Effect of Chemical Substituents on the Structure of Glassy Diphenyl

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Effect of Chemical Substituents on the Structure of Glassy Diphenyl Polycarbonates† M. S. Sulatha and Upendra Natarajan*,‡ Macromolecular Modeling and Simulation Laboratory, Polymer Chemistry Division, National Chemical Laboratory (NCL), Pune 411 008, India

bS Supporting Information ABSTRACT: Polycarbonates offer a wide variety of physical property behavior that is difficult to predict due to complexities at the molecular scale. Here, the physical structure of amorphous glassy polycarbonates having aliphatic and cycloaliphatic chemical groups is explored through atomistic simulations. The influence of chemical structure on solubility parameter, torsion distributions, radial distribution function, scattering structure factor, orientation distributions of phenylene rings and carbonate groups, and free volume distributions, leading to interchain packing effects, are shown. The effect of the cyclohexyl ring at the isopropylidene carbon as compared to the effect of the methyl groups positioned on the phenylene rings results in a larger reduction in the solubility parameter (δ). The interchain distance estimated for polycarbonates in this work is in the range of 5-5.8 Å. The o-methyl groups on the phenylene rings, as compared to a cyclohexyl ring, lead to higher interchain distances. The highest interchain distance is observed with a trimethylcyclohexylidene group at the isopropylidene carbon. Atomistic simulations reveal two different types of packing arrangement of nearest-neighbor chains in the glassy state, one type of which agrees with the NMR experimental data. The fundamental insights provided here can be utilized for design of chemical structures for tailored macroscopic properties.

1. INTRODUCTION Thermodynamic, mechanical, and dynamical properties of polymeric glasses are paramount to their behavior in many practical applications. Physical structure in the glassy phase, originating from effects of the chemical structure, affects the final properties and processing of these amorphous materials. Molecular scale physical structure in the glassy amorphous phase of polymers has been extensively studied by NMR spectroscopy, neutron scattering, wide-angle X-ray scattering, and infrared and Raman spectroscopy techniques. Molecular simulations can provide fundamental understanding toward the physical chemistry of glassy structures. Methods for generation and relaxation of glassy phase based on single-chain and multichain packing models, using Monte Carlo, energy minimization, and molecular dynamics approaches, have found tremendous utility in furthering the understanding of static conformational aspects and intermolecular structure of polymer glasses.1-9 Polycarbonates (PCs) constitute an important category of polymers and have been investigated by experiments spanning a wide range of structural chemistry on homopolymers, copolymers, and blends.10 Bisphenol A polycarbonate (BPAPC) is by far the most widely studied variety of polycarbonate, extensively investigated at a fundamental level, given its commercial applications which include bottles, shields, automotive parts, airplane windows, optical lenses, and compact disks. Simulation methods r 2011 American Chemical Society

with atomic detail applied to BPAPC have brought out various aspects of structure, thermodynamics, and dynamics aspects in the glassy state.11-15 These reports have utilized molecular mechanics simulations5,11,12 and MD simulations13-18 to understand the behavior of amorphous BPAPC: free volumes for small penetrant molecules;12 glass-transition prediction;13 small-penetrant diffusion using transition state approach;14 and crystalline, amorphous, and melt samples of BPAPC.15 Further, reports looked at entanglement analysis using coarse-grained chains,16 solubility of small organic molecules in the melt;17 mechanisms of plastic deformation;18a and strain-hardening.18b Attempts to discern possible link between macroscopic physical properties through underlying molecular mechanisms have sustained the interest in the field of macromolecular glass behavior.19 Amorphous PCs, chemically different from BPAPC, continue to evoke significant fundamental interest20 given the complex thermodynamic behavior. Molecular simulation studies of chemically substituted (i.e., structurally modified) PCs are very limited. Conformational analyses of model fragments and chains21,22 and optical properties23 have shown the influence of chemical structure on single-chain properties. Atomistic simulations of the Received: June 28, 2010 Revised: December 28, 2010 Published: January 28, 2011 1579

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The Journal of Physical Chemistry B

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Figure 1. Chemical structures of the polycarbonate repeat units and definition of torsion angles.

diffusivity of various penetrant gases in the amorphous phase of tetramethyl (TMPC) and tetrabromo (TBPC) derivatives of BPAPC24 have shown correlation between simulated free volume distribution and diffusional coefficient, consistent with experiment. Studies have investigated the transport behavior of gaseous diatomic molecules25 (O2 and N2) and CO226 in the copolymer poly(bisphenol A carbonate-co-4,40 -(3,3,5-trimethylcyclohexyl)diphenyl carbonate) (BPAPC-co-TMCPC). Simulated neutronscattering from atomistic models of cyclohexyl bisphenol polycarbonate (BPCPC) melts showed good agreement with experiment.27 Successful predictions of the Vogel-Fulcher temperature, conformational, and dynamic properties of BPAPC and substituted TMCPC in the melt were made by bondfluctuation Monte Carlo simulations on coarse-grained models.28 Off-lattice coarse-grained (CG) simulations of BPCPC and TMCPC have looked at equilibrated chain configurations in the melt state.29 Neutron scattering experiments have probed intermolecular order in glassy BPAPC30 and in melts27,31,32 of BPAPC, BPCPC, and TMCPC. Features of local packing and various intermolecular distances in glassy BPAPC were obtained by rotationalecho double resonance (REDOR) measurements on deuterated samples.33-37 2-D separated local field NMR studies of conformations in diphenyl carbonate38 and BPAPC in glassy state,39 using the orientation information of the chemical shift anisotropy (CSA) tensor, have revealed less than 10% of carbonate groups (denoted by torsion angle about C-O bond) being in cis conformation. The probability distribution of orientation of the phenylene rings with respect to the carbonate groups is quite broad.38 13C NMR spectroscopy studies have revealed different conformational dynamics of BPCPC in solution40a and glassy state40b and different activation energy barriers for the backbone phenylene rings having disparate structural disposition with respect to the cyclohexyl substituent group.41,42 We present atomistic simulations of five chemically different polycarbonates: poly(4,40 -isopropylidenediphenyl carbonate),

