Diffusion of radioactively tagged penetrants through rubbery polymers. I. Penetrants with very low solubility

The diffusion of radioactively tagged n-hexadecane, 1,7-heptanediol, and ethylene glycol has been studied in one polar and six nonpolar rubbery polymers. The penetrant–polymer pairs included some in which the two components were miscible in all proportions and some in which they were nearly incompatible (solubility of penetrant in polymer of the order of 1%). The theory for the thin smear method for measuring the diffusion coefficient was evaluated for incompatible pairs with two cases: case 2, when the rate-limiting step is diffusion through the polymer; and case 3, when the rate-limiting step is entry into the polymer across the penetrant–polymer interface. They are easily distinguished experimentally from each other and from case 1, which refers to completely miscible pairs. In examples of case 3, e.g., ethylene glycol with butadiene or styrene–butadiene rubbers, the half-time for saturating the polymer surface in contact with the penetrant was found to be several days at 25°C. The diffusion coefficients, when compared in four hydrocarbon rubbers, of n-hexadecane and 1,7-heptanediol were similar in magnitude even though in each rubber the hexadecane was soluble in all proportions and the diol only very slightly. The diffusion coefficient of ethylene glycol, despite its extreme thermodynamic incompatibility, appeared to be somewhat larger than those of the other penetrants.     

Sorption and diffusion of alcohols in amorphous polymers

The effects of polymer composition and penetrant molecular size on the solubility and diffusivity of alcohol vapors in a series of well characterized isoprene-methyl methacrylate copolymers and their corresponding homopolymers has been investigated at room temperature. The rate of sorption behavior changes progressively from Fickian to non-Fickian, to Case II to “Super Case II” transport with increasing methyl methacrylate (MMA) content in the polymers. The equilibrium solubility of the alcohols increases linearly with increasing penetrant molecular size for polymers which are above their glass transition temperature and decreases for polymers which are below their T_g. The solubility also initially increases as an approximately linear function of MMA content in the copolymers. At about 55 mole percent MMA, the sorbed concentration either levels off or passes through a maximum depending on the size of the penetrant. The apparent “diffusion coefficients” (D) decrease with increasing molecular volume of the penetrants. An exponential dependence was found between these two variables for PMMA. These “diffusion coefficients” also decrease exponentially with increasing MMA content in these polymers. However, at 55 mole percent MMA the copolymer undergoes a rubber to glass transition at the temperature of the experiments. On this basis, it is suggested that the hindered chain segmental motion contributes to the sorption process in addition to strictly thermodynamic considerations. Free volume theory can be used to explain the mechanism of diffusion through the rubbery polymers while the “hole” theory can be applied to explain the transport of the penetrants through the glassy polymers.     

Study of diffusion and sorption of bis-(2-chloroethyl)sulfide (SM) and bis-(2-chloroethyl)ether (OM) through polypropylene (PP) and biaxial-oriented polypropylene (bopp) films by the FTIR–ATR spectroscopic method

The diffusion of sulfur mustard (SM) and oxygen mustard (OM) in polypropylene (PP) and biaxial-oriented PP (BOPP) was measured using Fourier transform infrared–attenuated total reflectance (FTIR–ATR) spectroscopy, which allows one to study the diffusion of liquid through thin polymer films in situ. The temperature-dependent diffusion coefficients of OM and SM for PP and BOPP are also reported; these are in good agreement with the values obtained by the weight gain method. The activation energy of diffusion is determined by both methods. The polymer–penetrant interaction parameter (K) and transport number (n) are calculated for the system PP/OM and BOPP/OM by weight gain method. The “n” values indicate a Fickian mode of diffusion. © 1996 John Wiley & Sons, Inc.     

