Liquid-crystalline Casimir effect in the presence of a patterned substrate

Haddadan, Fahimeh Karimi Pour; Schlesener, F.; Dietrich, S.

doi:10.1103/physreve.70.041701

Cited by 20 publications

(9 citation statements)

References 46 publications

(73 reference statements)

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“…Beside surfaces with a homogeneous adsorption preference [14,15], the critical Casimir force has been investigated in the presence of a chem ically structured substrate [16], leading to a laterally varying adsorption preference, as well as in the presence of a substrate with a gradient in the adsorption preference [17]. Theoretical investigations of the critical Casimir force for inhomogeneous BC have considered the film geometry in the presence of a chemically striped substrate, studied within mean-field theory [46], within Gaussian approximation [47,48], and recently by MC simulations [8,39,44], The critical Casimir force in the presence of a chemically structured substrate has also been studied within the Derjaguin approximation for a sphere [49] and a cylindrical colloid [50] close to a planar wall. Inhomogeneous BC have been also considered within Gaussian approximation in Refs.…”

Section: Introductionmentioning

confidence: 99%

Critical Casimir force in the presence of random local adsorption preference

Toldin

2015

Phys. Rev. E

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We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.

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Section: Introductionmentioning

confidence: 99%

Critical Casimir force in the presence of random local adsorption preference

Toldin

2015

Phys. Rev. E

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“…Concerning the influence of patterned substrates on the liquid crystalline Casimir effect see Refs. [108][109][110].…”

Section: Basic Examples Of Fluctuation-induced Effective Forcesmentioning

confidence: 99%

Critical Casimir Effect: Exact Results

Dantchev¹,

Dietrich²

2022

Preprint

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In any medium there are fluctuations due to temperature or due to the quantum nature of its constituents. If a material body is immersed into such a medium, its shape and the properties of its constituents modify the fluctuations in the surrounding medium. If in the same medium there is a second body, modifications of the fluctuation due to the first one influence the modifications due to the second one. This mutual influence results in a force between these bodies. If the excitations of the medium, which mediate the effective interaction between the bodies, are massless, this force is longranged and nowadays known as a Casimir force. If the fluctuating medium consists of the confined electromagnetic field in vacuum, one speaks of the quantum mechanical Casimir effect. In the case that the order parameter of material fields fluctuates -such as differences of number densities or concentrations -and that the corresponding fluctuations of the order parameter are long-ranged, one speaks of the critical Casimir effect. This holds, e.g., in the case of systems which undergo a second-order phase transition and which are thermodynamically located near the corresponding critical point, or for systems with a continuous symmetry exhibiting Goldstone mode excitations. Here we review the currently available exact results concerning the critical Casimir effect in systems encompassing the one-dimensional Ising, XY, and Heisenberg models, the two-dimensional Ising model, the Gaussian and the spherical models, as well as the mean field results for the Ising and the XY model. Special attention is paid to the influence of the boundary conditions on the behavior of the Casimir force. We present results both for the case of classical critical fluctuations if the system possesses a critical point at a non-zero temperature, as well as the case of quantum systems undergoing a continuous phase transition at zero temperature as function of certain parameters. As confinements we consider the film, the sphere -plane, and the sphere -sphere geometries. We discuss systems governed by short-ranged, by subleading long-ranged (i.e., of the van der Waals type), and by leading long-ranged interactions. In order to put the critical Casimir effect into the proper context and in order to make the review as self-contained as possible, basic facts about the theory of phase transitions, the theory of critical phenomena in classical and quantum systems, and finite-size scaling theory are recalled. Whenever possible, a discussion of the relevance of the exact results towards an understanding of available experiments is presented. Hints about eventually applying the results towards their potential use in devices are also given.

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“…, (3.43) where p α = p for α = x, and p α = q for α = y. ii) if p = M and q = N : 45) where k x = 2πp/M , k y = 2πq/N , as well as all the other terms in the sum determining Λ are dimensionless. We again have to consider two sub-cases:…”

Section: The 3d Gaussian Modelmentioning

confidence: 99%

“…For the general case of O(n) systems there is no similarly thorough classification [38]. References [39][40][41][42][43][44][45][46][47] report on studies of the Casimir force in liquid crystals, and [48][49][50][51][52][53][54] describe investigations for 4 He and 3 He-4 He mixtures. In the case of Helium films, however, it is generally accepted that the boundary conditions are determined, in the region where the liquid behaves as a quantum liquid, by its quantum nature and, thus, cannot be easily influenced by modification of bounding surfaces, in that there are no surface fields that couple to the order parameter in such systems.…”

Section: Introductionmentioning

confidence: 99%

Manipulation and amplification of the Casimir force through surface fields using helicity

Dantchev

Rudnick

2017

Phys. Rev. E

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We present both exact and numerical results for the behavior of the Casimir force in O(n) systems with a finite extension in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems the Casimir force in certain temperature ranges is of the order of L −2 , both above and below the critical temperature, Tc, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one dimensional XY and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle and the three dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean field version of the three dimensional O(2) model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite size scaling.

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Liquid-crystalline Casimir effect in the presence of a patterned substrate

Cited by 20 publications

References 46 publications

Critical Casimir force in the presence of random local adsorption preference

Critical Casimir force in the presence of random local adsorption preference

Critical Casimir Effect: Exact Results

Manipulation and amplification of the Casimir force through surface fields using helicity

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