On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression

A mesoscopic, extended Doi theory for flows of nematic liquid crystals (LCs ) has been successfully applied by Rey to study extensional Row-induced, ho mogeneous phase transitions both for rod-like and disc-like molecular geome try. Rey analysed the two order parameters (eigenvalues) of the orientation tensor. Recently the authors generalized the flow-phase diagram (nematic c oncentration vs, flow rate) for rod-like nematics by analysing all tensor d egrees of freedom, i.e. by coupling the three director (eigenvector) degree s of Freedom. Here we record and discuss subtleties of the corresponding di agram for discotic LCs in uniaxial extension and uniaxial compression. We f ocus here on the induced stable orientation configurations. Uniaxial extens ion (an idealization of fibre how) yields a low concentration region of uni que oblate uniaxial states at every flow rate: a very small finite region o f bi-stable oblate and biaxial states: and the predominant region. encompas sing all concentrations above the pure I-N transition and all flow rates, w here the only stable steady state is a biaxial pattern. Furthermore, wherea s uniaxial states are 'unique', all biaxial states occur in a continuous fa mily, corresponding to an arbitrary positioning of the director pair in the plane transverse to the flow axis of symmetry. Uniaxial compression (an id ealization of film stretching how) of discotic LCs exclusively yields stabl e prolate uniaxial patterns.