Hard rectangles near curved hard walls: Tuning the sign of the Tolman length

Sitta, Christoph E.; Smallenburg, Frank; Wittkowski, Raphael; Löwen, Hartmut

doi:10.1063/1.4967876

Cited by 8 publications

(7 citation statements)

References 92 publications

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“…It converges to a finite value during the iteration. As in previous works, 59,[82][83][84] we combine this iteration with a direct inversion in the iterative subspace [85][86][87][88] to improve the convergence. The orientations of the rectangles are discretized in equidistant steps of ∆φ ≤ π/24 and a spatial Cartesian grid with step sizes ∆x = ∆y ≈ 0.03D is used.…”

Section: A Density Functional Theorymentioning

confidence: 99%

“…We do this for a two-dimensional system of hard rectangles and first study its bulk phase behavior in the flat and field-free case as a function of the particles' aspect ratio and number density. To tackle this problem, we propose a new DFT and perform complementary Monte Carlo (MC) computer simulations, showing stable isotropic, 34,47,59 nematic, 34,35,41,44,47,60 tetratic, [25][26][27][33][34][35]37,41,44,[60][61][62] and smectic 34,39,41,60 phases. Upon applying an aligning external field, the phase transition lines are shifted significantly and a binematic phase occurs at the expense of the tetratic phase.…”

Section: Introductionmentioning

confidence: 99%

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Liquid crystals of hard rectangles on flat and cylindrical manifolds

Sitta

Smallenburg

Wittkowski

et al. 2018

Phys. Chem. Chem. Phys.

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Using the classical density functional theory of freezing and Monte Carlo computer simulations, we explore the liquid-crystalline phase behavior of hard rectangles on flat and cylindrical manifolds. Moreover, we study the effect of a static external field which couples to the rectangles' orientations, aligning them towards a preferred direction. In the flat and field-free case, the bulk phase diagram involves stable isotropic, nematic, tetratic, and smectic phases depending on the aspect ratio and number density of the particles. The external field shifts the transition curves significantly and generates a binematic phase at the expense of the tetratic phase. On a cylindrical manifold, we observe tilted smectic-like order, as obtained by wrapping a smectic layer around a cylinder. We find in general good agreement between our density functional calculations and particle-resolved computer simulations and mention possible setups to verify our predictions in experiments.

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Section: A Density Functional Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Liquid crystals of hard rectangles on flat and cylindrical manifolds

Sitta

Smallenburg

Wittkowski

et al. 2018

Phys. Chem. Chem. Phys.

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“…4 in Sec. II A), we compute the ratio of the gas-wall interfacial tensions for the rough and flat surfaces: [52]…”

Section: B Two-gaussian Potentialmentioning

confidence: 99%

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

Egorov,

Binder

2020

Preprint

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The contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor rw), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form z wall (y) = ∆ cos(2πy/λ) , for a potential of short range σw acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be computed exactly, and corrections to Wenzel's equation are typically of order σw∆/λ 2 . For fixed rw and fixed σw the approach to Wenzel's result with increasing λ may be nonmonotonic and this limit often is only reached for λ/σw > 30. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases both for planar and corrugated walls, as well as the corresponding surface tensions. Again, deviations from Wenzel's results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret corresponding simulation results along similar lines. Wenzel's approach is found to generally hold when λ/σw 1, ∆/λ < 1, and conditions avoiding proximity of wetting or filling transitions.

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“…The chemical potential µ (i) is recalculated in every iteration step to maintain the desired area fraction and converges to a finite value in the iteration. As in previous works [53][54][55] , we combine this iteration with a direct inversion in the iterative subspace (DIIS) [56][57][58][59] to improve the convergence. The resolution of the spatial grid was chosen as ∆x = ∆y ≈ 0.03D and the discrete orientations of the particles are chosen in equidistant steps of ∆φ = 2π/48.…”

Section: B Density Functional Theorymentioning

confidence: 99%

Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory

Wittmann

Sitta

Smallenburg

et al. 2017

The Journal of Chemical Physics

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A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed measure theory and freely minimized numerically for hard discorectangles. The phase diagram, which involves stable isotropic, nematic, smectic, and crystalline phases, is obtained and shows good agreement with the simulation data. Our functional is valid for a multicomponent mixture of hard particles with arbitrary convex shapes and provides a reliable starting point to explore various inhomogeneous situations of two-dimensional hard rods and their Brownian dynamics.

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Hard rectangles near curved hard walls: Tuning the sign of the Tolman length

Cited by 8 publications

References 92 publications

Liquid crystals of hard rectangles on flat and cylindrical manifolds

Liquid crystals of hard rectangles on flat and cylindrical manifolds

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory

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