Atomistic methods molecular dynamics

Although the folding of short proteins has been simulated at the atomic level of detail [159,160], a simplified protein representation is often applied. Simplifications include using one or a few interaction centers per residue [161] as well as a lattice representation of a protein [162]. Some methods are hierarchical in that they begin with a simplified lattice representation and end up with an atomistic detailed molecular dynamics simulation [163]. 

Thermodynamic properties of a system can also be obtained from the atomistic considerations. Molecular dynamics or Monte Carlo methods have been successfully used to smdy polymers. The success stems from the fact that many properties can be projected from dynamics of relatively simple, oligomeric models. Unfortunately, miscibility strongly depends on the molecular weight and so far it cannot be examined by these methods. 

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... 

Related to the previous method, a simulation scheme was recently derived from the Onsager-Machlup action that combines atomistic simulations with a reaction path approach ([Oleander and Elber 1996]). Here, time steps up to 100 times larger than in standard molecular dynamics simulations were used to produce approximate trajectories by the following equations of motion ... 

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. 

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]. 

The aim of the force matching procedure is to obtain the effective pair-force between CG sites using the force data obtained from a detailed atomistic molecular dynamics (MD) trajectory. The current implementation of the force-matching method closely follows the formulation from Refs. [23, 24],... 

Molecular simulation methods can be a complement to surface complexation modeling on metal-bacteria adsorption reactions, which provides a more detailed and atomistic information of how metal cations interact with specific functional groups within bacterial cell wall. Johnson et al., (2006) applied molecular dynamics (MD) simulations to analyze equilibrium structures, coordination bond distances of metal-ligand complexes. 

The study of liquids near solid surfaces using microscopic (atomistic-based) descriptions of liquid molecules is relatively new. Given a potential energy function for the interaction between liquid molecules and between the liquid molecules and the solid surface, the integral equation for the liquid density profile and the liquid molecules orientation can be solved approximately, or the molecular dynamics method can be used to calculate these and many other structural and dynamic properties. In applying these methods to water near a metal surface, care must be taken to include additional features that are unique to this system (see later discussion). 

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

Figure 2 illustrates major modeling methods, i.e., ab initio molecular dynamic (AIMD), molecular dynamic (MD), kinetic Monte Carlo (KMC), and continuum methods in terms of their spatial and temporal scales. Models for microscopic and macroscopic components of a PEFC are placed in the figure in terms of their characteristic dimensions for comparison. While continuum models are successful in rationalizing the macroscopic behaviors based on a few assumptions and the average properties of the materials, molecular or atomistic modeling can evaluate the nanostructures or molecular structures and microscopic properties. In computational... 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

The development of multiscale simulation techniques that involve the atomistic modeling of various structures and processes still remains at its early stage. There are many problems to be solved associated with more accurate and detailed description of these structures and processes. These problems include the development of efficient and fast methods for quantum calculations at the atomistic level, the development of transferable interatomic potentials (especially, reactive potentials) for molecular dynamic simulations, and the development of strategies for the application of multiscale simulation methods to other important processes and materials (optical, magnetic, sensing, etc.). 

Two atomistic approaches have been presented briefly above molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the ab initio character of the method. However MD and TSA are valuable achievements, they are complementary in several... 

Experimental as well as theoretical methods have been widely employed to study such phenomena as solubility, the conformational structures, size change, and so on. Although these methods have been very successful, however, for example the experimental methods cannot reveal the detailed solvation structures to describe the interaction between solvent and polymer. Either theoretical methods are also not completely atomistic or they assume a certain molecular behavior. Molecular simulation methods, on the other hand, can produce most atomistic information about the solvation process. In this section we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. 

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