Orientational order and refractive indices in binary nematic mixtures

Mean field theory is used to calculate the temperature-composition phase diagram and component order parameters of binary nematic mixtures. Experimental values for the mixture order parameter of a binary nematic mixture close to the nematic/isotropic transition have been obtained from refractive index measurements. The experimental results qualitatively confirm the predictions of the theory.     

N.M.R. investigations and the molecular field theory of nematic mixtures

N.M.R. measurements have shown that the mixture E5 can be described by a single order parameter. Based on molecular field theory the nematic-isotropic transition and the temperature dependence of the order parameter in the nematic phase are considered for a binary mixture of nematogens. Guided by the results of the N.M.R. measurements the binary mixture is treated as an effective medium characterized by a single order parameter. Soft attractive forces are taken into account as well as the excluded volume. The coexistence of nematic and isotropic phases in the phase transition region is discussed in detail.     

Virtual isotropic‐nematic transitions in alkyl cyanobiphenyls

Pretransitional fluctuations in the isotropic phase of liquid crystalline and non‐liquid crystalline alkyl cyanobiphenyls have been investigated using light scattering and magnetic birefringence measurements. We find evidence for a virtual isotropic‐nematic phase transition in short‐chain alkyl cyanobiphenyls with no observable nematic phase. The measured temperature dependence of fluctuations is well‐described by mean‐field theory. Virtual phase transition temperatures extrapolated from separate light scattering and magnetic birefringence experiments are in good agreement. Landau–de Gennes model parameters for the compounds investigated are calculated from the experimental results.     

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.     

The Estimation of Statistical Parameters Determining the Relaxation Times of Nematic Elastomers: A Three‐Chain Network Model

A simplified “three‐chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean‐square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely‐jointed‐rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod‐like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively.     

Isotropic-nematic interfacial tension of hard and soft rods: application of advanced grand canonical biased-sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma(IN) in systems of hard and soft rods. For hard rods with LD=15, we obtain gammaIN approximately 1.4kBT/L2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.     

Computer simulation studies of anisotropic systems. XXII. An equimolar mixture of rods and discs: A biaxial nematic?

In principle, binary mixtures of rod-like and disc-like particles should exhibit a biaxial nematic phase, but in practice phase separation into two uniaxial nematic phases prevents this. Here, we report the results of a computer simulation study of an equimolar mixture of rods and discs in which phase separation is not allowed. The particles are confined to the sites of a simple cubic lattice in which each rod is surrounded by six discs and vice versa. Neighbouring particles interact such that they prefer to align with their respective symmetry axes orthogonal to each other. In contrast, the interaction between next nearest neighbours, which are either rods or discs, is such that their symmetry axes tend to be parallel. Monte Carlo simulations of this model mixture show that an orientationally ordered phase exists at low temperatures. This nematic phase has overall uniaxial symmetry and the particles have a negative second rank orientational order parameter, indicating that they tend to align at right angles to the director. The two interpenetrating sub-lattices containing either rods or discs, however, exhibit a biaxial nematic phase. The results of the simulation are found to be in reasonable agreement with the predictions of a molecular field theory for this model mixture. We have also investigated the behaviour of this mixture when the rods and discs are allowed to exchange between their lattice sites. The mixture is found to separate into two uniaxial nematic phases composed essentially of either rods or discs, as expected.     

Structural and dynamic properties of a new type of discotic nematic compounds

Thermodynamic, structural and dynamical properties of a new type of discotic compounds, a hydrocarbon without any heteroatoms, displaying a nematic discotic phase have been investigated by means of X-ray diffraction, electro-optical relaxation, and calorimetric studies. Of particular interest are the strength of the first order nematic—isotropic phase transition and the nature of the orientational fluctuations in the isotropic phase. The short range positional order was found to be biaxial in both the isotropic and the nematic phase. The isotropic phase displays strong pretransitional effects originating from orientational fluctuations in the neighbourhood of the transition to the nematic phase. The character of these pretransitional effects differs from that found for calamitic systems in that the number of correlated molecules g₂ is extremely large, of the order of 600 at the clearing temperature and the electro-optical relaxation time is very large, caused by the large value of g₂.     

