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Nature of the smectic- A 2 –smectic- C 2 transition: A calorimetric study
Abstract
The first high-resolution specific-heat measurement on octylphenyl-2-chloro-4-(p-cyano benzoyloxy) benzoate (DB8ClCN) is reported. At 390.2 K, the material undergoes a second-order phase transition from a bilayer smectic-A phase (Sm-A2) to a bilayer smectic-C phase (Sm-C2). On cooling, the specific heat of DB8ClCN is independent of temperature in the Sm-A2 phase and increases at Tc in a steplike fashion. In the Sm-C2 phase, the specific heat again becomes temperature independent. This is in striking contrast to previously reported Sm-A-Sm-C transition data, all of which conform to a Landau model with an unusually large sixth-order term.
... It is well known that pure substances, such as helium, glass, polymers and liquid crystals, show behaviour other than a first-order transition in their phase changes at constant pressure [7]. In the case of liquid crystals this situation usually occurs at the SmA-SmC phase transition, where second order-like is the most observed case, a situation well described by several authors [8,9]. The phase transition from SmA to SmC is related to the tilt angle of the mesophase and to how this order parameter is slightly (second order-like) or abruptly (first order) modified as the temperature decreases. ...
The synthesis and phase characterization of two liquid crystalline methacrylic monomers based on the -hexyloxysalicylaldimine group with octyl and decyloxy chain substitutions is presented. The liquid crystalline materials were characterized by polarizing optical microscopy, differential thermal analysis and X-ray diffractometry. Nematic and tilted smectic C phases were observed in the compounds. Their liquid crystalline properties where compared with previously studied samples of homologous compounds. In contrast to previous results, this structural modification induces pronounced enantiotropic first-order phase transitions between nematic and smectic C mesophases. A correlation between the phase transition behaviour and structural features of the sample is included.
IntroductionExperimental Methods and Typical ResultsDensityMetabolemeterHigh Pressure InvestigationsFluctuations and Liquid Crystal Phase TransitionsRe-entrant Phase Transitions in Liquid Crystals
IntroductionExperimental Methods and Typical ResultsDensityMetabolemeterHigh Pressure InvestigationsFluctuations and Liquid Crystal Phase TransitionsRe-entrant Phase Transitions in Liquid Crystals
Summary This document is part of Subvolume A of Volume 5 ‘Physical Properties of Liquid Crystals’ of Landolt-Börnstein - Group VIII Advanced Materials and Technologies.
Summary This document is part of Subvolume A of Volume 5 ‘Physical Properties of Liquid Crystals’ of Landolt-Börnstein - Group VIII Advanced Materials and Technologies.
Liquid crystal molecules with long aromatic cores and polar head groups are characterized by competition between two order parameters with incommensurate natural wave vectors. As a result, a rich variety of polymorphic smectic-A (and also smectic-C) phases are observed. Such polymorphism in “frustrated” smectic liquid crystals was first discovered experimentally [1] and discussed theoretically [2] in 1979 by the Bordeaux liquid crystal group. By 1983, this group, in collaboration with A. M. Levelut, had characterized the structures, determined the phase diagrams, and explored some of the physical properties of a large variety of these new thermotropic liquid crystal compounds [3-5].
Liquid crystals exhibit a rich variety of second-order phase transitions and multicritical points. In order to characterize fully the nature of the critical fluctuations at such transitions, it is necessary to employ a variety of experimental techniques. Among these are high-resolution calorimetric methods, which provide direct information about the energy fluctuations. Such heat capacity data in combination with scattering results can establish the universality class of a given transition and test various theories of liquid crystal behavior.
Summary This document is part of Subvolume A of Volume 5 ‘Physical Properties of Liquid Crystals’ of Landolt-Börnstein - Group VIII Advanced Materials and Technologies.
IntroductionThe Early Years up to About 1925The Second Phase from 1925 to 1959The Third Phase from 1960 to the Present TimeConclusions
References
We present a NMR study of the molecular order in a compound presenting three bilayer smectic mesophases: SA2: SC2 and SC? anticlinic-like). Two different models are proposed for the interpretation of the angular dependence of experimental dipolar splittings observed for the Sc2 and SC?, respectively. The results presented here are in agreement with the model initially proposed in the literature for the SC? mesophase. In particular we present here the estimation of the two tilt angles associated with the structure of the SC? phase.
