Doping-controlled ion diffusion in polyelectrolyte multilayers: Mass transport in reluctant exchangers

A new paradigm for nonlinear doping-controlled ion transport in soft condensed matter is presented, where the mobility of a minority "probe" ion is controlled by majority "salt" ion. The class of materials to which this paradigm applies is represented by ultrathin films of polyelectrolyte complexes, or multilayers. Intersite hopping of probe ions of charge v occurs only when the charge of the destination site, produced by clustering of monovalent salt ions, is at least -nu, conserving electroneutrality. Salt ions are reversibly "doped" into the multilayer under the influence of external salt concentration. In situ ATR-FTIR reveals that the doping level, y, is proportional to salt concentration. Because hopping requires coincidence, or clustering, of salt, a strongly nonlinear dependence of flux, J, on salt concentration is observed: Jsimilar to[NaCl](nu) similar toy(nu). This scaling was reproduced both by Monte Carlo simulations of ion hopping and by continuum probability expressions. The theory also predicts the observed scaling, though it underestimates the magnitude, of the strong selectivity of multilayers for ions of different charge.