Diffusion rate controlling

Film thickness is an important factor iu solvent loss and film formation. In the first stage of solvent evaporation, the rate of solvent loss depends on the first power of film thickness. However, iu the second stage when the solvent loss is diffusion rate controlled, it depends on the square of the film thickness. Although thin films lose solvent more rapidly than thick films, if the T of the dryiug film iucreases to ambient temperature duriug the evaporation of the solvent, then, even iu thin films, solvent loss is extremely slow. Models have been developed that predict the rate of solvent loss from films as functions of the evaporation rate, thickness, temperature, and concentration of solvent iu the film (9). 

Diffusivities in liquids are comparatively low, a factor of 10 lower than in gases, so it is probable in most industrial examples that they are diffusion rate controlled. One consequence is that L-L. reactions are not as temperature sensitive as ordinary chemical reactions, although the effect of temperature rise on viscosity and droplet size sometimes can result in substantial rate increase. On the whole, in the presnt state of the art, the design of L-L reactors must depend on scale-up from laboratory or pilot plant work. 

Much research into radiation effects on polymers is done with samples sealed under vacuum. However, polymer materials may, in practical applications, be subjected to irradiation in air. The effect of irradiation is usually substantially different in air, with increased scission at the expense of crosslinking, and the formation of peroxides and other oxygen-containing structures. Diffusion rates control the access of oxygen to radicals produced by the radiation, and at high dose rates, as in electron beams, and with thick samples, the behaviour may be similar to irradiation in vacuum. Surface changes may be quite different from bulk due to the relative availability of oxygen. 

Diffusion Rate Controlled Process If the rate of chemical reaction is much faster than the diffusion of water and EG through the solid amorphous phase, then the reaction can be considered to be at equilibrium throughout the pellet [21], The reaction rate is dependent upon the pellet size, the diffusivity of both water and EG, the starting molecular weight, and the equilibrium constants Ki and K5. In addition, the pellet can be expected to have a radial viscosity profile due to a by-product concentration profile through the pellet with the molecular weight increasing as the by-product concentrations decreases in the direction of the pellet surface [22-24],... 

Surface Diffusion Rate Controlled At high gas velocities, the pellet surface byproduct concentration is maintained at an equilibrium value determined by the by-product concentration in the gas. In this condition, the mass transfer from the surface is balanced by the diffusion within the pellet to the surface. However... 

The diffusion of dopants into, and out of, conducting polymers is important for possible applications in batteries, and as conductors or semiconductors. For conductors or semiconductors, the chief requirements are that the material can be doped in a reasonable time, but that it will then not lose dopant over periods of years. This is particularly important in determining junction stability in devices. In the case of batteries, on the other hand, rapid and reversible uptake and loss of dopants is needed, since the diffusion rate controls charging and discharging rates. In addition, the accessibility of the structure to oxygen, and other degradants, will be a factor in the stability of the polymer. 

Examples of accompanying chemical reactions influencing film and intraparticle diffusion rate control is afforded by instances where a counter-ion can react with the functional group or with the co-ion, for example ... 

All the previously described mechanism criteria rely in some way or another upon comparing the predictions of rate theory with the observations. The interruption test , first described by Kressman, is a favoured means of differentiating between film and particle diffusion rate control since it places no reliance upon theoretical boundary conditions or exchanger properties. 

For the TGA cumene hydroperoxide system, an ethanol water solvent was employed for monomer and initiator. The data clearly demonstrate maximum add-on with larger proportions of water in the system, providing greater hair swelling, consistent with diffusion rate control [87]. 

Comparing the last expression with Eq. 4.3-7, obtained for the shrinking-core model with diffusion rate controlling, shows that Pf — is nothing but the ratio of the time required to reach a given conversion to the time required to reach complete conversion. Sohn and Szekely showed that Eq. 4.4-8 leads to a remarkably accurate approximation to the results obtained by numerical integration. 

Kinetic data could be treated by the models given by Boyd et al. (1947), which is valid under the experimental conditions used. With diffusion rate controlling in the adsorption particles of spherical shape, the solution of the simultaneous set of differential and algebraic equations leads to (Reichenberg, 1953 Helfferich, 1962)... 

Kinetic studies have been made on the thermal decomposition of a poly(oxypropylene)triol-toluene di-isocyanate copolymer foam. Following a diffusion rate-controlled step, the cellular structure collapses to a viscous liquid and degradation then occurs on a random scission basis. Products of degradation of A-monosubstituted and A A-disubstituted polyurethanes have been analysed by direct pyrolysis in the ion source of a mass spectrometer. The mono-substituted polymers depolymerize quantitatively to di-isocyanates and diols, whereas the disubstituted materials decompose selectively to secondary amines, olefins, and carbon dioxide. The behaviour of the monosubstituted polymers has been confirmed in an i.r. study of the degradation of model compounds. A study of the thermal degradation in vacuum of polyurethanes prepared from butanediol, methylene bis(4-phenylisocyanate), and hexanedioic acid-ethylene glycol-propylene glycol polyesters has been reported and reaction mechanisms proposed. ... 

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