smectic-C Phase Transition Research Articles

Optical and calorimetric studies near the smectic-A to smectic-C tricritical point

Detailed heat capacity and birefringence measurements have been performed to investigate the transitional behavior near the orthogonal smectic-A to tilted smectic-C (Sm-A–Sm-C) phase transition on several liquid crystalline mixtures comprising of a rod-like mesogen and a hockey stick-shaped compound having substitution of methyl group in the lateral position. Both probing methods were found to be rather successful in assessing the phase transitional behavior with reasonably good accuracy. The data shows a divergent pretransitional excess above and below the transition temperature. Analysis of the data have been performed in detail with the renormalization-group expression with correction-to-scaling terms. The extracted effective critical exponents were observed in between the tricritical and 3D-XY limit. Detailed investigations carried out in this work reveal the dependence of the Sm-A–Sm-C phase transition on the width of the Sm-A phase and the existence of a broad tricritical range.

Dynamic renormalization group analysis of the chiral smectic-C to smectic-C phase transition

The chiral smectic-C to smectic-C (SmC -SmC) phase transition has been studied using dynamic renormalization group (DRG) analysis. Langevin equations are derived from the nonlinear elastic model of the SmC -SmC phase transition. The DRG equations are derived. The DRG analysis predicts the Kosterlitz-Thouless transition at low frequency limit and Kardar-Parisi-Zhang (KPZ) fixed point. The DRG calculation confirms that the SmC -SmC phase transition belong to the KPZ universality class.

Alignment and electro-optical properties of SmC* with direct transition to N* phases

ABSTRACTHighly first order silane end-group difluoroterphenyl liquid crystal was added to trifluoroterphenyl host with a nematic to smectic-C phase transition to increase its first order nature, achieve a higher cone angle and reduce its temperature dependence. Increasing concentration of the additive, caused a linear decrease and eventual disappearance of the nematic phase. A smectic-A phase was injected at 35% concentration, making the transition second order. Optical studies of the mixtures showed little dependence of the highest value of cone angle on concentration. The original host showed first order cone angle behavior and was used to fabricate a twisted FLC device.

Critical behavior at the isotropic to nematic, nematic to smectic-A and smectic-A to smectic-C phase transitions in a pyrimidine liquid crystal compound

High-resolution optical birefringence (∆n) measurement of a pyrimidine liquid crystal compound having nematic, smectic-A and smectic-C phases are reported. The high-resolution ∆n data are rather successful in assessing the critical anomaly at different phase transitions in the investigated compound with a reasonably good accuracy. The critical exponent β, describing the limiting behavior of the nematic order parameter close to the isotropic–nematic (I–N) phase transition, is found to be in good agreement with the tricritical hypothesis. The critical behavior at the nematic–smectic-A (N–Sm-A) and the smectic-A–smectic-C (Sm-A–Sm-C) phase transitions has been explored with the aid of a differential quotient extracted from the ∆n values. The yielded effective critical exponent α′ is appeared to be nearly tricritical in nature for the N–Sm-A phase transition. For the Sm-A–Sm-C phase transition, α′ exhibits a weak dependence on the fit range and assumes tricritical value for large temperature range considered, which again is found to be diminished slightly with reduction in the temperature range. Related critical amplitude quotient and corrections-to-scaling quotient are found to display deviations from the theoretical models. Such behavior signals the appearance of a non-Landau character for the orthogonal to tilted smectic phase transition in the investigated compound.

On a Molecular Based Q-Tensor Model for Liquid Crystals with Density Variations

In this article, we study the new Q-tensor model previously derived from Onsager's molecular theory by Han \textit{et al.} [Arch. Rational Mech. Anal., 215.3 (2014), pp. 741-809] for static liquid crystal modeling. Taking density and Q-tensor as order parameters, the new Q-tensor model not only characterizes important phases while capturing density variation effects, but also remains computationally tractable and efficient. We report the results of two numerical applications of the model, namely the isotropic--nematic--smectic-A--smectic-C phase transitions and the isotropic--nematic interface problem, in which density variations are indispensable. Meanwhile, we show the connections of the new Q-tensor model with classical models including generalized Landau-de Gennes models, generalized McMillan models, and the Chen-Lubensky model. The new Q-tensor model is the pivot and an appropriate trade-off between the classical models in three scales.

