Tc. Lubensky et H. Stark, THEORY OF A CRITICAL-POINT IN THE BLUE-PHASE-III-ISOTROPIC PHASE-DIAGRAM, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(1), 1996, pp. 714-720
In low to moderate chirality systems, there is a first-order phase tra
nsition 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 (1
995)] on high chirality systems show no transition. This suggests that
the isotropic phase and BP III have the same isotropic symmetry and t
hat there is a liquid-gaslike critical point in the temperature-chiral
ity plane terminating a line of coexistence. In this case the averaged
alignment tensor (Q(x)) is zero in both the isotropic phase and BP II
I. We introduce a scalar order parameter (psi) = [(del x Q) . Q] to de
scribe 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 a
t the fluctuations of Q around the critical point, we obtain formulas
for the Light scattering and the rotary power, which are in qualitativ
e agreement with experiments [J. B. Becker and P. J. Collings, Mel. Cr
yst. Liq. Cryst. 265, 163 (1995)] and need to be checked quantitativel
y.