Synthesis and mesomorphic properties of some derivatives of 2-methylcyclohex-2-ene-4-one-1-carboxylic and cis-2,6-dimethyl cyclohex-2-ene-4-one-1 -carboxylic acids

Mesomorphic derivatives prepared from ethyl esters of 2-methylcyclohex-2-ene-4-one-1-carboxylic and cis-2,6-dimethylcyclohex-2-ene-4-one-1-carboxylic acids have been synthesized. It has been shown that the compounds obtained are characterized by a lower nematic—isotropic transition temperature (10-20°C) and a considerably narrower nematic range in comparison with the analogous derivatives of 4-alkylcyclohex-3-ene-carboxylic and trans-4-alkylcyclohexane-carboxylic acid.     

Chiral induction of micellar cholesterics from lamellar phases

It is shown for the first time that induced micellar cholesterics can be obtained from lamellar phases within the sequence: lamellar—micellar nematic—micellar cholesteric—biphasic region—isotropic phase. The pitch is shortened by over 50 per cent when the temperature is raised within the cholesteric range of about 15 K.     

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.     

Statistical model of polar nematic polymers

The interaction in specially designed polymers may be dominated by the first rank P₁(cos β) type potential instead of the second rank P₂(cos β) type, as in conventional liquid crystal polymers (P₁(cos β) and P₂(cos β) are the first and second Legendre polynomials, respectively of the angle made by the polymer segments with respect to the preferred direction or director). The ordering of the polymers is envisaged in terms of the worm-like theory. The polymers show a polar nematic phase, that is a ferroelectric phase. These polymers have certain interesting properties, such as a second order polar nematic—isotropic transition, and related critical features. These materials are expected to exhibit giant dielectric responses. For more general polymer systems with interactions of both P₁(cos β) and P₂(cos β) types, we predict a peculiar phase behaviour.     

ESR spectra of trimeric heteronuclear clusters. I. Theory

A theory of the ESR spectra of trimeric heteronuclear clusters consisting of transition-metal ions has been developed. The theoretical model includes both isotropic exchange and Dzialoshinskii—Moriya antisymmetric interactions; it also takes into account the differences between g values of the individual ions. The energy levels of the interacting multielectronic ion system in a magnetic field have been found in theory. Radiofrequency transition probabilities have been determined for the canonical directions of the field. It is shown that the ESR spectrum exhibits peculiarities closely related to the non-linear behaviour of Zeeman levels.     

Ordering transition and demixing of a binary mixture of thick and thin rodlike molecules in the presence of an external field

The effect of an external field (electric/magnetic) on the phase behavior of the binary mixture of very long thick and thin rodlike particles is studied. Both the thick and thin particles possess positive but different susceptibility anisotropics (Delta alpha). The difference in the extent of interaction between the external field and the two species is varied by means of a coupling parameter (l = Delta alpha(thick)/Delta alpha(thin)). Isotropic-nematic phase transition and demixing phase transitions taking place both in the isotropic and nematic phases are examined as a function of field strength on the level of the second virial theory of Onsager in the range of 0 < l <1. The approximate sixth order Legendre polynomial expansion method is used to represent the excluded volume interaction between the rodlike particles. It is found that the isotropic phase becomes weakly nematic (paranematic) in the presence of external field and the field orients both components in the direction of the field even if the field does not have direct interaction with the thick component (l = 0). Analytical expressions are derived for the external field induced order parameters and birefringence. The increasing field destabilizes both types of demixing transitions (isotropic-isotropic and nematic-nematic) and the paranematic-nematic phase transition. Moreover it induces closed loop immiscibility, and upper and lower critical points terminating the paranematic-nematic phase coexistence may occur for low values of the coupling parameter. It is interesting that while the phase boundaries of the paranematic-paranematic demixing and the paranematic-nematic transitions are very sensitive to the value of the coupling parameter at low pressures, the paranematic-nematic and nematic-nematic phase boundaries are practically independent of the coupling parameter at high pressures.     

