Carl McBride

Anomalies in water as obtained from computer simulations of the TIP4P/2005 model: density maxima, and density, isothermal compressibility and heat capacity minima

The so-called thermodynamic anomalies of water form an integral part of the peculiar behaviour of this both important and ubiquitous molecule. In this paper our aim is to establish whether the recently proposed TIP4P/2005 model is capable of reproducing a number of these anomalies. Using molecular dynamics simulations we investigate both the maximum in density and the minimum in the isothermal compressibility along a number of isobars. It is shown that the model correctly describes the decrease in the temperature of the density maximum with increasing pressure. At atmospheric pressure the model exhibits an additional minimum in density at a temperature of about 200K, in good agreement with recent experimental work on super-cooled confined water. The model also presents a minimum in the isothermal compressibility close to 310K. We have also investigated the atmospheric pressure isobar for three other water models; the SPC/E and TIP4P models also present a minimum in the isothermal compressibility, although at a considerably lower temperature than the experimental one. For the temperature range considered no such minimum is found for the TIP5P model.

Heat capacity of water : a signature of nuclear quantum effects

In this note we present results for the heat capacity at constant pressure for the TIP4PQ/2005 model, as obtained from path-integral simulations. The model does a rather good job of describing both the heat capacity of ice I(h) and of liquid water. Classical simulations using the TIP4P/2005, TIP3P, TIP4P, TIP4P-Ew, simple point charge/extended, and TIP5P models are unable to reproduce the heat capacity of water. Given that classical simulations do not satisfy the third law of thermodynamics, one would expect such a failure at low temperatures. However, it seems that for water, nuclear quantum effects influence the heat capacities all the way up to room temperature. The failure of classical simulations to reproduce C(p) points to the necessity of incorporating nuclear quantum effects to describe this property accurately.

Quantum contributions in the ice phases: The path to a new empirical model for water—TIP4PQ/2005

With a view to a better understanding of the influence of atomic quantum delocalization effects on the phase behavior of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model in conjunction with the rigid rotor propagator proposed by Muser and Berne [Phys. Rev. Lett. 77, 2638 (1996)]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example, densities, structure, and relative stabilities.

Can simple models describe the phase diagram of water

The melting point of ice Ih for the TIP3P, SPC, SPC/E, TIP4P, TIP4P/Ew and TIP5P models has been determined by computer simulation. It has been found that the melting points of ice Ih for these models are 146, 190, 215, 232, 245 and 274 K respectively. Thus from the models of water available so far onl yT IP5P reproduces the experimental melting point of water. The relative stability of ice II with respect to ice Ih at the normal melting point has also been considered. Ice II is more stable than ice Ih for the TIP3P, SPC, SPC/E and TIP5P models. Only for the TIP4P and TIP4P/Ew models is ice Ih more stable than ice II at low pressures. The complete phase diagram for the SPC/E, TIP4P and TIP5P models has been computed. It has been found that SPC/E and TIP5P do not correctly describe the phase diagram of water. However, TIP4P provides a qualitatively correct description of the phase diagram of water. A slight modification of the parameters of the TIP4P model yields a new model, denoted as TIP4P/ice, which reproduces the experimental melting point of water and provides an excellent description of the densities of all ice phases.

The range of meta stability of ice-water melting for two simple models of water

A number of crystal structures of water have been ‘superheated’ in Monte Carlo simulations. Two well-known models for water were considered; namely the TIP4P model and the SPC/E model. By comparing the fluid–solid coexistence temperature to the temperature at which the solid becomes mechanically unstable and melts it is possible to determine the typical range of temperatures over which it is possible to superheat the ice phases in conventional simulation studies. It is found that the ice phases can be superheated to approximately 90 K beyond the fluid–solid coexistence temperature. Beyond this limit they spontaneously melt. This limit appears to depend weakly both on the type of ice phase considered and on the chosen model. Obviously only rigorous free energy calculations can determine the equilibrium fluid–solid coexistence of a model. However, a ‘rule of thumb’ is that, by subtracting 90 K from the mechanical stability limit of the ice phase one is provided with a first guess as to the equilibrium fluid–solid coexistence temperature.

