Investigations of nanoscale helical pitch in smectic-C*alpha and smectic-C* phases of a chiral smectic liquid crystal using differential optical reflectivity measurements

Variety of subphase emerging sequences, the frustration of three main phases, SmC_{A}^{*}, SmC^{*}, and SmA, and the long-range interlayer interactions

Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)2470-004510.1103/PhysRevE.96.012701], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of SmC_{A}^{*}, SmC^{*}, and SmA with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of SmC_{α}^{*} which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is SmC_{A}^{*}(SmC_{α}^{*})-1/4-1/3-2/5-3/7-1/2-SmC^{*}(SmC_{α}^{*}), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between SmC_{A}^{*}(SmC_{α}^{*}) and (SmC^{*})SmC_{α}^{*}. Moreover, the experimentally confirmed extraordinary subphase emerging sequence SmC^{*}-1/2-SmC_{α}^{*} appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from SmC_{A}^{*} and SmC^{*} to SmC_{α}^{*} is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence SmC_{A}^{*}-1/3-SmC^{*} does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.

Twist elastic constant in the SmC* phase of an antiferroelectric liquid crystal with and without photo-polymer networks

Chiral liquid crystalline phases with pitches that are comparable to visible wavelengths, all Bragg-reflect visible light. We measured Bragg reflections from the chiral SmC* phase of the antiferroelectric liquid crystal (AFLC), AS612, and explored how applied electric fields and polymer networks modify these reflections. From the critical field that unwinds the helix and destroys Bragg reflections, the twist elastic constant of the SmC* phase is determined. We estimate from this result, the elastic constant of polymer network, which when introduced into the liquid crystal matrix, fixes the helical pitch (and hence, Bragg peaks). These parameters are crucial for designing both FLC and AFLC displays since networks enhance the mechanical properties of the liquid crystal host while not affecting their optical properties.

Experimental evidence of soft mode in the smectic C(α)(*) phase of chiral ferroelectric liquid crystals

Dielectric properties of chiral smectic liquid crystals characterised by the occurrence of the C(α)(*) phase were investigated in the frequency range 10 Hz-1 MHz. In the range of existence of this phase the observed relaxation spectrum is composed of two kinds of mode, and not of a single one, as commonly thought. Phase modes of the Goldstone type coexist in it with an amplitude type soft mode. The share of the soft mode in the global value of electric permittivity ε can be dominant and attain 90%. A possible explanation for that effect is sought in the similarity to chiral phases of the de Vries type.

Complex superstructures in chiral liquid crystals: surface-induced helix destruction

The influence of surface anchoring in thin chiral ferroelectric liquid crystals on helical superstructures imposed onto smectic layers is studied by means of a simple model allowing surface anchoring through the self-depolarization effect. It is shown that, for narrow temperature ranges close to temperatures of tilting phase transitions, these interactions can destroy helices, leading to the emergence of complex, intertwined undulatory, and helical substructures with different, mainly short, pitches. Regions with both undulated and helical orderings are demonstrated to reveal different sizes and random distributions along the smectic layer normal. Assuming values of material model parameters, typical for liquid crystals being close to tilting phase transitions, the free energy of thin helical smectic liquid crystal systems is determined as a function of two variables. One of them specifies the helix period of the appropriate bulk system (unperturbed by surfaces), while the second describes the interplay between the surface anchoring and the liquid crystal elasticity. It is shown that the free energy exhibits a very complicated behavior within variable regions for which the regular helices or complex superstructures occur. The resulting sensitivity of the free energy on changes of these variables corresponds to the appearance of a large variety of complex superstructures with coexisting helices of different periods. This gives an explanation of the occurrence of intricate superstructures and provides new insight into the interplay between molecular and surface interactions near the tilting phase transitions.

Biaxial smectic-A* phase and its possible misidentification as a smectic-Cα* phase

The biaxial smectic-A* (Sm-A(B)*) phase, appearing in the phase sequence Sm-A*-Sm-A(B)*-Sm-C*, is analyzed using Landau theory. It is found to possess a helical superstructure with a pitch that is significantly shorter than the pitch of the Sm-C* helical superstructure. The Sm-A(B)*-Sm-C* transition can be either first or second order, and correspondingly there will be either a jump or continuous variation in the pitch. The behaviors of the birefringence and electroclinic effect are analyzed and found to be similar to those of a Sm-C(α)* phase. As such, it is possible that the Sm-A(B)* phase could be misidentified as a Sm-C(α)* phase. Ways to distinguish the two phases are discussed.

