Gas permeation in miscible homopolymer-copolymer blends: II. Tetramethyl bisphenol-A polycarbonate and a styrene/acrylonitrile copolymer

Gas sorption and transport properties for He, H₂, O₂, N₂, Ar, CH₄, and CO₂ at 35°C near atmospheric pressure have been obtained for miscible blends of tetramethyl bisphenol-A polycarbonate (TMPC) and a random copolymer of styrene with acrylonitrile (SAN) containing 9.5% by weight of acrylonitrile. All gas permeability, diffusion, and solubility coefficients obtained are lower than that calculated from the semilogarithmic additivity rule. These results are qualitatively interpreted by ternary solution theory and activated state theory which have been proposed to describe gas sorption and diffusion in miscible blends. The negative deviation of gas permeabilities for the blends from this rule can be explained semiquantitatively by free volume theory which takes volume contraction on mixing into account. The negative deviation increases with gas molecular size which results in larger ideal gas separation factors than that calculated from the additivity rule. For He/CH₄ and H₂/CH₄ pairs, the permselectivities for the blends are higher than that for either pure TMPC or SAN. The deviation from additivity for gas transport properties of TMPC/SAN blends is the opposite of that observed in the first paper of this series for PMMA/SAN blends. This can be attributed to the stronger interactions in TMPC/SAN blends than in PMMA/SAN blends.     

Antiplasticization of a polyamide: a positron annihilation lifetime spectroscopy study

In order to modify the transport properties of the amorphous polyamide Trogamid-T™, several additives with structural characteristics that produce antiplasticization have been tested. Positron annihilation lifetime spectroscopy (PALS) has been used to determine both the size of free volume holes and the number of holes (free fractional free volume). Polyvinyl phenol (PVPh), 1,5 dihydroxy naphthalene (Ndiol) and a hexafluorinated Bisphenol A (HFBA) were chosen according to the results of a preliminary study based on density and PALS measurements with 15% of additive blends. Their blends with Trogamid show different behaviours: HFBA behaves clearly as a plasticizer while the polyvinyl phenol acts as an antiplasticizer. Ndiol has a more special effect: blend densities are greater than additive whereas the hole size decreases.     

Effect of sorption behavior on transport properties of gases in polymeric membranes

The purpose of this work was to study the relationships between the gas sorption and transport properties in polymeric membranes. The intrinsic gas transport properties: permeation, diffusion, and sorption in a series of dense membranes with various carbonyl group densities were investigated. The poly(methyl methacrylate) (PMMA), polycarbonate (PC), and cyclic olefin copolymer (COC) membranes have similar helium permeability, but the helium permeability of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) membrane was very high. The variation of permeability for these four membranes consists with their fraction free volume. In this study, a direct relationship was found between the carbonyl group density and Langmuir affinity constant. Furthermore, dependence of the fractional free volume on the membrane Langmuir capacity constant was observed.     

Differential scanning calorimetric and free volume study of reactive compatibilization by EPM‐g‐MA of poly(trimethylene terephthalate)/EPDM blends

Differential scanning calorimetry (DSC) and positron annihilation lifetime measurements have been carried out to study the effect of the compatibilizer maleic anhydride grafted ethylene propylene copolymer (EPM‐g‐MA) in poly trimethylene terephthalate and ethylene propylene diene monomer (PTT/EPDM) immiscible blends. The DSC results for the blends of 50/50 and 30/70 compositions show two clear glass transition temperatures, indicating that the blends are two‐phase systems. With the addition of compatibilizer, the separation between the two glass transitions decreased, suggesting an increased interaction between the blend components with compatibilizer. At 5 wt % of compatibilizer, the separation between the T_gs reduced in both 50/50 and 30/70 blends. The positron results for the blends without compatibilizer showed an increase in relative fractional free volume, as the EPDM content in the blend is increased. This suggests the coalescence of free volume of EPDM with the free volumes of PTT due to phase separation. However, the effect of compatibilizer in the blends was clearly seen with the observed minimum in free volume parameters at 5% of the compatibilizer, further suggesting that this percent of compatibilizer seems to be the optimum value for these blends. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 740–747, 2006     

Positron annihilation and differential scanning calorimetric study of poly(trimethylene terephthalate)/EPDM blends

The blends of poly(trimethylene terephthalate) (PTT) and ethylene propylene diene monomer (EPDM) with different composition have been studied by positron lifetime technique (PLT) and differential scanning calorimetric (DSC) measurements. The DSC results for the blends of 50/50 and 40/60 show clear two glass transition temperatures indicating two-phase system. No melting point depression was observed for the blend system, which strongly supports the incompatibility. From the positron results an increase in free volume hole size and its concentration has been observed with the increase in EPDM content of the blend which indicates further that there is coalescence of free volumes of EPDM with the PTT to some extent and phase separation behavior continues. Another interesting aspect is that the relative fractional free volume exhibits neither negative nor positive deviation from the log additivity rule. It agrees well with the log additivity rule. The interchain interaction parameter evaluated from these results show some complex behavior. XRD results show the decrease in crystallinity of the blend with the increase in fractional free volume with the increase in concentration of EPDM.     

