Dependence of Elastic Properties of Vulcanized Rubber on the Degree of Cross-Linking

The results reported above demonstrate a progressive increase in the force of retraction τ at fixed elongation with increase in the fraction p of the structural units which are cross-linked from ρ=0.10×10−2 to 3.0×10−2. Over this range, τ at 100 per cent elongation increases about thirteenfold. Swelling measurements indicate that the increase in τ with ρ continues over an additional tenfold range in ρ. Previous assertions that the modulus of elasticity of soft gum rubber vulcanizates depends largely on chain interaction and entanglements other than those imposed by the cross-linkages, and that the modulus is, therefore, not directly related to the degree of cross-linking, are without foundation. The statistical theory of rubber elasticity expresses the force of retraction as a function of the temperature, vulcanizate structure and elongation; no arbitrary constants are involved. The magnitudes of τ for α=2 are in remarkably close agreement with the predictions of the theory over most of the range in ρ. This fact is of the utmost significance in confirmation of the statistical theory of rubber elasticity and of the analysis of the network structure of vulcanized rubber. On the other hand, τ increases less rapidly with ρ than the direct proportionality prescribed by theory. Forces of retraction are higher than the theory predicts at low degrees of cross-linking, and an opposite deviation is observed for values of ρ greater than about 1×10−2. Previous observations on Butyl rubber, vulcanized to p values from about 0.16×10−2 to 0.28×10−2 indicated forces of retraction (for infinite molecular weight M) which exceed by about threefold those predicted from the theory. This deviation is decidedly larger than has been observed here in the same range for ρ. A substantial part of the discrepancy observed for Butyl rubber may have arisen from failure to secure elastic equilibrium, however. Deviations in the values of τ from theory probably originate largely from oversimplifications in the treatment of the network structure. Entanglements of the sort previously discussed tend to enhance the restraints imposed on the chains when the rubber is elongated. Their percentage effect should be greatest for low degrees of cross-linking, hence the observed τ values are higher than theory at low degrees of cross-linking. “Intramolecular” cross-linkages, yielding short-circuit structures contributing nothing to the elastic reaction of the network, should become increasingly important at higher degrees of cross linking. Such wastage of cross-linkages may account for the low values of τ obtained for higher ρ values.