Topological rubber-elasticity theory. III. Comparison of rigidities computed for model tetra-functional networks with experiments

Abstract

A b initio comparison is made of the modulus computed for model tetrafunctional networks with experiments on poly(dimethyl–siloxane) (PDMS), polybutadiene (PB) and ethylene–propylene copolymer (EP) found in literature. The theory and computer programs presented in parts, I and II [K. Iwata, J. Chem. Phys. 76, 6363, 6375 (1982)] are improved further in the following points: (1) parameter L, which represents macroscopic shape of networks, is chosen as a parameter of topological distribution functions, (2) ‘‘THL network,’’ which has chain-connection pattern of tetrahedral lattice, is newly introduced as a model of tetrafunctional networks and (3) computer programs of part II are improved so that computational error becomes small enough for quantitative discussion. Reduced moduli, Ḡ=G/c0kT, are expressed in terms of the overlap parameter among strands, φ=(4πR3g/3)c0, and the volume expansion ratio relative to the as-formed volume, α, where c0 is the number concentration of elastically active strands and Rg, the unperturbed radius of gyration of the strands. It is found that (1) the shear modulus computed can be expressed in a compact form, Ḡtheor (φ,α)=Ḡph+φg(α), where Ḡph is a phantom network term and is far smaller than the second (i.e., topological) term, (2) a plot of Ḡexpt of PDMS, PB, and EP against φ produces a single curve, (3) qualitatively, Ḡtheor agree well with Ḡexpt but, quantitatively, Ḡtheor is overestimated by 50%–100%, (4) Ḡtheor is roughly proportional to α2/3, and (5) the Mooney constants 2C̄2, are far smaller than Ḡ. From these results it is concluded that the main source of rubber-elasticity is topological interaction among polymers.