Dynamics of tracer particles in gel-like media

Our previously proposed theory of kinetic arrest and activated barrier hopping in binary mixtures of hard and sticky spheres is applied to the problem of repulsive particle tracer diffusion. For a dynamically frozen matrix, a tracer kinetic arrest diagram is determined using a simplified version of ideal mode coupling theory. The matrix particles cluster more with increasing degree of attraction, resulting in extra free volume for tracer motion that shifts the onset of localization to higher volume fractions. At the nonergodicity transition, the tracer localization length is roughly its diameter and decreases exponentially with increasing matrix volume fraction. If the matrix is formed via thermoreversible gelation of a fluid, then the lifetime of the kinetically arrested state is a critical question. The naïve mode coupling theory localization boundary for a pure sticky particle fluid is computed and compared to the tracer localization boundary under dynamically frozen matrix conditions. Above a threshold degree of attraction, the matrix can be treated as effectively static for times less than the mean activated barrier hopping time, which grows strongly with increasing matrix particle stickiness.