Critical point for de-mixing of binary hard spheres

Hideki Kobayashi; Paul B. Rohrbach; Robert Scheichl; Nigel B. Wilding; Robert L. Jack

doi:10.1103/PhysRevE.104.044603

Critical point for de-mixing of binary hard spheres

Hideki Kobayashi
, Paul B. Rohrbach
, Robert Scheichl
, Nigel B. Wilding
, Robert L. Jack

School of Physics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

61 Downloads (Pure)

Abstract

We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble, and matching to the universal form for the $3d$ Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions, and the geometry of the underlying hard sphere packings.

Original language	English
Article number	044603
Journal	Physical Review E
Volume	104
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.104.044603
Publication status	Published - 8 Oct 2021

Bibliographical note

Funding Information:
We thank Daan Frenkel and Bob Evans for helpful discussions. This project was supported by the Leverhulme Trust (Grant No. RPG-2017-203). R.L.J. and H.K. are also grateful to the EPSRC for support in the later part of the project (Grant No. EP/T031247/1).

Funding Information:
Leverhulme Trust Engineering and Physical Sciences Research Council

Publisher Copyright:
©2021 American Physical Society

Keywords

cond-mat.stat-mech
cond-mat.soft

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10.1103/PhysRevE.104.044603

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title = "Critical point for de-mixing of binary hard spheres",

abstract = " We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble, and matching to the universal form for the \$3d\$ Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions, and the geometry of the underlying hard sphere packings. ",

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author = "Hideki Kobayashi and Rohrbach, \{Paul B.\} and Robert Scheichl and Wilding, \{Nigel B.\} and Jack, \{Robert L.\}",

note = "Funding Information: We thank Daan Frenkel and Bob Evans for helpful discussions. This project was supported by the Leverhulme Trust (Grant No. RPG-2017-203). R.L.J. and H.K. are also grateful to the EPSRC for support in the later part of the project (Grant No. EP/T031247/1). Funding Information: Leverhulme Trust Engineering and Physical Sciences Research Council Publisher Copyright: {\textcopyright}2021 American Physical Society",

year = "2021",

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doi = "10.1103/PhysRevE.104.044603",

language = "English",

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AU - Kobayashi, Hideki

AU - Rohrbach, Paul B.

AU - Scheichl, Robert

AU - Wilding, Nigel B.

AU - Jack, Robert L.

N1 - Funding Information: We thank Daan Frenkel and Bob Evans for helpful discussions. This project was supported by the Leverhulme Trust (Grant No. RPG-2017-203). R.L.J. and H.K. are also grateful to the EPSRC for support in the later part of the project (Grant No. EP/T031247/1). Funding Information: Leverhulme Trust Engineering and Physical Sciences Research Council Publisher Copyright: ©2021 American Physical Society

PY - 2021/10/8

Y1 - 2021/10/8

N2 - We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble, and matching to the universal form for the $3d$ Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions, and the geometry of the underlying hard sphere packings.

AB - We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble, and matching to the universal form for the $3d$ Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions, and the geometry of the underlying hard sphere packings.

KW - cond-mat.stat-mech

KW - cond-mat.soft

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DO - 10.1103/PhysRevE.104.044603

M3 - Article (Academic Journal)

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VL - 104

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 044603

ER -

Critical point for de-mixing of binary hard spheres

Abstract

Bibliographical note

Keywords

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