Monte Carlo simulation of complex isomerization, II. Effect of adsorption on product selectivity

The complex isomerization A=B=C over zeolite catalysts was simulated by the Monte Carlo method, and the effect of adsorption of molecules accompanied with chemical reaction upon the product selectivity has been investigated. The results show that the product selectivity is clearly related to the difference of equilibrium adsorption constants of molecules in the reaction. This suggests that the shape selectivity in zeolite-catalyzed reactions is the result of the channel structure and surface acidity of zeolite catalysts.     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Monte Carlo simulation of polymeric materials: Recent progress

Monte Carlo simulations are presented, dealing with phase diagrams of block copolymer melts and polymer blends, including the unmixing kinetics of the latter systems. The theoretical background is briefly reviewed: Ginzburg-type criteria reveal that in mixtures of long flexible polymers a “crossover” occurs from mean-field behavior (as described by Flory-Huggins theory) to nonclassical Ising-type behavior, and spinodal curves can be unusually sharp. This crossover is demonstrated by large scale simulations of the bond fluctuation model, and it is also shown that for symmetric mixtures the critical temperature scales with chain length as T_c α N. The prefactor in this relation is distinctly smaller than predicted by Flory-Huggins, but the Curro-Schweizer integral equation theory prediction T_c α √N is clearly ruled out. Tests of the Cahn theory on the initial stages of spinodal decomposition of polymer blends will also be reported. To conclude, the mesophase formation in block copolymers is discussed, and it is shown that the simulations agree very well with experiment. The pronounced chain stretching that already occurs in the disordered phase is compelling evidence against the validity of simple random phase approximation concepts for these systems. This shows how Monte Carlo simulations can assist in better understanding large classes of polymeric materials.     

Monte Carlo simulation of polymer mixtures: recent progress

The phase diagram of symmetrical polymer blends (A,B) confined into thin films is studied, considering both the effect of finite film thickness D and of surface forces at the confining walls that either prefer both the same species, or different species. In the case of <“>neutral<”> walls confinement enhances the compatibility of the blend. The critical temperature is depressed, the coexistence curve gets flattened (reflecting a crossover from 3‐dimensional to 2‐dimensional critical behavior). But if both walls preferentially attract species A, then also the critical composition of the blend is shifted to the A‐rich side of the phase diagram, and the coexistence curve exhibits a bulge just above the wetting transition temperature. If one wall attracts A and the other B, lateral phase separation sets in via a first order transition. Above this transition, an interface parallel to the walls is stabilized in the system.     

Estimation of radiation doses associated with natural radioactivity in sand samples of the north western areas of Pakistan using Monte Carlo simulation

Summary Activity concentrations of naturally occurring radionuclides, i.e., ²²⁶Ra, ²³²Th and ⁴⁰K, were measured in sand samples of north western areas of Pakistan using gamma-spectrometry. The measured ranges of activity concentrations for ²²⁶Ra, ²³² Th and ⁴⁰K were 36.9-51.9, 52.5-67.6 and 680-784 Bq ^. kg^-1, respectively. Associated external dose was calculated using Monte Carlo simulation technique. A theoretical model to determine the gamma dose rate at 1 m height from the sand was employed for calculation the mass attenuation coefficient and self absorption in sand slab for the gamma-energies of these radionuclides and their progeny. The weighted average values of the measured gamma dose rates were 3.3, 4.5 and 12.4 nGyh^-1 for ²²⁶Ra, ²³² Th and ⁴⁰K, respectively, with effective dose of 0.022±0.004 mSv ^. y^-1. Monte Carlo simulation shows that the sand slabs having more than 15 cm effective thickness contribute very little to the external gamma dose rate. The values of the external dose rate and annual effective dose were found to be much lower than the world average as well as from other countries of the world.     

A Monte Carlo simulation of radiation-induced conductivity of disordered solids

The Monte Carlo method was used to perform a theoretical study of the kinetics of radiation-induced conductivity under pulsed irradiation of a disordered solid with traps having different energy distributions. The kinetics of radiation-induced conductivity in a weak electric field was satisfactorily described by the Rose-Fowler-Vaisberg model. In a strong field, radiation-induced conductivity became a nonlinear field strength function because of distortions of the energy spectrum of trap centers.     

Evaluation of the self-absorption of 14C beta-rays in gel-suspension samples by Monte Carlo simulation

In order to investigate the self-absorption of the -rays from ¹⁴C in a gel-suspension sample, the Monte Carlo code, simulating the sequence of stages occurring in the sample, has been developed. The trajectory of the electron was calculated by the continuous slowing down approximation and the multiple Coulomb scattering theory. The effects of the self-absorption, strong quenching and particle size distribution of calcium carbonate on the output counting efficiency and the shape of the energy spectrum were evaluated.     

A Monte Carlo simulation of energy transfer processes in thermal unimolecular reactions. II. An applications to polyatomic dissociation

The Monte Carlo method has been used to provide a numerical solution to the ro-vibrational master equation for the low pressure unimolecular decomposition of a polyatomic molecule. This type of solution is made possible through the use of a simple exponential transition probability function, that represents the efficiency with which energy transfer takes place between the reactant molecule and an unspecified heat bath gas. The Monte Carlo technique is used to generate random variables that are distributed in a manner prescribed by the transition probability function. In the case of the present simulation, these variables correspond to random energy jumps induced in the molecule through single collision events. In order to account for the energy dependence of the vibrational state densities, we have proposed that vibrational relaxation in the polyatomic takes place from a single vibrational mode. Under equilibrium conditions we are able to show that with this assumption, the Monte Carlo model is capable of reproducing molecular quantities, such as the average vibrational energy per molecule and the vibrational specific heat, that compare favourable with the corresponding values calculated from equilibrium statistical mechanics. The model has been applied to a study of the low pressure unimolecular decomposition of a series of polyatomics. For three of the molecules, CH₄, CD₄, and C₂H₆ the agreement between the calculated and the high temperature experimental rate constants is very good. The calculations indicate that a significant proportion of the molecules that dissociate are rotationally as well as vibrationally excited. Very few of the reactive molecules have a vibrational energy content equal to or greater than E₀, the dissociation energy. The extent of rotational excitation is found to be temperature dependent.     

