Abstract
In this paper, a statistical model is developed to determine the number-average and weight-average molecular weights of a branched polymer system formed through random branching of polymer chains. The average properties of the branched structures formed by T-shaped junctions and by H-shaped junctions through random branching of polymer chains are compared in detail. The model indicates that the H-shaped chain connections can form a gel molecule while the T-shaped chain connections alone can not cause gelation. Because only the randomly branched polymers for an equilibrium system are considered (under Flory's simplifying assumptions), the present results would not be a rigorous proof that the H-shaped junctions are required to form a gel molecule in any type of reaction system. However, the present paper shows that the Macosko-Miller model can be applied to this type of problem in a straightforward manner. The gel point for the branched structures formed by H-shaped junctions can also be determined by the model.
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