Residual entropy of quasi-one-dimensional water systems

Abstract

Water systems allow for numerous configurations differing by the directions of hydrogen bonds. Formally defined configurational entropy is a measure of the number of hydrogen bond networks. In the case of ice it corresponds to experimentally known residual entropy. There exist numerous quasi-one-dimensional water systems with different morphologies: chains, ribbons, ice nanotubes, etc. In the present paper we determined residual entropy for different classes of quasi-one-dimensional systems: tapes of the types Tn(1), Tn(1)m(1), Tn(0)Am, Tn(2), Tn(2)m(2); double tapes 2T6(2), 2T5(2)7(2); square-net sheets; ice nanotubes, including helical ones. To do so we applied the transfer-matrix method. In the case of single tapes it provided the analytical solution while the residual entropy of the other systems is found numerically. The analytical and numerical results demonstrate that the dependence of the number of configurations on the morphology of the water system is non-trivial: the residual entropy is invariant with respect to some structural characteristics but it is strongly affected by others.