Intense laser light traversing a thin layer of nematic liquid crystal is an example of a simple, easy to realise physical system, that shows very complex behaviour. Light can turn the optical axis of ...this uniaxial medium while propagating through it, and the dynamical behaviour that results ranges from simple orientational instabilities, through low-dimensional chaotic behaviour, to spatiotemporal pattern formation. In this paper, we review recent advances in the theoretical description of the complex phenomena that light can induce in nematic liquid crystals. We discuss the various approximations made in the models, their range of applicability, and contrast their results with experimental observations. In particular, we discuss the achievements of the plane wave approximation in various geometries, and examine how the numerous bifurcation scenarios calculated from the models can be used to interpret observations. We treat with special emphasis the results achieved in the description of the strongly nonlinear regime, where experiments have revealed interesting bifurcations and chaotic behaviour. We also discuss the mostly open problems of transverse pattern formation and the effects that can be attributed to the finite cross-section of the laser beam.
Continuum theory is used to analyze the effect of an applied magnetic field on a ferronematic (i.e. dilute suspension of needle-like magnetic particles in nematic liquid crystal) with soft ...homeotropic anchoring between the ferroparticles and the director, and positive diamagnetic anisotropy of the liquid-crystalline matrix. It is shown that in infinite ferronematic a peculiar Fréedericksz-like transition takes place, at which by a threshold way the conditions of coupling on magnetic particles vary from homeotropic anchoring to planar one. The Fréedericksz transition field and saturation field are found as a functions of material parameters of a suspension. The continuum theory predicts the existence of three ferronematic phase (homeotropic, angular, and planar) with different relative orientations of the director and magnetization. The orientational structure of these ferronematic phases is studied.
The role of the elastic terms, linear in the spatial derivatives of the nematic director, on the director field is analyzed. We consider a nematic sample in the shape of a slab, limited by two ...identical surfaces, treated to induce homeotropic alignment. It is shown that these terms can be responsible for spontaneous Fréedericksz transitions induced by the thickness of the sample.
We show that magnetic colloids could increase the coupling of a liquid crystal to a week magnetic field. Magnetic Fréedericksz transition in a planarly oriented nematic liquid crystal doped with ...spherical ferromagnetic nanoparticles is considered theoretically. It is shown that even spherical nanoparticles could decrease a threshold of this transition because they strongly increase the magnetic field in the medium. This phenomenon indicates the possibility to use the considered system in magneto-optical displays.
Fréedericksz transitions between stationary planar deformation states, induced by cover surface interactions and by static external electric or magnetic field in a flat-parallel nematic liquid ...crystal cell, are studied theoretically in one-dimensional approximation. There is demonstrated that for initial stages of transition, when the deviation of director field from a boundary-induced state is small, the system of Euler-Lagrange equations for free-energy functional can be linearised and the threshold external field magnitudes can be deduced from eigenvalues of differential operator of second derivative for boundary eigenvalue problems with different boundary conditions. Different combinations of electric or magnetic field, parallel or perpendicular to the nematics layer boundaries, and different boundary conditions (including both strong and weak anchoring of nematics molecules) are analysed by using the same formalism. The considerations are based on Frank theory of static deformations of nematic liquid crystals. The formulae for the threshold fields, as depending on nematics and nematics-substrate coupling parameters, are derived. There are stated possible applications of these formulae to determining material parameters by exploiting threshold field magnitudes experimentally found.
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Dostopno za:
BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Le vieillissement physique est un sujet très actif en physique statistique car il ouvre la perspective d’une généralisation de la physique statistique à l’équilibre à des cas faiblement hors ...équilibre. Dans ce contexte où d’importants travaux ont été réalisés sur les polymères et les verres de spin, des travaux théoriques ont montré l’intérêt que pouvait apporter l’étude de système subissant une transition de phase du second ordre, les ingrédients théoriques étant plus simples. Nous avons donc étudié dans le détail la transition de Fréedericksz dans un cristal liquide qui est décrite par une transition du second ordre afin d’utiliser ensuite ce système pour faire une étude expérimentale du vieillissement au point critique. Nous avons alors montré que les équations usuellement utilisées (développement de l’énergie libre à la Landau) pour décrire la dynamique de cette transition ont un domaine de validité extrêmement mince qui n’est pas accessible expérimentalement. Il faut donc tenir compte des termes non linéaires de l’énergie libre pour décrire la dynamique du système, même dans le cadre de la réponse linéaire. Nous avons montré dans ce cadre le très bon accord entre la simulation numérique sans paramètre ajustable et les résultats expérimentaux. Nous avons ensuite étudié le comportement des fluctuations au voisinage du seuil de la transition et montré que lorsque la normalisation tenait bien compte du fait que la mesure est celle d’une variable quadratique, alors les fluctuations étaient d’amplitude maximale au seuil de la transition de Fréedericksz, comme on l’attend d’une transition du second ordre. L’étude de ces fluctuations permet alors de mesurer précisément la valeur du champ critique, ce qui est une mesure totalement nouvelle. Nous avons ensuite réalisé une étude de la dynamique des fluctuations du système lors de la réponse à une marche du paramètre de contrôle de la transition de Fréedericksz, et en particulier lors de trempes au point critique. Nous avons alors retrouvé les résultats prédits sur les systèmes de verres de spin, et nous montrons le lien entre la violation du théorème de fluctuation dissipation et l’évolution de la variance. Enfin nous avons monté un dispositif permettant de faire l’étude spatio-temporelle du système, nous avons montré que les 2 dispositifs mis en œuvre étaient limités par leur sensibilité dépendant de la valeur moyenne du paramètre d’ordre et nous proposons donc un autre système de mesure que nous n’avons pas eu le temps d’implémenter.