Effect of enantiomeric excess on the phase behavior of antiferroelectric liquid crystals

Null transmission ellipsometry and resonant x-ray diffraction are employed to study the effect of enantiomeric excess (EE) on the phase behavior of antiferroelectric liquid crystal 10OTBBB1M7. Phase sequence, layer spacing, and pitch of the helical structures of the smectic-C(α)* and smectic-C* phases are studied as a function of temperature and EE. Upon reducing EE, a liquid-gas-type critical point of the smectic-C(α)* to smectic-C* transition is observed, as well as the disappearance of the smectic-C(d4)* and the smectic-C(d3)* phases. Results are analyzed in a mean-field model.

Evolution of a rare sequence of surface transitions with temperature and film thickness

In free-standing smectic films, layers near the surfaces of the film often contain molecules tilted away from the layer normal, while in the bulk of the film the magnitude of the tilt decays exponentially with distance from the surface. We have identified the detailed molecular tilt orientations in the surface layers of films for one antiferroelectric liquid crystal compound. A series of five surface structures exists with different nonplanar tilt arrangements for each structure. The molecular orientations in the surface layers evolve with temperature. The polarization of the film also evolves with temperature, corresponding to the tilt arrangements. Using ellipsometric data, we reconstruct the changes in the magnitude and azimuthal direction of the tilt as functions of temperature. We have also studied films of several different thicknesses. We present a phase diagram for the five surface structures showing the dependence on temperature and film thickness.

Nonplanar tilts in very thin smectic films of one liquid-crystal compound

Surface effects cause tilted molecular arrangements in smectic layers near the surface of a free-standing liquid-crystal film in which the bulk of the film is in the smectic- A phase. One recent work has shown that the tilt directions in adjacent surface layers may be nonplanar. In this paper we study films with thicknesses of two to six smectic layers. Surface effects dominate in these very thin films. We show that the molecular tilts are nonplanar even in these very thin films.

Temperature-induced sign reversal of biaxiality observed by conoscopy in some ferroelectric Sm-C* liquid crystals

We have studied various ferroelectric liquid crystals to find the average molecular direction of the shortest axis in the perfectly unwound state by using tilted conoscopic measurements. We find that there exist two types of temperature dependencies of the biaxiality. Some materials exhibit increasing biaxiality while others show decreasing biaxiality with increasing temperature. The former shows a temperature-induced sign reversal of biaxiality. Three different physical mechanisms are identified as responsible for the emergence of biaxiality: (i) anisotropic fluctuations of the long molecular axis, (ii) a biased rotation around the long axis, and (iii) the local field effect. By means of a simple theoretical investigation, we conclude that these two types of trends are due mainly to the opposite signs of the biaxial order parameter C , which represents the second mechanism: the biased rotation around the long axis. This means that the central phenyl planes of molecules belonging to materials having biaxiality that increases with temperature are oriented on the average parallel to the tilt plane (the shortest index of refraction axis normal to the tilt plane), and, on the contrary, in those of the others molecules are oriented perpendicular to the tilt plane (the shortest index of refraction axis lying in the tilt plane). Thus, the direction of the phenyl ring plane of the liquid crystal molecules determines the different temperature dependencies of the biaxiality. It is also shown that the phenomenon of sign reversal of the biaxiality is due to the competitive contributions of the first and second physical mechanisms.

Smectic-C*alpha phase with two coexistent helical pitch values and a first-order smectic-C*alpha to smectic-C* transition

Previous results from Kundu using dielectric relaxation have suggested a reentrant antiferroelectric-ferroelectric-antiferroelectric transition in the compound LN36. Our comprehensive studies of this compound using differential optical reflectivity, nonadiabatic scanning calorimetry, null transmission ellipsometry, and resonant x-ray diffraction show that in fact LN36 exhibits the usual phase sequence for chiral smectic liquid crystals: SmA*-SmC*alpha-SmC*-SmC*FI1-SmC*A . Moreover, the SmC*alpha-SmC* transition is a first-order transition, characterized by a discontinuous change in the helical pitch. At temperatures just above the SmC*alpha-SmC* transition, two different values for the helical pitch are simultaneously observed for the first time.

Discontinuous change in the smectic layer thickness in ferrielectric liquid crystals

The temperature dependence of the thickness of thick free-standing films is studied using a high-resolution film thickness measurement technique. A small discontinuity in the temperature dependence of the smectic layer thickness at every phase transition between ferro-, ferri-, and antiferroelectric phases is observed. We show that the major contribution to it arises from a change in the smectic tilt angle.

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.