Studies on miscibility in homopolymer/ random copolymer blends by equation of state theory

The miscibility of poly(methyl methacrylate) (PMMA) and styrene-acrylonitrile random copolymers (SAN) blends was investigated on the basis of the Flory—Orwoll—Vrij equation of state theory. To obtain the equation of state parameters (P*, V*_sp, T*: characteristic parameters), the pressure—volume—temperature (PVT) behaviour was measured for PMMA and a series of SANs with various acrylonitrile contents. The exchange energy parameter X_ij was also calculated by fitting the theory to some phase diagrams of PMMA/SAN blends. The Flory—Huggins interaction parameter χ was separated into two contributions based on the equation of state theory for mixtures: the exchange energy term χ_inter and the free volume term χ_free. Both the temperature and copolymer composition dependences of χ_inter and χ_free were estimated by calculations using the equation of state parameters. There exists a region in which χ_inter is negative, leading to a miscibility window in PMMA/SAN blends. However, the immiscibility at high temperatures in the blends cannot be explained only by χ_inter; it is caused by the free volume contribution, χ_free. The miscibility window behaviour in PMMA/SAN blends may be explained within the framework of the equation of state theory.     

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     

Morphology effect on water sorption behavior in a thermoplastic modified epoxy resin system

Water sorption behavior in polyetherimide (PEI) modified diglycidyl ether bisphenol-A/4,4′-diaminodiphenyl sulfone (DGEBA/DDS) systems was investigated by gravimetric analysis, positron annihilation lifetime spectroscopy and scanning electron microscopy. The equilibrium water uptake showed strong composition-dependent, which suggested that hydrophilic groups rather than free volume were more significant in determining ultimate water sorption. While besides the number of hydrophilic groups and fractional free volume, morphology induced by phase separation was another key factor that decided the value of diffusion coefficient, which was chiefly responsible for the anomalous diffusion behavior observed at the beginning of co-continuous phase. In addition, morphology not only had the function of decreasing fractional free volume, but also changed the number of hydrophilic groups in epoxy rich regions, which obviously distinguished water sorption behavior in the blends from that in single component systems.     

Positron annihilation lifetime spectroscopy for miscibility investigations of styrene–butadiene–styrene copolymer/polystyrene blends

The free volume parameters of styrene–butadiene–styrene copolymer/polystyrene (SBS/PS) blends were investigated with positron annihilation lifetime spectroscopy (PALS) in this study. The behaviors of free volume distribution, average free volume, and relative fractional free volume revealed the difference of interfacial miscibility. Based on different models, inter‐chain interaction parameter β, geometric factor γ, and hydrodynamic interaction parameter α obtained from free volume data were employed to further determine the effect of molecular architecture and styrene content on the miscibility. The results suggest the better miscibility in star‐shaped SBS/PS blends than that of corresponding linear SBS/PS systems, even than that of systems containing more styrene unit. In addition, differential scanning calorimetry, dynamic mechanical analysis, and scanning electron microscopy, which are sensitive to heterogeneities in larger domain size, give different results of miscibility from free volume data. It should be attributed the difference of characterization scale. The mechanical property corroborates the results of miscibility. POLYM. ENG. SCI., 54:785–793, 2014. © 2013 Society of Plastics Engineers     