The smectic A-smectic C (A-C) transition in several compounds has been shown to be mean-field-like (MF) with a substantial tricritical crossover effect. However, a simple MF behaviour, i.e., with negligible tricritical influence, had not been reported till recently. The heat capacity measurements of the MIT group in two compounds exhibiting the bilayer A2−C2 transition revealed such a behaviour. It is of interest to investigate whether a simple MF behaviour can be observed for partially bilayer Ad−Cd and monolayer A−C1 transitions also. We report the first systematic order parameter measurements in the vicinity of the A2−C2, Ad−Cd and A1−C1 transitions. The data analysed in terms of power law and extended mean field expressions provide clear evidence of a simple MF behaviour in all three cases. The significance of this result is discussed.
A proton nuclear magnetic resonance (NMR) relaxation study of molecular dynamics in the liquid crystal 4-octylphenyl 2-chloro-4-(4-cyanobenzoyloxy)benzoate (DB8Cl) is presented. DB8Cl molecules possess a strong polar terminal group and form, in addition to the nematic phase, three different smectic phases: bilayer smectic A, bilayer smectic C, and anticliniclike smectic C phase. The proton spin-lattice relaxation times were measured in all mesophases over a broad frequency range of six decades by applying conventional and fast field-cycling NMR techniques. The parameters obtained in the analysis of the experimental data give quantitative information on molecular motions, particularly for the tilted smectic phases of DB8Cl. In contrast to former conjectures, we found that the low-frequency relaxation in the bilayer smectic C phases results from director fluctuations about the layer normal, which occur without distortion of the layers, and from layer undulations, similar to those in the smectic A phase. In the low-temperature bilayer smectic C phase, a considerable slowing-down of molecular translational diffusion is observed. It confirms indirectly the anticlinic character of this mesophase. Measurements of angular dependence of the relaxation times at 60 MHz support the conclusions obtained from the frequency dispersion data.
High-resolution x-ray diffraction studies have been performed on the polar liquid-crystal binary mixture of octyl- and decyl-oxyphenyl nitrobenxoyloxy benzoate (47.4 mole% DB8ONO2 + 52.6% DB10ONO2). At temperatures below 127 °C this mixture exhibits the phase sequence (with decreasing temperature) smectic-Ad—reentrant nematic Nd—reentrant nematic N1—smectic-A1—tilted smectic antiphase smectic- [Ctilde] -smectic-A2—smectic-C2. The development of lateral fluid antiphase fluctuations from the partial bilayer fluctuations in the smectic-A1 phase have been probed and analyzed as well as the transition from the tilted smectic antiphase to the tilted bilayer smectic-C2 phase that is accompanied by the occurrence of an intermediate smectic-A2 phase.
The phase diagram has been established for binary mixtures of nonyloxy-biphenyl cyanobenzoate (9OBCB) and pentylphenylcyanobenzoyloxy benzoate (DB5CN). These frustrated liquid crystals exhibit a rich variety of polymorphic smectic A (SA) and smectic C (SC) phases. X-ray and calorimetric studies have been made of SAd-S[Ctilde]-SC2 and SAd-SA1-S[Ctilde]-SA2SC2 phase sequences. Major emphasis is given to the tilted ribbon smectic (S[Ctilde])-bilayer smectic A (SA2) transition and the SA2-SC2 transition. The former is first order, but there is substantial pretransitional heat capacity in the S[Ctilde] phase that can be described by an inverted Landau model. The latter transition is second order and exhibits a classical Landau step in C p, in contrast to the behaviour of SA-SC transitions in non-polar systems where an extended Landau model with a large sixth order term is required.
In this work we present a proton NMR comparative study of the molecular order in the smectic C2 (), smectic C^* () and anticlinic smectic C phases ( and ) of two liquid crystalline compounds. The second moments of the experimental proton NMR spectra are well explained taking
into account two different molecular orientations models. From the analysis of our experimental results it was possible to
estimate the tilt angles for all the smectic C phases studied in this work.
