Phase diagram of transitions from an isotropic phase to nematic and smectic (uniaxial,biaxial) phases in liquid crystals with achiral molecules

The phase diagrams of transitions from an isotropic phase to nematic and smectic phases are investigated within a simple phenomenological model of the Landau thermodynamic potential. The conditions of the isomorphic phase transition between two uniaxial smectic phases and the direct transition from the isotropic phase to the uniaxial and biaxial smectic phases are determined. The behavior of the order parameters is described along different thermodynamic paths. The theoretical results are discussed using the example of liquid-crystal phases in compounds with banana-shaped achiral molecules.     

Spin nematic and antinematic states in a spin-3/2 isotropic non-Heisenberg magnet

The ground state phase diagram of a general isotropic spin-3/2 system with nearest-neighbor exchange is shown to contain unconventionally ordered spin nematic and antinematic states, as well as usual ferro- and antiferromagnetic phases. The two nematic phases have spontaneously broken rotational symmetry characterized by the long-range order of the nematic director u, as well as the broken time-reversal symmetry described by the pseudospin vector σ. Nematic phase differs from antinematic one by the type of ordering in σ vectors (uniform versus staggered). The ferromagnet-nematic and antiferromagnet-antinematic phase boundaries exhibit enhanced Sp(4) symmetry and correspond to the recently studied effective theory for spin-3/2 cold gases. We discuss optical properties and topological defects in the nematic phases.     

Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

We have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.     

Melting of lamellar phases in temperature sensitive colloid-polymer suspensions

We prepare a novel suspension composed of rodlike fd virus and thermosensitive polymer poly(N-isopropylacrylamide) whose phase diagram is temperature and concentration dependent. The system exhibits a rich variety of stable and metastable phases, and provides a unique opportunity to directly observe melting of lamellar phases and single lamellae. Typically, lamellar phases swell with increasing temperature before melting into the nematic phase. The highly swollen lamellae can be superheated as a result of topological nucleation barriers that slow the formation of the nematic phase.     

Kinetics of the isotropic–nematic phase transition in melted multi-component liquid crystal mixtures upon cooling

The kinetics of the phase separation and the nematic phase growth in two melted commercial multi-component liquid crystal mixtures upon cooling was studied using polarising optical microscopy and IR spectrometry. The droplets of the nematic phase revealed in the optical images across the phase transition were segmented and treated statistically. In the resulting size histograms of mixture B, two overlapping statistical ensembles related to two co-existing nematic phases were recognised; these phases were shown to be different in their chemical structures. In mixture A, any separation within the nematic phase was not found. The statistical ensembles of the nematic droplets were successfully described using the principles of irreversible thermodynamics. Analysis of the mean droplet diameter as a function of time allowed recognition of two regimes of the nematic phase evolution: (1) nucleation and rapid nucleus growth and (2) nucleus coalescence. Both the regimes were quantitatively described with the universal law for the cluster growth.     

Nematic-crystal transitions in liquid crystals

A lattice theory of phase transitions in a system of rod-like molecules is presented with application to liquid crystals. The first order transitions between nematic and crystal phases as well as between isotropic and nematic phases are obtained.     

Phase transitions in lyotropic nematic gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur. Received 15 February 2002 and Received in final form 14 June 2002     

Uniaxial and biaxial spin nematic phases induced by quantum fluctuations

It is shown that zero point quantum fluctuations completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin-2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry Dih4. There is a novel first-order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of 87Rb atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.     

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Electro-optical Kerr effect in the isotropic phase of the two antiferroelectric liquid crystal mixtures

We have experimentally studied for the first time the electro-optical Kerr effect and the pre-transitional behavior in the isotropic phase of two antiferroelectric liquid crystal mixtures, W-232 and W-204D, composed of rod-like ester molecules exhibiting the direct smectic-A to isotropic (SmA-I) phase transition. The Kerr law has been confirmed for the two compounds and the variation of inverse Kerr constant with temperature above the smectic–isotropic transition temperatures were determined. Both the mixtures with very broad antiferroelectric phase around room temperature have similar sequence of the phases (i.e., Cr-SmC*A-SmC*-SmA-I). Although, the pre-transitional behavior is usually complex in the isotropic phase of the chiral smectic liquid crystal compounds, the investigated compounds showed a similar behavior compared to that of nematic–isotropic behavior.     

