Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems

Reyes, Andrés Santos

doi:10.31338/uw.9788323517399.pp.203-298

Cited by 6 publications

(3 citation statements)

References 110 publications

(165 reference statements)

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“…Let us now use arguments similar to those conventionally used for isotropic potentials [13][14][15][16][17][18] to derive the structural properties of the mixture. Given a reference particle of species i, we focus on those particles to its right and denote by p…”

Section: Probability Densitiesmentioning

confidence: 99%

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

Maestre

Santos

2020

J. Stat. Mech.

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The equilibrium properties of a Janus fluid confined to a one-dimensional channel are exactly derived. The fluid is made of particles with two faces (active and passive), so that the pair interaction is that of hard spheres, except if the two active faces are in front of each other, in which case the interaction has a square-well attractive tail. Our exact solution refers to quenched systems (i.e., each particle has a fixed face orientation), but we argue by means of statistical–mechanical tools that the results also apply to annealed systems (i.e., each particle can flip its orientation) in the thermodynamic limit. Comparison between theoretical results and Monte Carlo simulations for quenched and annealed systems, respectively, shows an excellent agreement.

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Section: Probability Densitiesmentioning

confidence: 99%

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

Maestre

Santos

2020

J. Stat. Mech.

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show abstract

“…Let us now use arguments similar to those conventionally used for isotropic potentials [13,14,15,16,17,18] to derive the structural properties of the mixture. Given a reference particle of species i, we focus on those particles to its right and denote by p (ℓ,+) ij (r)dr the (conditional) probability that its ℓth right neighbor belongs to species j and is located at a distance between r and r + dr.…”

Section: Probability Densitiesmentioning

confidence: 99%

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

Maestre,

Santos

2020

Preprint

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The equilibrium properties of a Janus fluid confined to a one-dimensional channel are exactly derived. The fluid is made of particles with two faces (active and passive), so that the pair interaction is that of hard spheres, except if the two active faces are in front of each other, in which case the interaction has a square-well attractive tail. Our exact solution refers to quenched systems (i.e., each particle has a fixed face orientation), but we argue by means of statistical-mechanical tools that the results also apply to annealed systems (i.e., each particle can flip its orientation) in the thermodynamic limit. Comparison between theoretical results and Monte Carlo simulations for quenched and annealed systems, respectively, shows an excellent agreement.

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“…The importance of exact statistical-mechanical solutions, even in conditions of onedimensional confinement, cannot be overemphasized [53]. Not only do they represent academically important examples of statistical-mechanical methods at work [10,12,15,16,36,[70][71][72][73][74], but they also provide insights into some of the expected general properties in unconfined geometries, or can be exploited as a benchmark for approximations [2,3,11,14,17,18,21,69,78] or simulation methods [13,46]. Moreover, since one-dimensional systems can be seen as three-dimensional systems confined in a very narrow tube, they find a wide range of applications in physically important situations such as biological ion channels [19], binding of proteins on capillary walls [24], or carbon nanotubes [43,51].…”

Section: Introductionmentioning

confidence: 99%

Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

Montero

Santos

2019

J Stat Phys

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The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the trianglewell and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function g(r) was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of g(r) up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus-Yevick, and Martynov-Sarkisov closures. Finally, the Fisher-Widom and Widom lines are obtained in the case of the triangle-well model.

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Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems

Cited by 6 publications

References 110 publications

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

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