Sorption and transport of linear and branched ketones in biaxially oriented polyethylene terephthalate

Equilibrium sorption and kinetics of acetone, methyl ethyl ketone (MEK), methyl n-propyl ketone (MnPK), and methyl i-propyl ketone (MiPK) uptake in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were determined at 35 °C and low penetrant activity. Sorption isotherms for all penetrants were well described by the dual-mode sorption model. Sorption and desorption 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 and equilibrium solubility at fixed relative pressure decreased in the following order: acetone>MEK>MnPK>MiPK. Diffusion coefficients for each penetrant increased with increasing penetrant concentration.     

The desorption of ethane–butane mixtures from polyethylene

The desorption of mixtures of ethane and butane at atmospheric pressure from low-density polyethylene was investigated over the temperature range from 20 to 60°C. Desorbed penetrants were continuously trapped in glass tubes immersed in liquid nitrogen, and composition was determined as a function of time by means of gas chromatography. The ratio of the quantity of desorbed gas at any time t, q_t, to the quantity at complete desorption, q_∞, was used to determine diffusion coefficients and solubility constants. The diffusion coefficients for both ethane and butane increase with increasing butane concentration in the temperature interval investigated. The solubility of both penetrants can be correlated by Henry's law at 40, 50, and 60°C. However, at 20 and 30°C. the solubility constant for both penetrants increases with increasing butane concentration. This trend is consistent with experimental observations for single-component diffusion and solubility of several hydrocarbons in polyethylene, where increasing concentration of penetrant plasticizes the polymer, resulting in increasing diffusion coefficients and solubility constants.     

Sorption and diffusion of n-alkanes into bromobutyl rubber membranes

Sorption and diffusion of n-alkanes into bromobutyl rubber membranes were investigated in the temperature interval 25–60°C by a sorption gravimetric method. The Fickian diffusion equation was used to calculate the diffusion coefficients, which were dependent on the size of the alkanes, their interactions with the chain segments of the polymer and temperature. The diffusion coefficients varied from 0.34×10^?7 cm²/s (n-hexadecane) to 9.94×10^?7 cm²/s (n-hexane). The activation energy for diffusion varied from 14kJ/mol (n-hexane) heptane to 2.0kJ/mol for n-hexadecane. The sorption/swelling results are discussed in terms of first and second order kinetic equations. The molar mass between chain-entanglement-crosslinks was estimated from swelling data. The experimental and calculated results showed a systematic dependence on the increasing size of the alkanes. None of the solvents showed any degradative effects on the polymer.     

The diffusion of nonionic penetrants in polyamide

The diffusion behavior of nonionic penetrants in aqueous solution into nylon 6 was examined in the temperature range 5°–95°C. The Arrhenius plot of the diffusion coefficients is linear and its slope changes at 30–40°C higher than the glass transition temperature in water, as determined by dilatometry and viscoelastic measurements. The results are discussed in relation to the molecular size of the penetrant and the segmental motion of polymer chains.     

Studies on molecular transport of n‐alkanes through poly(tetrafluoroethylene‐co‐propylene) elastomeric membrane

Molecular transport of a series of n‐alkanes through commercial TFE elastomer (FA 150L) has been studied in the temperature range 30–50 °C using sorption‐gravimetric method. The Fickian diffusion equation was used to calculate the diffusion coefficients, which were dependent on the size of the alkanes and temperature. The diffusion coefficients at 30°C varied from 4.53 × 10^?8 cm²/s (n‐heptane) to 0.18 × 10^?8 cm²/s (n‐hexadecane). The liquid concentration profiles have also been computed using analytical solution of Fick's equation with the appropriate initial and boundary conditions and these were presented as a function of penetration depth of molecular migration and time of immersion. These results have been discussed in terms of molecular size of alkanes as well as temperature. In all the liquid penetrants, the transport phenomenon was found to follow the anomalous behavior. From the temperature dependence of diffusion and permeation coefficients, the Arrhenius activation parameters have been estimated. These parameters do not exhibit any systematic variation with the size of the penetrants. The resulting low diffusion coefficients, contribute to the superior barrier performance of the membrane, is due, in part, to the high glass transition temperature of Aflas? TFE elastomer. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2228–2235, 2006     

