Study on the gas permeabilities in styrene-butadiene rubber by molecular dynamics simulation

In this research, molecular dynamics (MD)simulations were used to study the transport properties of small gas molecules in the butadiene-styrene copolymer(SBR). The condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field was applied. The diffusion coefficients were obtained from MD (NVT ensemble) and the relationship between gas permeability; the chemical structure and free volume of butadiene-styrene copolymer were investigated. The results indicated that the diffusion coefficient of oxygen declined with increasing styrene content. The fraction of free volume (FFV) in butadiene-styrene copolymer was calculated. It was concluded that diffusion coefficient increased as the FFV increases, which is in accordance with the analysis of the small molecular hop through the free volume in polymer matrix. Subsequently, the glass transition temperatures of these copolymers were calculated by MD. The result showed that the glass transition temperature increased with increasing styrene content in polymer.     

Oxygen and carbon dioxide transport through high barrier polyester blends

The transport of oxygen and carbon dioxide through a set of random copolymer films based on poly(ethylene terephthalate) (PET) and poly(ethylene 2,6‐naphthalate) (PEN) were explored. Diffusivity and permeability of both gases decreased with increasing PEN content. The oxygen and carbon dioxide diffusion coefficients decreased 74 and 82% from pure PET to pure PEN, respectively. The presence of stiffer PEN moieties had an effect on the glass transition temperature (T_g) of PET/PEN blends and gas barrier. In the complete range of tested blends, the differential scanner calorimeter analysis displayed a single value of thermal glass transition temperature. As the PEN content was increased, the fractional free volume (FFV) and the diffusion coefficients of the blends were decreased. The Doolittle equation provided the best fit for diffusivity and FFV and showed that the gas transport behavior was better understood when it was taken into consideration the cohesive energy of blends. As the PEN content in films was increased, their rigidity and the glass/rubber transition temperature were increased, and their capacity to be penetrated by small molecules like O₂ and CO₂ was decreased. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Properties of random and block copolymers of butadiene and styrene. II. Melt flow

Flow curves, log (rate of shear) versus log (shear stress), as functions of temperature were obtained for several butadiene-styrene copolymers of fixed (25%) styrene content, differing in monomer sequence distribution. A random copolymer of constant composition along the polymer chain and narrow molecular weight distribution (MWD) exhibited behavior similar to linear, narrow MWD polybutadienes; the flow was Newtonian at low shear stresses, and the flow curves for various temperatures were accurately superimposable by a shift along the log (shear rate) axis. In a random copolymer varying in composition along the polymer chain, non-Newtonian behavior was more pronounced, and temperature-shear rate superposition did not succeed, a trend further perpetuated in copolymer of a single long styrene block sequence. The latter resemble branched polymers, as would be expected from association of the styrene blocks. With two styrene blocks, association produces network structures below the glass transition of polystyrene with consequent loss of flow. Disruption of these associations above T_g (styrene) imparts the greatest thermoplasticity to these elastomers. There is evidence, however, that some of the associations persist at temperatures well in excess of T_g (styrene).     

Effect of fractional free volume and Tg on gas separation through membranes made with different glassy polymers

The aim of this work is to study how the characteristics of the polymer used to manufacture gas separation membranes influence its permeability and selectivity. It has been shown that the gas diffusivity decreases with the kinetic diameter of the gas except for CO₂, probably due to its high condensability. While solubility increases with the gas condensation temperature and clearly with the glass transition temperature of the polymer for each gas. The permeabilities of CO₂, CH₄, O₂, N₂ increase for increasing glass transition temperatures. Nevertheless only the selectivity of CO₂ versus the other gases increases significantly when polymers with high glass transition are used. The Robeson limit in a selectivity‐versus‐permeability plot is approached for CO₂/CH₄ when T_g increases. This distance to the Robeson limit, for this pair of gases, results to decrease for increasing T_g. For the case of the O₂/N₂ selectivity remains approximately constant with an appreciable increase in permeability for polymers with increasing T_g. Permeability increases due to the corresponding increase in fractional free volume, FFV, that appears for increasing glass transition temperatures, T_g. This correlation of FFV with T_g has been confirmed by obtaining FFV by different methods. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Relationship between the gas transport properties and the refractive index in high‐free‐volume fluorine‐containing polyimide membranes

