High-concentration effects initial distribution

In calculations presented below we assume first one kind of defects to be immobile (Da = 0, k = 0) and their dimensionless initial concentration n(0) = 0.1 is not too high it is less than 10 per cent of the defect saturation level accumulated after prolonged irradiation [41]. Its increase (decrease) does not affect the results qualitatively but shorten (lengthen, respectively) the distinctive times when the effects under study are observed. To stress the effects of defect mobility, we present in parallel in Sections 6.3.1 and 6.3.2 results obtained for immobile particles A (D = 0, asymmetric case) and equal mobility of particles A and B (Da = Dq, symmetric case). In both cases only pairs of similar particles BB interact via elastic forces, (6.3.5), but not AA or AB. The initial distribution (t = 0) of all defects is assumed to be random, Y(r > 1,0) = -X (r,0) = 1 i/ = A,B. 

We assume here that the concentrations of monomer and initiator remain sensibly constant during the polymerization, and that any dependence of termination rate constants on macroradical size and concentration or autoacceleration effects can be neglected. Tliis means that the molecular weight distributions to be derived can be expected to apply to low-conversion polymers. Commercial macromolecules, whose polymerizations are often finished at high conversions, may have distributions that differ from those calculated here. Section 6.14.2 discusses the size distributions of such polymers. 

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. 

---