Binary mixtures of octyloxyphenyl-nitrobenzoyloxy benzoate (DB8ONO2) and decycloxyphenyl-nitrobenzoyloxy benzoate (DB10ONO2) exhibit a rich variety of smectic polymorphism. An ac calorimetric study has been carried out on six mixtures with mole percent X of the decyl homolog between 51 and 57, a range that includes the Sm-Ad-Nr-Sm-A1 point at X~=56. The sample with X=57 exhibits a first-order direct Sm-Ad-Sm-A1 transition, while the sample with X=51.3 exhibits two transitions-a second-order Sm-Ad-Nr transition with a very small excess heat-capacity peak and a tricritical Nr-Sm-A1 transition with a large heat-capacity peak. For samples with intermediate compositions, only weakly first-order Nr-Sm-A1 heat-capacity peaks are observed in the vicinity of the Sm-Ad-Nr-Sm-A1 point. All six investigated samples exhibit the Sm-A1-Sm-C~-Sm-C2 phase sequence at lower temperatures. The Sm-A1-Sm-C~ transition is a weakly first-order phase transition with pretransitional excess heat capacity below the transition temperature. In contrast, the Sm-C~-Sm-C2 transition is a weakly first-order inverted Landau transition with no pretransitional behavior in the Sm-C2 phase below the transition but a large mean-field excess heat capacity observed in the Sm-C~ phase above the transition.
A calorimetric characterization of a second-order nematic (N)-smectic-A2 (Sm-A2) transition and a detailed heat-capacity study of a Sm-A2-Sm-C2 (smectic-C2) transition have been carried out on 4'-n-heptyloxy-carbonylphenyl-4'-(4''-cyanobenzoyloxy) benzoate (7APCBB). The N-Sm-A2 heat capacity is well described by the three-dimensional XY model with critical exponent alpha=-0.007 and amplitude ratio A-/A+=0.98. The excess heat capacity DeltaCp associated with the Sm-A2-Sm-C2 transition increases in a steplike fashion from zero in the Sm-A2 phase to a constant value in the Sm-C2 phase. This behavior agrees with that observed previously in octylphenyl-2-chloro-4-(p-cyanobenzoyloxy) benzoate (DB8ClCN). In both cases, the Sm-A2-Sm-C2 behavior is markedly different from the Cp behavior at Sm-A-Sm-C transitions in nonpolar systems, all of which conform to a Landau model with a large sixth-order term.
In a substance with a substituted chlorine on the central ring of an alkylphenyl cyanobenzoyloxybenzoate we obtain evidence in a biaxial fluid medium for anomalies of periodicity similar to those initially found in the nematic and smectic A phases of the unsubstituted series (« DBn »). From X-ray studies, microscopic observations, D.S.C. recordings and magnetic measurements, a new mesomorphic nematic-smectic A2-smectic C2-smectic? sequence is reported. In the three smectic modifications there is a liquid-like order within the layers (even at short-range) and the layer thickness is close to two molecular lengths. The lowest temperature smectic phase seems to be a new lamellar structure with well defined layers. La substitution d'un chlore sur le noyau central d'un cyanobenzoyloxybenzoate d'alkylphényle offre un matériau qui permet de généraliser aux milieux fluides biaxes les anomalies de périodicité rencontrées initialement dans les phases nématique et smectique A de la série non substituée (« DB n »). En effet par analyse structurale RX, observations microscopiques, analyse enthalpique différentielle et mesures magnétiques, nous révélons une nouvelle séquence mésomorphe nématique-smectique A2-smectique C2-smectique ?. Dans les trois phases smectiques les couches sont liquides (même à courte portée) avec une période de modulation proche de deux fois la longueur moléculaire. La phase smectique basse température apparaît comme une nouvelle structure lamellaire avec des couches bien séparées.
The first observation of a smectic-A phase with two collinear incommensurate density modulations is reported. X-ray diffraction studies of this incommensurate phase reveal reflections corresponding to both partially bilayer (Ad) and bilayer (A2) periodicities, the relative intensities of the two reflections being strongly temperature dependent.
We have carried out a detailed study of the smectic-A-smectic-C transition in butyloxybenzylidene heptylaniline (40.7) using high-resolution x-ray, heat-capacity, and light scattering techniques. Although the order-parameter data are consistent with heliumlike critical behavior, the data as a whole are uniquely described by a mean-field Landau model with an anomalously large sixth-order term.
The smectic state has been known for over a century but is currently being very actively investigated. We review the polymorphism associated with one-dimensional ordering, critical phenomena characteristic of the several phase transitions encountered in these systems, together with their very special dynamical properties.
Alternating current microcalorimetry was used to measure the specific heat of 4-n-pentylphenylthiol-4′-n-octyloxybenzoate in the nematic, smectic-A, and smectic-C phases. Critical exponents were found to be consistent with the superfluid analogy of de Gennes for the nematic to smectic-A transition, i.e., α=α′=0 (logarithmic divergence). For the smectic-C to smectic-A transition, the data were consistent with α′=-0.54 and inconsistent with the superfluid analogy.
