tda-segmentor: A tool to extract and analyze local structure and porosity features in porous materials

Local geometrical features of a porous material such as the shape and size of a pore or the curvature of a solid ligament do often affect the macroscopic properties of the material, and their characterization is necessary to fully understand the structure-property relationships. In this contribution, we present an approach to automatically segment large porous structures into such local features. Our work takes inspiration from techniques available in Topological Data Analysis (TDA). In particular, using Morse theory, we generate Morse-Smale Complexes of our structures that segment the structure, and/or its porosity into individual features that can then be compared. We develop a tool written in C++ that is built on the topology toolkit (TTK) library, an open source platform for the topological analysis of scalar data, with which we can perform segmentation of these structures. Our tool takes a volumetric grid representation as an input, which can be generated from atomistic or mesh structure models and any function defined on such grid, e.g. the distance to the surface or the interaction energy with a probe. We demonstrate the applicability of the tool by two examples related with analysis of porosity in zeolite materials as well as analysis of ligaments in a porous metal structure. Specifically, by segmenting the pores in the structure we demonstrate some applications to zeolites such as assessing pore-similarity between structures or evaluating the accessible volume to a target molecule such as methane that can be adsorbed to its surface. Moreover, once the Morse-Smale complexes are generated, we can construct graph representations of the void space, replacing the entire pore structure by a simply connected graph. Similarly, the same tool is used to segment and generates graphs representing the solid structure and we show how they can be used to correlate structure and mechanical properties of the material. The code is published as open-source and can be accessed here: https://github.com/AMDatIMDEA/tda-segmentor