The liquid-crystal dimer 1'',7''-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB) exhibits two liquid-crystalline mesophases on cooling from the isotropic phase. The high-temperature phase is nematic; the identification and characterization of the other liquid-crystal phase is reported in this paper. It is concluded that the low-temperature mesophase of CB7CB is a new type of uniaxial nematic phase having a nonuniform director distribution composed of twist-bend deformations. The techniques of small-angle x-ray scattering, modulated differential scanning calorimetry, and dielectric spectroscopy have been applied to establish the nature of the nematic-nematic phase transition and the structural features of the twist-bend nematic phase. In addition, magnetic resonance studies (electron-spin resonance and (2)H nuclear magnetic resonance) have been used to investigate the orientational order and director distribution in the liquid-crystalline phases of CB7CB. The synthesis of a specifically deuterated sample of CB7CB is reported, and measurements showed a bifurcation of the quadrupolar splitting on entering the low-temperature mesophase from the high-temperature nematic phase. This splitting could be interpreted in terms of the chirality of the twist-bend structure of the director. Calculations using an atomistic model and the surface interaction potential with Monte Carlo sampling have been carried out to determine the conformational distribution and predict dielectric and elastic properties in the nematic phase. The former are in agreement with experimental measurements, while the latter are consistent with the formation of a twist-bend nematic phase.

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This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of alpha,omega-bis[(4-cyanobiphenyl-4'-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density p(eq)(beta(A),beta(B)) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simultaneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer alpha-[(4-cyanobiphenyl)-4'-yloxy]-omega-(4-decylanilinebenzylidene-4'-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases.

This paper reports a novel liquid crystal phase having the characteristics of a twist-bend nematic phase formed by a non-symmetric ether-linked liquid crystal dimer. The dimer 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB) exhibits two liquid-crystalline phases on cooling at a sufficiently high rate from the isotropic phase. The high temperature mesophase has been reported in the literature as nematic and confirmed in this study. The other mesophase is metastable and can be supercooled giving rise to a glassy state. Its identification and characterization are based on optical textures, broadband dielectric spectroscopy, calorimetry, measurements of both splay and bend elastic constants in the nematic phase and miscibility studies. It is concluded that the low temperature mesophase exhibits the characteristics of a twist-bend nematic phase. Dielectric measurements enable us to obtain the static permittivity and information about the molecular dynamics in the isotropic phase, in the nematic mesophase and across the isotropic-to-nematic phase transition. Two orientations, parallel and perpendicular to the director, have been investigated. In the high temperature nematic mesophase, the dielectric anisotropy is found to be positive. Measurements of the parallel component of the dielectric permittivity are well-explained by the molecular theory of dielectric relaxation in nematic dimers (M. Stocchero, A. Ferrarini, G. J. Moro, D. A. Dunmur and G. R. Luckhurst, J. Chem. Phys., 2004, 121, 8079). The dimer is modelled as a mixture of cis and trans conformers and the model allows an estimate of their relative populations at each temperature. The nematic-to-isotropic phase transition has been exhaustively studied from the accurate evolution of the heat capacity and the static dielectric permittivity data. It has been concluded that the transition is first order in nature, but close to tricritical. The nature of the nematic-to-the novel liquid crystal phase transition is difficult to analyze to the same extent because of insufficient precision. Only observations at cooling rates of 10 K min(-1) or higher were possible because on heating from the glassy state, the twist-bend nematic mesophase crystallizes at temperatures far below the nematic-nematic phase transition.

We propose an intrinsic molecular chirality tensor based only on nuclear positions. The chirality tensor gives rise to two universal chirality indices, the first giving information about absolute chirality, and the second about the anisotropy chirality, i.e., the degree of chirality in different spatial directions. The formalism is derived using simple models obtained from the theory of optical activity. The indices are calculated analytically for a right angled tetrahedron, and numerically for a small selection of molecules.