🍩 Database of Original & NonTheoretical Uses of Topology
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Persistent Homology Analysis of Ion Aggregations and HydrogenBonding Networks (2018)
Kelin XiaAbstract
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and their associated water hydrogenbonding networks still remains a challenging problem. In this paper, a newlyinvented mathematical method called persistent homology is introduced, for the first time, to quantitatively analyze the intrinsic topological properties of ion aggregation systems and hydrogenbonding networks. The two most distinguishable properties of persistent homology analysis of assembly systems are as follows. First, it does not require a predefined bond length to construct the ion or hydrogenbonding network. Persistent homology results are determined by the morphological structure of the data only. Second, it can directly measure the size of circles or holes in ion aggregates and hydrogenbonding networks. To validate our model, we consider two wellstudied systems, i.e., NaCl and KSCN solutions, generated from molecular dynamics simulations. They are believed to represent two morphological types of aggregation, i.e., local clusters and extended ion networks. It has been found that the two aggregation types have distinguishable topological features and can be characterized by our topological model very well. Further, we construct two types of networks, i.e., Onetworks and H2Onetworks, for analyzing the topological properties of hydrogenbonding networks. It is found that for both models, KSCN systems demonstrate much more dramatic variations in their local circle structures with a concentration increase. A consistent increase of largesized local circle structures is observed and the sizes of these circles become more and more diverse. In contrast, NaCl systems show no obvious increase of largesized circles. Instead a consistent decline of the average size of the circle structures is observed and the sizes of these circles become more and more uniform with a concentration increase. As far as we know, these unique intrinsic topological features in ion aggregation systems have never been pointed out before. More importantly, our models can be directly used to quantitatively analyze the intrinsic topological invariants, including circles, loops, holes, and cavities, of any networklike structures, such as nanomaterials, colloidal systems, biomolecular assemblies, among others. These topological invariants cannot be described by traditional graph and network models.