The dependence of gas permeation on system size in glassy polymers has been tested by creating several models containing different numbers of molecules of the same chain length for the ODPA-ODA homopolyimide and by subsequently determining the permeation characteristics of helium. Eight "standard size" 4150-atom, a 6225-atom, and a much more expensive computationally 56025-atom systems were generated using hybrid pivot Monte Carlo (PMC)-molecular dynamics (MD) single-chain sampling. Following the careful relaxation of the polyimide matrices, helium atoms were then inserted into these systems, and MD simulations were carried out at the same applied external conditions of constant temperature and pressure tensor. Average densities for the pure matrices all fell within 0.7% of the experimental value. Energetic and structural properties as well as solubilities and characterization of the void space were also found to be number independent, thus showing that the preparation procedure gives reproducible and reliable results. Helium diffusion was analyzed over periods up to 20 ns using different approaches, such as observation of the individual trajectories, mean-square displacements, distributions of penetrant displacements components, and van Hove correlation functions. No number dependence could be detected, whether the gas molecules were in the anomalous or in the Fickian regime.

Fully atomistic molecular dynamics (MD) simulations have been carried out on a series of bulk melt pure PEO oligomers and PEO oligomer−silica systems, which differed by their macromolecular end groups. A realistic hybrid model of a silica nanoparticle combining an ionic core as well as the fine-tuning of the surface thickness and number of OH groups per unit surface area was used. The PEO oligomers were decorrelated in all systems under study in order to prevent any artifacts related to the preparation procedure. Significant changes were found to occur in the immediate vicinity of the interface with flattened PEO backbones arranged in densily packed shells and stabilized by the added PEO−silica interactions. Their conformations were also more coiled in order to better adapt to the surface structure. While methyl end groups did not show special characteristics other than their steric effect, hydroxyl end groups had a much higher affinity for the surface and tended to position themselves perpendicular to the surface, thus forming dynamic hydrogen-bonding complexes between the hydroxyl oxygens and the silanol hydrogens. The range of influence of the nanoparticle was evident for structural properties only up to two or three molecular layers, 10−15 Å, but was approximately twice that for dynamical ones.

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Molecular dynamics (MD) simulations are undertaken on a series of five copolyimides based on two different dianhydrides: the flexible 4,4′-oxydiphthalic dianhydride (ODPA) and the rigid bulky bicyclo(2.2.2)-oct-7-ene-2,3,5,6-tetracarboxylic dianhydride (BCDA). The diamines are respectively 4,4′oxydi(phenylamine) (ODA), 2-trifluoride-4,4′-oxydi(phenylamine) (CF 3ODA) and 2-methoxy-4,4′-oxydi-(phenylamine) (MeOODA). These are potential candidates for gas separation membranes, and the effects of increasing BCDA content in ODPA/BCDA copolyimides as well as adding trifluoromethyl or methoxy substituents on the ODA are studied at the molecular level. Amorphous long-chain models are built using a hybrid pivot Monte Carlo/MD sampling preparation procedure. The reproducibility of this approach is tested on a series of eight independently prepared systems. Densities, cohesive energies, Hildebrand parameters, conformational characteristics, intermolecular structures, and the available void spaces are analyzed for each system under study. Both the BCDA moiety and the trifluoromethyl substituent on the diamine are found to have similar consequences on the properties of the copolyimide by decreasing chain cohesion and increasing the available void space. This is related to the steric effect of the BCDA dianhydride, while the trifluoromethyl combines both steric and electronic repulsion. The steric effect of the methoxy substituent on the diamine is not strong enough to significantly differ from the unsubstituted system.

Fluorinated polyimides are interesting polymer materials for gas separation applications because of their good mechanical, thermal, and transport properties. We have performed molecular dynamics simulations (MD) of CO2 sorption and desorption in three fluorinated polyimides: 6FDA-6FpDA, 6FDA-6FmDA, and 6FDA-DAM. These polyimides are known to vary significantly in their gas permeation properties. A stepwise procedure was used to insert CO2 molecules into the previously prepared polymer matrices in order to mimick the experimental procedure of progressive loading and to avoid the necessity of preswelling the samples. An iterative technique was then used to estimate the vapor pressure of CO2 that would have to be applied in order to obtain the imposed uptake. The resulting sorption isotherms are found to be in relatively good agreement with their respective experimental curves, and the trend in solubility was reproduced (6FDA-DAM > 6FDA-6FpDA > 6FDA-6FmDA). Desorption isotherms were also calculated starting from systems corresponding to an applied pressure of 60 bar. Hysteresis was evident even upon immediate unloading. Changes in volume, void space, potential energies, etc., have been characterized and compared to experimental data and to theories of gas sorption and plasticization in glassy polymers.

