Monte Carlo methods complex fluids

Siepmann, J. I., Monte Carlo methods for simulating phase equilibria of complex fluids,... 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

MONTE CARLO METHODS FOR SIMULATING PHASE EQUILIBRIA OF COMPLEX FLUIDS... 

Monte Carlo methods offer a useful alternative to Molecular Dynamics techniques for the study of the equilibrium structure and properties, including phase behavior, of complex fluids. This is especially true of systems that exhibit a broad spectrum of characteristic relaxation times in such systems, the computational demands required to generate a long trajectory using Molecular Dynamics methods can be prohibitively large. In a fluid consisting of long chain molecules, for example, Monte Carlo techniques can now be used with confidence to determine thermodynamic properties, provided appropriate techniques are employed. 

Molecular dynamics (MD) methods are nearly as old as the Metropolis Monte Carlo method. The first applications of MD techniques for molecular simulation were made to simple fluids. Simulations for complex liquids such as water followed, and the first MD simulation of a biomacromolecule was performed over 10 years ago. Since then, the MD technique has been used extensively in the study of biomolecules, and the increased utility of this technique parallels closely the development of computer resources. 

The Monte Carlo method has been used extensively to investigate the properties of simple fluids such as noble gases as well as more complex liquids such as water. The results of such computations are considered quite reliable even for a system consisting of... 

To some extent, this article also illustrates that, over the. last decade, Monte Carlo methods for simulation of complex fluids have evolved significantly. Their advent has led to computational efficiency gains of several orders of magnitude. As a result, the problems that can be addressed today by Monte Carlo simulation are significantly more involved than those investigated just a few years ago. 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

In the investigation of Ortiz et al. [104], a stochastic method is presented which can handle complex Hermitian Hamiltonians where time-reversal invariance is broken explicitly. These workers fix the phase of the wave function and show that the equation for the modulus can be solved using quantum Monte Carlo techniques. Then, any choice for its phase affords a variational upper bound for the ground-state energy of the system. These authors apply this fixed phase method to the 2D electron fluid in an applied magnetic field with generalized periodic boundary conditions. 

One of the earliest particle-based schemes is the Direct Simulation Monte Carlo (DSMC) method of Bird [126]. In DSMC simulations, particle positions and velocities are continuous variables. The system is divided into cells and pairs of particles in a cell are chosen for collision at times that are determined from a suitable distribution. This method has seen wide use, especially in the rarefied gas dynamics community where complex fluid flows can be simulated. 

In this review, almost all of the simulations we have described use only classical mechanics to describe the nuclear motion of the reaction system. However, a more accurate analysis of many reactions, including some of the ones that have already been simulated via purely classical mechanics, will ultimately require some infusion of quantum mechanical methods. This infusion has already taken place in several different types of reaction dynamics electron transfer in solution, > i> 2 HI photodissociation in rare gas clusters and solids,i i 22 >2 ° I2 photodissociation in Ar fluid,and the dynamics of electron solvation.22-24 Since calculation of the quantum dynamics of a full solvent is at present too time-consuming, all of these calculations involve a quantum solute in a classical solvent. (For a system where the solvent is treated quantum mechanically, see the quantum Monte Carlo treatment of an electron transfer reaction in water by Bader et al. O) As more complex reaaions are investigated, the techniques used in these studies will need to be extended to take into account effects involving electron dynamics such as curve crossing, the interaction of multiple electronic surfaces and other breakdowns of the Born-Oppenheimer approximation, the effect of solvent and solute polarization, and ultimately the actual detailed dynamics of the time evolution of the electronic degrees of freedom. 

A generalization of these population balance methods to reactions with arbitrary RTD was given by Rattan and Adler [126]. They expanded the phase space of the distribution functions to include the life expectation as well as concentration of the individual fluid elements i/ (C, A, 0- The population balance then reduces to all of the previous developments for the various special cases of segregated or micromixed flow, the perfect macromixing coalescence-redispersion model, and can be solved as continuous functions or by discrete Monte Carlo techniques. Goto and Matsubara [127] have combined the coalescence and two-environment models into a general, but very complex, approach that incorporates much of the earlier work. 

There is no single, perfect, and all-comprising model for predicting fuel cell properties on all length- and time scales. As shown in Figure 3.2, the density functional theory (DFT) can be applied at the atomistic scale (10 m) chemical reactions in the three-phase boundary (TPB) the molecular Dynamics (MD) and Monte Carlo (MC) methods, based on classical force fields, can be employed to describe individual atoms or clusters of catalyst materials at the nano-Zmicro-scale (10 —10 m) the particle-based methods (e.g. DPD) or mesh-based methods, for example Lattice-Boltzmann (LB), are used to solve the complex fluid flows in the porous media at the meso-scopic scale (10 10 m) and at the macroscopic scale (>10 m), continuum models... 

Brownian Dynamics Continuum Solvation Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Monte Carlo Simulations for Complex Fluids Monte Carlo Simulations for Liquids Poisson-Boltzmann Type Equations Numerical Methods Rates of Chemical Reactions Supercritical Water and Aqueous Solutions Molecular Simulation Transition State Theory. 

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