Long-Range Spatial Correlations of Particle Displacements and the Emergence of Elasticity

Elijah Flenner and Grzegorz Szamel
Phys. Rev. Lett. 114, 025501 – Published 14 January 2015
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Abstract

We examine correlations of transverse particle displacements and their relationship to the shear modulus of a glass and the viscosity of a fluid. To this end we use computer simulations to calculate a correlation function of the displacements, S4(q;t), which is similar to functions used to study heterogeneous dynamics in glass-forming fluids. We show that in the glass the shear modulus can be obtained from the long-time, small-q limit of S4(q;t). By using scaling arguments, we argue that a four-point correlation length ξ4(t) grows linearly in time in a glass and grows as t at long times in a fluid, and we verify these results by analyzing S4(q;t) obtained from simulations. For a viscoelastic fluid, the simulation results suggest that the crossover to the long-time t growth of ξ4(t) occurs at a characteristic decay time of the shear stress autocorrelation function. Using this observation, we show that the amplitude of the long-time t growth is proportional to η where η is the viscosity of the fluid.

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  • Received 12 May 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.025501

© 2015 American Physical Society

Authors & Affiliations

Elijah Flenner and Grzegorz Szamel

  • Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA

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Vol. 114, Iss. 2 — 16 January 2015

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