Phase transition and rheological bihavior of freely - jointed rod - like polymer solution in a steady flow

Abstract

The effects of polymer chain flexibility and elongational flow field on the isotropic-nematic phase transition were studied by applying a freely-jointed rods model to the Onsager theory. The theory was developed on the assumption that the non-equilibrium condition was treated as a pseudo-equilibrium state. The velocity field could be regarded as a potential in a steady state and this potential term was added into an equilibrium equation. In order to obtain accurate orientational distribution functions, the modified Onsager``s integral equation was numerically solved on a grid of points real space, uasing a simple iterative method. The biphasic region becomes wider and the difference of order parameters between the coexisting phases becomes larger as the flexibility increases. Also, the onset concentration of highly ordered nematic phase becomes lower, the biphasic region narrower and a difference of the order parameters between the coexisting phases smaller as the stretching rate increases. It is shown that there exists a critical point at a sufficiently high stretching rate, which means the existence of a stable monophase above the critical point. There exists not only a unstable biphasic state but also a stable biphasic state in a weakly stretching rate. Thus the order parameter has double values in this stable biphasic region. Finally a conclusion is made that the effects of the elongational flow field on the rod-like systems are more pronounced when the system is close to or in the biphasic state. Applying an iterative method to the medified Onsager``s integral equation by introducing a flow term, the rheological properties of rod-like polymer solution such as viscosity, first and second normal stress coefficients were calculated on the basis of molecular kinetic approach of Kuzuu and Doi in steady flows. By using this theory with the Leslie-Ericksen type equation, the nonlinear viscoelasticity was predicted. Theoretical values of shear viscosities were in ...