Primary chain

In the case of filled rubbers, the network is represented by a huge chain of contour length L = NL, where N is the number of primary chains of length L. The observable (macroscopic) free energy is given by Equation 22.9, where Z(n) is the replicated partition function that is estimated by functional integration over the continuous chain conformations ... 

One of the calculation results for the bulk copolyroerization of methyl methacrylate and ethylene glycol dimethacrylate at 70 C is shown in Figure 4. Parameters used for these calculations are shown in Table 1. An empirical correlation of kinetic parameters which accounts for diffusion controlled reactions was estimated from the time-conversion curve which is shown in Figure 5. This kind of correlation is necessary even when one uses statistical methods after Flory and others in order to evaluate the primary chain length drift. 

If the degree of cross-linking p is small (and the primary chain length therefore great), 0 =tf s, giving... 

A molecule whose first primary chain was formed early in the polymerization will, on the average, acquire more branches than a molecule originated later even among those originating in the same time inter-... 

Chain scission will have the effect of decreasing the primary chain length, which, of course, is a highly important factor in respect to the vulcanizate network structure. 

A copolymer in which blocks of one polymer are inserted in a primary chain of the other or where the arrangement of the different monomers is not random but in distinct multiple monomer blocks. Blocking... 

The two polymer substrates investigated as part of the study of DBDPO mixtures were polypropylene (PP) and linear high density polyethylene (HDPE). while both PP and HDPE decompose by similar random chain scission, radical mechanisms, chain transfer occurs much more teadily during the pyrolysis of PP because of the presence of the tertiary hydrogens. In addition, only primary chain end radicals are formed when the HDPE chain cleaves homolytically. Therefore, a comparison of the PP/DBDPO and the HDPE/DBDPO mixtures volatile product distributions was undertaken. 

High functionality precursors of/ > 10-20 are primary chains if they participate in crosslinking by vulcanization each monomer unit of primary chain is a potential site for crosslinking. Also, dendrimers and random hyperbranched polymers of higher molecular weight, rank among high-functionality precursors. 

In stepwise reactions, all functional groups take part in bond formation. Their reactivity can be considered independent of the size and shape of the molecules or substructures they are bound to (Flory principle). If such a dependence exists, it is mainly due to steric hindrance. In chain reactions only activated sites participate in bond formation if propagation is fast relative to initiation, transfer and termination, long multifunctional chains are already formed at the beginning of the reaction and they remain dissolved in the monomer. Free-radical copolymerization of mono- and polyunsaturated monomers can serve as an example. The primary chains can carry a number of pendant C=C double bonds... 

In earlier times, polymer networks were generally prepared by reactions between small monomers and by vulcanization of primary chains. Successively, the notion of a precursor developed for a preformed polymer molecule carrying functional groups, or a distribution of them. Synthesis of precursors and their use in network build-up have been motivated by the following needs ... 

The exact formula was derived by Schulz [80] and the asymptotic equation is due to Zimm [81]. Schulz derived the distribution for/chains that are coupled together, where it has no influence whether one has a head to tail coupling of most probable distributions or whether these distributions are coupled onto a star center. Zimm recognized that the asymptotic form can be efficiently used to describe the distributions of fractions. The index o refers to the primary (most probable) chain distribution and p is the extent of reaction for this primary chain. 

Rule 6 orients the molecule, collecting the vertices and edges in the proper order. To accomplish this, all root nodes are collected. Starting from each root, the primary chain of the notation is chosen using the longest path of notation symbols, breaking any tie by choosing the chain which ends in the latest notation symbol (Rule 2). 

The free-radical crosslinking polymerization can be regarded as a special example of specific diffusion control, in which the tendency to microgel formation and decrease of apparent reactivity of Internal double bonds depends on the size of the mlcrogel which in turn depends on the molecular weight of the primary chain. Polymerization of diallyl monomers exhibits much less of these features (W) because the degree of polymerization of their primary chains is extremely low due to degradative chain transfer. 

This theoretical model allows to predict the variation of complexation degree 6 and the molecular weight of the complex versus PAA concentration, molecular weight of the primary chains (PAA, polybase), concentration ratio r - [polybase]/[PAA], acrylate ratio p, and the minimvim chain length 1 (27). The theoretical predictions about the evolution of the system are confirmed by experimental results. For instance, in figure 12 (DP ). - which is the num-... 

Table 7.1 compares vc/v0 according to the two criteria. Values for primary chains with exponential distribution (Mw/Mn = 2) are also included. The number of active strands according to the Scanlan criterion is larger by a factor of 1.5 at the gel point. The ratio decreases slowly with increasing y and finally approaches a value of unity for large numbers of crosslinks per primary chain. Both expressions approach the form vc = v0y for sufficiently large values of y. 

Table 7.1. Concentrations of elastically effective strands according to the Flory and Scanlan criteria for random crosslinking of monodisperse primary chains...

Values in parentheses were obtained at the same gel fraction wg by calculations for primary chains with an exponential distribution of lengths. 

Langley (255) has developed a refined definition of the Ferry trapping factor, and he also accounts theoretically for effects of the primary chain distribution and... 

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