poly(4,40 -cyclohexyldiphenyl carbonate), poly(4,40 -(3,3,5-trimethylcyclohexyl)diphenyl carbonate), poly(4,40 -cyclohexyl 2,20 -dimethyldiphenyl carbonate), and poly(4,40 -isopropylidene-2,20 dimethyldiphenyl carbonate). These polycarbonates have repeating units with the following chemical modifications as compared to BPAPC: (i) cyclohexylidene group at the CR carbon, BPCPC; (ii) trimethylcyclohexylidene group at CR, TMCPC; (iii) methyl groups at the ortho position of the phenylene rings, DMPC; and (iv) cyclohexylidene group at CR and methyl groups on phenylene rings, DMBPC (see Figure 1). Reports have looked at these polycarbonates as potential candidates for providing high glass transition temperature and as materials for gas-separation membranes. These structures have interesting glass transition behavior and free volume properties.10,41,42 Through amorphous atomistic models, the conformational features and packing of chains, torsion distributions, structure factors, radial distribution functions, intermolecular correlations of phenylene rings and carbonate groups, and the free volume distributions are obtained to observe the connection between chemical structure and glassy state properties.

2. SIMULATION METHOD AND COMPUTATIONAL DETAILS The well-parametrized PCFF force field43 successfully applied to polar polymers in the past was used to describe all interactions. Bonded out-of-plane potential interactions and cross terms up to third order were included. Static dielectric constant 3.17 corresponding to the value for BPAPC was used for all polycarbonates, as the different aliphatic chemical substituents of the hydrocarbon type in these PCs are not expected to significantly alter the value. Computations were carried out using Cerius2 chain generation, molecular mechanics and molecular dynamics modules.44 Isolated single polymer chains were generated by assigning random values to backbone torsions. These chains were relaxed using potential energy minimization (steepest descent and conjugate 1580

dx.doi.org/10.1021/jp105954z |J. Phys. Chem. B 2011, 115, 1579–1589

The Journal of Physical Chemistry B gradient methods) and by short canonical molecular dynamics (NVT) runs at 300 K. From the sample set of energy-minimized chains, one chain corresponding to the lowest energy was used for the construction of the amorphous bulk structures using the RIS-based “amorphous-cell” scheme.2,4-6,11,12 The cell sizes used here are sufficient given the results from earlier reports and persistence length of BPAPC, while the same is expected to hold for the substituted polycarbonate chains. The number of repeat units in each type of polycarbonate chain (Table 3S, Supporting Information) was such that the edge lengths of simulation cells was =32 Å based on the experimental density values41,42 for these polymers, corresponding to typical high molecular weights for these PCs. Initial guess structures (>100) were generated for each type of PC by packing a polymer chain in a periodic box with minimum image convention. Use of different vdW scale factor values (that determine the allowable center-ofmass approach distances between two atoms) was explored during the amorphous structure building procedure.2,4-6,44 This feature available with the Amorphous Builder of Cerius2 provides the possibility of variation of vdW scale factors in the generation of well-packed amorphous samples depending on the polymer chemical structure. A lower value of the scale factor reflects a smaller approach distance between the centers of the nonbonded atoms. A value 1 pertaining to very high repulsive interatomic interaction potential energy would mean full overlap of the hardsphere radii of the two approaching atoms. For BPAPC, three scale factors 0.3, 0.4, and 0.5 resulted in successful generation of amorphous cells. For substituted PCs, amorphous samples were constructed using values 0.3 and 0.4. The potential energy of amorphous structures is minimized by standard steepest descent and conjugate gradient methods. Twenty samples out of 100 initial bulk structures were chosen for each chemically different polycarbonate based on energy minimization. The chain dimensions in these samples were found to be close to those of their respective RIS models.5,22 The potential energies were further minimized and these structures were subjected to a short molecular dynamics run of 5 ps at 300 K. Nonbonded interactions defined by vdW and Coulombic terms were truncated at 15.5 Å using a fifth-order spline switching function (12.5-15.5 Å). Structures corresponding to the final snapshot of the MD trajectory were further subjected to energy minimization using conjugate gradient method until the gradient of energy with respect to atom coordinate variations was obtained to be smaller than 0.1 kcal/(mol Å). A final set of 10 independently generated amorphous structures corresponding to BPAPC, BPCPC, TMCPC, DMBPC, and DMPC were used for performing further equilibration and sampling of properties using NVT MD simulations. MD simulations were performed at 300 K using Nose thermostat45 and Verlet algorithm46 with time step 1 fs. All atoms were treated explicitly and all degrees of freedom involving atoms were allowed to vary without constraints. An initial stage of 100 ps MD simulations was performed on each sample. Samples of TMCPC and DMBPC required MD runs of longer duration for acceptable energetics. For BPAPC and BPCPC, after 110-160 ps of simulations, the structures were found sufficiently relaxed with respect to potential and kinetic energies. While the claim is not that these structures represent truly equilibrated glassy states, the structural properties presented here in this paper are static in nature and these are compared for a series of polycarbonates with chemically different repeat units. The simulation procedures are appropriate considering the number of independent samples generated via

