Structural characterization of ice polymorphs from self-avoiding walks

Topological properties of crystalline ice structures are studied by means of self-avoiding walks on their H-bond networks. The number of self-avoiding walks, C-n, for eight ice polymorphs has been obtained by direct enumeration up to walk length n = 27. This has allowed us to determine the 'connective constant' or effective coordination number mu of these structures as the limit of the ratio C-n/Cn-1 for large n. This structure-dependent parameter mu is related with other topological characteristics of ice polymorphs, such as the mean and minimum ring size, or the topological density of network sites. A correlation between the connective constant and the configurational entropy of hydrogen-disordered ice structures is discussed. (C) 2014 Elsevier B.V. All rights reserved.