Mixing time of molecules inside of nanoporous gold

Nanoporous gold is a two-component material consisting of metallic gold and a disordered network of pores. Using three-dimensional tomography data collected from a real nanoporous gold sample, we propose a new class of graphs for modeling the porous network of nanoporous gold. Roughly speaking, the graphs of this class are created by combining many copies of a constituent graph S in a particular way. For the graphs in this class we construct an estimate of the mixing time of a random walk on these graphs in terms of the mixing time of a random walk restricted to the constituent graph S. The mixing time can be used to measure the rate of diffusion of molecules through the porous network of nanoporous gold. Our estimate of the mixing time is useful for understanding how the "local" connectivity of the pores affects the rate of diffusion of molecules through a larger segment of the pore network and therefore may be used to identify nanoporous metals with high diffusion rates for particular applications.