A micromechanics model for molecular diffusion in materials with complex pore structure

Molecular diffusion in fully saturated porous materials is strongly influenced by the pore space, which, in general, is characterized by a complex topological structure. Hence, information on macroscopic diffusion properties requires up-scaling of transport processes within nano-pores and micro-pores over several spatial scales. A new model in the framework of continuum micromechanics is proposed for predicting the effective molecular diffusivity in porous materials. Considering a representative volume element, characterizing a porous material without any information about the pore space microstructure complexity, the uniform flux is perturbed by recursively embedding shape information hierarchically in the form of the ESHELBY matrix-inclusion morphology to obtain the effective diffusivity as a function of the recurrence level and the porosity. The model predicts a threshold value for the porosity, below which no molecular diffusion can occur because of the presence of isolated pore clusters that are not connected and unavailable for transport. The maximum porosity, below which no molecular transport is possible, is predicted as one-third for spherical inclusions. The model allows for extensions to more complex morphologies of the inclusions. We also identify, that the effects of the micro-structure on molecular transport are characterized by porosity dependent long-range and short-range interactions. The developed framework is extended to incorporate realistic pore size distributions across several spatial scales by means of a distribution function within the hierarchical homogenization scheme. Available experimental results assert the model predictions.