The Effect of Diffusion Limitation

While there have been several studies on the synthesis of block copolymers and on the molecular weight evolution during solution as well as bulk polymerizations (initiated by iniferters), there have been only a few studies of the rate behavior and kinetic parameters of bulk polymerizations initiated by iniferters. In this paper, the kinetics and rate behavior of a two-component initiation system that produces an in situ living radical polymerization are discussed. Also, a model that incorporates the effect of diffusion limitations on the kinetic constants is proposed and used to enhance understanding of the living radical polymerization mechanism. 

Thus diffusion limitations decrease the yield twofold. These results may be generalized to include interface and intraparticle diffusion for bidisperse catalysts [5]. The effect of diffusion limitation on the concentration distribution over the reactor length can be calculated from Equations 8.24, 8.29 and 8.33. An example of such calculations is shown in Figure 8.4 for the case CM = 0, DtA = D and kjkx = 0.1. Although the rate of... 

Thus, even tliough measurements are taken at open circuit, it is clearly advantageous to use highly conducting solutions whenever possible, and this becomes essential if we wish to study the rate of fast reactions. These considerations become even more critical when the effects of diffusion limitation are included, as we shall see. 

Figure 15K represents a typical response of the electrochemical inteqjhase to constant current pulses of different magnitude. For a sufficiently low current density, a true steady state is reached before the effect of diffusion limitation can be observed. As the current density is increased, diffusion limitation sets in earlier. Extrapolation of the potential to zero time can sometimes be employed to estimate a correct value of the activation overpotential, as shown in this Fig. 15K. If such extrapolation is not practical, one may use a higher concentration of the reactant, to increase the ratio x /x (i.e., to...

For the Andrussow process the effect of diffusion limitation is to ensure that the composition of the gas phase at the catalyst surface is richer in NH3 and less rich in methane and oxygen than the bulk gas composition. This implies that the maximum HCN synthesis rates are achieved with surface CH4/NH3 and air/fuel ratios lower than those prevailing in the bulk gas phase. 

Certain rough criteria can be made for the importance of internal diffusion in terms of the general Thiele modulus, h. Consider first the case of the first order reaction in the slab. It is clear from the left-hand curve of Fig. 6.7 that if h is less than I the effect of diffusion limitation is not serious, whereas... 

In polymerization processes carried out in batch, the viscosity of the polymer/monomer solution will increase progressively with the conversion of the monomer, because the polymer concentration and its molecular mass both go up. Therefore, the effects of diffusion limitation may increase progressively or even appear quite suddenly at a certain degree of conversion. 

Why is a peak observed in this type of measurement In the experiment shown in Figure 15.1 the sweep is started at a potential of—0.2 V versus the standard potential for the Fe /Fe couple, where no Faradaic reaction takes place. At about -0.05 V, the anodic current starts to increase with potential. Initially, the current is activation controlled, but as the potential becomes more positive, diffusion limitation sets in. The observed current is the inverse sum of the activation and the diffusion limited currents, (cf. Eq. (1.5)). As time goes on, the activation-controlled current increases (due to the increase in potential with time) but the diffusion-controlled current decreases. As a result, the observed current increases first, passes through a maximum and then decreases. At higher sweep rates each potential is reached in a shorter time, when the effect of diffusion limitation is less, hence the peak current is found to increase with sweep rate. 

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