Entropy‐Driven Phase Transitions in Colloids: From spheres to anisotropic particles

Dijkstra, Marjolein

doi:10.1002/9781118949702.ch2

Cited by 36 publications

(38 citation statements)

References 190 publications

(292 reference statements)

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“…The problem of determining the equilibrium phase behavior of hard sphere mixtures is substantially more challenging and richer than that for identical hard spheres, including the possibilities of metastable or stable fluidfluid and/or solid-solid phase transitions (apart from stable fluid or crystal phases). While much research remains to be done, considerable progress has been made over the years, 54,55,[185][186][187][188][189][190][191][192][193][194][195][196][197] which we only briefly touch upon here for both additive and nonadditive cases. In additive hardsphere mixtures, the distance of closest approach between the centers of any two spheres is the arithmetic mean of their diameters.…”

Section: Equilibrium and Metastable Behaviormentioning

confidence: 99%

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Perspective: Basic understanding of condensed phases of matter via packing models

Torquato

2018

The Journal of Chemical Physics

134

139

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Packing problems have been a source of fascination for millennia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals, and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.

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Section: Equilibrium and Metastable Behaviormentioning

confidence: 99%

“…6,51 Moreover, the classic hard-sphere model provides a good description of certain classes of colloidal systems. 18,[52][53][54][55] Note that the hard-core constraint does not uniquely specify the hard-sphere model; there are an infinite number of nonequilibrium hard-sphere ensembles, some of which will be surveyed.…”

Section: Introductionmentioning

confidence: 99%

Perspective: Basic understanding of condensed phases of matter via packing models

Torquato

2018

The Journal of Chemical Physics

134

139

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“…Model. Many computational models of spheroidal particles have been developed to study structure and thermodynamic phase behaviors (42,(58)(59)(60) and jamming transitions (61) of ellipsoids. Here we use an interparticle potential proposed in refs.…”

Section: Methodsmentioning

confidence: 99%

Self-organization into ferroelectric and antiferroelectric crystals via the interplay between particle shape and dipolar interaction

Takae

Tanaka

2018

Proc. Natl. Acad. Sci. U.S.A.

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Ferroelectricity and antiferroelectricity are widely seen in various types of condensed matter and are of technological significance not only due to their electrical switchability but also due to intriguing cross-coupling effects such as electro-mechanical and electro-caloric effects. The control of the two types of dipolar order has practically been made by changing the ionic radius of a constituent atom or externally applying strain for inorganic crystals and by changing the shape of a molecule for organic crystals. However, the basic physical principle behind such controllability involving crystal-lattice organization is still unknown. On the basis of a physical picture that a competition of dipolar order with another type of order is essential to understand this phenomenon, here we develop a simple model system composed of spheroid-like particles with a permanent dipole, which may capture an essence of this important structural transition in organic systems. In this model, we reveal that energetic frustration between the two types of anisotropic interactions, dipolar and steric interactions, is a key to control not only the phase transition but also the coupling between polarization and strain. Our finding provides a fundamental physical principle for self-organization to a crystal with desired dipolar order and realization of large electro-mechanical effects.

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“…(13). Additionally, Q bulk 2 = A(A − A bulk ex )/2, with A bulk ex the orientationally averaged excluded area between two particles in the bulk, which is given by Eq.…”

Section: B Low-density Expansion Of the Tolman Lengthmentioning

confidence: 99%

“…This is achieved best for simple model systems of classical statistical mechanics. Hard objects have been studied extensively in this respect as temperature scales out and density is the only relevant thermodynamic parameter [11][12][13]. In three spatial dimensions, hard spheres near a hard wall have received considerable attention [14,15].…”

Section: Introductionmentioning

confidence: 99%

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

Sitta

Smallenburg

Wittkowski

et al. 2016

The Journal of Chemical Physics

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Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and a hard circular obstacle surrounded by particles are considered. We focus on moderate bulk densities (corresponding to area fractions up to 50 percent) where the bulk phase is isotropic and vary the aspect ratio of the rectangles and the curvature of the wall. The Tolman length, which gives the leading curvature correction of the interfacial tension, is found to change sign at a finite density, which can be tuned via the aspect ratio of the rectangles.

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Entropy‐Driven Phase Transitions in Colloids: From spheres to anisotropic particles

Cited by 36 publications

References 190 publications

Perspective: Basic understanding of condensed phases of matter via packing models

Perspective: Basic understanding of condensed phases of matter via packing models

Self-organization into ferroelectric and antiferroelectric crystals via the interplay between particle shape and dipolar interaction

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

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