Phase separation and gelation of polymer-dispersed liquid crystals

Polymerization-induced phase separation in polymer-dispersed liquid crystal is studied by computer simulations in two dimensions. The domain morphology resulting from phase separation is investigated by solving the coupled set of equations for the local volume fraction and the nematic order parameter, taking into account the viscoelastic effects and gelation due to polymerization. Comparing the morphology of phase separation by temperature quench, it is shown that the viscoelastic effects and gelation enable the polymer-rich phase to form a stable interconnected domain even when the polymer component is minority. The experimental evidence consistent with this characteristic feature is also given.     

Nucleus growth in liquid crystals

The phase ordering kinetics of various liquid crystalline materials from well known series (PCH, CCH, nO. m, BCH and CB) when turning from a disordered to an ordered phase induced by a rapid temperature quench have been investigated. The process of phase ordering can generally be described by the growth of a characteristic length L. The exponents n of the theoretically predicted universal growth law L (t) tn have been determined. In this paper we present in particular the results for the kinetics of phase formation which takes place under the mechanism of nucleus growth. As characteristic length we chose the diameter of the nuclei. We obtained values for n between 0.5 and 1 dependent on the depth of the temperature quench. These results for mainly spherical shaped nematic and smectic germs are discussed in terms of the Allen-Cahn theory for the movement of an antiphase boundary (APB). As a lower limiting value, 0.5 confirms the classical theory, while 1 as an upper limiting value can be explained by the introduction of a volume driving force.     

Kinetics of the nematic ordered phase growth during a temperature quench of an isotropic siloxane-azomethine polymer

Kinetics of the nucleus growth during a deep temperature quench across the isotropic to nematic phase transition was experimentally investigated for a siloxane-azomethine polyether at cooling rates of 10 and 20°C min^-1. Nematic droplets revealed in the optical images during the phase separation were treated statistically and the resulting statistical size distributions were described using the model of reversible aggregation. Analysis of the time-dependent distribution parameters allowed two processes involved in liquid crystal phase ordering to be identified: nucleus growth and nucleus coarsening. Both regimes are quantitatively described using the universal growth law.     

Nematic to smectic-A phase transition in mixture of liquid crystal and nonmesogenic impurities: existence of tricritical point

Experiments on the mixture of liquid crystals and nonmesogenic impurities showed the significant role of nonmesogenic impurities on the nematic–smectic-A phase transition. Using both Flory–Huggins theory of isotropic mixing and Landau–de Gennes theory, we present a phenomenological theory that discusses the role of such impurities on the nematic–smectic-A phase transition in a mixture of smectic liquid crystal and nonmesogenic impurities. We discuss the impact of nonmesogenic impurities on the order parameters, Frank elastic constants (splay and bend) and transition temperature of the nematic–smectic-A phase transition. Our theoretical results show that there exists a tricritical point for which the second-order nematic–smectic-A phase transition becomes first order at a tricritical point by increasing the concentration of nonmesogenic solute. We find a remarkable agreement between theoretical and experimental results.     

Pentaerythritol Derived Tetrapode Exhibiting a Nematic-Like Mesophase at Ambient Temperatures

The nematic liquid-crystalline phase exhibits average orientational order, with no positional organisation. So-called modulated nematic phases exhibit this same orientational order with an additional spatially periodic modulation of the nematic director, the most common of which is the twist-bend nematic phase. We report a pentaerythritol derived tetrapode which exhibits a nematic-like mesophase at ambient temperature, and we denote this new mesophase ‘N_X’ to indicate a nematic phase of unknown structure. X-ray scattering experiments refute the possibility of positional order, yet optical textures are consistent with a periodic structure. We suggest that the mesophase exhibited by this material is a new type of nematic-like mesophase with some form of modulated structure. We find the N_X phase to exhibit an electrooptic response consistent with a nematic-like phase.     

Phase separation kinetics in mixtures of flexible polymers and low molecular weight liquid crystals

A dynamic Monte Carlo (MC) simulation is performed to investigate the phase behavior of mixtures of flexible polymers and low molecular weight thermotropic liquid crystals (LCs). The polymer is represented by three‐dimensional self‐avoiding lattice chains, while the LC is described by the Lebwohl‐Lasher nematogen model. The initially homogeneous rod‐coil mixture is, following a deep quench, separated into an isotropic phase rich in coils and a nematic phase rich in rods. The underlying spinodal decomposition (SD) process is then simulated and studied extensively. This is the first simulation of SD in a rod‐coil mixture where the nematic ordering is included. Concentration fluctuations with a conserved order parameter are thus coupled with orientation fluctuations with a nonconserved order parameter. It is found that the early stage SD in the rod‐coil mixture still exhibits the dominant spatial wavelength and that the scalar scattering functions in the late stage of SD obey the Furukawa scaling law. The kinetic difference between the so‐called isotropic and anisotropic SD regions is, however, much less pronounced than predicted recently by the mean‐field theory.     

