Modulus of natural rubber cross-linked by dicumyl peroxide. III. Some molecular interpretations, possible refinements of theory, and conclusions

Abstract
The shear modulus G = 5.925 × 10 - 3(fp - 0.45)T+G* (Part I), its energy component G* = 0.0684 (fp - 0.45)+ 2.70 (Part II), and the number of effective suh-chains per unit volume ve = (G - G*)/RT are given detailed molecular consideration. G is given in Mdyn cm-2 for rubber cross-linked by adding p parts of dicumyl peroxide per hundred of rubber, and heating until a fraction f of the peroxide is decomposed. ve is found to be approximately twice the density of cross-links, after a correction for impurities and chain ends is made. It can not be computed as G/RT since only the entropy component of modulus is related to ve. The sub-chains for the most highly cross-linked rubbers studied had a molecular weight of about 575 g mol-1, corresponding to about 8 isoprene units. The modulus corresponding to no added cross-links is not zero. It is determined chiefiy by the energy component of the modulus; it does not arise from entanglements. The "front factor" is found to be unity. An extensive literature survey yields values of the quantity RTΨ(v 2), where Ψ (v 2) is the Flory- Rehner equation function of v 2, the equilibrium volume fraction obtained by swelling the cross-linked rubber. RTψ (v 2) is found to be greater than G - G* but not as large as G itself.

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