Diffusion rate, influencing factors

The retarding influence of the product barrier in many solid—solid interactions is a rate-controlling factor that is not usually apparent in the decompositions of single solids. However, even where diffusion control operates, this is often in addition to, and in conjunction with, geometric factors (i.e. changes in reaction interfacial area with a) and kinetic equations based on contributions from both sources are discussed in Chap. 3, Sect. 3.3. As in the decompositions of single solids, reaction rate coefficients (and the shapes of a—time curves) for solid + solid reactions are sensitive to sizes, shapes and, here, also on the relative dispositions of the components of the reactant mixture. Inevitably as the number of different crystalline components present initially is increased, the number of variables requiring specification to define the reactant completely rises the parameters concerned are mentioned in Table 17. 

There is a whole spectrum of heterogeneous catalysts, but the most common types consist of an inorganic or polymeric support, which may be inert or have acid or basic functionality, together with a bound metal, often Pd, Pt, Ni or Co. Even if the support is inert its structure is of vital importance to the efficiency of the catal ic reaction. Since the reactants are in a different phase to the catalyst both diffusion and adsorption influence the overall rate, these factors to some extent depending on the nature and structure of the support. 

Studies in the field of electrochemical kinetics were enhanced considerably with the development of the dropping mercury electrode introduced in 1923 by Jaroslav Heyrovsky (1890-1967 Nobel prize, 1959). This electrode not only had an ideally renewable and reproducible surface but also allowed for the first time a quantitative assessment of diffusion processes near the electrode s surface and so an unambiguous distinction between the influence of diffusion and kinetic factors on the reaction rate. At this period a great number of efectrochemical investigations were performed at the dropping mercury efectrode or at stationary mercury electrodes, often at the expense of other types of electrodes (the mercury boom in electrochemistry). 

Leakage through a synthetic liner is controlled by Fick s first law, which applies to the process of liquid diffusion through the liner membrane. The diffusion process is similar to flow governed by Darcy s law except that it is driven by concentration gradients and not by hydraulic head. Diffusion rates in membranes are very low in comparison with hydraulic flow rates even in clays. In synthetic liners, therefore, the factor that most influences liner performance is penetrations. Synthetic liners may have imperfect seams or pinholes, which can greatly increase the amount of leachate that leaks out of the landfill. 

This study showed that the overall crystallization processes for mor-denite, zeolite X, and zeolite A were similar. However, the physical properties of the crystallizing system determine the rate-limiting step for a particular zeolite synthesis. In the case of mordenite in which both the viscosity of the batch composition and the morphology of seed crystals were varied, it was observed that diffusion in the liquid phase was the ratedetermining step. For zeolite X the actual growth rate on the crystal-liquid interface was the rate-limiting factor as shown by identical conversion rates for the seeded and unseeded systems. For zeolite A in the system chosen, both processes influenced the conversion rate. 

The external factors comprise the nature of the membrane, the substrate concentration in the aqueous phase and any other external species that may participate in the process. They may strongly influence the transport rates via the phase distribution equilibria and diffusion rates. When a neutral ligand is employed to carry an ion pair by complexing either the cation or the anion, the coextracted uncomplexed counterion will affect the rate by modifying the phase distribution of the substrate. The case of a cationic complex and a counteranion is illustrated schematically in Figure 10 (centre). 

Another peculiar feature of the grafting of acrylic acid is the break observed in the conversion curves particularly at low dose rates. The interpretation of this effect proposed above does not account for the fact that no break is observed with other monomers except at much higher grafting ratios (2, 4). These striking differences in kinetics for systems which in principle should exhibit comparable behavior are presumably related to differences in diffusion rates and polymer-polymer and polymer-monomer compatibilities. Little is known at present on the factors which govern these effects and on their influence on the kinetics. 

PVC is often used in food packaging and blood bags. This study concerns mass transfers between plasticised PVC, having been subjected to a treatment, and liquid food or food simulants. The treatment reduces the diffusion of the plasticiser and the influence of some factors of this processing were investigated. A mathematical model, able to simulate these mass transfers and to quantify treatment parameters, is proposed to quantify the diffusion rate in terms of an average diffusion coefficient. 16 refs. 

It was stated, that macroporous carbons of plant origin show better properties in dynamic than in static conditions. It is cormected with relationship of quantity of macropores and diffusion rate. Greater differences in classsification are observed at lower equilibrium concentrations (0,1 and 0,01 mg/dm ) in static adsorption. Therefore direct factors of Freundlich s isotherms influencing adsorption capacities at different concentrations should be considered. It was stated that angle of slope, adsorption rate in static conditions, shape of breaktrough curves in dynamic conditions... 

Two mtyorlactors affect droplet size and density in the PIPS process types and relative concentration of materials used and cure temperature. The cure temperature influences the rate of polymerization, viscosity of the polymer, diffusion rate of the liquid crystal and solubility of the liquid crystal in the polymer. Each factor is affected differently by the cure temperature with the result that droplet size varies in a complex manner with cure temperature (Figure 5) and must therefore be empirically determined for each formulation. 

On heating, many hydrides dissociate reversibly into the metal and Hj gas. The rate of gas evolution is a function of both temperature and /KH2) but will proceed to completion if the volatile product is removed continuously [1], which is experimentally difficult in many systems. The combination of hydrogen atoms at the metal surface to yield Hj may be slow [2] and is comparable with many heterogeneous catalytic reactions. While much is known about the mobility of H within many metallic hydride phases, the gas evolution step is influenced by additional rate controlling factors. Depending on surface conditions, the surface-to-volume ratio and the impurities present, the rate of Hj release may be determined by either the rate at which hydrogen arrives at the solid-gas inteifece (diffusion control), or by the rate of desorption. 

It should be borne in mind that the reactions of lead azide and water-carbon dioxide are reversible, and the extent of lead azide deterioration will be influenced by a number of factors which include temperature, the partial pressure of reactants, diffusion rates, container dead space, and leakage from the container. 

Using another electrical analog approach, Klute (26,27) arrived at a similar expression in which the impedance factor was termed the "transmission function." In both cases, however, the properties of the conducting phase are considered not to be influenced by the crystalline phase. Although this was found to be true for sorption, Michaels et al asserted that the crystallites would reduce the mobility of the chains in the amorphous phase and, thus, further reduce penetrant diffusion rates. The "chain... 

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