Estimation of diffusivities and solubilities from sorption studies

Abstract

AbstractTechniques and results are reported for the joint estimation of kinetic (diffusion) and equilibrium (solubility) properties of gas—polymer systems. Pressure decreasing with time is measured in a closed, isothermal system as gas diffuses radially into a cylindrical mass of polymer held in a sintered steel or glass container. Polyethylene and polystyrene with various gases have been studied at temperatures up to 227°C. and pressures to 650. Gas pressures are raised “incrementally” to minimize (and to study) the dependence of diffusivities on concentration and pressure and to improve solubility estimation. Data collection techniques have evolved from hand recording of time, temperature, and pressure to use of an automatic analog and digital recording system. Pressures are converted to moles by use of an empirical equation of state based on published P—V—T data. Fourier's equation for radial diffusion from a closed well‐mixed solution into an infinite cylinder and some approximations thereto serve as a frame of reference for analysis of the data. Least squares estimates of the diffusivity and solubility are obtained by a numerical iteration process on an electronic computer. Some of the effects of departures from applicability of Fourier's equation are overcome by extrapolating series of estimetes of diffusivities and solubilities obtained from systematically censoring the data.