Linkage weighted average

If we regard it as a cross-linked polymer, we require ywj the weight average degree of polymerization if all cross-linkages were severed. This operation would amount to replacing each tetrafunctional unit, or pair of cross-linked units, with two bifunctional units. The extent of reaction p would not be affected. Hence, according to Eq. (VIII-8)... 

Problem 7.19 Consider a sample containing discrete polymer molecules that can be interconnected either during forther polymerization or by a separate reaction on the macromolecules. Suppose some of the molecules are cross-linked by linkages formed between randomly selected monomer units in them. Show by probability considerations that a sufficient condition for gelation occurs when the polymer sample contains one cross-linked unit per weight average molecule or one cross-link per two polymer chains. 

In Example 5.9, aggregation of clusters was carried out by the weighted average linkage methods. In general, the distance to a new object or cluster k (labeled in the example by a star) is computed by forming the average between the individual distances of objects A and B to object i. 

Unsaturated polyesters have a widespread field of applications. In almost all cases, unsaturation in these materials is introduced by the acid component when the prepolymers are manufactured. These prepolymers can be of either the structoterminal or structopendant type depending on the location of the unsaturated linkages. The average molecular weight is in the range of 1-5 x 10. ... 

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