Molecular model for solubility of gases in flexible polymers

We propose a model for a priori prediction of the solubility of gases in flexible polymers. The model is based on the concept of ideal solubility of gases in liquids. According to this concept, the mole fraction of gases in liquids is given by Raoult's law with the total pressure and the vapor pressure of the gas, where the latter may have to be extrapolated.

However, instead of considering each polymer molecule as a rigid structure, we estimate the effective number of degrees of freedom from an equivalent freely jointed bead-rod model for the flexible polymer. In this model, we associate the length of the rods with the molecular weight corresponding to a Kuhn step.

The model provides a tool for crude estimation of the gas solubility on the basis of only the monomer unit of the polymer and properties of the gas. A comparison with the solubility data for several gases in poly(dimethylsiloxane) reveals agreement between the data and the model predictions within a factor of 7 and that better model results are achieved for temperatures below the critical temperature of the gas.

The model predicts a decreasing solubility with increasing temperature (because of the increasing vapor pressure) and that smaller gas molecules exhibit a lower solubility than larger ones (e.g., CH4 has a smaller solubility than CO2), which agrees with the experimental data.