Induced helical structure of nematics in a magnetic field

Abstract

Nematics MBBA, EBBA, PBBA, BBBA, 5CB, 8OCB and PCH5 doped with chiral 2-(4′-phenylbenzylidene)-p-menthan-3-one are studied. A numerical solution in terms of the Landau-de Gennes theory is obtained to describe the experimental temperature dependence of P/P ₀, where P ₀ corresponds to P in zero magnetic field. The angle of tilt θ from the plane perpendicular to the helical axis is evaluated and the domain wall energy in a constant magnetic field analysed. To take into account the helical structure deformation, the helicoidal order parameter G is defined, so that G = 0 in the N phase and G = 1 with d?/dz = const. and θ = 0 in the N* phase. The relaxation of the helical structure to the equilibrium state (N* → N) is shown to be determined by the domain wall energy with the magnetic field H ≠ 0.     

Molecular field theory for polar,biaxial bent-core nematics

We have studied a polar, biaxial nematic liquid crystal formed from bent-core molecules using molecular field theory. The model includes a simple Heisenberg-form dipolar intermolecular interaction in addition to the usual quadrupolar nematic interaction, and mimics a system consisting of nematogenic bent-core molecules with a large transverse dipole along the bisector of the two molecular arms. Such systems are regarded as good candidates for biaxial nematic liquid crystals. In principle, the molecular dipoles can align, thus stabilising the ordering of the minor axes. Our calculations predict that, for suitable values of the bent-core interarm angle, the biaxial nematic phase can be stabilised at higher temperatures than in the absence of the transverse dipole. In general, the transverse macroscopic polar order stabilises the biaxial nematic phase. In particular, for a large enough dipolar interaction, the Landau point in the pure biaxial nematic develops into a line of first-order polar biaxial nematic-to-isotropic phase transitions.     

Molecular dynamics simulation of the cybotactic region in gas-expanded methanol-carbon dioxide and acetone-carbon dioxide mixtures

Local solvation and transport effects in gas-expanded liquids (GXLs) are reported based on molecular simulation. GXLs were found to exhibit local density enhancements similar to those seen in supercritical fluids, although less dramatic. This approach was used as an alternative to a multiphase atomistic model for these mixtures by utilizing experimental results to describe the necessary fixed conditions for a locally (quasi-) stable molecular dynamics model of the (single) GXL phase. The local anisotropic pair correlation function, orientational correlation functions, and diffusion rates are reported for two systems: CO2-expanded methanol and CO2-expanded acetone at 298 K and pressures up to 6 MPa.     

Channel confined active nematics

Active nematics is a popular model fluid for active matter. The popularity comes from the fact that several biological systems involving cells and cytoskeletal elements closely match active nematic fluid. Moreover, the theory of active nematics is amenable for analytical and computational developments. This review discusses different flow states and flow transitions exhibited by channel confined active nematics. The discussions based on experimental and theoretical investigations reveal the role of inherent hydrodynamic instabilities, the unique fluid properties, and the bounding geometry in dictating the behavior of active nematic fluids in channel confinements. The discussions also highlight the current and outstanding research questions in the field.     

Viscoelastic coefficients of glass-forming nematics

In this paper, we report measurements of the viscoelastic properties of nematic liquid crystals which exhibit a glass transition in the nematic phase. We have studied the Freedericksz transition in planar cells with a magneto-optical method. K₁ was determined from the critical field, and the rotational viscosity, γ₁, from the response time for the director orientation by the external field. We found a temperature dependence of γ₁ of the Vogel type, with absolute values ranging over several orders of magnitude, and K₁ values similar to those of conventional thermotropic low molar mass nematics.     

Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.     

Phase diagram of Gaussian-core nematics

The authors study a simple model of a nematic liquid crystal made of parallel ellipsoidal particles interacting via a repulsive Gaussian law. After identifying the relevant solid phases of the system through a careful zero-temperature scrutiny of as many as eleven candidate crystal structures, they determine the melting temperature for various pressure values, also with the help of exact free energy calculations. Among the prominent features of this model are pressure-driven reentrant melting and the stabilization of a columnar phase for intermediate temperatures.     

The elastic constants of nematics

Abstract

It is pointed out that some often cited molecular statistical calculations of the elastic constants of nematics are based on a postulated instead of a derived expression for the distortion free energy density. In particular attention is paid to the contradictory results of Priest and Poniewierski and Stecki for hard rod systems. The appropriate way to calculate the elastic constants of hard rod models from first principles is discussed briefly.     

Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

A surface-induced transition in polymeric nematics

New polymeric liquid crystals can be treated as standard nematic liquid crystals when only their bulk properties are at issue, but they exhibit peculiar surface properties. The most striking one is that biaxial distributions may be induced on a confining surface. On continuously varying the surface anchoring conditions, we find a first-order phase transition from planar to homeotropic alignment in the bulk. Moreover, the decay towards these uniaxial states is radically different in the two cases: it is asymptotically exponential in the former, whereas it happens abruptly at a finite depth in the latter. There is precisely one surface biaxial distribution that induces bistability between these decay modes: it depends on the elastic constants in the Landau-de Gennes free energy functional. The analysis of the model we propose can prove useful in detecting the sign of the difference between splay and bend constants.     

Characterization of lyotropic nematics in cylindrical capillaries

Procedures for characterization of lyotropic nematics in cylindrical capillaries by optical microscopy in orthoscopic geometry are presented. Typical textures due to surface alignment allow unambiguous characterization of N_c (cylindrical micelles) and N_d (discotic micelles) phases. Typical textures due to the compromise between surface and magnetic alignment allow unambiguous definition of the sign of the diamagnetic anisotropy susceptibility δχ. The textures allow also estimates of anisotropies of elastic constants for N_d lyomesophases.     

