Pretransitional Behavior Research Articles

Constraining late-time transitions in the dark energy equation of state

One of the most compelling goals of observational cosmology is the characterisation of the properties of the dark energy component thought to be responsible for the recent acceleration of the universe, including its possible dynamics. In this work we study phenomenological but physically motivated classes of models in which the dark energy equation of state can undergo a rapid transition at low redshifts, perhaps associated with the onset of the acceleration phase itself. Through a standard statistical analysis we have used low-redshift cosmological data, coming from Type Ia supernova and Hubble parameter measurements, to set constraints on the steepness of these possible transitions as well as on the present-day values of the dark energy equation of state and in the asymptotic past in these models. We have also studied the way in which these constraints depend on the specific parametrisation being used. Our results confirm that such late-time transitions are strongly constrained. If one demands a matter-like pre-transition behaviour, then the transition is constrained to occur at high redshifts (effectively in the matter era), while if the pre-transition equation of state is a free parameter then it is constrained to be close to that of a cosmological constant. In any case, the value of dark energy equation of state near the present day must also be very similar to that of a cosmological constant. The overall conclusion is that any significant deviations from this behaviour can only occur in the deep matter era, so there is no evidence for a transition associated with the onset of acceleration. Observational tools capable of probing the dynamics of the universe in the deep matter era are therefore particularly important.

Coupling of emergent octahedral rotations to polarization in (K,Na)NbO3 ferroelectrics

Perovskite potassium sodium niobates, K1−xNaxNbO3, are promising lead-free piezoelectrics. Their dielectric and piezoelectric characteristics peak near x = 0.5, but the reasons for such property enhancement remain unclear. We addressed this uncertainty by analyzing changes in the local and average structures across the x = 0.5 composition, which have been determined using simultaneous Reverse Monte Carlo fitting of neutron and X-ray total-scattering data, potassium EXAFS, and diffuse-scattering patterns in electron diffraction. Within the A-sites, Na cations are found to be strongly off-centered along the polar axis as a result of oversized cube-octahedral cages determined by the larger K ions. These Na displacements promote off-centering of the neighboring Nb ions, so that the Curie temperature and spontaneous polarization remain largely unchanged with increasing x, despite the shrinking octahedral volumes. The enhancement of the properties near x = 0.5 is attributed to an abrupt increase in the magnitude and probability of the short-range ordered octahedral rotations, which resembles the pre-transition behavior. These rotations reduce the bond tension around Na and effectively soften the short Na-O bond along the polar axis – an effect that is proposed to facilitate reorientation of the polarization as external electric field is applied.

Impact of ferroelectric and superparaelectric nanoparticles on phase transitions and dynamics in nematic liquid crystals.

Results of broadband dielectric spectroscopy (BDS) studies of pure liquid crystalline (4-pentyloxy-4-biphenylcarbonitryle) 5OCB and its nanocolloids with BaTiO_{3} nanoparticles (NPs) under varying pressure and temperature are presented. The notable impact of NPs on phase transitions and dynamics was found. Particularly strong impact on pretransitional behavior was observed for relatively low concentrations of NPs, which can be related to the NPs-induced disorder. There are also notable differences between pressure and temperature paths of studies for nanocomposites, absent for the pure LC compound. For instance, tests focused on the translational orientational decoupling via the fractional Debye-Stokes-Einstein relation yielded S=0.71 and S=0.3 for the temperature and pressure paths, respectively: S=1 is for the complete coupling. The possible theoretical frame of observed phenomena is also proposed.

Pretransitional behavior of the nonlinear dielectric effect for the liquid-solid transition in nitrobenzene.

The nonlinear dielectric effect describes changes of dielectric permittivity induced by the strong electric field. This report shows the evidence for the critical-like pretransitional behavior for the liquid-solid transition in the supercooled nitrobenzene. Hallmarks of such behavior extend even above the melting temperature. A method for the analysis of pretransitional effects, avoiding the biasing impact of the noncritical background contribution, is proposed.

Electro-optical Kerr effect of azo-dye-doped liquid crystals using nulled intensity method

ABSTRACTThe electro-optical Kerr effect and pre-transition behavior have been investigated for different concentration of dimethyl-aminoazobenzene dye-doped nematic liquid crystal by using the nulled intensity method. Measurement results have showed that the molecular reorientation of liquid crystals induced by photoisomerization of azo dyes come about to increase an amount of Kerr constant at low percentages of dye concentration. Additionally, the results of pre-transition temperature which were obtained by extrapolating the invers Kerr constant as a function of temperature have been found to be in good agreement with predictions of the Landau-De Gennes model.