The refractive index and gas transport properties (i.e., permeability, diffusivity, and solubility) in the 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride (6FDA)‐based polyimides were systematically investigated in terms of their polymer fractional free volumes (FFVs). The permeability and diffusion coefficients of the 6FDA‐based polyimide membranes to hydrogen, oxygen, nitrogen, methane, and carbon dioxide were correlated with their FFVs, which were estimated with van Krevelen's group contribution method. Linear correlations were also observed between the gas transport properties and the refractive index of these polyimides. We described FFV as a function of the refractive index based on the Lorentz–Lorenz equation. Linear correlations were observed between their refractive‐index‐based FFVs and the gas permeability, diffusivity, and solubility coefficients of these 6FDA‐based polyimides membranes. However, the FFVs of the 6FDA‐based polyimides calculated from refractive index were 1.16–1.37 times larger than their FFV values. This FFV was dependent on the free‐volume space and optical factors, such as the refractive index and molar refraction, which affected the electronic structure and the interactions between the gas molecules and the polymer segments. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Chain structure,linear viscoelasticity and extensional rheology of poly(4-vinyl biphenyl-stat-styrene) statistical copolymers

A series of statistical copolymers of 4-vinylbiphenyl and styrene were prepared via free radical polymerization to investigate the effect of the comonomer ratio on their microstructure and rheological properties. The glass transition temperature of the copolymers follows a nonlinear monotonic decreasing dependence with increasing styrene content which is well described by the Gordon-Taylor equation. WAXS measurements reveal that both the backbone to backbone and the inter-phenyl distances (d₁ and d₂, respectively) are decreasing functions of the styrene content in the copolymers. The apparent monomeric friction coefficient, calculated from dynamic frequency sweeps in the linear viscoelastic regime, decreases exponentially with the styrene content in the copolymer. We postulate that the strong effect of the copolymer composition on the friction coefficient is due to the larger overlapping distance between phenyl rings of adjacent polymer chains (d_overlap), giving rise to stronger aromatic π–π interactions, which in turn results in stronger friction between adjacent chains. The increase in d_overlap and monomeric friction coefficient also leads to a significant increase in the extensional strain hardening measured during extensional startup flow measurements.     

Molecular simulation on penetrants diffusion at the interface region of organic-inorganic hybrid membranes

Detailed atomistic structures of blend (class I) and chemical tethered (class II) poly vinyl alcohol (PVA)-silica hybrid membranes were constructed to investigate the diffusion behavior of small molecules at the interfacial region. Stronger interaction between PVA and silica, as well as more appropriate interfacial morphology which was evaluated by interchain distance, chain mobility and free volume were found in class II hybrid membranes due to the presence of covalent bonds. The effects of interfacial morphology on diffusion behavior of small molecules including benzene and cyclohexane were tentatively explored, and found that diffusion coefficients were closely related to fraction of free volume (FFV). Subsequently, the diffusion selectivity was calculated by the ratio of FFV probed by benzene and cyclohexane molecules. Hopefully, this study will offer some important qualitative insight into the transport phenomena within organic-inorganic hybrid membranes.     

The effect of styrene grafting on the diffusion and solubility of organic liquids in polyethylene

The effect of grafting styrene onto low-density polyethylene on the diffusion and solubility of benzene and n-hexane in the graft copolymer has been investigated. The diffusion coefficient at zero concentration D_{c = 0} for both benzene and n-hexane decreased with the amount of styrene grafting in the polyethylene–styrene graft copolymer membrane. The free volume parameters of the polyethylene–styrene graft copolymer were calculated using benzene and n-hexane as the diffusing species. Results show that there is a large decrease in free volume as grafting proceeds and the effect is more pronounced at low levels of grafting. Solubility was found to be a function of the per cent grafting, there being a 50%–90% increase in benzene solubility in a 26% graft compared to polyethylene. The increase in solubility for n-hexane was considerably lower. The effect of crystallinity on the free volume parameters has also been calculated.     