A theory for the diffusion of large molecules in amorphous polymers above Tg

A general theory of diffusion of large molecules in rubbery amorphous polymers is of interest for the scientific understanding and with regard to material design and process optimization. A broadly applicable model would be useful in developing controlled transport of plasticizers and other additives through polymeric substances. A diffusion model is presented which has been developed for large molecular penetrants above the T_g of the amorphous polymer allowing for required increase in redistribution of the free volume of the polymer structure, as well as the penetrant size and shape. Applicability of the model is demonstrated by comparing theoretically developed diffusion curves for DNOP and DNDP in PVC vs. their weight fractions at 82°C and 91°C. These theoretically derived plots are compared with experimental D vs. w₁ curves for these systems generated at lower temperature.     

Sorption,desorption, diffusion,and permeation of aliphatic alkanes into santoprene thermoplastic rubber

The molecular transport characteristics of Santoprene rubber in the presence of n-alkanes, cyclohexane, 2,2,4-trimethylpentane, and 1,2,3,4-tetrahydronaphthalene at 25, 40, 55, and 70°C have been studied using a sorption gravimetric technique. From the sorption and desorption studies, the diffusion coefficients have been calculated and used in the discussion of the transport results. It was observed that these data depend on the size of the penetrants. Furthermore, efforts were made to evaluate the permeation coefficients, molar mass between crosslinks, and the kinetic rate constants. These data showed a systematic dependence on the penetrant size. Activation parameters for the process of diffusion and permeation have been calculated from the temperature dependence of the transport coefficients. © 1995 John Wiley & Sons, Inc.     

The effect of sorbed penetrants on the aging of previously dilated glassy polymer powders. I. Lower alcohol and water sorption in poly(methyl methacrylate)

Sorption kinetics and equilibria for methanol, ethanol, and n-propanol in 0.544 μm diameter poly(methyl methacrylate) microspheres were determined at 35°C over a wide range of relative pressures. Sorption isotherms were concave to the pressure axis at low relative pressures and convex to the pressure axis at higher relative pressures. These results, considered in the context of recently reported data for high pressure sorption of gases in polymeric glasses, suggest that the S-shaped isotherms reported here are examples of a generalized isotherm which describes sorption behavior of all penetrants in glassy polymers if an appropriate range of concentration is traversed by the experimental protocol. The effects of dialating the microspheres by preswelling with methanol were studied by subsequent low pressure sorption of water, methanol, ethanol, and n-propanol at 35°C. The preswollen microspheres exhibited initially higher sorption capacities than the as-Received samples, but tended to consolidate with time following the preswelling treatment. The aging process, monitored by periodic short-term sorption with the various penetrant probes, was arrested by contacting the microspheres with an activity of n-propanol sufficient to maintain a sorbed concentration of approximately 1 wt %. The aging was significantly retarded by the presence of low concentrations of water and ethanol. Conversely, the aging process appeared to be essentially unaffected by the presence of correspondingly low concentrations of methanol. The complex kinetics describing the sorption of the various penetrants ranged from Fickian diffusion to polymer relaxation-controlled absorption, depending upon penetrant, relative pressure, and prior exposure history. The low temperature preswelling of the microspheres markedly increased the rate of sorption as well as the respective apparent equilibrium sorption.     

The effect of sorbed penetrants on the aging of previously dilated glassy polymer powders. IV

