The transport of gases and vapors in polymeric systems is of great interest for various applications, among the others for membranes technology. Therefore, solubility and the permeability of low molecular weight species in glassy and rubbery polymers are of great importance, and their prediction based on reliable models are highly needed.
In this work, use is made of a simple and fundamental approach recently proposed for the description of gas and vapor solubility and permeability, which considers the diffusion coefficient as the product of two contributions, the penetrant mobility (a purely kinetic parameter), and the thermodynamic factor (accounting for the dependence of the penetrant chemical potential on its concentration) .
The nonequilibrium thermodynamic approach (NET-GP) provides the description of the thermodynamic properties of the solute/polymer mixtures in the glassy state, and in particular of the solubility coefficient as well as of the thermodynamic factor for diffusion ; the penetrant mobility, on the other hand, is endowed with a simple exponential dependence on penetrant concentration. The simple and general expression derived for penetrant diffusivity and permeability requires two adjustable parameters only: the penetrant infinite dilution mobility L0, and the plasticization factor b, accounting for its dependence on concentration.
The resulting model is able to describe successfully all the different experimental behaviors of gas and vapor permeability in glassy polymers as a function of upstream pressure and even the non-monotonous behavior known as plasticization effect [3-5], and can also be employed for the a priori estimation of the permeability and selectivity properties, on the basis of the pure polymer and penetrant properties.
Indeed, the NET-GP model can be used predictively for the solubility coefficient, while the two mobility parameters of the model are endowed with a precise physical meaning which allow to relate them with pure polymer and penetrant properties through simple and effective correlations. In fact, the infinite dilution mobility depends on the penetrant size (e.g. critical volume), and on the polymer fractional free volume, while the plasticization factor is related to the swelling induced by the diffusant in the matrix, readily estimated by the NET-GP. On the other hand, the membrane sieving ability (diffusion selectivity) is strictly related to its cohesive energy, and the thermodynamic model readily provides the solubility selectivity contribution.
Thus, the model can be applied to obtained to a simple method for the calculation of permeability and selectivity of various gas pairs in glassy polymers. This can be then applied to the analysis of the upper bound correlations provided by Robeson , often employed in the evaluation of the membrane separation performance.
Noteworthy, the same approach can provide on one hand the detailed description of the permeability behaviors with pressure or temperature with a remarkable accuracy and, on the other hand, it also offers an estimation a priori of the permeability and selectivity of the various penetrants of interest, on the basis of simple physical correlations.
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