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Monte Carlo and relaxed using MD simulations (despite the extent of which being short), in order to cover the phase space. The procedures used here are as extensive if not more compared to those used in earlier studies on BPAPC and other amorphous polymer solely by potential energy minimization method. The values of the mean-squared end-to-end distance, radius of gyration, and solubility parameter of BPAPC are in agreement with the corresponding experimental values. This ensured the validity of these simulated structures in the present work. The atom stresses (not given explicitly here) were observed to be low, thereby indicating sufficient relaxation that is necessary to be achieved in order to estimate physical and thermodynamic properties of the glassy state of amorphous polymers. For TMCPC, DMBPC, and DMPC after 120-200 ps depending on the structure, energies were found to be oscillating at average values. This was followed by 40 ps sampling simulations for physical properties on all equilibrated amorphous cells. Trajectories were recorded every 0.5 ps for analysis. The final snapshot structure of the sampling run, for each independently generated statistical sample, was energy minimized and used for calculation of the cohesive energy densities and solubility parameters (Ecoh and δ). Radial distribution functions and scattering curves over the sample set were obtained from 40 ps trajectories of sampling runs. For each PC, as many as 10 different (in the phase space as generated by RIS Monte Carlo technique) samples were simulated by energy minimization and MD (which corresponds to a sampling of different possible structural states for the same PC). We have calculated the static structural properties averaged over 10 samples for each PC.

3. RESULTS AND DISCUSSION 3.1. Cohesive Energies and Solubility Parameters. Simulated Ecoh and δ values, averaged over the ensemble of microstructures, for each PC are given in Table 1. The calculated dispersive van der Waals interaction energy per atom (averaged over the set of samples) is relatively higher for TMCPC and DMBPC due to increased steric interactions from multiple chemical substitutions. The difference between bulk and single chain vdW energies is lowest for TMCPC followed by that for DMBPC, which is due to largest repulsive energies between the atoms in the glassy structures in these two polycarbonates. These polycarbonates show electrostatic energy values that are relatively less cohesive as compared to those in the packing structures of BPAPC, DMPC, and BPCPC. ΔEvdW and ΔECoulomb are relatively more positive for substituted polycarbonates as compared to BPAPC. The best available experimental δ values for BPAPC47,48 are 9.92 and 9.82 (cal/cm3)1/2 in excellent agreement with the value 9.96 (cal/cm3)1/2 from our simulations. These aliphatic substituted bisphenol PCs show lower solubility parameters as compared to BPAPC. Lower values of CED exemplify reduced intermolecular forces in the bulk state and lower levels of energy stabilization of these PCs. Dispersive nonbonded interactions are found to play a dominant role in determining the CED of these polymers. The relative orders of the difference in vdW energy between the single chain and the bulk, among these polycarbonates, follow the same pattern as the CED and δ. The extent of reduction in δ by the presence of a trimethylcyclohexylidene group at the CR carbon (TMCPC) is greater than that due to presence of the methyl groups on the phenylene rings (DMPC). Our simulations yield lowest values of CED and δ for TMCPC. Additional methyl groups on the substituent cyclohexylidene 1581



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Table 1. Chain Statistics and Solubility Parameters of Amorphous Bulk Polycarbonates from Atomistic Simulationsa cohesive energy density (CED) (cal/cm3) PC

a

Ær2æ/M (Å2 3 mol 3 g-1)

vdW

Coulomb

total

solubility parameter (cal/cm3)1/2

BPAPC

1.06 ( 0.22 (1.12)

91.74

7.48

99.23 ( 2.1

9.96 ( 0.11

BPCPC

0.95 ( 0.12 (0.96)

86.30

6.02

92.33 ( 2.8

9.60 ( 0.14

TMCPC

0.79 ( 0.12 (0.84)

71.11

4.41

75.54 ( 2.3

8.69 ( 0.13

DMBPC

0.85 ( 0.21 (0.80)

80.36

4.11

84.48 ( 3.3

9.19 ( 0.18

DMPC

0.94 ( 0.17 (0.86)

83.92

4.88

88.98 ( 2.0

9.43 ( 0.11

The values in parentheses given for Ær2æ/M correspond to the limiting values of polycarbonates as obtained from RIS models22 at 300 K.

group in TMCPC are responsible for significant vdW repulsive interactions and relatively lower levels of attractive packing energies in the amorphous state thus leading to lower intermolecular interaction energies.. This is in accordance with the interchain distances (packing) from the scattering structure factor analysis described in a later section of this paper. The δ value estimated for TMPC (tetramethylbisphenol polycarbonate) from experimental measurements48 is 9.2 (cal/cm3)1/2 for DMPC which is lower than the value seen for BPAPC. The present simulations yield a value of 9.4 (cal/cm3)1/2 for DMPC which is intermediate between those for TMPC and BPAPC. Specifically, compared to BPAPC, higher δ values are reported for chloral polycarbonate (10.1), tetrabromobisphenol polycarbonate (10.2), and dicyanobisphenol polycarbonate (10.9) which clearly shows an increase in δ due to polar substituents.47,48 Thus, the lower values of CED and δ for substituted PCs (that are devoid of any polar groups and where the substituents are purely aliphatic in nature) when compared to BPAPC are in accordance with experimental observations. 3.2. Conformations. The Ær2æ/M values of the relaxed amorphous structures are given in Table 1. The torsion angle distributions averaged over the ensemble of energy-optimized structures are shown in Figure 2. The probability for trans conformations of the carbonate group (φ2, φ3) is significantly higher as compared to cis. NMR experiments of bulk amorphous BPAPC have shown that less than 10% of all carbonate groups are in the cis conformation; hence trans-trans is dominant as compared to cis-trans.38,39 IR and Raman scattering studies49 on amorphous BPAPC have shown substantial preference for cis-trans (φ2, φ3) conformations at room temperature, in line with earlier atomistic models5 of BPAPC. We see that, in BPAPC, torsion values of the phenylene rings with respect to the carbonate group (φ1 and φ4) are distributed in the entire conformational range with peak maxima at their respective RIS states. 2D-separation field NMR experiments also suggest a disordered distribution for this dihedral angle with the population maxima at 55.38 The torsions representing highly interdependent conformations about the isopropylidene group φ5 (φ6) are restricted within a range of 50-150 with maximum probability at 54. The dihedral angle distribution for BPAPC in the present work is in agreement with the published data from NMR experiments. Experiments suggest that O-Cphenylene dihedral angle (φ1 and φ4) is widely distributed with population maxima where the C-O-C plane forms an angle of 55 with the phenyl ring. In the present work, this dihedral distribution is broad with maxima at 54. From our present simulations, the (φ2, φ3) torsion distribution is predominantly trans,trans as is corroborated from experiments, although the probability of the (cis,trans) conformers is higher than that observed experimentally. This would possibly arise from the amorphous cell building procedure.

