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

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 86, Issue 4, 2012, Pages

  Xu, H ^a   Wittmer, J P ^b   Polinska P ^b   Baschnagel, J ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

D DIMENSIONS; FIRST DERIVATIVE; GLASS FORMER; HIGHER DERIVATIVES; ISOTROPIC LIQUID; LENNARD JONES; PAIR POTENTIAL; POLYDISPERSES;

BINARY MIXTURES;

ELASTIC MODULI;

EID: 84868350504     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.046705     Document Type: Article

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35. Apart from the Born term C B α β γ δ and the stress-fluctuation term C F α β γ δ, there is a kinetic contribution C K α β γ δ and in prestressed systems (as in the systems considered numerically by us) an explicit contribution from the applied stress to the experimentally relevant elastic moduli resulting from an infinitesimal strain applied to the reference state.
36. For systems with finite mean shear stress, various stress-fluctuation formulas must be changed and especially Eq. for the shear modulus G must be modified.
37. The trivial kinetic energy contributions to the elastic moduli are removed as far as possible from the presentation since MC results are also considered here.
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39. If plotted as a function of the number of configurations sampled, the compression modulus for both models is seen to decrease first with sampling time t before leveling off at a finite value. Similar behavior has been observed for polymeric systems.
40. A similar, albeit very small, impulsive correction arises for the "configurational temperature" being the ratio of the mean-squared forces acting on the particles and the mean divergence of these forces. See Eq. (7.2.11) of Ref..
41. For our low-temperature MC simulations, we use in addition to the standard local jump moves both longitudinal and (more importantly) transverse plane waves with wave vectors commensurate with the simulation box. The amplitudes of the collective displacement fields for each wave vector are chosen as implied by continuum theory. If such collective displacements are included, the shear stress for one given quenched configuration can be shown to be negligible as required.
42. It is well known that two-point correlations, as measured by the pair correlation function g (r), do barely change at the glass transition. Please note that the shear modulus G computed according to Eq. is a properly defined thermodynamic correlation function characterizing not only two-point, but also three- and four-point correlations. Apparently, these higher static correlations change qualitatively at the glass transition.
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..