Model calculations of the phase behaviour of rod-like particles in solution: Polydisperse systems having asymmetric distributions of rod-lengths

Abstract

Model calculations have been made of the phase behaviour, and compositions of the phases in the biphasic range, for polydisperse rod-like particles in solution. The special cases of a most-probable distribution (m.p.d.), an empirically modified most-probable distribution and asymmetric Gaussian distributions are considered. It is shown that the presence of species of very low molecular length in the m.p.d. result in v o ϱ∗∗ , the volume fraction of polymer for which the system becomes wholly-anisotropic, being close to unity and thus the biphasic range for the case of this distribution is far larger than that normally found experimentally. The empirically-modified m.p.d. gives a narrower biphasic range than that for the m.p.d. Calculations for the asymmetric Gaussian distribution make it clear that v o ϱ∗∗ is determined by the low molecular length species in the distribution whilst v o ϱ∗ , the volume fraction of polymer at which the system goes from isotropic to biphasic, is determined by the high molecular length species of the distribution. It is suggested that these distributions and those considered earlier are unable to adequately explain the observed dielectric and viscosity behaviour of rod-like molecules in solution. It is necessary to introduce a small high molecular weight tail to a chosen distribution in order to obtain agreement betwee between the calculate and the observed behaviour.