Computer simulation of polymer networks: swelling by binary Lennard-Jones mixtures

The swelling of regular, tightly meshed model networks is investigated by a molecular-dynamics-Monte Carlo hybrid technique. The chemical equilibrium between two simulation boxes representing the gel phase and a solvent bath, respectively, is obtained by subjecting the Lennard-Jones particles of a binary mixture, serving as explicit solvent, to the particle transfer step of Gibbs ensemble-Monte Carlo. The swelling behavior, especially preferential absorption of a single component, whose dependence on temperature, pressure, and fluid composition is studied, also depends significantly on the size of the central simulation cell. These finite-size effects correlate well with those exhibited by the density of solvent-free (dry) networks. A theoretical expression, whose derivation is based on network elasticity (of dry networks) yields finite-size scaling behavior in good accord with simulation results for both dry networks and gels in contact with solvent baths. This expression can be used to extrapolate the swelling behavior of simulated finite systems to infinite system size.     

Behavior of a polymer chain immersed in a binary mixture of solvents

The behavior of a polymer chain immersed in a binary solvent mixture is investigated via a single-polymer simulation using an effective Hamiltonian, where the solvent effects are taken into account through a density-functional theory for polymer-solvent admixtures. The liquid-liquid phase separation of the binary solvent mixture is modeled as that of a Lennard-Jones binary fluid mixture with weakly attractive interactions between the different components. Two types of energetic preferences of the polymer chain for the better solvent-(A) no preferential solvophilicity and (B) strong preferential solvophilicity-are employed as polymer-solvent interaction models. The radius of gyration and the polymer-solvent radial distribution functions are determined from the simulations of various molar fractions along an isotherm slightly above the critical temperature of the liquid-liquid phase separation. These quantities near the critical point conspicuously depend on the strength of the preferential solvophilicity. In the case where the polymer exhibits a strong preferential solvophilicity, a remarkable expansion of the polymer chain is observed near the critical point. On the other hand, in the case where the polymer has no preferential solvophilicity, no characteristic variation of the polymer conformation is observed even near the critical point. These results indicate that the expansion of a polymer chain enhances the local phase separation around it, acting as a nucleus of demixing in the vicinity of the critical point. This phenomenon in binary solvents near the liquid-liquid critical point is similar to the expansion of the polymer chain in one-component supercritical solvents near the liquid-vapor critical point, which we have reported [T. Sumi and H. Sekino J. Chem. Phys. 122, 194910 (2005)].     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.     

Molecular simulation of binary mixture adsorption in buckytubes and MCM-41

MCM-41 and buckytubes are novel porous materials with controllable pore sizes and narrow pore size distributions. Buckytubes are carbon tubes with internal diameters in the range 1–5 urn. The structure of each tube is thought to be similar to one or more graphite sheets rolled up in a helical manner. MCM-41 is one member of a new family of highly uniform mesoporous silicate materials produced by Mobil, whose pore size can be accurately controlled in the range 1.5–10 nm. We present grand canonical Monte Carlo (GCMC) simulations of single fluid and binary mixture adsorption in a model buckytube, and nonlocal density functional theory (DFT) calculations of trace pollutant separation in a range of buckytubes and MCM-41 pores. Three adsorbed fluids are considered; methane, nitrogen and propane. The GCMC studies show that the more strongly adsorbed pure fluid is adsorbed preferentially from an equimolar binary mixture. Ideal adsorbed solution theory (IAST) is shown to give good qualitative agreement with GCMC when predicting binary mixture separations. The DFT results demonstrate the very large increases in trace pollutant separation that can be achieved by tuning the pore size, structure, temperature and pressure of the MCM-41 and buckytube adsorbent systems to their optimal values.     

An analysis of the swelling equilibrium of an ionic polymer network in a binary liquid mixture

An equation which represents the swelling equilibrium of an ionic polymer network in a binary liquid mixture is introduced and evaluated numerically. Discontinuous volume changes are obtained with pertinent values of the parameters. From two types of dependence of the degree of ionic dissociation on the composition of a liquid mixture, two types of volume transitions of an ionic gel are illustrated. One is the transition typically seen in acrylamide gels, and the other is a re-entrant transition typical of isopropylacrylamide gels. The selective dissolution factor of two liquids into a swollen polymer network also becomes discontinuous in accordance with the discontinuous volume change. Transition points and the spinodal line are calculated from a generalized form of the free energy change of the swollen gel system. © 1994 John Wiley & Sons, Inc.     

