The effect of plasticization on the transport of gases in and through glassy polymers

The effects of plasticization on the transport of gases and vapors in and through glassy polymers are examined from the viewpoint of the “dual-mode” sorption model with partial immobilization. The analysis assumes the existence of two penetrant populations with different mobilities in the Henry's law and Langmuir domains of the glassy polymers. These mobilities are characterized by their mutual diffusion coefficients D_D and D_H. The plasticization of the polymer by penetrant gases is reflected in the concentration dependence of D_D and D_H. Expressions for the effective (apparent) diffusion and permeability coefficients are derived assuming that D_D and D_H are exponential functions of the penetrant concentration in the polymers. The results of this study are compared with a similar analysis which assumed the existence of a single mobile penetrant population. The present analysis provides information on the effects of plasticization on the penetrant transport in the Henry's law and Langmuir domains separately. The effects of antiplasticization or clustering of penetrant molecules on the effective diffusion and permeability coefficients are also examined.     

Effects of physical aging on solubility,diffusivity, and permeability of propane and n-butane in poly(4-methyl-2-pentyne)

The effects of physical aging on the solubility, diffusivity, and permeability of propane and n-butane in a hydrocarbon-based disubstituted polyacetylene, poly(4-methyl-2-pentyne) (PMP), were studied. As the relative pressure of propane and n-butane increased, the solubility of both hydrocarbons increased. Like other glassy polymers, the sorption isotherms for propane and n-butane in all PMP films were concave to the relative pressure axis, indicating dual-mode sorption behavior. The diffusion of propane and n-butane in PMP followed typical Fickian diffusion in a plane sheet. The propane diffusivity in both the unaged and aged films increased with increasing concentration of propane sorbed in the film. The n-butane diffusivity in aged films also increased with increasing n-butane concentration. However, unaged films showed the opposite behavior: the diffusivity decreased with increasing n-butane concentration. These diffusion phenomena are a consequence of the interplay between thermodynamic and mobility factors. The permeabilities of propane and n-butane decreased monotonically with increasing penetrant concentration, similar to the behavior observed in other common glassy polymers. The relaxation of the nonequilibrium excess free volume in PMP films induced the decrease in both solubility and diffusivity. As a result, the permeability of propane and n-butane in PMP decreased upon physical aging. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2407–2418, 2004     

Transport of hexane vapor in polystyrene at 25°C I. Analysis of integral sorption data

A series of measurements of integral n-hexane vapor sorption at 25°C and moderate activity, in polystyrene microspheres of varying radii, exhibits typical non-Fickian behavior: nonoverlap of curves of fractional uptake versus (square root of time)/radius. The data are examined in light of a sorption isotherm indicating hexane solubility in excess of that predicted by the Flory–Huggins equation, up to the hexane activity at which the glass transition apparently occurs. A transport analysis is developed based on the assumption that below the transition temperature T_g the rate of sorption is limited by the rate of polymer chain relaxations induced by the penetrant, which facilitate hexane entry into, and immobilization in, glassy microvoids.     

Pure hydrocarbon sorption properties of poly(1-trimethylsilyl-1-propyne) (PTMSP), poly(1-phenyl-1-propyne) (PPP), and PTMSP/PPP blends

Propane and n-butane sorption in blends of poly(1-trimethylsilyl-1-propyne) (PTMSP) and poly(1-phenyl-1-propyne) (PPP) have been determined. Solubilities of propane and n-butane increased as the PTMSP content in the blends increased. This result is consistent with the higher free volume of PTMSP-rich blends and the better thermodynamic compatibility between PTMSP and these hydrocarbons. Propane and n-butane sorption isotherms were well described by the dual-mode model for sorption in glassy polymers. PTMSP/PPP blends are strongly phase-separated, heterogeneous materials. A noninteracting domain model developed for sorption in phase-separated glassy polymer blends suggests that sorption in the Henry's law regions (i.e., the equilibrium, dense phase of the blends) is consistent with the model. However, Langmuir capacity parameters in the blends are lower than predicted from the domain model, suggesting that the amount of nonequilibrium excess free volume associated with the Langmuir sites depends on blend composition. © 1996 John Wiley & Sons, Inc.     

