Casimir-like interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals

Haddadan, Fahimeh Karimi Pour; Naji, Ali; Podgornik, Rudolf

doi:10.1039/c8sm02328j

Cited by 6 publications

(12 citation statements)

References 30 publications

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“…and Z is the sample partition function for a given con guration of the disorder elds. For the current model, we have [26]…”

Section: Modelmentioning

confidence: 99%

“…The special case of a nondisordered sm-A [26] follows from our formalism, when the disorder variance is set to zero.…”

Section: Modelmentioning

confidence: 99%

“…Using equations ( 10)-( 12) and the path-integral methods discussed in references [32,33], we nd (see reference [26] for complementary details not reiterated here)…”

Section: Fourier Diagonalizationmentioning

confidence: 99%

“…The uctuation-induced interactions within this model, which was rst pursued in the absence of the disorder [11,26] were shown to be attractive (for similar, or symmetric, boundary conditions on the two substrates) and to depend on a characteristic length as well as layer spacing [26]. Motivated by these ndings, we now generalize the setup to include also quenched and annealed surface disorder in the direction of the so-called easy axis of the surface anchoring and study the consequent disorder-induced modi cation of the uctuation interaction force.…”

Section: Introductionmentioning

confidence: 99%

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Surface alignment disorder and thermal Casimir forces in smectic-A liquid crystalline films

Haddadan

Naji

Podgornik

2020

J. Phys.: Condens. Matter

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Disorder components in surface anchoring orientation of a smectic-A liquid crystalline lm (occurring, e.g., due to surface contamination sources) modify the thermal pseudo-Casimir interaction mediated between the bounding surfaces of the lm. By considering a plane-parallel slab with bounding surfaces positioned normal to the layering eld of the lm, we study the anchoring disorder effects by assuming that the disorder source is present on one of the two substrates, producing a Gaussian-weighted distribution for the preferred molecular anchoring orientation (easy axis) on that substrate, with a nite mean and variance or, more generally, with a homogeneous in-plane, two-point correlation function. We show that the presence of disorder, either of quenched or annealed type, leads to a signi cant reduction in the magnitude of the net pseudo-Casimir force between the con ning substrates of the lm. This force can be attractive or repulsive depending on the boundary conditions. In the quenched case, the interaction force reduction is a direct consequence of an additive free energy term dependent on the variance of the disorder, while in the annealed case, the suppression of the interaction force can be understood based on a disorder-renormalized, effective anchoring strength. We predict a regime of behavior, exhibiting non-monotonic dependence for the interaction pressure as a function of separation. We also show that, by increasing the disorder variance, the interaction pressure changes sign and becomes a monotonically decreasing function of the separation between the substrates.

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“…and Z is the sample partition function for a given con guration of the disorder elds. For the current model, we have [26]…”

Section: Modelmentioning

confidence: 99%

“…The special case of a nondisordered sm-A [26] follows from our formalism, when the disorder variance is set to zero.…”

Section: Modelmentioning

confidence: 99%

“…Using equations ( 10)-( 12) and the path-integral methods discussed in references [32,33], we nd (see reference [26] for complementary details not reiterated here)…”

Section: Fourier Diagonalizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Surface alignment disorder and thermal Casimir forces in smectic-A liquid crystalline films

Haddadan

Naji

Podgornik

2020

J. Phys.: Condens. Matter

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“…It seems that further experiments on Casimir-Lifshitz torques with liquid crystals are within experimental reach presently or in the near future. Apart from the Casimir-Lifshitz torques, liquid crystals exhibit diverse other Casimir fluctuation phenomena and so might prove to be an abundant source of a variety of distinct Casimir phenomena [30,31]. The simplest way to theoretically describe the anisotropy of liquid crystals is by approximating them as uniaxial half spaces with a unique orientation [32].…”

Section: Introductionmentioning

confidence: 99%

Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals

Broer,

Lu,

Podgornik

2021

Preprint

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We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid crystals, which can be treated like bloc birefringent media. In particular, we find that the torque deviates considerably from its usual sinusoidal behavior as a function of the misalignment angle. In the case of a birefringent crystal faced with a cholesteric liquid one, the Casimir-Lifshitz torque decreases more slowly as a function of distance than in the nematic case. In the case of two cholesteric liquid crystals, either in the homochiral or in the heterochiral configuration, the angular dependence changes qualitatively as a function of distance. In all considered cases, finite pitch length effects are most pronounced at distances of about 10 nm.

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Path integrals for higher derivative actions

Dean¹,

Miao²,

Podgornik³

2019

J. Phys. A: Math. Theor.

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We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with bending rigidity as well as a number of models for electrolytes. The approach used is based on the relation between quadratic path integrals and Gaussian fields and we also show how it can be extended to the evaluation of even higher order path integrals.

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Casimir-like interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals

Cited by 6 publications

References 30 publications

Surface alignment disorder and thermal Casimir forces in smectic-A liquid crystalline films

Surface alignment disorder and thermal Casimir forces in smectic-A liquid crystalline films

Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals

Path integrals for higher derivative actions

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