Lech Longa

Landau theory of the nematic-isotropic phase transition

Abstract A review is given of the wide variety of predictions that results from a Landau-type of description of the nematic-isotropic phase transition. This includes a discussion of the nature of the order parameter and of the various types of possible phases, of the influence of external fields, and of the effect of inclusion of spatial variations of the order parameter. The various predictions are compared with the available experimental results. It is concluded that there is still no clear picture about the nature of the singularity near the nematic-isotropic phase transition. Though the assumption of classical (mean-field) critical behaviour seems to be incorrect, there is no conclusive proof which alternative applies.

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Abstract Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and ...

Simple model of induced smectic phases in binary mixtures of liquid crystals

The origin of the occurrence of induced smectic phases (ISP) in binary mixtures of liquid crystals is discussed. First the experimental evidence is reviewed, which leads to a division in strong complexing (electron–donor–acceptor complex as indicated by a charge–transfer band) and weak complexing, where only indirect evidence is available. Within the mean field approximation a theoretical model is given in which the influence of complex formation on the nematic–smectic‐A transition temperature is investigated for ideal orientational order. The ISP mechanism is attributed to the dispersive interactions between the complexes. However, in principle in a two‐component mixture without complexing also ISP can be obtained due to interactions involving permanent dipoles. From fits to experimental phase diagrams and from estimates of parameters it follows that the first mechanism is more likely. Three nonstandard groups of phase diagrams with characteristic maxima of minima are predicted. The location of the extre...

Landau-De Gennes Theory of Biaxial Nematics Reexamined

Recent experiments report that the long-looked-for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations, we concentrate on some elementary theoretical issues concerned with the classical sixth-order Landau-de Gennes free energy expansion in terms of the symmetric and traceless tensor order parameter Q alpha beta. In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple, critical, and tricritical points and with multiple (reentrant) biaxial and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.

ROUNDOFF-INDUCED COALESCENCE OF CHAOTIC TRAJECTORIES

Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of precision of calculations. Two generic behaviors of the average coalescence time are identified: exponential or linear. In both cases no synchronization occurs if iterations are done with {\em infinite} precision.

MOLECULAR DYNAMICS SIMULATIONS OF A GAY-BERNE NEMATIC LIQUID CRYSTAL : ELASTIC PROPERTIES FROM DIRECT CORRELATION FUNCTIONS

We report molecular dynamics simulations of a Gay–Berne nematic liquid crystal at constant temperature and density/pressure using the generalization of an algorithm recently proposed by Toxvaerd [Phys. Rev. E 47, 343 (1993)]. On the basis of these simulations the absolute values of the Oseen–Zocher–Frank elastic constants K11, K22, and K33 as well as the surface constants K13 and K24 have been calculated ab initio within the framework of the direct correlation function approach of Lipkin et al. [J. Chem. Phys. 82, 472 (1985)]. The angular coefficients of the direct pair correlation function, which enter the final equations, have been determined from the computer simulation data for the pair correlation function of the nematic by combining the Ornstein–Zernike relation and the Wiener–Hopf factorization scheme. The unoriented nematic approximation has been assumed when constructing the reference state of Lipkin et al. By an extensive study of the model over a wide range of temperatures, densities and pressu...

On the tricritical point of the nematic–smectic A phase transition in liquid crystals

Using the Landau expansion simple formulas are found that allow for systematic calculations of the tricritical temperature for a given molecular model. The theory is applied to some molecular models of the nematic–smectic A (NA) phase transition of liquid crystals. It is shown exactly that for a large class of molecular theories the NA tricritical temperature depends only on the couplings between the two lowest order translational order parameters and the orientational degrees of freedom. The relative importance of these couplings on tricritical behavior is studied in detail in the mean‐field approximation. Numerical analysis is carried out for various molecular models of the smectic A phase including the McMillan model and its generalizations. It is shown that for an experimentally relevant class of models, the presence of second and higher order harmonics does not influence the tricritical temperature in an essential way, which means that the coupling between orientational and translational degrees of f...

Computer simulation studies of anisotropic systems. XXVII. The direct pair correlation function of the Gay–Berne discotic nematic and estimates of its elastic constants

Monte Carlo simulations have been performed for a discotic liquid crystal composed of Gay–Berne particles. On the basis of these simulations for the nematic phase, a subset of the spherical harmonic expansion coefficients of the direct pair correlation function (DPCF) were determined from the pair distribution function (PDF) by solving the Ornstein–Zernike (OZ) equation. This was achieved by generalizing the Wiener–Hopf factorization scheme for the numerical solution of the OZ equation. Only the expansion coefficients gl1,l2,l(r) (lα⩽4) of the PDF in the laboratory frame were used when solving the OZ equation; this means that the DPCF so obtained is equivalent to that for a nematic in which the director is randomly distributed. From the DPCF, the scaled Oseen–Zocher–Frank elastic constants K11*, K22*, and K33*, as well as the surface constant K13*, have been calculated from the subset of expansion coefficients. Generally, we find that K33*

Density functional approach to study the elastic constants of biaxial nematic liquid crystals

A density functional theory for bulk and surface elastic constants of biaxial nematic liquid crystals is developed. It is based on a functional Taylor expansion of the free energy of a distorted biaxial nematic with respect to the one-particle distribution function. Detailed microscopic expressions for the biaxial elastic constants of bulk and surface deformations are derived by expanding further the distribution functions into symmetry-adapted Wigner matrices. The final expressions depend on generalized orientational order parameters characterizing the biaxial nematic and on expansion coefficients of the direct pair correlation function. The case where the expansions are truncated at the lowest nontrivial order with respect to the momentum index of the Wigner matrices is analyzed in detail. It gives only six distinct, nonzero bulk elastic constants. The mixed elastic constants, which measure distortions of more than one director, vanish within this approximation. As in the uniaxial case, a splay-bend deg...

Elastic Constants of Nematic Liquid Crystals From Molecular Dynamics Simulations

Abstract The Frank-Oseen elastic constants K 11, K 22 and K 33 as well as the surface constants K 13 and K 24 have been calculated for Gay-Berne nematic liquid crystal with anisotropy parameters k = 3 and k′ = 5. In deriving the elastic constants a direct correlation function approach of Poniewierski and Stecki1 in a version proposed by Lipkin et al. 5 was choosen. The final formulas have been expressed in terms of the orientational order parameters and of the angular coefficients of the direct correlation function of an unoriented nematic. The latter have been determined exactly from the molecular dynamics simulations in the NVT ensemble. Results for the surface elastic constants, qualitatively different than those obtained from all previous treatments, clearly show that the surface deformations are strongly sensitive to details of the direct correlation function. Obtained values of surface elastic constants are partly negative and an order of magnitude smaller than bulk elastic constants.