Layer-Scale Optical Chirality of Liquid-Crystalline Phases L. E. Hough and N. A. Clark Department of Physics, University of Colorado, Boulder, Colorado 80309, USA (Received 26 February 2005; published 31 August 2005) We present a model for the optical chirality of layered liquid-crystalline phases. The model demon- strates that uniform stacking of chiral layers can lead to significant collective optical rotation, even in the absence of a superlayer helix. We predict the optical rotation of the B2 phases of bent-core liquid crystals, which can have optical rotation as large as 1000 times the molecular optical activity. DOI: 10.1103/PhysRevLett.95.107802 PACS numbers: 61.30.2v, 42.70.Df, 78.20.Ek Gyrotropy or optical chirality is an important property of chiral materials, in particular, chiral liquid crystals (LCs). These materials exhibit a variety of chiral optical effects, including the spectacular Bragg reflection and photonic band gap effects from macroscopically helical chiral ne- matic and smectic (SmC  or SmCA) phases [1,2]. Chiral nematic LCs show giant divergent pretransitional optical rotation (OR) produced by helical molecular orientation within nematiclike correlation volumes at temperatures just above the isotropic to cholesteric transition [3,4]. These phenomena have been modeled by a variety of analytical and numerical methods in which the medium consists of optically achiral molecular elements (either uniaxial or weakly biaxial) assembled into macroscopi- cally chiral superstructures [4 –9]. In all of these models, the observed and predicted optical activity of the super- molecular structures is much greater than that which would be expected from isolated chiral molecules. Optical rotations of linearly polarized light by 0:1 to 1 deg=m in the visible and near UV wavelength ranges have recently been observed in isotropic but optically active (dark-conglomerate) phases of bent-core molecules. This work has renewed interest in the origins of optical rotation in LC phases [10,11]. In order to explain the dark- conglomerate observations, Ortega et al. recently modeled the SmC A P A with a locally achiral dielectric tensor with optic axes rotating continuously and a pitch of two layers. This work indicates that layer-scale structural chirality can lead to observable optical rotation [12]. Furthermore, Olson et al. have observed chiral optical effects in a single layer of freely suspended B2 films [13]. With only one layer present no superlayer structure exists. The optical modeling employed therefore was based on the chirality of the layer itself. They modeled the layer as two uniaxial halves whose optic axes were oriented along the arms of the tilted, bent-core molecule. In a freely suspended film, the finite system size makes this optical structure chiral, even though the stacking of such layers would form an achiral bulk structure. These observations led us to explore the consequences of introducing layer chirality into the optical modeling of bulk chiral smectic LC phases. These effects should be particularly important when superlayer helixing and asso- ciated strong optical rotatory effects are absent. Previous models of bulk optical activity in LCs have assumed chiral helical supermolecular organization of achiral elements [Fig. 1(b)], which produces the colossal visible wavelength OR observed in chiral nematic and SmC LCs (  100 deg=m), roughly 10 6 times larger than that arising from the optical activity of individual molecules (  1 deg=cm) [Fig. 1(a)]. Here we demonstrate that the uni- form achiral stacking of chiral layers produces significant collective chiral optical activity, generating OR in bent- core systems of magnitude   1 deg=m, approxi- mately 10 4 times the individual molecule value and the dominant OR effect in the absence of supermolecular helixing. We refer to the collective optical activity of chiral layers as layer optical chirality (LOC), which has not been widely studied in LCs because their optical properties are generally dominated either by birefringence or by super- molecular helixing. However, in helix-free situations where the macroscopic birefringence is small, LOC can be the dominant bulk optical effect. This occurs, for ex- ample, in the ‘‘orthoconic’’ tilted chiral smectics [14], and in the recently discovered ‘‘dark conglomerate’’—both of which are believed to be locally chiral tilted smectics. Here we calculate the LOC of bent-core systems, though our approach is also appropriate for any chiral layered phase. Figure 1 illustrates the layer optical model for the ap- plication to B2-based bent-core phases, which are particu- larly good candidates for this approach. As shown in the space-filling model of the compound W508 [15] in Figs. 1(f) and 1(g), the layer structure is dominated by two distinct sublayers of elongated, nearly uniaxially bi- refringent arms connected in a bent fashion by a covalent linker at the center of the molecule. The layers are capped at their ends by a sublayer of aliphatic tails at the interface with the adjacent layer. Since the plane containing the arms is tilted with respect to the layer normal, z, as shown in Fig. 1(f), the layer structure is C2 symmetric about y. The layer structure is also chiral if mirror reflection symmetry about the x-z plane is absent, a condition caused by the distinct nature of the layer center (linker) and layer edge interfaces that generate a net polar structure. Thus both PRL 95, 107802 (2005) PHYSICAL REVIEW LETTERS week ending 2 SEPTEMBER 2005 0031-9007= 05=95(10)=107802(4)$23.00 107802-1  2005 The American Physical Society