Structure and stability of isotropic states of hard platelet fluids

David Cheung, Lucian Anton, Michael P. Allen, Andrew J. Masters, Jonathan Phillips, Matthias Schmidt

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.
LanguageEnglish
Article number041201
Number of pages13
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume78
Issue number4
DOIs
Publication statusPublished - Oct 2008

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Platelets
platelets
Fluid
fluids
Density Functional
Correlation Function
Closure
closures
simulation
Simulation
oblate spheroids
Function Approximation
Spatial Structure
Functional Analysis
Elongation
reference systems
Stability Analysis
Vanish
Integral Equations
Thermodynamics

Keywords

  • thermodynamics
  • isotropic states
  • platelet fluids

Cite this

Cheung, David ; Anton, Lucian ; Allen, Michael P. ; Masters, Andrew J. ; Phillips, Jonathan ; Schmidt, Matthias. / Structure and stability of isotropic states of hard platelet fluids. In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics . 2008 ; Vol. 78, No. 4.
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Structure and stability of isotropic states of hard platelet fluids. / Cheung, David; Anton, Lucian; Allen, Michael P.; Masters, Andrew J.; Phillips, Jonathan; Schmidt, Matthias.

In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics , Vol. 78, No. 4, 041201, 10.2008.

Research output: Contribution to journalArticle

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AU - Cheung, David

AU - Anton, Lucian

AU - Allen, Michael P.

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AB - We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

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