Calculation of the residual entropy of Ice Ih by Monte Carlo simulation with the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method

Understanding the impact of ammonium ion substitutions on heterogeneous ice nucleation

Understanding the mechanisms underpinning heterogeneous ice nucleation in the presence of ionic inclusions is important for fields such as cryopreservation and for improved models of climate and weather prediction. Feldspar and ammonium are both present in significant quantities in the atmosphere, and experimental evidence has shown that feldspar can nucleate ice from ammonium-containing solutions at temperatures warmer than water alone. In recent work, Whale hypothesised that this increase in nucleation temperature is due to an increase in configurational entropy when an ammonium ion is included in the ice hydrogen bond network (T. F. Whale, J. Chem. Phys., 2022, 156, 144503). In this work, we investigate the impact of the inclusion of an ammonium ion on the hydrogen bond network by direct enumeration of the number of structures found using Rick's algorithm. We also determine the energy of these systems and thus compare the effects of enthalpy and entropy to test Whale's hypothesis. We find that the inclusion of an ammonium ion increases the total number of configurations under conditions consistent with a realistic surface charge. We also find that the enthalpic contribution is dominant in determining the location of the ammonium ion within the structure, although we note that this neglects other practicalities of ice nucleation.

Exact results for the residual entropy of ice hexagonal monolayer

Since the problem of the residual entropy of square ice was exactly solved, exact solutions for two-dimensional realistic ice models have been of interest. In this work, we study the exact residual entropy of ice hexagonal monolayer in two cases. In the case that the external electric field along the z-axis exists, we map the hydrogen configurations into the spin configurations of the Ising model on the kagome lattice. By taking the low temperature limit of the Ising model, we derive the exact residual entropy, which agrees with the result determined previously from the dimer model on the honeycomb lattice. In another case that the ice hexagonal monolayer is under the periodic boundary conditions in the cubic ice lattice, the residual entropy has not been studied exactly. For this case, we employ the six-vertex model on the square lattice to represent the hydrogen configurations obeying the ice rules. The exact residual entropy is obtained from the solution of the equivalent six-vertex model. Our work provides more examples of the exactly soluble two-dimensional statistical models.

Ring population statistics in an ice lattice model

We calculate the distribution probability of hexagonal six-site rings in the disordered state of a cubic or hexagonal ice lattice model with ice rules perfectly obeyed. The mean-field distribution obtained is in significant agreement with those, slightly different among them, obtained by Monte Carlo simulations of the cubic or hexagonal model. The results are discussed in connection with the equilibrium and non-equilibrium transition from disorder to ferroelectric proton order.