Solubility and diffusivity of methylmethacrylate and butylacrylate monomers in a MMA–BA copolymer

Mutual diffusion coefficients and sorption isotherms of methyl methacrylate (MMA) and butyl acrylate (BA) monomers in methyl methacrylate‐butyl acrylate copolymer (MMA‐BA) have been measured by gravimetric sorption. MMA is found to have higher solubility and diffusion rates in the copolymer than BA. Sorption data for MMA were interpreted using classical Flory‐Huggins thermodynamic theory with a constant interaction parameter (χ). A modified version of this theory has been applied to correlate the sorption data of BA, which exhibit a temperature and concentration‐dependent χ parameter. For MMA, the isotherm data reveal enhanced polymer‐solvent interactions with increasing temperature, while for BA the data indicate a drive toward phase separation with increasing temperature. Despite the difference in thermodynamic behavior, both monomers are found to exhibit Fickian diffusion and the diffusivity data are correlated reasonably well with the Vrentas‐Duda free volume theory. Some deviation between the free‐volume correlation and the experimental data is observed at the lowest temperature and BA concentration examined. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1996–2006, 2007     

Effect of blend composition on diffusivity and solubility of small molecules in polystyrene/poly(vinyl methyl ether) blends

The capillary column inverse gas chromatography technique was used to determine diffusivity and solubility data for several solvents in polymer blends composed of polystyrene and poly(vinyl methyl ether) (PVME). Diffusivity behaved as expected, increasing as the concentration of PVME increased in the blend. Knowing only the free‐volume parameters for the pure polymers, the free‐volume theory was successfully applied to predict the dependence of the diffusion coefficients on the blend composition. Transport in blends above the glass transition temperature is controlled by free volume, and the effect of concentration fluctuations is minimal at the temperatures studied. Experimental data show an increase in the partition coefficient of some solvents in the blends with respect to the pure polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2071–2082, 2007     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

Transport of toluene/methyl ethyl ketone mixtures in polyisobutylene

In this study, the diffusion behavior of methyl ethyl ketone (MEK)/toluene mixtures, with MEK molar fractions (x₁) in the liquid source lower than 0.2, in polyisobutylene (PIB) was investigated with vapor‐sorption Fourier transform infrared attenuated total reflectance (FTIR‐ATR) spectroscopy. FTIR‐ATR Fickian diffusion models for both binary and ternary systems were used to determine diffusion coefficients. Obtained diffusion coefficients for MEK from the binary diffusion model did not agree with those determined previously for the diffusion of MEK/toluene mixtures, with x₁ > 0.2, in PIB. When the ternary diffusion model was used, the main‐term and cross‐term diffusion coefficients of MEK were comparable. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 908–914, 2001     

Gas transport in vulcanized natural rubber‐cellulose. II. Composites

This work reports the transport of carbon dioxide, oxygen, and nitrogen in amorphous membranes of vulcanized natural rubber reinforced with regenerated cellulose. The values of the permeability coefficient of carbon dioxide, oxygen, and nitrogen in the composites with 25% of cellulose, measured at 25 °C and 15 cmHg of pressure, are roughly one‐third of those measured in the same conditions for these gases in natural rubber. The isotherms representing the variation of both the permeability and diffusion coefficients of the gases with pressure present a relatively sharp increase in the region of low pressures, attributed to changes in the free volume. The analysis of the permeability characteristics of the membranes in terms of the free‐volume theory suggests that gas transport is severely hindered in both the cellulose phase and the cellulose–rubber interphase of the composites. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 393–402, 2000     

Sorption of methanol/MTBE and diffusion of methanol in 6FDA–ODA polyimide

This article discusses the diffusion and solubility behavior of methanol/methyl tert‐butyl ether (MTBE) in glassy 6FDA–ODA polyimide prepared from hexafluoroisopropylidene 2,2‐bis(phthalic anhydride) (6FDA) and oxydianiline (ODA). The diffusion coefficients and sorption isotherm of methanol vapor in 6FDA–ODA polyimide at various pressures and film thicknesses were obtained with a McBain‐type vapor sorption apparatus. Methanol/MTBE mixed‐liquid sorption isotherms were obtained by head‐space chromatography and compared with a pure methanol sorption isotherm obtained with a quartz spring balance. Methanol sorption isotherms obtained with the two methods were almost identical. Both methanol sorption isotherms obeyed the dual‐mode model at a lower activity, which is typical for glassy polymer behavior. The MTBE was readily sorbed into the polymer in the presence of methanol, but the MTBE sorption isotherm exhibited a highly nonideal behavior. The MTBE sorption levels were a strong function of the methanol sorption level. Methanol diffusion in the polymer was analyzed in terms of the partial immobilization model with model parameters obtained from average diffusion coefficients and the dual‐mode sorption parameters. Simple average diffusion coefficients were obtained from sorption kinetics experiments, whereas the dual‐mode sorption parameters were obtained from equilibrium methanol sorption experiments. An analysis of the mobility and solubility data for methanol indicated that methanol tends to form clusters at higher sorption levels. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2254–2267, 2000     

