Diffusion-controlled region

When intraparticle diffusion occurs, the kinetic behaviour of the system is different from that which prevails when chemical reaction is rate determining. For conditions of diffusion control 0 will be large, and then the effectiveness factor tj( 1/ tanh 0, from equation 3.15) becomes. From equation 3.19, it is seen therefore that rj is proportional to k Ul. The chemical reaction rate on the other hand is directly proportional to k so that, from equation 3.8 at the beginning of this section, the overall reaction rate is proportional to k,n. Since the specific rate constant is directly proportional to e"E/RT, where E is the activation energy for the chemical reaction in the absence of diffusion effects, we are led to the important result that for a diffusion limited reaction the rate is proportional to e E/2RT. Hence the apparent activation energy ED, measured when reaction occurs in the diffusion controlled region, is only half the true value ... 

A further important result which arises because of the functional form of is that the apparent order of reaction in the diffusion controlled region differs from that which is observed when chemical reaction is rate determining. Recalling that the reaction order is defined as the exponent n to which the concentration CAm is raised in the equation for the chemical reaction rate, we replace f(CA) in equation 3.8 by CJ . Hence the overall reaction rate per unit volume is (1 - e)rjkCA. When diffusion is rate determining, tj is (as already mentioned) equal to f1 from equation... 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first order, whereas a second-order reaction has an apparent order of 3/2 when strongly influenced by diffusional effects. Because k and n are modified in the diffusion controlled region then, if the rate of the overall process is estimated by multiplying the chemical reaction rate by the effectiveness factor (as in equation 3.8), it is imperative to know the true rate of chemical reaction uninfluenced by diffusion effects. 

Activation energy per mole for chemical reaction Apparent activation energy per mole in diffusion controlled region... 

In the course of catalytic oxidation, the production rate of intermediates that finally generate CO2 and H2O is also limited by rx. Some intermediates are the chemisorbed species that form surface donors and acceptors, and the other intermediates are the excited species. Both the generation rate of carriers originated from the surface states and the production rate of the excited species is governed by rx- Thus the dependence of CTL intensity on flow velocity should agree with that of rx in the diffusion-controlled region. 

In conclusion it may be said that equations (3a) and (4) adequately represent the changes of termination and propagation constants in the diffusion-controlled regions for the emulsion polymerization of styrene. 

There are two critical values, and x n2], of the layer thickness which divide this dependence into the reaction controlled and diffusion controlled regions with regard to components A and B, respectively. 

Let the convective-diffusion-controlled region be defined as those sets of conditions (Pe, R, A/kT) for which the rate may he calculated to within 10% by ignoring London forces. Similarly, let the London-force-controlled region be those sets of conditions for which the rate may be calculated to within 10% by ignoring Brownian motion. These definitions suggest a method for determining limits for the regions. 

The product selectivity of the complex isomerization can be improved by the pore entrance deactivation when the reaction is operated in diffusion-controled region, However, effectiveness of thezeolite catalysts at higher Thiele modulus is already small, and it will be decreased further by the pore entrance deactivation. Therefore, to obtain higher selectivity and remain suitable activity, the pore entrance of zeolite catalysts should be modified properly. 

The Avrami analysis was performed on the crystallization data. The DLI measurements provided high Avrami exponents in the blends, but the analysis on the DLI data is extremely inaccurate because of all the difficulties inherent to the method. The IR measurements show Avrami exponents that range from 2.5 to 1.5 for PET and PBT. These studies were made on the diffusion-controlled region. It is our belief that the Avrami analysis strongly depends on the method used to follow the crystallization and always has to be accompanied with direct observations on the morphology. 

Chemical reaction is only rate determining in a first low temperature domain, situated roughly below 1000°C. In a second, medium temperature domain the gaseous reactant is gradually depleted inside the porous particle, so that the reaction proceeds at the rate at which internal diffusion supplies new reactants. In this internal diffusion controlled region the apparent energy of activation falls off to half its initial value. 

Thus a single equation in terms of the derivative of epoxy conversion is obtained, so that the global kinetic constants can be obtained as the intercept and slope of the linear fit at low conversions (far from the diffusion controlled region) of the expression ... 

In the course of the previous sections, several striking differences between the two epoxy systems were noted concerning the conversion at vitrification, the diffusion-controlled region in non-isothermal experiments, the critical heating rates, etc. These differences can be related to the chemical structure of the monomers, which influence the reactivity and the growing network structure. 

Figure 2.19 Cole-Cole plot for a 200mCcm" (9500 A) PPy/NaC104 film showing a longer diffusion-control region at low oxidation levels.

In the diffusive control region, a linear dependence between t] and Da can be observed in a log-log plot ... 

In the diffusion-controlled region where the electrode overpotential is high enough, the current is proportional to the square root of the angular velocity of the electrode according to the Levich equation ... 

When the free energy change (AG) for electron transfer is more negative than -lOKcal/mol, the rate is practically in diffusion controlled region. The present system falls in this category. 

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