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.     

Sorption and diffusion of water in poly(vinylpyrrolidone)

The effect of molecular mass, thermal prehistory, physical state, and three-dimensional chemical crosslinked structure of a polymer on dissolution and diffusion in the PVP-water system has been studied. The kinetic dependences of sorption that correspond to the Fickian or pseudonormal type have been measured. In a certain concentration range, sorption is accompanied by transition of the system to the rubbery state. In the glassy state, the negative concentration dependence of the diffusion coefficient related to the nonequilibrium state of the polymer sorbent is observed. Sorption isotherms are described by S-shaped curves. It has been shown that the thermal prehistory of the polymer sorbent has the most pronounced effect on its sorption behavior. The effect of molecular mass is insignificant, while three-dimensional chemical crosslinks in PVP manifest themselves only in the region of the rubbery state. In accordance with the double sorption model, the experimental isotherms are represented as the superposition of two isotherms described by the Langmuir and Flory-Huggins equations. For the glassy state of the polymer sorbent, the degree of the nonequilibrium state has been estimated. With due regard for the excess free volume, the detailed thermodynamic analysis of isotherms has been performed; namely, the pair interaction parameters and the free energy of mixing have been calculated. The state of water in the polymer has been examined within the framework of hydrate contributions and clusterization 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     

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.     

Sorption and pervaporation properties of sulfonyl‐containing polyimide membrane to aromatic/non‐aromatic hydrocarbon mixtures

Sorption of single‐component vapors of benzene (Bz), n‐hexane (Hx), and cyclohexane (Cx), and of binary liquid mixtures of Bz/Hx and Bz/Cx in a polyimide from 3,3′,4,4′‐diphenylsulfone‐tetracarboxylic dianhydride (DSDA) and 2,8(6)‐dimethyl‐3,7‐diaminobenzothiophene‐5,5‐dioxide (DDBT) were investigated in detail at 333 K. Sorption and desorption of vapors followed the non‐Fickian kinetics and the sorption isotherms were concave to the vapor activity. For the binary liquids, the sorption isotherms of the Bz component were concave to the Bz composition in feed, whereas those of Hx and Cx were convex because of competitive sorption. As a result, the solubility selectivity was much larger than the sorption ratio of pure liquids. The concentration‐averaged diffusion coefficients of Bz (D̄_Bz) and Hx (D̄_Hx) were evaluated using the sorption and pervaporation data of the polyimide membrane toward the binary mixtures. A kind of coupling effect of the coexisting component on D̄ was observed. That is, D̄ of penetrant with smaller molecular size (Hx and Bz for Bz/Hx and Bz/Cx systems, respectively) was reduced by the presence of penetrant with larger molecular size (Bz and Cx, respectively) and vice versa. D̄_Bz was similar to D̄_Hx, but much larger than D̄_Cx. The difference in PV behavior between Bz/Hx and Bz/Cx systems for glassy polymer membranes was understood based on the aforementioned features of sorption and diffusion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2954–2964, 2000     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

Analysis of transport behavior in polymer powders

Vapor sorption studies on powder samples of glassy polymers have provided data which supplement results obtained on conventional film specimens and aid in the elucidation of glassy-state transport mechanisms. For uniform spherical particles of sub-micron size, sorption kinetics at very low activities of organic vapors follow a simple Fickian diffusion model. The short diffusion path in such samples allows determination of the very low diffusivities characteristic of the glassy state in experiments of conveniently short duration. Deviations from the Fickian, uniform-sphere model are observed in several circumstances: Particle size non-uniformity retards the approach to diffusion equilibrium. Sorption data at substantial vapor activities show an apparently similar slow approach to equilibrium which can be related to the contribution of a relaxation-controlled mode of sorption. The effects of particle non-uniformity and of relaxation processes can be distinguished by appropriate experimental design, and models for both have been developed. Sorption rate data obtained under Fickian diffusion conditions can be used to characterize particle size distribution. Sorption kinetics on uniform-sphere powders, conversely, can be analyzed through a diffusion-plus-relaxation model to distinguish and quantify the roles of the two transport modes more clearly than is possible with polymer film specimens. Polymer powder vapor solubility isotherms show significant variations with sample history which can be interpreted in terms of free volume changes and glassy state relaxations. This discussion, based on a study of vapor sorption by poly(vinyl chloride) samples, indicates that powder sorption measurements are also likely to be of general value in the study of other glassy polymers.     

