Monte Carlo simulation for the modification of polymer via grafting

Monte Carlo method has been applied to investigate the kinetic of grafting reaction in free radical copolymerization. The simulation is quits in agreement with that of theoretical and experimental results. It proves that the Monte Carlo simulation is an effective method for investigating the grafting reaction of free radical copolymerization. (C) 2000 Elsevier Science Ltd. All rights reserved.

Monte Carlo simulation of phase behavior of polymer blends with special interactions

Full Paper: The phase, behavior of A-B-random copolymer/C-homopolymer, blends with special interaction was studied by a. Monte, Carlo simulation in two dimensions. The interaction between I segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. The simulation results showed that the blend became two large co-continuous phase domains at lower segment-B component compositions, indicating that the blend showed spinodal decomposition. With an increase of the segment-B component, the miscibility between the copolymer,and the polymer was gradually improved up to being miscible. In addition, it was found that segment B tended to move to the surface of the copolymer phase in the case of a lower component of segment B. On the other hand, if was observed that the average, end-to-end distances ((h) over bar) for both copolymer and polymer changed slowly with increasing segment-B component of the copolymer up to 40%, thereafter they increased considerably with increasing segment B component. Moreover, it was found that the (h) over bar of the copolymer was obviously shorter than that of the homopolymer for the segment-B composition, region from 0% to 80%. Finally, a, phase diagram showing I phase and - II phase regions under the condition of constant-temperature is presented.

Monte-Carlo simulation of surface crack growth rate for offshore structural steel E36-Z35

The Monte- Carlo method is used to simulate the surface fatigue crack growth rate for offshore structural steel E36-Z35, and to determine the distributions and relevance of the parameters in the Paris equation. By this method, the time and cost of fatigue crack propagation testing can be reduced. The application of the method is demonstrated by use of four sets of fatigue crack propagation data for offshore structural steel E36-Z35. A comparison of the test data with the theoretical prediction for surface crack growth rate shows the application of the simulation method to the fatigue crack propagation tests is successful.

A Generalized Soft-Sphere for Monte Carlo Simulation

A new collision model, called the generalized soft-sphere (GSS) model, is introduced. It has the same total cross section as the generalized hard-sphere model [Phys. Fluids A 5, 738 (1993)], whereas the deflection angle is calculated by the soft-sphere scattering model [Phys. Fluids A 3, 2459 (1991)]. In virtue of a two-term formula given to fit the numerical solutions of the collision integrals for the Lennard-Jones (6-12) potential and for the Stockmayer potential, the parameters involved in the GSS model are determined explicitly that may fully reproduce the transport coefficients under these potentials. Coefficients of viscosity, self-diffusion and diffusion for both polar and nonpolar molecules given by the GSS model and experiment are in excellent agreement over a wide range of temperature from low to high.

Permeability of Fractal Porous Media by Monte Carlo Simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based oil the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.

Pressure and thermal effects on elastic properties of single crystal alpha-Al2O3 from Monte-Carlo simulation

A rectangular structural unit cell of a-Al2O3 is generated from its hexagonal one. For the rectangular structural crystal with a simple interatomic potential [Matsui, Mineral Mag. 58A, 571 (1994)], the relations of lattice constants to homogeneous pressure and temperature are calculated by using Monte-Carlo method at temperature 298K and 0 GPa, respectively. Both numerical results agree with experimental ones fairly well. By comparing pair distribution function, the crystal structure of a-Al2O3 has no phase transition in the range of systematic parameters. Based on the potential model, pressure dependence of isothermal bulk moduli is predicted. Under variation of general strains, which include of external and internal strains, elastic constants of a-Al2O3 in the different homogeneous load are determined. Along with increase of pressure, axial elastic constants increase appreciably, but nonaxial elastic constants are slowly changed.

Quantum Monte Carlo study of the CO interaction with a dimer model surface for Cr(110)

The chemisorption of CO on a Cr( 110) surface is investigated using the quantum Monte Carlo method in the diffusion Monte Carlo (DMC) variant and a model Cr2CO cluster. The present results are consistent with the earlier ab initio HF study with this model that showed the tilted/ near-parallel orientation as energetically favoured over the perpendicular arrangement. The DMC energy difference between the two orientations is larger (1.9 eV) than that computed in the previous study. The distribution and reorganization of electrons during CO adsorption on the model surface are analysed using the topological electron localization function method that yields electron populations, charge transfer and clear insight on the chemical bonding that occurs with CO adsorption and dissociation on the model surface.

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Quantum and variational monte-carlo interaction potentials for li2 (x1-sigma-g+)

<span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">Optimized trial functions are used in quantum Monte Carlo and variational Monte Carlo calculations of the Li</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">2</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">(X&nbsp;</span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">1</sup><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">&Sigma;</span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">+</sup><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">g</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron&mdash;nuclear and electron&mdash;electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy&nbsp;</span><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">E</em><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">L</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">&nbsp;(</span><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">E</em><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">L</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">&nbsp;��� &Psi;</span><sup style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">&minus;1</sup><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><em style="border: 0px; font-size: 13px; margin: 0px; padding: 0px; vertical-align: baseline; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px; text-align: justify; word-spacing: -1px">H</em><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">&Psi;</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">, where &Psi;</span><sub style="border: 0px; font-size: 0.75em; margin: 0px; padding: 0px; line-height: 0; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; text-align: justify; word-spacing: -1px">T</sub><span style="color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; font-size: 13px; line-height: 20px; text-align: justify; word-spacing: -1px">&nbsp;denotes a trial function) over a fixed sample. At the equilibrium separation, the variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.</span>

Optimization of tried wave-function in quantum monte-carlo method

A method for optimizing tried wave functions in quantum Monte Carlo method has been found and used to calculate the energies of molecules, such as H-2, Li-2, H-3+, H-3 and H-4. Good results were obtained.

Monte Carlo Modeling of Micro Scale Gas Flows

An information preservation (IP) method has been used to simulate many micro scale gas flows. It may efficiently reduce the statistical scatter inherent in conventional particle approaches such as the direct simulation Monte Carlo (DSMC) method. This paper reviews applications of IP to some benchmark problems. Comparison of the IP results with those given by experiment, DSMC, and the linearized Boltzmann equation, as well as the Navier-Stokes equations with a slip boundary condition, and the lattice Boltzmann equation, shows that the IP method is applicable to micro scale gas flows over the entire flow regime from continuum to free molecular.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.