The Complex Ginzburg-Landau Equation for Beginners

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Low-voltage-driven electromechanical effects of swollen liquid-crystal elastomers

We experimentally investigate, in detail, electromechanical effects in liquid-crystal elastomers (LCEs) previously swollen with low-molecular-weight liquid crystals (LMWLCs). Both polydomain (POLY) and monodomain (MONO) LCEs were studied. We used a well known LMWLC, 4-n-pentyl-4-cyanobiphenyl (5CB) as a solvent. After swelling POLY and MONO LCEs (LSCE) with 5CB, shape changes were measured by recording the displacement of the edge of the swollen LCE at different voltages, V, and temperature. With 100 µm distance between electrodes, measurable shape changes (~1–20 µm) are observed with small voltages (V~0.5–10 V). In particular, we note that, compared to unswollen L(S)CEs, a dramatic ~200 times decrease of the threshold field was found for electromechanical effects in swollen L(S)CEs. While swollen MONO LCEs showed electromechanical effects in the planar geometry, homeotropic MONO swollen with homeotropically oriented 5CB did not. This is easy to understand because, in the homeotropic case, the liquid-crystal preferred axis is already aligned with the field so the field has no reorienting effect. The inverse of the response time when the field was switched on in both POLY and MONO was proportional to E2, which is the same field dependence as the response time of LMWLCs. When the field was switched off, the relaxation time showed a field dependence different from that of LMWLCs that we attribute to relaxation of the LCE network

Dynamics of line defects in nematic liquid crystals

FWN – Publicaties zonder aanstelling Universiteit Leide

Dynamical test of phase transition order

FWN – Publicaties zonder aanstelling Universiteit Leide

Standard and Embedded Solitons in Nematic Optical Fibers

A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wavepackets of transverse magnetic (TM) modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations (PDEs) which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order derivative nonlinearity, governing the dynamics for the amplitude of the wavepacket. In this derivation the dispersion, self-focussing and diffraction in the nematic are taken into account. Although the resulting nonlinear $PDE$ may be reduced to the modified Korteweg de Vries equation (mKdV), it also has additional complex solutions which include two-parameter families of bright and dark complex solitons. We show analytically that under certain conditions, the bright solitons are actually double embedded solitons. We explain why these solitons do not radiate at all, even though their wavenumbers are contained in the linear spectrum of the system. Finally, we close the paper by making comments on the advantages as well as the limitations of our approach, and on further generalizations of the model and method presented.Comment: "Physical Review E, in press

Tilt order parameters, polarity and inversion phenomena in smectic liquid crystals

The order parameters for the phenomenological description of the smectic-{\it A} to smectic-{\it C} phase transition are formulated on the basis of molecular symmetry and structure. It is shown that, unless the long molecular axis is an axis of two-fold or higher rotational symmetry, the ordering of the molecules in the smectic-{\it C} phase gives rise to more than one tilt order parameter and to one or more polar order parameters. The latter describe the indigenous polarity of the smectic-{\it C} phase, which is not related to molecular chirality but underlies the appearance of spontaneous polarisation in chiral smectics. A phenomenological theory of the phase transition is formulated by means of a Landau expansion in two tilt order parameters (primary and secondary) and an indigenous polarity order parameter. The coupling among these order parameters determines the possibility of sign inversions in the temperature dependence of the spontaneous polarisation and of the helical pitch observed experimentally for some chiral smectic-{\it $C^{\ast}$} materials. The molecular interpretation of the inversion phenomena is examined in the light of the new formulation.Comment: 12 pages, 5 figures, RevTe

Crystallization of the ordered vortex phase in high temperature superconductors

The Landau-Khalatnikov time-dependent equation is applied to describe the crystallization process of the ordered vortex lattice in high temperature superconductors after a sudden application of a magnetic field. Dynamic coexistence of a stable ordered phase and an unstable disordered phase, with a sharp interface between them, is demonstrated. The transformation to the equilibrium ordered state proceeds by movement of this interface from the sample center toward its edge. The theoretical analysis dictates specific conditions for the creation of a propagating interface, and provides the time scale for this process.Comment: 8 pages and 3 figures; to be published in Phys. Rev. B (Rapid Communications section

Non-singular disclinations of strength S = + 1 in nematics

It is shown that the energy of a screw disclination of strength + 1 [1] (2 π rotation of the director around the line) is reduced if the molecules are allowed to relax out of the plane perpendicular to the line. This solution has no singularity on the axis, r = 0. The calculation is done in the case of the anisotropic elasticity [2] for the pure splay-bend and twist-bend cases. It satisfies de Gennes' [3] molecular field. The line energy of the solution does not depend upon the size R of the specimen. When R becomes smaller than a critical value of the order of several molecular lengths, the Frank solution with an isotropic (or nematic) core is preferable.On montre que les lignes de singularité de rang + 1 dans les nématiques (S = + 1 correspondent à une rotation de 2 π du directeur autour de la ligne) sont d'énergie minimale lorsque le directeur a une composante hors du plan perpendiculaire à la ligne et se trouve parallèle à la ligne le long de celle-ci. On fait le calcul de la configuration et de l'énergie dans les cas des déformations purement astrales (splay-flexion) et purement circulaires (torsion-flexion), en tenant compte de l'anisotropie des constantes élastiques. Ces solutions satisfont à la condition de champ moléculaire de de Gennes. L'énergie de la ligne ne dépend pas de la taille R de l'échantillon (supposé cylindrique). Pour R inférieur à une valeur critique de l'ordre de quelques longueurs moléculaires, la solution de Franck avec cœur (isotrope ou nématique) est préférable

Smectic X : the first truly ferroelectric liquid crystal

We report the identification of the first truly ferroelectric liquid crystal in a compound which also shows chiral C, I and G' phases at higher temperatures. In the new phase the director can be oriented in a bistable way with an electric field V in a time τ such that V.ln τ is proportional to temperature. Furthermore, when the field is turned off, the orientation remains. This behaviour indicates a fundamental difference between the new phase and bulk chiral smectics.Nous présentons des résultats expérimentaux permettant d'identifier la première mésophase véritablement ferroélectrique dans un composé qui présente également des phases C, I et G' à plus haute température. Dans cette nouvelle phase, le directeur s'oriente de façon bistable sous un champ électrique V. Le temps caractéristique τ de ce processus est tel que V.ln τ est proportionnel à la température. De plus, l'échantillon reste orienté même après la suppression du champ. Ce comportement indique une différence fondamentale entre cette nouvelle phase et les smectiques chiraux en volume