Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Urrutia, Ignacio; Szybisz, L.

doi:10.1063/1.3319560

Cited by 10 publications

(30 citation statements)

References 68 publications

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“…It can also be readily applied to systems of AO particles in spaces with dimensions other than three (discs and hyper-spheres), with V o r taken from Ref. [60].…”

Section: Discussionmentioning

confidence: 99%

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

Paganini

Pastorino

Urrutia

2015

The Journal of Chemical Physics

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We study a system of few colloids confined in a small spherical cavity with event driven molecular dynamics simulations in the canonical ensemble. The colloidal particles interact through a short range square-well potential that takes into account the basic elements of attraction and excluded-volume repulsion of the interaction among colloids. We analyze the structural and thermodynamic properties of this few-body confined system in the framework of inhomogeneous fluids theory. Pair correlation function and density profile are used to determine the structure and the spatial characteristics of the system. Pressure on the walls, internal energy, and surface quantities such as surface tension and adsorption are also analyzed for a wide range of densities and temperatures. We have characterized systems from 2 to 6 confined particles, identifying distinctive qualitative behavior over the thermodynamic plane T - ρ, in a few-particle equivalent to phase diagrams of macroscopic systems. Applying the extended law of corresponding states, the square well interaction is mapped to the Asakura-Oosawa model for colloid-polymer mixtures. We link explicitly the temperature of the confined square-well fluid to the equivalent packing fraction of polymers in the Asakura-Oosawa model. Using this approach, we study the confined system of few colloids in a colloid-polymer mixture.

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“…It can also be readily applied to systems of AO particles in spaces with dimensions other than three (discs and hyper-spheres), with V o r taken from Ref. [60].…”

Section: Discussionmentioning

confidence: 99%

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

Paganini

Pastorino

Urrutia

2015

The Journal of Chemical Physics

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“…It also checks the robustness of approximate Eqs. (42,43) that would be good approximations for any fluid at low density. Using Eq.…”

Section: Accuracy Of Truncation In the Low Curvature Expansionmentioning

confidence: 99%

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

Urrutia¹

2016

Phys. Rev. E

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We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical, and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension γ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to γ(R) and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed.

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“…Few-body fluid-like systems of HS with one or two particles confined in cavities with different geometries, including the spherical, cuboidal and cylindrical cases, were analytically solved in the canonical ensemble in Refs. [10][11][12]. Those works make it possible to explore on exact grounds the corresponding open systems with M = 2.…”

Section: The Few Hs System In a Spherical Confinementmentioning

confidence: 99%

An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement

Urrutia

Castelletti

2012

The Journal of Chemical Physics

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This paper presents a modified grand canonical ensemble which provides a new simple and efficient scheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalism is implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-like system with up to three particles confined in a spherical cavity. In addition, the partition function of this system was used to analyze the surface thermodynamic properties of the many-HS system and to derive the exact curvature dependence of both the surface tension and adsorption in powers of the density. The expressions for the surface tension and the adsorption were also obtained for the many-HS system outside of a fixed hard spherical object. We used these results to derive the dependence of the fluid-substrate Tolman length up to first order in density.

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Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Cited by 10 publications

References 68 publications

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

Structure, thermodynamic properties, and phase diagrams of few colloids confined in a spherical pore

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement

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