### Abstract

Exact geometrical relations valid for hard sphere (HS) fluids are used to derive analytical expressions for the cavity formation energy equal to the free energy cost of insertion of a HS solute into a HS solvent and the contact value of the solute-solvent pair distribution function (PDF) in the limit of the infinite solute dilution. In contrast to existing relations from the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state, the derived expressions are self-consistent and result in correct asymptotics when the solute size goes to infinity. The proposed equations are tested against Monte Carlo simulations at diameter ratios d in the range 1≤d≤3.5 and three reduced densities 0.7. 0.8, and 0.9. The BMCSL theory is shown to systematically underestimate contact PDF values as compared to simulations both for finite solute concentrations and in the infinite dilution limit calculated by extrapolation of the results obtained at several concentrations. These infinite-dilution values of the solute-solvent PDF at contact calculated from simulations are in excellent agreement with the analytical expression derived in the paper. An analogy to the BMCSL equation for HS mixtures is used to extend this equation into the range of finite concentrations of the solute. The proposed equation is found to agree well with our simulation results.

Original language | English (US) |
---|---|

Pages (from-to) | 5815-5820 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 107 |

Issue number | 15 |

State | Published - Oct 15 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*107*(15), 5815-5820.

**Cavity formation energy in hard sphere fluids : An asymptotically correct expression.** / Matyushov, Dmitry; Ladanyi, Branka M.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 107, no. 15, pp. 5815-5820.

}

TY - JOUR

T1 - Cavity formation energy in hard sphere fluids

T2 - An asymptotically correct expression

AU - Matyushov, Dmitry

AU - Ladanyi, Branka M.

PY - 1997/10/15

Y1 - 1997/10/15

N2 - Exact geometrical relations valid for hard sphere (HS) fluids are used to derive analytical expressions for the cavity formation energy equal to the free energy cost of insertion of a HS solute into a HS solvent and the contact value of the solute-solvent pair distribution function (PDF) in the limit of the infinite solute dilution. In contrast to existing relations from the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state, the derived expressions are self-consistent and result in correct asymptotics when the solute size goes to infinity. The proposed equations are tested against Monte Carlo simulations at diameter ratios d in the range 1≤d≤3.5 and three reduced densities 0.7. 0.8, and 0.9. The BMCSL theory is shown to systematically underestimate contact PDF values as compared to simulations both for finite solute concentrations and in the infinite dilution limit calculated by extrapolation of the results obtained at several concentrations. These infinite-dilution values of the solute-solvent PDF at contact calculated from simulations are in excellent agreement with the analytical expression derived in the paper. An analogy to the BMCSL equation for HS mixtures is used to extend this equation into the range of finite concentrations of the solute. The proposed equation is found to agree well with our simulation results.

AB - Exact geometrical relations valid for hard sphere (HS) fluids are used to derive analytical expressions for the cavity formation energy equal to the free energy cost of insertion of a HS solute into a HS solvent and the contact value of the solute-solvent pair distribution function (PDF) in the limit of the infinite solute dilution. In contrast to existing relations from the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state, the derived expressions are self-consistent and result in correct asymptotics when the solute size goes to infinity. The proposed equations are tested against Monte Carlo simulations at diameter ratios d in the range 1≤d≤3.5 and three reduced densities 0.7. 0.8, and 0.9. The BMCSL theory is shown to systematically underestimate contact PDF values as compared to simulations both for finite solute concentrations and in the infinite dilution limit calculated by extrapolation of the results obtained at several concentrations. These infinite-dilution values of the solute-solvent PDF at contact calculated from simulations are in excellent agreement with the analytical expression derived in the paper. An analogy to the BMCSL equation for HS mixtures is used to extend this equation into the range of finite concentrations of the solute. The proposed equation is found to agree well with our simulation results.

UR - http://www.scopus.com/inward/record.url?scp=0342642807&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0342642807&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0342642807

VL - 107

SP - 5815

EP - 5820

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 15

ER -