Effect of penetrant-induced isothermal glass transition on sorption,dilation, and diffusion behavior of polybenzylmethacrylate/CO2

The effect of a penetrant-induced isothermal glass transition on sorption, dilation, and diffusion behavior was studied in a single experimental run for CO₂ in cast polybenzylmethacrylate films. The dual-mode type sorption isotherms below the glass transition temperature of the polymer changed to linear ones above a certain concentration. Meanwhile, partial molar volume of CO₂ determined from the dilation of the films above the concentration gave a value very close to the one reported for rubbery polymers, and diffusion coefficients became less concentration-dependent. The results were conformable to the concept of unrelaxed volume in glassy polymers. © 1996 John Wiley & Sons, Inc.     

Dual-mode analysis of subatomspheric-pressure CO2 sorption and transport in Kapton H polyimide film

Sorption kinetics and equilibria as well as permeabilities and diffusion time lags for CO₂ in Kapton polyimide film have been studied at temperatures from 35 to 55°C and pressures up to 0.78 atm. The sorption/desorption cycles indicate that the diffusivity of CO₂ increases with increasing local penetrant concentration in the polymer. Both the permeability and time lag decrease with increasing upstream CO₂ pressure. All of these results are described well by theoretical expression based on the dual-mode theory of sorption and transport in glassy polymers.     

Sorption of carbon dioxide in fluorinated poyimides

Sorption isotherms of CO₂ for ten fluorinated polyimides measured at 35°C and up to about 25 atm are analyzed according to the dual-mode sorption model. Sorption properties for these polyimides are compared with those for other glassy Polymers including unfluorinated polyimides. The glassy polymers with higher glass transition temperatures T_g tend to show greater CO₂ sorption. Introduction of a ? C (CF₃)₂? linkage into the repeat unit of the main chain increases the sorption by 20–80%. For glassy polymers, including the fluorinated and unfluorinated polyimides, the Langmuir affinity constant b and Henry's law solubility constant k_D are correlated with the content of functional (carbonyl or sulfonyl) groups [FG], and composite parameter reflecting the magnitude of both [FG] and free-space fraction V_F, respectively, with some exceptions. The Langmuir capacity constant C′_H is correlated with T_g, but there are two correlation lines; one for unfluorinated polyimides and a different one for other glassy polymers including fluorinated polyimides. The slope of the former group is smaller probably because of smaller differences in thermal probably because of smaller differences in thermal expansion coefficients in rubbery and glassy states. Most fluorinated polyimides show greater solubility of CO₂ than unfluorinated polyimides and other glassy polymers, because of their larger C′_H and k_D. © 1993 John Wiley & Sons, Inc.     

CO2 sorption in poly(ethylene terephthalate) above and below the glass transition

High-pressure CO₂ sorption data in semicrystalline poly(ethylene terephthalate) (PET) are presented for temperatures ranging from 25 to 115°C. The results are described by Henry's law above the glass-transition temperature of PET, while a dual-mode sorption model comprised of a Henry's law and a Langmuir isotherm applies in the glassy state. The disappearance of the Langmuir capacity of the polymer above T_g presumably results from the elimination of regions of localized lower density which are frozen into the glass upon quenching from the rubbery state. Exposure of PET to a high CO₂ pressure produced a systematic variation in the apparent sorption equilibria. Correlation of the Langmuir capacity of PET with the dilatometric parameters of the polymer provides a useful framework for understanding the origin of the Langmuir sorption mode and for interpreting annealing and conditioning effects in glassy polymers.     

