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.
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21 March 2011
Research Article|
March 15 2011
Thermodynamics of d-dimensional hard sphere fluids confined to micropores
Hyungjun Kim;
Hyungjun Kim
a)
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
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William A. Goddard, III;
William A. Goddard, III
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
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Kyeong Hwan Han;
Kyeong Hwan Han
3Department of Chemistry and School of Molecular Science (BK21),
Korea Advanced Institute of Science and Technology
, Daejeon 305-701, South Korea
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Changho Kim;
Changho Kim
3Department of Chemistry and School of Molecular Science (BK21),
Korea Advanced Institute of Science and Technology
, Daejeon 305-701, South Korea
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Eok Kyun Lee;
Eok Kyun Lee
3Department of Chemistry and School of Molecular Science (BK21),
Korea Advanced Institute of Science and Technology
, Daejeon 305-701, South Korea
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Peter Talkner;
Peter Talkner
4Institut Physik,
Universität Augsburg
, D-86135 Augsburg, Germany
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Peter Hänggi
Peter Hänggi
4Institut Physik,
Universität Augsburg
, D-86135 Augsburg, Germany
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a)
Electronic mail: linus16@kaist.ac.kr.
J. Chem. Phys. 134, 114502 (2011)
Article history
Received:
November 08 2010
Accepted:
February 20 2011
Citation
Hyungjun Kim, William A. Goddard, Kyeong Hwan Han, Changho Kim, Eok Kyun Lee, Peter Talkner, Peter Hänggi; Thermodynamics of d-dimensional hard sphere fluids confined to micropores. J. Chem. Phys. 21 March 2011; 134 (11): 114502. https://doi.org/10.1063/1.3564917
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