The discrete RIS values derived from conformational energy calculations22 on small segments of BPAPC are 50 for φ1 (φ4), 0 for φ2 (φ3), and 50 for φ5 (φ6), and the distributions for the amorphous samples retain their peak maxima at these values. The equatorial (φ6) and axial (φ5) backbone phenylene rings in cyclohexyl-substituted polycarbonates show distinctly different dihedral angle distribution. For PCs with cyclohexyl group, φ5 (axial) and φ6 (equatorial) are not equivalent. Equatorial phenylene rings exhibit a broad distribution in the entire possible range from -180 to 180 whereas the axial phenylene ring are restricted to the range 70-125 in BPCPC and DMBPC. The distribution for the axial ring in TMCPC is, however, significantly narrower due to 1,4-diaxial interactions from the methyl groups on the cyclohexyl ring. φ1 and φ4 distributions for BPCPC and TMCPC are similar to that of BPAPC which shows that the cyclohexyl group as positioned in the polycarbonate chain does not influence the state of torsion angles of the carbonate group in the bulk packed state. Restricted rotations about these Ph-oxy bonds are brought about solely by substituents in the ortho position of the backbone rings, as observed for DMPC and DMBPC. The Ph-oxy torsion (φ1 and φ4) in DMPC and DMBPC is centered around 100 due to steric overlap from the o-Me groups.22 Relatively dense population of torsions at their respective rotational isomeric states occur, although accompanied by a large fluctuation. Conformations energetically unfavorable for the unperturbed chain are observed in the glassy state, though with a lower probability. Although the distributions are broader, maximum probabilities for the various torsions are clustered around their respective intramolecular RIS states.22 This suggests that intramolecular interactions play a large role in the most probable conformations in the bulk, and deviation from these low-energy states is dictated by the intermolecular chain interactions. 3.3. Radial Distribution Functions. The radial distribution function (RDF) profiles are shown in Figure 3. Key features of the RDFs of a few atom pairs common to all five polycarbonates are as follows: (i) intermolecular correlations between the isopropylidene carbons in the range 6-6.5 Å; (ii) these are also observed between carbonyl carbons (cz-cz) within 4-4.5 Å; (iii) weak correlations are observed between the carbonyl oxygens (oo-oo) at ∼3 - 3.5 Å; and (iv) short-range order between the carbonyl carbon atoms and the isopropylidene carbon atoms (cz-c) are observed at around 5.5 Å. Local ordering is also observed for the carbonate oxygen-isopropylidene carbon atom pairs, where a prominent peak at 5.8 Å is seen, with strong order at 7 and 8 Å. A peak of lower intensity at 7.9 Å in this pair arises solely due to intermolecular interactions. Extensive rotational-echo double resonance (REDOR) measurements used to determine local packing in glassy deuterated 1582



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Figure 2. Torsion distributions. Thick dark lines indicate RIS torsions (ref 22) using conformational analysis of isolated bisphenyl and carbonate fragments.

BPAPC have led to reports of various intermolecular distances.34-37 Very short correlation distances were observed: (i) phenylene ring carbon to phenylene ring deuterium distance 2.6 Å, (ii) ringcarbon to methyl-deuterium distance 3.2 Å,35 and (iii) an average intermolecular distance 3.8 Å between carbonyl carbon and nearest-neighbor methyl deuterons.34 90% of the quaternarycarbonyl intermolecular distances were within (20% of an average distance 5.6 Å as found by using DRAMA and CEDRA dephasing spins in the 13C-13C dipolar coupling NMR experiments in BPAPC.36 REDOR studies on a homogeneous blend of carbonate 13C labeled BPAPC and CF3 labeled BPAPC showed that at least 75% of carbonate carbon 13C 3 3 3 F3 nearest neighbors are separated by a narrow distribution of distances 4.7 ( 0.3 Å with most of the 13C 3 3 3 F3 vectors having a preferred orientation relative to the polycarbonate main chain axis. This combination of distance and orientational constraints has been interpreted in terms of local order in the packing the carbonate group of one chain relative to the isopropylidene moiety in a neighboring chain.37 The RDF data for BPAPC from our simulations indicates existence of local order between carbonyl carbons (cz-cz) in the

