Transport processes molecular modelling

In summary, this discussion illustrates the general importance of transport processes in many (electro)catalytic reactions. These have to be addressed properly for a detailed (and quantitative) understanding of the molecular-scale mechanism. Because of the problems associated with the direct identification of the reaction intermediates (see above), experiments on nanostructured model electrodes with a well-defined distribution of reaction sites of controlled, variable distance and under equally well-defined transport conditions (first attempts in this direction are described in [Lindstrom et al., submitted Schneider et al., 2008]), in combination with detailed simulations of the ongoing transport processes and theoretical calculations of the... 

Chemical mass is redistributed within a groundwater flow regime as a result of three principal transport processes advection, hydrodynamic dispersion, and molecular diffusion (e.g., Bear, 1972 Freeze and Cherry, 1979). Collectively, they are referred to as mass transport. The nature of these processes and how each can be accommodated within a transport model for a multicomponent chemical system are described in the following sections. 

This section provides a comprehensive overview of recent efforts in physical theory, molecular modeling, and performance modeling of CLs in PEFCs. Our major focus will be on state-of-the-art CLs that contain Pt nanoparticle electrocatalysts, a porous carbonaceous substrate, and an embedded network of interconnected ionomer domains as the main constituents. The section starts with a general discussion of structure and processes in catalyst layers and how they transpire in the evaluation of performance. Thereafter, aspects related to self-organization phenomena in catalyst layer inks during fabrication will be discussed. These phenomena determine the effective properties for transport and electrocatalytic activity. Finally, physical models of catalyst layer operation will be reviewed that relate structure, processes, and operating conditions to performance. 

Self-consistent approaches in molecular modeling have to strike a balance of appropriate representation of the primary polymer chemistry, adequate treatment of molecular interactions, sufficient system size, and sufficient statistical sampling of structural configurations or elementary transport processes. They should account for nanoscale confinement and random network morphology and they should allow calculating thermodynamic properties and transport parameters. 

Another moderately successful approach to the theory of diffusion in liquids is that developed by Eyring (E4) in connection with his theory of absolute reaction rates (P6, K6). This theory attempts to explain the transport phenomena on the basis of a simple model for the liquid state and the basic molecular process occurring. It is assumed in this theory that there is some unimolecular rate process in terms of which the transport processes can be described, and it is further assumed that in this process there is some configuration that can be identified as the activated state. Then the Eyring theory of reaction rates is applied to this elementary process. 

Physical transport processes and mixing ratio. The concentration profile of a minor constituent in an atmosphere is often expressed as a mixing ratio by volume or a mole fraction rather than the concentration by atmospheric modelers. Physical transport processes involve vertical and horizontal mixing by turbulence and molecular diffusion. The molecular diffusion process can be ignored in the stratosphere since it is important only above about 40 km. 

A series of articles were published by Ennari et al. on MD simulation of transport processes in Poly(Ethylene Oxide) and sulfonic acid-based polymer electrolyte.136,137 The work was started by the determination of the parameters for the ions missing from the PCFF forcefield made by MSI (Molecular Simulations Inc.), to create a new forcefield, NJPCFF. In the models, the proton is represented as a hard ball with a positive charge. Zhou et al. used the similar approach to model Nation.138 The repeating unit of Nafion (Fig. 17) was optimized using ab initio VAMP scheme. The protons were modeled with hydronium ions. Three unit cell or molecular models were used for the MD simulation. The unit cell contains 5000 atoms 20 pendent side chains, and branched Nafion backbone created with the repeating unit. Their water uptakes or water contents were 3, 13, or 22 IEO/SO3, which correspond to the room temperature water uptakes at 50% relative humidity (RH), at 100% RH, and in liquid water respectively.18 The temperature was initially set at a value between 298.15 and 423.15 K under NVE ensemble with constant particle number, constant volume (1 bar), and constant energy. 

Atomistic molecular modeling techniques have proven to be a very useful tool for the investigation of the structure and dynamics of dense amorphous membrane polymers and of transport processes in these materials. By utilizing these methods, information can be obtained that is not accessible by experimental means. 

This model, based on the earlier work of Fujita (18), currently appears to be the most effective theory to describe diffusion both above and below Tg. It adopts the notion that all transport processes are governed by the availability of free volume in the system. Free volume is a useful concept representing a specific volume V/v present as holes of the order of molecular (monomeric) dimensions or smaller, which together with the specific volume of the molecules themselves, Vo, gives the total specific volume, V... 

Somewhat closer to the designation of a microscopic model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller cells of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable average length of the elementary diffusion jump must be known. But in the framework of this type of microscopic model, it is not possible to determine this parameter from first principles . 

In the light of the previous discussion it is quite apparent that a detailed mathematical simulation of the combined chemical reaction and transport processes, which occur in microporous catalysts, would be highly desirable to support the exploration of the crucial parameters determining conversion and selectivity. Moreover, from the treatment of the basic types of catalyst selectivity in multiple reactions given in Section 6.2.6, it is clear that an analytical solution to this problem, if at all possible, will presumably not favor a convenient and efficient treatment of real world problems. This is because of the various assumptions and restrictions which usually have to be introduced in order to achive a complete or even an approximate solution. Hence, numerical methods are required. Concerning these, one basically has to distinguish between three fundamentally different types, namely molecular-dynamic models, stochastic models, and continuous models. 

In S. typhimurium a combination of two concurrent processes, either mechanisms 1 and 3 or mechanism 2, would explain the observed results. The former would account for the rapid phase of iron uptake while the latter would explain the slower penetration rate of the intact chelate. In this organism the iron of ferrioxamine B is again rapidly assimilated, and the chelate enters at a slower pace, but no information on the mechanism can be gleaned from the chromic complexes as they are not transported. It is possible that the active isomer has not been tested in this system. An inspection of molecular models implies that four trans isomers might exist (79). 

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