Diffusion rates, bulk

Isotopic exchange reaction rates and oxygen diffusion coefficients of Pt/M-CZ, S-CZ and R-CZ at 41 are listed in Table V (Dong et al., 2004a). The surface diffusion rate for R-CZ (Rg) is nearly 4 times larger than the bulk diffusion rate or the equilibrium isotopic exchange rate (R ), while it is... 

Since in some cases the previously described alloy, dealloyed, and controlled-crystal-face catalysts also develop porous/hollow structures, it is of particular interest to determine to what extent the hollow structure affects the high ORR activities seen in those catalysts. Focus points for future research should include (i) developing scalable synthesis techniques and (ii) determining whether the surface and bulk diffusion rates of Pt in these hollow structures, relative to the fuel cell life, are sufficiently slow for this type of catalyst to be practical. 

Silicon nitride is a highly covalent material, which means bulk diffusion rate is too low to give densification. Therefore, sintering additives are used to obtain the fully desified material. The added metal oxides (MgO, Al203,Y203, rare... 

If the exchange is governed by diffusion away from the surface, then a stretched-exponential type of behavior F(t) = r(0) exp[-(t/r) ] is observed for the decay in the surface excess of the initially adsorbed pol5mier. The value of the exponent p can vary between 0 and 1, depending on the rate of readsorption and the bulk diffusion rates (35,36). If diffusion is slow and the chain exhibits a strong tendency to readsorb, p will have a small value p < 1/2). The time constant for exchange in this case scales as where D is the diffusion coefficient of the polymer chain in the matrix of adsorbed chains. 

In the limiting case where Dcnsat/ sb(1 9h) (this corresponds to conditions where D is low, the membrane is thick, 9h is not close to unity, and fcgB is high), the permeation rate is limited by the bulk diffusion rate in the membrane, and the surface-bulk transfer step is in quasiequilibrium (Ssb osb). It gives, as an approximation, the same expression for X versus 9h as in the charging conditions (Equation 2.12a) except that this equation applies only to the region of the bulk close to the entry surface ... 

Since amorphous films have no grain boundaries, they are expected to show lower diffusion rates than films that have grain boundaries, since grain boundary diffusion rates are higher than bulk diffusion rates. Amorphous conductive materials, such as 758125, have been proposed as a diffusion barrier film in semiconductor metallizations. Nucleation on a surface can be modified from a disordered state to an ordered state by carefully controlled concurrent ion bombardment. 

The simulation of molecules in solution can be broken down into two categories. The first is a list of elfects that are not defined for a single molecule, such as diffusion rates. These types of effects require modeling the bulk liquid as discussed in Chapters 7 and 39. The other type of effect is a solvation effect, which is a change in the molecular behavior due to the presence of a solvent. This chapter addresses this second type of effect. 

Adsorption systems employing molecular sieves are available for feed gases having low acid gas concentrations. Another option is based on the use of polymeric, semipermeable membranes which rely on the higher solubiHties and diffusion rates of carbon dioxide and hydrogen sulfide in the polymeric material relative to methane for membrane selectivity and separation of the various constituents. Membrane units have been designed that are effective at small and medium flow rates for the bulk removal of carbon dioxide. 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

Sinee the kinetie proeesses oeeur eonseeutively, the solution eoneentration adjusts itself so that the rates of the two steps are equal at steady state. In most eases, more than one meehanism influenees a erystal s growth rate. If the different meehanisms take plaee in parallel, then the meehanism resulting in the faster growth eontrols the overall rate. If the proeesses take plaee in series, as in the ease of bulk diffusion followed by surfaee reaetion, then the slower meehanism will eontrol the overall rate. 

The role of bulk diffusion in controlling reaction rates is expected to be significant during surface (catalytic-type) processes for which transportation of the bulk participant is slow (see reactions of sulphides below) or for which the boundary and desorption steps are fast. Diffusion may, for example, control the rate of Ni3C hydrogenation which is much more rapid than the vacuum decomposition of this solid. 

While it is inherently probable that product formation will be most readily initiated at sites of effective contact between reactants (A IB), it is improbable that this process alone is capable of permitting continued product formation at low temperature for two related reasons. Firstly (as discussed in detail in Sect. 2.1.1) the area available for chemical contact in a mixture of particles is a very small fraction of the total surface (and, indeed, this total surface constitutes only a small proportion of the reactant present). Secondly, bulk diffusion across a barrier layer is usually an activated process, so that interposition of product between the points of initial contact reduces the ease, and therefore the rate, of interaction. On completion of the first step in the reaction, the restricted zones of direct contact have undergone chemical modification and the continuation of reaction necessitates a transport process to maintain the migration of material from one solid to a reactive surface of the other. On increasing the temperature, surface migration usually becomes appreciable at temperatures significantly below those required for the onset of bulk diffusion within a product phase. It is to be expected that components of the less refractory constituent will migrate onto the surfaces of the other solid present. These ions are chemisorbed as the first step in product formation and, in a subsequent process, penetrate the outer layers of the... 

The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the... 

In addition, assuming that the rate-determining step is the bulk diffusion (i.e.,ka/(DJt) lholds), we can derive the minimum dissolution current observed after the fluctuation-diffusion current, that is,... 

For example, for alkyl (8-16) glycoside (Plantacare 818 UP) non-ionic surfactant solution of molecular weight 390 g/mol, an increase in surfactant concentration up to 300 ppm (CMC concentration) leads to a significant decrease in surface tension. In the range 300 < C < 1,200 ppm the surface tension was almost independent of concentration. In all cases an increase in liquid temperature leads to a decrease in surface tension. This surface tension relaxation is a diffusion rate-dependent process, which typically depends on the type of surfactant, its diffusion/absorption kinetics, micellar dynamics, and bulk concentration levels. As the CMC is approached the absorption becomes independent of the bulk concentration, and the surfactant... 

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