LOCAL STABILITY OF BIAXIAL NEMATIC PHASES BETWEEN 2 CYLINDERS

We consider a nematic liquid crystal confined between two cylinders of radii r(1) > 0 and r(2) > r(1). We suppose that the lateral surfaces induce a uniaxial anchoring with the optic axis aligned along the radi al direction, and we study the equilibrium configurations which minimi ze the free energy functional. This problem has been already studied u nder the assumption that the nematic remains uniaxial in the whole tub e, with fixed degree of orientation s. We allow the nematic to become biaxial between the surfaces, and include in the free-energy functiona l an internal potential which favours uniaxiality. We prove that, if t he internal potential is neglected (i.e. if biaxiality can arise at no cost), the free energy minimizer is biaxial in the whole volume (exce pt, of course, on the lateral surfaces, where it must be uniaxial). Th e minimizer is unique, and no bifurcation arises for any value of rho := r(1)/r(2).We arrive at new results also when the internal potential is at work: an exact solution, obtained in a special case, proves the existence of a bifurcation at a critical value of rho; approximate mi nimizers show how biaxiality fades away in the bulk as the potential i s magnified, and numerical studies illustrate the features of the most general minimizers. (C) 1997 Elsevier Science Ltd.