A Theoretician’s Approach to Nematic Liquid Crystals and Their Applications

Majumdar, Apala; Lewis, Alexander H.

doi:10.1007/978-981-10-2502-0_8

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…[25][26][27][28][29][30][31][32] Eq. ( 1) thus provides a natural theoretical framework for the description of smoothly modulated nematic phases, and has been successfully used in recent years for the analytical 59,60 and numerical 59,61 modelling of a number of experimentally-relevant systems. However, its main shortcoming lies in the coarse-graining of all bulk particle properties into the three K i scalars -understood as free parameters arising from basic mean-field symmetries, and often taken to be equal for the sake of simplicity.…”

Section: Microscopic Theory Of Liquid-crystal Elasticitiesmentioning

confidence: 99%

Perturbative density functional methods for cholesteric liquid crystals

Tortora

Doye

2017

The Journal of Chemical Physics

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We introduce a comprehensive numerical framework to generically infer the emergent macroscopic properties of uniaxial nematic and cholesteric phases from that of their microscopic constituent mesogens. This approach, based on the full numerical resolution of the Poniewierski-Stecki equations in the weak chirality limit, may expediently handle a wide range of particle models through the use of Monte-Carlo sampling for all virial-type integrals. Its predictions in terms of equilibrium cholesteric structures are found to be in excellent agreement with previous full-functional descriptions, thereby demonstrating the quantitative validity of the perturbative treatment of chirality for pitch lengths as short as a few dozen particle diameters. Furthermore, the use of the full angle-dependent virial coefficients in the Onsager-Parsons-Lee formalism increases its numerical efficiency by several orders of magnitude over that of these previous methods. The comparison of our results with numerical simulations however reveals some shortcomings of the Parsons-Lee approximation for systems of strongly non-convex particles, notwithstanding the accurate inclusion of their full effective molecular volume. Further potential limitations of our theory in terms of phase symmetry assumptions are also examined, and prospective directions for future improvements discussed

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Section: Microscopic Theory Of Liquid-crystal Elasticitiesmentioning

confidence: 99%

Perturbative density functional methods for cholesteric liquid crystals

Tortora

Doye

2017

The Journal of Chemical Physics

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“…Instead of treating the active gel through a theory based on the LEP formulation for liquid crystals [4][5][6], we include the corresponding terms into the Beris-Edwards theory that uses Q-tensors to describe liquid crystals and is a popular field of research across the theoretical literature [23,[42][43][44][45], see also the recent overviews [46,47], as a more general alternative theory for liquid crystals. In a subsequent step, we express the two-dimensional Q-tensor in terms of the director field and an additional scalar order parameter to obtain an Ericksen-type model introduced in [38], for which we then derive the thin-film model in §3.…”

Section: Formulations Of Active Liquid Crystal Models (A) Beris-edwards Model For An Active Gelmentioning

confidence: 99%

“…This hydrolysis of ATP fuels the molecular motors (and is also used for the polymerization and depolymerization of the actin filaments). Instead of treating the chemical potential difference as a local quantity or a fixed constant as is done for the Leslie-Ericksen-Prodi formulation [12,24,25], we include the corresponding terms into the Beris-Edwards theory that uses Q-tensors and is popular in the liquid crystal literature [11,16,29,53,54] nd the recent overview [2,28] as a more general alternative theory for liquid crystals. In a subsequent step, we express the Q-tensor in terms of the director field and an additional scalar order parameter to obtain the Ericksen model, for which we then derive the thin film model in section 3.…”

Section: Formulations Of Active Liquid Crystals 21 Beris-edwards Mode...mentioning

confidence: 99%

Thin-film models for an active gel

2018

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In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamcs in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Lesli-Erickson-Parodi theory. Analytic expression are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure. *

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Placement of an Obstacle for Optimizing the Fundamental Eigenvalue of Divergence Form Elliptic Operators

Chorwadwala

Roy

2021

Advances in Mechanics and Mathematics

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A Theoretician’s Approach to Nematic Liquid Crystals and Their Applications

Cited by 4 publications

References 33 publications

Perturbative density functional methods for cholesteric liquid crystals

Perturbative density functional methods for cholesteric liquid crystals

Thin-film models for an active gel

Placement of an Obstacle for Optimizing the Fundamental Eigenvalue of Divergence Form Elliptic Operators

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