxanes, (c) carbon atoms in phenyl rings, and (d) spiro carbon atoms. A common feature in the g(r) is that H2O exhibits a peak at the shortest distance because it has the smallest size among the three solvents, which is in contrast to CH3Cl with a peak at the longest distance. More importantly, different profiles are observed in the g(r) for the four different types of atoms in PIM-1. As shown in Figure 5a, the peak around nitrogen atoms in cyano groups drops in the order of CH3OH > H2O > CHCl3, implying CH3OH has the strongest interaction with cyano groups. A similar trend is observed in Figure 5b around oxygen atoms in dioxanes, except that CHCl3 exhibits a higher peak than H2O because of the favorable interaction between CHCl3 and carbon atoms in dioxanes. It is also seen in Figure 5c,d that both CHCl3 and CH3OH have a higher peak than H2O around carbon atoms. Overall, the structural analysis in Figure 5 reveals that polar cyano and dioxane groups interact more preferentially with hydrophilic CH3OH and H2O, whereas less polar carbon atoms favor the interaction with hydrophobic CHCl3. This is a consistent with the interaction energies discussed above. As evidenced from the mean-squared displacements (MSDs), residual solvents and polymer chains exhibit distinct mobility. Figure 6 shows that the MSDs of CHCl3 and CH3OH are considerably smaller than H2O and the mobility decreases in the order of H2O > CH3OH > CHCl3. The decreasing order could

Figure 6. Mean-squared displacements of solvent molecules in PIM-1/ solvent membranes.

be attributed to two factors. First, the molecular weight increases as H2O < CH3OH < CHCl3. However, H2O tends to form clusters with weight heavier than CH3OH, thus the molecular weight may not be the major factor. Second, the interaction strength with polymer increases with increasing degree of hydrophobicity H2O < CH3OH < CHCl3. Consequently, we speculate the second factor may play a more dominant role in governing the mobility of solvents. Figure 7 shows the MSDs of polymer chains in PIM-1/solvent membranes. Compared with residual solvents, the mobility of polymer chains is negligible. Nevertheless, the mobility increases in the same order as observed in Figure 6. The reason is that solvent molecules in membrane can be considered as a part of membrane skeleton. Therefore, the mobility of solvent and polymer is cooperative and a larger mobility of the former 11237

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Figure 7. Mean-squared displacements of polymer chains in PIM-1/ solvent membranes.

Table 3. Solubility Coefficients S [10
3 cm3 (STP)/ cm3 cmHg] and Diffusion Coefficients D (10
8 cm2/s) of H2 in PIM-1/Solvent Membranes solvent

Ssim

Sexp16

Dsim

Dexp16

PIM-1/CH3OH

5.04 ( 0.05

6.6

6471 ( 481

5000

PIM-1/CHCl3

4.75 ( 0.10

6.9

3513 ( 423

2900

PIM-1/H2O

4.21 ( 0.03

2.7

2326 ( 604

1000

facilitates the mobility of the latter. Moreover, Figure 7 indicates the mobility of polymer chains is enhanced in the presence of residual solvent. This is because solvent
polymer interaction leads to a relatively weaker polymer
polymer interaction and a looser polymer network. Such a phenomenon is analogous to the plasticization of polymer membranes, e.g., in our recent study on CO2-included plasticization of 6FDA-ODA polyimide.29 3.3. Sorption and Diffusion of H2. Table 3 lists the solubility coefficients of H2 in PIM-1/solvent membranes. Good agreement is found between the predicted and experimental data. The solubility decreases following PIM-1/CH3OH > PIM-1/CHCl3 > PIM-1/H2O, which is in accord with the decreasing order of FFV in the three membranes and implies the solubility is proportional to the free volume. As observed experimentally,16 the solubility in the presence of solvent is smaller compared against that in dry PIM-1 membrane. The reason is that solvent molecules can bind/block sorption sites and thus lead to a reduction in H2 sorption. This effect induced by residual solvent was also observed for the solubility of N2 in 6FDA-mPDA.14 Furthermore, it is noteworthy that PIM-1 exhibits the largest solubility than other polymers reported to date, due to the existence of microporous structure and polar sorption sites. This is unique for glassy PIM-1 because a large solubility is usually observed in rubbery polymers. In a polymer membrane, a gas molecule is trapped in a void and may jump into a neighboring void if the energy barrier is sufficiently low. The jumping occurs rapidly with a time frame shorter than the residence time in a void. The frequency of jumping depends on the energy barrier, which in turn is governed by the intrinsic properties of membrane and gas molecule. This process proceeds repeatedly as a result of the opening and close of voids in polymer matrix and leads to gas diffusion. In general, diffusion can be described by mean-squared displacement (MSD) versus time t as MSD(t)  tγ, where γ is the signature

Figure 8. Mean-squared displacements of H2 in PIM-1/solvent membranes. The inset is in log
log scale.

