On the Second-Order Transition of a Rubber

The view that the glass transition has a thermodynamic basis is extended to a cross-linked rubber. The elevation of the second-order transition temperature as a function of the number of cross-links is found to be (T(X) - T(0))/T(0) =KX/1 - KX, where T(X) is the transition temperature for a rubber with degree of cross-linking X. The constant K is to first order independent of material. Also a relation involving no adjustable parameter is derived for the ratio of second-order transition temperatures to deformation. It is T(λ)/T(1)=exp (G(Σλ ² - 3)/2ΔC T ₀) where ΔC is the value of the specific heat discontinuity per cm³ at the transition and T ₀ is the temperature at which the modulus G is measured. Available experimental evidence from five separate investigations agrees with these predictions.