Dynamic Monte-Carlo Simulation

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

The tests in the two previous paragraphs are often used because they are easy to perform. They are, however, limited due to their neglect of intermolecular interactions. Testing the effect of intennolecular interactions requires much more intensive simulations. These would be simulations of the bulk materials, which include many polymer strands and often periodic boundary conditions. Such a bulk system can then be simulated with molecular dynamics, Monte Carlo, or simulated annealing methods to examine the tendency to form crystalline phases. 

K. A. Fichthorn, W. H. Weinberg. Theoretical foundations of dynamical Monte Carlo simulations. J Chem Phys 95 1090-1096, 1991. 

R. B. Pandey, A. Milchev, K. Binder. Semidilute and concentrated polymer solutions near attractive walls Dynamic Monte Carlo simulation of density and pressure profiles of a coarse-grained model. Macromolecules 50 1194-1204, 1997. 

Enzyme reactions, like all chemical events, are dynamic. Information coming to us from experiments is not dynamic even though the intervals of time separating observations may be quite small. In addition, much information is denied to us because of technological limitations in the detection of chemical changes. Our models would be improved if we could observe and record all concentrations at very small intervals of time. One approach to this information lies in the creation of a model in which we know all of the concentrations at any time and know something of the structural attributes of each ingredient. A class of models based on computer simulations, such as molecular dynamics, Monte Carlo simulations, and cellular automata, offer such a possibility. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Korzeniewski C, Kardash D. 2001. Use of a dynamic Monte Carlo simulation in the study of nucleation-and-growth models for CO electrochemical oxidation. J Phys Chem B 105 8663-8671. 

A quantitative analysis [34], based on the adsorption isotherms and the intercrystalline porosity, yielded the remarkable result that a satisfactory fit between the experimental data and the estimates of Aong-range = Pinter Anter following Eqs. (3.1.11) and (3.1.12) only lead to coinciding results for tortuosity factors a differing under the conditions of Knudsen diffusion (low temperatures) and bulk-diffusion (high temperatures) by a factor of at least 3. Similar results have recently been obtained by dynamic Monte Carlo simulations [39—41]. 

In a few instances, quantum mechanical calculations on the stability and reactivity of adsorbates have been combined with Monte Carlo simulations of dynamic or kinetic processes. In one example, both the ordering of NO on Rh(lll) during adsorption and its TPD under UHV conditions were reproduced using a dynamic Monte Carlo model involving lateral interactions derived from DFT calculations and different adsorption... 

A Dynamic Monte Carlo Simulations of Lattice Polymers. 27... 

In the dynamic Monte Carlo simulations described earlier, we used a crystalline template to suppress supercooling (Sect. A.3). If this template is not present, there will be a kinetic interplay between polymer crystallization and liquid-liquid demixing during simulations of a cooling run. In this context, it is of particular interest to know how the crystallization process is affected by the vicinity of a region in the phase diagram where liquid-liquid demixing can occur. 

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

FaUer, R. and de Pablo, J.J., Constant pressure hybrid molecular dynamics-Monte Carlo simulations, J. Chem. Phys., 116, 55, 2002. 

Kotelyanskii, M.J., Suter, U.W. A dynamic Monte Carlo method suitable for molecular simulations. J. Chem. Phys. 1992, 96, 5383-8. 

Molecular dynamics, Monte Carlo simulations (Haile, 1992), and very recently applications of cellular automata to drug research (Kier and Cheng,... 

As stated in Sec. 3.1, only ideal systems will be considered in this section. This definition implies that there is no intramolecular reaction, a condition which is satisfied in practice for very low concentrations of Af monomers (f >2), in the A2 + Af chainwise polymerization. To take into account intramolecular reactions it would be necessary to introduce more advanced methods to describe network formation, such as dynamic Monte Carlo simulations. 

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