Transport versus Kinetic Control

If it is intended to study the reaction kinetics, that is, the dependence rate upon variables such as reaction pressures or temperature, it is important to be sure that the surface reaction is the slowest of all those forming the catalytic cycle, and that therefore mass transport to and from the surface are not rate limiting. Symptoms of mass transport limitation include the following. 

The rate is proportional to the catalyst weight W or surface area As to a power less than unity. 

The conversion is not accurately proportional to the inverse of the reactant flow rate F. 

Thus for kinetic control the rate r should be proportional to the contact time T so that 

The temperature coefficient is low, corresponding to an apparent activation energy of 10-15 kJ mol gaseous diffusion processes do not in fact obey the Arrhenius equation, their rates being proportional to 

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Erosion is typically characterized by either occurring on the surface or in the bulk. Surface erosion is controlled by the chemical reaction and/or dissolution kinetics, while bulk erosion is controlled by diffusion and transport processes such as polymer swelling, diffusion of water through the polymer matrix, and the diffusion of degradation products from the swollen polymer matrix. The processes of surface and bulk erosion are compared schematically in Fig. 1. These two processes are idealized descriptions. In real systems, the tendency towards surface versus bulk erosion behavior is a function of the particular chemistry and device geometry (Tamada and Langer, 1993). Surface erosion may permit the... 

Fig. 2.3 Rate-limiting steps in mineral dissolution (a) transport-controlled, (b) surface reaction-controlled, and (c) mixed transport and surface reaction control. Concentration (C) versus distance (r) from a crystal surface for three rate-controUing processes, where is the saturation concentration and is the concentration in an infinitely diluted solution. Reprinted from Sparks DL (1988) Kinetics of soil chemical processes. Academic Press New York 210 pp. Copyright 2005 with permission of Elsevier...

Factors analogous to those affecting gut absorption also can affect drug distribution and excretion. Any transporters or metabolizing enzymes can be taxed to capacity—which clearly would make the kinetic process nonlinear (see Linear versus Nonlinear Pharmacokinetics ). In order to have linear pharmacokinetics, all components (distribution, metabolism, filtration, active secretion, and active reabsorption) must be reasonably approximated by first-order kinetics for the valid design of controlled release delivery systems. 

In the simplest case E is the potential applied between two electrodes in solution and / is the current flowing in the circuit. Curve a in Fig. lA represents the dependence of current on potential when the process is controlled by the kinetics of the reaction alone. Curve b takes into account the effects of mass transport. These concepts are explained in detail in the section that follows. In actual measurement the potential E is always measured versus a fixed reference electrode and instead of the current one refers to the current density on the electrode being studied, but at this point we need not concern ourselves with these refinements. 

Guy, Ch. and Schott, J. (in press), Multisite Surface Reaction versus Transport Control during the Hydrolysis of a Complex Oxide, Chem. Geol. Kinet. (spec, issue). 

The multiphasic nature of the intra-particle diffusion plot confirms the presence of both surface and pore diffusion. In order to predict the actual slow step involved, the kinetic data were further analysed using Boyd kinetic expression. Equation A.22 was used to calculate B( values at different time t. The linearity of the plot of B( versus time was used to distinguish whether surface and intra-particle transport controls the adsorption rate. It... 

FIG. 37 Kinetics of irreversible adsorption under the diffusion controlled transport at a planar surface expressed as the versus (t/tch) dependencies (where t = l/(Sgit ) D is the... 

FIG. 52 Adsorption kinetics of latex particles on mica under the diffusion-controlled transport (AFM method [9]) the particle coverage versus the adsorption time t dependence curve 1, / = 5 X 10-3 curve 2,1= IQ- M. The continuous lines represent the exact theoretical results derived numerically [2] and the dashed line shows the limiting results calculated from Eq. (170). (From Ref. 2.)... 

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