Patterns in Thin Liquid Crystal Films and the Divergence (“Surfacelike”) Elasticity

Lavrentovich, Oleg D.; Pergamenshchik, V. M.

doi:10.1142/s0217979295000926

Cited by 100 publications

(93 citation statements)

References 35 publications

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“…Thus, these terms are often neglected when surface effects are not important. Surface-like terms have been the object of intense research activity, encompassing both theoretical and experimental issues [13]. The saddle-splay contribution has been shown to be responsible for the induction of spontaneous deformation and pattern formation in nematic layers [26,27].…”

Section: Molecular Theories For the Elastic Constants Of Nematicsmentioning

confidence: 99%

“…Calculations were performed in the same molecular frame for all conformers and the average values then evaluated according to Equation (13), with the orientational distribution function of the undeformed nematic phase. The Saupe ordering matrix of a mesogen was also obtained in this way and then diagonalised.…”

Section: Predictions For Schiff's Bases and Thiadiazole Derivativementioning

confidence: 99%

“…He predicted the dependence of elastic constants on the orientational order parameter, K , S 2 [6], which he could then test experimentally [7]. Moreover, he derived an expression for the elastic free energy, hence denoted as the 'Nehring-Saupe' form [8,9]; this contains the secondorder splay-bend contribution, which has been the object of intense debate in subsequent years [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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The theory of elastic constants

Ferrarini

2010

Liquid Crystals

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The elastic theory of liquid crystals can be traced back to the early 1930s, but the origin of the molecular theory of elastic constants must be postponed to more than 30 years later, when Alfred Saupe wrote his famous papers on this subject. At approximately the same time, the seminal works by Priest and Straley also appeared. Since then, several theories have been developed to connect intermolecular interactions to curvature deformations, on a quite different length-scale, in liquid crystals. This field was particularly alive between the end of the 1970s and the beginning of the 1980s, in parallel with experimental investigations. In more recent times, a renewed interest was aroused by the controversy about the second-order splay-bend contribution, which appears in the Nehring-Saupe expression for the deformation energy density. In the first part of the present contribution the molecular theory of elastic constants is briefly reviewed. This paper focuses on the effects of molecular structure on the elastic constants of thermotropic nematics and the ability of different models to account for them. A few classical examples are discussed to illustrate these issues. The second part of this paper is dedicated to our recent 'Surface Interaction' model, a molecular field approach based on the Maier-Saupe theory, implemented into a framework allowing for atomistic molecular modelling. The theoretical background is outlined, then some new results are reported and the insights derived from a realistic molecular representation are discussed. We conclude that, after about 40 years of theoretical investigations, there is a general consensus on the importance of the molecular shape in determining the elastic constants of nematics: for fairly rigid compounds these can be simply related to the length-to-width ratio, but for the general case of non-rigid mesogens the molecular flexibility and shape curvature have to be taken into account

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Section: Molecular Theories For the Elastic Constants Of Nematicsmentioning

confidence: 99%

Section: Predictions For Schiff's Bases and Thiadiazole Derivativementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The theory of elastic constants

Ferrarini

2010

Liquid Crystals

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“…From the basic research side the main interest is connected to the formation of various types of defects and to how these defects are related to the elastic and ultimately to the molecular properties of the material. Experimentally a great amount of work has been performed by various groups [4,5]. Theoretically the approach has normally been based on continuum elastic theories [2,3], although recently computer simulations have also been applied to study the involved phenomena [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Simulations of Topological Defects in Nematic Liquid Crystal Films

Chiccoli

Pasini

Feruli

et al. 2003

Molecular Crystals and Liquid Crystals

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“…The crucial feature of the present MC simulations is the type of boundary conditions (BC) imposed onto the system through layers of spins with suitably fixed orientations. We mimic a hybrid aligned nematic (HAN) cell [9]. The spins of the bottom layer, z 0, have random fixed orientations in the horizontal ͑x, y͒ plane, while those of the top layer, z h, are fixed along the surface normal.…”

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confidence: 99%

Monte Carlo Simulations of Stable Point Defects in Hybrid Nematic Films

et al. 1997

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Monte Carlo (MC) simulations based exclusively on nearest-neighbor intermolecular interactions reveal the existence of stable long-range deformations and topological defects in a thin nematic film confined between two surfaces with antagonistic (normal and tangential) molecular orientations. Thus the MC technique allows one to describe a delicate balance of bulk elasticity and surface energy usually treated only with macroscopic theories. [S0031-9007(97)04727-3] PACS numbers: 61.30. Cz, 61.30.Gd, 64.70.Md There are three well-known mechanisms that lead to the formation of topologically stable defects [1] in systems with spontaneously broken symmetry. The first one is fast quench through phase transitions [2,3]. The defects appear as a result of the combination of domains with a different (but uniform within each domain) phase of the order parameter. These defects annihilate in the phase ordering process. Second, defect networks can emerge as stable structures to minimize the bulk energy. Wellknown examples are Abrikosov lattices in superconductors and the so-called twist grain boundary [4,5] and blue phases [6] of liquid crystals (LC). In both the above mechanisms the presence of bounding surfaces plays no significant role in the formation of the defects. Contrary to this, in the third mechanism stable defects appear as a topological response of the system to a closed bounding surface. For example, for spherically bounded liquid crystal droplets the Poincaré and Gauss theorems guarantee the existence of defects provided the anisotropic surface energy WR 2 overweights the bulk elastic energy KR (i.e., the system size R is larger than R C K͞W ), where K is an effective elastic constant and W is the anchoring coefficient [7]. A similar phenomenon occurs when one disperses sufficiently large particles in the liquid crystal bulk [8]. The above topological mechanisms do not work, however, when the boundary is not closed or when the socalled Euler characteristic of the boundary is zero (as in the case of a torus).In this Letter we report the results of Monte Carlo (MC) simulations with purely microscopic molecular interactions that show the appearance of stable topological defects for a system in which none of the above three mechanisms appears to be called to action. Defects appear in nematic films with hybrid boundary conditions when the film thickness h is much smaller than its lateral size L. Although similar results are established experimentally and on the basis of continuum theory [9], neither microscopic theory derivations nor computer simulations of such stable defects exist for this LC system. MC simulation is a particularly attractive technique to study defects [10], since it provides a way of determining equilibrium molecular organizations starting in principle from an arbitrary one. More interestingly the technique can be used to examine the relative stability of a configuration used as a starting one, to see if and how it evolves into another one of lower free energy.Here we deal with a model where the ...

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Patterns in Thin Liquid Crystal Films and the Divergence (“Surfacelike”) Elasticity

Cited by 100 publications

References 35 publications

The theory of elastic constants

The theory of elastic constants

Simulations of Topological Defects in Nematic Liquid Crystal Films

Monte Carlo Simulations of Stable Point Defects in Hybrid Nematic Films

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