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Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

H. Xu

J. P. Wittmer*, P. Polińska, and J. Baschnagel

  • LCP-A2MC, Institut Jean Barriol, Université de Lorraine & CNRS, 1 bd Arago, 57078 Metz Cedex 03, France

  • Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France

  • *joachim.wittmer@ics-cnrs.unistra.fr
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Phys. Rev. E 86, 046705 – Published 31 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.046705

Abstract

The truncation of a pair potential at a distance rc is well known to imply, in general, an impulsive correction to the pressure and other moments of the first derivatives of the potential. That, depending on rc, the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G(T) around the glass transition temperature Tg.

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  43. Since such a thermodynamic relation may be questioned for the strongly frozen systems, we have also determined G using the mechanical definition by linear regression from the observed conjugated instantaneous shear strain and stress. This yields the same values as Eq. (40).

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Phys. Rev. E 86, 046705– Published 31 October, 2012
  • Received 1 August 2012

©2012 American Physical Society

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