Rate constant for initiation

Autocatalytic rate constant for initiation Fraction active polymer in CFSTR with dead polymer Fraction by-pass in by-pass CFSTR... 

Rate constants for initiator decomjosition and radical reactions in aqueous laiase. The rate coefficient for KgSgOg thermal decoiposition has been calculated at the relevant teiperature according to Kolthoff and Hiller (W). The... 

A great deal of confusion exists in the definitions chosen by different authors (and by the same authors on different occasions) for the rate constants for initiation and termination. The factor 2 expressing the fact that two radicals are created or destroyed in the respective processes is sometimes incorporated in the rate constants. Here we have consistently taken kd, h, and kt to represent the rate constants for the reactions as ordinarily written, hence the 2 is not included in the rate constant. Results expressed otherwise have been converted to this basis. 

In general, however, rate-constants for initiation, k, for at least one termination, and for various transfer reactions must also be known. If the real initiator is formed from precursors by an antecedent reaction, such as... 

Several authors have attempted to calculate the rate-constant for initiation from their observed d[P +]/d . However, it follows from our theory that the alleged k, which we designate by kk and which was calculated from... 

The effect of temperature on the rate and degree of polymerization is of prime importance in determining the manner of performing a polymerization. Increasing the reaction temperature usually increases the polymerization rate and decreases the polymer molecular weight. Figure 3-13 shows this effect for the thermal, self-initiated polymerization of styrene. However, the quantitative effect of temperature is complex since Rp and X depend on a combination of three rate constants—kd, kp, and kt. Each of the rate constants for initiation, propagation, and termination can be expressed by an Arrhenius-type relationship... 

Rate laws for radical chain reactions initiated by thermolysis are 1.5 order, first order in the component reacting in the rate-controlling step, and 0.5 order in the initiator. When the initiator is the same component as that reacting in the ratecontrolling step, the reaction will be 1.5 order in this reagent. When chain reactions are initiated by photolysis instead of thermolysis, the rate constant for initiation, the... 

The rate of radical generation or production (Rpr) is related to the rate constant for initiator decomposition, c, by Equation 10.3 where [I] is the instantaneous initiator concentration. The factor of 2 is included because two initiator or primary radicals are... 

The approach to the stationary state in a chain system is not instantaneous but takes a finite time which may be calculated from the kinetic mechanism if the individual rate constants for initiation and termination arc known. For the homogeneous chain reaction represented by case 1 Benson has shown how to calculate both the time ta required to reach any fraction a of the stationar37 -state concentration of X, and the fraction of reaction Fa occurring in that time. For thermal initiation ta is given by... 

Avhere kh represents the second-order specific rate constant for branching of the chain centers C, is the zero-order specific rate constant for initiation of chain centers at the walls, ktw is the diffusion-controlled temiination rate constant for capture of radicals at the walls, and P is the total pressure. On solving for (C) we find... 

This situation differs from that in transient state experiments, in which Eq. (32) is not satisfied and the surface coverages still build up in time [Y ] = [Y ],. Therefore, the ratio of the rates of production, (time dependent. Boudart (34) has pointed out, in the general context of polymerization kinetics, that the evolution in time of this ratio, when normalized by its steady-state value k Kk -I- k ), is a function of kp only, provided that the rate constant for initiation k, is large with respect to both k and k, (34). From a comparison of the transient state distribution with the steady-state one an absolute value for kp therefore can be found. The value of k, then follows from the steady-state value of a = kp/(kp -I- k,) via Eq. (33). 

Table 26. Rate constants for initiation step (a) in 20, in 1 mol solvents l70bj = 0.18 M. min, in several...

A fourth and probably the most useful method of determination of initiator eflSciency is based on the dead-end effect in polymerization technique which is treated in a later section. This technique allows treatment of kinetic data obtained under dead-end conditions to evaluate both the rate constant for initiator decomposition (kj) and the initiator efficiency (/) under experimental conditions. 

Using the data published by Ivan et. al. (47) and our own conclusions, the relative rate constants for initiation from internal allylic, tertiary and normal secondary chlorine can approximately be given as 1, 1, and 2 10 respectively. On the other hand, topical relative concentrations of these structures are 2, 10 and 10 > respectively, in an ordinary PVC. With respect to all uncertainties this shows that the total contribution from random dehydrochlorination is of the same order as that from internal allylic chlorine. In agreement with our earlier conclusion (3 8) the dominating influence of initiation from tertiary is obvious. 

Rate constant for initial weight loss / 1 dM, V, df ftm0 Molecular weight against time Molcular weight vs. conversion Introduction of chain transfer... 

Both the intracrystalline and intercrystalline (or external) acid sites of the zeolite are decreased by the silica binder. The changes in the intracrystalline acidity of the zeolite are reflected in its propane aromatization activity the activity is reduced significantly by the silica binder. The aromatics selectivity and the dehydrogenation / cracking and aromatization / cracking activity ratios and aromatization/(methane + ethane) mass ratio are also affected appreciably by the silica binder. The shape selectivity of the zeolite is increased markedly by the silica binder. Also because of the binder, the deactivation rate constant for initial fast deactivation is decreased but for the later slow deactivation is increased. 

The initiation step consists of two reactions in series. The first is the production of free radicals, which can be accomplished in many ways. The most common method, however, involves the use of a thermolabile compound, called an initiator (or catalyst), which decomposes to yield fre Radicals when heated. Thus, the homolytic dissociation of an iiiitiator I yields a pair of radicals R, as shown by Eq. (6.3), where kd is the rate constant for initiator dissociation at the particular temperature. Its magnitude is usually of the order of 10 -10 s (Being derived from the initiator, R is referred to as an initiator radical and often as a primary radical.) The second step of the initiation process is the addition of the radical R to a monomer molecule as shown in Eq. (6.4), where RM is the monomer-ended radical containing one monomer unit and an end group R. The rate constant for the reaction is ki. For a vinyl monomer, this second step involves opening the r-bond to form a new radical ... 

KtAc etfiyl acetate k rate constant for initiator-... 

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