INDEX diffusion-controlled

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

The data for the isothermal crystallization of [IX-Cg] from the glassy state were analyzed by the same method as that for the polyethers. Avrami s index obtained was between 2.1 and 2.2, i.e., n = ca. 2. This value, n = 2, suggests that the crystals grow two-dimensionally, if the nucleation process is heterogeneous and the growth process is diffusion-controlled. 

By now this basic formulation has had many interpretations. For example (Activity) has been used to refer to coke-on-catalyst, amine index of the material, reference to conversion in some specific chemical test who knows what else. The value of n, reported in various studies as ranging from 0 to 12, has been represented to indicate diffusion control (0.5) up to essentially "... we don t know what is going on here. .. (12). .. ". The factor is a proportionality constant specific to catalyst, operating conditions and chemical reaction. Voorhies model, based on time-on-stream observations, is obviously not general, but it is a good place to start. 

Procedures outlined in previous sections were used to compute the curves in Fig. 1.8. Three variables arc shown. The abscissa is the chemical rate applicable if all the surface is available. It is the chemical rate built into the catalyst. The ordinate represents values of an index that combines all diffusional tendencies of the particle. Moving in the direction of more diffusion control decreases this index. For example, higher porosity increases (providing it is not accomplished by decreasing the pore radius), increasing total pressure decreases Dg (and thus and increasing the pellet diameter, Pp, lowers both the effectiveness factor and mass transfer coefficient. Parameters on the curves are pellet rates. The ratio between the pellet rate and the intrinsic chemical rate is the effectiveness factor. 

The polymers produced by Ziegler-Natta polymerization normally have very wide molecular weight distributions. The polydispersity index PDI (= Myj/Mn) is 5-20 for polyethylene and 5-15 for polypropylene. The cause of the wide dispersity is not precisely known. Some workers believe that the propagation reaction becomes diffusion controlled after a few percent conversion and it is this which is responsible for the large dispersity. Some other workers believe that the rate constants are dependent upon the molecular size. 

The term C, is the 20% index at time t and represents the amount of cleaved disulfide at time f is the 20% index at time zero and represents the total amount of disulfide before oxidation and a represents the fiber radius, assumed to be 40 pm. Considering these assumptions, one obtains an approximate diffusion coefficient of 1.8 x lO cm /min. This diffusion coefficient is of the anticipated magnitude, suggesting that the oxidation of the disulfide bond in hair by alkaline hydrogen peroxide is a diffusion-controlled reaction. 

As a rule, the saturation index is a useful qualitative guide in connection with diffusion-controlled corrosion, but certain types of organic and inorganic particles as well as complex ions may prevent salt deposition on the surface and thereby make the SI invalid [8.10]. 

The closed extrusion process is a liquid (core mixture)-liquid (shell mixture) diffusion control process. The key parameters for controlling the refractive index distribution in this process are the compositions of the reactant mixtures, pump speed, the temperature and the length of the diffusion zone. In our previous study, we have shown that the refractive index distribution of the GRIN polymer fibers was significantly affected by the monomer composition of the reactant mixtures and the temperature of the diffusion zone (13). The refractive index difference between the... 

Material-invariance of the relative drop in oxygen index with increasing temperature is explained by the fact that the diffusion-controlled intermixing with oxygen is the determinant process rather than the thermal decomposition which follows the Arrhenius law. Diffusion processes are known to fit to a plot against the 3/2 power of temperature. 

In case of reaction control or ash layer diffusion-control, SCM is a single parameter model, and Treaction or rash as characteristic time. The above equations show that, to achieve any conversion of Xb, for the diffusion of gas film, r oc °, when R increases, the index decreases, and for ash diffusion con-... 

In the case of PE irradiation, it has been established that the superficial oxidized layer undergoes essentially chain scission, whereas the behavior of nonoxidized core layers is dominated by crosslinking therefore, the samples become more and more heterogeneous as the dose increases and a skin core structure appears. If in an inert medium, y-rays penetrate in all directions of the material in an oxidative medium, the phenomenon is oxygen diffusion-controlled. A depth distribution will exist in the variation of carbonyl index, crystallinity, melting point, degradation products, and so on. 

Very much more is known about the theory of concentration gradients at electrodes than has been mentioned in this brief account. Experimental methods for observing them have also been devised, based on the dependence of refractive index on concentration (the Schlieren method) by means of interferometry (O Brien, 1986). Nevertheless, the basic concept of an effective diffusion-layer thickness, treated here as varying in thickness with fi until the onset of natural convection and as constant with time after convection sets in (though decreasing in value with the degree of disturbance, Table 7.10), is a useful aid to the simple and approximate analysis of many transport-controlled electrodic situations. A few of the uses of the concept of 8 will now be outlined. 

The various data obtained for the kinetics of graft copolymerization onto PTFE films demonstrate that this reaction is complicated by the fact that the rate of diffusion of the monomer may become the controlling factor. It seems interesting at this point to compare and discuss together the results obtained with the different monomers. Table I summarizes the data obtained for autoacceleration indexes (/ ), dose-rate exponents (a), and over-all activation energies E, with styrene, acrylic acid, and vinylpyridine. Several conclusions can be derived from an examination of these data. 

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