Solution of a molecular statistical model for chiral nematic liquid crystals

A molecular statistical model for the chiral nematic phase of liquid crystals is investigated. The model is treated in the molecular field approximation. The resulting set of coupled integral equations for the order parameters and the pitch determining equation are solved numerically. The model hamiltonian consists of a nematic and a twist producing term. If only the nematic term is present, the model is known to have a first order phase transition. The model containing only the twist producing term is shown to exhibit a second order phase transition. The order parameters and wave length are presented for three ratios of the coupling constants in the case that both interactions are present.     

Magnetic alignment of aqueous CTAB in nematic and hexagonal liquid crystalline phases investigated by spin-1 NMR

Spin-1 NMR has been used to characterize the magnetically aligned nematic and hexagonal liquid crystalline phases of aqueous cetyltrimethylammonium bromide (CTAB). A nematic/hexagonal biphasic region has been identified for the first time in this system. The nematic phase is characterized by an order parameter of smaller magnitude and greater temperature dependence. Magnetic alignment kinetic rates of the two phases differ greatly, with the nematic phase showing magnetic alignment much faster than the hexagonal phase. Equilibration has been monitored over time by measuring the change in quadrupole splitting as a function of temperature. As the sample equilibrates the temperature dependence of the splitting decreases logarithmically. This work also demonstrates how the phase and order of the liquid crystal can be manipulated during the early part of equilibration.     

Effects of temperature on the alignment and electrooptical responses of a nematic nanoscale liquid crystalline film

The surface-induced alignment and electrooptical (EO) dynamics of a 50-nm-thick liquid crystalline (4-n-pentyl-4'-cyanobiphenyl; 5CB) film were studied at three temperatures: 25 and 33 degrees C (near the crystalline-nematic and nematic-isotropic transition temperatures, respectively) and 29 degrees C (a median temperature in the stability region of the nematic phase). The ZnSe surfaces that entrap the liquid crystal (LC) film have been polished unidirectionally to produce a grooved surface presenting nanometer-scale corrugations, a structure that induces a planar and homogeneous orientation in the nematic phase. The present work attempts to understand the influences of temperature on the surface-induced alignment and corresponding EO dynamics of the material. Step-scan time-resolved spectroscopy measurements were made to determine the rate constants for the electric-field-induced orientation and thermal relaxation of the 5CB film. The field-driven orientation rates vary sensitively with temperature across a range that spans the stability limits of the nematic phase; the relaxation rates, however, vary very little across this same temperature range. We propose that these differences in LC behavior arise as consequence of the interplay of the temperature dependence of the elastic constants, viscosity, and degree of orientational order of the LC medium. A simple theoretical model provides some understanding of these behaviors.     

On the Uniaxial–Biaxial Nematic Phase Transition in Liquid‐Crystalline Polymers and Elastomers

We study how the uniaxial–biaxial nematic phase transition changes its nature when going from a low‐molecular‐weight liquid crystal to a liquid‐crystalline elastomer or polymer (the latter above the Maxwell frequency) and find a qualitative change due to the presence of a coupling to the strain field in these materials. While this phase transition can be of second‐order in low‐molecular‐weight materials, as is also experimentally observed, we show here that the order of this phase transition is changed generically to no phase transition at all or to a first‐order phase transition in mean‐field approximation. We analyze the influence of an external mechanical stress field above the uniaxial–biaxial nematic phase transition and find that either biaxial nematic order is induced, which is linear or quadratic in the stress intensity, or no response to an external stress results at all, depending on the relative orientation of the applied shear with respect to the director of the uniaxial nematic phase.     

Bifurcational analysis of the isotropic-discotic nematic phase transition in the presence of extensional flow

A bifurcational analysis is performed on a version of Doi's equation of nematodynamics that describes the non-equilibrium isotropic-discotic nematic phase transition in the presence of steady uniaxial extensional flow. The disc-like molecular geometry and the degenerate extensional flow-induced orientation are shown to be the source of a complex bifurcation and multistability behaviour involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. Depending on the temperature and the extension rate, the isotropic-discotic nematic transition, involving the two biaxial nematic phases and the uniaxial paranematic phase, may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. A validation procedure on the validity of the predictions is implemented. The predictions presented here find practical applications in the industrial spinning of mesophase carbon fibres, and also provide new results that increase the present fundamental understanding of the rheology of discotic nematic liquid crystals.     

Interplay between shear flow and elastic deformations in liquid crystals

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.     

Morphology of spinodal decompositions in liquid crystal-colloid mixtures

We study the morphology of spinodal decompositions (SDs) in mixtures of a liquid crystal and a colloidal particle by solving time-dependent Landau-Ginzburg equations for a conserved order parameter (concentration) and two nonconserved order parameters (orientation and crystallization). We numerically examine the coupling between concentration, nematic ordering, and crystalline ordering in two dimensional fluid mixtures, coexisting a nematic and a crystalline phase. On increasing the concentration of colloidal particles, we have three different SDs: a nematic order-induced SD, a phase-separation-induced SD (PSD), and a crystalline-order-induced SD (CSD). In NSD, the phase ordering can lead to fibrillar and cellular networks of the minority colloidal-particle-rich phase in early stages. In the PSD, we find a bicontinuous network structure consisting of a nematic phase rich in liquid crystal and a crystalline phase rich in colloidal particles. In the CSD, nematic droplets can be formed in a crystalline matrix. Asymmetric mixtures of a liquid crystal and a colloidal particle lead to rich varieties of morphologies.     

