Empty space and how things move around in it

by 1971- Willmore, Franklin Ted

The Cavity Energetic Sizing Algorithm (CESA) method of int Veld 7 is extended to characterize the nonspherical nature of free volume. The new technique is introduced with reference to simple model fluids (water, hard spheres, and a Lennard-Jones fluid) and then applied to polymers of interest to membrane scientists. A set of shape parameters is introduced, characterizing nanopores in terms of surface area, volume, radius of gyration, and span. Results are presented for a Lennard-Jones fluid and a hard sphere fluid, and for the high free volume polymers (poly-trimethyl-silyl-propane) poly(1-trimethylsilyl-1-propyne) (PTMSP) and a random copolymer of 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole (TFE/BDD). PTMSP is observed to have an average free volume cluster span of 1.43 nm, compared to TFE/BDD with an average cluster span of 0.98 nm, consistent with the markedly higher permeability of CO2 observed in PTMSP. An additional method for measuring free volume is introduced, similar to a method introduced by Greenfield and Theodorou69-72, which measures free volume relative to a specific probe. The method captures 1-3 times the fractional cavity volume captured by CESA. Free volume measurements are presented for a set of polysulfones with respect to noble gas 11, 73 probes. 17