bulk. The average intramolecular distance between adjacent carbonyl carbon atoms along the BPAPC backbone is 10-11 Å. The cz-cz RDF for BPAPC has a peak at about 4.5 Å which arises solely due to intermolecular interactions. Thus, the intermolecular distance between carbonyl carbons, from the present simulations, is roughly in the same range ((20% of 5.6 Å) as reported earlier using NMR measurements.36 The RDF for the cz-c3 pair (carbonyl carbon-methyl carbon) in BPAPC shows two peaks, one at 3.9 Å of lower intensity and another at 7.4 Å which is of a higher intensity. The intramolecular distance for this pair in BPAPC is in the range 6.5-7.5 Å. Therefore, the higher intensity peak is due to this intramolecular correlation and the peak at 3.9 Å arises exclusively from nearest-neighbor chain interactions in agreement with 3.8 Å from NMR data.34 For the c-c (isopropylidene carbon) atom pair, the maxima at 6.4 Å for BPAPC is due to proximity of an isopropylidene carbon of one chain to the isopropylidene carbon of the nearest-neighbor chain. Along a chain, the intramolecular distance for this pair is about 11-13 Å. For the cz-c pair, shoulder peak at 4.8-5.4 Å arises from the arrangement of carbonyl carbon of one chain relative to the isopropylidene carbon of the nearest-neighbor chain. Another 1583



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Figure 3. Total radial distribution functions of the different atom pairs in PCs as obtained from simulations.

strong pointer to the local short-range order for BPAPC in the bulk as observed from the present simulations is the oo-oo RDF (oo is the carbonyl oxygen of the CdO), which shows a broad peak at 3-4 Å that arises exclusively due to proximity of these groups between the nearest-neighbor chains. The intramolecular distance for the carbonyl oxygens along a chain is in the range of 10-12 Å. The analysis of the RDF data for BPAPC clearly indicates alignment of nearest-neighbor chains with a short-range local order. Intermolecular distances between the isopropylidene carbons (c-c), carbonyl oxygens (oo-oo), and carbonyl carbons (cz-cz) suggest the respective groups in neighboring chains are nearer to each other (for, e.g., carbonyl carbon of one chain nearer to the carbonyl carbon of the nearest-neighbor chain). Another possibility arises from the short distances as observed in the cz-c RDF, which suggest proximity of carbonyl carbon of one chain relative to the isopropylidene carbon of the nearest-neighbor chain. Recent NMR experiments corroborate the latter structural arrangement where a preferred distance and orientation between the isopropylidene moiety of one chain and the carbonate moiety of the nearest-neighbor chain was revealed.37 At least 75% of the carbonyl carbon to F3 (fluorinated methyl at the isopropylidene group) were separated by a narrow distribution of distances 4.7 ( 0.3 Å. Schaefer et al. suggest that nearest-neighbor carbonyl carbon distances of 6 Å as obtained from previous 2D 13C NMR experiments36 arise from chains that are packed with two carbonyl carbons as nearest neighbors with no orientational preferences but not as tightly packed as carbonyl-isopropylidene pairs.37 DMPC shows similar RDF distribution patterns as BPAPC. In all the PCs, short-range local order is observed between the isopropylidene carbons (c-c), carbonyl carbons (cz-cz), and carbonyl oxygens (oo-oo) which suggest a favorable packing of nearest-neighbor chains with similar groups close to each other. As in BPAPC, preferred short intermolecular distances for the cz-c pair (4.8-5.8 Å) is also seen, which suggests the alignment of carbonate group of one chain adjacent to the isopropylidene carbon (BPAPC, DMPC) or cyclohexylidene carbon (BPCPC, TMCPC, DMBPC) of the nearest-neighbor chain. Correlation between the nearest-neighbor cyclohexyl groups could not be

Figure 4. Neutron scattering structure factors of bulk polycarbonates obtained from atomistic simulations.

elucidated from the RDFs here, as the intramolecular peak is of higher probability and the intermolecular peak just could not be differentiated. To summarize, there seems to be two different types of packing of nearest-neighbor chains which is common to all PCs in this study. Analysis of the various RDFs reveals interchain distances of the order of 5-6 Å for the PCs studied here. In the case of BPAPC, calculated distances between the nearest neighbors is about 5 Å from NMR experiments37 which is in agreement with the RDF as well as analysis of scattering data (described in the next section) from the present work. 3.4. Scattering Structure Factors. The static structure factors obtained from the simulations are given by X Æbi æÆbj æðsin krij Þ SðkÞ ¼ ð1Þ krij ij where b corresponds to the scattering lengths of atoms, k is the magnitude of the scattering vector and indices i and j run over all atoms in the chain. These are shown in Figure 4. The observed experimental maxima for BPAPC appear at k values 1.27, 3.1, and 5.3 Å-1. The present simulations for BPAPC show peak positions at k values 1.23, 3.1, and 5.4 Å-1, in good agreement with data from neutron scattering experiments.50,51 The results of the scattering curves presented in earlier reports27,29 show amorphous halo peak for BPAPC at 1.27 Å-1 ascribed to correlation between neighboring chains and the shoulder peak at 0.5 Å-1 ascribed to intramolecular correlations along the chain. 1584



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Table 2. Comparison between Neutron Scattering Data from Simulations and Experimental Values k (Å-1) present atomistic

d (Å) present atomistic

PC

simulationsa

experimentalb

simulationsa

experimentalb

BPAPC

1.23

1.27 (1.21)c

5.10

4.93 (5.19)

BPCPC TMCPC

1.22 1.09

1.26 1.23 (1.20)

5.15 5.76

4.98 5.12 (5.23)

DMBPC

1.17

-

5.37

-

DMPC

1.15

-

5.46

-

a As obtained from simulations in the present study. b The experimental values are from refs 27 and 31. c For comparison, the values given in parantheses are those obtained from coarse-grained simulations of polymer melts as given in ref 29.

