Mössbauer studies of bound diffusion in a model polymer system

Iron hydroxide particles with diameters of about 3 nm have been precipitated in a network of polymer chains of sulfonated polystyrene, cross-linked by divinylbenzene. The dynamics of these iron particles has been investigated by Mössbauer spectroscopy. The spectra were analyzed using a generalized Brownian oscillator model, in which the bound diffusion proceeds in an arbitrary potential. Samples with different degrees of cross-linkage have been investigated. The water content of the samples was varied, and the viscosity of the water was increased by the addition of sucrose solution. It can be shown that the size of the cages formed by the polymer chains essentially determines the type of diffusion. If the iron hydroxide particles have no free space, the dynamics is determined by the polymer network. With an increase of the free volume, the iron hydroxide particles show the typical behavior of bound diffusion in a hard cage. By increasing the size of the cage further, one attains a situation close to free diffusion. Varying the viscosity of the solvated liquid in a sample with a given cage size leads to a dynamics of the iron hydroxide particles that shows the expected dependence on the diffusion constant D. It should be noted that some of the samples show unusually broad Mössbauer spectra, with a half width up to 500 mm/s.