Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials

Abstract: 3D bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Due to their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity $\phi_1=1/2$: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective transport properties via closed-form microstructure-property formulas. Specifically, we estimate the recently introduced time-dependent diffusion spreadability exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in the extreme porosity limits by identifying the corresponding optimal structures.