High-frequency elastic moduli of two-dimensional Yukawa fluids and solids

Abstract

An approach to calculate high-frequency bulk and shear modului of two-dimensional (2D) weakly screened Yukawa fluids and solids is presented. Elastic moduli are directly related to sound velocities and other important characteristics of the system. In this article we discuss these relations and present exemplary calculation of the longitudinal, transverse, and instantaneous sound velocities and derive a differential equation for the Einstein frequency. Simple analytical results presented demonstrate good accuracy when compared with numerical calculations. The obtained results can be particularly useful in the context of 2D colloidal and complex (dusty) plasma monolayers.

Practical formula for the shear viscosity of Yukawa fluids

“…46 Quantitatively, this means that the Einstein frequency is not expected to change much across the fluid-solid phase transition. Indeed, for weakly screened Yukawa systems the Einstein frequency is only slightly higher in a fluid phase as compared to an ideal crystal, as has been recently shown theoretically 54,55 and documented experimentally (using a strongly coupled dusty plasma). 56 According to the Lindemann melting rule, Ω E ∝ T m /ma 2 at the melting point, and this immediately leads to the scaling of Eq.…”

Collective modes of two-dimensional classical Coulomb fluids

“…For an ideal crystalline lattice the summation involved represents just the lattice sum for the dipole-dipole (∝ r −3 ) potential. 32,82 For the triangular lattice this yields Ω 2 E 0.399256ω 2 0 .…”

Unified description of sound velocities in strongly coupled Yukawa systems of different spatial dimensionality

“…In particular, the dependence g(x; Γ, κ) on κ is known to be very weak for weakly screened (κ is not much larger than unity) Yukawa fluids. [80][81][82] The excess energy at strong coupling can be very accurately approximated as u ex M fl Γ M cr Γ, where M fl and M cr can be referred to as the fluid and crystalline Madelung constants (M fl ∼ M cr ). 83 This reflects the fact that for soft repulsive interactions the dominant contribution to the excess energy comes from static correlations.…”