Coarse-grained kinetic Monte Carlo simulations

T. O. Drews, R. D. Braatz, and R. C. Alkire, Int. J. Multiscale Comput., 2, 313 (2004). Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives. 

Graham and Olmsted [166,167] used coarse-grained kinetic Monte Carlo simulations to simulate anisotropic nucleation based on the chain configurations obtained from a molecular flow model, the Graham-Likhtman and Milner-McLeish (GLaMM) model [168,169].These simulations confirm the power law with exponent 4 up to reasonably high shear rates (molecular stretch up to 3 to 4). They actually found an exponential dependence on the square of the molecular stretch. A practical problem of such an expression is that it contains an extra parameter besides the prefactor for the stretch, there is a prefactor for the exponential function as a whole, which gives the quiescent sporadic creation rate. Since quiescent nucleation is predominantly athermal, this parameter cannot be determined for common melts. 

Coarse-grained Stochastic Processes and Kinetic Monte Carlo Simulation for the Diffusion of Interacting Particles. J. Chem. Phys., 119, 9412-9427. 

Katsoulakis, M.A. Vlachos, D.G. Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles. J. Chem. Phys. 2003, 119, 9412-9428. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

This chapter discusses a staged multi-scale approach for understanding CO electrooxidation on Pt-based electrodes. In this approach, density functional theory (DFT) is used to obtain an atomistic view of reactions on Pt-based surfaces. Based on results from experiments and quantum chemistry calculations, a consistent coarse-grained lattice model is developed. Kinetic Monte Carlo (KMC) simulations are then used to study complex multi-step reaction kinetics on the electrode surfaces at much larger lengthscales and timescales compared to atomistic dimensions. These simulations are compared to experiments. We review KMC results on Pt and PtRu alloy surfaces. 

Further informatimi can be obtained using coarse-grained methods such as Kinetic Monte Carlo (KMC) [125]. These simulations which can include much larger systems and the results evaluated in much longer times could be particularly useful to investigate degradation processes such as those discussed in this chapter. 

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