Residual entropy of twisted and helical ice nanotubes

Abstract

To study the properties of ice nanotubes, the exact statistics of proton disorder are of interest. In this paper, a new version of the transfer-matrix method is applied to compute the number of defect-free configurations in twisted and helical ice nanotubes. For the calculation of the transfer matrices themselves, this new version of the transfer-matrix method uses small conditional matrices of size 2 x 2 or 4 x 4. For different types of nanotubes, the number of proton configurations in the unit cells of different lengths and the asymptotic values of the residual entropy are presented. For wide tubes, the convergence of the residual entropy to the entropy of the well-known two-dimensional ice model is discussed.