On the Elastic Constants of a Nematic Liquid Crystal

Schiele, K.; Trimper, Steffen

doi:10.1002/pssb.2221180132

Cited by 89 publications

(75 citation statements)

References 18 publications

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“…This question has already been discussed in the literature in the mean field approximation [15][16][17]. Here we present a systematic approach to the problem.…”

Section: Oseen-frank Theory and Landau-ginzburg-de Gennes Expansionmentioning

confidence: 89%

“…Special cases of second and third order expansions have already been proposed in the literature ( 16,17,18,26]. However, they failed to recognize the minimal set of independent invariants in third order of the orientation tensor Q.…”

Section: Discussionmentioning

confidence: 99%

“…This degeneracy of the elastic constants cannot be removed even by adding the missing term (4b) to the expansion (4a). A possible way out of this difficulty is to include higher order terms, like Q(oQ)(oQ) where Q(oQ)(oQ) denotes the class of all independent S0(3)-invariants built up from the tensor Q~pQ&.y Q~'"·"· Such a programme has been carried out partially, by Schiele and Trimper [16] for nematics and has further been generalized by Berremann and Meiboom [17] and Poniewierski and Sluckin [18]. In [ 17] the OZF elastic constants are calculated under the assumption that Q is uniaxial (5) In third order of the expansion the degeneracy of K 11 and K 33 is removed.…”

Section: (3 B)mentioning

confidence: 99%

“…is the mean field part of OZF free energy [15][16][17]. The mean field formula (26b) leads to the well-known degeneracy of the splay and bend elastic constants…”

Section: Oseen-frank Theory and Landau-ginzburg-de Gennes Expansionmentioning

confidence: 99%

See 3 more Smart Citations

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Longa

Monselesan²,

Trebin³

1987

Liquid Crystals

151

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Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau--de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermodynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data.

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“…This question has already been discussed in the literature in the mean field approximation [15][16][17]. Here we present a systematic approach to the problem.…”

Section: Oseen-frank Theory and Landau-ginzburg-de Gennes Expansionmentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: (3 B)mentioning

confidence: 99%

“…is the mean field part of OZF free energy [15][16][17]. The mean field formula (26b) leads to the well-known degeneracy of the splay and bend elastic constants…”

Section: Oseen-frank Theory and Landau-ginzburg-de Gennes Expansionmentioning

confidence: 99%

See 2 more Smart Citations

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Longa

Monselesan²,

Trebin³

1987

Liquid Crystals

151

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show abstract

“…In eq. (2) the prefactors L n with n = 1, 2 or 3 are linear combinations of the Frank elastic constants, K n [26]:…”

mentioning

confidence: 99%

Confinement Induced Splay-to-Bend Transition of Colloidal Rods

et al. 2012

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We study the nematic phase of rodlike fd -virus particles confined to channels with wedgestructured walls. Using laser scanning confocal microscopy we observe a splay-to-bend transition at the single particle level as a function of the wedge opening angle. Lattice Boltzmann simulations reveal the underlying origin of the transition and its dependence on nematic elasticity and wedge geometry. Our combined work provides a simple method to obtain the splay-to-bend elasticity ratios and offers a way to control the position of defects through the confining boundary conditions. PACS numbers:Packing and confinement problems emerge in fields ranging from biology to engineering. In biological systems the organization of the cell is determined, among other things, by the packing of fibril-like particles (actin filaments, DNA) [1,2]. An example of the subtlety of packing phenomena is the plethora of liquid crystalline phases that can be found in arrangements of anisotropic particles by increasing concentration [3,4]. Confinement of liquid crystals adds to the complexity, since the interactions of the particles with the walls may lead to structures that compete with those formed in the bulk [5,6]. Many of the next generation liquid crystal display devices exploit this interplay by using structured or patterned surfaces as an essential element of their design [7,8]. Very recently, the ordering at sawtoothed structures has been studied theoretically within a Landau-De Gennes framework [9,10], with a focus on the wetting behaviour. In this Letter, in a combined experimental and theoretical effort, we show the rich phenomenology that emerges when confining a nematic liquid crystal to a microfluidic channel with a wedge structured wall. We seek to disentangle how the wedge geometry and elasticity of the fd -virus' nematic phase determine the adopted deformation in the wedge. We introduce a new method for estimating elastic constants suitable to colloidal and biological systems, as an alternative to previous methods using magnetic fields [11] or light scattering [12]. Specifically, we determine the transition from a splay to a bend director field, with increasing wedge angle.We use the fd -virus, which is an excellent model liquid crystal system for both static and dynamic behaviour [13][14][15][16]. The virus' contour length and diameter are 0.88 µm and 6.6 nm, respectively. These dimensions allow for the 3D determination of the position and orientation of individual particles by means of laser scanning confocal microscopy (LSCM). Thus we obtain detailed mechanistic insights on a single particle level of the director field. Moreover, due to the relatively large size of the particles, we can study effects of wall structures that are, when translated to the scale of thermotropic liquid crystals, very small and inaccessible. The particles were grown following standard protocols [17] and dispersed in 20 mM tris buffer at pH 8.15 with 100 mM NaCl and 15% EtOH. The ethanol was added to prevent the growth of bacteria. The virus concent...

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Elastic Properties of Nematic Liquid Crystals

Stannarius¹

1998

Handbook of Liquid Crystals Set

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On the Elastic Constants of a Nematic Liquid Crystal

Cited by 89 publications

References 18 publications

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Confinement Induced Splay-to-Bend Transition of Colloidal Rods

Elastic Properties of Nematic Liquid Crystals

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