Model of a disclination core in nematics

The core structure of a disclination line of strength 1 in uniaxial nematics is determined by using a space-dependent mean-field approach somehow based on the rod-like molecular model. It is shown that, due to distortion, biaxiality arises at all points of the defect core, except at the centre line where symmetry dictates uniaxiality; the orientational distribution of the rod-like molecules is there 'oblate', however. Although, as is well known, the configuration of a 1 defect is stable only under limiting conditions (as compared with either escaping in the axial direction or splitting into two 1/2 lines), the simple example developed here is indicative of a method which can readily be extended to more realistic, if mathematically more complex, situations such as 1/2 lines, layers close to solid boundaries, etc.     

New lyotropic nematics of double chain surfactants

The phase behaviour of N,N-dialkyl-N,N-dimethyl ammonium bromide double chain surfactants was investigated by polarization microscopy, ²H-N.M.R. spectroscopy, and surface and magnetic field alignment in order to find new lyotropic nematic systems. Decanol was utilized to cause a rod to disc transition in the nematic phase. The sign of the anisotropy of the diamagnetic susceptibility Δx was inverted by substituting the bromide counter-ion with the benzenesulphonate ion. The phase behaviour was modified within a wide range by varying the length of the two alkyl chains. Using these tools we were able to prepare any of the four kinds of uniaxial nematic phases: rod-like and disc-like aggregates with both negative and positive anisotropy of the diamagnetic susceptibility. Several new binary, ternary and quaternary systems of these double chain surfactants and some experiments are described to classify the different nematic phases.     

The alignment of cybotactic groups in a nematic mesophase by an electric field

The anomalous electric field alignment of the nematic mesophase of 4,4′-dimethoxyazoxybenzene, as inferred from the electron resonance spectrum of dissolved vanadyl acetyl acetonate, is discussed. A model, based on the alignment of cybotactic groups with their planes parallel to the electric field, is able to account for the major features of the angular dependence of the spectrum. The analysis shows that, at 125°C, the molecular axes are inclined at least 13° to the plane of the cybotactic group.     

An old model for magnetic nematics

A mean-field treatment is given of the off-lattice Krieger-James model of ordered fluids, which reduces to the more familiar Maier-Saupe liquid crystal (Heisenberg fluid) in the absence of ferromagnetic (nematic) interactions. As in the lattice version, isotropic, nematic and ferromagnetic nematic phases are found, but the nematic-ferronematic transition can either change order at a tricritical point, or terminate at a critical end point on the ferronematic-isotropic coexistence curve. In addition it is argued that the sequence of phase diagram topologies, as a function of the relative weights of ferromagnetic and nematic contributions to the free energy, should be similar to that obtained on varying the elongation of dipolar spheroids.     

Molecular structure of proline

The molecular structures of the two lowest-energy conformers of proline, Pro-I and Pro-II, have been characterized by ab initio electronic structure computations. An extensive MP2/6-31G* quartic force field for Pro-I, containing 62,835 unique elements in the internal coordinate space, was computed to account for anharmonic vibrational effects, including total zero-point contributions to isotopomeric rotational constants. New re and improved r0 least-squares structural refinements were performed to determine the heavy-atom framework of Pro-I, based on experimentally measured (A. Lesarri, S. Mata, E. J. Cocinero, S. Blanco, J. C. Lopez, J. L. Alonso, Angew. Chem. 2002, 114, 4867; Angew. Chem. Int. Ed. 2002, 41, 4673) rotational constant sets of nine isotopomers and our ab initio data for structural constraints and zero-point vibrational (ZPV) shifts. Without the ab initio constraints, even the extensive set of empirical rotational constants cannot satisfactorily fix the molecular structure of the most stable conformer of proline, a 17-atom molecule with no symmetry. After imposing the ab initio constraints, excellent agreement between theory and experiment is found for the heavy-atom geometric framework, the root-mean-square (rms) residual of the empirical rotational constant fit being cut in half by adding ZPV corrections. The most significant disparity, about 0.07 A, between the empirical and the best ab initio structures, concerns the r(N...H) distance of the intramolecular hydrogen bond. Some of the experimental quartic centrifugal distortion constants assigned to Pro-II have been corrected based on data obtained from a theoretical force field.     

Molecular structure of thiourea

The molecular structure of thiourea has been investigated under C(s), C(2), and C(2v) symmetry constraints. At the coupled-cluster level in conjunction with a triple-ζ basis set, only the C(2) conformer has been found to be a real minimum on the potential energy surface. Its equilibrium structure has therefore been accurately evaluated using both theoretical and experimental data. With respect to the former, high-level quantum-chemical calculations at the coupled-cluster level in conjunction with correlation-consistent basis sets ranging in size from triple- to quintuple-zeta have been carried out. Extrapolation to the complete basis-set limit as well as core-correlation effects and inclusion of full treatment of triple excitations in the cluster operator have been considered. On the basis of the vibrational ground-state rotational constants available for five isotopic species and the corresponding computed vibrational corrections, the semiexperimental equilibrium geometry of thiourea has also been determined for the first time.     

Molecular structure of benzene

The molecular structure of benzene has been determined by combining the average distances obtained by the present electron diffraction study and the moments of inertia reported by Cabana et al. The following thermal average bond distances have been determined: r_g(C-C) = 1.399 ± 0.001 Å and r_g (C-H) = 1.101 ± 0.005 Å. The uncertainties represent the estimated limits of error. The C-H distance of this molecule is similar to vinyl C-H distances.