Solid state rate processes

The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. 

G.H. Vineyard. Frequency factors and isotope effects in solid state rate processes. J. Chem. Phys. Solids, 3(1-2) 121-127, 1957. 

The application of absolute reaction rate theory to a chemical change at an interface is only useful if the calculations refer to an identified, or at least reliably inferred, model of the controlling bond redistribution step. This is a problem, because it is particularly difficult to characterize the structures of the immediate precursors to reaction in many solid state rate processes of interest. The activated species are inaccessible to direct characterization because they are usually located between reactant and product phases. The total amount of reacting material present within this layer, often of molecular dimensions, is small and irreversible chemical and textural changes may accompany opening of such specialized structures for examination or analysis. Moreover, the presence of metallic and/or opaque, ill-crystalUzed product phases may prevent or impede the experimental recognition of participating intermediates or essential textural features. 

The cooperative movement of large numbers of atoms represents an alternative, and in some ways more precise [83], mechanism of reaction in addition to the well-established interface advance and diffusion-controlled processes which are considered throughout this book. Examination of the possible participation of crystallographic shear in the reactions of solids has been largely restricted to refractory oxides, but comparable or related behaviour could, in principle, operate in a variety of other solid state rate processes. 

Vineyard G. H., Erequency Eactors and Isotope Effects in Solid State Rate Processes, J. Phys. 

Note also that we have just introduced the concepts of nuclei and nucleation in our study of solid state reaction processes. Our next step will be to examine some of the mathematics used to define rate processes in solid state reactions. We will not delve into the precise equations here but present them in Appendices at the end of this chapter. But first, we need to examine reaction rate equations as adapted for the solid state. 

Figure 5.3 Effect of nitrogen gas flow rate on the solid-state polycondensation process for PET reaction conditions, 259°C for 7h initial Mn, 16500, with a particle size of 0.18-0.25 mm data obtained by gas chromatographic analysis, employing a column of dimensions 8ft x 0.7.5 in o.d. [5]. Reproduced from Hsu, L.-C., J. Macromol. Sci., Phys., B1, 801 (1967), with permission from Marcel Dekker...

Besides the pressure (vacuum) and the flow rate of the gas, temperature is the major experimental variable in SSP and is of the highest importance for the economy of the process. Temperature dependence data for the solid-state polycondensation process are shown in Figures 5.4-5.7. According to the results... 

In Eqs. (3.58) and (3.59), the kt are the reaction rate constants. We will see in Chapter 4 that many solid-state ceramic processes involve simultaneous mass transport (diffusion), thermal transport, and reaction. 

As in solution phase electrochemistry, selection of solvent and supporting electrolytes, electrode material, and method of electrode modification, electrochemical technique, parameters and data treatment, is required. In general, long-time voltam-metric experiments will be preferred because solid state electrochemical processes involve diffusion and surface reactions whose typical rates are lower than those involved in solution phase electrochemistry. 

Table 1.1 provides typical values for atomic diffusivities in the solid, liquid, and gas states. As you can see, sohd-state diffusivities tend to be many orders of magnitude slower than liquid- or gas-phase diffusivities. Thus, solid-state diffusion often tends to be a rate-limiting step in many solid-state kinetic processes. 

Compare and contrast gas, liquid, and solid-state diffusion processes. Predict and model (quantitatively) diffusion processes in all three phases of matter. Provide reasonable ballpark estimates for the approximate rates of diffusion in all three phases of matter. 

In corrosion, phenomena other than mass transport in the electrolyte can slow down the establishment of steady state conditions, including adsorption, precipitation or film growth. Especially, solid state transport processes in passive oxide films are generally slow (Chap. 6) and as a consequence the measured current density will depend on the sweep rate, even if from a solution mass transport point of view steady state prevails (t 1). Polarization curves measured under these conditions are sometimes called pseudo-steady-state polarization curves. When reporting such data one should always indicate the sweep rate used. 

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