Liquid structure computer simulation

S. V. Shiyanovskii, 1.1. Smalyukh, and O. D. Lavrentovich, Computer simulations and fluorescence con-focal polarizing microscopy of structures in cholesteric liquid crystals, p. 229, in Defects in liquid crystals computer simulations, theory and experiments (Kluwer Academic Publishers, Netherland, 2001). 

Monte Carlo simulations are an efficient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an efficient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic effects are included. 

Essentially, the RISM and extended RISM theories can provide infonnation equivalent to that obtained from simulation techniques, namely, thermodynamic properties, microscopic liquid structure, and so on. But it is noteworthy that the computational cost is dramatically reduced by this analytical treatment, which can be combined with the computationally expensive ab initio MO theory. Another aspect of such treatment is the transparent logic that enables phenomena to be understood in terms of statistical mechanics. Many applications have been based on the RISM and extended RISM theories [10,11]. 

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... 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

Keywords liquid crystals, Gay-Berne, computer simulations, phase structure... 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

Another remarkable feature of thin film rheology to be discussed here is the quantized" property of molecularly thin films. It has been reported [8,24] that measured normal forces between two mica surfaces across molecularly thin films exhibit oscillations between attraction and repulsion with an amplitude in exponential growth and a periodicity approximately equal to the dimension of the confined molecules. Thus, the normal force is quantized, depending on the thickness of the confined films. The quantized property in normal force results from an ordering structure of the confined liquid, known as the layering, that molecules are packed in thin films layer by layer, as revealed by computer simulations (see Fig. 12 in Section 3.4). The quantized property appears also in friction measurements. Friction forces between smooth mica surfaces separated by three layers of the liquid octamethylcyclotetrasiloxane (OMCTS), for example, were measured as a function of time [24]. Results show that friction increased to higher values in a quantized way when the number of layers falls from n = 3 to n = 2 and then to M = 1. 

It has been proposed recently [28] that static friction may result from the molecules of a third medium, such as adsorbed monolayers or liquid lubricant confined between the surfaces. The confined molecules can easily adjust or rearrange themselves to form localized structures that are conformal to both adjacent surfaces, so that they stay at the energy minimum. A finite lateral force is required to initiate motion because the energy barrier created by the substrate-medium system has to be overcome, which gives rise to a static friction depending on the interfacial substances. The model is consistent with the results of computer simulations [29], meanwhile it successfully explains the sensitivity of friction to surface film or contamination. 

This chapter is concerned with the application of liquid state methods to the behavior of polymers at surfaces. The focus is on computer simulation and liquid state theories for the structure of continuous-space or off-lattice models of polymers near surfaces. The first computer simulations of off-lattice models of polymers at surfaces appeared in the late 1980s, and the first theory was reported in 1991. Since then there have been many theoretical and simulation studies on a number of polymer models using a variety of techniques. This chapter does not address or discuss the considerable body of literature on the adsorption of a single chain to a surface, the scaling behavior of polymers confined to narrow spaces, or self-consistent field theories and simulations of lattice models of polymers. The interested reader is instead guided to review articles [9-11] and books [12-15] that cover these topics. 

Clearly, any measurement that differentiates between the properties of high and low temperature forms of H20(as), and/or delineates the relationship between H20(as) and liquid H20, can be used to test the hypotheses advanced vis a vis their structures. These and the experimental tests suggested, together with the construction of continuous random network models more sophisticated than that for Ge(as), the increased use of computer simulation, and exploitation of the available experimental information to guide the choice of appproximations in a statistical mechanical theory should increase our understanding of H20(as) and, uitimately, liquid H20. 

Urahata, S.M., and Ribeiro, M.C.C., Structure of ionic liquids of l-alkyl-3-methy-limidazolium cations A systematic computer simulation study, ]. Chem. Phys., 120, 1855-1863, 2004. 

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