In Table 2, peak positions obtained from the present simulation study are shown along with reported data from scattering experiments and earlier atomistic as well as coarse-grain simulation studies. The structure factors obtained from experiments on BPAPC, BPCPC, and TMCPC are available in the low k range (k e 2.2 Å-1).27,31,32 Experimental data shows the amorphous halo for BPCPC at 0.01 Å-1 lower than that for BPAPC (1.26 vs 1.27 Å-1) and the present simulation also yields the same difference for this peak (1.22 vs 1.23 Å-1). For TMCPC, the amorphous halo from experiments is seen at 1.23 Å-1 and coarse-grain simulations showed two peaks at 1.1 and 1.2 Å-1.32 The present simulations yielded a single peak at 1.09 Å-1 for TMCPC. For DMBPC and DMPC also, the amorphous halo is found to be at a lower value (1.17 and 1.15 Å-1) when compared to BPAPC. There is no reported experimental data on these PCs to compare with the present simulation results. While comparing the distance (d) between the neighboring chains, the present simulations tend to overestimate the values for TMCPC, when compared to experimental data. This has been noted also in the case of coarse-grained TMCPC melt simulations.32 The relative trend in the distance between the neighboring chains (d) among the different PCs is found to be in agreement with the experimental neutron scattering measurements (Table 2). More importantly, the present simulations yield a distance of about 5 Å between the nearest-neighbor chains in BPAPC from the neutron scattering analysis (as well as from RDFs) is in agreement with NMR data.37 Our results show that, in the glassy phase, the presence of the cyclohexyl substituent (BPCPC), gives a small increase in the interchain distance, while additional methyl groups on cyclohexyl ring (TMCPC) give the largest interchain distance among the PCs studied here. The presence of the methyl groups on the backbone phenylene rings leads to an increase in the interchain distance, as observed experimentally and by coarse-grain simulations.31,32 We clearly observe that the ortho-substituting methyl groups located on the phenylene rings (5.46 Å for DMPC) are responsible for appreciable changes in the interchain distances as compared to the influence of the CR substituting cyclohexyl group (5.15 Å for BPCPC). The d value for DMBPC, which has both these types of chemical modifications, is higher than that for BPCPC, but is only slightly lower as compared to DMPC. DMBPC has two different types of substitutions, a cylochexyl group as well as methyls on backbone phenyl rings, but still has slightly lower interchain distance compared to DMPC (methyl groups on the backbone phenyl rings). The interchain distance in DMBPC is

smaller than that in TMCPC. This aspect shows that methyl groups as positioned on the cyclohexyl rings lead to a larger separation of the neighboring chains as compared to the effect induced by these groups positioned on the phenylene rings. The d values from our simulations are reasonable when we compare these to experimental bulk amorphous densities of these polycarbonates. BPAPC and BPCPC have similar densities, and the interchain distances for these polymers are also similar. TMCPC has the lowest density among these polycarbonates, and the maximum value of interchain distance as obtained from our simulations is in accordance with its lower density. DMBPC has a higher bulk density (experimental) than DMPC, and our simulation shows a smaller interchain distance for DMBPC, consistent with experiment. Approximate correlation lengths (ξ) can be calculated from the width of the amorphous halos of the simulated scattering curves. Experimental data suggest that the chains in TMCPC are less densely packed than in BPAPC and also less correlated with each other. Previous atomistic simulation studies on BPCPC and TMPC underestimated these correlation lengths as the amorphous halos obtained were much broader than those derived from experiments. The present simulations also yielded very broad amorphous halos and hence the correlation lengths were not calculated. The discrepancy observed in the width of the amorphous halo could be due to the finite size of the amorphous cells used in the simulations, as reported earlier,27 which is about 32 Å, and the experimental correlation lengths of some of these polycarbonates are in the range 19-27 Å. 3.5. Orientations of Phenylene Rings and Carbonate Groups. The orientation correlations of nearest-neighbor phenylene ring planes were determined as per the earlier procedure adopted for rings in polystyrene and BPAPC.52 The phenylene rings in BPAPC are known to show preference for a parallel alignment of their longitudinal 1,4-axis (i.e., smaller angles between their 1,4-axes), while the orientations between their planes were random, as seen from 13C polarization transfer NMR experiments. The carbonate groups show equal preference for both parallel and perpendicular orientations as seen from their distance-factor spectra.52 As seen in Figure 5, for the neighboring ring planes within distance 3.5-6 Å, the probability to have either parallel or perpendicular orientations is almost identical, in agreement with results from earlier experimental report.52 In the 6-10 Å distance range, the angle distribution clearly showed preference for perpendicular alignment of ring planes. For the chemically substituted PCs, the pattern is similar to that for BPAPC. The ring planes show no preference for a particular orientation, at separation distance less than 6 Å. As the inter-ring distance increases, perpendicular orientations are strongly preferred. For BPAPC, the distributions give a higher probability for near-perpendicular orientations of carbonate planes, as shown in Figure 6. For the substituted PCs as well, the carbonate planes have higher probabilities for perpendicular orientations of neighboring groups as well as groups separated by more than 6 Å. The difference is that the likelihood for a near-perpendicular orientation of carbonate planes within 4-6 Å distance is greater for the substituted PCs. 3.6. Free Volume Distributions. The results of the Voronoi tessellation (polyhedra) analysis and the calculation of the available fractional free volume (FFV) are shown in Figure 7. Higher probability for vacant tetrahedrons in the volume range 7-10 Å3 is seen for all polycarbonates. Cyclohexyl-group polycarbonates BPCPC and DMBPC show a similar trend with respect to tetrahedrons of smaller sizes (7-10 Å3), but the 1585



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Figure 5. Angle orientation distributions between the phenyl ring planes. The fractional contributions of the ring pairs from which the distributions were plotted for the distance intervals 3.5-6 in the order for various polycarbonates are (a) BPAPC, 0.256; (b) BPCPC, 0.251; (c) TMCPC, 0.185; (d) DMBPC, 0.14; and (e) DMPC, 0.20.