Correlation of penetrant transport with polymer free volume: Additional evidence from block copolymers

The transport rates of methanol and water through a series of PEBAX® block copolymers were measured and correlated with the fractional free volume. Excellent agreement between the logarithm of the diffusion coefficient and the inverse of the fractional free volume of the polymer was observed. This provides new evidence of the utility of the free volume theory to describe the transport of highly condensable vapours. Correlation was also quite good when the logarithmic additivity relationship was employed. This relationship has been previously shown to correlate the properties of homogenous blends with copolymer composition. The successful use of this theory for a series of blends that exhibit two glass transition temperature is discussed.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Molecular dynamics simulations to compute diffusion coefficients of gases into polydimethylsiloxane and poly{(1,5‐ naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide]}

Diffusion coefficients of N₂, O₂, CO₂ and CH₄ at 298 K in polydimethylsiloxane (PDMS) and poly{[(1,5‐naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide]} (6FDA‐1,5‐NDA) polymers have been estimated using molecular dynamics (MD) simulations. Estimated diffusion coefficients in PDMS decrease systematically with increasing size of the penetrant gas molecules following the experimental observations. For 6FDA‐1,5‐NDA polymer, diffusion coefficients decrease in the same order of magnitude, but differ in their sequential order, due to varying side group interactions of the polymer with the gaseous molecules. Cohesive energy density, solubility parameter and free volume of the polymers were determined using MD simulations. Reliability and accuracy of the simulations have been tested typically with the computed values of the diffusion coefficient of O₂ in PDMS polymer, which compare well with the literature data. X‐ray scattering profiles of 6FDA‐1,5‐NDA have been generated to understand the interrelationship between the morphology and diffusion coefficients. The radial distribution function was evaluated to find the contribution of atoms that are important in understanding the molecular interactions during gas diffusion in polymers. Copyright © 2007 Society of Chemical Industry     

Diffusion of radioactively tagged penetrants through random and block styrene–butadiene copolymers and filled cis-polybutadiene

The diffusion of radioactively tagged n-hexadecane in trace amounts has been studied in 22 random styrene–butadiene (SBR) copolymers with different styrene contents and butadiene microstructures; in several SBR block copolymers with different average block lengths (also diffusion of tagged 1,1-diphenyl ethane); in a triblock SBR copolymer cast from different solvents and also molded at elevated temperature; and in cis-polybutadiene filled to different extents with carbon black, calcium carbonate, and microglass spheres. The diffusion coefficient in random SBR copolymers decreased with increasing content of styrene and/or vinyl configuration and could be correlated with fractional free volume on the basis of linear additivity of the cis, trans, vinyl, and styrene moieties. In SBR block copolymers, the diffusion coefficient increased with increasing average block sequence length. For the triblock copolymer, the diffusion coefficient was approximately the same for samples molded or cast from solvents which are good for polybutadiene, but was far smaller for a sample cast from ethyl acetate, in which the polystyrene domains are probably lamellar. The effect of fillers on diffusion in cis-polybutadiene was compared with calculations on the basis of several theoretical models.     

分子动力学模拟预测壳聚糖的玻璃化转变温度

为了预测壳聚糖的玻璃化转变温度,在COMPASS力场和恒温恒压（NPT）系综条件下,利用分子动力学模拟方法,在343～543 K温度范围内研究了壳聚糖的玻璃化转变行为,通过模拟体系在不同温度下的比体积、回转半径和能量参数,获得了壳聚糖的玻璃化转变温度(T_g)。研究结果表明,壳聚糖的比体积、回转半径、内能随温度有规律的变化并在T_g处发生转折。模拟计算得到的壳聚糖的T_g与实验方法获得的值基本相符,分子动力学方法可用于壳聚糖玻璃化转变温度的预测。其中,通过回转半径-温度曲线获得的T_g与实验值最相符,回转半径是影响玻璃化转变的一个重要因素,可用于预测聚合物的玻璃化转变温度。     