Radial distribution functions and densities for the SPC/E, TIP4P and TIP5P models for liquid water and ices Ih, Ic, II, III, IV, V, VI, VII, VIII, IX, XI and XII

Monte Carlo computer simulation studies have been undertaken for virtually all of the ice phases as well as for liquid water for three of the most popular model potentials; namely SPC/E, TIP4P and TIP5P. Densities have been calculated for specific thermodynamic state points and compared to experimental results. The SPC/E and TIP4P models overestimate the solid densities by about 2%. The TIP5P model overestimates the solid densities by about 5-10%. The structural pair correlation functions between oxygen-oxygen, hydrogen-hydrogen and oxygen-hydrogen atoms were also obtained from the simulations. (These are available as ESIt). It has been found that SPC/E and TIP4P structural predictions are rather similar, with the only exception of ice II for which differences are visible between these two models. Predictions from the TIP5P are clearly different from those of the other models, especially for ices Ih and II. For the higher density ices structural differences between the models are rather small. Experimental data would be highly desirable to test the structural predictions of the different models of water. This is especially true for ice II. We have also found that the oxygen-oxygen correlation function of high density amorphous (HDA) water presents the same broad features as those exhibited by ice XII.

Phase behavior of attractive and repulsive ramp fluids : Integral equation and computer simulation studies

Using computer simulations and a thermodynamically self-consistent integral equation we investigate the phase behavior and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid demixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighborhood of the liquid-liquid transition region, leading to a phase diagram with a somewhat complicated topology. This solidification at moderate densities is also present in the repulsive ramp fluid, but in this case inhibits the fluid-fluid separation.

The fluid-solid equilibrium for a charged hard sphere model revisited

The global phase diagram of a system of charged hard spheres, composed of positive and negative ions of the same size, is obtained by means of computer simulations. Thermodynamic integration and Einstein crystal calculations are used to determine the free energies of the different possible solid structures. In this way, the fluid–solid and solid–solid phase transitions are located. Gibbs–Duhem integration is used to trace the full coexistence curves between the different phases involved. Three different solid structures are found to be stable for the model considered; namely, a cesium chloride structure (CsCl), a substitutionally disordered close packed structure which is faced centered cubic (fcc), and a tetragonal ordered structure with a fcc arrangement of atoms if the charge of the ions is not considered. At high temperatures, freezing leads to the substitutionally disordered close packed structure. This solid structure undergoes an order–disorder transition at low temperatures transforming into the t...

Liquid crystal phase formation for the linear tangent hard sphere model from Monte Carlo simulations

Monte Carlo simulations have been performed for the linear tangent hard sphere model. The models considered in this work consisted of m=3, 4, 5, 6, and 7 monomer units. For the models m=3 and m=4 we find an isotropic fluid and an ordered solid. For the m=5 model we find the sequence of phases isotropic–nematic–smectic A on compression, and the sequence solid–smectic A–isotropic on expansion. We suggest that the nematic phase for this model is meta stable. For the model m=6 we observe the phase sequence isotropic–nematic–smectic A on compression, and the sequence ordered solid–smectic A–nematic–isotropic on expansion. We observe a similar sequence on expansion of the m=7 model. The results for the m=7 model are in good agreement with those of Williamson and Jackson [J. Chem. Phys. 108, 10294 (1998)]. It was suggested by Flory [Proc. R. Soc. London, Ser. A 234, 73 (1956)] that liquid crystal phases could exist for length to breadth ratios ⩾5.437, i.e., m⩾6. In this work we place the lower bound at m⩾5.

MOLECULAR DYNAMICS SIMULATIONS OF A FLEXIBLE LIQUID CRYSTAL

Molecular dynamics simulations have been performed for a liquid crystal composed of a Gay—Berne core site with two alkyl chains of different length (C7 and C3) at either end of the molecule. Calculations have been carried out for 512 molecules in the NVT ensemble for simulation times of up to 8.0ns at two distinct densities. The liquid crystal phases of the material have been fully characterized by measurements of orientational order parameters and radial distribution functions in each phase. Results are also presented for conformational distributions and effective torsional potentials of the system. We conclude that models of this nature represent a powerful approach to the study of flexibility in mesogenic systems and open up possibilities for predicting both the phase behaviour and bulk properties of liquid crystals based solely on a prior knowledge of intermolecular interactions.