Nonlinear Viscoelasticity of Concentrated Solution of Rod-like Polymers

Abstract

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

A rheological study of the order-disorder conformational transition of xanthan gum

“…26,35,36 However, the data superimpose at low angular frequency or shear rates. These observations are qualitatively in agreement with the theoretical description of the nonlinear viscoelasticity of concentrated solutions of rod-like polymers proposed by Yuzuu and Doi,37 which predicts that the complex viscosity should dominate the steady shear viscosity in the nonlinear area.…”

A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension

“…From the conservation statement for the conventional Eulerian form of the distribution function (1.1 b), we derived in I the conservation statement for the new, Lagrangian form. This equation is Moments may be recast in the reference configuration, by taking the point of view that (1.2) is really an expression of a coordinate transformation for each material point; hence for an initially isotropic orientation distribution (AR, 0) = 1/4n), we have This same technique was used by Kuzuu & Doi (1980) and earlier by Okagawa, Cox & Mason (1973) in studies of suspension mechanics without Brownian motions. The same idea works well when Brownian motions are included, as in the present work.…”

Rheological properties of a semi-dilute solution of rodlike macromolecules. II. Transient flows

“…The three functions Y(y), Yi (7), and Y2(7) are related by the formulas Y(y) = 3(uxuz) + y(u2u2), Yi(7) = 3 (u2 -u2), and Y2(7) = 3 {u2 -u2) to orientational averages of quadratic and quartic functions of the direction cosines ua = ü-éa (a = x, y, z) of the rod axis. The origins of the quadratic and quartic terms are, respectively, the diffusive (Brownian) and convective contributions to the bead velocities; cf.…”