Osmotically active and passive counterions in inhomogeneous polymer gels

The concepts of osmotically passive and active counterions are introduced for spatially inhomogeneous polyelectrolyte systems. Osmotically passive counterions appear as a result of the trapping of counterions in wells of inhomogeneously distributed electric potential. This effect is additional to the well-known Onsager-Manning condensation (i.e. condensation on the line of charges), which also produces counterions that are osmotically passive. The simplest theory of the swelling of inhomogeneous polyelectrolyte gels taking into account the effect of osmotically passive counterions is developed. It is shown that such gels swell less than the corresponding counterparts with homogeneously distributed charges on the gel chains because osmotically passive counterions are no longer contributing to the exerting of osmotic pressure. Some experimental confirmations of the effect of osmotically passive counterions are discussed.