We report measurements of the tilt angle Φ and the planar spacing dC near the second-order SmC-SmA transition in 4-n-pentyl-phenylthiol-4′-n-octyloxybenzoate (8S̅ 5). We find that the ratio Φ/invcos(dC/dA) is constant (1.2 ± 0.1) through the C phase, supporting a simple molecular-tilt model for the transition. For 5×10-3>1-T/Tc>3×10-5, Φ exhibits mean-field behavior. A simple Ginzburg-criterion argument indicates that the true critical region should be unobservably small for most A-C transitions.
High-resolution ac calorimetric measurements have been made on azoxy-4,4′-di-undecyl-α-methylcinnamate (AMC-11), butyloxybenzylidene heptylaniline (4O.7), heptyloxybenzylidene hexylaniline (7O.6), and heptyloxybenzylidene butylaniline (7O.4). The heat capacity CP exhibits a sharp, asymmetric peak near the second-order smectic-A—smectic-C transition. The CP values increase in the smectic-C phase as the transition temperature Tc is approached and then decrease abruptly at Tc. These data are well described by a mean-field Landau model and are not consistent with the heliumlike critical behavior expected from the de Gennes model. It is also shown that it is very difficult to distinguish between meanfield and XY critical behavior on the basis of data obtained only in the smectic-C phase.
An ac calorimetric technique has been used to study the nematic—smectic-A (N-SmA) and nematic-isotropic (N-I) transitions in octyloxycyanobiphenyl (8OCB) along a series of isobars between 1 atm and 2 kbar. The excess heat capacity ΔCp(NA) associated with the essentially second-order N-SmA transition is found to diminish rapidly with pressure and is not observed for p>1.5 kbar. The variation in ΔCp(NA) with reduced temperature is not consistent with a logarithmic singularity but can be characterized by a critical exponent α=α′=0.25±0.05 for all the pressures studied. The excess heat capacity at the N-I transition is almost independent of pressure; these data suggest but do not clearly establish quasitricritical behavior. Details of the experimental method and the fitting procedures are given.
Experimentally we present high-resolution ac calorimetry measurements on a liquid-crystal compound exhibiting a smectic-A—smectic-C (SmA-SmC) phase transition which is shown to be mean-field-like. In the light of this experimental result, a simple and convincing argument, based on the mean-field theory, is given to explain why non-mean-field critical exponents were obtained in many of the studies on the SmA-SmC transition. The theory not only gives an excellent fit to our data for temperatures below the transition temperature but also provides a qualitative prediction on the size of the deviation from the linear relationship between (Tc-T) and the square of the order parameter. The predicted deviation is consistent with x-ray measurements on the order parameter of another liquid-crystal compound.
We report measurements of the tilt angle ψ near the second-order
SmA-SmC transition in azoxy-4,4'-di-undecyl-α-methylcinnamate.
Data analysis shows that this transition, which belongs to the same
universality class as 4He, has, in the absence of a
constraining field, a critical exponent β=0.36+/-0.005.
We discuss the nature of the order in the main smectic phases (A, C, and B) together with the related phase transitions. (1) The B phase may correspond to a plastic crystal, or to a system of weakly coupled solid layers: to discriminate between these two models, acoustical studies using shear waves appear to be most promising, (2) the transitions A ⟷ N, C ⟷ N, C ⟷ A (where N stands for nematic) may be of second order in certain cases, which will allow for a number of interesting experiments. The C ⟷ A transition should be very similar to the λ transition of helium, and some critical exponents which are not accessible in helium could be measured here. The N ⟷ A transition is similar to the onset of superconductivity in a metal. A bend (or twist) deformation tends to suppress the A phase just as a magnetic field destroys superconductivity. In the N phase the twist and bend elastic constants should show pretransitional anomalies. The C ⟷ N transition is more complex. A tentative calculation suggests that here all three elastic constants should show pretransitional anomalies.
We present dielectric measurements of the « DB8Cl » cyano compound which exhibits a Smectic A2 → Smectic C2 → Smectic ? sequence of bilayered fluid smectic phases. In particular a new perpendicular relaxation is observed in the S? which we interpret as indicative of a dipole ordering. A simplified model taking this result into account is proposed. Nous présentons des mesures diélectriques effectuées sur le composé cyané « DB8Cl » qui présente la séquence de phases smectiques fluides bicouches : Smectique A2 → Smectique C2 → Smectique ?. Nous observons en particulier une nouvelle relaxation perpendiculaire en phase S?, qui vraisemblablement traduit un ordre de dipôles. Un modèle simplifié rendant compte de ce résultat est proposé.