9. Obtaining the Tortuosity Factor as a Function of Crystallinity in Polyethylene Membranes

When a gas flows through a polymeric membrane, the diffusion process is affected by the tortuosity factor (τ) and the chain immobilization factor (β) as two impedance elements which affect the diffusion in systems with large molecules. In this chapter, a thermodynamic framework to obtain values for the tortuosity and the chain immobilization parameters in semicrystalline polymeric membranes is presented. A thermodynamic expression for the factors τ and β in terms of the activation entropy and the cohesion energy of the polymeric structure was obtained. The model was applied to experimental data obtained for linear low-density polyethylene (LLDPE) membranes with different percentages of crystallinity and with different densities (0.94, 0.93, 0.92, 0.91, 0.90, and 0.87 g/cm³). Experimental measurements for diffusion and permeability of oxygen, methane, ethane, ethylene, propane, propylene, and helium were performed by the time-lag method. The temperature and pressure were of 30 °C and 1 bar, respectively, throughout all the diffusion and permeability analyses. Finally, to understand the differences between the parameters characterizing the immobilization of the chains and the tortuosity, with respect to the diffusion of gases, a thermodynamic analysis using helium was done.