Theory of transport of ions and macroions in heterogeneous polymer materials

We have developed a general theory to describe transport of ionic species in disordered polymer materials by considering electrostatic binding/unbinding of mobile ions with the matrix. The contributions to ionic conductivity from ion hopping among spatially correlated domains and direct sliding along the skeletons of the matrix are taken into account in deriving closed-form formulas. The theory is valid for the mobility of both electrolyte ions and charged macromolecules. When the charged macromolecule is topologically frustrated, extreme violations of Einstein’s law of mobility emerge during practical time scales of experimentation. Comparison between the predictions of the theory and experimental results on ionic conductivity will be presented.