On the theory of self-diffusion in a polymer gel

The problem of self-diffusion in a random medium consisting of a solvent and a fixed set of scattering centers (obstacles) is discussed. A new equation describing diffusion of a Brownian particle in such a system is derived. We find that the self-diffraction coefficient of the particle depends on the concentration of scattering centers like D/D₀=1-A√C ₀-BC₀+⋯, where A and B are positive constants, depending on the size of particle and repulsive range of scatterers, and D ₀ is the diffusion coefficient in a pure solvent.