Measurement of splay elastic constant and rotational viscosity of an induced nematic binary system

ABSTRACTWe investigated the temperature dependence of the splay elastic constant (K11) and rotational viscosity (γ1) of a binary liquid crystal system comprising 5-trans-n-butyl-2-(4-isothiocyanatophenyl)-1,3-dioxane (4DBT) and 4-cyano-4′-n-undecyloxy-biphenyl (11OCB), exhibiting induced nematic phase. Both the splay elastic constant and rotational viscosity increased following lowering of the temperature. In the vicinity of smectic A-nematic (SmA-N) transition, both the relaxation time and rotational viscosity exhibited a strong pretransitional behaviour. The critical exponent (ν) presented here led to valuable qualitative information about the pre-transitional behaviour of the rotational viscosity data near the SmA-N phase transition. The extracted ν values ranging between 0.336 and 0.352 are in fair agreement with those predicted in the de Gennes model as compared to that by the mean-field model.

Hydrogen bonding intermolecular effect on electro-optical response of doped 6PCH nematic liquid crystal with some azo dyes

Previous studies on the electro-optical responses of dye-doped liquid crystal have shown that dopant material have a considerable effect on their electro-optical responses. Despite the studies carried out on electro-optical properties of dye-doped liquid crystal, no attention has been paid to study of the interaction and structural effects in this procedure. In this paper, linear dyes and with similar structure were selected as dopants. The only difference in used dyes is the functional groups in their tails. So, doping of these dyes into liquid crystals determines the influence of interaction type on electro-optical behaviours of the doped systems. Therefore, in this work, two aminoazobenzene (“A-dye”: hydrogen bond donor) and dimethyl-aminoazobenzene (“B-dye”) dyes with different compositional percentages in liquid crystal host were used. Electro-optical Kerr behaviour, the pre-transition temperature and third order nonlinear susceptibility were investigated. The obtained results effectively revealed that type of interactions between the dye and liquid crystal is determinative of behavioral difference of doped system, compared to pure liquid crystal. Also, pre-transitional behaviour and thereupon Kerr electro-optical responses were affected by formed interactions into doped systems. In other words, it will be shown that addition of any dopants in liquid crystal, regardless of the nature of interactions, cannot cause appropriate electro-optical responses. In fact, type of dye, nature of interactions between dopant and liquid crystalline host as well as concentration of dye are the key factors in selecting the appropriate liquid crystal and dopant dye.

Impact of BaTiO(3) nanoparticles on pretransitional effects in liquid crystalline dodecylcyanobiphenyl.

The pretransitional behavior of dodecylcyanobiphenyl (12CB) (isotropic-smectic-A-solid mesomorphism) with d=50nmBaTiO(3) nanoparticles (NPs) linked to the cubic phase was monitored via temperature studies of dielectric constant. Tests were carried out in the isotropic, liquid crystal mesomorphic, and solid phases. For each phase transition the same value of the critical exponent α∼0.5 was obtained, including nanocolloids. All phase transitions show the weakly discontinuous nature. The temperature metric of the discontinuity ΔT notably decreases when adding nanoparticles. The addition of nanoparticles first decreases the dielectric constant by approximately 50% in comparison with pure 12CB, but already for a concentration ∼x=0.4% NP an increase over 50% takes place. It is notable that for the latter concentration unique hallmarks of the pretransitional effect emerge also for the solid-mesophase transition. All these indicate the important impact of nanoparticles on multimolecular mesoscale fluctuations.

Spherical microparticles with Saturn ring defects and their self-assembly across the nematic to smectic-A phase transition.

We report experimental studies on the Saturn ring defect associated with a spherical microparticle across the nematic (N) to smectic-A (SmA) phase transition. We observe that the director distortion around the microparticle changes rapidly with temperature. The equilibrium interparticle separation and the angle between two quadrupolar particles in the N phase are larger than those of the SmA phase. They are almost independent of the temperature in both phases, except for a discontinuous jump at the transition. We assembled a few particles using a laser tweezer to form a two-dimensional colloidal crystal in the N phase. The lattice structure of the crystal dissolves irreversibly across the N-SmA phase transition. The results on the pretransitional behavior of the defect are supported by the Landau-de Gennes Q-tensor modeling.