Water vapor/propylene sorption and diffusion behavior in PVA-P(AA-AMPS) blend membranes by GCMC and MD simulation

Detailed atomistic structures of blend membranes (poly vinyl alcohol (PVA)/(acrylic acid-co-2-acrylamido-2-methylpropylsulfonic acid) (P(AA-AMPS)) were constructed to investigate the sorption and diffusion behavior of gas molecules (water and propylene) in the membranes. Interaction and miscibility between PVA and P(AA-AMPS) were calculated, and it was found that strong intermolecular interaction resulted in good miscibility of PVA and P(AA-AMPS) in the blend. The polymer chains mobility and free volume properties of the blend membranes were characterized. The sorption quantities and sorption sites of water and propylene in the blend membranes were calculated using Grand Canonical Monte Carlo (GCMC) method. The diffusion coefficients of water in the blend membranes were calculated by molecular dynamics (MD) simulation. The simulated results of the membrane structure (chain mobility, free volume properties), the sorption quantities and diffusion coefficients of water/propylene in the blend membranes showed the identical changing trends as the experimental results. Hopefully, this study could offer qualitative insight into the mass transport phenomena within the blend membranes.     

Polymer–CO2 systems exhibiting retrograde behavior and formation of nanofoams

The sorption of compressed gases in polymers causing a reduction in the glass transition temperature (T_g) is well established. There is, however, limited information on polymer–gas systems with favorable interactions, producing a unique retrograde behavior. This paper reports on using a combination of established techniques of in situ gravimetric and stepwise heat capacity (C_p) measurements using high‐pressure differential scanning calorimetry (DSC) to demonstrate the occurrence of this behavior in acrylonitrile–butadiene–styrene copolymer (ABS)–CO₂ and syndiotactic poly(methyl methacrylate) (sPMMA)–CO₂ systems. The solubility and diffusion coefficient of CO₂ in the range 0 to 65 °C and pressures up to 5.5 MPa were determined, which resulted in a heat of sorption of ? 15.5 and ? 15 kJ mol^?1, and an activation energy for diffusion of 28.3 and 32.1 kJ mol^?1 in the two systems, respectively. The fundamental kinetic data and the changes in C_p of the polymer–gas systems were used to determine the plasticization glass transition temperature profile, its relationship to the amount of gas dissolved in the polymer, and hence the formation of nano‐morphologies. Copyright © 2006 Society of Chemical Industry     

Molecular simulations of gas transport in nitrile rubber and styrene butadiene rubber

Nitrile rubber (NBR, 39:61 wt% of acrylonitrile:butadiene) and styrene butadiene rubber (SBR, 50:50 wt% of styrene:butadiene) matrices have been equilibrated by molecular dynamics (MD) simulations. Transition-state approach is used to calculate the diffusion and solubility coefficients of small penetrants in these matrices, indicating quite low values in NBR and reasonable agreement with experimental results. MD simulations have been performed to analyze water diffusion in these matrices. Aggregation of water molecules is observed in the hydrophobic matrix SBR. MD simulations with fictitious nonpolar water molecules inhibit aggregation and lead to enhanced diffusion in SBR. In NBR there is a slight increase in diffusion for fictitious water molecules. The lower diffusion constants in NBR result from slower local relaxation of the matrix due to tighter intermolecular packing and higher cohesive energy density. The free volume distribution that affects solubility coefficients is not a major determining factor for the diffusion coefficients in these matrices.     

Diffusion behavior of benzene/cyclohexane molecules in poly(vinyl alcohol)-graphite hybrid membranes by molecular dynamics simulation

