Three-dimensional square water in the presence of an external electric field

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.