Critical behaviour of a polar-polar binary system from optical birefringence measurements

ABSTRACTHigh resolution measurements of optical birefringence (Δn) have been carried out to study the critical behaviour at the nematic-isotropic (N–I) and smectic A-nematic (SmA–N) phase transitions in a binary system composed of nonyloxycyanobiphenyl (9OCB) and heptylcyanobiphenyl (7CB). From a fitting procedure compatible with the weakly first order nature of the N–I transition, the order parameter critical exponent β at the N–I transition has been found to be in well agreement with the tricritical hypothesis. The pretransitional behaviour at the SmA–N transition has been investigated with the aid of a differential parameter extracted from Δn data and the yielded critical exponent α has been found to be non-universal in nature. A weak birefringence have been found to develop on approaching the N–I transition temperature, which is tentatively attributed to surface induced ordering. In this case, a treatment identical to that for the SmA–N transition yields a tricritical nature for the N–I transition in the investigated mixtures. Such an outcome has also appeared to be in well agreement with those obtained from the direct analysis of the Δn data (i.e. in parameterisation of β).

Topological defect transformation and structural transition of two-dimensional colloidal crystals across the nematic to smectic-A phase transition.

We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N) to smectic-A(SmA) phase transition. When approaching the SmA phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the SmA phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q-tensor modeling accounting for the increasing elastic anisotropy.

Critical behavior of optical birefringence at the nematic–smectic A phase transition in a binary liquid crystal system

We report the measurement of optical birefringence (Δn) of a binary liquid crystal system consisting of decyloxycyanobiphenyl (10OCB) and heptylcyanobiphenyl (7CB) by means of a high resolution temperature scanning technique. The birefringence data are found to be rather successful in studying the nature of the transition and the critical behavior at the nematic–smectic A (N–SmA) phase transition in these mixtures. In the vicinity of N–SmA phase transition the optical birefringence (Δn) data exhibit strong pretransitional behavior which gets enhanced as the nematic region diminishes. The critical exponent (α), when plotted against the McMillan ratio (TNA/TNI), a uniform crossover from second order to first order behavior have been observed with a tricritical point (TCP) at x10OCB=0.587. The 3D-XY limit for the N–SmA phase transition would hypothetically reach at the McMillan ratio equal to 0.937 for this binary system.

Dielectric studies and critical behaviour in the vicinity of nematic–isotropic phase transition of a smectogenic binary mixture showing induced nematic phase

The phase diagram of a binary mixture composed of compounds, one having NCS terminal group (4DBT, showing smectic A1 phase) and the other with CN terminal group (11OCB, showing smectic Ad phase), exhibiting induced nematic phase in a certain concentration range (0.100 < x4DBT < 0.951) is reported here. Results of the static dielectric parameters measurement on this binary system within the entire mesomorphic range are presented. Evidence of strong pretransitional behaviour near the nematic–isotropic (N–I) phase transition, indicating the influence of tricritical behaviour, is observed. Precise determination of discontinuity (ΔT) and the critical exponent (α) of N–I phase transition have been carried out. Moreover, the order parameter critical exponent β is correctly predicted by the tricritical hypothesis through the dielectric anisotropy data for all the investigated mixtures.

Soft memory in a ferroelectric nanoparticle-doped liquid crystal.

A small quantity of BaTiO(3) ferroelectric nanoparticles (FNP) was doped in a liquid crystal (LC), and the LC + FNP hybrid was found to exhibit a nonvolatile electromechanical memory effect in the isotropic phase. The permanent dipole moment of the FNPs causes the LC molecule to form short-range pseudonematic domains surrounding the FNPs. The FNP-induced short-range orders become more prominent in the isotropic phase when the global nematic order is absent. These short-range domains, being anisotropic in nature, interact with an external electric field, exhibiting a Fréedericksz-type transition. When the field is turned off, these domains stay oriented, showing a hysteresis effect due to the absence of any long-range order and restoring forces in the isotropic phase. The hysteresis graph for this memory effect shows a significant pretransitional behavior on approaching the nematic phase from the isotropic phase.

Critical behavior of dielectric permittivity in the vicinity of nematic–isotropic and smectic–nematic phase transitions in smectogenic binary mixtures

We report the phase diagram of a binary mixture composed of compounds, one having NCS terminal group (5DBT, showing smectic A1 phase) and the other with CN terminal group (10OCB, showing smectic Ad phase), exhibiting induced nematic phase in a certain concentration range (0.05<x5DBT<0.95). Measurement of static dielectric parameters on this binary system within the whole mesomorphic range is being reported. Pretransitional behavior at the nematic–isotropic and the smectic A–nematic phase transitions has been studied by measuring the static dielectric parameters in the entire mesomorphic range. Precise determination of discontinuity (ΔT) and the critical exponent (α) has been carried out for the nematic–isotropic phase transition. Effective molecular dipole moment and the angle of inclination with respect to the molecular long axis have been determined. High resolution density measurement is also carried out for one concentration x5DBT=0.301 and from the molar volume so obtained, the discontinuity (ΔT) of the transition and the critical exponent are measured. Additionally, the nature of the N–SmA phase transition has been studied for a few mixtures from dielectric anisotropy measurements to explore the critical behavior of the N–SmA phase transition.