Refusing to twist: demonstration of a line hexatic phase in DNA liquid crystals

We report conclusive high resolution small angle x-ray scattering evidence that long DNA fragments form an untwisted line hexatic phase between the cholesteric and the crystalline phases. The line hexatic phase is a liquid-crystalline phase with long-range hexagonal bond-orientational order, long-range nematic order, but liquidlike, i.e., short-range, positional order. So far, it has not been seen in any other three dimensional system. By line-shape analysis of x-ray scattering data we found that positional order decreases when the line hexatic phase is compressed. We suggest that such anomalous behavior is a result of the chiral nature of DNA molecules.     

Pretransitional dielectric properties of nematogenic 4-cyanophenyl-4′-n-heptylbenzoate

This article presents results of the static and dynamic dielectric studies performed for mesogenic 4-cyanophenyl-4′-n-heptylbenzoate in the isotropic (I) and nematic (N) phases. Pretransitional phenomena are observed in the vicinity of I–N phase transition as an anomalous temperature behavior of both the static and the dynamic dielectric properties of the compound. The temperature dependence of the static permittivity is correlated with the entropy change induced by the probing electric field while an anomalous behavior of the dielectric relaxation directly points out for a subdiffusional Brownian rotation of mesogenic molecules in the vicinity of the phase transition.     

Synthesis and characterization of wide range mesogenic esters based on asymmetrical 2,5-disubstituted 1,3,4-thiadiazole

A homologous series of new 13 esters, 4-(5-(p-tolyl)-1,3,4-thiadiazol-2-yl)-phenyl-4-alkoxybenzoate, (IV_n), based on 1,3,4-thiadiazole core has been synthesized. The structures of these esters were confirmed by Fourier transform infrared spectroscopy, proton nuclear magnetic resonance and mass techniques. Their mesophases behavior was investigated with hot-stage polarizing optical microscope and differential scanning calorimetry. The thermal stability for most of these derivatives was measured by thermal gravimetric analysis. All the target esters showed enantiotropic mesomorphic behaviors with nematic and nematic/smectic C phases. The phase transition temperatures and liquid crystalline properties were affected by the nature of heterocyclic ring and the length of the alkoxy chain. Only the nematic phase was observed in the first 10 derivatives, (n = 1–10), while the last 3, (n = 12, 16 and 18) showed nematic and smectic C phases. These compounds demonstrated high liquid crystalline ranges, both in heating and cooling cycles. The mesomorphic results obtained were compared with the reported analogs of similar constituents.     

Reexamining the phase diagram of the Gay—Berne fluid

This work reexamines and updates earlier investigations on the phase behaviour of the Gay-Berne liquid crystal model, concentrating on the effect of varying temperature. Constant volume and constant pressure Monte Carlo simulations are combined for systems consisting of N = 500 molecules along different isotherms over the reduced temperature range 0.60 ≤ T ≤ 1.25. As in previous simulation studies of the model, the study identifies nematic and smectic B phases on compressing the isotropic fluid, the particular phase sequence depending on temperature. The nematic phase is found to be stable with respect to the isotropic phase for reduced temperatures T ≥ 0.75. In the temperature range 0.75 ≤ T ≤ 1.25, the phase boundaries of the isotropic-nematic transition are obtained by computing the Helmholtz free energy of both phases from thermodynamic integration. From the simulation data, the relative volume change at the isotropic-nematic transition is about 2%, and this value appears to be rather insensitive to changes in temperature. On compressing the nematic phase, the Gay-Berne fluid undergoes a strong first-order transition to the smectic B phase. This transition is studied by using constant pressure simulation, and the coexistence properties are estimated from the limits of mechanical stability of the nematic phase. Larger relative volume changes are found at the transition than those suggested by previous studies, with typical values increasing up to 10.5% as the temperature is decreased. The results are consistent with the existence of strong coupling between nematic and smectic order parameters. For temperatures T ≤ 0.70 the nematic phase is no longer stable, and the phase sequence isotropic-smectic B is observed. Therefore, the Gay-Berne model exhibits an isotropic-nematic-smectic B triple point. Extrapolating the present simulation data, this triple point is located approximately at reduced temperature T_INB ? 0.70 and reduced pressure P_INB ? 1.825.     

Lamellar phase of stacked two-dimensional rafts of actin filaments

We examined liquid crystalline phases of the cytoskeletal polyelectrolyte filamentous (F-)actin in the presence of multivalent counterions. As a function of increasing ion concentration, the F-actin rods in either an isotropic or a nematic phase will transform into a new and unexpected lamellar phase of cross-linked rafts (L(XR) phase), before condensing into a bundled phase of parallel, close-packed rods. This behavior is generic for alkali earth divalent ions Mg2+, Ca2+, Sr2+, and Ba2+, and the structural transitions are achieved without any architecture-specific actin-binding linker proteins.     