Electric-field induced isotropic to smectic-C phase transition

The theoretical observation of the critical point for the isotropic to smectic-C phase transition in the presence of the electric field is reported. The influence of an external electric field on the isotropic to smectic-C phase transition has been studied using Landau phenomenological theory. Analytic results are given for the phase boundary, stability limits, and location of the critical points of the isotropic to smectic-C phase transition with positive dielectric anisotropy. Topological classification of phase diagrams in the field–temperature coordinates is performed.

Liquid Crystalline Symmetrical 3,6-Diaryl-1,2,4,5-Tetrazines

A new series of symmetrical 3,6-diphenyl-1,2,4,5-tetrazines with four alkoxy tails were synthesized along with new examples with two alkoxy tails. Mesogenic properties were studied by differential scanning calorimetry and polarizing optical microscopy. The influence of the number and length of alkoxy chains attached to the 3,6-diphenyl-1,2,4,5-tetrazine core is discussed. Compared with the two-tailed tetrazines, 6 the four-tailed liquid crystalline tetrazines, 5e–g possess lower smectic-C phase transitions, and clearing point temperatures.

CdSe nanoparticles dispersed in ferroelectric smectic liquid crystals: Effects upon the smectic order and the smectic-Ato chiral smectic-Cphase transition

Spherical CdSe nanoparticles, surface-treated with oleylamine and tri-octylphosphine, dispersed in ferroelectric liquid crystals, can efficiently target disclination lines, substantially altering the macroscopic properties of the host compound. Here we present an ac calorimetry and x-ray diffraction study demonstrating that for a large range of nanoparticle concentrations the smectic-A layer thickness increases monotonically. This provides evidence for enhanced accumulation of nanoparticles at the smectic layers. Our results for the Smectic-A (SmA) to chiral smectic-C (SmC) phase transition of the liquid crystal S-(+)4-(2'-methylbutyl)phenyl-4'-n-octylbiphenyl-4-carboxylate (CE8) reveal that the character of the transition is profoundly changed as a function of the nanoparticle concentration. Large transition temperature shifts are recorded. Moreover, the heat-capacity peaks exhibit a crossover trend to a step-like anomaly. This behavior may be linked to the weakening of the SmA and SmC order parameter coupling responsible for the observed near-tricritical, mean-field character of the transition in bulk CE8. At lower temperatures, the presence of nanoparticles disrupts the phase sequence involving the tilted hexatic phases most likely by obstructing the establishment of long-range bond-orientational order.

Isotropic to chiral smectic-C phase transition in chiral smectic-C elastomers

A phenomenological Landau-like theory is presented, which describes the isotropic to chiral smectic-C (I-SmC⁎) phase transition in chiral smectic-C (SmC⁎) elastomers and polymers. The coupling between elastic strain, SmC⁎ order parameters and polarization is examined and piezoelectric and ferroelectric effects are predicted. While this phase transition is first order in low-molecular-weight SmC⁎ materials, we show here that the order of this transition does not change in SmC⁎ elastomers. The effect of the electric field in SmC⁎ elastomers is examined. The temperature dependence of the anomalous heat capacity and the nonlinear dielectric effect in the isotropic phase above the I-SmC⁎ phase transition in SmC⁎ elastomers are calculated.

Isotropic micellar to tilted lamellar phase transition in lyotropic liquid crystals

We extend our previous phenomenological model for the isotropic micellar to lamellar (smectic-A) phase transition to the isotropic micellar to tilted lamellar (smectic-C) (I–Lt) phase transition in lyotropic liquid crystals. We analyze the influence of micellar concentration on the I–Lt phase transition. The conditions for the I–Lt phase transition and the stability conditions of the tilted lamellar phase are calculated. The temperature dependence of the non-linear dielectric effect in the isotropic micellar phase above the I–Lt phase transition is calculated. Within this model the I–Lt phase transition is found to be always first order.

