Transport processes in solids

Carbonell, RG Sarti, GC, Coupled Deformation and Mass-Transport Processes in Solid Polymers, Industrial and Engineering Chemistry Research 29, 1194, 1990. 

Solid-state electrochemistry — is traditionally seen as that branch of electrochemistry which concerns (a) the -> charge transport processes in -> solid electrolytes, and (b) the electrode processes in - insertion electrodes (see also -> insertion electrochemistry). More recently, also any other electrochemical reactions of solid compounds and materials are considered as part of solid state electrochemistry. Solid-state electrochemical systems are of great importance in many fields of science and technology including -> batteries, - fuel cells, - electrocatalysis, -> photoelectrochemistry, - sensors, and - corrosion. There are many different experimental approaches and types of applicable compounds. In general, solid-state electrochemical studies can be performed on thin solid films (- surface-modified electrodes), microparticles (-> voltammetry of immobilized microparticles), and even with millimeter-size bulk materials immobilized on electrode surfaces or investigated with use of ultramicroelectrodes. The actual measurements can be performed with liquid or solid electrolytes. 

Fig. 1-1. Transport processes in solid-liquid soil reactions—Nonactivated processes 1. Transport in the soil solution, 2. Transport across a liquid film at the solid-liquid interface, 3. Transport in a liquid-filled micropore. Activated processes 4. Diffusion of a sorbate at the surface of the solid, 5, Diffusion of a sorbate occluded in a micropore, 6. Diffusion in the bulk of the solid.

Beside the gas coulometry, solid state coulometry is used to investigate transport processes in solid conductors. In such a way, the transference number of solid conductors (e.g., Ag in a—Agl,... 

Defects are mandatory for additional transport processes in solids, among them diffusion and ionic conductance. The latter is an important property for sensors. It is encountered mainly in ionic crystals, e.g. in metal oxides. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

The classification of wastewater in terms of size distribution is normally done from a practical point of view. Typically, a distinction is made between soluble, colloidal and suspended components (Figure 3.6). While this definition for determining what solids are is rational as far as physical transport processes in sewers are concerned, when dealing with the microbial processes for sewer conditions, an extension of the solids definition is required. Particles larger than about 10-4 pm cannot be transported through the cell wall and are, therefore, from a microbial point of view, considered particles. 

The distribution of elements between the solid and the liquid phase is of primary importance for the transport processes in the environment. In addition, the uptake of elements in plants and other living organisms is determined by the speciation of the element in that phase. 

It is important to differentiate between two terms that are widely used in the literature, namely chemical kinetics and kinetics . Chemical kinetics is defined as the investigation of chemical reaction rates and the molecular processes by which reactions occur where transport (e.g., in the solution phase, film diffusion, and particle diffusion) is not limiting. On the other hand, kinetics is the study of time-dependent processes. Because of the different particle sizes and porosities of soils and sediments, as well as the problem to reduce transport processes in these solid phase components, it is difficult to examine the chemical kinetics processes. Thus, when dealing with solid phase components, usually the kinetics of these reactions are studied. 

As aforementioned, the introduction of carbon nanomaterials is an effective strategy to take on some of the contemporary challenges in the field of DSSCs. In particular, enhanced charge injection and charge transport processes in carbon nanomaterial-doped electrodes, efficient carbon nanomaterial-based, iodine-free, quasi-solid state electrolytes, and the use of novel nanographene hybrids as dyes are some of the most stunning milestones. All of these milestones are considered as solid proof for the excellent prospect of carbon nanomaterials in DSSCs. The major goal of this chapter is to... 

D.c. electrical conductivity, thermal conductivity, Seebeck effect and Hall effect are some of the common electron-transport properties of solids that characterize the nature of charge carriers. On the basis of electrical properties, solid materials may be classified into metals, semiconductors, and insulators where the charge carriers move in band states (Fig. 6.1) there are other semiconductors and insulators where charge carriers are localized and their motion involves a diffusive process (Honig, 1981). We shall briefly present the important relations involved in interpreting the transport phenomena in solids. 

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

We have discussed point defects in elements (A) and in nearly stoichiometric compounds having narrow ranges of homogeneity. Let us extend this discussion to the point defect thermodynamics of alloys and nonmetallic solid solutions. This topic is of particular interest in view of the kinetics of transport processes in those solid solutions which predominate in metallurgy and ceramics. Diffusion processes are governed by the concentrations and mobilities of point defects and, although in inhomogeneous crystals the components may not be in equilibrium, point defects are normally very close to local equilibrium. 

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Lautenberger, C. and Fernandez-Pello, C. Pyrolysis modeling, thermal decomposition, and transport processes in combustible solids. In Faghri, M. and Sunden, B. (eds.). Transport Phenomena in Fires. Boston, MA WIT Press, 2008, pp. 209-259. 

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