Mathematically modelling competitive ion absorption in a polymer matrix

A recent publication [Linden et al., RSC Adv., 2014, 4, 25063-25066] describing a material with extreme efficiency and selectivity for adsorbing copper opens up the possibility of large scale purification technologies and new materials for prevention of biological growth, both in bulk and on surfaces. On the molecular scale, the material's efficiency and selectivity depends on competitive metal ion diffusion into a nanometer thin polymer film and on competitive binding of metal ions to specific ligand sites. We present and explore two reaction-diffusion models describing the detailed transport and competitive absorption of metal ions in the polymer matrix studied in [Linden et al., RSC Adv., 2014, 4, 25063-25066]. The diffusive transport of the ions into an interactive, porous polymer layer of finite thickness, supported by an impermeable substrate and in contact with an infinite electrolyte reservoir, is governed by forced diffusion equations, while metal ion binding is modelled by a set of coupled reaction equations. The qualitative behavior observed in experiments can be reproduced and explained in terms of a combination of (a) differing ion diffusive rates and, effectively, (b) an ion exchange process that is superimposed on independent binding processes. The latter's origin is due to conformational changes taking place in the polymer structure in response to the binding of one of the species. The results of simulations under a diverse set of parameter conditions are discussed in relation to experimental observations.