Free volume,excess entropy and mechanical behavior of polymeric glasses

Free volume fraction of the Williams-Landel-Ferry(WLF)-Doolittle type has been applied to the analysis of the nonequilibrium state for the glassy polymers. The free volume fraction is a two parameter variable since it depends on the free volume and the occupied volume. The excess entropy is derived from the mixing of vacant and occupied sites, and for polymers a factor is added which corresponds to disordering the molecular segments. A relationship between the excess entropy and enthalpy is derived. For a given level of fractional free volume, there is a unique rate constant associated with changing that level of the fractional free volume. The reciprocal of this rate constant, which depends on the exponential order of the fractional free volume, can be considered as a time constant for changing the molecular conformational probability, and its value is in the order of the average dielectric relaxation time in the corresponding state. When mechanical deformation is. imposed with a rate which is too fast as compared to this time constant, the deformation without a change in the conformational probability, i.e., the reversible elastic deformation, will ensue. In contrast, a sufficiently slow deformation will be accompanied by a change in fractional free volume and the excess entropy, and the above-mentioned time constant will change with deformation. Since dilation will tend to shorten this time constant, tensile deformation will result in reducing the modulus accompanied by the increase in entropy. Shear deformation is considered as a mixture of compression and tension, where only tension contributes to a change in entropy, and the net result is the strain softening which can be predicted from the tensile behavior. Uniaxial compression is controlled by the shear behavior, and the excess entropy and the fractional free volume increase, while the occupied volume decreases with strain. A constitutive relationship has been proposed which accounts for the effects of temperature, pressure, strain rates and thermal history on nonlinear viscoelastic behavior of polymeric glass.     

Free volume as an internal material parameter to probe interfaces in ternary polymer blends: A positron lifetime study

A new method to characterize individual interfaces in ternary polymer blends from experimentally measured fractional free volume from Positron Annihilation Lifetime Spectroscopy (PALS) has been developed. By this, we derive the composition dependent miscibility level in ternary polymer blends. This method has its genesis in KRZ (Kirkwood–Risemann–Zimm) theory which introduces hydrodynamic interaction parameter as a measure of excess friction generated at the interface between dissimilar polymer chains resulting in energy dissipation. The method successfully applied for binary blends has been theoretically modified to suit ternary blends in the present work. The efficacy of this method has been tested for two ternary blends namely polycaprolactone/poly(styrene‐co‐acrylonitrile)/poly(vinyl chloride) (PCL/SAN/PVC) and polycaprolactone/poly(vinyl chloride)/poly(vinyl acetate) (PCL/PVC/PVAc) in different compositions. We obtained a maximum effective hydrodynamic interaction (α_eff) of ?12.60 at composition 80/10/10 of PCL/PVC/PVAc while PCL/SAN/PVC showed ?1.60 at 68/16/16 composition. These results suggest that these compositions produce high miscibility level as compared to other compositions. DSC measurements have also been used to supplement positron results. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3335–3344, 2013     

Microstructure and miscibility of acrylonitrile–butadiene rubber/ethylene–propylene–diene monomer blends studied by positron annihilation spectroscopy

The free‐volume properties and miscibility of ethylene–propylene–diene monomer/acrylonitrile–butadiene rubber blends with poly(vinyl chloride) used for compatibilization were investigated with positron annihilation lifetime spectroscopy and Doppler broadening of annihilation radiation. The results showed that the ortho‐positronium annihilation lifetimes and intensities as well as the S parameter had a linear relationship with a negative slope as a function of the weight percentage of acrylonitrile–butadiene rubber, which indicated the miscibility of the blend. The filling effect of silica on the free‐volume properties of an ethylene–propylene–diene monomer/acrylonitrile–butadiene rubber (75/25) blend was also examined. On the other hand, a correlation between the size and concentration of the free‐volume holes and the electrical and mechanical properties of the aforementioned blends was established. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Investigation of the glass transition and viscoelastic properties of polycarbonate/multi-walled carbon nanotube composites by positron annihilation lifetime spectroscopy

The influences of free volume and temperature on the viscoelastic properties of polycarbonate (PC)/multi-walled carbon nanotube (MWNT) composites were investigated by positron annihilation lifetime spectroscopy (PALS) and dynamic mechanical analysis (DMA). Three methods, including PALS, DMA and differential scanning calorimetry were used to determine the glass transition temperature (T_g) of PC/MWNT composites. The experimental results indicated that the higher the MWNT contents, the lower the T_g, which attributes to the large free volume hole and the enhanced polymer mobility in PC/MWNT composites with higher MWNT contents. The effect of MWNTs on viscoelastic property has been investigated in detail. A direct linear relationship between fractional free volume and viscoelastic property has been obtained using the Williams–Landel–Ferry equation based on free volume theory, which indicates that the free volume plays an important role in determining the viscoelastic property.     