Uniform, submicron-diameter polystyrene (PS) and poly(methylmethacrylate) (PMMA) microspheres were dilated by preswelling with pure organic vapors followed by rapid removal of the preswelling penetrant by protracted evacuation of the preswelling chamber to a pressure of 10^?3 mm Hg. Aging of the preswollen polymers was carried out both in vacuum and in the presence of various penetrants at sorbed concentrations typically less than 2 wt%. Inferences about relaxations of the polymers were based upon changes in concentrations of the penetrants within the microspheres, at a given temperature and penetrant activity, which result from aging in vacuum or in the presence of penetrant. The kinetics of the relaxations were monitored by probing the expanded glasses with relatively low concentrations of penetrants. In general, the continuous presence of these low concentrations of probe molecules either arrested or retarded the ensuing relaxation as compared with the aging that occurred in vacuum. A series of lower monohydric alcohols, lower n-alkanes, and some other similar penetrants were used as probes to test explicitly and systematically the effects of size and structure of the penetrant contacting the polymer during aging on the decay of excess sorption capacity of the preswollen glassy polymers. Decay of excess sorption in the presence of penetrant was evident only when molecularly small penetrants with interactive functional groups, alcohols for example, were sorbed into preswollen PMMA. This result suggested that the relaxation occurring in the presence of penetrant involved specific interactions between the penetrants and the carbonyl groups in the PMMA.     

Sorption/desorption properties of ethanol,toluene, and xylene in poly(dimethylsiloxane) membranes

Sorption/desorption kinetics and sorption equilibria have been determined for ethanol, toluene, and xylene vapors in a poly(dimethylsiloxane) membrane containing about 32 wt % silica resin at 25°C. Dependence of diffusion coefficient on vapor activity and sorption isotherms have been compared to identify the transport mechanisms of those penetrants in the PDMS membrane. The analysis of Zimm–Lundberg clustering functions showed that all three penetrants had a tendency to form clusters and ethanol molecules might be immobilized by the residual silanol groups within the silica resin in the membrane. The diffusion coefficient of toluene was roughly constant and that of xylene slightly decreased as increasing the vapor activity due to the competing effects of penetrant clustering and solvent swelling of polymer. The diffusion coefficient of ethanol versus activity exhibited a maximum due to the effects of ethanol immobilization and cluster formation. The freevolume effect by solvent swelling to diffusion was obscured by either penetrant clustering or immobilization for the three penetrant–polymer systems. © 1994 John Wiley & Sons, Inc.     

Molecular transport of n‐alkanes into PU/PBMA interpenetrating polymer network systems

The methylene diisocyanate (MDI) and toluene diisocyanate (TDI) based polyurethane/polybutyl methacrylate (PU/PBMA‐50/50) interpenetrating polymer network (IPN) membranes have been prepared. The molecular migration of n‐alkane penetrants such as hexane, heptane, octane, nonane, and decane through PU/PBMA (50/50) membranes has been studied at 25, 40, and 60°C using a weight gain method. From the sorption results, diffusion (D) and permeation (P) coefficients of n‐alkane penetrants have been calculated. Molecular migration depends on membrane‐solvent interactions, size of the penetrants, temperature, and availability of free volume within the membrane matrix. Attempts have been made to estimate the parameters of an empirical equation and these data suggest that molecular transport follows Fickian mode. From a study of temperature dependence of transport parameters, activation energy for diffusion (E_D) and permeation (E_P) have been estimated from the Arrhenius relation. Furthermore, sorption results have been interpreted in terms of enthalpy (ΔH) and entropy (ΔS) of sorption. The liquid concentration profiles have been computed using Fick's equation with appropriate initial and boundary conditions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 739–746, 2003     

Permeation of N-butane,propane and ethane through ethylcellulose

The permeation of n-butane, propane, and ethane in ethylcellulose has been measured over a pressure range from 25 to 200 mm Hg and over the temperature range from 30 to 70°C. The permeation and diffusional time lag of each of the three gases in ethylcellulose is pressure dependent. Transport of the gases through ethylcellulose can be described by the partial immobilization model. It was found that, in general, the Langmuir-mode species diffusion coefficients are lower than the Henry's law species diffusion coefficients. The logarithm of diffusion coefficients at zero penetrant concentration varies linearly with the square of the molecular diameter of n-butane, propane, and ethane permeating through ethylcellulose. This relationship suggests that the diffusion process depends upon the availability of sufficient cross-sectional area for the penetrant to diffuse. An Arrhenius temperature dependence was observed for permeation coefficients and diffusion coefficients for n-butane, propane, and ethane in ethylcellulose. The activation energy of diffusion at zero penetrant concentration is directly proportional to the square of the gas molecular diameter and the entropy of activation. This observation is consistent with the view that the activation energy of diffusion is associated with the energy required to produce a space of sufficient cross-section for the diffusion molecule to pass.     

