Regular Solution Theory for Polymer Permeation Transients: A Toolkit for Understanding Experimental Waveshapes

The accurate measurement of permeation is important at the product design stage for a variety of industries as diverse as conveyance methods for oil and gas produced fluids, such as mixtures of carbon dioxide, methane, hydrogen sulfide, water, and hydrocarbons, and in polymer-lined, unbonded flexible risers and flow lines through connectors and valves, hydrogen and methane gas carrying domestic lines, hydrogen storage tanks, sulfur hexafluoride circuit breakers for high power-carrying lines, oxygen through display technology, and drug delivery. It would also be appropriate to monitor the permeation rate through the polymer, composite, and elastomeric layers during the in-service times where applications allow. In the future, any alteration in the short term and long-term transport rates could be analyzed in terms of an initial alteration or degradation of the polymeric materials and, in some cases, metallic components. Crucially, such measurements would serve as an early warning system of any change in a polymeric material that could result in the loss of function of the fluid of a gas containing barrier material. Most experimental determinations are made through recording flux transients (varying flux) through permeation cells in which a polymer membrane or film separates a donor compartment (usually an infinite supply) and an acceptor compartment and in which membrane transport is considered to be slow. Treatment of the resulting experimental data is usually, but not always, undertaken through comparison with a steady-state model based on Fickian diffusion through the membrane, so as to extract the membrane permeability, the diffusion coefficient of the permeant, and the solubility of the permeant in the membrane phase. However, in spite of these measurements being undertaken routinely using closed cell manometric or continuous flow methods, there is a lack of literature in which experimental flux transients are provided, and in several cases, it is clear that the experimental data do not conform to the expected model of slow, Fickian diffusion through the membrane, even though experiments are performed at temperatures much higher than the glass transition temperature of the polymer membrane. In this paper, we first re-examine the classical model for an infinite source and extend it to account for (1) molecular interactions between membrane and permeant, using regular solution theory, (2) slow transport in the acceptor phase, and (3) slow kinetics across the membrane|acceptor interface. We demonstrate that all three aspects can cause permeation flux transients to exhibit unusual, nonclassical waveshapes, which have nevertheless been experimentally realized without rationalization. This enables the development of an algorithmic toolkit for the interpretation of permeation flux transients, so as to provide reliable and accurate data analysis for experimentalists.