Anomalous transport of penetrants in glassy polymers

Solutions are presented for the Fickian and non-Fickian equations describing the case of penetrant transport in a glassy polymer. Due to associated macromolecular relaxation, a sharp penetrant front is observed which separates the glassy core from the rubbery (gel-like) layer at the surface. Concentration profiles are compared and general comments about Fickian versus non-Fickian transport in polymers are made.     

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.     

Fine characterization of the ethylene and ethane sorption in poly(amide 12-block-tetramethylenoxide) copolymer/AgBF4 membranes

Ethylene/ethane sorption characteristics were determined for dry Pebax™ (poly(amide 12-block-tetramethylenoxide) copolymer)/AgBF₄ membranes by using an electronic microbalance. The membranes containing 0.7 and 22 wt.% AgBF₄ showed a dual-mode sorption isotherm. The ethane isotherms for all the membranes were of the Henry-type, which is the normal sorption for gases in rubbery polymers. The abnormal presence of Langmuir sorption sites only for ethylene in the rubbery copolymer, never reported sofar, is attributed to the silver-based specific complexation sites. The silver salt which dissolved in limited amounts in the rubbery copolymer had a much smaller Langmuir sorption capacity than the salt that crystallized in the copolymer. The sorption kinetics indicate that the crystallized salt did adsorb slowly ethylene according to a zeroth-order kinetics, but not ethane. The gas uptake kinetics resulting from a step of the pressure surrounding the copolymer exhibited one stage for ethane but two stages for ethylene. For the latter, there was first a fast Fickian sorption stage, then a drift of the zeroth-order sorption of ethylene on salt crystals, which contributes for a large part to the total uptake. The zeroth-order sorption suggests that the sorbed ethylene amount in the second-stage is independent of the crystal-surface coverage. The value of the Fickian diffusion coefficient calculated by fitting the kinetics with a solution of the second Fick’s law was 5 × 10⁻¹² m²/s for both ethylene (the first stage) and ethane, and is typical for small organic compounds in a rubbery material.     

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.     

Analysis of the kinetics of vapor absorption/desorption in/from silicone rubber and cellulose acetate membranes in the presence of stagnant boundary layers

The application of an interferometric technique (optical thickness meter, OTM) to the measurement of vapor sorption kinetics in both rubbery and glassy polymers is presented. In this technique, the membrane is formed by casting on a suitable glass surface and interferometry is applied in situ. The use of a carrier gas loaded with penetrant vapor introduced a stagnant boundary layer (SBL) effect which had to be corrected, in order to determine true sorption kinetics. The said SBL effect was estimated, on the basis of existing theory for the silicone rubber–methylene chloride (SR/MC) system and found to be more pronounced in the case of desorption. Upon correction for this effect, Fickian sorption curves were obtained; which yielded nearly constant values of the diffusion coefficient, not materially different for absorption and desorption, in line with theoretical expectation.Cellulose acetate–methylene chloride (CA/MC) was then studied as an example of a glassy polymer–vapor system, where the SBL effect distorts the absorption kinetic curve in the same way as the non-Fickian mechanism of sorption inherent in this kind of polymer–penetrant system. Here, the vapor sorption data were corrected using the results obtained from the Fickian SR/MC system. The corrected results were checked by comparison with independent data reflecting the true kinetic behavior of CA/MC, obtained with a vacuum balance apparatus (VBA), which is free of SBL effects. It is shown that this novel method of applying the SBL correction was reasonably successful in favorable circumstances, while a criterion is provided to identify cases where reasonably reliable correction is not possible.     

Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

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     

Interdiffusion kinetics of miscible polymer/polymer laminates investigated by atomic force microscopy

The miscibility of poly(vinyl chloride)/poly(n-butyl methacrylate) (PVC/PnBMA) blend and the interdiffusion kinetics of PVC/PnBMA laminates have been investigated by differential scanning calorimetry (DSC) and atomic force microscopy (AFM), respectively. This blend exhibited a lower critical solution temperature behavior. Below 120℃, DSC results showed each blend with different PVC contents exhibited only a single glass transition temperature which increased with PVC content, indicating that PVC and PnBMA were miscible. After PVC/PnBMA laminates were annealed at different temperature for different time, a smooth cross-section across interface was prepared by ultramicrotoming. Combined with topography and phase images of tapping mode AFM, the relative concentration profile, interface width and the relationship between interface width and annealing time could be obtained. In a regime of rubbery/rubbery interdiffusion, the diffusion obeyed a typical Fickian Case-Ⅰ behavior where the interface width was proportional to the square root of annealing time. The mutual diffusion coefficient was in good agreement with that obtained from DSC and positron annihilation lifetime spectroscopy. However, in the regime of glassy/rubbery interdiffusion, the diffusion followed a typical Case-Ⅱ behavior where the interface width was proportional to annealing time. These results imply that AFM is a reliable and powerful tool for the investigation of polymer/polymer interdiffusion at a level of polymer chain size.     