Density effect on the isotropic to smectic-C phase transition

The phenomenological model of the isotropic to smectic-C phase transition with the inclusion of the density change is examined in a simple way. The analysis shows that the density variation shifts the isotropic to smectic-C transition temperature but does not change first order character of the transition. The pressure dependence of the transition temperature and other thermodynamic quantities are calculated. The theoretical results are found to be in good qualitative and quantitative agreement with experiments.

Structure–property correlation of a hockey stick-shaped compound exhibiting N-SmA-SmCa phase transitions

We report the measurement of birefringence, dielectric constant, splay, bend elastic constants and rotational viscosity in the nematic phase (N) of a hockey stick-shaped compound exhibiting smectic-A (SmA) and anticlinic smectic-C (SmCa) phase transitions at lower temperature. It is found that the physical properties are significantly different than calamitics and partially similar to the bent-core liquid crystals. It exhibits the positive dielectric and the negative elastic anisotropy. The optical and the thermal measurements show that all the transitions are first order. The rotational viscosity is comparatively higher than calamitic liquid crystals and exhibits weak pre-transitional divergence. The temperature dependent static dielectric measurements indicate antiparallel correlation of both the longitudinal and the transverse components of dipole moments in both the smectic phases. The parallel component of the dielectric constant exhibits a single Debye type relaxation in all the phases. The activation energy in the N, SmA and SmCa phases are comparatively larger than that of the respective phases of calamitic liquid crystals and can partially be attributed to the higher rotational viscosity of the hockey stick-shaped compound.

Tricritical behavior of the smectic-A to smectic-C phase transition in a liquid crystal mixture

A phenomenological approach to the description of the smectic-A to smectic-C phase transition in a liquid crystal mixture is proposed. The problem of the first or second order transition is explored by means of the variation of the concentration. The influence of the concentration on this transition is discussed by varying the coupling between the concentration variable and the order parameters. We show that a tricritical point on the smectic-A to smectic-C phase transition line can be achieved under certain conditions. The theoretical prediction is found to be in good qualitative agreement with experimental results.

Non-linear dielectric effect in the isotropic phase of ferroelectric liquid crystals

We use a phenomenological model to find theoretically the non-linear dielectric effect (NDE) in the isotropic phase above the isotropic to chiral smectic-C ( I-SmC * ) phase transition. We find an analytical expression for the NDE in the isotropic phase above the I-SmC * phase transition. The temperature dependence of the NDE is presented in the isotropic phase of the I-SmC * phase transition.

Tilt Angle, Spontaneous Polarization and LF Dielectric Relaxation Investigations in the Chiral Nematic and Smectic-C* Phases of a Hydrogen Bonded Ferroelectric Liquid Crystal (HBFLC)—11 bpa

Investigations of tilt angle, spontaneous polarization and Low frequency (5 Hz - 10 MHz) dielectric relaxations are reported in a chiral hydrogen bonded liquid crystal, HBFLC, viz., 11 bpa. Isotropic to chiral nematic (IN*) and chiral nematic to chiral smectic-C (N*SmC*) phase transition temperatures determined by dielectric method agree with reports of TM and DSC. Temperature variation of order parameter (viz., primary order parameter tilt θ (T) and secondary order parameter spontaneous polarization P S (T) relevant to SmC* phase) studied through critical exponents β 1 and β 2 agree with Mean-Field predictions. Influence of hydrogen bonding on the growth of relevant order parameters is discussed. Dielectric dispersion revealed a collective motion (i.e., Goldstone mode GM) around ∼ 100 Hz. Other two higher frequency relaxation processes (viz., Type–I and –II) observed in the N* and SmC* phases are explained on the basis of a molecular dipole model. The influence of bias field on G.M. is studied in SmC* phase. The off-centred non-Debye's dispersion is studied through the Cole-Davidson theory. HF relaxations of Type-I and –II are explained as reorientation of dipole distinctly configured on the molecular frame. Soft mode relaxation in SmC* phase follows ferroelectric Curie-Weiss law. Arrhenius shift of relaxation frequency fR reveals higher activation energy for Type-II and lower energy for Type-I reorientation. The influence of hydrogen bonding on ferroelectricity in LCs is studied in terms of phase stability, tilt angle and polarization in SmC* phase in the wake of reports in other FE materials.

