Statistical thermodynamics to assess probability of water channel formation in membrane

Abstract

In this work, the probability of water channel formation was calculated for several polymeric materials, and with that information, the desalination capacity of each material was assessed. Using a 3D lattice model for a flat sheet, the Gibbs free energy change (ΔG) that results from the formation of the first water channel from the top to the bottom surface of the sheet was calculated as a function of the hydrophilicity/-phobicity of the polymeric material (w), the total fraction of water in the 3D lattice (x), and the thickness of the lattice (n). With this result, an equation was further derived to evaluate (xb) the fraction of water which is related to the channel formation, and (xb/x), the ratio of xb to x. It was found that the values of xb are closely related to the fractional free volume (FFV) measured by positron annihilation lifetime spectroscopy (PALS) and the percent free volume of percolated open spaces where water could pass through obtained by molecular dynamics simulation (MDS).These equations were then used to assess the usefulness of each material for making reverse osmosis membranes. When xb is too large, too many channels form, and those channels join to form large pores through which salt can pass, rendering reverse osmosis unsuccessful. On the other hand, when xb is too small, not enough water channels are formed, so reverse osmosis cannot occur then either. It was found that xb was too small for polyvinylidene fluoride (PVDF) and polyethersulfone (PES); suitable for cellulose acetate (CA), aromatic polyamide (APA) and aromatic polyamidehydrazide (APAH); and too large for cellophane (CE). This paper determines which circumstances allow water to form channels in a membrane, and it provides a novel method to assess a material's suitability for reverse osmosis.