Self-diffusion of non-interacting hard spheres in particle gels

Different kinds of particle gels were simulated using a process of random aggregation of hard spheres. The mean square displacement of Brownian spherical tracer particles through these rigid gels was monitored and the average diffusion coefficient, normalized with the free diffusion coefficient (D), was obtained. For each gel structure the effect of the gel volume fraction (φ) and size ratio of the tracer (d) on the relative diffusion coefficient was investigated systematically. The volume fraction that is accessible to the tracers (φ(a)) was determined in each case. D was found to be approximately the same if φ(a) was the same, independent of φ, d and the gel structure. However a different behaviour is found if the tracers can penetrate the strands of the gel. A state diagram of d versus φ is given that shows the critical values (d(c), φ(c)) at which all tracers become trapped. Different values are found for different gel structures. The dependence of D on φ/φ(c) is independent of d, while the dependence of D on d/d(c) is independent of φ.