Understanding the effects of incorporated inorganic particles in organic-inorganic hybrid membranes at molecular level is crucial to design hybrid membranes with tailored structure and desired properties. In this study, molecular dynamics simulation has been employed to investigate the effects of graphite particle on the diffusion behavior of benzene and cyclohexane in poly(vinyl alcohol)-graphite hybrid membranes. Firstly, the non-bonding interaction energies between PVA polymer and graphite particle with different amount of hydroxyl and carboxyl groups were calculated by DREIDING force field. Next, polymer chain mobility was analyzed by mean-square displacement (MSD) and glass transition temperature (T_g), and found that incorporation of graphite particle into PVA increased the polymer chain mobility. Free volume characteristics of membranes were investigated by Connolly surface, and found that free volumes in PVA-graphite hybrid membranes were larger than those in PVA control membranes. This simulation result showed the same tendency with the PALS measurement. Finally, the diffusion coefficients of benzene and cyclohexane in the membranes were calculated by Einstein relation, and found that the diffusion coefficients in hybrid membranes were larger than those in the control membrane. Furthermore, it was found that the diffusion coefficients of benzene and cyclohexane in the membranes exhibited exponential relation with the inverse fractional free volumes and agreed well with the free volume theory.     

High internal phase emulsion foams: Copolymers and interpenetrating polymer networks

High internal phase emulsion (HIPE) copolymer and interpenetrating network foams were prepared from 2‐ethylhexyl acrylate (EHA), styrene (S) and divinylbenzene (DVB) using a unique process. The morphologies, thermal properties and dynamic and static mechanical properties of these foams were investigated. The glass transition temperatures and damping properties of the EHA/S copolymer foams vary with its composition. IPN foams with very broad tan 5 peaks were obtained. The damping properties of IPN foams were tailored through changing copolymer composition and monomer composition. The IPN foams based on a copolymer foam and styrene had a broader tan δ peak, a higher glass transition temperature and a higher modulus than tne copolymer foams of similar overall styrene contents. It is therefore possible to prepare novel damping foams based on polyHIPE foams through the synthesis of interpenetrating polymer networks.     

Relationship between gas transport properties and fractional free volume determined from dielectric constant in polyimide films containing the hexafluoroisopropylidene group

The dielectric constant and gas transport properties (i.e., permeability, diffusivity, and solubility) in 2,2′‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride (6FDA)‐based polyimides were systematically investigated in terms of their polymer fractional free volumes (FFVs) at 30°C. The permeability and diffusion coefficients of the 6FDA‐based polyimide films to hydrogen, oxygen, nitrogen, methane, and carbon dioxide were correlated with their FFVs estimated using van Krevelen's group contribution method. There appeared, however, small linear correlation coefficients. Linear correlations were also observed between the gas transport properties and dielectric constant of these polyimides. This study described FFVas a function of the dielectric constant based on the Clausius‐Mossotti equation. It was found that the gas permeability and diffusion coefficients of these 6FDA‐based polyimide films increased as their dielectric constant‐based FFV increased. A better linear relationship was observed between the gas transport properties and the FFV determined from the polymer dielectric constant in comparison to that estimated using the group contribution method. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Miscible blends of styrene–cinnamic acid copolymers with poly(ethyl methacrylate)

Differential scanning calorimetry and inverse gas chromatography have been used to investigate the miscibility behaviour of blends of poly(ethyl methacrylate) (PEMA) with styrene–cinnamic acid statistical copolymers PSCA5, PSCA8, PSCA23 having compositions of, respectively, 5, 8 and 23 mol% of cinnamic acid. Several probes with different chemical nature and polarity have been used to determine the polymer–solute and polymer–polymer interaction parameters. DSC and CPGI measurements indicate that poly(ethyl methacrylate) is miscible with each poly[(styrene)‐co‐(cinnamic acid)] copolymer as established from the observation of a single composition‐dependent glass transition temperature. This deduction is corroborated by the IGC data; comparison of the experimental retention volume of the blend with the algebraic average retention volumes of the pure components, together with negative values of the apparent polymer–polymer interaction parameter, establish the miscibility of the studied systems. Furthermore, the polymer–polymer interaction parameters are found to show marked probe dependence; this is discussed in terms of the Δχ effect. As indicated by the variation of the glass transition temperature with blend composition, the application of the Kwei and the Schneider approaches to the calorimetric results suggests the occurrence of strong specific interactions within the blends; the strength of these intermolecular interactions increases with the cinnamic acid content in the PSCA copolymer. © 2001 Society of Chemical Industry