Atomistic Simulations of Liquids

The basic idea behind an atomistic-level simulation is quite simple. Given an accurate description of the energetic interactions between a collection of atoms and a set of initial atomic coordinates (and in some cases, velocities), the positions (velocities) of these atoms are advanced subject to a set of thermodynamic constraints. If the positions are advanced stochastically, we call the simulation method Monte Carlo or MG [10]. No velocities are required for this technique. If the positions and velocities are advanced deterministically, we call the method molecular dynamics or MD [10]. Other methods exist which are part stochastic and part deterministic, but we need not concern ourselves with these details here. The important point is that statistical mechanics teUs us that the collection of atomic positions that are obtained from such a simulation, subject to certain conditions, is enough to enable aU of the thermophysical properties of the system to be determined. If the velocities are also available (as in an MD simulation), then time-dependent properties may also be computed. If done properly, the numerical method that generates the trajectories 

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This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

Wilson JA (1977) A Generalized Configuration - Dependent Band Model for Lanthanide Compounds and Conditions for Interconfiguration Fluctuations. 32 57-91 Wilson MR (1999) Atomistic Simulations of Liquid Crystals. 94 41-64 Winkler H, see Trautwein AX (1991) 78 1-96... 

Bulk atomistic simulations of liquid crystal mesophases are extremely time-consuming and currently represent the limit of what can be achieved with today s computers. However, in the past few years a number of (mainly) united-atom models of small mesogens have started to appear in the literature. These simulations are sununarised in Table 2, and snapshots of molecules taken from a MD simulation of CCH5 are shown in Fig. 7. Many of the studies in Table 2 suffer from common drawbacks, namely small numbers of moleeules and rather short simulation... 

Table 3. Diffusion constants from atomistic simulations of liquid crystals.

Abrams, C.F. and Kremer, K. (2003) Combined coarse-grained and atomistic simulation of liquid bisphenol A-polycarbonate liquid packing and intramolecular structure. Macromolecules, 36 (1), 260-267. 

Table 1. Atomistic simulations of bulk liquid crystals... 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Bhargava, B.L., and Balasubramanian, S., Refined potential model for atomistic simulations of ionic liquid, /. Chem. Phys., 127, 114510, 2007. 

The simulation models also correctly predicted the diffusivities of hydronium and methanol in a wide range of temperature (Fig. 19). Methanol is a neutral species and weakly interacts with Nation backbone. It is not surprising that the present MD models that do not consider chemical interaction between the molecules can still correctly evaluate the diffusivity of methanol. Because the present experimental setup is limited for liquid samples, whether or not the permeability of diffusivity is strongly depends on water content has not been examined. In summary, this work provided benchmark for the atomistic simulation of the transport processes in Nation at water content above 3 although at some points, the errors can be 100%. 

R. H. Boyd and P. V. K. Pant, Polym. Prepr. ACS, Div. Polym. Chem., 30(2), 30 (1989). Atomistic Simulation of a Polymeric Glass Starting from an Equilibrated Liquid. 

Atomistic Simulations of Neat Ionic Liquids - Structure and Dynamics... 

The potential energy functions for both water and biomolecules are important in making atomistic simulations of biomolecules in solution quantitative. Water, as a liquid with many unique properties that are important for life on earth, must be modeled with... 

Sylvester, M. F., Yip, A., and Argon, A. S. (1991) Investigations by atomistic simulation of structural and dynamic differences in the glassy and liquid states of atactic polypropylene, in Computer Simulation of Polymers, edited by Roe, R. J., Upper Saddle River, NJ Prentice Hall, pp. 105-121. 

Kelkar MS, Shi W, Maginn EJ (2008) Determining the accuracy of classical force fields for ionic liquids atomistic simulation of the thermodynamic and transport properties of 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtS04]) and its mixtures with water. Ind Eng Chem Res 47 9115-9126... 

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