A density-functional theory study of the confined soft ellipsoid fluid

A system of soft ellipsoid molecules confined between two planar walls is studied using classical density-functional theory. Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ans?tze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF's). The first is a numerical DCF obtained from simulations of bulk soft ellipsoid fluids and the second is taken from the Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic‐to‐nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau–de Gennes model for rod‐like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic‐isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic–nematic interface and the substrate–nematic–isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Texture formation under phase ordering and phase separation in polymer-liquid crystal mixtures

Computational modeling of texture formation in coupled phase separation-phase ordering processes in polymer/liquid crystal mixtures is performed using a unified model based on the nematic tensor order parameter and gradient orientation elasticity. The computational methods are able to resolve defect nucleation, defect-defect interactions, and defect-particle interactions, as well as global and local morphological features in the concentration and order parameter spatiotemporal behavior. Biphasic structures corresponding to polymer dispersed liquid crystals (PDLCs), crystalline filled nematic (CFNs), and random filled nematics (RFNs) are captured and analyzed using liquid crystal defect physics and structure factors. Under spinodal decomposition due to concentration fluctuations, the PDLC structure emerges, and the nucleation and repulsive interaction of defects within nematic droplets leads to bipolar nematic droplets. Under spinodal decomposition due to ordering fluctuations, the CFNs structure emerges, and the stable polymer droplet crystal is pinned by a lattice of topological defects. For intermediate cases, where the mixture is unstable to both concentration and nematic order fluctuations, the RFN structure emerges, and polymer droplets and fibrils are pinned by a defect network, whose density increases with the curvature of the polymer-liquid crystal interface. The simulations provide an information of the role of topological defects on phase separation-phase ordering processes in polymer-liquid crystal mixtures.     

Rigid rod molecules as liquid crystal thermosets. II. Rigid rod esters

Nine rigid rod ester monomers endcapped with maleimide, nadimide, and methylnadimide groups were prepared and studied by DSC and hot stage polarized light microscopy. All of the monomers showed thermotropic nematic liquid crystalline phases and could be thermally crosslinked in the nematic phase. The nematic texture was maintained in the crosslinked solid state. The nematic phase range was enlarged by B-staging the monomeric compounds. Heating the monomers for a short period of time in the nematic phase lowered the crystal to nematic transition temperatures and increased the nematic to isotropic transition temperatures. A nonequilibrium phase diagram was proposed to explain the melting behavior of these reactive liquid crystal thermoset materials.     

Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.     

Determination of the elastic constants of nematic liquid crystals by means of the affine transformation model

In this paper the affine connection approach will be used to calculate the elastic constants of nematic liquid crystals. Following this approach, which was originally conceived to compute the nematic viscosity coefficients, an expression for the elastic constants, without adjustable free parameters, will be formulated in terms of a temperature dependent metric, whose non‐isotropic part is proportional to the tensorial order parameter of the nematic phase. The dependence of the elastic constants on the scalar order parameter, in the geometry of the nematic molecules, and in the anisotropic part of the molecular interaction, will be determined.     

Isotropic–nematic phase separation and demixing in mixtures of spherical nanoparticles with length‐polydisperse nanorods

An extension of Onsager theory is developed to simulate isotropic–nematic phase separation in a mixture of spheres with length‐polydisperse system of rods. This work is motivated by recent experimental data on nanorod liquid crystals. Prior theoretical investigations indicate that both polydispersity and the presence of spheres should increase the biphasic–nematic phase transition, that is, the nematic cloud point. Results indicate that the phase diagrams undergo drastic changes depending upon both particle geometry and rod length polydispersity. The key geometric factor is the ratio between the sphere diameter and the rod diameter. In general, length fractionation is enhanced by the addition of spheres, which may be experimentally advantageous for separating short nanorods from a polydisperse population. Simulation results also indicate that the nematic cloud and shadow curves may cross one another because of the scarcity of spheres in the shadow phase. In general, these results do indicate that the nematic cloud point increases as a function of sphere loading; however, in certain areas of phase space, this relationship is nonmonotonic such that the nematic cloud point may actually decrease with the addition of spheres. This work has application to a wide range of nanoparticle systems, including mixtures of spherical nanoparticles with nanorods or nanotubes. Additionally, a number of nonspherical particles and structures may behave as spheres, including crumpled graphene and tightly coiled polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Phase equilibria and photopolymerisation-induced phase transitions of mesogenic diacrylate monomer and low molecular mass liquid crystal mixture

Experimental phase diagrams of binary mesogenic mixtures of reactive mesogenic diacrylate (RM257) monomer and low molar mass liquid crystals (E7) were determined by means of differential scanning calorimetry and optical microscopy. The combined free energy densities of Flory–Huggins for liquid–liquid demixing, Maier–Saupe for nematic ordering, and phase field free energy for crystal solidification was proposed to describe the phase diagrams of the starting E7/RM257 mixtures. The phase diagram thus constructed is an ideal mixing type, exhibiting a narrow loop of isotropic + nematic (I + N) coexistence region followed by the crystal + nematic (Cr1 + N) region in descending order of temperature. Of particular interest is the permanent fixation of the mesophase structures upon photopolymerisation of neat RM257 in the corresponding nematic and crystalline phases. Upon photopolymerisation of a low RM257 content mixture in both isotropic and nematic states, the nematic–isotropic transition of E7 was found to persist. The permanent structural anchoring is seen upon photo-curing of the 90/10 RM257/E7 mixture in the crystalline state.     

