Mean-field theory of ice phase stability

Predicting nonpolymeric materials structure with real-space self-consistent field theory

Polymer self-consistent field theory of the Edwards-Helfand kind is the state-of-the-art method for predicting the morphologies of block copolymer materials. The methodology of block copolymer self-consistent field theory is transported to classical density functional theory such that a wide range of self-consistent field theory tools can be applied to completely nonpolymeric materials, such as liquid crystal, molecular, or colloidal systems. This allows for the prediction of structure in nonpolymeric condensed matter systems without any prior knowledge of the possible phases, using calculations that take a fraction of the time needed for simulations. The approach is applied to a simple interaction site density functional theory representing adsorbed nitrogen molecules, and plastic crystal as well as herringbone phases are found in the phase diagram.

A potential model for the study of ices and amorphous water: TIP4P/Ice

The ability of several water models to predict the properties of ices is discussed. The emphasis is put on the results for the densities and the coexistence curves between the different ice forms. It is concluded that none of the most commonly used rigid models is satisfactory. A new model specifically designed to cope with solid-phase properties is proposed. The parameters have been obtained by fitting the equation of state and selected points of the melting lines and of the coexistence lines involving different ice forms. The phase diagram is then calculated for the new potential. The predicted melting temperature of hexagonal ice (Ih) at 1 bar is 272.2 K. This excellent value does not imply a deterioration of the rest of the properties. In fact, the predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.

The melting temperature of the most common models of water

The melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E,TIP3P,TIP4P, TIP4P/Ew, and TIP5P) is obtained from computer simulations at p = 1 bar. Since the melting temperature of ice I(h) for the TIP4P model is now known [E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 (2004)], it is possible to use the Gibbs-Duhem methodology [D. Kofke, J. Chem. Phys. 98, 4149 (1993)] to evaluate the melting temperature of ice I(h) for other potential models of water. We have found that the melting temperatures of ice I(h) for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T = 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I(h) with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II (so that ice I(h) is not a thermodynamically stable phase for these models). For TIP4P and TIP4P/Ew, ice I(h) is the stable solid phase at the standard melting point. The location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters.

Combinatorial entropy and phase diagram of partially ordered ice phases

A close analytical estimate for the combinatorial entropy of partially ordered ice phases is presented. The expression obtained is very general, as it can be used for any ice phase obeying the Bernal-Fowler rules. The only input required is a number of crystallographic parameters, and the experimentally observed proton site occupancies. For fully disordered phases such as hexagonal ice, it recovers the result deduced by Pauling, while for fully ordered ice it is found to vanish. Although the space groups determined for ice I, VI, and VII require random proton site occupancies, it is found that such random allocation of protons does not necessarily imply random orientational disorder. The theoretical estimate for the combinatorial entropy is employed together with free energy calculations in order to obtain the phase diagram of ice from 0 to 10 GPa. Overall qualitative agreement with experiment is found for the TIP4P model of water. An accurate estimate of the combinatorial entropy is found to play an important role in determining the stability of partially ordered ice phases, such as ice III and ice V.