Physical aging is an active subject in statistical physics as it could lead to the generalization of equilibrium statistical physics to weakly out of equilibrium systems. In this context, where polymers and spin glasses have already been extensively studied despite not still well understood, theoretical works have shown new interests in systems undergoing a second order phase transition, where model ingredients are based on simpler physical arguments. Therefore, we studied in details a second order phase transition in liquid crystals : the Fréedericksz transition, in order to monitor experimentally aging at its critical point. We showed that the equations usually proposed to describe the dynamics of the transition (Landau like development of the free energy) have a very limited domain of validity, not accessible experimentally. In fact, one has to take into account the non-linearities, even in the vicinity of the Fréedericksz threshold and in the linear response regime. In this framework, we found a very good agreement between numerical simulations (no adjustable parameters) and experimental results. Then, we studied the behavior of fluctuations in the vicinity of the transition threshold and showed that, when ones takes into account the quadratic dependence of the measured variable, the fluctuations have a maximal amplitude at the threshold, as expected in a second order phase transition. This experimental study of fluctuations provides a new method to precisely measure of the value of the Fréedericksz threshold. A detailed analysis of the system dynamic fluctuations during quenches, and in particular, critical quenches was also performed, and we found the same behavior as predicted on spin glasses. The relation between fluctuation-dissipation theorem violation and variance evolution during the quench could be established. In parallel, we designed an experimental set-up to study the spatio-temporal fluctuations and also used a classical one, which both have sensitivity limits due to the mean value of the order parameter. We therefore propose a third set-up which could not be implemented due to a lack of time, that should overcome these difficulties.
We demonstrate experimentally that the transverse shape of the laser beam can strongly affect the laser-induced molecular reorientation in nematic liquid crystals. In this paper we studied only the ...case of elliptical beam cross-section. In this case, a relatively strong extra-torque was observed tending to reorient the liquid crystal director parallel to the ellipse major axis. The extra-torque is zero for circular beam cross-section and increases as the beam cross-section becomes more and more elliptical.
This work reports on the implementation of an an iterative procedure to solve the non-linear problem of wave propagation in homeotropic Nematic Liquid Crystals (N-LC). The nematic structure of the ...crystal molecules is strongly dependent on the applied external electromagnetic field. In our case, a monochromatic plane wave is normally incident on the liquid crystal, which is sandwiched between two glass layers. The orientation of these molecules, called the directors, determine the dielectric tensor properties of the medium. A Mode-Matching Technique (MMT) was used to accurately solve for the governing fields in each of the subdivided layers composing the crystal, whereas an explicit finite-difference scheme with relaxation was implemented to solve for the directors' orientation. The non-linear problem was also solved using a more efficient implicit finite difference scheme characterized by a faster convergence rate. Obtained computational results were compared to published data indicating good agreement.
In a liquid crystal cell, under a given boundary condition and an externally applied field, the liquid crystal is in director field configuration that minimizes the total free energy of the system. ...When an external electric field is applied to the liquid crystal, it will reorient because of the dielectric interaction between the liquid crystal and the applied field. This field‐induced reorientation of the liquid crystal is referred to as the Fréedericksz transition. Anchoring strength of alignment layers in liquid crystal devices has profound effects on the electro‐optical properties of the devices. This chapter considers how to measure anchoring strengths. In liquid crystal devices it is highly desirable that the alignment layer has a pretilt angle such that the reorientation of the liquid crystal is well controlled and uniform. Large pretilt angles can be measured by using the magnetic ‘null’ method.
We measure, under stationary conditions, the power spectrum of the transmitted and scattered light intensity in a planar nematic liquid crystal cell as a function of the applied voltage in the ...neighbourhood of the electrically-induced splay Fréedericksz transition. The Fréedericksz threshold is independently determined using a standard interferometric technique. The low-frequency noise spectral density of the transmitted light displays a well defined peak at the critical voltage; this feature is instead hidden in the scattering noise. We critically examine the performances of these different experimental techniques and show that noise measurements are an adequate tool to study orientation transitions in nematic liquid crystals.