Phase separations in liquid crystal-colloid mixtures

We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.     

Theory of volume phase transitions of side-chain liquid crystalline gels

We present a mean field theory to describe volume phase transitions of side-chain liquid crystalline gels. Three different uniaxial nematic phases (N(1), N(2), and N(3)) are defined by using orientational order parameter S(m) of side-chain liquid crystals (mesogens) and S(b) of backbone chains. We derive the free energy for the three nematic phases of side-chain liquid crystalline gels dissolved in isotropic solvents and calculate the swelling curve of the gel, the order parameters of a backbone chain and of side-chain liquid crystals, and the deformation of the gel as a function of temperature and an electric field. We find isotropic-nematic (N(1), N(2), and N(3)) and N(1)N(2) phase transitions of the gels, depending on the interaction between a backbone chain and a side-chain liquid crystal.     

Thermodynamics of activated phase transitions of 8CB: DSC and MC calorimetry

The present paper reports the heating rate effect on the phase transitions of a pure liquid crystal octylcyanobiphenyl (8CB) with use of Differential Scanning Calorimetry (DSC) and Modulation Calorimetry (MC) techniques. The DSC runs were taken at various temperature ramp rates from 20 to 0.5 K/min for heating and cooling scans. Well-defined endothermic/exothermic peaks were found at the melting/crystallization, smectic-A to nematic (SmA-N), and nematic to isotropic (N-I) transitions on heating/cooling scans, respectively. All transitions shift in temperature significantly with different ramp rates. The temperature shift of C(p) peaks between heating and cooling scans indicates the order of the transitions. In addition, all transitions follow an Arrhenius behavior. The activation energy of a transition increases as the total energy involved in the transition decreases. The respective enthalpy and entropy change of each transition provides information on the Gibbs free energy. The significance of the results is discussed in terms of the order of transitions. A comparative analysis of MC and DSC techniques highlights the significance of the two techniques. MC is a practicable tool for observing the phase dynamics whereas DSC is a good tool for studying the rate kinematics of the transitions.     

Molecular Dynamic Simulation of Side-Chain Liquid Crystalline Elastomer Under Load

Summary: We present a molecular dynamic simulation of a side chain liquid crystalline elastomer (LCE) under load. The LCE is composed of a flexible tetrafunctional diamond like network with rod-like mesogens attached to the network. As a precursor of the LC elastomer a flexible polymer network in a low molecular liquid-crystal (LC) solvent was used. The phase behavior of the LCE under uniaxial stretching up to the deformations of λ = 1.5 and 2.0 at different densities was studied. As in the non-stretched case upon density increase an isotropic to nematic phase transition occurs. However, in contrast to thermotropic side chain LC elastomers the stress induced shift transition is not observed. The stretching slightly increases the anisotropy of translational diffusion of mesogens in the nematic state. The stress-strain dependence for LCE both in the isotropic and the nematic states is obtained. Elastic modulus increases at high values of order parameter.     

Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch_H) is derived as a function of a usual orientational order parameter and an order parameter of the Ch_H phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch_H phase. Depending on the temperature and the strength of the external field, we find the second-order N–Ch_H and Ch_H–Ch phase transitions and the first-order paranematic (pN)–N, pN–Ch_H and pN–Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field.     

Bifurcational analysis of the isotropic-nematic phase transition of rigid rod polymers subjected to biaxial stretching flow

A bifurcational analysis is performed on Doi's equation of nematodynamics that describes the non-equlibrium isotropic-nematic phase transition of rigid rod polymers in the presence of steady biaxial stretching flow. The symmetry of the flow and of the governing order parameter equations are shown to be the source of a rich bifurcation, symmetry breaking, and multistability behavior involving two physically equivalent biaxial nematic phases, one uniaxial nematic phase and one uniaxial paranematic phase. According to the relative intensity of the nematic ordering field and stretching rate, the uniaxial isotropic-biaxial nematic transition may be continuous (2nd order), discontinuous (1st order), or it may exhibit a tricritical non-equilibrium phase transition point. The solutions to the Doi equations of nematodynamics are found to be consistent with those of Khokhlov and Semenov [Macromolecules 15 , 1272 (1982)], which are based on a version of the Onsager theory of isotropic-nematic phase transitions. The present simulations provide a useful guide for orientation control in biaxial stretching flows.     

Multiple Polar and Non-polar Nematic Phases

Liquid-crystal materials exhibiting up to three nematic phases are reported. Dielectric response measurements show that while the lower temperature nematic phase has ferroelectric order and the highest temperature nematic phase is apolar, the intermediate phase has local antiferroelectric order. The modification of the molecular structure by increasing the number of lateral fluorine substituents leads to one of the materials showing a direct isotropic-ferronematic phase transition.