Atomistic structural models, effect

Finally, Honeycutt" has applied blend PRISM theory at an atomistic RIS model level to study the effect of tacticity (stereochemical differences) on the phase behavior of a commercially important binary polymer mixture. Tacticity is found to result in significant changes of the computed spinodal boundaries, which serves to again emphasize the importance of monomer structure and local packing on the free energy of mixing. 

The objective of CL modeling is to establish relations between fabrication procedures and conditions, structure, effective properties of transport and reactions, and performance, which evolves over a wide range of scales, from atomistic-dominated processes at supported catalyst nanoparticles to the operation in a fuel cell at the macroscopic device level. As discussed above, separate approaches in theory and modeling are considered at different scales, which allow one to focus on essential features under specific conditions. For example, atomistic scale models can predict physical properties of materials with ideal, theoretical or proposed micro-structures imder... 

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]. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

Many solvents do not possess the simple structure that allows their effects to be modeled by the Langevin equation or generalized Langevin equation used earlier to calculate the TS trajectory [58, 111, 112]. Instead, they must be described in atomistic detail if their effects on the effective free energies (i.e., the time-independent properties) and the solvent response (i.e., the nonequilibrium or time-dependent properties) associated with the... 

Equation 1.3 represents a system of usually several thousand coupled differential equations of second order. It can be solved only numerically in small time steps At via finite-difference methods [16]. There always the situation at t + At is calculated from the situation at t. Considering the very fast oscillations of covalent bonds, At must not be longer than about 1 fs to avoid numerical breakdown connected with problems with energy conservation. This condition imposes a limit of the typical maximum simulation time that for the above-mentioned system sizes is of the order of several ns. The limited possible size of atomistic polymer packing models (cf. above) together with this simulation time limitation also set certain limits for the structures and processes that can be reasonably simulated. Furthermore, the limited model size demands the application of periodic boundary conditions to avoid extreme surface effects. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Two broad classes of technique are available for modeling matter at the atomic level. The first avoids the explicit solution of the Schrodinger equation by using interatomic potentials (IP), which express the energy of the system as a function of nuclear coordinates. Such methods are fast and effective within their domain of applicability and good interatomic potential functions are available for many materials. They are, however, limited as they cannot describe any properties and processes, which depend explicitly on the electronic structme of the material. In contrast, electronic structure calculations solve the Schrodinger equation at some level of approximation allowing direct simulation of, for example, spectroscopic properties and reaction mechanisms. We now present an introduction to interatomic potential-based methods (often referred to as atomistic simulations). 

Theoretical methods offer the opportunity to explore structure-property relationships in ideal metal-ceramic interfaces. Ultimately, improved understanding of the causal sequence leading to a particular interface structure and set of properties would enable further optimization of manufacturing parameters. Atomistic modeling constitutes the perfect laboratory in this respect. Within the limits of the specific approximations used for interatomic interactions, physical properties may be resolved to arbitrary accuracy and competing effects may be separated. 

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