Phase sequences and long-range interactions in ferroelectric liquid crystals

Definite existence of subphases with eight- and ten-layer unit cells as studied by complementary methods, electric-field-induced birefringence and microbeam resonant x-ray scattering

A mixture of two selenium-containing compounds, 80 wt. % AS657 and 20 wt. % AS620, are studied with two complementary methods, electric-field-induced birefringence (EFIB) and microbeam resonant x-ray scattering (μRXS). The mixture shows the typical phase sequence of Sm-C_{A}^{*}-1/3-1/2-Sm-C^{*}-Sm-C_{α}^{*}-Sm-A, where 1/3 and 1/2 are two prototypal ferrielectric and antiferroelectric subphases with three- and four-layer unit cells, respectively. Here we designate the subphase as its q_{T} number defined by the ratio of [F]/([F]+[A]), where [F] and [A] are the numbers of synclinic ferroelectric and anticlinic antiferroelectric orderings in the unit cell, respectively. The electric field vs temperature phase diagram with EFIB contours indicates the emergence of three additional subphases, an antiferroelectric one between Sm-C_{A}^{*} and 1/3 and antiferroelectric and apparently ferrielectric ones between 1/3 and 1/2. The simplest probable q_{T}'s for these additional subphases are 1/4, 2/5, and 3/7, respectively, in the order of increasing temperature. The μRXS profiles indicate that antiferroelectric 1/4 and 2/5 approximately have the eight-layer (FAAAFAAA) and ten-layer (FAFAAFAFAA) Ising unit cells, respectively. The remaining subphase may be ferrielectric 3/7 with a seven-layer unit cell, although the evidence is partial. These experimental results are compared with the phenomenological Landau model [P. V. Dolganov and E. I. Kats, Liq. Cryst. Rev. 1, 127 (2014)2168-039610.1080/21680396.2013.869667] and the quasimolecular model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)1063-651X10.1103/PhysRevE.68.051703].

Effect of an external electric field on the smectic-Ctilted* phases

We are interested in the chiral tilted smectic subphases, smectic-C(tilted)(*), including commensurate structures as well as the incommensurate smectic-C(α)(*) one. The continuum theory defines two scalar order parameters I and J, which can be coupled with an external electric field through a linear term I × E and a dielectric term J × E(2). We have calculated the changes due to these terms in the phase diagrams in the (α,η) plane, where α comes from the spontaneous twist and η measures the strength of the biaxial order. The coupling with an external electric field induces the expansion of the areas with spontaneous polarization and the appearance of an electroazimuthal effect.

Effect of dipolar interaction in molecular crystals

In this paper we investigate the ground state and the nature of the transition from an orientational ordered phase at low temperature to the disordered state at high temperature in a molecular crystal. Our model is a Potts model which takes into account the exchange interaction J between nearest-neighbor molecules and a dipolar interaction between molecular axes in three dimensions. The dipolar interaction is characterized by two parameters: its amplitude D and the cutoff distance r(c). If the molecular axis at a lattice site has three orientations, say the x, y or z axes, then when D = 0, the system is equivalent to the 3-state Potts model: the transition to the disordered phase is known to be of first order. When D ≠ 0, the ground-state configuration is shown to be composed of two independent interpenetrating layered subsystems which form a sandwich whose periodicity depends on D and r(c). We show by extensive Monte Carlo simulation with a histogram method that the phase transition remains of first order at relatively large values of r(c).

Field-induced transitions between multilayer phases of polar smectic liquid crystals

Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] reported the discovery of a novel multilayer phase in polar liquid crystals. The phase was unambiguously assigned to a six-layer antiferroelectric structure (Sm-C(d6)(*)) by resonant x-ray diffraction. This discovery lead to essential progress in understanding the nature of polar phases. However, more recently, Chandani et al. [Liq. Cryst. 38, 663 (2011)] in the same material clearly identified the novel phase as a ferrielectric five-layer structure (Sm-C(d5)(*)) by the electric-field-induced birefringence. This contradiction seemed to be a mystery. In this paper we show that the two experiments are in agreement. Phenomenological Landau theory of the phase transitions shows that both phases (Sm-C(d6)(*) and Sm-C(d5)(*)) exist and transform into each other in a relatively low electric field.