Proton NMR relaxation study of molecular dynamics of chromonic liquid crystal Edicol Sunset Yellow

Proton nuclear magnetic resonance (¹H NMR) relaxometry, over about five decades in Larmor frequency, and pulsed field gradient NMR were used to study the molecular dynamics in the chromonic nematic and isotropic phases of stacked molecules of the binary mixture composed by Edicol Sunset Yellow (ESY) and deuterated water. Our results evidence that in both phases collective motions are responsible for the spin-lattice relaxation dispersion in the Larmor frequency range below 1 MHz. In the nematic phase, the collective motion are attributed to columnar undulations within the stacked molecules, while, in the isotropic phase, the results are explained by local order fluctuations due to the formation of the stacks. The high frequency dispersion was explained by individual molecular motions like rotations around and perpendicular to the stack axis, and also self-diffusion.     

Coassembly of Nanorods and Nanospheres in Suspensions and in Stratified Films

The entropically driven coassembly of nanorods (cellulose nanocrystals, CNCs) and nanospheres (dye‐labeled spherical latex nanoparticles, NPs) was studied in aqueous suspensions and in solid films. In mixed CNC‐latex suspensions, phase separation into an isotropic latex‐NP‐rich and a chiral nematic CNC‐rich phase took place; the latter contained a significant amount of latex NPs. Drying the mixed suspension resulted in CNC‐latex films with planar disordered layers of latex NPs, which alternated with chiral nematic CNC‐rich regions. In addition, fluorescent latex NPs were embedded in the chiral nematic domains. The stratified morphology of the films, together with a random distribution of latex NPs in the anisotropic phase, led to the films having close‐to‐uniform fluorescence, birefringence, and circular dichroism properties.     

The structure and conformation of a mesogenic compound between almost zero and almost complete orientational order

The conformational distributions in molecules that form liquid crystalline phases are predicted to depend strongly on orientational order. Results are presented here to test this hypothesis. The mesogen 4‐hexyloxy‐4′‐cyanobiphenyl (6OCB) has been studied by NMR spectroscopy in the isotropic phase and in the nematic phase. In the isotropic phase the field‐induced orientational ordering produces small dipolar couplings between ¹³C and ¹H nuclei, which were determined from the ¹³C spectra. Couplings between ¹H nuclei were also obtained using 2D selective refocusing experiments. In the nematic phase, both ¹H–¹H dipolar couplings and quadrupolar splittings for deuterium nuclei were measured for partially‐deuterated samples. Both proton and deuterium spectra were also obtained for 6OCB in an equimolar mixture with 4‐(ethoxybenzylidene)‐4′‐butylaniline (EBBA). This mixture exhibits SmA and SmB phases. The data obtained from these experiments has been analysed to yield the probability distribution of the conformations in this molecule generated by rotations about bonds. It is found that there is a substantial influence of the orientational order of the molecules on these distributions.     

Equilibrium phase diagram of polystyrene and 8CB

The experimental equilibrium phase diagram of a mixture of linear polystyrene of molecular weight M_w = 44,000 g/mol and 4‐cyano‐4′‐n‐octyl‐biphenyl (8CB) is established. The three transitions smectic A‐nematic, nematic‐isotropic, and isotropic‐isotropic are observed. The first two are observed both by optical microscopy and differential scanning calorimetry (DSC) while the isotropic‐isotropic transition could be seen only via optical microscopy. Two series of samples with the same compositions were independently prepared and yielded consistent results both by microscopy and DSC. Measurements of sample compositions with less than 50 weight % of 8CB were influenced by the vicinity of the glass transition temperature (T_g) of the polymer in the mixture. This quantity is also determined by DSC as a function of composition. A single T_g is observed, which decreases with composition of the LC. Other thermodynamic quantities such as the enthalpy variations of LC in the nematic‐isotropic transition and the fraction of LC contained in the droplets are also considered. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1841–1848, 1999