Pretransitional effects near the smectic-A–smectic-C*phase transition of hydrophilic and hydrophobic aerosil networks dispersed in ferroelectric liquid crystals

A detailed x-ray scattering and high-resolution ac calorimetric study has been carried out near the smectic-A to chiral smectic-C phase transition of liquid-crystal compounds 4-(2-methyl butyl) phenyl 4-n-octylbiphenyl-4-carboxylate (CE8) and p-( n-decyloxy) benzylidene-p-amino-(2-methylbutyl) cinnamate (DOBAMBC) confined in hydrophilic and hydrophobic aerosil nanoparticle networks. The character of the transition, which is mean field near a tricritical point in bulk, is changed dramatically with an increase of aerosil-induced disorder. X-ray measurements revealed pretransitional behavior and compression of the smectic layers, phenomena that are strongly pronounced in high aerosil concentrations. A theoretical model that takes into account the interplay of relevant mechanisms is proposed to explain the observed phenomena. The effect of chirality on the interaction of liquid crystals with aerosils is discussed.

A phenomenological theory of the isotropic to chiral smectic-C phase transition

In this paper we discuss the direct isotropic to chiral smectic-C phase transition on the basis of a phenomenological theory. The model free energy is written in terms of the coupled order parameters including the spontaneous polarization. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a direct isotropic to chiral smectic-C phase transition is possible when compared to other phase transitions. On the basis of this model the isotropic-smectic-C* transition is always of first order. The theoretical predictions are compared with the available experimental results.

Phase Transitions and Soft Elasticity of Smectic Elastomers

Smectic-C elastomers can be prepared by cross-linking, e.g., liquid crystal polymers, in the smectic-A phase followed by a cooling through the smectic-A to smectic-C phase transition. This transition from D(infinityh) to C(2h) symmetry spontaneously breaks rotational symmetry in the smectic plane as does the transition from a smectic-A to a biaxial smectic phase with D(2h) symmetry. We study these transitions and the emergent elasticity of the smectic-C and biaxial phases in three related models and show that these phases exhibit soft elasticity analogous to that of nematic elastomers.

Surface-induced molecular tilt above the smectic-A-smectic-C phase transition in a nonchiral liquid crystal.

A polyimide-coated substrate was rubbed in such a way as to possess two competing easy axes for liquid crystal alignment. On cooling a homeotropically aligned liquid crystal through the smectic-A phase toward the smectic-C phase transition, an increasing tilt of the molecules relative to the layer normal was observed. The tilt was localized to within a smectic-C correlation length of the interface, and was found to increase monotonically with the rubbing strength associated with the preparation of the polyimide surface. The results are discussed in light of the dual easy axis model [T. Shioda et al., Phys. Rev. E 67, 041706 (2003)], and suggest that the two easy axes are not mutually orthogonal.

Tilt order parameters, polarity, and inversion phenomena in smectic liquid crystals.

The order parameters for the phenomenological description of the smectic-A to smectic-C phase transition are formulated on the basis of molecular symmetry and structure. It is shown that, unless the long molecular axis is an axis of twofold or higher rotational symmetry, the ordering of the molecules in the smectic-C phase gives rise to more than one tilt order parameter and to one or more polar order parameters. The latter describe the indigenous polarity of the smectic-C phase, which is not related to molecular chirality but underlies the appearance of spontaneous polarization in chiral smectics. A phenomenological theory of the phase transition is formulated by means of a Landau expansion in two tilt order parameters (primary and secondary) and an indigenous polarity order parameter. The coupling among these order parameters determines the possibility of sign inversions in the temperature dependence of the spontaneous polarization and of the helical pitch observed experimentally for some chiral smectic-C* materials. The molecular interpretation of the inversion phenomena is examined in the light of this formulation.