A novel connectivity factor for morphological characterization of membranes and porous media: A simulation study on structures of mono-sized spherical particles

Abstract

In this study, we propose to define a connectivity factor as the inverse of the diffusional tortuosity to measure quantitatively the connectivity of whatever type of structure. The concept of connectivity used here is related to the diffusional accessibility of the structure voids. This definition of connectivity factor arises from the consideration that, if we ideally imagine to decrease progressively the porosity of a regular structure, the porosity itself reaches a limit value below which the inner pores are not interconnected anymore. This leads to an evident situation of zero connectivity and infinite tortuosity, where there is no continuous diffusion path able to connect the structure voids. According to the proposed definition, the connectivity factor is comprised within [0, 1], with zero corresponding to a completely disconnected structure and unity to a completely connected one. To show the efficacy of the presented approach, a case study on the regular structure of mono-sized (mono-disperse) spherical particles (Simple Cubic (SC), Face-Centred Cubic (FCC), Body-Centred Cubic (BCC) and Tetragonal structures) is provided. In particular, the tortuosity of such structures is evaluated by Computational Fluid Dynamics simulations, calculating the connectivity factor consequently. The morphological modification with porosity is induced by changing the surface-surface interparticle distance, allowing us to take both positive (detached particles) and negative values (overlapping particles). For each structure, a comparison between the calculated trends and some correlations of literature is made, and a novel "hidden" morphological parameter has been identified, that is, the here-called Limit Porosity Value, below which the connectivity is zero. The presented approach represents a systematic methodology to quantify the connectivity of any structure and to compare the morphology of membranes, catalysts, and porous media in general.