Figure 6. Angle orientation distributions between the carbonate planes in polycarbonates. The fractional contributions of carbonate pairs from which the distributions were plotted for the distance intervals 4-6 Å in the order for various polycarbonates are (a) BPAPC, 0.254; (b) BPCPC, 0.278; (c) TMCPC, 0.31; (d) DMBPC, 0.266; and (e) DMPC 0.215.

Figure 7. Voronoi volume distributions in bulk amorphous polycarbonates from atomistic simulations.

volume available in the larger size range is lower in the case of DMBPC. Gas permeability and selectivity studies in a series of structurally different polycarbonates have been looked at over the past few years extensively, and researchers have tried to find a correlation between permeability and polymer structure.25,41,42,53-57 Polycarbonates with structural characteristics inhibiting interchain

packing resulting in a higher fractional free volume, as compared to that seen in BPAPC, along with a restricted intrachain rotational mobility (smaller conformational entropy), were found to exhibit higher permeability as compared to BPAPC. Relative to what is seen in BPAPC, a flexible cyclohexyl substituent (BPCPC) is found to facilitate closer packing and lower gas permeability53 as compared to the trimethylcyclohexyl group in TMCPC.25,42 Positronium annihilation lifetime spectroscopic studies of BPAPC and a few substituted PCs have clearly shown that the average hole volume has an inverse correlation with the bulk density.58 Predictive models based on empirical correlations have proposed that the gas diffusion and permeability are controlled by the polymer chemical structure and specific volume.59,60 Further refinements of these have been suggested60 wherein the gas diffusivity in addition to being dependent on FFV was found to be strongly influenced by the chain stiffness and cohesive energy density. The free volume of the simulated bulk structures here was calculated as the ratio of the available volume to the cell volume, averaged over the ensemble of energy relaxed equilibrated structures for each polycarbonate. The values obtained were 0.308 1586



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Table 3. Voronoi Volume Distributions in Polycarbonate Bulk Structures Voronoi free vola

available vol/

PC

(peak max) (Å3)

cell vol (ratio)

FFVb

BPAPC BPCPC

9.5 (0.11); 19.5 (0.08) 9.5 (0.09); 20.5 (0.09)

0.308 0.301

0.164 0.156

TMCPC

6.5 (0.08); 22.5 (0.07)

0.329

0.190

DMBPC

9.5 (0.10); 19.5 (0.07)

0.293

0.113

DMPC

9.5 (0.12); 19.5 (0.07)

0.306

0.149

a

Probability of occurrence of the peak is given in parentheses. b Fractional free volumes reported in refs 41,42 and 53. For DMBPC and DMPC, FFV is calculated from the specific free volume given in ref 41.

(BPAPC), 0.301 (BPCPC), 0.329 (TMCPC), 0.293 (DMBPC), and 0.306 (DMPC). The FFV varies as TMCPC > BPAPC ≈ DMPC > BPCPC > DMBPC. Except for TMCPC, the substituted polycarbonates have lower FFV than BPAPC. DMBPC has the lowest free volume among this set of polycarbonates. FFV for correlating with experimental gas permeabilities is calculated as (V - Vo)/V, where Vo is the polymer occupied specific volume and V is the measured polymer specific volume (inverse of the experimental density). The calculated free volumes from the present amorphous cell simulations and the FFV reported from experimental derivation are given in Table 3. While absolute values of FFV calculated from these two different approaches are not expected to be identical, we are interested only in the relative trend among these polycarbonates. The simulated results for probe radius value 0.5 Å are used for our analysis, following previous study61 wherein the best agreement between MD (atomistic) simulated FFV and that calculated through empirical approach (i.e., using density and the Bondi’s method) was obtained by using a probe radius value 0.4 Å. The values obtained from the present simulations follow the same trend as that reported from previous experimental report41,42,53 where gas permeabilities of a series of polycarbonates have been correlated with FFV. Polycarbonates having methyl substituents at 3,30 positions on the backbone phenylene rings (DMPC)41 as well as those having cyclohexyl group at CR carbon (BPCPC)53 show lower gas permeability than that exhibited by BPAPC, due to the closer intermolecular packing and lower FFV available to diffusant molecules. For BPCPC, the lower free volume is explained on the basis of a better packing in the bulk brought about due to the flexible cyclohexyl substituent.53 On the other hand, TMCPC with additional methyl groups on the cyclohexyl ring has a higher free volume which inhibits chain packing and results in a higher gas permeability value.42 The higher free volume observed for TMCPC from our simulations points to a relatively loosely packed structure which is also confirmed by the simulated scattering structure factor and interchain distance. Oxygen permeability in DMBPC was found to be lowest among a series of 24 structurally different polycarbonates.41 Our simulations yield the lowest value of FFV for DMBPC in agreement with its poor permeability properties. Interchain distance calculated from scattering structure factor is found to be largest for TMCPC among these polycarbonates. Also supporting this is the higher fractional free volumes calculated for this simulated bulk amorphous polymer. Interchain distance in DMBPC is found to be smaller than in TMCPC, which gets to the realization that the methyl substitutions on backbone phenylene rings are less effective in separating out

neighboring chains than those methyls present on the cyclohexyl group. Interestingly the free volume is the lowest for DMBPC polycarbonate, which brings out the type of chemical substituent that provides the most efficient packing. No correlation between free volume and Tg is observed in these polycarbonates. In principle, the free volume in the glassy state (below Tg) is tantamount to the value at the thermodynamic Tg, and as per present knowledge in the field of polymer science, it is related via the Doolitle equation to the Tg value in terms of the universal WLF coefficient (denoted as either “b” or “C2”) and the volumetric thermal expansion coefficient in the melt state (sufficiently above thermodynamic Tg). To our knowledge, no experimental PVT data is available in the literature for these substituted polycarbonates; and, therefore, we can only compare the simulated free volume from our simulations to those available experimentally using PALS. The experimental data for the free volume of such substituted polycarbonates are not available in the literature to our knowledge.

