Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres

Mansoori, G. Ali; Carnahan, Norman F.; Starling, K.E.; Leland, Thomas W.

doi:10.1063/1.1675048

Cited by 2,036 publications

(1,131 citation statements)

References 21 publications

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“…(15) [14]. In contrast, the original White-Bear version of FMT, which is based on a different mixture generalization of the CS pressure [25,26] does not possess this feature of self-consistency, i.e. the derivative of Φ WB with respect to n 3 does not yield exactly the CS pressure [11].…”

Section: Morphological Thermodynamicsmentioning

confidence: 99%

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Hansen-Goos¹,

Roth²

2006

J. Phys.: Condens. Matter

197

286

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Abstract. In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.

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Section: Morphological Thermodynamicsmentioning

confidence: 99%

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Hansen-Goos¹,

Roth²

2006

J. Phys.: Condens. Matter

197

286

View full text Add to dashboard Cite

show abstract

“…The next two terms describe the steric interactions between the particles. The first of the two is the Mansoori et al [12] free energy expression for a binary hard sphere mixture, and the latter is the Carnahan-Starling free energy [17] for the smaller particles in the B phase. For R 1 R 2 , the Mansoori term reduces to the CarnahanStarling expression for monodisperse spheres.…”

Section: Volume 89 Number 15 P H Y S I C a L R E V I E W L E T T E Rmentioning

confidence: 99%

“…They account for the steric interactions between the particles. is the excess free energy per particle, derived from the Mansoori et al equation of state [12]. ''Smoothed'' densities ' ' p1 and ' ' p2 are introduced in the last two terms of (1) using the Tarazona weighted density approximation [13].…”

mentioning

confidence: 99%

Entropically Driven Formation of Hierarchically Ordered Nanocomposites

et al. 2002

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Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly in such materials, where the system undergoes a nanoscale ordering of the particles along with a phase transformation in the copolymer matrix. Furthermore, the selfassembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties. DOI: 10.1103/PhysRevLett.89.155503 PACS numbers: 81.07.Pr, 61.46.+w, 83.80.Uv The self-assembly of hard and soft components into nanostructured composites can facilitate the development of novel biomimetic [1], photonic [2], and electronic [3,4] materials. By themselves, binary mixtures of hard particles that differ in size or shape can self-assemble into a startling array of ordered structures [5,6]. Soft block copolymers can ''microphase separate'' into spatially periodic lamellar, cylindrical, spherical, or more complicated mesophases [7]. Using theoretical methods, in this Letter we conduct the first investigations into the cooperative behavior and novel structures that can potentially emerge when these two disparate ordering phenomena are coupled. Focusing on a small volume fraction of bidisperse spheres in AB diblocks, we isolate a system that simultaneously exhibits a structural change in the system of particles and a transformation in the microstructure of the copolymer matrix, creating in a single process a nanocomposite that potentially exhibits unique optoelectronic properties. Furthermore, these morphological changes are driven entirely by entropic effects involving all of the species. Our results indicate that the blending of particle mixtures and block copolymers can be exploited to create materials with new morphologies and functions.To characterize the diblocks in our system, we let f denote the fraction of A segments per chain. The enthalpic interaction between an A segment and a B segment is described by the dimensionless Flory-Huggins parameter, AB . Both the larger (referred to as p 1 ) and smaller (p 2 ) spheres are preferentially wetted by the A blocks. That is, the Flory-Huggins interaction parameter between the particles and A is taken as p1A p2A 0, and the interaction parameter between the different particles and the B species is set equal to AB ( AB p1B p2B). The radii of the p 1 and p 2 particles are denoted by R 1 and R 2 , respectively, and are given in units of R 0 , the root-meansquare end-to-end distance of the chain. These nanoparticles are comparable in size to the copolymers, and this correspondence of scales contributes to the unique structural organization within these nanocomposites.To determine the structure of the mixture, we now modify our previous SCF/DFT approach [8][9][10], which combines a self-consistent field theory (SCF) for diblocks with a density funct...

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“…[5][6][7] The optimized design of these devices requires the mechanistic spatiotemporal understanding of ionic arrangement and charge transport in electrolytes. Although the physicochemical aspects of electrolyte solutions have been extensively studied, a series of recent experimental and computational results [8][9][10][11][12][13][14][15][16][17][18][19] reflects knowledge gaps even in the context of basic science. 3,16,[20][21][22][23][24] A robust spatiotemporal framework is thus required to advance electrochemically-based industrial applications of highlyconcentrated electrolytes, e.g., fuel cells ∼1M (mol/liter) and batteries ∼10M.…”

mentioning

confidence: 99%

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory

Gavish

Elad

Yochelis

2017

J. Phys. Chem. Lett.

108

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The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and under-screening, which all impact the emergence of fluid/solid interfaces, and transport in these systems. Since these phenomena are not captured by existing mean field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquids. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing free energy that consists of short and long range interactions, together with a dissipation mechanism via Onsagers' relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as 1

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Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres

Cited by 2,036 publications

References 21 publications

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Entropically Driven Formation of Hierarchically Ordered Nanocomposites

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory

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