Solvent diffusion in amorphous polymers: Polystyrene–solvent systems

The inverse gas chromatography (IGC) technique was used to obtain the partition and diffusion coefficients of solvents in polystyrene over a wide range of temperatures. Infinite dilution experiments were performed with three solvents: toluene, benzene, and hexane. Finite concentration data were measured for the polystyrene–toluene system at various concentrations from 110 to 180 °C. For the finite concentration region, the modified capillary column model used by Tihminlioglu and Danner (J Chromatogr A 1999, 845, 93–101) was used to calculate diffusion and thermodynamic data. Finite concentration thermodynamic data were also calculated with the retention theory approach and compared with the capillary column model. The experimental IGC results are in good agreement with data from other experimental techniques. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1965–1974, 2000     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

Poly(propylene imine) dendrimers as plasticizers for polyvinyl chloride

Fourth and fifth generation poly(propylene imine) dendrimers and methyl and benzyl functionalized copolymers of these dendrimers are solution blended with poly(vinyl chloride) (PVC). The methyl‐derivative copolymer is observed to be dispersed in PVC as judged by optical and dynamic scanning calorimetry measurements. This dispersion leads to a substantial reduction in the glass transition temperature and a commensurate plasticization effect, demonstrating that functionalized dendrimer copolymers can successfully plasticize semicrystalline polymers. This plasticization is thought to occur as a result of additional free volume from the highly branched structure of the dendrimer. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1970–1975, 2007     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Free radical ring‐opening polymerization of cyclic allylic sulfides: Liquid monomers with low polymerization volume shrinkage

The free radical polymerization of four methylated cyclic allylic sulfides was examined with reference to their polymerization volume shrinkage and the effect of ring size on reactivity. The compounds examined were 2‐methyl‐5‐methylene‐1,3‐dithiane ( 5 ) (solid), 2‐methyl‐6‐methylene‐1,4‐dithiepane ( 6 ) (liquid), 6‐methyl‐3‐methylene‐1,5‐dithiacyclooctane ( 7 ) (liquid), and 6,8‐dimethyl‐3‐methylene‐1,5‐dithiacyclooctane ( 8 ) (liquid). The monomers were stable materials not requiring any special handling or storage conditions. They were polymerized in bulk using thermal azobisisobutyronitrile (AIBN, VAZO88) and photochemical initiators (Ciba DAROCUR 1173) and in benzene solutions (AIBN, 70 °C). The six‐membered ring monomer 5 was unreactive whereas seven‐membered ring monomer 6 polymerized to high conversion in bulk. In addition, 6 did not polymerize in benzene solution at 70 °C at [ 6 ] = 1.25M. Eight‐membered ring monomers 7 and 8 polymerized in bulk to complete conversion with thermal and photochemical initiators to give lightly crosslinked materials. Near complete conversion to soluble polymers could be obtained in solution polymerizations in benzene. Soluble polymers were also obtained in photochemical initiated bulk polymerizations by lowering initiator concentrations or length of irradiation. The methyl substituent had no effect on which allylic carbon–sulfur bond fragmented in the ring‐opening step. The polymerization volume shrinkages of monomers 7 and 8 were 1.5 and 2.4% respectively and together with monomer 4 (1.5–2.0% shrinkage) are the best available liquid free radical ring‐opening monomers that can be polymerized in bulk at room temperature. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 202–215, 2001     

Sorption and diffusion of oxygen in plasticized ethyl cellulose films of varying degrees of substitution

Plasticized films cast from ethyl cellulose were examined to evaluate the effect of the degree of substitution, DS, and the plasticizer content on the sorption and diffusion of oxygen. Sorption and permeation measurements were performed over a temperature range of 25–65°C on three different types of ethyl cellulose in the DS range 1.7–2.5 that had been plasticized with organic esters of comparatively low molecular weight. Sorption coefficients were determined by the pressure decay method, and permeability coefficients were measured independently according to ASTM D-1434-66. The diffusion coefficients were calculated assuming Fickian transport, and were compared to the values directly obtained from the evaluation of the sorption kinetics. The permeability coefficient indicates that there is a significant improvement of the barrier properties of the materials when the DS is reduced and when the plasticizer content is at the absolute minimum required. It was found that the variation in the magnitude of the permeability coefficient is related to the value of the diffusion coefficient, which is governed by the chemical composition of the mixtures. In contrast, the solubility of oxygen was determined by the physical state of the polymer matrix and increased rapidly at temperatures significantly below the glass transition temperature. Using an ergodic model, the diffusion coefficients obtained were related to the size distribution of microvoids in the materials and relative values for the diffusion coefficient were computed as a function of DS and temperature. The model calculates the concentration (number per volume) of voids that are large enough to be occupied by a penetrant molecule. It was assumed that the unoccupied volume fraction as a function of the cohesive energy density follows a Boltzmann distribution. The cohesive energy density and the unoccupied volume fraction of the polymer-plasticizer mixtures were calculated by fitting the Simha-Somcynsky equation of state to pressure-volume-temperature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 639–653, 1997     

