Reaction kinetics mesoscale models

The mathematical modeling of polymerization reactions can be classified into three levels microscale, mesoscale, and macroscale. In microscale modeling, polymerization kinetics and mechanisms are modeled on a molecular scale. The microscale model is represented by component population balances or rate equations and molecular weight moment equations. In mesoscale modeling, interfacial mass and heat transfer... 

In the last section, we discussed the use of QC calculations to elucidate reaction mechanisms. First-principle atomistic calculations offer valuable information on how reactions happen by providing detailed PES for various reaction pathways. Potential energy surfaces can also be obtained as a function of electrode potential (for example see Refs. [16, 18, 33, 38]). However, these calculations do not provide information on the complex reaction kinetics that occur on timescales and lengthscales of electrochemical experiments. Mesoscale lattice models can be used to address this issue. For example, in Refs. [25, 51, 52] kinetic Monte Carlo (KMC) simulations were used to simulate voltammetry transients in the timescale of seconds to model Pt(l 11) and Pt(lOO) surfaces containing up to 256x256 atoms. These models can be developed based on insights obtained from first-principle QC calculations and experiments. Theory and/or experiments can be used to parameterize these models. For example, rate theories [22, 24, 53, 54] can be applied on detailed potential energy surfaces from accurate QC calculations to calculate electrochemical rate constants. On the other hand, approximate rate constants for some reactions can be obtained from experiments (for example see Refs. [25, 26]). This chapter describes the later approach. 

There are two approaches to modeling the SOFC electrochemistry at the mesoscale an elementary kinetics-based model and a modified Butler-Volmer model. In the elementary kinetics-based model, the electrochemical reactions of the SOFC are modeled exactly, whereas in the modified Butler-Volmer model, the phenomenological Butler-Volmer equation is solved based on the local Faradaic current density. 

It is meaningful to examine the relation between microscale model, mesoscale model, and micromodel. For reaction kinetics, microscale and mesoscale models adopt the same kinetics that based on element reaction system. For diffusion, mesoscale model embodies two diffusion mechanisms (one for micropores and another for mesopores and macropores), and microscale model considers one diffusion mechanism since it only has micropores. No diffusion was considered within the macropores. It is obvious that the mesoscale model possesses the same theoretical foundation as the microscale model, but its application scope has been enlarged compared to the microscale model. Therefore, it could be reliably used as a tool to derive some parameters, such as effective chemical kinetics and effective diffusion parameters, for macroscale model. In the section following, we discuss the method on how to link the microscale kinetics to the lumped macroscale kinetics via the mesoscale modeling approach. 

This is followed in Section 26.4 by a discussion of mesoscale modehng of the SOFC electrodes in which the SOFC electrodes are explicitly resolved and the detailed reactive transport and electrochemistry is modeled. Section 26.5 briefly describes nanoscale approaches for modeling the transport and reactions of species in the SOFCs, which are suitable for elucidating kinetic and mechanistic issues relevant to SOFC performance. 

The mesoscale multiregion model discussed above may open a way to link the microscale kinetics to the macroscale kinetics. The macroscale kinetics derived from microscale kinetics at least ensures that the reaction mechanism at the microscale can be correctly reflected. As mentioned by Campbell (1994), knowing a mechanism can give an intelligent way to extrapolate kinetics to unknown conditions. As far as we know, there is no MTO macroscale kinetics at present derived direcdy from microscale kinetics. 

---