Gel formation by main-chain fracture of long-chain polymers

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Abstract
The conditions are examined under which the fracture of main-chain bonds in a long-chain polymer, which would normally result in a decrease in average molecular weight, can nevertheless result in formation of a network of infinite extent (gel). It is assumed that the two end-groups produced at a fractured site can attack neighbouring molecules, and link them ­ selves to them. For an initially random distribution it is shown that gel formation will first occur when one molecule in three is thus fractured. The sol fraction is found to equal ( i /3 r ) 2 , where r/i is the average number of fractures per molecule; with increasing fracture density the sol therefore tends to zero. Where only a proportion of the fractures result in linking, the sol fraction decreases to a limiting value. Expressions are derived for many of the parameters of the sol and gel fractions and for the swelling. The results obtained are compared with those for crosslinking of polymers with a similar molecular weight distribution. To distinguish the process considered in this paper from that usually referred to as crosslinking, the term endlinking is proposed.

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