Theory of microphase separation on side-chain liquid-crystalline polymers with flexible spacers

We model a melt of monodisperse side-chain liquid-crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded-volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free-energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases or phases with modulated wave vector but without nematic ordering. Such microphases are the result of the competition between the incompatibility among the blocks and the connectivity constraints imposed by the spacer and the backbone. Also the effects of the polymerization degree and structural conformation of the monomeric units on the phase behavior of the side-chain liquid-crystalline polymers are studied.     

A generic equation of state for liquid crystalline phases of hard-oblate particles

A generic equation of state (EoS) is developed for the hard cylindrical disc model to describe the isotropic phase of hard cut-sphere particles introducing a correction parameter to incorporate the negative contributions from higher-order virial coefficients. The isotropic–nematic–columnar phase diagram of hard cut-sphere fluids is investigated combining the new EoS with a scaled Onsager free energy for the nematic phase and an extended cell theory for columnar phase. By mapping the virial coefficients of an oblate spherocylinder on to those of the cylindrical disc (which are known algebraically), the new generic EoS is used to describe the isotropic and nematic phases of hard oblate spherocylinder particles. The predictions of the generic EoS are compared with available simulation data.     

Orientational order parameter studies in two symmetric dimeric liquid crystals – an optical study

The optical technique developed by [W. Kuczynski, B. Zywucki, and J. Malecki, Determination of orientational order parameter in various liquid-crystalline phases, Mol. Cryst. Liq. Cryst. 381 (2002), pp. 1–19; B.J. Zywucki and W. Kuczynski, IEEE transactions on optical phenomena – The orientational order in nematic liquid crystals from birefringence measurements, Dielectr. Electr. Insul. 8 (2001), pp. 512–515] is fabricated and used to determine the orientational order parameter in two dimeric liquid crystalline compounds nematic and SmA phases of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) homologous series. The compounds studied are 5.O8O.5 and 5.O10O.5 which exhibit nematic and SmA, and nematic phases, respectively. The orientational order parameter in both the phases of nematic and SmA phases of the compound one and the nematic phase of the compound two are obtained using the principle of Newton's rings which gives directly the birefringence, δn of the liquid crystal dimer. The merits of the technique used are presented over the conventional techniques for the determination of orientational order parameter. The results for the two compounds are compared with those values estimated from n _e, n _o and density using the two internal field models due to Vuks and Neugebauer applicable to nematic phase.     

Tetrahedral Order in Liquid Crystals

We review the impact of tetrahedral order on the macroscopic dynamics of bent-core liquid crystals. We discuss tetrahedral order comparing with other types of orientational order, like nematic, polar nematic, polar smectic, and active polar order. In particular, we present hydrodynamic equations for phases, where only tetrahedral order exists or tetrahedral order is combined with nematic order. Among the latter, we discriminate between three cases, where the nematic director (a) orients along a fourfold, (b) along a threefold symmetry axis of the tetrahedral structure, or (c) is homogeneously uncorrelated with the tetrahedron. For the optically isotropic T_d phase, which only has tetrahedral order, we focus on the coupling of flow with, e.g., temperature gradients and on the specific orientation behavior in external electric fields. For the transition to the nematic phase, electric fields lead to a temperature shift that is linear in the field strength. Electric fields induce nematic order, again linear in the field strength. If strong enough, electric fields can change the tetrahedral structure and symmetry leading to a polar phase. We briefly deal with the T phase that arises when tetrahedral order occurs in a system of chiral molecules. To case (a), defined above, belong (i) the non-polar, achiral, optically uniaxial D2d phase with ambidextrous helicity (due to a linear gradient free energy contribution) and with orientational frustration in external fields, (ii) the non-polar tetragonal S4 phase, (iii) the non-polar, orthorhombic D2 phase that is structurally chiral featuring ambidextrous chirality, (iv) the polar orthorhombic C2v phase, and (v) the polar, structurally chiral, monoclinic C2 phase. Case (b) results in a trigonal C3v phase that behaves like a biaxial polar nematic phase. An example for case (c) is a splay bend phase, where the ground state is inhomogeneous due to a linear gradient free energy contribution. Finally, we discuss some experiments that show typical effects related to the existence of tetrahedral order. A summary and perspective is given.