Topological cell-openness index for porous materials

TL;DR

This paper introduces a topological method using Betti numbers to estimate pore openness in porous materials, providing an alternative to traditional gas pycnometry and revealing additional structural insights.

Contribution

The authors develop a Betti number-based cell-openness index that improves pore characterization and offers new structural information beyond existing methods.

Findings

Significant correlations between the index and physical quantities in simulated structures.

The method can identify mismatches between traditional and topological measures.

Betti curves help estimate characteristic feature sizes in porous structures.

Abstract

We propose a method of estimating the proportion of open and closed cells in a porous material based on measuring Betti numbers on the structures. Based on this method, we define a cell-openness index {\tau} which can be used instead of or complementary to the proportion of open-celled volume reported by gas pycnometry, which is the current gold standard for pore type characterization. We discuss in what types of structures mismatches between the two measures can occur and how such mismatches convey additional information about the structure. We also demonstrate initial examples of significant correlations between {\tau} and measurable physical quantities in numerically generated structures. We also discuss how Betti curves can be used to estimate characteristic feature sizes in porous structures.