Chain dissociation rate

The initial distribution is therefore not Gaussian if the chain dissociation rate p, or recombination rate a, depends on the end-to-end distance. 

The first term Vg (t) gives the number of chains that were initially active and remain active until time r. It is therefore a steadily decreasing function of the time it goes down to 0 at r = oo in most cases. It can reach a finite value at t = oo when the chain dissociation rate P(r) vanishes in a certain finite region of r. 

Let us next consider the special case where the chain dissociation rate (r) is a constant. This limit is called the Green-Tobolsky limit (GT limit). Since r)= o iP ir) = 0), we And from (9.70a,b)... 

Because the reactive group is attached on the chain end, it is pulled by the tension / from the chain. Hence, the potential barrier for the associative group to dissociate is effectively reduced to A — /a. The chain dissociation rate is therefore enhanced to... 

Fig. 9.4 (a) Modulus-frequency master curve for the chain dissociation rate p r) = The... 

Fig. 9.17 Nonlinear stress relaxation of the transient network model with a quadratic chain dissociation rate under a constant shear deformation for y = 0.5. The decay rate is fixed as (a) /3q = 0 and (b) /3q = 1. The total number Ve of active chains and the number Vg of chains that remain active from the initial state are shown on a logarithmic scale. These are normalized by the stationary value of Ve. The shear stress hxy, the first normal stress difference N, and the second normal stress difference N2 are shown in the unit of Ve B T. (Reprinted with permission from Ref. [19].)...

In this appendix, we study in detail a specific form of the chain dissociation rate... 

Kiessling et al,48 reported a similar increase in the inhibitory activity of synthetic polymers of increasing lengths that possess Man residues in a hemagglutination assay with ConA. The authors concluded that the enhanced inhibitory activities of the longer chain polymers were largely due to a combination of statistical and chelation effects and therefore slower dissociation rates. 

The rate of dissociation has been measured by oxygen uptake in the presence of an inhibitor of chain reactions as in the case of hexaaryl-ethanes. Since the uptake of oxygen obeys the same kinetic law, it is a reasonable extrapolation to suppose that here too the rate-determining step is a dissociation into radicals. When one of the phenyl groups in triphenylmethyl is replaced by a cyclohexyl group, the rate of dissociation of the ethane is reduced by a factor of 170.38 Some dissociation rate parameters are given in Tables III A and B. 

A selection of data for a series of alcohols with a- and ft-CD is shown in Table 11. The association rate constants remained constant, showing no dependence on chain length of the alcohols for binding in both a- and /i-CD. However, the dissociation rate constant did decrease with the alcohol s chain length in both sizes of cyclodextrin. This decrease in dissociation rate constant could be related to the fact that the larger guests are more hydrophobic. The dissociation rate constants were smaller... 

Rate equations of considerable complexity can result from chain reactions, such as the reaction of bromine with hydrogen in the gas phase between 200 and 300 °C to form hydrogen bromide. These are reactions in which a chain carrier is created in an initiation step (here, a Br- atom from dissociation of Br2) and goes on to create more carriers (Br + H2 — HBr + H-, followed by H + Br2 -4 HBr + Br-, and so on) until a recombination step ends the chain. The rate equation for HBr formation has been shown to be ... 

Worsfold found that the degree of association as measured from viscosity was less than that indicated by the light scattering and spectroscopic results. It was therefore concluded that the association dissociation rates were comparable to the chain entanglement lifetime. As a consequence, Worsfold concluded that viscosity measurements involving concentrated solutions of poly(dienyl)lithium in the entanglement regime could not detect the presence of, for example, star-shaped tetramers if the equilibrium... 

For the purpose of determining the chain termination type, Figure 5.9 shows the dependence of the methane oxidation rate on the chain initiation rate, which is characterized by the elementary reaction of H202 dissociation (k ) to hydroxyl radicals and described by the following kinetic equation ... 

Figure 3. Effect of side chain, proximal basicity, and solvent on CO and 02 dissociation rates. B= Im, R= vinyl unless otherwise noted. Solvent is aqueous detergent. Exact conditions vary but are internally consistent in any column. aR = ethyl. bVariations in kinetic method and...

When a dormant species or alkoxyamine dissociates homolytically, a carbon-centered radical and a stable nitroxide radical are formed (Scheme 2). This is a reversible process and the reversible reaction is very fast - close to diffusion-controlled rates. With increasing temperature, the dissociation rate will increase, which will increase the concentration of the polymeric radicals (P ). These will have a chance to add to monomer before being trapped again, which allows growth of the polymer chains. The nitroxide is an ideal candidate for this process since it only reacts with carbon-centered radicals, is stable and does not dimerize, and in general couples nonspecifically with all types of carbon-centered radicals (at close to diffusion-controlled rates). 

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