4. CONCLUSIONS The influence of chemical groups and aliphatic substituents on the physical structure in amorphous glassy phase in a series of PCs is explored by molecular simulations. CED is lowered by the aliphatic substituent groups present in the PCs studied here. The cyclohexylidene group at the CR carbon (BPCPC) gives a greater reduction in δ and CED as compared to the effect of the methyl groups on the backbone phenylene rings (DMPC), which is supported by simulated data on the interchain distances (packing) obtained from scattering structure factor analysis. The additional methyls, as on the substituent cyclohexylidene group, as in TMCPC, shows the lowest value of CED and δ are responsible for significant repulsive interactions. Analysis of the RDFs show aspects of distance between nearestneighbor groups in excellent agreement with NMR spectroscopy results from previous studies. Specific features directly related to packing of chains in the bulk are seen. The present simulations show two different types of packing arrangement of nearestneighbor chains in the bulk common to all PCs studied here. The arrangement in which the isopropylidene carbon of one chain is in close proximity to the carbonate carbon of the neighboring chain which is observed in the bulk structures studied here has been noted from REDOR NMR experiments. Nearest-neighbor distances between the carbonyl carbons (4.5 Å) and isopropylidene carbons (6-6.5 Å) are also observed, pointing to the arrangement of these groups as nearest neighbors in the bulk. The present simulations yield a distance of about 5 Å between the nearest-neighbor chains in BPAPC from the neutron scattering analysis (as well as from RDFs) in agreement with NMR data.37 Further substituent groups do not signifacntly increase the interchain distances which for the different polycarbonates studied here is in the range of 5-5.8 Å. The cyclohexyl substituent (BPCPC) gives a small increase in interchain distance, and the additional methyl groups on cyclohexyl ring (TMCPC) lead to the largest distance between neighboring chains. Also, relative to BPAPC, the cyclohexylidene group (BPCPC) does not give appreciable changes in the interchain distance, as compared to having the o-methyl group substituents located on the phenylene rings as in DMPC. However, methyl groups positioned on the cyclohexyl rings lead to a larger separation of neighboring chains in the bulk state when compared to the effect of their positioning on the phenylene rings. The nearest-neighbor phenylene ring 1587


The Journal of Physical Chemistry B planes show no preference for a particular orientation at smaller separation distances. The orientation between nearest-neighbor carbonate groups (interchain) is preferentially normal. The probability for a near-perpendicular orientation of carbonate planes within 4-6 Å distance is greater for the substituted polycarbonates. On the basis of conclusions derived from the trend in the behavior of gas permeabilities in a series of polycarbonates from previous experiments in the literature, the simulations here reaffirm the correct trend as a function of chemical structure. The simulations show that, except in the case of the heavily substituted TMCPC, the fractional free volume is lower in the glassy structures of these chemical-substituted polycarbonates. DMBPC, which has the lowest free volume (closest interchain packing) within this set of poylcarbonates, shows that this type of substitution leads to efficient packing. The interchain distance in DMBPC is also lower than TMCPC, which suggests the chains are closely packed with reduced free volume. Gas permeability of polycarbonates depends on the available free volume to the diffusants. Lower free volume for DMBPC in conjunction with its free rotating chain statistics for the phenylene rings irrespective of the ortho methyl groups leads to lower gas permeation values. On the other hand, higher free volume in TMCPC due to the bulky trimethyl cylcohexylidene group, higher interchain distance, and restricted rotations of the phenyl rings (axial phenyl ring in particular) result in a loosely packed structure with higher gas permeability values. Atomistic models for the substituted PCs presented here thus bring about differences in the macroscopic properties such as gas permeation as affected by subtle changes in the chemical structure in these PCs. To understand more about the packing of chains and their arrangement in the bulk, detailed studies probing the orientations of the different structuiral groups in the PC chain along with refined NMR experiments are required.

’ ASSOCIATED CONTENT

bS

Supporting Information. Atom typing and force-field parameters, simulation box parameters. Details of the number of repeat units in the chains, amorphous periodic cubic box (cell) parameters, cell volumes, and specified experimental densities for the five polycarbonates. Potential energies, chain dimensions, and cohesive energies of all minimized structures after sampling simulations. Contributions to potential energy from bonded and nonbonded interactions for all samples. Variation of potential energy during MD simulations for some cells. The relaxed structures (snapshots) of the polycarbonates subsequent to sampling run times. Free volume distributions and averaged characteristics. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: 91-44-22574184. Fax: 91-44-22574150, 91-44-22574152. Present Addresses ‡

Present address: Department of Chemical Engineering, Indian Institute of Technology (IIT) Madras, Chennai 600 036, India.

’ ACKNOWLEDGMENT M.S.S. thanks the Council of Scientific and Industrial Research, CSIR India (New Delhi), for a Senior Research Fellowship.

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Effect of Chemical Substituents on the Structure of Glassy Diphenyl

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