Phase equilibria in athermal solutions of rigid macromolecules containing freely jointed segments of different length

Abstract

The formation of a liquid crystalline phase in athermal solutions of long chains consisting of freely jointed rod-like segments of different length has been analysed by means of the methods developed by Flory in 1956 and 1978. The necessity is pointed out to take into account in a rigorous manner the dispersion of segment orientations in the nematic phase. Phase diagrams have been constructed for the case of two segments of different length (axis ratios x a and x a , x a > x b ). It has been shown that at x b / x a > 0·2 (system I) the solution of chains consisting of mesogenic segments can be approximated by a model of monodisperse chains with axis ratio x w given by a weighted average of x a and x b . In system II, where only the longer segments ( x a ) are mesogenic, the mesophase region gets rapidly narrower when the shorter segments are incorporated into the macromolecular chains; if their volume fraction ν b is larger than 0·1, the phase transition occurs practically without any mesophase region at an almost constant value of ν a . In system III where x b / x a < 0·2 the anisotropic character of shorter segments manifests itself only at sufficiently high concentrations. The phase diagram of system III is intermediate between those of systems I and II.