Generalized Langevin-Debye model of the field dependence of tilt, birefringence, and polarization current near the de Vries smectic-A*to smectic-C*liquid crystal phase transition

In chiral smectic-A (Sm-A) liquid crystals, an applied electric field induces a tilt of the optic axis from the layer normal. When these materials are of the de Vries type, the electroclinic tilt susceptibility is unusually large, with the field-induced director reorientation accompanied by a substantial increase in optical birefringence with essentially no change in the smectic layer spacing. In order to account for the observed electro-optic behavior, we assume that the molecular orientation distribution in the Sm-A has two degrees of freedom: azimuthal orientation and tilt of the molecular long axis from the layer normal, with the tilt confined to a narrow range of angles. We present a generalized Langevin-Debye model of the response of this orientational distribution to applied field that gives a field-induced optic axis tilt, birefringence, and polarization dependence that agrees well with experimental measurements and reproduces the double-peaked polarization current response characteristic of a first-order Sm-A(*)-Sm-C(*) transition. Additionally, we find that the measured field-induced polarization and the Langevin-Debye model predictions can be quantitatively described as pre-transitional behavior near the tricritical point of a recently published generalized 3D XY model of interacting hard rods confined to reorient on a cone in the presence of an applied field.

Distortion-sensitive insight into the pretransitional behavior of 4-n-octyloxy-4′-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4′-cyanobiphenyl (8OCB) with isotropic (I)–nematic (N)–smectic A (SmA)–crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I–N and N–SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid–fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τc(T−TC)−ϕ. In the immediate vicinity of the I–N transition a novel anomaly has been found: Δτ ∝ 1/(T − T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the ‘background behavior’. Experimental results are confronted with the comprehensive Landau–de Gennes theory based modeling.

Anomaly of Pretransitional Behavior at the Nematic–Smectic-A Phase Transition of Amphiphilic Liquid Crystals with a Hydrophilic Group

In order to clarify the origin of the X-ray diffraction peak corresponding to the smectic-like layer ordering appearing even in the nematic phase over a wide temperature range above the nematic-smectic A (NA) phase transition in liquid crystal (LC) molecules with a hydroxy group, we investigated the critical behavior of bend elastic constants and the correlation length of the smectic-like ordering in the N phase. It is found that cybotactic clusters with the transient layer ordering grow up extremely even far above the NA phase transition, and the critical exponent of the correlation length of the cybotactic clusters is estimated anomalously larger than that of conventional LC materials. Furthermore, we measured diffusion constants parallel and perpendicular to the director in the N phase, and concluded that cybotactic clusters with the smectic layer ordering create a finite potential barrier to prevent diffusion of the molecules parallel to the director as well as the true smectic A layer structure.

Aggregation, pretransitional behavior, and optical properties in the isotropic phase of lyotropic chromonic liquid crystals studied in high magnetic fields

We report results on the high-field magneto-optical response of four aqueous, lyotropic, chromonic liquid crystal formulations in the isotropic phase. Measurements of the field-induced birefringence at temperatures above the isotropic-nematic coexistence region at high magnetic fields reveal qualitative differences in different materials; these differences can be attributed to the nature of aggregation and are discussed within the context of competing aggregation models. Extending these measurements to very high fields and large optical phase differences reveals the presence of an unexpected optical phenomenon: magnetic field-induced circular birefringence, measured in the Voigt geometry, in a system containing no molecularly chiral species. Possible origins of this effect are discussed.

Dielectric pre-transitional behavior in the vicinity of isotropic–blue phase III transition

Pre-transitional effects have been observed from the study of static dielectric permittivity () and its temperature derivatives () near the isotropic to blue phase-III (I–BPIII) transition in a highly polar T-shaped liquid crystalline material having a stable BPIII phase which persists over a comparatively wide range of temperature (∼8°C). The pre-transitional behavior near I–BPIII transition is found to be very similar to that observed in isotropic–nematic (I–N) transition. Landau–de Genes and Maier–Saupe approaches, used earlier to describe anomalous behavior of εS near the I–N transition, have been implemented to investigate the present pre-transitional behavior near the I–BPIII transition. The value of critical exponent (α) for the I–BPIII transition is found to be close to that of the reported I–N transition. Temperature-dependent behavior of and have also been interpreted in terms of field-induced increments of basic thermodynamic quantities, namely internal energy, entropy, and Helmholtz free energy.