Surface-aligning field in smectic liquid-crystal films

Two modified mean-field J(1)-J(2) models are studied to explain the surface reduction of twisting power in the helical smectic-C*(α) phase in free-standing liquid crystal films. Profiles of the surface interlayer interaction are calculated from the experimental results. The calculations reveal the existence of a strong surface field and indicate that the surface field is the reason for the observed reduced twisting power near the surface region. Our results provide a quantitative study of the interlayer interactions through surface effects in smectic liquid crystals.

Continuum theory of tilted chiral smectic phases

We show that the sequence of distorted commensurate phases observed in tilted chiral smectics is explained by the gain in electrostatic and elastic energies due to the lock-in of the unit cell to a number of layers which is the integer closest to the ratio of the helix pitch over the smectic layer thickness of the subjacent Sm-Cα∗ phase. We also explain the sign change of the helicity in the middle of the sequence by a balance between two twist sources one intrinsic and another due to the distortion of the Sm-Cα∗.

Theoretical analysis of continuous pitch evolution and reversed phase sequence in antiferroelectric liquid crystals

Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted Sm C(alpha)* phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted Sm C* phase appeared below the four-layer Sm CFI2* phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.

Discovery of a novel smectic-C{*} liquid-crystal phase with six-layer periodicity

We report the discovery of a new smectic-C{*} liquid-crystal phase with six-layer periodicity by resonant x-ray diffraction. Upon cooling, the new phase appears between the SmC{alpha}{*} phase having a helical structure and the SmC{d4}{*} phase with four-layer periodicity. This SmC{d6}{*} phase was identified in two mixtures which have an unusual reversed SmC{d4}{*}-SmC{*} phase sequence. The SmC{d6}{*} phase shows a distorted clock structure. Three theoretical models have predicted the existence of a six-layer phase. However, our experimental findings are not consistent with the theories.

Thickness dependent phase behavior of antiferroelectric liquid crystal films

Free standing films of a liquid crystal compound with simple surface enhanced order were studied. The resultant phase diagram demonstrates that (1) the short helical pitch smectic-C(alpha)* phase disappears below a film thickness of 10 layers, and (2) the temperature window of a distorted 4 layer smectic-C(FI2)* phase increases dramatically upon decreasing film thickness. The experimental findings were attributed to the reduced dimensionality and enhanced surface effects in thin films. The results of the smectic-C(alpha)* phase are consistent with what have been reported for helically ordered magnetic thin films, with a noticeable difference due to the opposite effect of the surface on ordering in the two systems.

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

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.

Effects of doping on an unusual smectic- C*alpha-smectic-C*FI2-smectic-C* phase sequence

The compound 10OHF has a partially inverted phase sequence, unique among the series of nOHF homologous compounds and all other known liquid crystals, with the smectic-C*FI2 (SmC*FI2) phase occurring at higher temperature than the smectic-C* (SmC*) phase. We present ellipsometric data to identify the phase sequences of 9OHF, 10OHF, 11OHF, and 12OHF. Binary mixtures of 10OHF with C11, a compound with the typical phase sequence among the smectic phases, show that the unusual phase sequence of 10OHF stabilizes upon mixing and that SmC*FI2 predominates over SmC* throughout the entire mixing phase diagram. In thin films of some mixtures, surface interactions induce a reentrant SmC*FI2-SmC*-SmC*FI2 transition in the rest of the film.

Experimental study of high-temperature smectic- C_{FI2}{ *} phase in chiral smectic liquid crystals that exhibit phase-sequence reversal

