Phase behaviour computer simulations

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

As shown in section C2.6.6.2, hard-sphere suspensions already show a rich phase behaviour. This is even more the case when binary mixtures of hard spheres are considered. First, we will mention tire case of moderate size ratios, around 0.6. At low concentrations tliese fonn a mixed fluid phase. On increasing tire overall concentration of mixtures, however, binary crystals of type AB2 and AB were observed (where A represents tire larger spheres), in addition to pure A or B crystals [105, 106]. An example of an AB2 stmcture is shown in figure C2.6.11. Computer simulations confinned tire tliennodynamic stability of tire stmctures tliat were observed [107, 1081. 

Computer simulations therefore have several inter-related objectives. In the long term one would hope that molecular level simulations of structure and bonding in liquid crystal systems would become sufficiently predictive so as to remove the need for costly and time-consuming synthesis of many compounds in order to optimise certain properties. In this way, predictive simulations would become a routine tool in the design of new materials. Predictive, in this sense, refers to calculations without reference to experimental results. Such calculations are said to be from first principles or ab initio. As a step toward this goal, simulations of properties at the molecular level can be used to parametrise interaction potentials for use in the study of phase behaviour and condensed phase properties such as elastic constants, viscosities, molecular diffusion and reorientational motion with maximum specificity to real systems. Another role of ab initio computer simulation lies in its interaction... 

In principle, the expressions for pair potentials, osmotic pressure and second virial coefficients could be used as input parameters in computer simulations. The objective of performing such simulations is to clarify physical mechanisms and to provide a deeper insight into phenomena of interest, especially under those conditions where structural or thermodynamic parameters of the studied system cannot be accessed easily by experiment. The nature of the intermolecular forces responsible for protein self-assembly and phase behaviour under variation of solution conditions, including temperature, pH and ionic strength, has been explored using this kind of modelling approach (Dickinson and Krishna, 2001 Rosch and Errington, 2007 Blanch et al., 2002). 

This also favours the occurrence of temperature-dependent disorder. Computer simulation of structural variations and comparison of both theoretical and experimental behaviour of the integral intensities of structure-sensitive diffraction reflections allow one to prove the presence of the temperature-dependent disorder of the Fe(C12Gm)3(B i-C4H9)2 molecules in crystals. The thermal expansion anomalies and the relative shift of the molecules preced the phase transition and, presumably, promot its realization in this crystal [282]. 

Various physical and chemical properties useful to understand the solubility of RTlLs have been smdied, among which dielectric properties are crucially important. However, there are, at least, two problems in the study of dielectric properties. One problem concerns the experimental techniques and the other, the scientific aspects. Furthermore, there arises a basic question about how the permittivity derives, assunting that ILs are homogeneous. This is related to the interconnection polar to non-polar domains as predicted by computer simulation and evidenced by experiments. In addition, anomalous phase separation behaviour has been reported for binary systems of RTILs with some organic compounds. 

In previous papers we have reported on some detailed studies on the behaviour of the order parameter C, (T) which was assimilated to the correlation length for critical fluctuations accessible by means of neutron small-angle scattering as well some measurements on the molecular dynamics across the two phase transitions as explored by neutron quasielastic scattering as well as computer simulations. 

The two extremes, using instantaneous and cumulative phase predictions discussed above, provide only the framework for the total variability, which can be expected in the reservoir filling history studied here. Unravelling the evolution of petroleum fluid compositions in the Snorre Field through time would require a model resolution far exceeding what can be handled in reasonable computing time. The approach shown allows, however, a prediction of fluid properties, which is much closer to the natural fluid compositions than previously possible. This compositional kinetic scheme is the first of its kind to allow reasonable petroleum phase behaviour assessment in the simulation of basin evolution and hydrocarbon migration. 

Due to the rapid development of computer performance in the last few years, the molecular dynamics simulation method can now be used in order to get more detailed information on the phase behaviour of surfactant molecules at the air/water interface, provided that the number of molecules does not exceed a certain threshold value. With these computer simulation methods, it is possible to directly calculate molecular parameters such as the average tilt angle of the surfactant molecules adsorbed in the monolayer. 

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