Transport of organic vapors and liquids in poly(vinyl chloride)

This paper reviews research since 1980 on the equilibria and kinetics of transport of small organic molecules in rigid and plasticized PVC. The forms of both the solubility isotherms and the sorption kinetics are shown to change as the PVC/penetrant system undergoes a glass-rubber transition with an increase of either temperature or penetrant concentration. The isotherms are of “dual-mode” form (concave to the activity axis) for the glassy state, and show an inflection to Flory-Huggins form when the penetrant concentration exceeds C_g, the transition composition at the experimental temperature. The solubility at a given penetrant activity is governed primarily by the PVC/penetrant interaction parameter, χ. Sorption kinetics are Fickian for conditions producing small changes of concentration in either the glassy or rubbery state. For sorption into initially unplasticized PVC, kinetics are anomalous if the final penetrant concentration is between about C_g/2 and C_g, and Case II if C_g is exceeded. The magnitude of the Fickian diffusion coefficients depends largely on the geometric factors of molecular size and shape of the penetrant; this dependence is much steeper in the glassy than in the rubbery state. Recent results show that carbon dioxide displays both high diffusivity and substantial solubility in PVC under high pressure; this combination makes compressed CO₂ uniquely useful in accelerating the absorption of low-molecular-weight additives into PVC.     

Kinetics and equilibria of sulfur dioxide sorption in kapton polyimide

The kinetics and equilibria of SO₂ sorption in Kapton polyimide film have been measured at 25°C for pressures up to 58 cm Hg using a quartz spring balance. The observed equilibria are described well by the dual-mode model for sorption of penetrants in glassy polymers. Observed hysteresis in sorption-desorption cycling indicates that the diffusivity of SO₂ increases markedly with increasing local penetrant concentration in the polymer. The concentration dependence of the effective average diffusion coefficient is described well by an expression from dual-mode theory. The Langmuir component of the sorption population has an extremely low mobility compared to that of the Henry's law component; in fact, the so-called “total immobilization” limiting case, which assigns a zero diffusion coefficient to this component, appears to be satisfactory under the conditions studied. These results, coupled with published results for other penetrants, suggest that the degree of immobilization of the Langmuir population depends to a great extent on the condensability and/or the molecular size of the penetrant. Predictions of the SO₂ diffusion time lag and permeability in Kapton as functions of the upstream SO₂ pressure are presented and discussed in terms of the dual-mode theory.     

Sorption and transport of linear alkane hydrocarbons in biaxially oriented polyethylene terephthalate

Equilibrium sorption and uptake kinetics of n‐butane and n‐pentane in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were examined at 35 °C and for pressures ranging from 0 to approximately 76 cmHg. Sorption isotherms were well described by the dual‐mode sorption model. Sorption kinetics were described either by Fickian diffusion or a two‐stage model incorporating Fickian diffusion at short times and protracted polymer structural relaxation at long times. Diffusion coefficients increased with increasing penetrant concentration. n‐Butane solubility was lower than that of n‐pentane, consistent with the more condensable nature of n‐pentane. However, n‐butane diffusion coefficients were higher than those of n‐pentane. Infinite‐dilution, estimated amorphous phase diffusion and solubility coefficients were well correlated with penetrant critical volume and critical temperature, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1160–1172, 2001     

Relationships between chemical structures and solubility,diffusivity, and permselectivity of 1,3-butadiene and n-butane in 6FDA-based polyimides

The solubility, diffusivity, and permselectivity of 1,3-butadiene and n-butane in seven different polyimides synthesized from 2,2-bis (3,4-carboxyphenyl) hexafluoropropane dianhydride (6FDA) were determined at 298 K. The influence of chemical structures on physical and gas permeation properties of 6FDA-based polyimides was studied. Solubility of 1,3-butadiene in 6FDA-based polyimides can be described by a dual-mode sorption model. 1,3-Butadiene-induced plasticization is considered to be associated with the increasing permeabilities of 1,3-butadiene and n-butane and the decreasing permselectivity of 1,3-butadiene vs. n-butane in the mixed gas system containing a high concentration of 1,3-butadiene. It was found that controlling the solubility of 1,3-butadiene in an unrelaxed volume in 6FDA-based polyimides is very important to maintain the high permselectivity of 1,3-butadiene vs. n-butane in the mixed gas system. Changing the  C(CF₃)₂ linkage to a  CH₂ ,  O linkage, removing methyl substituents at the ortho position of the imide linkage, and changing the p-phenylene linkage to an m-phenylene linkage in the main chains in some 6FDA-based polyimides are effective to decrease fractional free volume and restrict the solubility of 1,3-butadiene in the unrelaxed volume of a polymer matrix. The 6FDA-based polyimides restricting the solubility of 1,3-butadiene in an unrelaxed volume exhibit high separation performance in the 1,3-butadiene/n-butane mixed gas system compared with conventional glassy polymers and, therefore, are potentially useful membrane materials for the separation of 1,3-butadiene and n-butane in the petrochemical industry. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2941–2949, 1999     

