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

Abstract

Sound velocities in classical single-component fluids with Yukawa (screened Coulomb) interactions are systematically evaluated and analyzed in one-, two-, and three spatial dimensions (D = 1, 2, 3). In the strongly coupled regime the convenient sound velocity scale is given by Q 2 /∆m, where Q is the particle charge, m is the particle mass, n is the particle density, and ∆ = n −1/D is the unified interparticle distance. The sound velocity can be expressed as a product of this scaling factor and a dimension-dependent function of the screening parameter, κ = ∆/λ, where λ is the screening length. A unified approach is used to derive explicit expressions for these dimension-dependent functions in the weakly screened regime (κ 3). It is also demonstrated that for stronger screening (κ 3), the effect of spatial dimensionality virtually disappears, the longitudinal sound velocities approach a common asymptote, and a one-dimensional nearest-neighbor approximation provides a relatively good estimate for this asymptote. This result is not specific to the Yukawa potential, but equally applies to other classical systems with steep repulsive interactions. An emerging relation to a popular simple freezing indicator is briefly discussed. Overall, the results can be useful when Yukawa interactions are relevant, in particular, in the context of complex (dusty) plasmas and colloidal suspensions.

Lindemann melting criterion in two dimensions

“…The latter is proportional to the universal scaling factor Q 2 /∆m, where ∆ = n −1/D is the interparticle separation. The proportionality constant is ≃ 0.440 in 3D and 0.495 in 2D [47]. The fluid-solid phase transition takes place at Γ m ≃ 175 in 3D [57] and Γ m ≃ 135 in 2D [6].…”

“…Taking into account the strong inequality c 2 l ≫ c 2 t (which holds in both 2D and 3D soft interacting particle systems [45][46][47]) we arrive at the 2D melting conditions…”

“…The sound velocities have been evaluated using the approach described in Refs. [47,71]. The dashed curve shows the application of a simplified melting indicator of Eq.…”

Instantaneous shear modulus of Yukawa fluids across coupling regimes

“…Recently, a unified description of elastic moduli of strongly coupled Yukawa systems of different spatial dimensionality has been proposed (main results are expressed in terms of the longitudinal and transverse sound velocities, directly related to elastic moduli). 60 In this approximation the elastic moduli are related to the internal energy of Yukawa solids using relatively weak sensitivity of the RDFs to the screening parameter at weak screening and the fact that the internal energy is dominated by the static contribution. The excess contribution to the instantaneous shear modulus is then expressed in terms of Madelung constant and its first two derivatives with respect to κ (for details see Ref.…”

“…The excess contribution to the instantaneous shear modulus is then expressed in terms of Madelung constant and its first two derivatives with respect to κ (for details see Ref. 60). Using the ion sphere model 61,62 as a proxi for the Madelung constant the following expression can be derived 60…”