Computer simulation of the liquid crystal formation in a semi-flexible polymer system

Molecular dynamic simulations are reported for system of semi-flexible linear rod-like molecules. The molecules are composed of N_c tangent soft spheres, connected by elastic springs. Rigidity is introduced by additional springs between all pairs of spheres along the molecule. The formation of only a nematic LC phase is shown for all systems with N_c = 8 and different flexibility. The effect of flexibility on the order parameter and the volume fraction at the LC phase transition is compared with theoretical predictions by Khokhlov-Semenov and with available simulation data. The dependence of the anisotropy of diffusion on chain flexibility in LC phase was studied. The polymer brushes consisting of flexible and semi-flexible (composed of linear rod-like segments) chains were simulated at different grafting densities. Height of brush, order parameter, distribution of density and chain ends in brush were obtained in both cases and compared with theoretical predictions.     

Computer simulation of geminate recombination in non-crystalline polymer solids

A computer simulation method is applied to model geminate charge recombination in non-crystalline polymer solids that exhibit charge transport anisotropy due to different intra- and interchain hopping rates. We investigate how the electron escape probability is affected by both the degree of charge transport anisotropy and morphology of polymer systems.     

Crystallization of a binary Lennard-Jones mixture

Transition interface path sampling combined with straightforward molecular dynamics simulation was applied to study the mechanism and kinetics of the crystallization of an undercooled 3:1 binary Lennard-Jones mixture with diameter ratio 0.85 and equal interaction strengths. We find that this mixture freezes via the formation of crystalline clusters consisting of a fcc-rich core and a bcc-rich surface layer, with an excess of large particles and particle species distributed randomly. A detailed comparison reveals that the transition mechanism is similar to that of the pure fluid but occurs with much smaller nucleation rates even at comparable degrees of undercooling. Also, the growth of the crystalline cluster in the mixture proceeds at a pace about 1 order of magnitude slower than in the pure system. Possibly, this slow dynamics of the mixture is related to the occurrence and subsequent relaxation of icosahedral structures in the growing crystal as well as in the liquid surrounding it.     

Computer simulation of the formation of polymer networks

Complex crosslinked polymer structures can be quite easily modeled with the aid of computers. BTOSYM's implementation of an algorithm that has been developed by Eichinger and his co-workers over the last few years is described. This algorithm allows us to model both random (as in sulfur-cured rubber) and site-specific (as in end-linked silicones) crosslinking reactions. The simulation method provides detailed information on gel points, cycle rank, modulus of elasticity and other characteristics of the networks as they are formed. Illustrative results obtained with the program are presented.     

Evaporation of a binary liquid mixture

An apparatus was designed to measure the evaporation rates of the components comprising a binary liquid mixture, from a horizontal surface, under condi Evaporation studies were conducted on the ethanol-water system. The effects on the evaporation rate of air velocity and liquid composition were investiThe experimental evaporation rates were shown to depend on vapour pressure driving force. For the pure component, the evaporation exhibited a direct li For ethanol-water mixtures the total and ethanol component evaporation increased with increasing ethanol concentration, while that of the water compone     

Permeation of binary gas mixture through glassy polymer membranes with concentration-dependent diffusivities

An analytical solution has been obtained for the modified dual-mode mobility model for a single gas proposed by Zhou and Stern and extended to a binary gas mixture to describe the pressure dependence of mean permeability coefficients for CO₂ and CH₄ mixtures in homogeneous cellulose triacetate membranes. The permeabilities calculated from the model fitted the corresponding experimental results quite well. Permeation experiments for equimolar CO₂ and CH₄ mixture in a homogeneous membrane of methyl methacrylate and n-sbutyl acrylate copolymer were performed along with sorption experiments for pure CO₂ and CH₄ to test the applicability of the model. The experimental permeabilities were close to those calculated from the model.     

Surface-directed phase separation via a two-step quench process in binary polymer mixture films with asymmetry compositions

Surface-directed phase separation via a two-step quench process in asymmetry polymer mixtures is numerically investigated by coupling the Flory-Huggins-de Gennes equation with the Cahn-Hilliard-Cook equation. Two distinct situations, i.e., the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed, respectively. The morphology and evolution dynamics of the phase structure, especially the secondary domain structure, are analyzed. The wetting layer formation mechanisms during the two-step quench process are examined. The simulated results demonstrate that different secondary domain structures in these two situations can be induced by the second quench with deeper quench depth, which can be used to tailor phase morphology. It is also found that, in the second quench process, the evolution of the wetting layer thickness can cross over to a faster growth when the preferential component is the minority component. In this situation, the formation mechanism of the wetting layer will change and is eventually determined by the second quench depth. However, when the preferential component is the majority component, a deeper second quench depth corresponds to a slower growth of the wetting layer thickness. The chemical potential is calculated to explain the difference regarding the growth dynamics of the wetting layer thickness between these both situations.     

