Predictive Approach for the Solubility and Permeability of Binary Gas Mixtures in Glassy Polymers Based on an NETGP-NRHB Model

Abstract

The NETGP-NRHB lattice-fluid model describes the sorption thermodynamics of penetrants in amorphous polymer−penetrant mixtures locked in an out-of-equilibrium "glassy" state. It accounts for the nonrandom distribution of mean-field contacts and voids and for the possible occurrence of specific interactions. In this contribution, we assess the suitability of the NETGP-NRHB model to interpret the sorption thermodynamics of binary penetrant mixtures in glassy polymers. Moreover, adopting the gradients of NETGP-NRHB penetrant chemical potentials as driving forces for their diffusive fluxes, a self-consistent framework is proposed to predict the permeability of light gas binary mixtures in glassy polymer membranes once all of the model parameters are obtained by nonlinear regression of data of the corresponding binary and pure component subsystems. This approach is validated against solubility data of CO 2 /CH 4 and CO 2 /C 2 H 4 mixtures in glassy amorphous poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and poly(methyl methacrylate) (PMMA), respectively, and permeability data of CO 2 /CH 4 mixtures in three glassy amorphous polymer membranes (PAr, PSf, PH); all of the data are taken from the literature. In particular, solubility data are investigated up to a CH 4 partial pressure of 15 atm at a fixed CO 2 partial pressure equal to 5.1 atm for the system CO 2 /CH 4 /PPO and up to a CO 2 partial pressure of 4 atm at a fixed C 2 H 4 partial pressure equal to 2.09 atm for the system CO 2 /C 2 H 4 /PMMA. Permeability data are investigated at a fixed upstream molar concentration of the binary gas mixture equal to 0.5 by changing the total pressure up to 18 atm for the systems CO 2 /CH 4 /PAr and CO 2 /CH 4 /PSf and up to 14 atm for the system CO 2 /CH 4 /PH; the downstream total pressure is equal to 0 atm for all of the systems. All of the experimental sets of data are obtained at 35 °C. Solubility and permeability predictions for the ternary systems compare very well with all experimental literature data without additional parameters besides those required for the corresponding binary subsystems.

Modelling changes in glass transition temperature in polymer matrices exposed to low molecular weight penetrants

“…Its value is commonly retrieved by measurements performed on the pure polymer at the temperature of interest at atmospheric pressure. ksw,i represents a corrective phenomenological factor [21], which accounts for the instantaneous elastic swelling of the glassy polymeric matrix induced by sorption of the i- th penetrant [21,43,44]. Finally, Pi is the partial pressure of the i- th penetrant in the external fluid phase.…”

“…It suffices here to recall that the internal state variables of the NETGP–NRHB model, Γij and ναβ appearing in the expression of the chemical potential of the penetrants present in the polymer phase are still dictated by the minimization conditions of the Gibbs energy [21,40] (see equations (S5)–(S7) reported in the electronic supplementary material) and that the same scaling parameters and associated mixing rules of the NRHB model are adopted. The ‘mean-field’ penetrant–polymer binary interaction parameters, k ij , take the same values independently of the state of the mixture (glassy or rubbery) [21,44]. One can determine the value of k ij for a given couple of polymer–penetrant using the NETGP–NRHB model to fit pseudo-equilibrium solubility data for a glassy polymer–penetrant mixture and then use this value in the procedure for the evaluation of the glass–rubber map.…”

“…The value of ρp0 of PMMA has been set equal to 1.172 g cm −3 according to [43]. We remark that the use of the parameter k sw is necessary in view of the wide pressure range of the experimental data [44]. The value of k 12 determined in this way must be regarded, at least in principle, as being independent of the state (rubbery or glassy) of the polymer–penetrant mixture and has been used to predict the glass-to-rubber map reported in figure 6 along with experimental data taken from [42].…”

“…To improve the predictive capability, one could account for the temperature dependence of the binary interaction parameter, k ij , [44,45], that is generally assumed to take the following linear form: kij=kij,0+aT⋅T.…”

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

“…The NE approach can be applied to the SAFT and PC-SAFT EoS as well, yielding the NE-SAFT and NE-PC-SAFT models, respectively [155], which are better-suited to describe polar and associating species, but no explicit expression is available for the chemical potential due to the higher complexity of the free energy expression [156]. Application of the NET-GP framework to the Non-Random Hydrogen Bonding (NRHB) EoS [87,88] has been reported as well [157,158], also in the mixed-gas case [159,160].…”