A Monte Carlo simulation of the inhomogeneous Lebwohl-Lasher lattice model

A Monte Carlo computer simulation of a modified Lebwohl-Lasher model is presented. The model consists of a set of interaction centres placed at the sites of a cubic lattice. The angular part of the pair potential is a second Legendre polynomial of the relative orientation between the two particles, like that of the Lebwohl-Lasher model. Each particle interacts with its six nearest neighbours with an attractive anisotropic potential differing in strength for the four horizontal and the two vertical neighbours. Various values of the in-plane to out-of-plane coupling ratio δ have been considered, i.e. δ = 0.75, 0.5, 0.1, 0.0. The latter case corresponds to the limiting situation of a two-dimensional lattice. Systems with a 1000 particles have been simulated for δ = 0.75, 0.5 and 0.1 while a sample of 3600 particles has been investigated for the two-dimensional lattice. Comparisons are made with available simulations and with mean field theory. We find that the molecular field theory predictions worsen as the effective coordination number is decreased. Energy, specific heat, second and fourth rank order parameters have been evaluated for the various models. We also present, for the first time, a way of approximately reconstructing the pair distribution, G(r₁₂, ω₁₂), using maximum entropy and second and fourth rank two particle order parameters.     

A simple Monte Carlo program for simulation of X-ray transport

A Monte Carlo-based program for treatment of photon transport, restricted to photon energies used in medical diagnostics, is developed. Only the photoabsorption and Compton scattering of photons are taken into account, a justifiable assumption for the energies involved. We can simply separate contributions of reflection events with one, two, three, or more successive collisions of X-rays with electrons of the target. This gives us insights and information about photon transport which otherwise would be inaccessible.     

A Monte Carlo simulation of diffusion-controlled reactions in inhomogeneous systems

A random-walk model has been developed to treat the kinetics of reactions taking place in spurs at different solute concentrations. The dependence of the molecular yields on solute concentration has been studied using Monte Carlo techniques for simulation of the formation of spurs and of the random movement of the reactive species.     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

A rapidly convergent simulation method: Mixed Monte Carlo/stochastic dynamics

Although Monte Carlo and molecular dynamics are the primary methods used for free energy simulations of molecular systems, their application to molecules that have multiple conformations separated by energy barriers of ≥ 3 kcal/mol is problematic because of slow rates of convergence. In this article we introduce a hybrid simulation method termed MC-SD which mixes Monte Carlo (MC) and stochastic dynamics (SD). This new method generates a canonical ensemble via alternating MC and SD steps and combines the local exploration strengths of dynamics with the barrier-crossing ability of large-step Monte Carlo. Using calculations on double-well potentials and long simulations (10⁸ steps of MC and 1 μs of SD) of the simple, conformationally flexible molecule n-pentane, we find that MC-SD simulations converage faster than either MC or SD alone and generate ensembles which are equivalent to those created by classical MC or SD. Using pure SD at 300 K, the conformational populations of n-pentane are shown to be poorly converged even after a full microsecond of simulation. © 1994 by John Wiley & Sons, Inc.     

Grafted polymer layers under variable solvent conditions: A Monte Carlo simulation

Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been predicted by previous theories.     

Plastic and glassy crystalline states of methane: A Monte Carlo simulation study

A Monte Carlo simulation study has been carried out on the glassy crystalline phases of methane obtained by annealing or quenching the plastic (orientationally disordered) phase. Different cooling rates lead to different states of the glass. Temperature variation of the reorientational parameter suggests the presence of a transition between the plastic and glassy crystalline phases.     

Polymer chains confined into tubes with attractive walls: A Monte Carlo simulation

A bead-spring off-lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, D_T², is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short-range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three-dimensional and quasi-one-dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time-dependent mean-square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N² and to N³ play a role in the reptative motion of the chain in the tubes.     

A comprehensive Monte Carlo simulation of styrene atom transfer radical polymerization

<正>An optimized and high-performance Monte Carlo simulation is developed to take thorough account of four different cases of termination in styrene ATRP.According to the simulation results,the bimolecular termination rate constant sharply drops throughout the polymerization when either chain-length dependency of termination rate constant,gel effect,or both together is applied to the simulation.In addition,as expected,the initiator is quickly decomposed at the early stages of the polymerization.The concentration of the catalyst in lower oxidation state decreases at first and then plateaus at higher conversion;furthermore,the steady concentration of M_t~nY/L in the polymerization is the highest when the chain-length-dependent diffusion-controlled termination rate constant is employed in the simulation.The rates of deactivation and chain end degradation reactions are also smaller in this case.Therefore,the fraction of dormant chains is higher throughout the reaction and consequently the portion of dead polymers decreases.Besides,molecular weight increases linearly with conversion;however,when neither gel effect nor chain-length dependency of termination rate constant is considered,the molecular weight deviates from linearity at the end of the reaction.The peak of chain length distribution shifts toward higher molecular weight too during the reaction.Finally,the molecular weight distribution broadens at higher conversion;however, the chain length distribution of polymers produced under conditions of applying chain-length-dependent diffusion-controlled termination rate constant is narrower.