Multiaxial deformations of end‐linked poly(dimethylsiloxane) networks. III. Effect of entanglement density on strain‐energy density function

Strain‐energy density functions (W) of end‐linked polydimethylsiloxane (PDMS) networks with different entanglement densities were estimated as a function of the first and second invariants I₁ and I₂ of Green's deformation tensor on the basis of the quasi‐equilibrium biaxial stress‐strain data. Entanglement densities in the PDMS networks were controlled by varying the precursor PDMS concentration (?₀) in end‐linking. The deduced functional form of W W = C₁₀(I₁ ? 3) + C₀₁(I₂ ? 3) + C₁₁(I₁ ? 3)(I₂ ? 3) + C₂₀(I₁ ? 3)² + C₀₂(I₂ ? 3)²] is independent of the degree of dilution at network preparation. The contribution of each term in I₁ and I₂ to total energy depends on whether the precursor PDMS solution before end‐linking belongs to the concentrated regime ?₀ > ?_c where many entanglement couplings of precursor chains exist or the moderately concentrated regime ?₀ < ?_c where pronounced entanglement couplings of precursor chains are absent. These results suggest that the rubber elasticity of the end‐linked networks is significantly influenced by the entangled state of precursor chains before end‐linking, and the extra terms in the estimated W that are absent in the prediction of the classical rubber elasticity theories W = C (I₁ ? 3)] mainly originate from the effect of trapped entanglements. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2780–2790, 2002