Distorsion d'UNE Lamelle Nématique Sous Champ Magnétique Conditions d'ANCRAGE Aux Parois

Rapini, Alessandro; Papoular, M.

doi:10.1051/jphyscol:1969413

Cited by 804 publications

(489 citation statements)

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“…f bulk is the Frank energy with a single elastic constant K, n being the director, regularized to permit defects where |n| deviates from unity over a small region of size δ [25,26]. For f anch , we adapt the Rapini-Popoular form [6] to our diffuse-interface formalism, with A being the anchoring energy density. Now we have the total free energy density for the two-phase material:…”

Section: Theoretical Model and Numerical Methodsmentioning

confidence: 99%

“…Perhaps the most fundamental issue is the interfacial tension. Continuum models and mean-field and atomistic calculations have predicted the easy axis on the interface and the magnitude of the interfacial energy [6][7][8][9][10]. A somewhat more advanced issue is the interfacial rheology, i.e., the dynamic coupling between the interfacial configuration and a flow field.…”

Section: Introductionmentioning

confidence: 99%

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Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Yue

Feng

et al. 2005

Journal of Colloid and Interface Science

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Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.  2005 Elsevier Inc. All rights reserved.

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Section: Theoretical Model and Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Yue

Feng

et al. 2005

Journal of Colloid and Interface Science

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“…Thus it is a function of the difference between the actual surface order parameter and the "easy" or ideal surface order parameter. It may be explicitly expressed in the manner of Rapini and Papoular [35] in terms of anchoring angles or the corresponding vector products as shown in Eq. (2).…”

Section: Predicting Morphologymentioning

confidence: 99%

“…Using the expressions for the anchoring energy density [35,36] and the elastic strain energy provided in Eqs. (1) and (2), the free energy functional G[n(r)] is defined in Eq.…”

Section: Predicting Morphologymentioning

confidence: 99%

Understanding and controlling the morphology of styrene–isoprene side-group liquid crystalline diblock copolymers

Osuji

Chen

Mao

et al. 2000

Polymer

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In side-chain liquid crystalline diblock copolymers, driving forces for ordering of the material may be provided by the chemical incompatibility between the blocks and by the liquid crystalline nature of one of the blocks. We study the microstructure and its development from initially isotropic solutions in side-group liquid crystalline copolymers based on styrene-isoprene diblocks. Hierarchical structure from the 5 Å to the 500 Å length scale is observed, the product of coherent block copolymer microphase separation and liquid crystalline mesophase formation. The presence of cylindrical microdomains of either the poly(isoprene-LC) or poly(styrene) block markedly increased the thermal stability of the LC. Confinement of the LC to cylindrical microdomains strongly inhibited defect formation within the mesophase after suitable orientation and thermal treatment, readily manifested by the significantly improved optical clarity of these samples versus LC matrix or LC lamellar samples. We consider the relative stabilities of parallel-transverse, perpendicular-parallel, parallel-parallel and transverse-perpendicular arrangements of the microdomain and mesophase structures in interpreting the development of structure in these materials under oscillatory shear. ᭧

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“…The orientational alignment energy distributed in the surface layer can be written in the Rapini-Papolar form (Rapini & Papoular 1969) as F w = dr [f w (z; n)], with an energy density 12) in whichw(z) is the distributed alignment strength that varies with z and extends from 0 to h.…”

Section: Orientational Alignment Energymentioning

confidence: 99%

A scaling approach to the derivation of hydrodynamic boundary conditions

2008

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We show hydrodynamic boundary conditions to be the inherent consequence of the Onsager principle of minimum energy dissipation, provided the relevant effects of the wall potential appear within a thin fluid layer next to the solid wall, denoted the surface layer. The condition that the effect of the surface layer on the bulk hydrodynamics must be independent of its thickness h is shown to imply a set of consistent 'scaling relationships' between h and the surface-layer variables/parameters. The use of the scaling relations, in conjunction with the surface-layer equations of motion derived from the Onsager principle, directly leads to the hydrodynamic boundary conditions. We demonstrate the surface-layer scaling process both physically and mathematically, and relate the parameters of the boundary conditions to those in the surface-layer equations of motion. In spatial regions outside the surface layer, equivalence between the use of surface-layer dynamics and boundary conditions is numerically demonstrated for Couette flows. As an application of the present approach, we derive the liquid-crystal hydrodynamic boundary conditions in which the rotational and translational dynamics are coupled.

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Distorsion d'UNE Lamelle Nématique Sous Champ Magnétique Conditions d'ANCRAGE Aux Parois

Abstract: On étudie l'influence sur la transition de Freedericks des conditions d'ancrage : 1) Angle fini d'ancrage ; 2) Energie d'ancrage finie. Cette influence se traduit par une diminution des constantes d'élasticité apparentes

Cited by 804 publications

References 0 publications

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Understanding and controlling the morphology of styrene–isoprene side-group liquid crystalline diblock copolymers

A scaling approach to the derivation of hydrodynamic boundary conditions

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