Thermodynamic-scaling Monte Carlo method

There are many different routes for calculating phase equilibria that are covered in detail in other chapters of this volume thermodynamic scaling Monte Carlo (chapter by Valleau), Gibbs-Duhem integration along coexistence lines (chapter by Kofke), and pseudo-ensemble methods (chapter by de Pablo and Escobedo). Thus these methods are not discussed here. 

Valleau, J. P., Thermodynamic scaling methods in Monte Carlo and their application to phase equilibria, Monte Carlo Methods Chem. Phys. 1999,105, 369-404... 

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. 

Kiyohara, K. Spyriouni, T. Gubbins, K. E. Panagiotopoulos, A. Z., Thermodynamic scaling Gibbs ensemble Monte Carlo a new method for determination of phase coexistence properties of fluid, Mol. Phys. 19%, 89, 965-974. 

THERMODYNAMIC-SCALING METHODS IN MONTE CARLO AND THEIR APPLICATION TO PHASE EQUILIBRIA... 

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