The atomistic simulation of the gas permeability of poly(organophosphazenes). Part 1. Poly(dibutoxyphosphazenes)

Self-diffusion and solubility coefficients of six gas molecules (He, Ne, O₂, N₂, CH₄, and CO₂) in two poly(dibutoxyphosphazenes)—poly[bis(n-butoxy)phosphazene] (PnBuP) and poly[bis(sec-butoxy)phosphazene] (PsBuP)—have been investigated by means of molecular simulation using the COMPASS molecular mechanics force field. Diffusion coefficients were obtained from molecular dynamics (NVT ensemble) using up to 3 ns simulation time. Solubility coefficients were obtained by means of a Grand Canonical Monte Carlo (GCMC) method. Results of both simulations were in generally good agreement with experimental data with the exception of the simulation results for gas solubility in PsBuP where differences from the data may be attributed to microcrystallinity of the experimental sample. In the case of diffusivity, diffusion coefficients correlated well with the square of the effective diameter of the diffusing gas. Similarly a good correlation was found between the solubility coefficients obtained by GCMC simulation of sorption isotherms and the Lennard-Jones potential well depth parameter, ϵ/k.

The transition-state model of Gusev and Suter was used to determine free volume and free volume distribution for PnBuP, PsBuP, and poly[bis(iso-butoxy)phosphazene] (PiBuP). The diffusion coefficient for a given gas in each polyphosphazene was found to correlate exponentially with its accessible free volume fraction. A model for the distribution of accessible free volume, derived from the Cohen–Turnbull theory for the self diffusion of a liquid of hard spheres, was found to provide excellent fit with the simulation results.