of different types of diffusion. Specifically, γ < 1, > 1, and = 1 correspond to sub-, super-, and normal-diffusion, respectively. Subdiffusion is usually observed within a short time and attributed to the structural correlation of immediate environment that retards diffusion. Superdiffusion occurs under convective or hydrodynamic transport. Normal (also called Einstein) diffusion takes place if molecules move randomly. Figure 8 shows the MSDs of H2 in PIM-1/solvent membranes. As indicated by the inset, the MSDs scale with t after approximately 1000 ps. This implies that H2 reaches normal diffusion in the three PIM-1/solvent membranes after 1000 ps. Consequently, diffusion coefficient can be estimated using the Einstein equation D¼

1 d lim 6N dt t f ¥

N

∑ ÆjrkðtÞ
rkð0Þj2 æ k¼1

ð6Þ

It is commonly recognized that diffusion is faster in a membrane with a larger FFV, which is observed in Table 3. The diffusion coefficients in the PIM-1/solvent membranes decrease in the hierarchy of PIM-1/CH3OH > PIM-1/CHCl3 > PIM-1/H2O. The trend is consistent with the decreasing order of FFV. The presence of solvent molecules reduces free volume and diffusion coefficient. Particularly, H2O clusters occupy the large-size voids in PIM-1/H2O and cause the largest reduction in free volume and diffusion. For the same reason, the diffusion in wet PIM-1 membrane is slower than that in dry PIM-1 membrane as experimentally observed.16 It is interesting to compare gas diffusion in PIM-1 with that in other polymer membranes and porous structures. As a result of its microporous feature, PIM-1 has diffusion coefficient larger than most glassy polymers, though smaller than extremely permeable poly[1-(trimethylsilyl)-1propyne], poly(4-methyl-2-pentyne) and Teflon AF.19 However, the diffusion coefficients in PIM-1 are 2
3 orders of magnitude lower than in zeolites and MOFs.30,31 This is because the pores/ voids are irregular in amorphous PIM-1, but well-defined and highly ordered in zeolites and MOFs. Table 3 also compares the simulated and experimental diffusion coefficients of H2. Fairly good agreement is found despite one-fold overestimation by simulation in PIM-1/H2O membrane. There are a number of factors that would cause the discrepancy between simulation and experiment. (1) Simulation predicts self-diffusion coefficient, whereas experiment typically reports transport diffusion coefficient by time-lag measurement. The self- and transport diffusion coefficients are identical only at 11238

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The Journal of Physical Chemistry C infinite dilution, but experimental condition is usually at finite pressure/concentration. (2) Accurate prediction of diffusion coefficient requires not only an accurate force field, but also a well-equilibrated model membrane. It was found that the equilibration procedure to construct a model membrane may affect gas diffusion.32 (3) With self-avoiding random-walk method to build a membrane, anisotropy may exist and leads to nonuniform distribution of polymer chains. Even if simulated density is close to experimental value, the void distribution in a model membrane may differ from that in a real membrane. (4) Polymer chain length also plays a role in gas diffusion.33 A model membrane built with short polymer chains tends to have a larger fractional free volume than that with long polymer chains. Consequently, diffusion coefficient predicted in the former is greater. The average molecular weight of PIM-1 samples was measured to be 370 000 g/mol,16 which implies the degree of polymerization is approximately 797. In our simulation, however, the PIM-1 model has 15 monomers and this would lead to faster diffusion than experimentally observed. In addition, short polymer chains have a greater mobility, which in turn facilitates gas diffusion.

4. CONCLUSIONS We have examined how residual solvents (CH3OH, CHCl3, and H2O) in PIM-1 affect the microscopic structure of membrane and gas permeation. It is observed that the fractional free volumes and large-size voids in PIM-1/solvent membranes decrease following CH3OH > CHCl3 > H2O, which is in accordance with the measurements by positron annihilation lifetime spectroscopy. Among the three solvents, CHCl3 interacts most strongly with hydrophobic PIM-1. However, H2O does not preferentially interact with PIM-1 and thus aggregates into clusters. The average interaction energies predicted for CHCl3, CH3OH, and H2O are
16.3,
9.6, and
7.0 kcal/mol, respectively, which agree well with available experimental data. Consequently, a structure
property relationship is proposed between the critical volume of solvent and interaction energy, and might be useful for the prediction of interaction energies for other solvents. The analysis of radial distribution functions reveals that cyano and dioxane groups in PIM-1 interact preferentially with hydrophilic CH3OH and H2O, whereas carbon atoms favor the interaction with hydrophobic CHCl3. It is found that the mobility of residual solvent decreases as H2O > CH3OH > CHCl3, opposite to the increasing hierarchy of molecular weight and interaction strength with PIM-1. The mobility of polymer is vanishingly small but facilitated by solvent due to the cooperative interactions between polymer and solvent. Both solubility and diffusion coefficients of H2 in PIM-1/ solvent membranes decrease in the order of CH3OH > CHCl3 > H2O, which follows the decreasing order of free volume. The predicted coefficients are in fairly good agreement with experimental results. The solubility and diffusion coefficients are smaller compared with those in dry PIM-1 membrane in the absence of solvent. This is because solvent molecules bind/block sorption sites and decrease free volume, thus leading to a reduction in both sorption and diffusion. Finally, it is interesting to note that gas solubility/diffusion in PIM-1 appear to be larger/ faster than in many other polymer membranes, as a consequence of the intrinsic microporous structure.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: (65) 65165083. Fax: (65) 67791936.

