Physical properties Monte Carlo methods

Recendy, Ronova and Pavlova54 suggested a set of relations between the conformational rigidity and some physical properties of the aromatic polymers. The conformational rigidity is correlated to the Kuhn statistical segment A calculated by die Monte Carlo method ... 

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 ... 

The best-known physically robust method for calculating the conformational properties of polymer chains is Rory s rotational isomeric state (RIS) theory. RIS has been applied to many polymers over several decades. See Honeycutt [12] for a concise recent review. However, there are technical difficulties preventing the routine and easy application of RIS in a reliable manner to polymers with complex repeat unit structures, and especially to polymers containing rings along the chain backbone. As techniques for the atomistic simulation of polymers have evolved, the calculation of conformational properties by atomistic simulations has become an attractive and increasingly feasible alternative. The RIS Metropolis Monte Carlo method of Honeycutt [13] (see Bicerano et al [14,15] for some applications) enables the direct estimation of Coo, lp and Rg via atomistic simulations. It also calculates a value for [r ] indirectly, as a "derived" property, in terms of the properties which it estimates directly. These calculated values are useful as semi-quantitative predictors of the actual [rj] of a polymer, subject to the limitation that they only take the effects of intrinsic chain stiffness into account but neglect the possible (and often relatively secondary) effects of the polymer-solvent interactions. 

In contrast, the first class of applications can require very precise solutions. Increasingly, computers are being used to solve very well defined but difficult mathematical problems. For example, as Dirac [1] observed in 1929, the physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are completely known and it is only necessary to find precise methods for solving the equations for complex systems. In the intervening years fast computers and new computational methods have come into existence. In quantum chemistry, physical properties must be calculated to chemical accuracy (say, 0.001 Rydberg) to be relevant to physical properties. This often requires a relative accuracy of 10s or better. Monte Carlo methods are used to solve the electronic... 

Martin M G and J I Siepmann 1999. Novel Configurational-bias Monte Carlo Method tor Branched Molecules Transferable Potentials for Phase Equilibria. 2 United-atom Description of Branched Alkanes Journal of Physical Chemistry 103 4508-4517 Metropolis N, A W Rosenbluth, M N Rosenbluth, A H Teller and E Teller 1953 Equation of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21 1087-1092 Okamoto Y and U H E Hansmann 1995. Thermodynamics of HeUx-coU Transitions Studied by Multicanomcal Algorithms. Journal of Physical Chemistry 99 11276-11287 Panagiotopoulos A Z 1987. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Molecular Physics 61.813-826 Pangali C, M Rao and B J Berne 1978 On a Novel Monte Carlo Scheme for Simulating Water and Aqueous Solutions Chemical Physics Letters 55 413-417. 

A new, valuable type of experiment are computer simulations of network properties. Computer simulations are well established both in equilibrium and non-equilibrium physics of systems of linear chains and have been used for the study of networks and melts. The effect of the topological constraints on the stress-strain behaviour of tetrafunctional networks with a regular structure has been investigated by Elyashevich and Remeev using Monte Carlo methods to generate Marko-... 

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

A complete model for the description of plasma deposition of a-Si H should include the kinetic properties of ion, electron, and neutral fluxes towards the substrate and walls. The particle-in-cell/Monte Carlo (PIC/MC) model is known to provide a suitable way to study the electron and ion kinetics. Essentially, the method consists in the simulation of a (limited) number of computer particles, each of which represents a large number of physical particles (ions and electrons). The movement of the particles is simply calculated from Newton s laws of motion. Within the PIC method the movement of the particles and the evolution of the electric field are followed in finite time steps. In each calculation cycle, first the forces on each particle due to the electric field are determined. Then the... 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (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... 

Because the physical description is correct and consistent, the method allows for arbitrary division of a system into different subsystems, which may be described either on the quantum-mechanical (QM) or the molecular mechanics (MM) level, without significant loss of accuracy. This allows for performing fully MM molecular simulations (Monte Carlo, molecular dynamics), which can subsequently be followed by performing QM/MM calculations on a selected number of representative snapshots from these simulations. These QM/MM calculations then give directly the solvent effects on emission or absorption spectra, molecular properties, organic reactions, etc... 

Up to now, numerous studies have been conducted on their synthesis [9,10], treatment [5,13] and physical properties [4], However only limited number of studies has been carried out on die adsorption of gas in CNTs, including experimental works [8,11] and molecular simulations [3,7,14-lS]. Adsorption behavior depends strongly on the microporous structure of the particular adsorbent. In this work the effect of pore size on the adsorption behavior is of interest. The adsorption equilibria of methane, ethane and their mixture into SWNTs were studied by using a Grand Canonical Monte Carlo (GCMC) method. We reported equilibrium isotherms of methane and ethane, and the selectivity from their equimolar mixture. 

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