Gravimetric study of high-pressure sorption of gases in polymers

A gravimetric method for determining precisely the solubility of gases in polymers at high pressure is described. The solubilities of N₂ and CO₂ in low-density polyethylene (LDPE); CO₂ in polycarbonate (PC); and N₂, CH₄, C₂H₆, and CO₂ in polysulfone (PSUL) have been measured as a function of pressure up to 50 atm. Most of the measured sorption isotherms agreed closely with published data, but reproducible and time-dependent hysteresis in the sorption of CO₂, C₂H₆, and CH₄ in glassy polymers, PC, and PSUL, was observed in this study for the first time. Like the well known conditioning effect of high-pressure CO₂ on the sorption capacity of glassy polymers, these hysteresis phenomena are believed to be due to the plasticizing effect of sorbed gases. On the basis of the current data, the dual-mode sorption model including the plasticization by sorbed gas is discussed and a primitive equation for the concentration of sorbed gases in a quasiequilibrium state of sorption or desorption is proposed.     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Diffusion-controlled penetration of polymethyl methacrylate sheets by monohydric normal alcohols

The kinetics of ethanol, n-propanol, and n-butanol penetration, sorption, and dimensional swelling in 2 mm poly(methyl methacrylate) sheets were determined over the temperature range 50–95°C. At 50°C, Case II relaxation-controlled transport dominated the observed sorption and penetration kinetics for all three alcohols. At higher temperatures, diffusion of swelling penetrant to the relaxing boundary contributes increasingly to the observed sorption kinetics. In addition, as the temperature is raised, the completion of sorption lags significantly behind the penetration of the relaxing boundary to the sheet midplane. p]The activation energy describing low temperature penetration is significantly higher than the activation energy describing the temperature dependence of high temperature penetration. A distinct transition in the penetration kinetics is apparent for all three alcohols at approximatively 65°C. Independent Clash—Berg determinations of the T_g of the alcohol-swollen sheets indicate that the transition in behaviour is not related to a thermal transition in the polymer, but rather to the generation of diffusional resistance in the high temperature penetration experiments which is comparable to the otherwise rate-determining Case II relaxations dominant in low temperature penetration. At high temperatures, the overall activation energy reflects the combination of diffusional absorption and the more highly activated relaxation-controlled transport. At low temperatures, diffusion of penetrant to the relaxing boundary is rapid compared with the slow, rate determining relaxations and, therefore, the concentration of penetrant is everywhere uniform within the already swollen shell. The extra-ordinarily high apparent activation energy describing the temperature dependence of the initial sorption rate at low temperature reflects the endothermic enthalpy of sorption of alcohols in PMMA as well as the strong coupling between relaxation rate and the penetrant concentration driving the rate determining relaxations. p]Clash—Berg measurements of the temperature dependence of the ten second shear moduli in partially swollen sheets, completely swollen sheets, and unswollen sheets suggest a T_g of approximatively 40°C in the alcohol-swollen PMMA. Moreover, an analysis of the Clash—Berg measurements suggests that the properties of the swollen regions of partially penetrated sheets are identical to the properties of the completely swollen sheets.     

Polymer drying. V. Intramolecular-rotor fluorescence studies of evaporation from liquid-saturated poly(styrene-co-divinylbenzene)

The fluorescence intensity and residual weight of poly(styrene-co-divinylbenzene) saturated with a < 0.003M solution of a intramolecular-rotor-fluorescent probe-molecule in a volatile liquid were monitored simultaneously as the system evaporated at 23°C to virtual dryness. The “breakpoints” in the pattern for fluorescence increase coincided with the “breakpoints” in the kinetics of desorption with respect to the number, α_t of residual sorbed volatile molecules per phenyl group in the polymer, showing that both time-studies reflect the same physical changes in the system that occur reproducibly as α_t decreases monotonically through α′_s and α′_g the compositions that signal respectively incipient elimination of volatile molecules immobilized by adsorption to polymer, and incipient transition of the system from the rubbery state to the glassy state. The fluorescence intensity attained its asymptotic limit before α_t became equal to α_g the composition identified earlier to be that which marks completion of the transition to the glassy state.