Chain termination constants

The experimentally measured direct chain termination constant was found to be 5.5 X 103 Mole"1 sec."1. However, this value was not considered very accurate because there is a large correction to the measured oxidation rates for oxygen evolved in the self-reactions of COO radicals at the relatively high photo-initiation rates required to reduce the importance of thermal initiation from the added COOH. A more accurate value of 2.9 X 103 mole"1 sec."1 was calculated from the limiting value of fcpC/[2fc fdirect)]"1/2 at high [COOH] for the AIBN thermally initiated reaction at 30 °C. combined with the measured value of Jcp for neat cumene (0.18 Mole"1 sec."1). 

In general, if rarh = 1 and if the chain termination constants for oxidations of A alone and B alone are the same ( ideal reactivities), then the total rates of oxidation of mixtures at constant rate of initiation are a linear function (for ideal solutions) of the volume % of B in the A—B feed. Russell (30,31, 32) and Alagy and co-workers (1, 2,3,4, 8, 33) have shown for several systems that when B has a higher termination constant than A and when B is sufficiently reactive, B can reduce (sometimes fourfold) the rate of oxidation to less than the ideal rate. A secondary objective was to see if there were any other important abnormalities (particularly rates much greater than ideal) in co-oxidations of hydrocarbons. 

Ito s model [68] bears resemblances to the model of Ref. [35], but is different by two aspects. Firstly, it assumes that the constant rate of the chain termination depends on the number of monomeric units (so-called polymerization degree) of tn and n radical chains taking part in the termination reaction and represents the sum of the independent contributions of m and n. Secondly, the dependence of the chain termination constant on the length of chains under two types of conditions is described the first condition is < n, controlled by segmental diffusion, and the second one is m > controlled by the reptation diffusion. In the reptation chemical mechanism of diffusion in the deep states of conversion the macroradicals move snake-like between the network joints. De Gennes connected a reptative moving of macroradicals with the dynamic properties of the medium with the use of scaling ratios [37-40] as applied in Refs. [41-46] for the description of constant chain termination in the late conversion state. 

Two types of functions in the models for the description of the polymerization processes at moderate and high conversions have been described in the literature [47-53, 57-61, 63, 70-75]. For example, in Ref. [63] until the depth of conversion 7-0,6, the kinetics of the polymerization process are described by a change of the bimolecular chain termination rate constant parameters of the propagation and initiation efficiency are assumed to be constant values. Decreasing the chain termination constant rate via especial empirical dependence has been introduced for values of F > 0,6. Decreasing the chain termination constant rate for F < 0,6 is determined via the coefficients of the translational and segmental diffusion of the macroradicals ... 

Ur is a chain termination constant rate limited by the translational diffusion and is calculated via the coefficients of the self-diffusion of the macroradicals and the size R of their balls ... 

On the basis of the free volume model in Ref. [70] the diffusion-controlled chain termination constant is described via all processes as follows ... 

We can conclude on the basis of data presented in Tables 7.2-7.5 that the parameter P and the monomolecular chain termination constants rate k, depend on temperature. This proves the activation nature of constant k,. 

Note that, when comparing values of the monomoleeular chain termination constants rate which have been obtained in Ref. [16] via a kinetic model with two... 

Throughout this section we have used mostly p and u to describe the distribution of molecular weights. It should be remembered that these quantities are defined in terms of various concentrations and therefore change as the reactions proceed. Accordingly, the results presented here are most simply applied at the start of the polymerization reaction when the initial concentrations of monomer and initiator can be used to evaluate p or u. The termination constants are known to decrease with the extent of conversion of monomer to polymer, and this effect also complicates the picture at high conversions. Note, also, that chain transfer has been excluded from consideration in this section, as elsewhere in the chapter. We shall consider chain transfer reactions in the next section. 

The most remarkable feature of the antibody molecule is revealed by comparing the amino acid sequences from many different immunoglobulin IgG molecules. This comparison shows that between different IgGs the amino-terminal domain of each polypeptide chain is highly variable, whereas the remaining domains have constant sequences. A light chain is thus built up from one amino-terminal variable domain (Vl) and one carboxy-terminal constant domain (Cl), and a heavy chain from one amino-terminal variable domain (Vh), followed by three constant domains (Chi, Ch2. and Chs). 

Which mechanism of termination will be preferably applied depends largely on the monomer used. Thus, methyl methacrylate chains terminate to a large extent by disproportionation, whereas styrene chains tend to termination by combination. The ratios of termination rate constants 8 = ktJkic (for disproportionation, td, combination,, c) are 5 == 0 and 5 = 2 for styrene [95] and methyl methacrylate [96], respectively. In the case of styrene, however, the values of 8 reported in the literature are at variance. Berger and Meyerhoff [97] found 8 = 0.2, at 52°C. Therefore, it is possible that a fraction of styrene terminates by disproportionation. 

It is commonly found that polymers are less stable particularly to molecular breakdown at elevated temperatures than low molecular weight materials containing similar groupings. In part this may be due to the constant repetition of groups along a chain as discussed above, but more frequently it is due to the presence of weak links along the chain. These may be at the end of the chain (terminal) arising from specific mechanisms of chain initiation and/or termination, or non-terminal and due to such factors as impurities which becomes built into the chain, a momentary aberration in the modus operandi of the polymerisation process, or perhaps, to branch points. 

The absolute rate constants for attack of carbon-centered radicals on p-benzoquinone (38) and other quinones have been determined to be in the range I0M08 M 1 s 1.1 -04 This rate shows a strong dependence on the electrophilicity of the attacking radical and there is some correlation between the efficiency of various quinones as inhibitors of polymerization and the redox potential of the quinone. The complexity of the mechanism means that the stoichiometry of inhibition by these compounds is often not straightforward. Measurements of moles of inhibitor consumed for each chain terminated for common inhibitors of this class give values in the range 0.05-2.0.176... 

North and coworkers106 168 proposed that chains terminate with a rate constant which is determined by the rate of diffusion. Thus... 

The desorption and termination constants were calculated for a copolymer from the corresponding homopolymer constants as discussed in Nomura and Fujita (12.) The homopolymer desorption coefficients were calculated from the appropriate chain transfer constants and radical diffusivities in the aqueous and polymer phases using an extension of the desorption theory developed by Nomura and Fujita (12.). The homopolymer termination constants were corrected for the Trommsdorff effect by using the Friis and Hamielec (12) correlation. 

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

The termination constants kt found previously (see Table XVII, p. 158) are of the order of 3 X10 1. mole sec. Conversion to the specific reaction rate constant expressed in units of cc. molecule" sec. yields A f=5X10". At the radical concentration calculated above, 10 per cc., the rate of termination should therefore be only 10 radicals cc. sec., which is many orders of magnitude less than the rate of generation of radicals. Hence termination in the aqueous phase is utterly negligible, and it may be assumed with confidence that virtually every primary radical enters a polymer particle (or micelle). Moreover the average lifetime of a chain radical in the aqueous phase (i.e., 10 sec.) is too short for an appreciable expectation of addition of a dissolved monomer molecule by the primary radical prior to its entrance into a polymer particle. 

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