Topological rubber elasticity theory. II. SCL networks

Abstract

The theory presented in part I [Iwata, J. Chem. Phys. 76, 6363 (1982)] is applied to networks having a simple-cubic-lattice (SCL) regular connection pattern, for which the projection matrix Γ* is computed easily. Derivatives of elastic free energies in regard to parameter λ for macroscopic deformation ∂F̃e/∂λ are computed numerically for isotropic deformations (swelling or deswelling) and for simple deformations (extension or contraction under swelling by α times). The initial arrangement of junction points r0 is assumed to be exactly SCL, and δ = d0/νb is chosen as one of parameters in the calculation, where d0 is an end-to-end distance of the strands at the time of network formation, ν is a degree of polymerization in regard to the strands, and b is a statistical length per monomer. A repeating cell is chosen as a cube composed of 3×3×3 ( = 27) junction points and 3×27 ( = 81) strands. The following are found in this work. (1) Among four terms ∂F0,ph/∂λ, ∂F̃0,top/∂λ, ∂F̃1/∂λ, and ∂F̃2/∂λ of the derivative of the elastic free energy, the principal term is ∂F̃0,top/∂λ, which comes from the topological interaction among the strands; the phantom network term ∂F0,ph/∂λ is only a small correction to the net stress. (2) In isotropic deformations, the elastic free energy takes a minimum at λ0, a little below λ = 1; for compression below λ0, a strong postitive inner pressure, which comes from the topological repulsive forces among the strands, arises. (3) In simple deformations, the Mooney–Rivlin term appears for unswollen systems and it disappears as swelling of the network proceeds. Experimental plans are proposed which will reveal the existence of the topological repulsive interactions in the networks.