Computer simulation basic techniques

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

The world of colloidal particles is large and fasdnating. Basic simulation techniques rapidly lead to challenging questions and new things to be discovered. Computer simulations are close enough to experiments to allow intellectual inspiration as well as a quantitative comparison of the results. We have reviewed the basic simulation techniques and their principal implementation but could only briefly mention advanced techniques and results. A survey of the recent literature shows the variety of physical effects present in colloidal systems and accessible to computer simulations. 

Molecular spectra can be analyzed for spectrometric or for spectroscopic purposes. The term spectrometric usually refers to compound identification (linking a signal to a known structure) and to the determination of its concentration. The term spectroscopic stands for interpretation of the spectrum in terms of structure (chemical, electronic, nuclear, etc.). In this chapter we will look as some theoretical and practical aspects of a key spectrometric application of bioEPR, namely, the determination of the concentration of paramagnets, also known as spin counting. Subsequently, we consider the generation of anisotropic powder EPR patterns in the computer simulation of spectra, a basic technique that underlies both spectrometric and spectroscopic applications of bioEPR. 

Because time is explicitly present in the formulations of MD, this technique is the most straightforward way of computer simulating the motion of penetrant molecules in amorphous polymer matrices (97-99). The MD method allows one to look at a truly atomistic level within the system as it evolves in time. Recently, excellent reviews on the use of MD for simulating penetrant diffusion in polymers have been published (96-99). A summary of the basic concepts and some relevant results obtained so far with MD will be presented bellow. 

In this chapter we focus on a few selective new VCD applications reported in the last 5 years, along with a brief review of the basic experimental techniques and theoretical methods. The remainder of this chapter is organized as follows. In the next section, we will present the VCD experimental technique with a short review of VCD instrumentation and some recent developments, and describe the usual procedure to obtain VA and VCD measurements in solution and in thin film states. In Sect. 3 the associated VCD computational simulations will be illustrated. This includes a brief historical overview of the theory development, and some basics related to VCD calculations, as well as the typical procedure of carrying out VCD simulations. The main part of this chapter deals with the diverse applications of VCD spectroscopy, focusing on the new developments in the last 5 years. Since there are a large number of publications which are dedicated to AC determinations of many interesting and important chiral molecules, a comprehensive review of all... 

First-principles simulations are techniques that generally employ electronic structure calculations on the fly . Since this is a very expensive task in terms of computer time, the electronic structure method is mostly chosen to be density functional theory. Apart from the possibility of propagating classical atomic nuclei on the Born-Oppenheimer potential energy surface represented by the electronic energy V (R ) = ji(R ), another technique, the Car-Parrinello method, emerged that uses a special trick, namely the extended Lagrangian technique. The basic idea... 

However, we do not know exactly to what extent simulated amorphous atomic structures depend upon the rate of quenching. It is known, for example, that in the ion implantation technique for the preparation of amorphous metals, one can achieve effective rates of cooling of 10 K/s (see, e.g. Ref. [15], p. 27) which is already close to that achievable in computer simulations. The resulting atomic structures are basically the same as those obtained by quenching techniques with six orders of magnitude smaller rates of cooling. 

MC and MD are versatile techniques that have been shown to be powerful methods of enhancing our understanding of molecular behavior both of carbon surfaces and of the many other solid adsorbents presently in use. Although this chapter has dealt with the basics of computer simulation, there are many areas where simulators have been active that have not been dealt with in the chapter (e.g., see Chapters 5, 6, 8—10, and 15). 

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. 

The Avrami equationhas been extended to various crystallization models by computer simulation of the process and using a random probe to estimate the degree of overlap between adjacent crystallites. Essentially, the basic concept used was that of Evans in his use of Poisson s solution of the expansion of raindrops on the surface of a pond. Originally the model was limited to expansion of symmetrical entities, such as spheres in three dimensions, circles in two dimensions, and rods in one, for which n = 2,2, and 1, respectively. This has been verified by computer simulation of these systems. However, the method can be extended to consider other systems, more characteristic of crystallizing systems. The effect of (a) mixed nucleation, ib) volume shrinkage, (c) variable density of crystallinity without a crystallite, and (random nucleation were considered. AH these models approximated to the Avrami equation except for (c), which produced markedly fractional but different n values from 3, 2, or I. The value varied according to the time dependence chosen for the density. It was concluded that this was a powerful technique to assess viability of various models chosen to account for the observed value of the exponent, n. 

Above we have listed only very basic MD and MC algorithms, and the interested reader is referred to the literature for more information. Introductory texts on computer simulation methods are abundant. Somewhat older but still one of the best is Ref. 6. Also highly recommendable is Ref. 7. A special text on the details of MC is Ref. 8. Simulation techniques especially for polymers are discussed in Ref. 9. 

The adsorbent surface is a source of an external force field which strongly affects the behavior of adsorbate molecules. In contrast to the experiments, the molecular structure of the adsorbent surface is completely known and assumed a priori in computer simulations. However, computer generation of physically realistic surfaces is not simple and requires answers to many important questions. There are three possible approaches to this problem (1) attempt to build the relatively primitive model which is able to reflect basic features of the system (2) try to construct a model that is as similar as possible to the real material carefully studied by means of modem experimental techniques (3) in the simulation procedure, attempt to mimic the manufacturing process used to produce the real adsorbent [280]. 

Additionally, there is process simulation steady-state flow sheet simulators and dynamic flow sheet simulators. Steady-state flow sheet simulators have been widely used in chemical process engineering since the 1960s. Steady-state simulators describe the process as a set of modules connected by flows of material and energy between them. The modules correspond to mass and energy balances together with physical and thermodynamic data necessary for calculations. The calculations may be performed using one of two basic techniques. The sequential approach computes modules one by one, in a direction that generally follows that of the physical flows in the system (Leiviska, 1996). 

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