Metropolis Monte Carlo, structural

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

In Zeolite A. An extensive series of papers concerned with the sorption location and isotherms of Xe in zeolite A have been published (118-122). The locations of sorbates and their structures were investigated by using Metropolis Monte Carlo simulations of zeolite A models (118, 119). Initially, an idealized truncated cuboctahedron was used, with Si and Al atoms occupying vertices and O atoms occupying the midpoints of line segments (118). Subsequent calculations were based on the positions of atoms in... 

When applying a SA approach to crystal structure prediction, a Metropolis Monte Carlo scheme [20], rather than molecular dynamics [28], is usually chosen to sample the configurational space (different possible candidate structures). In practice, this scheme proceeds by comparing the quality (value of the cost function) of a new candidate structure with the current candidate structure. The new candidate is either rejected or used to replace the current candidate struc-... 

In its role as a catalyst, the surface condition of the as-leached nickel nanostructure is highly important. In particular, the sites occupied on the surface of the catalyst by any residual aluminium atoms are of interest. In order to investigate the surface configuration of as-leached surfaces a Metropolis Monte Carlo (MMC) model is subsequently applied. As a starting point the MMC model exploits the nano-porous structure already predicted by the kMC approach. The MMC model aims to simulate the appearance of Al-rich surface configurations that are routinely observed in experiment. 

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. 

RMC is a variation of the standard Metropolis Monte Carlo (MMC) method (Metropolis et al., 1953 see also Chapters l and 5). The principle is that we wish to generate an ensemble of atoms, i.e. a structural model, which corresponds to a total structure factor (set of experimental data) within its errors. These are assumed to be purely statistical and to have a normal distribution. Usually the level and distribution of statistical errors in the data is not a problem, but systematic errors can be. We shall initially consider materials that are macro-scopically isotropic and that have no long range order, i.e. glasses, liquids and gases. The basic algorithm, as applied to a monatomic system with a single set of experimental data, is as follows ... 

In a random search, one can move from one region of the energy-surface to a completely unconnected region in a single step. A commonly applied method is the Metropolis Monte Carlo scheme that starts with a minimized conformation A of a molecule. Then a random move on the energy-landscape is carried out (e.g. torsion angles are rotated by a random amount) and the structure is minimized. The potential energy of the output structure B is evaluated. If < Epot (A), the new conformation is accepted. 

Most of the above simulations are performed on three-dimensional simple cubic lattices with periodic boundary conditions in all directions. (Some of the early studies were based on two-dimensional square lattices but have since been updated.) Additionally, all of the works discussed in this section (except where noted otherwise) use the standard Metropolis Monte Carlo algorithm discussed in detail in Sec. III. B, but the major difference lies in the selection of which of the components contribute to the total energy of the system. Other differences include the lattice rearrangement methodology and parameters such as surfactant structure, temperature, composition, lattice size, and dimensionality. The specifics of each model are summarized below. 

Due to the lack of experimental data available, alternative methods for properly estimation are needed [3]. Such methods include modelling at both the macroscopic and microscopic scales. At the macroscopic scale, the development of theoretical EoS is needed for accurate prediction of properties and phase equilibria calculations. At the molecular level. Molecular Dynamics (MD) and Metropolis Monte Carlo simulations are used for the elucidation of microscopic structure and the prediction of thermodynamic and transport properties. Liu et al. [7] evaluated a series of force fields in their ability to predict properties of CO2-H2O systems and concluded that different force fields produce optimal results in different ranges of temperatures and pressures. 

Abstract. The interlamellar domain of semicrystalline polyethylene is studied by means of off-lattice Metropolis Monte Carlo simulations using a realistic united atom force field with inclusion of torsional contributions. Both structural as well as thermal and mechanical properties are discussed for systems with the 201 crystal plane parallel to the interface. In so doing, important data is obtained which is useful for modeling semicrystalline polyethylene in terms of multiphase models. Here, we review the main results published previously by us (P.J. in t Veld, M. Hiitter, G.C. Rutledge Macromolecules 39, 439 (2006) M. Hiitter, P.J. in t Veld, G.C. Rutledge Polymer (in press), (2006)]. 

To characterize the structure and to quantify the mechanical and thermal properties of the interlamellar, non-crystalline material. Metropolis Monte Carlo simulations have been performed [22-26] on systems kept in metastable equilibrium [27,28]. Here, we give a summary of our most recent results for a realistic model for polyethylene including torsion interactions. For more details the reader is referred to the original publications [29,30], Throughout the manuscript, we concentrate our attention on the 201 crystal surface, because it was found to be energetically favored in simulations [25] and predominant... 

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