Pretransitional behavior of a water in liquid crystal microemulsion close to the demixing transition: evidence for intermicellar attraction mediated by paranematic fluctuations

We present a study of a water-in-oil microemulsion in which surfactant coated water nanodroplets are dispersed in the isotropic phase of the thermotropic liquid-crystal penthyl-cyanobiphenyl (5CB). As the temperature is lowered below the isotropic to nematic phase transition of pure 5CB, the system displays a demixing transition leading to a coexistence of a droplet-rich isotropic phase with a droplet-poor nematic. The transition is anticipated, in the high T side, by increasing pretransitional fluctuations in 5CB molecular orientation and in the nanodroplet concentration. The observed phase behavior supports the notion that the nanosized droplets, while large enough for their statistical behavior to be probed via light scattering, are also small enough to act as impurities, disturbing the local orientational ordering of the liquid crystal and thus experiencing pretransitional attractive interaction mediated by paranematic fluctuations. The pretransitional behavior, together with the topology of the phase diagram, can be understood on the basis of a diluted Lebwohl-Lasher model which describes the nanodroplets simply as holes in the liquid crystal.     

Density-functional study of model bidisperse ferrocolloids in an external magnetic field

We present phase diagrams of a model bidisperse ferrocolloid consisting of a binary mixture of dipolar hard spheres (DHSs) under the influence of an external magnetic field. The dipole moments of the particles are chosen proportional to the particle volume to mimic real ferrocolloids, and we focus on dipole-dominated systems where isotropic attractive interactions are absent. Our results are based on density-functional theory in the modified mean-field (MMF) approximation. For one-component DHS fluids in external fields, and for corresponding mixtures dominated by one of the components, MMF theory predicts the tricritical point of the transition between an isotropic gas and a ferromagnetic liquid occurring at zero field to be changed into a critical point separating two magnetically ordered phases of different density. The corresponding critical temperature displays a nonmonotonic dependence on the field strength. Completely different behavior is found for the critical temperature related to the demixing phase transitions appearing in strongly asymmetric mixtures [G. M. Range and S. H. L. Klapp, Phys. Rev. E 70, 061407 (2004)]. For such systems, we find a monotonic decrease of the demixing critical temperature with increasing field. The field strength dependence of the critical temperature can therefore be tuned between nonmonotonic and monotonic behaviors just by changing the composition of the mixture--e.g., by adjusting the chemical potentials. This allows us to efficiently control the influence of external magnetic fields on the phase behavior over a large temperature interval.     

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.     

Dipolar and dispersion interactions in nematogens A computer simulation study

A classical system, consisting of identical cylindrically symmetric particles, with centres fixed on a simple-cubic lattice, may or may not support nematic—like orientational order depending on the interaction potential. For example, a Lebwohl-Lasher potential model produces orientational order, as does an anisotropic London—de Boer dispersion potential restricted to nearest neighbours, although increasing its range destroys the orientational order and brings about a staggered configuration of the system. In consequence, a Maier-Saupe molecular field treatment is appropriate in the first two cases, but not in the last. On the other hand, according to computer simulation results, a purely dipolar interaction produces a low temperature antiferroelectric phase which can be regarded as an extreme case of a nematogen. We carried out Monte Carlo simulations on a potential model defined by a linear combination of dipolar and full ranged London-de Boer dispersion terms, in order to study their competition. To save computer time and yet monitor the physically relevant changes, we have varied their relative weights, while keeping fixed both the temperature and the anisotropy parameter in the dispersion potential. Simulation results show that in energetic terms the two interactions are cooperative, whereas in structural terms their interplay brings about first a weak but recognizable increase of nematic ordering, and then its collapse with the onset of the staggered configuration.     

Orientational ordering in hard rectangles: The role of three-body correlations

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient B3 is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parametrized distribution function, for various particle aspect ratios in the range of 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N(u)) and isotropic-tetratic nematic (N(t)) spinodals and to study the order of these phase transitions. We find that the relative stability of the N(t) phase with respect to the isotropic phase is enhanced by the introduction of B3. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N(t) phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.     

Three-body contribution to the helium interaction potential

Two nonadditive three-body analytic potentials for helium were obtained: one based on three-body symmetry-adapted perturbation theory (SAPT) and the other one on supermolecular coupled-cluster theory with single, double, and noniterative triple excitations [CCSD(T)]. Large basis sets were used, up to the quintuple-zeta doubly augmented size. The fitting functions contain an exponentially decaying component describing the short-range interactions and damped inverse powers expansions for the third- and fourth-order dispersion contributions. The SAPT and CCSD(T) potentials are very close to each other. The largest uncertainty of the potentials comes from the truncation of the level of theory and can be estimated to be about 10 mK or 10% at trimer's minimum configuration. The relative uncertainties for other configurations are also expected to be about 10% except for regions where the nonadditive contribution crosses zero. Such uncertainties are of the same order of magnitude as the current uncertainties of the two-body part of the potential.     

