X-Ray Study of the Hexatic-B-to-Smectic-APhase Transition in Liquid-Crystal Films

Abstract

X-ray studies of thick, free-standing films of the liquid-crystal compound «-butyl 4'-nhexyloxybiphenyl-4-carboxylate (460BC) have determined the critical behavior at the threedimensional hexatic-5-to-smectic-^4 phase transition. The position and width of the scattering peaks exhibited 1 -a singularities in agreement with theory and heat-capacity results. Measurements on two-layer films of 460BC provided evidence for a continuous, twodimensional, hexatic-to-liquid transition.PACS numbers: 64.70.Ew, 68.60. + qThe layered hexatic-i? liquid-crystal phase is the only three-dimensional (3D) physical system in which "hexatic" order has been observed. 1,2 This ordering involves a long-range sixfold symmetric, orientational alignment of the "bonds" connecting neighboring in-plane molecules even though their in-plane positional correlations remain short ranged and is characterized by a local order parameter \lf(T) = e 6i0(r) where 0(7) is the angle between the "bonds" and some reference axis. 3 The loss of bond-orientational order upon heating the hexatic-i? phase results in a layered phase with liquidlike inplane order-the smectic-^ phase. Heat-capacity studies 4 of the hexatic to smectic-^ (hex-A ) transition in the liquid-crystal compound 650BC found the transition to be continuous with a large, nearly symmetric heat-capacity peak and critical exponent a ~ 0.6. This heat-capacity behavior implies large hexatic fluctuations which couple to the density fluctuations, causing sixfold symmetric x-ray scattering with a singular critical temperature dependence for both the position and width of the scattering peaks. In this Letter we present measurements of this singular behavior at the 3D hex-^4 transition and evidence for a continuous (2D) hexatic-liquid transition. The 3D measurements involved thick films (several hundred molecular layers) while the 2D measurements were on two-layer films. The films were free standing and thus substrate-free.The liquid-crystal compound studied was «-butyl 4'-«-hexyloxybiphenyl-4-carboxylate (460BC). In comparison to 650BC, this compound exhibited the hexatic and smectic-^ phases over wider temperature ranges. Furthermore, the range of stability for two-layer films was enhanced, and this material showed no crystalline surface-ordering transition as observed in 650BC. 1 Heat-capacity measurements 5 on 460BC indicated that the hex-^4 transition was first order, but only weakly so. The heat capacity, C p , could be fitted by a power-law divergence up to 30 mK of T c . Explicitly C p -A ± r a± , where t = \(T -T c )/T c \, the upper and lower signs refer to T > T c and T < T c , respectively, and the fitted parameters were A + /A ~ = 0.75 ± 0.03 and a + = a" =0.49 ±0.02. Unfortunately, 460BC films rupture when cooled from the hexatic phase into a monoclinic crystalline phase, and so the hexaticcrystal transition could not be studied.For our structural studies, the layers of the liquid-crystalline phase were aligned by drawing free-standing films across a 6x6-mm 2 hole in a glass cover slide....

Hexatic Order and Liquid Density Fluctuations

“…The results to be presented below are in excellent agreement with experiments on both liquid crystals 4 and xenon adsorbed on graphite. 3 They are also very general; indeed, they apply to a wide range of liquids whose local densities are coupled to other, primary order parameters.…”

“…The dimensionality d = 3 for bulk liquid crystals, 4,8,9 while d = 2 for thin liquidcrystal films and gas monolayers. 3 ' 4 Equation (3) defines the hexatic order parameter ^(7) in terms of p- (7).…”

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

“…The temperature dependence of ξ 0 (T ) obtained for the single-domain case [see Fig. 3(b)] is in agreement with the previous results [8,11,12,25,26]. The correlation lengths ξ n (T ) associated with the higher harmonics of BO order [see Fig.…”

Recent developments in the physics of liquid crystals

“…The scattering in the A phase (a) is independent of X.For temperatures below the smectic A-hexatic B transition ((b) and (c)), the X-scan develops a peak which is direct evidence of hexagonal bond-orientational order(from Pindak et al (1981)).The smectic A-hexatic B transition has been studied by high-resolution X-ray and calorimetric techniques (Huang et aI. 1981,Davey et al 1984, Pitchford et al 1986, Nounesis et al 1986, Mahmood et al 1986) but the nature of the transition is still not clearly elucidated.…”