Lamellar morphology induced by two-step surface-directed spinodal decomposition in binary polymer mixture films

A novel process for obtaining ordered morphology on the basis of two-step surface-directed spinodal decomposition is numerically investigated. The formation mechanism and evolution dynamics of this process are also discussed in detail. The calculated results of the chemical potential demonstrate that the equilibration state at the first quench affects the competition between the surface potential and the chemical potential in the bulk, leading to a surprising lamellar structure at the second further quench. It is also found that the lamella formation obeys the logarithmic growth. These results could provide a new approach for fabricating ordered structure of polymer materials and stimulate experimental studies based on this subject.     

Adsorption of gas-water binary systems in carbon micropores: Computer simulation

The adsorption of gas-water mixture in micropores of carbon materials at 298 K has been studied using computer simulation. Methane, nitrogen, ammonia, carbon dioxide, and hydrogen sulfide were considered as gas components. In the grand canonical ensemble Monte-Carlo simulation of adsorption, the displacement of a gas component from a pore as a result of the formation of water microclusters was observed for all systems studied. Cluster growth conditions on graphite-like and activated surfaces differ significantly. The comparative stability of adsorbed gas-water mixtures has been determined for all gases.     

Computer simulation for the pervaporation process of wate/ethanol mixture through interpenetrating polymer network (IPN) membranes

In this study, the pervaporation behavior of EtOH-water mixture through interpenetrating polymer network (IPN) membranes was predicted. The pervaporation characteristics of single component membranes were modelled according to the “six coefficients model” proposed by Brun [J. Membrane Sci., 23 (1985) 257]. In the case of the IPN membrane, two models were proposed according to the phase structure of the IPN. For a uniphase membrane with no phase separation, the compositional averages of the single component membrane coefficients were used. In the case of the phase separated IPN, two cases exist. The first is the island and sea model: one phase is continuous and the other is discrete. The second is the cocontinuous model, in which two continuous phases exist. For these cases the permeation rate and separation factor of the IPN membrane were calculated using the experimental sorption data and pure component values for each IPN composition. Comparison with the experimental data indicates that these models could be to predict the performances of IPN membranes depending on the morphology of the IPN.     

Computer simulation of dilute polymer solutions in transient elongational flows

The behaviour of polymer molecules in solution flowing through a succession of contraction‐expansion zones was simulated using the Brownian dynamics method. The velocity profile of the flow field calculated previously, assuming that the flow modification in dilute polymer solution is negligible, was used. In the vicinity of the cell symmetry axis the flow can be described as an oscillatory elongational planar flow. The dumbbell with conformation‐dependent friction and elastic coefficients was chosen as a model for the polymer chain. When the initial state of the polymer chain entering the first contraction zone had corresponded to a gaussian coil the initial increase in the polymer deformation along the flow direction was observed. After some time independent of the flow rate, the amplitude of deformation gradually decreased to the stationary value further in the cell where the polymer deformation followed the flow oscillations. The amplitude of the deformation oscillations showed the critical behaviour: they increased for flow rates less than a critical value and did not change with further increase in the flow rate.     

Construction of a disorder variable from Steinhardt order parameters in binary mixtures at high densities in three dimensions

Using molecular dynamics simulation, we investigate the structural disorder in crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of N(1) + N(2) = 4096 particles at a low temperature in three dimensions. The size ratio σ(2)/σ(1) between the large and small particles is either 1.2 or 1.4. The crossovers among these states occur, as the composition of the large particles c = N(2)/(N(1) + N(2)) is varied. We define a disorder variable D(j) for each particle j in terms of local bond order parameters based on spherical harmonics (Steinhardt order parameters). Stacking faults and grain boundaries in fcc polycrystal and mesoscopic structural heterogeneity in glass are then visualized. At small c, disturbances of large particles is stronger for larger σ(2)/σ(1). At large c, the transition between glass and polycrystal occurs nearly discontinuously at c = c(c) ~ 0.8. At σ(2)/σ(1) = 1.4, microphase separation occurs in polycrystal states with c > c(c), where fcc crystal grains comprising the large particles are enclosed by amorphous layers composed of the two particle species.