Pervaporation separation of n‐heptane/organosulfur mixtures with PDMS membrane: Experimental and modelling

In this paper, polydimethylsiloxane (PDMS) pervaporation membrane was employed to simulate the desulfurization process of gasoline where n‐heptane was selected to stand for gasoline. A modified solution–diffusion model is proposed to account for the mass transport of penetrants in the polymer membrane. In the model, the group contribution method (the UNIFAC‐ZM model) is applied to calculate the activity of penetrants in the polymer membrane, and the free volume theory with some modifications is employed to describe the diffusion behaviour of the penetrants. The effects of operating temperature and feed concentration on pervaporation properties were investigated to validate the model. It has been shown that the results predicted by the solution–diffusion model are in good agreement with the experimental values.     

Diffusion of saturated hydrocarbons in low density polyethylene (LDPE) films

The diffusion coefficients at zero penetrant concentration, D₀, of n-heptane, n-heptane, n-octane, n-decane, and 2,2,4-trimethylpentane (TMP) in LDPE were obtained in the range of 25–50°C, using the desorption method. The dependence of D₀ on the size and shape of the penetrant is reported. It was found that D₀ decreases with increasing penetrant molecule size. The activation energies of diffusion in the temperature range of 25–50°C increase with increasing penetrant molecule size and are independent of temperature. The results are interpreted in terms of the free volume theory and semiquantitative estimates of the free volume parameters are reported.     

Diffusion of low molecular weight substances into a laminar film. I: Rigorous solution of the diffusion equation in a composite film of multiple layers

A rigorous solution of the diffusion of penetrant into a laminar film comprised of multilayers of m components is presented by an orthogonal-expansion method. As the simplest practical cases of m ? 2 and m ? 3, with stepwise distribution of both diffusion coefficients and solubility coefficients at the boundary between respective layers, the diffusion properties in the transient state are analyzed in detail. That is, changes in the penetrant concentration distribution within the laminar film and the total amount of penetrant sorbed within the film both with time after exposing the film to an atmosphere of fixed penetrant concentration are calculated for A–B as well as A–B–A type layer arrangements. The calculation is performed while keeping (L₂/L₁) at a constant value of 2.0 but varying the diffusion coefficient ratio of (D₁/D₂) from 10² to 10^?2, and/or varying the solubility coefficient ratio of (S₁/S₂) from 1 to 10, where L₁ and (L₂ ? L₁) are the thickness D₁ and D₂ are the diffusion coefficients of penetrant, and S₁ and S₂ are the solubility coefficients in the A-component and B-component, respectively. The sorption curves deviate considerably from those of Fickian curves of homogeneous film with (D₁/D₂) ? 1 in their respective ways. The results obtained here can be applied to the diffusion in a single component polymer film having a surface layer with different diffusion properties from that of the inner side of the film caused by differing distributions in molecular orientation or degrees of crystallinity.     

Effects of chain stiffness and penetrant size on penetrant diffusion in simple polymers: deduced relations from simulation and PRISM theory

Molecular dynamics simulations in the NVT ensemble were performed for a repulsive system of bead-spring polymer chains with angle constraints. The diffusion coefficients of spherical penetrants were measured for different size penetrants as the angle constraints were varied. The scaling of the diffusion coefficient with penetrant size varies as a function of chain stiffness from liquid-like behavior to polymeric behavior. Free volume distributions were calculated from both simulation and PRISM theory. It is found that free volume distributions and mean void size are constant with chain stiffness although the diffusion coefficient changes by a factor of two. This suggests that while free volume is necessary for diffusion to occur, binary collisions and chain relaxation also play a role in determining penetrant diffusion. The relative contributions of these factors to the diffusion coefficient may change as a function of chain stiffness.