Instantaneous shear modulus of Yukawa fluids across coupling regimes

Abstract

The high frequency (instantaneous) shear modulus of three-dimensional Yukawa systems is evaluated in a wide parameter range, from the very weakly coupled gaseous state to the strongly coupled fluid at the crystallization point (Yukwa melt). This allows us to quantify how shear rigidity develops with increasing coupling and inter-particle correlations. The radial distribution functions (RDFs) needed to calculate the excess shear modulus have been obtained from extensive molecular dynamics (MD) simulations. MD results demonstrate that fluid RDFs appear quasi-universal on the curves parallel to the melting line of a Yukawa solid, in accordance with the isomorph theory of Roskilde-simple systems. This quasi-universality, allows to simplify considerably calculations of quantities involving integrals of the RDF (elastic moduli represent just one relevant example). The calculated reduced shear modulus grows linearly with the coupling parameter at weak coupling and approaches a quasi-constant asymptote at strong coupling. The asymptotic value at strong coupling is in reasonably good agreement with the existing theoretical approximation.

Dispersion relations of Yukawa fluids at weak and moderate coupling

“…Recent theoretical results regarding the onset and simple description of transverse waves in strongly coupled Yukawa fluids can be found elsewhere [6,14]. The process of shear rigidity emergence with increasing coupling and interparticle correlations in Yukawa systems, starting from the weakly coupled gaseous regime, has been also investigated [45].…”

Elastic properties of Yukawa crystals

“…A distinctive feature of Ref. 13 is that it takes into account the background contribution to the internal energy, [12,14] while in our work, it is not done. For quantities, which do not depend on the elementary cell volume change, this difference is not relevant.…”

Three-dimensional structure of a string-fluid complex plasma

“…4a, c, e). Comparison of the first peaks of g(r) with those for the Yukawa melt allows us to estimate the relative coupling parameter [31] Γ m /Γ ≃ 1.25, where Γ m is the coupling parameter at melting. c) polar angle distribution function p(θ) for two experimental data sets, simulated Yukawa melt and simulated anisotropic complex plasma.…”