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The finite deformation elasticity of gels of stiff rodlike polymer chains is discussed theoretically. Unlike a rubber composed of flexible polymer chains, the elasticity of this system is energetic, and arises from the elastic deformation of the stiff chains which are forced to bend under macroscopic strain. The stress‐strain curve of this system is shown to be nonlinear even if the bending of the rods is small, and has a characteristic S‐shaped form which is unlike that of a rubber. The effect of orientational order is also discussed.

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ABSTRACT:The nonlinear viscoelasticity of concentrated solutions of rod-like polymers in the isotropic phase was studied theoretically based on the molecular diffusion equation of DoiEdwards. Rheological functions were calculated for both shear and elongational flows in a steady, and transient state. The viscoelastic properties of this system were found to be very similar to those of flexible polymers despite the difference in molecular shape and the mechanism of Brownian motion: e.g., shear thinning, normal stresses, and stress overshoot were predicted for rod-like polymers.KEY WORDSThe viscoelastic properties of concentrated solution of rod-like polymers are very important from the stand point of industrial application. 1 In the past ten years, several experimental and theoretical studies have been reported. 2 -6 Though the transient flow and elongational flow are important in fiber or film formation processes, the studies so far carried out are mostly concerned with the linear viscoelasticity, or the steady-state simple shear flow. In this paper, we study theoretically the nonlinear viscoelasticity of this system under simple shear and elongational flows in both the steady state, and the transient state. We show that the viscoelastic properties of this system are qualitatively very similar to those of flexible polymers.The Brownian motion of rigid rod-like polymers in a concentrated solution in the isotropic phase has been discussed by Doi 7 and Doi-Edwards, 8 • 9 and the formula for calculating the stress tensor for a given velocity gradient is presented in ref 9.According to 9 given the history of the velocity gradient, the stress at time t can be calculated as follows.Let u be the unit vector parallel to a rod and f(u; t) be its orientatiorial-distribution function at