Residual entropy of ice nanotubes and ice layers

A relatively simple algorithm is presented for the complete enumeration of all H-bond networks in finite fragments of ice nanotubes and ice layers with periodic boundary conditions. This algorithm is based on the well-known transfer matrix method and it includes a convenient procedure for calculation of the elements of transfer matrices themselves. To facilitate this, it is necessary to specify only very small local matrices of sizes 2×2 or 4×4. We present exhaustive statistics of H-bonds arrangements for finite-size zigzag- and armchair-like ice nanotubes, for the fragments of hexagonal monolayer and bilayer and also for ice nanotubes consisting of stacked n$n$-membered rings. Using the new algorithm, we have also calculated the specific residual entropy for the infinite two-dimensional lattices. The agreement with the well-known solution for a square ice model demonstrates the reliability of the obtained results.