Mesoscale simulation techniques

In terms of applicable length scales and timescales, the KMC method generally ranks between molecular dynamics methods and mesoscale simulation techniques (Figure 1). Subramanian and his coworkers have recently reviewed modeling and simulations in lithium-ion battery research, including the importance of KMC in describing detailed electrochemical events, such as the growth of the passive solid electrolyte interphase (SEI) layer. 

Keywords Binary fluid mixtures, Colloids, Complex fluids, Hydrodynamics, Mesoscale simulation techniques. Microemulsions, Folymers, Red blood cells. Vesicles, Viscoelastic fluids... 

In the short time since Malevanets and Kapral introduced MFC dynamics as a particle-based mesoscale simulation technique for studying the hydrodynamics of... 

Of all the topics discussed in this text, mesoscale simulations are probably at the most infantile stage of development. The idea of the mesoscale calculations is very attractive and physically reasonable. However, it is not as simple as one might expect. The choice of bead sizes and parameters is crucial to obtaining physically relevant results. More complex bead shapes are expected to be incorporated in future versions of these techniques. When using one simulation technique to derive parameters for another simulation, very small errors in a low-level calculation could result in large errors in the final stages. 

The evolving structural characteristics of CLs are particularly important for further analysis of transport of protons, electrons, reactant molecules (O2), and water as well as for the distribution of electrocatalytic activity at Pt-water interfaces. In principle, the mesoscale simulations allow relating these properties to the choices of solvent, ionomer, carbon particles (sizes and wettability), catalyst loading, and hydration level. Explicit experimental data with which these results could be compared are still lacking. Versatile experimental techniques have to be employed to study particle-particle interactions, structural characteristics of phases and interfaces, and phase correlations of carbon, ionomer, and water in pores. 

A comparison of mesoscopic simulation methods with MD simulations has been performed by Denniston and Robbins.423 They study a binary mixture of simple Lennard-Jones fluids and map out the required parameters of the mesoscopic model from their MD simulation data. Their mapping scheme is more complete than those of previous workers because in addition to accounting for the interfacial order parameter and density profiles, they also consider the stress. Their mapping consists of using MD simulations to parameterise the popular mesoscale Lattice Boltzmann simulation technique and find that a... 

The methods developed in this book can also provide input parameters for calculations using techniques such as mean field theory and mesoscale simulations to predict the morphologies of multiphase materials (Chapter 19), and to calculations based on composite theory to predict the thermoelastic and transport properties of such materials in terms of material properties and phase morphology (Chapter 20). Material properties calculated by the correlations presented in this book can also be used as input parameters in computationally-intensive continuum mechanical simulations (for example, by finite element analysis) for the properties of composite materials and/or of finished parts with diverse sizes, shapes and configurations. The work presented in this book therefore constitutes a "bridge" from the molecular structure and fundamental material properties to the performance of finished parts. 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

EDMD is a very effective simulation technique for studying protein folding or mesoscale behavior, like protein sdf-assembly, " with several orders of magnitude greater effidency than traditional MD. The ability of EDMD to give accurate dynamics has also been demonstrated (see Reference 24). 

Molecular simulation techniques can obtain the microscopic information that cannot be detected by current experimental conditions, but the conventional simulation methods stiU have inherent limitations with special mesoscopic scales of various complex forces and complex structure. It is necessary to establish a new mesoscale method that considers the chemical reaction and transport to the larger system at the same time. The roughness and chemical properties of catalyst supporting interface have great influence on chemical and physical adsorption stability of clusters. The problem is that the system is too large for traditional simulation in nano-/micro-/mesoscale. We need a new mesoscale method to study the effect of interface roughness on physical/chemistry phenomena. 

One could also expect that mesoscale simulations will become important tool in studies of nanoparticle cytotoxicity. Over the past decade, the number of products containing nanoparticles (i.e. dimensions <100 nm) has increased dramatically. As these nanoparticles are introduced into various media (mainly polymer matrices), they are functionahzed with different Ugands and surfactants to achieve better dispersions. The simulation techniques discussed in this chapter may help to understand, from a quahtative aspect, how the interaction of nanoparticles with cell membranes wiU depend not only on the type of surface modification but also on the particle size and shape. 

When hydrodynamic effects are not expected to be important, it is often convenient to simulate without explicit solvent molecules. This approach can stUl be justified even when hydrodynamic flow becomes relevant, but solvent-related degrees of freedom have to be incorporated on a certain coarse-grained level. To reproduce hydrodynamic effects in the continuum limit, mesoscale hydrodynamic techniques... 

The dynamical behavior of macromolecules in solution is strongly affected or even dominated by hydrodynamic interactions [6,104,105]. Erom a theoretical point of view, scaling relations predicted by the Zimm model for, e.g., the dependencies of dynamical quantities on the length of the polymer are, in general, accepted and confirmed [106]. Recent advances in experimental single-molecule techniques provide insight into the dynamics of individual polymers, and raise the need for a quantitative theoretical description in order to determine molecular parameters such as diffusion coefficients and relaxation times. Mesoscale hydrodynamic simulations can be used to verify the validity of theoretical models. Even more, such simulations are especially valuable when analytical methods fail, as for more complicated molecules such as polymer brushes, stars, ultrasoft colloids, or semidilute solutions, where hydrodynamic interactions are screened to a certain degree. Here, mesoscale simulations still provide a full characterization of the polymer dynamics. 

Many of the mesoscale techniques have grown out of the polymer SCF mean field computation of microphase diagrams. Mesoscale calculations are able to predict microscopic features such as the formation of capsules, rods, droplets, mazes, cells, coils, shells, rod clusters, and droplet clusters. With enough work, an entire phase diagram can be mapped out. In order to predict these features, the simulation must incorporate shape, dynamics, shear, and interactions between beads. 

Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

In principle, mesoscale methods can provide a means for connecting one type of simulation to another. For example, a molecular simulation can be used to describe a lipid. One can then derive the parameters for a lipid-lipid potential. These parameters can then be used in a simulation that combines lipids to form a membrane, which, in turn, can be used to compute parameters describing a membrane as a flexible sheet. Such parameters could be used for a simulation with many cells in order to obtain parameters that describe an organ, which could be used for a whole-body biological simulation. Each step, in theory, could be modeled in a different way using parameters derived not from experiment but from a more low-level form of simulation. This situation has not yet been realized, but it is representative of one trend in computational technique development. 

The applicability of mesoscale techniques to systems difficult to describe in any other manner makes it likely that these simulations will continue to be used. At the present time, there is very little performance data available for these simulations. Researchers are advised to carefully consider the fundamental assumptions of these techniques and validate the results as much as possible. 

Polymers are difficult to model due to the large size of microcrystalline domains and the difficulties of simulating nonequilibrium systems. One approach to handling such systems is the use of mesoscale techniques as described in Chapter 35. This has been a successful approach to predicting the formation and structure of microscopic crystalline and amorphous regions. 

An alternative mesoscale approach for high-level molecular modeling of hydrated ionomer membranes is coarse-grained molecular dynamics (CGMD) simulations. One should notice an important difference between CGMD and DPD techniques. CGMD is essentially a multiscale technique (parameters are directly extracted from classical atomistic MD) and it... 

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