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Journal of Chemical Physics / Volume 134 / Issue 11 / ARTICLES / Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

J. Chem. Phys. 134, 114502 (2011); http://dx.doi.org/10.1063/1.3564917 (11 pages)

Thermodynamics of d-dimensional hard sphere fluids confined to micropores

Hyungjun Kim1,2, William A. Goddard, III1,2, Kyeong Hwan Han3, Changho Kim3, Eok Kyun Lee3, Peter Talkner4, and Peter Hänggi4

1Center for Materials Simulations and Design, Graduate School of EEWS (WCU), Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
2Materials and Process Simulation Center (MC 139-74), California Institute of Technology, Pasadena, California 91125, USA
3Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
4Institut Physik, Universität Augsburg, D-86135 Augsburg, Germany

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(Received 8 November 2010; accepted 20 February 2011; published online 15 March 2011)

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss’ interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. GENERAL FORMULATION
    1. The second virial coefficient of confined fluids: Free volume approach
    2. Free energy and pressure tensor components
    3. Asymptotic behavior of pressure in the limit of wide and narrow slits
  3. COMPARISON WITH MOLECULAR DYNAMICS SIMULATION RESULTS
    1. Two-dimensional channel
    2. Three-dimensional channel
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

entropy, equations of state, fugacity, liquid theory, molecular dynamics method, porosity

PACS

  • 65.20.De

    General theory of thermodynamic properties of liquids, including computer simulation

  • 61.20.Ja

    Computer simulation of liquid structure

  • 64.10.+h

    General theory of equations of state and phase equilibria

  • 61.20.Gy

    Theory and models of liquid structure

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3564917

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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