Thermodynamic Model
Gas transport through glassy polymers involves multiple distinct modes of penetrant immobilization. The dual-sorption theory describes this behavior by combining Henry’s law dissolution with Langmuir cavity filling. These two modes represent different microstructural environments within the polymer matrix.
Henry’s law describes absorption into the dense polymer matrix, while Langmuir sorption describes the filling of microvoids or free-volume elements.
Mathematical Description
Total penetrant concentration is expressed as the sum of the two independent populations. The dual-sorption theory uses a non-linear equation where the Henry’s law term is proportional to pressure, and the Langmuir term is a hyperbolic function of pressure. The parameters include the Henry’s law solubility coefficient, the Langmuir capacity parameter, and the Langmuir affinity constant.
These constants are derived by fitting experimental isotherm data across a wide range of pressures.
Physical Separation
The glassy state of polymers maintains a non-equilibrium excess free volume that provides pre-existing gaps for penetrant molecules. Under the dual-sorption theory, molecules in the Langmuir mode are largely immobilized within these gaps, while the Henry mode molecules remain mobile and contribute to diffusion. As pressure increases, the Langmuir sites become saturated, causing the overall solubility coefficient to decrease and approach the Henry’s law limit.
This saturation explains the downward curvature observed in gas solubility isotherms for glassy polymers. When the polymer undergoes physical aging, the excess free volume collapses, which significantly reduces the Langmuir capacity parameter.
Material Evaluation
Membrane design for gas purification depends on accurate solubility predictions. Industrial engineers use the dual-sorption theory to evaluate how plasticizing gases like carbon dioxide affect polymer performance over time. Characterization involves testing polymer membranes under varying pressures and temperatures to extract the three primary parameters.
This systematic testing ensures that the membranes retain their selectivity under high-pressure industrial operating conditions.