’ ACKNOWLEDGMENT The authors gratefully acknowledge the National Research Foundation of Singapore (R-279-000-261-281) for support. ’ REFERENCES (1) Bernardo, P.; Drioli, E.; Golemme, G. Ind. Eng. Chem. Res. 2009, 48, 4638. (2) Ockwig, N. W.; Nenoff, T. M. Chem. Rev. 2007, 107, 4078. (3) Shao, L.; Low, B. T.; Chung, T.-S.; Greenberg, A. R. J. Membr. Sci. 2009, 327, 18. (4) Sridhar, S.; Smitha, B.; Ramakrishna, M.; Aminabhavi, T. M. J. Membr. Sci. 2006, 280, 202. (5) Xiao, Y. C.; Chung, T. S.; Guan, H. M.; Guiver, M. D. J. Membr. Sci. 2007, 302, 254. (6) Low, B. T.; Chung, T. S.; Chen, H.; Jean, Y.-C.; Pramoda, K. P. Macromolecules 2009, 42, 7042. (7) Ribeiro, C. P.; Freeman, B. D. Macromolecules 2008, 41, 9458. (8) Sen, S. K.; Banerjee, S. J. Membr. Sci. 2010, 350, 53. (9) Karayiannis, N. C.; Mavrantzas, V. G.; Theodorou, D. N. Macromolecules 2004, 37, 2978. (10) Spyriouni, T.; Boulougouris, G. C.; Theodorou, D. N. Macromolecules 2009, 42, 1759. (11) Heuchel, M.; Hofmann, D.; Pullumbi, P. Macromolecules 2004, 37, 201. (12) Heuchel, M.; B€ohning, M.; H€olck, O.; Siegert, M. R.; Hofmann, D. J. Polym. Sci., Part B 2006, 44, 1874. (13) Abou-Hussein, R.; Wu, S.; Zhang, L.; Mark, J. E. J. Inorg. Organomet. Polym. Mater. 2008, 18, 100. (14) Joly, C.; Le Cerf, D.; Chappey, C.; Langevin, D.; Muller, G. Sep. Purif. Tech. 1999, 16, 47. (15) Kostina, Y.; Bondarenko, G.; Alentiev, A.; Yampolskii, Y. Vysokomol. Soedin. 2006, 48, 41. (16) Budd, P. M.; McKeown, N. B.; Ghanem, B. S.; Msayib, K. J.; Fritsch, D.; Starannikova, L.; Belov, N.; Sanfirova, O.; Yampolskii, Y.; Shantarovich, V. J. Membr. Sci. 2008, 325, 851. (17) Fang, W. J.; Zhang, L. L.; Jiang, J. W. Mol. Simul. 2010, 36, 992. (18) McKeown, N. B.; Budd, P. M. Chem. Soc. Rev. 2006, 35, 675. (19) Budd, P. M.; Msayib, K. J.; Tattershall, C. E.; Ghanem, B. S.; Reynolds, K. J.; McKeown, N. B.; Fritsch, D. J. Membr. Sci. 2005, 251, 263. (20) Theodorou, D. N.; Suter, U. W. Macromolecules 1985, 18, 1467. (21) Theodorou, D. N.; Suter, U. W. Macromolecules 1986, 19, 139. (22) NIST Chemistry WebBook; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, 2011. (23) Smith, W.; Yong, C. W.; Rodger, P. M. Mol. Simul. 2002, 28, 385. (24) Gelb, L. D.; Gubbins, K. E. Langmuir 1998, 14, 2097. (25) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726. (26) Ban, S.; Vlugt, T. J. H. Mol. Simul. 2008, 35, 1105. (27) Yampolskii, Y.; Alentiev, A.; Bondarenko, G.; Kostina, Y.; Heuchel, M. Ind. Eng. Chem. Res. 2010, 49, 12031. (28) Dill, K. A.; Bromberg, S. Molecular Driving Forces; Garland Science: New York, 2010. (29) Zhang, L. L.; Xiao, Y. C.; Chung, T. S.; Jiang, J. W. Polymer 2010, 51, 4439. (30) Smit, B.; Maesen, T. L. M. Chem. Rev. 2008, 108, 4125. (31) Keskin, S.; Liu, J.; Rankin, R. B.; Johnson, J. K.; Sholl, D. S. Ind. Eng. Chem. Res. 2009, 48, 2355. (32) Meunier, M. J. Chem. Phys. 2005, 123, 134906. (33) Gestoso, P.; Meunier, M. Mol. Simul. 2008, 34, 1135.

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