Extension of the Hamaneh-Taylor model using the macroscopic polarization for the description of chiral smectic liquid crystals

Abstract

Chiral smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate Sm-Calpha* phase. We carried out an extension of the phenomenological model recently presented by Hamaneh and Taylor based on the distorted-clock model. The salient feature of this model is that it links the appearance of phases to a spontaneous microscopic twist: i.e., an increment alpha of the azimuthal angle from layer to layer. The balance between this twist and an orientational order parameter J gives the effective phase. We introduce a second orientational order parameter I , which physical meaning comes from the macroscopic polarization; the effect of an applied electric is also studied. We derive phase diagrams and correlate them to our experimental results under field showing the sequence of phases versus temperature and electric field in some compounds.

Continuum theory of tilted chiral smectic phases

“…This looks like previous theories [9,10,15] which make use only of the 2D-uniaxial invariant missing somewhat the other terms which are at the origin of the Hamaneh- Taylor (H&T) theory [23,26,27].…”

“…in Sm-C * F i1 if the angle µ is much larger than 2π/3 as reported in literature [26], the opposite sign comes again. 4.…”

“…taking the definitions of µ and Φ 0 given in the figure (5), one finds [26] that the polarization P S is proportional to I = (1 + 2 cos µ)/3 while the macroscopic quadrupole Θ ij is a function of θ, I…”

“…H&T have introduced the angles ∆ϕ and α to describe the distance from the XY model and the parameter J = cos 2ϕ ≤ 1 to describe the biaxial Ising-like tendency [23,27]. We have further defined the parameter −1 ≤ I = cos ϕ ≤ 1 that measures the in-plane uniaxial character [26].…”

“…The phase diagrams in the plane (0 α π , 0 η 1) have been computed by H&T [23,27] with the J 2 term and Dhaouadi [26] (I 2 ) together with their behavior under an applied electric field (-I.E) in the last case.…”