CO2和O2在聚乳酸/聚偏二氟乙烯共混物中扩散行为的分子动力学模拟研究

采用分子动力学模拟方法研究了CO₂和O₂分子在聚乳酸/聚偏二氟乙烯（PLA/PVDF）共混物中的扩散行为;通过菲克第一定律和Einstein关系式计算了共混物体系模型的自由体积分数以及CO₂和O₂分子在体系中的扩散系数,研究探讨了自由体积分数与探头半径的关系及自由体积分数与扩散系数的关系。结果表明,当PLA/PVDF共混物中PLA和PVDF的质量比为9∶1时,CO₂和O₂气体分子的扩散系数均为最小,共混物阻隔性能最好;共混体系中小分子的动力学半径越小,扩散系数越大;自由体积分数随硬球探头模型中探头半径的增大而减小;不同共混物体系中,自由体积分数的变化趋势与扩散系数一致,与Fox和Flory的自由体积理论相符。     

Solute and penetrant diffusion in swellable polymers. VII. A free volume-based model with mechanical relaxation

Penetrant transport through and solute release from continuously swelling polymers is viewed as a process associated with major structural changes in the polymer morphology. Changes in the diffusivities of penetrant and solute reflect a free volume mechanism for transport. The polymer is initially glassy with a uniform dispersion of solute. After the system is placed in contact with a thermodynamically good penetrant, a glassy/rubbery phase transition occurs at a well defined swelling interface. The Fickian equations with concentration-dependent diffusivities and moving boundaries are solved simultaneously in polymer-fixed coordinates. A constitutive relation is used to describe the effect of macromolecular relaxations on the rate of volume expansion as the polymer swells. The penetrant fractional uptake, solute fractional release, sample dimensions, swelling front position, and instantaneous swelling interface number are determined and related to the nature of the swelling process.     

Comparison of hydrogen bonding interaction between PMMA/PMAA blends and PMMA-co-PMAA copolymers

A series of miscible PMMA/PMAA blends and PMMA-co-PMAA copolymers with different compositions were prepared in this study. T_gs of PMMA-co-PMAA copolymers are significantly higher than average values or from the Fox equation. The proton spin-lattice relaxation time in the rotating frame (T_1ρ^H) determined by high resolution solid state ¹³C nuclear magnetic resonance indicates single composition-dependent from all blends and copolymers, implying a good miscibility with chain dynamics on a scale of 1-2 nm. However, T_1ρ^Hs of copolymers are still smaller than those of blends, implying that degrees of homogeneity of copolymers are higher than those of blends. On the basis of Kovacs' free volume theory, the free volume of the copolymer obtained is decreased which is another indication of greater homogeneity of the copolymer than that of the corresponding blend. According to Fourier transform infrared spectroscopy analyses, the above results can be rationalized that the hydrogen bonding interaction of the copolymer is stronger than the blend.     

Relationship between free volume properties and structure of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) membranes via various crystallization conditions

The relationship between the crystalline structure and the free volume properties within the amorphous phase of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) membranes, which were prepared via isothermal crystallization processes at various crystallization temperatures, was investigated. From the data of positron annihilation lifetime (PAL) spectroscopy over a temperature range of 25–90 °C, the temperature dependence of free volume size, amount, distribution, and relative fractional free volume and thermal expansion behaviors of free volume were discussed. The existence of a rigid-amorphous fraction (RAF) which constrained long-range motions in the semi-crystalline polymer was demonstrated by DSC trace and considered to interpret the temperature dependence of those free volume properties. Based on the crystallization conditions, the effect of the crystallization rate of PHBV polymer was proposed to explain the thermal expansion coefficients of free volume size. The membranes crystallized at faster crystallization rate would accompany higher thermal expansion coefficients of free volume size and the larger free volume size at higher temperatures. Larger distribution of the free volume size and higher thermal expansivity of o-Ps lifetime dispersion (dσ/dt) of isothermally melt-crystallized membranes were observed as a result of the bimodal distribution of the lamellar periodicity, which was obtained by small-angle X-ray scattering (SAXS), and less amount of RAF than that of a cold-crystallized membrane. Conclusively, free volume size and thermal expansion of the free volume in PHBV membranes were affected by the kinetics of crystallization; comparatively, the total amount of free volume and fractional free volume were determined by the final crystallinity. The size distribution of free volume was associated with the crystalline lamellar structure which was dominated by the crystallization conditions.     

Constitutional and configurational influences on the viscoelastic data of methyl substituted hydrocarbon macromolecular systems

Summary From viscoelastic measurements on the melts of non-entangled atactic head-to-tail and of head-to-head — tail-to-tail polypropylenes over a broad region of temperatures and frequencies it is concluded that the head-to-tail macromolecules are the significantly less mobile ones. Equimolar blends of both components show up one-phase behaviour. A tendency towards beginning incompatibility may be concluded, however, from some characteristics of the blend: Additional transition in the glassy state, at 210. 3 K, increased fractional free volume and raised zero shear melt viscosity.