1,721,035 research outputs found
ON THE K13 SURFACE-LIKE ELASTIC-CONSTANT AN EXPERIMENTAL-METHOD TO TEST DIFFERENT THEORETICAL-MODELS
No full textOldano and Barbero showed that, due to the presence of the surface-like elastic constant K13 in the expression of the elastic free energy density, F2, in a nematic liquid crystal, the functional F2 is unbounded from below and thus it is impossible to find an equilibrium director distortion. In particular, they showed that the surface-like elastic constant favours a discontinuity of the director-field at the interfaces. In recent years two quite different theoretical approaches have been proposed to eliminate the mathematical difficulties related to the K13 problem. Barbero et al., expanded the free energy functional F up to the fourth order in the director derivatives and showed that the minimization problem becomes mathematically well posed. A strong subsurface director distortion on a length scale of the order of the molecular length is predicted by using this approach. This point has been critized by V. Pergamenshchik who considers the subsurface strong distortion as an artefact of theory and proposes an alternative method to account for the effect of K13. This method is virtually coincident with that already proposed by Hinov on the basis of an a priori assumption. In this paper we discuss some direct consequences of these two different approaches and we propose two simple experimental measurements which should lead to different results depending on which model is the correct one, allowing in this way a test of the different theoretical models
The effects of curvature on nematic liquid crystals confined in a cylindrical cavity
No full textIt has been shown that the surface free energy for a smooth interface between a nematic liquid crystal (NLC) and an isotropic medium contains four different contributions: a standard anchoring term, an elastic term and two curvature terms, In this paper we show that the four coefficients that enter the surface free energy can be obtained from suitable experiments performed on NLCs confined in a cylindrical cavity. It is also shown that the new surface free energy provides a satisfactory explanation for an apparent discrepancy of some previous experimental results. (C) 1998 Elsevier Science B.V
Measurements of the azimuthal anchoring energy at a polyimide-nematic interface with a new transmitted light method
No full textA new transmitted light method has been used to measure the azimuthal anchoring energy coefficientWat the interface between the nematic liquid crystal 5CB and a rubbed polyimide substrate. This method overcomes the typical drawbacks of the transmitted light methods and provides an unambiguous measurement of the director rotation at the surface. The contributions of the bulk director distortion are very small and can be easily separated from those due to the anchoring. The measurements can be performed also in the critical case of somewhat strong anchoring. The small optical anisotropy of the orienting layer (polyimide)can be also taken into account
RESUMMATION OF HIGHER-ORDER TERMS IN THE FREE-ENERGY DENSITY OF NEMATIC LIQUID-CRYSTALS
No full textThe presence of the surfacelike elastic constant K13 in the expression of the elastic free-energy density F2 for a nematic liquid crystal (NLC) makes the free-energy functional unbounded from below. A discontinuity of the director field has been predicted to occur at the interfaces of the NLC. In recent years two very different theoretical approaches have been proposed to bypass mathematical difficulties related to the K13 problem. Hinov and Pergamenshchik [Mol. Cryst. Liq. Cryst. 148, 197 (1987); 178, 53 (1990), and references therein; Phys. Rev. E 48, 1254 (1993)] consider the surface director discontinuity is an artifact of theory and make the assumption that the director field must be sought in the class of continuous functions. With this assumption a well defined solution for the equilibrium director field can be found and new phenomena are predicted to occur. Barbero and co-workers [Nuovo Cimento D 12, 1259 (1990); Liq. Cryst. 5, 693 (1989)] expanded the free-energy functional F up to the fourth order in the director derivatives (second-order elastic theory) and showed that the minimization problem now becomes mathematically well posed. A strong subsurface director distortion on a length scale of the order of the molecular length is predicted to occur by using this approach. The macroscopic consequence of the strong subsurface distortion is an apparent renormalization of the anchoring energy as far as the long-range bulk distortion is concerned. In the first part of this paper we propose a simple and rigorous test based on the general principles of mechanics to establish the internal consistency of these very different theoretical approaches. The second-order elastic theory is found to satisfy this test, while the Hinov-Pergamenshchik model is found to be in contrast with it. In the second part of this paper we make a systematic expansion of the free energy at any order in the director derivatives and we analyze the physical effects of the higher-order contributions that were disregarded by the second-order theory. At any expansion order a strong subsurface director distortion is predicted to occur and its macroscopic effect is shown to be equivalent to an apparent renormalization of the anchoring energy. Therefore, the main qualitative predictions of the second-order elastic theory remain satisfied at any expansion order, although the quantitative behavior of the system is found to be greatly affected by higher-order contributions
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
THE K-13 SURFACE-LIKE ELASTIC-CONSTANT - ANALYSIS OF THE PREDICTIONS OF DIFFERENT THEORETICAL-MODELS
No full textIn recent years two very different theoretical approaches have been proposed to by-pass the mathematical difficulties related to the problem of finding the director-field in a nematic liquid crystal when the surface-like elastic constant K-13 is different from zero. Barbero et al. expanded the free energy functional up to the fourth order in the director derivatives and showed that, under these conditions, the minimisation problem now becomes correctly set from the mathematical point of view. A strong subsurface director distortion on a length scale of the order of the molecular length is predicted by using this approach. Hinov and V. Pergamenshchik consider the subsurface strong distortion as an artefact of theory and propose an alternative method to account for the effect of K-13. In this paper we analyze the consequences of these different theoretical approaches in the case of a nematic layer with a tilted director orientation at one interface and in the presence of a magnetic field. In this special case (tilted alignment), we show that, for every value of K-13, the Hinov-Pergamenshchick method predicts very unusual phenomena, whilst no anomalous macroscopic phenomenon is predicted by the second order elastic theory. According to this latter theory, the macroscopic behaviour of the system is demonstrated to be fully equivalent to that predicted by the first order Frank theory (K-13 = 0) if the actual easy axis at the interfaces and the anchoring energy are substituted by an ''effective easy axis'' and an ''effective anchoring energy.'' A simple experimental method to test the different predictions of the two theories is proposed
On the validity of the elastic expansion of the free energy of nematic liquid crystals
No full textThe elastic free energy F-el of nematic liquid crystals is a truncated power expansion of the free energy F in the gradients of the director field n(r). In principle, the cut-off distortion length for F-el could be estimated from the direct comparison between the elastic terms and the higher order ones. However, in the case of dispersion interactions, the higher order elastic constants diverge and this comparison is not possible. The divergence of the higher order constants poses some doubt about the internal consistency of the elastic expansion itself. In this paper, we use a molecular model of a nematic liquid crystal to calculate the total free energy and its elastic approximation. The two free energies are calculated numerically for some director configurations as a function of the characteristic distortion length L-dis. A good agreement between the two free energies is found for slow director fields, and large deviations are observed only if L-dis approximate to a, where a is the molecular length. This result demonstrates the validity of the elastic expansion and shows that the higher order terms affect only the behavior at very short length scales. (C) 1999 Elsevier Science B.V
A REFLECTOMETRIC METHOD TO MEASURE THE AZIMUTHAL ANCHORING ENERGY OF A NEMATIC LIQUID-CRYSTAL
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