74 research outputs found
THE PHENOMENOLOGICAL FUNCTIONS THAT CHARACTERIZE THE SURFACE FREE-ENERGY DENSITY OF NEMATIC LIQUID-CRYSTALS - A MICROSCOPIC ANALYSIS
No full textIn recent paper, Faetti proposed a new phenomenological expression for the surface free energy density F-s of a nematic Liquid crystal in contact with an isotropic substrate. F-s depends on director n, on the unit vector k orthogonal to the interface and on their gradients at the interface. Five different terms appear in the expression of F-s. The first term is the standard anchoring energy contribution, the second and third terms are elastic contributions that depend on the surface tangential director gradients, the fourth and fifth terms are new geometrical contributions that account for the effect of a local curvature of the interfaces. The expression of the surface free energy density is characterized by five phenomenological functions W(n(k)), K-13*(n(k)), K-24*(n(k)), A(1)(n(k)) and A(2)(n(k)) where n(k) is the scalar product n . k. In this paper we give the first microscopic calculation of these new surface functions by using a simplified microscopic model of intermolecular interactions. Surface functions A(1)(n(k)), A(2)(n(k)), and K-24*(n(k)) are found to be of the same order of magnitude of the Frank bulk elastic constants, whilst K-13*(n(k)) = 0. The geometric surface functions A(1)(n(k)) and Az(nk) satisfy the simple relation A(1)(n(k)) = -n(k)(2) A(2)(n(k)). Both the results K-13*(n(k)) = 0 and A(1)(n(k)) = n(k)(2) A(2)(n(k)) are shown to be a direct consequence of the invariance with respect to the transform n --> -n of the interaction energy between molecules
Comment on "Phenomenological approach to the problem of the K13-surface-like elastic term in the free energy of a nematic liquid crystal
No full textIn a recent paper [Phys. Rev. E 48, 1254 (1993)], an alternative procedure is proposed for obtaining the nematic director field that minimizes the total free energy of a nematic liquid crystal. In this Comment we show that this solution does not correspond to a minimum of the free energy
Splay-bend surface elastic constant of nematic liquid crystals: A solution of the Somoza-Tarazona paradox
No full textThe Nehring-Saupe [J. Chem. Phys. 54, 337 (1971); 56, 5527 (1972)] elastic free energy of nematic liquid crystals (NLCs) contains the splay-bend elastic constant K-13, which affects only the elastic surface free energy. Several years ago, Somoza and Tarazona [Mol. Phys. 72, 991 (1991)]. showed that the value of K-13 depends on the nonlocal to local mapping that is used to define the local elastic free energy. Then they concluded that the splay-bend constant is not a well-defined physical parameter. In the present paper we show that the Somoza-Tarazona result comes from an inconsistent treatment of the boundary effects. If all the boundary effects are correctly taken into account in an elastic approach, the elastic surface free energy contains an effective elastic constant K-13(eff) that is mapping independent. K-13(eff) is the sum of three different constants: the classical Nehring-Saupe bulk constant K-13 and two specific interfacial constants K-1 and K-h. While each surface constant (K-13, K-1, and K-h) depends on the kind of nonlocal to local mapping, the resulting surface constant K-13(eff)=K-13+K-1+K-h is mapping independent. Using a simple molecular model of the intermolecular interactions, we obtain explicit expressions of K-13(eff) in terms of the characteristic parameters of the intermolecular energy. In the final part of this paper we discuss the meaning and the physical consequences of the elastic surface free energy F-s. We show that F-s is a semimacroscopic; parameter that provides an approximate elastic description of the interfacial layer. Furthermore, we point out that the elastic surface free energy should not be confused with the thermodynamic surface free energy that appears in a consistent continuum theory of NLCs
THE EFFECT OF A FINITE ANCHORING ENERGY ON THE TRANSIENT PERIODIC STRUCTURES IN NEMATIC LIQUID-CRYSTALS
No full textElastic effects of long range quadrupolar interactions in nematic liquid crystals
No full textWe discuss the role of the quadrupolar interaction in nematic liquid crystal samples in the shape of a slab limiting the study to planar deformations. Our analysis shows that this interaction gives rise to a bulk energy density that, in the elastic approximation, depends linearly on the second spatial derivative and quadratically on the first spatial derivative of the nematic orientation. We show that this bulk energy density can be separated in a surfacelike term, which gives rise just to a surface contribution, plus a term having the usual form. Both terms depend on the first derivative of the tilt angle and are proportional to the square of the electrical quadrupolar density. The bulk term, quadratic in the first derivative of the tilt angle, renormalizes the usual elastic energy density connected to the shea-range forces. The bulk elastic constant of quadrupolar origin can be negative and one order of magnitude smaller than the effective elastic constants for typical nematic liquid crystals. According to our analysis this interaction is responsible for an elastic anisotropy proportional to the square of the electrical quadrupolar density, which depends on the nematic orientation. The surfacelike term is proportional to the first derivative of the tilt angle. It calls mind to the splay-bend elastic term, although the tilt angle dependence is more complicated. The relevant elastic constant is of the same order of magnitude as the bulk one, due to the same interaction. We evaluate also the energy density in the surface layers, where the quadrupolar interaction is restricted by the surface. In this case we show that the free energy contribution due to the surface layers is reduced to a classical anchoring energy. The solution of the variational problem by means of a simple version of the density functional theory is presented. [S1063-651X(98)11612-4]
THEORY OF SURFACELIKE ELASTIC CONTRIBUTIONS IN NEMATIC LIQUID-CRYSTALS
