THES, atomistic simulations

The author is grateful for the contributions of many collaborators to the work reviewed here. Nir Goldman and M. Riad Manaa played a central role in the atomistic simulations. W. Michael Howard, Kurt R. Glaesemann, P. Clark Souers, Peter Vitello, and Sorin Bastea developed many of the thermochemical simulation techniques discussed here. This work was performed under the auspices of the U. S. Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. 

For the atomistic simulation of the kaolinite interface it is assumed that surfaces are planar. Irregularities such as steps, kinks and ledges, which are present on real surfaces, are omitted for the present treatment. For kaolinite the energy of the 001 basal surface was evaluated using a suitable cell containing 425 atoms. 

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

The simulation models also correctly predicted the diffusivities of hydronium and methanol in a wide range of temperature (Fig. 19). Methanol is a neutral species and weakly interacts with Nation backbone. It is not surprising that the present MD models that do not consider chemical interaction between the molecules can still correctly evaluate the diffusivity of methanol. Because the present experimental setup is limited for liquid samples, whether or not the permeability of diffusivity is strongly depends on water content has not been examined. In summary, this work provided benchmark for the atomistic simulation of the transport processes in Nation at water content above 3 although at some points, the errors can be 100%. 

Figure 19. Methanol permeability as a function of temperature and diffusiv-ity data evaluated using the atomistic simulation method.138 Reprinted from Journal of Electrochemical Society, X. Zhou, Z. Chen, F. Delgado, D. Brenner, R. Srivastava, J. Electrochem. Soc. 154, B82 (2007)- Reproduced by permission of the Electrochemical Society.

Another important result from the atomistic simulations was that the stress-strain response of a region of material around an interface that debonded could be represented by an elastic fracture analysis at the next higher size scale if the interface was assumed to be larger than 40 A. Hence, an elastic fracture criterion was used in the microscale finite element analysis, which focused on void-crack... 

Nowdays the atomistic simulation of diffusional processes in polymers is a domain of vivid research activity which already shows remarcable results and brings continously new achievements. The second section of this chapter is devoted to a concise presentation of this topic. 

On the other hand, based on the rapid progress which was recorded in the last decade in the atomistic simulation of diffusion processes in polymers one may be confident that these computational methods will be one day able to cope with the prob-... 

One-way, top-down methods. These involve a transfer of information from the CG simulation to the atomistic simulation, e.g. using a CG model to enhance... 

Lyubartsev has also developed a multiscale parameterisation method that has been used to systematically build a CG model of a DMPC bilayer. Lyubartsev uses an inverse Monte Carlo method to generate the CG parameters from an underlying atomistic simulation. The atomistic simulation trajectory is analysed to generate the radial distribution functions (RDFs) for the CG bead model. These RDFs can be converted into pairwise interaction potentials between the beads. The... 

RDFs calculated from a CG simulation using these initial interaction potentials differ from those calculated from the atomistic simulation. An inverse Monte Carlo algorithm is therefore used to iteratively refine these interaction potentials by correcting them by the difference between the CG and atomistic RDFs. This is essentially the same method that was used by Shelley et al to derive the parameters between the CG lipid head group particles, and is also similar to the Boltzmann inversion method, " which also uses an iterative procedure that uses RDFs measured from atomistic simulations to derive CG interaction potentials. Lyubartsev has used this method to fully parameterize his own CG model of DMPC. 

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. 

Leontidis E, Forrest B M, Widmann A H and Suter U W1995 Monte Carlo algorithms for the atomistic simulation of condensed polymer phases J. Chem. Soc. Farad. Trans. 91 2355- 68... 

Baig, C., Alexiadis, O., and Mavrantzas, V. G. 2010. Advanced Monte Carlo algorithm for the atomistic simulation of short- and long-chain branched polymers Implementation for model h-shaped, aSaaS multiarm (pom-pom), and short-chain branched polyethylene melts. Macromolecules, 43(2) 986-1002. 

Computational techniques have extensively been used to stu(fy the interfacial mechanics and nature of bonding in CNT-polymer composites. The computational studies can be broadly classified as atomistic simulations and continuum methods. The atomistic simulations are primarily based onMD simulations and DFT [105-110], The main focus of these techniques was to understand and stndy the effect of bonding between the polymer and nanotube (covalent, electrostatic or vdW forces) and the effect of friction on the interface. The continuum methods extend the continuum theories of microme-chanics modeling and fiber-reinforced composites (elaborated in the next section) to CNT-polymer composites [111-114] and explain the behavior of the composite from a mechanics point of view. 

In order to simulate fluid flow, heat transfer, and other related physical phenomena over various length scales, it is necessary to describe the associated physics in mathematical terms. Nearly all the physical phenomena of interest to the fluid dynamics research community are governed by the principles of continuum conservation and are expressed in terms of first- or second-order partial differential equations that mathematically represent these principles (within the restrictions of a continuum-based firamework). However, in case the requirements of continuum hypothesis are violated altogether for certain physical problems (for instance, in case of high Knudsen number rarefied gas flows), alternative formulations in terms of the particle-based statistical tools or the atomistic simulation techniques need to be resorted to. In this entry, we shall only focus our attention to situations in which the governing differential equations physically originate out of continuum conservation requirements and can be expressed in the form of a general differential equation that incorporates the unsteady term, the advection term, the diffusion term, and the source term to be elucidated as follows. 

This chapter discusses the form and parameterization of the potential energy terms that are used for the atomistic simulation of polymers. The sum of potential terms constitutes a molecular force field that can be used in molecular mechanics, molecular dynamics, and Monte Carlo simulations of polymeric systems. Molecular simulation methods can be used to determine such properties as PVT data, selfdiffusion coefficients, modulus, phase equilibrium, x-ray and neutron diffraction spectra, small molecule solubility, and glass transition temperatures with considerable accuracy and reliability using current force fields. Included in the coverage of Chapter 4 is a review of the fundamentals of molecular mechanics and a survey of the most widely used force fields for the simulation of polymer systems. In addition, references to the use of specific force fields in the study of important polymer groups are given. 

TABLE 4.1. Literature citations (1990-2005) for force fields used in the atomistic simulations of polymers. 

Usually, it is necessary to calculate stress of every atom in order to analyze the relations between the stress states of atoms and the onset of defects. The stress in the atomistic simulation mn on plane m and in the n-direction can be given by... 

Theodorou, D.N. Variable-connectivity Monte Carlo algorithms for the atomistic simulation of long-chain polymer systems. Bridging Time Scales Molecular Simulations for the Next Decades, Nielaba, P., Mareschal, M., Cicotti, G., Eds. Springer Verlag Berlin, 2002, 67-127. 

It is interesting to note that the true power of the atomistic simulations lies in following three major areas ... 

Simple Flexible Boundary Conditions for the Atomistic Simulation of Dislocation Core Structure and Motion. 

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