Lyotropic structures in a thermotropic liquid crystal

We have investigated the nature of didodecyldimethylammonium bromide (DDAB)/water aggregates dispersed in 4-n-pentyl-4'-cyanobiphenyl thermotropic liquid crystal (5CB). The structure of this microemulsion has been probed by small-angle neutron and X-ray scattering experiments far above the nematic-to-isotropic phase transition temperature of the solvent. Our data show that the stability of this system is controlled by strong attractive van der Waals interactions between spherical inverted micelles. These interactions also explain why other swollen mesophases in related cosurfactant/DDAB/water/5CB phase diagrams are not observed. When approaching the isotropic-to-nematic phase transition, scattering experiments additionally confirm the predominance of an increasing attractive interaction due to the 5CB paranematic fluctuations.     

Induced isotropic scattering from liquid carbon dioxide

The lineshape of the isotropic induced scattering has been measured from polarized and depolarized Rayleigh bands of CO₂ fluid. A comparison with other “collision-induced” spectra has been performed. It is argued that the scattering is dominated by two- and three-body interactions.     

Multiscale coarse-graining and structural correlations: connections to liquid-state theory

A statistical mechanical framework elucidates the significance of structural correlations between coarse-grained (CG) sites in the multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105). If no approximations are made, then the MS-CG method yields a many-body multidimensional potential of mean force describing the interactions between CG sites. However, numerical applications of the MS-CG method typically employ a set of pair potentials to describe nonbonded interactions. The analogy between coarse-graining and the inverse problem of liquid-state theory clarifies the general significance of three-particle correlations for the development of such CG pair potentials. It is demonstrated that the MS-CG methodology incorporates critical three-body correlation effects and that, for isotropic homogeneous systems evolving under a central pair potential, the MS-CG equations are a discretized representation of the well-known Yvon-Born-Green equation. Numerical calculations validate the theory and illustrate the role of these structural correlations in the MS-CG method.     

Monte Carlo simulations on mesophase formation using dipolar Gay-Berne model

We report the results of a Monte Carlo simulation of polar particles interacting via the Gay-Berne potential combining dipole-dipole interactions. Simulations were carried out on a system of 256 particles with either a zero dipole moment or longitudinal dipole moment located at the centre of the molecule. The system was found to spontaneously form nematic, smectic and crystal phases from an isotropic phase with a random configuration as temperature was decreased, irrespective of values of the dipole moment. The results do not give any indication of a net polarization even in the system with a strong dipole moment (μ* = 2.00). The transition temperature from the isotropic to nematic phase is not sensitive to the value of the dipole moment within the limits of statistical error, while the transition from the nematic to smectic phase depends on the strength of dipole moment. At lower temperatures forming the smectic or the crystal phase, the translational order along the director increases with increasing dipole moment. The dipolar interactions contribute to the long range ordering.     

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.     

A study of critical phenomena and dissipative nanostructures in self-organizing polymer systems

A research methodology based on scaling concepts is developed in detail for nonequilibrium polymer systems. Melt-crystallized linear high-density polyethylene is chosen as an example. In flexible-chain semicrystalline polymers, the transition from a solid isotropic or oriented state to a melt or from a solid isotropic state to an oriented state below the critical degree of polymerization occurs through necking at a nonzero external field on the combined line of first- and second-order phase transitions. A melt is a symmetric phase with a zero order parameter. Lamellar and fibrillar semicrystalline phases are phases with inherent order parameters that are periodic functions of one coordinate, and the neck draw ratio is another order parameter. At the critical degree of polymerization, all the phases are identical. In terms of the fluctuation theory of phase transitions and critical phenomena, the quantitative dependence of macroscopic properties on nanostructure parameters in this polymer material is revealed. The neck draw ratio and the draw ratio at break are macroscopic properties. The structure is characterized by the average thickness of amorphous layers. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the probability of collision of chain ends. In turn, this probability is proportional to the average thickness of amorphous layers in an isotropic sample. The problems of dynamic scaling and entanglements are discussed.