Argon sorption and partial molar volume in poly(ethyl methacrylate) above and below the glass transition temperature

Sorption and dilation isotherms for argon in poly(ethyl methacrylate) (PEMA) are reported for pressures up to 50 atm over the temperature range 5–85°C. At temperatures below the glass transition (T_g=61°C), sorption isotherms are well described by the dual-mode sorption model; and isotherms above T_g follow Henry's law. However, isotherms for dilation due to sorption are linear in pressure at all temperatures over the range investigated. Partial molar volumes of Ar in PEMA are obtained from these isotherms. The volumes are approximately constant above T_g (about 40 cm³/mol), whereas the volumes below T_g are smaller and dependent on both temperature and concentration (19–26 cm³/mol). By analyzing the experimental data according to the dual-mode sorption and dilation model, the volume occupied by a dissolved Ar molecule and the mean size of microvoid in the glass are estimated to be 67 129 ų, respectively. The cohesive energy density of the polymer is also estimated as 61 cal/cm³ from the temperature dependence of the dual-mode parameters.     

Gas sorption in poly(vinyl benzoate)

High-pressure sorption (up to 50 atm) for CO₂, N₂, and Ar in poly(vinyl benzoate) (PVB) was studied at temperatures from 25 to 70°C by a gravimetric method utilizing an electromicrobalance. The results are described by Henry's law above the glass transition temperature T_g for all gases. The dual-mode sorption model, Henry's law plus a Langmuir isotherm, applies to the sorption isotherms of N₂ and Ar in the glassy state, and the dual-mode parameters are given. For CO₂, a new type of sorption isotherm is observed below T_g. The isotherm is concave to the pressure axis in the low-pressure region and turns into a straight line with increasing CO₂ pressure which can be extrapolated back to the coordinate origin. The linear part of the isotherm is characteristic of the rubbery state, while the nonlinear part stems from glassystate behavior. The “glass transition solubility” of CO₂, at which PVB film changes from the glassy to the rubbery state, decrease as the temperature increases. The disappearance of microvoids, that is, the decrease of the Langmuir capacity, may be due to a large plasticizing effect of sorbed CO₂. The difference between the N₂ and Ar isotherms and the CO₂ isotherm is discussed from this standpoint.     

Diffusion in atactic polystyrene above the glass transition point

Diffusivities and solubilities in the system n-pentane-polystyrene were measured for low penetrant concentrations at several temperatures above the glass transition temperature. The relatively sharp changes in the activation energy of diffusion and the heat of solution near 150°C. are interpreted tentatively as indicating that a second-order transition exists in atactic polystyrene above the glass transition temperature. Evidence indicating the existence of this transition has been obtained by other techniques and the effects observed in this study should also be present in the diffusion of other penetrants in polystyrene. Correlation of these and other available data for diffusion in polystyrene as a function of the molecular size of the penetrant indicates that specific thermodynamic interactions between polymer and penetrant have little influence on the diffusion process.     

Sorption and diffusion of water vapor in polyimide films

Sorption and diffusion of water vapor are investigated gravimetrically for polyimide films. The activity dependence of the solubility and diffusion coefficients, S and D, respectively, is classified under four types: (1) constant S and D type, (2) dual-mode sorption and transport type, (3) dual-mode type followed by a deviation due to a plasticization effect at high vapor activity, and (4) constant S and D type followed by a deviation due to water cluster formation at high activity. For the dual-mode type, the Henry's law component is much larger than the Langmuir component except at low activity, and therefore deviation in behavior from the first type is small. S is larger for polyimides with higher content of polar groups such as carbonyl, carboxyl, and sulfonyl. D is larger for polyimides with a higher fraction of free space, with some exceptions. The polyimide from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and dimethyl-3,7-diaminodibenzothiophene-5, 5-dioxide belongs to the third type and displays both large S and large D. The polyimide from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride and 4,4′-oxydianiline belongs to the fourth type, and has the largest D but rather small S because of the hydrophobic C(CF₃)₂ groups. © 1992 John Wiley & Sons, Inc.     