We report the results of an experimental study of a recently observed phase sequence reversal of smectic-C_{FI2}{ *} [ SmC;{ *}(q_{T}=1/2); a four layer antiferroelectric] phase appearing in the temperature range above the smectic-C{ *} (SmC;{ *}) phase from the results of optical birefringence, spontaneous polarization, selective reflection, conoscopy, and dielectric spectroscopy. The SmC_{FI2}{ *} phase is observed in an antiferroelectric liquid crystalline compound, 10OHF, in a temperature range above that of SmC{ *} phase and is found to be thermodynamically monotropic, i.e., it appears only upon cooling from SmC_{alpha}{ *} phase. This is also unstable as if it is once transformed to SmC{ *} by the application of the bias, it does not return to its original state unless the sample is heated and cooled again in the absence of the bias. Nevertheless this phase is stabilized by the addition of a chiral smectic compound 9OTBBB1M7 (abbreviated as C9), having a wide temperature range of the SmC_{FI2}{ *} phase. The temperature range of the low temperature SmC{ *} decreases with increase in the concentration of C9 and for a concentration of 55 wt. %, SmC{ *} disappears and the transition takes place directly from SmC_{FI2}{ *} to the crystalline phase on cooling. The existence of such a high-temperature SmC_{FI2}{ *} phase is also supported by a phenomenological model.

Investigation into liquid crystalline smectic-C* subphase stability using chiral and achiral dopants

In this paper we investigate the influence of chiral and achiral dopants on a chiral smectic liquid crystal material, which exhibits a rich phase sequence, including the antiferroelectric phase and the three-layer intermediate smectic (SmC*FI1) phase. Using polarized optical microscopy, differential scanning calorimetry, and x-ray diffraction we find that small amounts of achiral dopant have the ability to significantly broaden the SmC*FI1 phase, whereas an oppositely-handed dopant (otherwise identical to the host material) destabilizes the phase. This work clearly indicates that bulk chirality strongly influences SmC*FI1 phase formation and that steric effects also play an important role. Interestingly, addition of the shorter achiral molecule (8CB) was observed to increase the smectic layer spacing, most likely by suppressing interdigitation of alkyl chains between adjacent smectic layers. Control of the SmC*FI1 phase width using mixtures in this way is clearly important for effective phase characterization, and could potentially lead to commercially viable materials with a stable SmC*FI1 phase over a large temperature range.

Unique pitch evolution in the smectic-C+alpha phase

Employing resonant x-ray diffraction, we observed unique pitch evolutions in the smectic-C*(alpha) phase in mixtures of two antiferroelectric liquid crystals. Our results show that the pitch in this phase continuously evolves across 4 layers, contradicting a theoretical model that predicts that the smectic-C*(FI2) phase intervenes in the smectic-C*(alpha) phase. The phase sequences we found can be explained by another model that includes one type of long-range interaction among smectic layers.

Range of interlayer interactions in smectic- C liquid crystals

The fact that the elastic constant for bending a layer of smectic- C liquid crystal along its c director differs from the value for bending in the perpendicular direction has recently been shown to give rise to interactions between distant layers. The effect of this entropy-induced interaction is to favor a parallel or antiparallel alignment of the c directors in these nonadjacent layers. We calculate in detail the range and strength of this interaction in both infinite and finite samples, and find the results to depend mainly on the ratio of the average layer bending elastic constant to the layer compression modulus. At low values of this ratio, the interlayer interaction is of long range in a bulk sample, while at high values of the ratio it decays as the inverse cube of the interlayer distance. For a sample confined between rigid substrates parallel to the layers, the interaction is greatly reduced. For a free-standing film the interaction may be enhanced if the surface tension is weak, but may be diminished if the surface tension is strong.

Smectic-Calpha*-smectic-C* phase transition and critical point in binary mixtures

We have investigated the smectic-Calpha*-smectic-C* (SmCalpha*-SmC*) transition in a series of binary mixtures with resonant x-ray diffraction, differential optical reflectivity, and heat capacity measurements. Results show that the phases are separated by a first-order transition that ends at a critical point. We report the observation of such a critical point. We have proposed the appropriate order parameter and obtained values of two critical exponents associated with this transition. The values of the critical exponents suggest that long-range interactions are present in the SmCalpha*-SmC* critical region.

Surface-induced multiple reentrant transitions

We have studied tilted surface layers in the bulk SmA temperature window of one liquid crystal using null transmission ellipsometry. Five distinct nonplanar surface structures were observed. We present analyses of the tilt and azimuthal profiles of the structures and examine the transitions between the structures. The transitions are identified as a double reentrant synclinic-anticlinic-synclinic-anticlinic transition. Meanwhile, the transitions also display reentrant ferroelectric-antiferroelectric-ferroelectric behavior.

Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC*FI2-SmC* phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the SmC*FI2 phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.