Functionality and Observed Versus Predicted Gel Points

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Abstract
An ambiguity in use of the term functionality is pointed out. The two most widely used relations (Flory, and Stockmayer and Kahn) connecting extent of reaction at the gel point and functionality are examined. The relations are shown mathematically to lead to the same result when all assumptions and definitions are considered. Measured gel points of polyesters are compared with those predicted by the equation. Deviations were less than 10% of the predicted values. An ambiguity in definition has been observed for the word functionality which has led to unnecessary confusion of thought. It is believed that this confusion has often occurred and has been seen in the literature quite recently [1,2]. On the one hand, functionality has been used to mean the number of chain ends united at the branch points in a polymer network. Since branch points can unite no fewer than three chain ends, functionality in this sense can take on values of three or greater. Networks are most often three or four functional. If more than one type of branch point is present, the average functionality can be calculated as a fraction with a value above three.