Synthesis and gas permeation properties of poly(4-methyl-2-pentyne)

Poly(4-methyl-2-pentyne) [PMP] is an amorphous, glassy, di-substituted acetylene-based polymer. PMP has a low density of 0.78 g/cm³ and a high fractional free volume of 0.28. The permeabilities for helium, hydrogen, nitrogen, oxygen, carbon dioxide, methane, ethane, propane, and n-butane were determined at temperatures from 20 to 65°C and pressures from 10 to 150 psig. PMP is the most permeable purely hydrocarbon-based polymer known; its permeabilities are only exceeded by poly(1-trimethylsilyl-1-propyne) [PTMSP] and poly(1-trimethylgermyl-1-propyne) [PTMGeP]. The oxygen permeability of PMP at 25°C is 2700 × 10⁻¹⁰ cm³(STP) cm/cm² s cmHg and the nitrogen permeability is 1330 × 10⁻¹⁰ cm³(STP) cm/cm² s cmHg. The high gas permeabilities in PMP result from its very high free volume, and probably, interconnectivity of the free-volume-elements. For a glassy polymer, PMP exhibits unusual organic vapor permeation properties. Permeabilities in PMP are higher for large, condensable gases, such as n-butane, than for small, permanent gases such as helium. The permeabilities of condensable gases and permanent gases decrease as the temperature is increased. This behavior is completely unexpected for a glassy polymer and has been observed previously in only high-free-volume glassy PTMSP.     

Dilation of poly[1-(trimethylsilyl)-1-propyne] during sorption of n-nonane

The linear expansion and contraction in the principal planar directions of poly[1-(trimethylsilyl)-1-propyne] film were measured concurrently with the sorption of n-nonane at 35°C. After the first sorption cycle, in which the polymer exhibited markedly nonisotropic volumetric dilation, the polymer expanded and contracted reproducibly during subsequent multiple sorption and desorption cycles. These reversible dilation isotherms were reproducible from sample to sample. The fractional change in length was identical in arbitrarily selected, orthogonal directions in the plane of the film, suggesting that the expansion and dilation of the sample are isotropic. When plotted versus the activity of n-nonane, the linear expansions in the plane of the film are slightly concave to the activity axis, reaching levels over 10% at the highest activities. The experimental partial specific volume of the polymer is near its pure component value but that of the penetrant is much less than its pure component value. Moreover, the magnitude of dilation observed is described rather closely by the dilation which would result solely from the Henry's law portion of sorption, assuming zero volume-change of mixing. These results are consistent with the explicit notions of “hole-filling” associated with the Langmuir mode in the dual-mode model. © 1993 John Wiley & Sons, Inc.     

Swelling and sorption in polymer–CO2 mixtures at elevated pressures

Experimental data on gas sorption and polymer swelling in glassy polymer—gas systems at elevated pressures are presented for CO₂ with polycarbonate, poly(methyl methacrylate), and polystyrene over a range of temperatures from 33 to 65°C and pressures up to 100 atm. The swelling and sorption behavior were found to depend on the occurrence of a glass transition for the polymer induced by the sorption of CO₂. Two distinct types of swelling and sorption isotherms were measured. One isotherm is characterized by swelling and sorption that reach limiting values at elevated pressures. The other isotherm is characterized by swelling and sorption that continue to increase with pressure and a pressure effect on swelling that is somewhat greater than the effect of pressure on sorption. Glass transition pressures estimated from the experimental results for polystyrene with CO₂ are used to obtain the relationship between CO₂ solubility and the glass transition temperature for the polymer. This relationship is in very good agreement with a theoretical corresponding-states correlation for glass transition temperatures of polystyrene-liquid diluent mixtures.