Theory of a critical point in the blue-phase-III–isotropic phase diagram

In low to moderate chirality systems, there is a first-order phase transition between the isotropic phase and the blue phase III (BP III) in chiral liquid crystals. Recent experiments [Z. Kutnjak, C. W. Garland, J. L. Passmore, and P. J. Collings, Phys. Rev. Lett. 74, 4859 (1995); J. B. Becker and P. J. Collings, Mol. Cryst. Liq. Cryst. 265, 163 (1995) on high chirality systems show no transition. This suggests that the isotropic phase and BP III have the same isotropic symmetry and that there is a liquid-gaslike critical point in the temperature-chirality plane terminating a line of coexistence. In this case the averaged alignment tensor 〈Q(x)〉 is zero in both the isotropic phase and BP III. We introduce a scalar order parameter 〈ψ〉=〈(∇×Q)⋅Q〉 to describe both phases and develop a Landau-Ginzburg-Wilson Hamiltonian in ψ and Q, which can be motivated by a coarse-graining procedure. Our model predicts that the isotropic-to-BP-III transition is in the same universality class (Ising) as the liquid-gas transition. By looking at the fluctuations of Q around the critical point, we obtain formulas for the light scattering and the rotary power, which are in qualitative agreement with experiments [J. B. Becker and P. J. Collings, Mol. Cryst. Liq. Cryst. 265, 163 (1995) and need to be checked quantitatively. © 1996 The American Physical Society.