Solid state transport rates

Mukherjee studied the gas phase equilibria and the kinetics of the possible chemical reactions in the pack-chromising of iron by the iodide process. One conclusion was that iodine-etching of the iron preceded chromis-ing also, not unexpectedly, the initial rate of chromising was controlled by transport of chromium iodide. Neiri and Vandenbulcke calculated, for the Al-Ni-Cr-Fe system, the partial pressures of chlorides and mixed chlorides in equilibrium with various alloys and phases, and so developed for pack aluminising a model of gaseous transport, solid-state transport, and equilibria at interfaces. 

The oxygen partial pressure affects the defect concentrations in an oxidic solid and therefore also the diffusivity in nonstoichiometric oxide ceramic compounds. The oxygen gas pressure then affects the apparent reaction rate through the solid state diffusion rates even when there is no mass transport through the gas phase during sintering. 

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. 

The latter reaction mechanism is favored by most researchers. The presence of NO2 with H2S greatly enhances silver sulfidation and when high relative humidity is added, the rate of sulfidation is extremely rapid and is limited by gas-phase diffusion even at high flow rates. Therefore, the solid-state transport of silver atoms from the bulk is faster than the interfacial reaction and does not affect the rate. 

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... 

The high temperature XRPD technique can be used to investigate the dynamics of solid-state ion exchange of zeolites. Data suggest that the rate of Cd2+ ion transport in the zeolite Y micropores controls the rate of the solid-state ion exchange. 

In industrial PET synthesis, two or three phases are involved in every reaction step and mass transport within and between the phases plays a dominant role. The solubility of TPA in the complex mixture within the esterification reactor is critical. Esterification and melt-phase polycondensation take place in the liquid phase and volatile by-products have to be transferred to the gas phase. The effective removal of the volatile by-products from the reaction zone is essential to ensure high reaction rates and low concentrations of undesirable side products. This process includes diffusion of molecules through the bulk phase, as well as mass transfer through the liquid/gas interface. In solid-state polycondensation (SSP), the volatile by-products diffuse through the solid and traverse the solid/gas interface. The situation is further complicated by the co-existence of amorphous and crystalline phases within the solid particles. 

To increase the PET molecular weight beyond 20 000 g/mol (IV = 0.64 dL/g) for bottle applications, with minimum generation of acetaldehyde and yellowing, a further polycondensation is performed in the solid state at low reaction temperatures of between 220 and 235 °C. The chemistry of the solid-state polycondensation (SSP) process is the same as that for melt-phase polycondensation. Mass-transport limitation and a very low transesterification rate cause the necessary residence time to increase from 60-180 minutes in the melt phase to... 

Experimental determination of Ay for a reaction requires the rate constant k to be determined at different pressures, k is obtained as a fit parameter by the reproduction of the experimental kinetic data with a suitable model. The data are the concentration of the reactants or of the products, or any other coordinate representing their concentration, as a function of time. The choice of a kinetic model for a solid-state chemical reaction is not trivial because many steps, having comparable rates, may be involved in making the kinetic law the superposition of the kinetics of all the different, and often unknown, processes. The evolution of the reaction should be analyzed considering all the fundamental aspects of condensed phase reactions and, in particular, beside the strictly chemical transformations, also the diffusion (transport of matter to and from the reaction center) and the nucleation processes. 

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. 

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