Ion aggregation in high salt solutions. IV. Graph-theoretical analyses of ion aggregate structure and water hydrogen...

Ions in high salt solutions form a variety of ion aggregates, from ion pairs to clusters and networks. Their influences on water hydrogen bonding (H-bonding) network structures have long been of great interest. Recently, we have shown that the morphological structures of ion aggregates can be analyzed by using a spectral graph analysis theory, where each ion cluster or ion network is represented by a properly defined graph with edges and vertices. Here, to further examine the network properties of ion aggregates and water H-bonding networks in high salt solutions, we consider a few representative graph-theoretical descriptors: clustering coefficient, minimum path length, global efficiency, and degree distribution of ion aggregates. From the molecular dynamics trajectories, these graph theoretical properties of ion aggregates and water structures in NaCl and kosmotropic solutions are calculated and shown to be strongly dependent on the two types of ion aggregate structures, i.e., ion cluster and ion network. Ion clusters in high NaCl solutions exhibit typical behaviors of scale free network. The corresponding graph theoretical properties of ion networks in high KSCN solutions are notably different from those of NaCl ion clusters and furthermore they are very similar to those of water hydrogen-bonding network. The present graph-theoretical analysis results indicate that the high solubility limits of KSCN and other ion-network-forming salts might originate from their ability to form a large scale morphological network that can be intertwined with co-existing water H-bonding network. Furthermore, it is shown that the graph-theoretical properties of water H-bonding network structures do not strongly depend on the nature of dissolved ions nor on the morphological structures of ion aggregates, indicating that water's H-bonding interaction and network-forming capability are highly robust. We anticipate that the present graph-theoretical analysis results of high salt solutions would provide important information on the Hofmeister ion effects on water structure.