No full textIn a recent paper we carried out a systematic expansion of the free-energy density of nematic liquid crystals (NLC's) in the director derivatives for planar director distortions and small director angles. At any order of expansion, the director distortion is the superposition of a standard long-range bulk director distortion and a very-short-range subsurface distortion. The bulk macroscopic distortion is found to be the same as that which is obtained using the Frank elastic form of the free-energy density and an effective anchoring energy function f(s) which implicitly contains the surfacelike elastic constant K13 and all higher-order elastic constants. In this paper we generalize this theoretical result and extend it to the case of large director angles using the Gibbs theory of interfacial phenomena. Furthermore we extend the theoretical analysis to the more general case of nonplanar director distortions. An alternative theoretical expression of the first-order free-energy density that does not present mathematical problems, and allows us to study any kind of director distortion in NLC's, is proposed. In the nonplanar case, both of the surfacelike elastic constants K)3 and K24 are shown to make explicit contributions to the first-order free-energy density. Recent theoretical and experimental results concerning the elastic behavior of a NLC sample enclosed in a cylindrical cavity are reanalyzed in terms of the present theoretical procedure. Rough estimates of the surfacelike elastic constants K13 and K24 are obtained from the analysis of the experimental results. A surface orientational transition, which makes it possible to measure the K13 surfacelike elastic constant, is predicted to occur at a critical value of the radius R of the cylindrical cavity
van der Waals induced distortions in nematic liquid crystals close to a surface
No full textBy a discrete-layer model, we investigate theoretically the alignment of a nematic liquid crystal close to a hat amorphous substrate. We show that the presence Df van der Waals interactions induces a strong distortion Idealized in a few molecular lengths. We compare these predictions with that of a continuum model recently developed by some of us. In the continuum model, we derive approximate analytical expressions for the distortion profile, showing that, asymptotically, the distortion decays as the inverse of the distance from the substrate. The amplitude of the distortion according to the two models is different, but the main qualitative features remain unchanged. We show that the main distorting mechanism can be attributed to an effective surface field. The existence of a subsurface distortion is compatible with some recent measurements of the alignment of the first molecular layer, performed with optical second-harmonic generation techniques
EXPERIMENTAL INVESTIGATION OF SURFACE DEFORMATIONS AT THE NEMATIC-ISOTROPIC INTERFACE - A NEW METHOD TO MEASURE THE NEHRING-SAUPE ELASTIC-CONSTANT K-13 (+)
No full textStructural deformations of a nematic-isotropic interface induced by magnetic field have been predicted some years ago by de Gennes. In this paper we extend the de Gennes' theory in order to account for the finite anchoring energy of the director at the interface, for the anisotropy of the elastic constants K11 and K33 and for the effect of the elastic constant K13 introduced by Nehring and Saupe. We obtain a simple analytical expression which relates the maximum tilt angle of the interface to the surface director polar angle, to the elastic constants, to the surface tension and to the magnetic field. Therefore a measurement of this tilt furnishes a direct method to measure the K13 constant which cannot be measured by standard techniques. The predictions of the theory have been verified experimentally at the nematic-isotropic interface of the liquid crystal 4-cyano-4'-n-heptylbiphenyl (7CB). Both the geometry and the magnetic field-dependence of the surface deformations are found to agree satisfactorily with the theoretical predictions. An upper limit to the elastic constant K13 is obtained from the experiment.Les déformations structurelles de l'interface nématique-isotrope d'un cristal liquide nématique dans un champ magnétique ont été étudiées théoriquement par de Gennes. Dans cet article nous généralisons la théorie de de Gennes en prenant en considération l'anisotropie des constantes élastiques, l'énergie d'ancrage finie et l'effet de la constante élastique K13 de Nehring et Saupe. Nous trouvons une expression analytique simple qui relie l'angle maximum d'inclinaison de l'interface à l'angle polaire du directeur en surface, aux constantes élastiques, à la tension superficielle et au champ magnétique. Nous montrons que la mesure de cette inclinaison peut permettre d'obtenir l'énergie d'ancrage et la constante élastique K13. Les prévisions de la théorie ont été vérifiées expérimentalement à l'interface nématique-isotrope du cristal liquide 7CB. La géométrie et la dépendance en champ magnétique des déformations de la surface sont en accord satisfaisant avec les prédictions théoriques. On déduit des expériences une borne supérieure à la constante élastique K13
MOLECULAR-ORIENTATION AND ANCHORING ENERGY AT THE NEMATIC-ISOTROPIC INTERFACE OF 7CB
No full textThe properties of the nematic-isotropic interface of the nematic liquid crystal 7CB are studied by optical reflectometry. It is found that at the interface the director is tilted with respect to the vertical axis. Measurements are reported of the tilt angle θt, of the thickness of the interface, and of the anchoring energy.Nous étudions par réflectométrie optique les propriétés de l'interface nématique-isotrope du cristal liquide 7CB. Nous mesurons l'épaisseur de l'interface, l'angle polaire du directeur à l'interface et son énergie d'ancrage
Refractive indices of liquid crystals E7 and K15 in the mid- and near-IR regions
No full textThis paper presents the results of refractive-index measurements of the extraordinary and ordinary rays in nematic liquid crystals (NLCs) using a refractometric technique in the mid-IR (gimel = 10.6 mu m) and near-IR (gimel = 1550 nm) regions for NLC E7 and at (gimel = 1550 nm) regions for NLC K15. The optical anisotropy of NLC E7 at 10.6 mu m is determined independently by means of the interferometric method in order to compare it with the results obtained by the refractometric technique. (c) 2006 Optical Society of America
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