Rate of gas transport in glassy polymers: a free volume based predictive model

Abstract

Free volume theories of diffusion developed in the literature successfully treat penetrant transport behavior in rubbery polymers. The potential of such a free volume theory to predict the gas transport behavior in glassy polymers is explored here, duly taking into account the excess hole free volume present in the glassy state. The calculations require values for three model parameters appearing in the theory of diffusion which are obtained by fitting experimental gas permeability data in rubbery polymers. The calculations also require an estimate for the hole free volume in the gas-polymer mixture. This is obtained by fitting experimental gas sorption data in rubbery and glassy polymers to a free volume based theory of gas sorption developed here. Thus, the calculation of gas permeability in glassy polymers is strictly predictive in the sense that no use is made of experimental permeation data in the glassy state. I. Introduction Free volume concepts have been successfully used for the quantitative description of equilibrium and transport properties of polymeric systems. The equation of state models of Flory (1965, 1970), Prigogine (Prigogine et al., 1953a-c; Prigogine, 1957), Patterson (Patterson, 1969; Patterson and Delmas, 1970), and Sanchez and Lacombe (1976,1978) are examples of how the free volume concept has been employed in the quantitative treatment of equilibrium behavior. The treatment of viscosity of polymer melts by Williams et al. (1955) (see also Ferry, 1970) and of diffusion by Cohen and Turnbull (1959), Fujita (1961), and Vrentas and Duda (1977a,b, 1979,1986) are some examples of free volume based treatments of transport behavior. Given the success of free volume models in describing diffusion behavior in rubbery polymers, it is natural to explore whether they can be employed also to describe the permeability behavior of gases in glassy polymers. Specifically, we show in this paper that, from our knowledge of sorption behavior in rubbery and glassy polymers and of diffusion behavior in rubbery polymers, we can reasonably predict the permeability of gases through glassy polymer membranes without using any experimental permeability data in the glassy state.