Virial Coefficients and Equations of State for Hard Polyhedron Fluids

Irrgang ME, Engel M, Schultz AJ, Kofke DA, Glotzer SC (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Langmuir American Chemical Society

Book Volume: 33

Pages Range: 11788-11796

Journal Issue: 42

DOI: 10.1021/acs.langmuir.7b02384

Abstract

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on thermodynamic properties, even in moderate-density fluids. Only the second virial coefficient is known analytically for general convex shapes, so higher-order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating virial coefficients up to B4 and numerically evaluating them to B8. Using virial coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow et al. (J. Chem. Phys. 2012, 137, 204102) is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fluids of arbitrary hard convex bodies are too complicated to be described in a general way at high densities, so the high-precision state data we provide can serve as a reference for future work in calculating state data or as a basis for thermodynamic integration.

Authors with CRIS profile

Michael Engel Lehrstuhl für Multiscale Simulation of Particulate Systems

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

University at Buffalo. State University of New York US United States (USA) (US) University of Michigan US United States (USA) (US)

How to cite

APA:

Irrgang, M.E., Engel, M., Schultz, A.J., Kofke, D.A., & Glotzer, S.C. (2017). Virial Coefficients and Equations of State for Hard Polyhedron Fluids. Langmuir, 33(42), 11788-11796. https://dx.doi.org/10.1021/acs.langmuir.7b02384

MLA:

Irrgang, M. Eric, et al. "Virial Coefficients and Equations of State for Hard Polyhedron Fluids." Langmuir 33.42 (2017): 11788-11796.

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