Extensive molecular dynamics (MD) simulations of 6FDA-6FpDA, 6FDA-6FmDA, and 6FDA-DAM polyimides with CO 2 weight percentages up to ∼30%, were carried out to characterize the atomic level features associated with CO 2 diffusivity in these glassy matrices. The fluorinated polyimide models were first loaded with CO 2 in increments of 2% in order to mimic the experimental procedure of progressive loading and to avoid the necessity of artificially preswelling the simulation boxes. The sorption phase was then followed by a progressive desorption phase in decrements of 2%. This work covered nominal CO 2 concentrations up to ∼200 cm 3 (STP) cm -3 and amounted to a total of more than 80 simulations of 5000 ps each at 308 K, as well as an additional 20 simulations at higher temperatures. In all cases, CO 2 trajectories display the basic hopping-type mechanism, i.e. a combination of oscillations within available free volumes in the polymer matrix associated with occasional jumps from one site to another. There are no longlived interactions with either the polymer or with the other penetrants, and thus, CO 2 is a very mobile penetrant free to access any part of the matrix free-volume. Diffusion coefficients, D CO 2 , at 308 K were estimated from a novel trajectory-extending kinetic Monte Carlo (TEKMC) method, which, based on the actual CO 2 trajectories during the MD production runs, allowed us to extend them by more than 3 orders of magnitude. These estimates of D CO 2 compare very well with those obtained by a high-temperature Arrhenius extrapolation approach and with experimental evidence. Activation energies for diffusion are also validated by experimental data. All three polyimide models are able to reproduce both experimental penetrant-induced plasticization and sorption-desorption hysteresis during the few nanoseconds time scale available to MD simulations. The D CO 2 are found to be very closely linked to the volume swelling-contraction behavior. They tend to remain low up to the start of plasticization and to be directly correlated to the gradual transition to an almost linear increase in volume at higher concentrations. The sorption-desorption hysteresis can be related to a fairly limited increase in polymer local mobility upon volume dilation, which means that the system is not able to come back to its initial structure upon desorption.

Gas permeation has been studied in two fully atomistic molecular models of a glassy polyimide, which differ by their chain configurations and packing. The first polyimide system is an isotropic 56 025-atom bulk model of the amorphous phase while the second is a 141 100-atom model of an actual membrane. The preparation procedure of the membrane was based loosely on the experimental solvent-casting process. The membrane model exhibits density oscillations at the interfaces with chains being aligned and flattened parallel to it. The structuration persists throughout the membrane, and this leads to the gas diffusing in a slightly anisotropic way in the center of the membrane model. However, the diffusion coefficient obtained using either approximate analytical solutions or numerical solutions to the one-dimensional diffusion equation as well as a time-lag approach was found to be very similar to that in the bulk, which was evaluated from mean-square displacements, probability density distributions of displacement vector components, and the van Hove self-correlation function. Solubilities obtained from Widom's insertion technique and from the equilibrium density of gas within the matrix were in very good agreement for the membrane model. Despite a small drop in solubility in the region corresponding to the density peak of the polymer at the interface, the solubility coefficient also remained similar to that of the bulk. The changes in configurations and the high-density interface have thus little effect on the permeability of the gas used in this case.

Molecular dynamics (MD) simulation holds great promise as a source of otherwise elusive information concerning ionic conduction mechanisms occurring in the amorphous phases of polymer electrolytes. However, most polymer/salt complexes have a multiphase character at temperatures of interest. Insights into crystalline phases may thus prove meaningful in the subsequent design of strategies to decrease the degree of crystallinity in these systems. We report here the full details of a molecular dynamics model (‘‘md’’ model) for the crystalline phase of the widely used host-polymer poly(ethylene oxide) (PEO). Force-field and computational parameters are optimized to give realistic behavior for crystalline PEO. Analyses of the structure and dynamics obtained from the MD simulations performed at 300 K include mean-square displacements, x-ray powder diffractograms, distributions of bond and torsion angles, and radial distribution functions. These are compared with experimental data, the static x-ray determined PEO structure and that obtained using a ‘‘tethered’’ model, in which the atoms are attached by springs to their initial crystalline positions, and allowed to move according to their experimental mean-square displacements. Agreement is good, but the reliability of the x-ray refined positions is questioned.