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

Wittmann, René; Sitta, Christoph E.; Smallenburg, Frank; Löwen, Hartmut

doi:10.1063/1.4996131

Cited by 42 publications

(38 citation statements)

References 89 publications

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“…1c) with an aspect ratio p = 10 that well reflects the experimental parameters. The interaction between these particles is described by a free energy functional constructed as an extension of fundamental measure theory 43,67,68 to account for anisotropic particle shapes 45,69 . These geometrical functionals derived from first principles are exact in the low-density limit and have proven very reliable for highly packed systems.…”

Section: Methodsmentioning

confidence: 99%

“…Overlapping parameter space. Our experiment and theory are designed, such that they can both tackle hard rods with a comparable anisotropy that is sufficiently high to ensure that the smectic phase is stable over a large range of densities 45,70 . Systems with variable inclusion size ratios b and the radii R out of the circular outer wall ranging between 1.9L ≤ R out ≤ 5.7L are covered by both approaches.…”

Section: Methodsmentioning

confidence: 99%

“…This combination of curved geometry and nontrivial topology is triggering certain characteristic defect patterns. In our study we uniquely combine real-space microscopy of colloidal samples with modern first-principles density functional theory (DFT) 42 based on geometric fundamental measures 43 which provides a full microscopic description of inhomogeneous and orientationally disordered smectics 44,45 . A plethora of different states with characteristic defect topologies is observed in perfect agreement between theory and experiment up to the microscopic nuances in the defect shape and wall alignment.…”

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confidence: 99%

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Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

et al. 2021

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Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

et al. 2021

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“…In passive lyotropic liquid-crystalline systems, particle density and shape determine both structural and dynamical properties. The isotropic-nematic (IN) transition in a system of hard rods with aspect ratio L /σ = 20 at ϕ ≈ 0.2 ( 36 ) is a lower bound for the IN transition for our semiflexible filaments. To investigate the effect of filament density, we show in Fig.…”

Section: Resultsmentioning

confidence: 95%

Filamentous active matter: Band formation, bending, buckling, and defects

et al. 2020

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Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

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“…Therefore, using recently developed theoretical frameworks, including exactly solvable models, one can potentially use these treatments to solve domain-domain PDFs of experimentally studied spherical vesicles [38][39][40][41][42][43][44]. Since, the complete physical description of both intra-and inter-domain correlations, and lipid phase separation is still a work in progress, the applicability of alternative computational approaches to interpret experimental data should be of interest [45][46][47][48][49][50].…”

Section: Discussionmentioning

confidence: 99%

Models for randomly distributed nanoscopic domains on spherical vesicles

2018

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The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size-a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.

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

Cited by 42 publications

References 89 publications

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

Filamentous active matter: Band formation, bending, buckling, and defects

Models for randomly distributed nanoscopic domains on spherical vesicles

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