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, Mel. 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 (psi) = [(del x Q) . Q] to describe both phases and develop a Landau-Ginzburg-Wilson Hamiltonian in psi 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, Mel. Cryst. Liq. Cryst. 265, 163 (1995)] and need to be checked quantitatively.