Permeation of water through polar and nonpolar polymers and copolymers: Determination of the concentration‐dependent diffusion coefficient

The diffusion and permeation properties of liquid water through different polar and nonpolar polymers and copolymers were studied with a highly sensitive permeameter. The transient permeation fluxes through the polar polymer films could be fitted well only with an exponential equation for the diffusivity concentration dependence; this empirical exponential equation represented the diffusion plasticization effect of water on the materials. For the hydrophobic polyolefins, this exponential equation was no longer valid, and another form of the equation was empirically found to account for the reduction of the water diffusivity with the extent of the permeation. Such a negative plasticization effect might be attributed to the formation of water clusters in the polyolefins. The values of the diffusion coefficient of water in the dry polar polymers were smaller than those in dry polyolefins, but the opposite behavior was found for the permeability because it was much more favorable for water sorption in the polar polymers than in the hydrophobic polyolefins. For the ethylene–vinylacetate copolymers, the plasticization effect of water on its own diffusion was negative for the sample with a low vinyl acetate (VA) content; it became nil at 19 wt % VA and positive at higher VA contents. This increase in the extent of the water sorption with the increase in the VA content led to a steady increase in the water permeability in the poly(ethylene‐co‐vinylacetate) copolymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1998–2008, 2000     

Prediction and estimation of solvent diffusivities in polyacrylate and polymethacrylates

The relationship between polymer side‐chain length and the hole free volume that is effective for solvent diffusion was investigated for polyacrylates and polymethacrylates on the basis of free‐volume theory. Measurements of a polymer's viscoelasticity and solvent diffusivity provided experimental evidence for polymer segment mobility, and the results indicated that hole free volume in a linear polymer increases with hydrocarbon side‐chain length. Because the molecular mechanisms of polymer viscoelasticity and diffusivity are identical, the free‐volume parameters obtained for polyacrylates and polymethacrylates by measuring the polymer viscoelastic‐temperature dependence can reliably be used in predicting the solvent diffusion coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1393–1400, 2003     

Local free volume and structural relaxation studied with photoisomerization of azobenzene and persistent spectral hole burning in poly(alkyl methacrylate)s at low temperatures

The final extent of trans‐to‐cis photoisomerization of an azobenzene probe in various amorphous polymers has been used in previous studies for estimating local free volume and its fluctuation in polymer solids. However, there have been few studies on what kinds of molecular motion cause the fluctuation of local free volume at low temperatures. The onset of local structural relaxation (molecular motion) can be observed with temperature cycling experiments in persistent spectral hole burning (PSHB). Thus, in the present article, the fluctuation of local free volume observed in trans‐to‐cis photoisomerization of azobenzene is related to the local structural relaxation observed in PSHB for poly(alkyl methacrylate)s with various ester groups, i.e., methyl (PMMA), ethyl (PEMA), n‐propyl (PnPMA), isopropyl (PiPMA), and isobutyl (PiBMA) groups. In the final cis fraction, rapid decrease, from 20 to 4 K in PEMA, PnPMA, and PiPMA, and from 86 to 20 K in PiBMA, is observed. These temperature regions of the rapid decrease in final cis fraction in these polymers agree well with those where the hole width in PSHB temperature cycling experiments begins to increase for the same polymers. For example, PEMA begins its ester ethyl group rotation at 17 K, which was primarily observed with PSHB, causing the drastic decrease in final cis fraction of azobenzene from 20 to 4 K. The final cis fractions at 4 K for these poly(alkyl methacrylate)s reflect the intrinsic sizes of the local free volume, except in the case of PMMA, and are compared with the reported results of positron annihilation lifetime measurements. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3098–3105, 2000     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Homopolymerization of methyl methacrylate and styrene: Determination of the chain‐transfer constant from the Mayo equation and the number distribution for n‐dodecanethiol

Chain‐transfer constants were evaluated for n‐dodecanethiol in the homopolymerization of styrene (S) and methyl methacrylate (MMA). The polymerizations were carried out in benzene at 50 °C with different amounts of 2,2′‐azobisisobutyronitrile as the initiator. The new chain length distribution (CLD) analytical method was used and compared to the traditional Mayo method. The chain‐transfer‐constant values were independent of the initiator concentration and slightly higher (by a factor of 1.1 for MMA and 1.2 for S) when obtained according to the CLD method compared to the Mayo method. The chain‐transfer constant for S was 20 times higher than for MMA. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 170–178, 2000     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003