Multi-scale models Coarse-graining methods

In the following, the key issues and related models at different scales in PEMFCs are outlined in Section 3.2. In Section 3.3, the multi-scale strategies across neighboring scales are summarized and compared. The typical applications based on coarse-grained molecular dynamics (CG-MD) method areal so exhibited to discuss the multi-scale modeling techniques in PEMFC. However, there are still some major challenges and limitations in these modeling and simulations, as summarized in Section 3.4. 

The methods discussed here merely represent the beginning of increasingly complex computational architectures, where more than one QM method may be combined with other QM methods, MM methods, continuum electrostatic approaches and coarse-grained models in a coherent multi-scale framework. With such developments, increasingly complex chemical and biological systems can be analyzed computationally in a routine and realistic fashion. 

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. 

Carbonaceous particles can be coarse-grained in various ways, building upon a new technique called multi-scale coarse graining (MS-CG) [125-127]. In this method, the CG potential parameters are systematically obtained from atomistic-level interactions [127]. Using this technique, a model was built for semispherical carbon particles based on CG nonpolar sites in the C60 system. 

Multicomponent melts that are commonly found in such varied situations as material fabrification, reinforcement, blending, and so on are discussed in the chapter by Muller ( Computational Approaches for Structure Formation in Multi-component Polymer Melts ). Only equilibrium properties are discussed along with computational approaches for coarse-grained models in the mean field approximation. Both hard-core and soft-core models are used to cover a multitude of scales of length, time, and energy. Attention is also paid to methods that go beyond the mean field approximation. 

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