Generalized constitutive equation for polymeric liquid crystals: Part 2. non-homogeneous systems

Abstract The Hamiltonian formulation of equations in continuum mechanics through Poisson brackets was used in Ref. 1 to develop a constitutive equation for the stress and the order parameter tensor for a polymeric liquid crystal. These equations were shown to reduce to the homogeneous Doi equations as well as to the Leslie-Ericksen-Parodi (LEP) constitutive equations under small deformations [1]. In this paper, these equations are fitted against the non-homogeneous Doi equations through the simulation of the spinodal decomposition of the isotropic state when it is suddenly brought into a parameter region in which it is thermodynamically unstable. Linear stability analysis reveals the wavelength of the most unstable fluctuation as well as its initial growth rate. Results predicted from this theory compare well with the predictions of Doi for the spinodal decomposition using an extended molecular rigid-rod theory in terms of the distribution function. This completes the development of a generalized constitutive equation for polymeric liquid crystals initiated in Part 1.