I n d . E n g . C h e m . R e s . 1987,26,433-438 Milam, E. E.; Crow, W. B.; Myers, J. R. Corrosion 1977, 33, 240. Nicolet, M-A.; Banwell, T. C.; Paine, B. M. In Ion Implantation and Zon Beam Processing of Materials; Hubler, G. K., Holland, 0. W., Clayton, C. R., White, C. W., Eds.; North-Holland: New York, 1984; pp 3-11. Preece, C. M., Hirvonen, J. K., Eds. Ion Implantation Metallurgy; The Metallurgical Society of AIME: Warrendale, PA, 1980. Sartwell, B. D.; Campbell, A. B.; Needham, P. B., Jr. In Ion Implantation in Semiconductors; Chernow, F., Borders, J. A., Brice, D. K., Eds.; Plenum: New York, 1977; pp 201-212.
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Sartwell, B. D.; Walters, R. P.; Wheeler, N. S.; Brown, C. R. In Corrosion of Metals Processed by Directed Metal Beams; Clayton, C. R., Preece, C. M., Eds.; The Metallurgical Society of AIME: Warrendale, PA, 1982; pp 53-74. Smidt, F. A., Ed. Ion Implantation for Materials Processing; Noyes Data: Park Ridge, NJ, 1983.
Received f o r review February 7, 1985 Revised manuscript received September 3, 1986 Accepted November 7, 1986
Sorption and Diffusion of Gases in Glassy Polymers Eizo Sada,* Hidehiro Kumazawa, Hiroshi Yakushiji, Yukio Bamba, and Kazuhiko Sakata Department of Chemical Engineering, Kyoto University, Kyoto 606, J a p a n
Shao-Ting Wang Department of Chemical Engineering, T i a n j i n University, Tianjin, China
T h e sorption and diffusion of carbon dioxide and methane in glassy polymer films of polystyrene and polycarbonate were measured over a temperature range of 20 deg below the glass transition temperature and pressures up t o 3 MPa. T h e sorption equilibrium for each system was described by a dual-mode sorption model. T h e Henry’s law constant and Langmuir affinity constant depend on temperature via a van’t Hoff type equation. T h e Langmuir capacity constant was found t o decrease monotonically t o zero as the temperature increases to the glass transition temperature. The permeability data for each system were well represented by the dual-mode mobility model based on gradients of concentration as well as chemical potential. T h e temperature dependence of the diffusion coefficients of Henry’s law and Langmuir modes was consistent with a n Arrhenius-type equation. T h e permeability expression was derived by incorporating a contribution of intermode jumps, and the contribution was numerically discussed in one of the present systems. The sorption of gases in glassy polymers is generally more complex than in rubbery polymers and the sorption equilibria have been described in terms of dual-mode sorption model, first suggested by Barrer et al. (1958), for many gas-glassy polymer systems. In the dual-mode sorption model, penetrant molecules are retained in the polymer in two distinct ways, namely, Henry’s law dissolution and Langmuir adsorption. This dual-mode concept a t sorption equilibrium has been well developed, whereas a parallel treatment for permeation of both dissolved and adsorbed molecular populations has not been well established yet as stated in the following. In an earlier stage of the theoretical treatment of diffusion in such a dual-mode system, it was assumed that there is always local equilibrium between dissolved and adsorbed molecules and the adsorbed molecules are completely immobilized, whereas the dissolved molecules execute diffusive movements (Vieth and Eilenberg, 1972). As the experimental results on permeability coefficients and time lags have been accumulated, however, the possibility that adsorbed molecules might be only partially rather than completely immobilized, i.e., execute diffusive movements, has been introduced. Petropoulos (1970) first suggested that the driving force for diffusion of dissolved and adsorbed molecules should be based on the gradients of chemical potential rather than concentration, and two distinct penetrant molecules, respectively, contribute to the total diffusion flux. Paul and Koros (1976) and Koros et al. (1978b) utilized the driving force based on the gradients of concentration in the course of analyses of a series of their experimental data. In both treatments, two penetrant molecules are assumed to diffuse in parallel, being locally in sorption equilibrium with each other. Recently,
Barrer (1984) has suggested that two kinds of penetrants should execute diffusive movements within the two respective modes and jumps between the two modes. In this paper, the sorption isotherms of carbon dioxide and methane in typical glassy polymer film samples of polystyrene and polycarbonate were measured over a temperature range of 20 deg below the glass transition temperature and pressures up to 3 MPa, and the sorption parameters were determined. The permeabilities of these gases in the same polymer samples were measured for upstream pressures up to 2.5 MPa over the same temperature range. In conjunction with measured sorption data, a gas diffusion mechanism has been discussed by comparing it with the existing transport models proposed by Petropoulos (1970), Paul et al. (1976), and Barrer (1984).
Theoretical Background The isotherm of sorption of gases in glassy polymers has been found to be satisfactorily described by a so-called dual-mode sorption model, which postulates a combination of Langmuir-type trapping in preexisting microvoids plus Henry’s law sorption (Barrer et al., 1958). Quantitatively, this may be written as c = C D + CH = kDP + cH’bP/(l + b p ) (1) The two sorbed populations, which are termed the Henry’s law population and Langmuir population, can execute diffusive movements with different mobilities. This approach has been called the dual-mode mobility model. The diffusion flux obtained from the dual-mode mobility model driven by the gradients of chemical potential has been given by Petropoulos (1970), viz.,
0888-588518712626-0433$01.50/0 0 1987 American Chemical Society
434 Ind. Eng. Chem. Res., Vol. 26, No. 3, 1987
After integrating eq 2 over p from p1to pz with J constant under steady state assuming sorption and diffusion parameters constant, one gets
Therefore, permeability
(P),which is defined by
P = Jl/(p1 - PZ)
+ DHD) - k a D H I ( P 1 - P2) (1 + b p i ) ( l + b p z )
ICH’b(DHH
(4)
(14)
Therefore, the permeability (P),which is defined by eq 4,can be given as
is written as
When bp,
If CD is replaced with kDp, eq 13 may be written as
