Phase Transitions and Phase Diagrams in Liquid Crystalline Polymers

Abstract

It is trivial to recall that the simplest and commonest model to represent a LMM is the anonymous uncharacteristic rigid rod shown in Fig. 1. Indeed liquid crystalline properties are readily associated to molecular or supramolecular anisotropy and therefore the first modelization of a macromolecular mesogen do not differ from this simple picture: Fig. 1 can serve as well provided one considers possible an infinite lengthening of this object. However this seemingly simple modification has non negligible outcomes, both theoretical and practical. First, the steric interactions in assemblies of such very long rods become a major parameter in the occurence of an anisotropic state. The great achievement of early theoretical works by Onsager and Flory is to have introduced the axial ratio x = L/d (Fig. 1) to account for these repulsive forces. Refined models including now attractive interactions¹ show that the isotropic-nematic transition is expected only within a given range of axial ratio limited by an upper critical value (≈6) (Fig. 2). In addition the order parameter at the transition for long rods comes out to be close to 1, significantly higher than the value from the Maier and Saupe’s theory (≈0.43) which describes satisfactorily the behavior of short LMMs. What system seems more suitable than a sequence of phenyl rings to make up rigid-rod polymers ? In order to test this model and evaluate the meaning and the limitations of the phase diagram in Fig. 2, let us consider the Table 1 which presents some relevant characteristics of polyphenylenes: H - {- ø) -}_n - H.