Topological cell-openness index for porous materials

We propose a method of estimating and parametrising the proportion of open and closed cells in a porous material based on measuring Betti numbers on the structures. We define a cell-openness index τ which can be used to complement 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 demonstrate examples of significant correlations between τ and measurable physical quantities in both numerical and experimental structures. We also discuss how Betti curves can be used to estimate characteristic feature sizes in porous structures.