Thermodynamics and dynamics of two-dimensional systems with dipolelike repulsive interactions

Abstract

Thermodynamics and dynamics of a classical two-dimensional system with dipolelike isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical approximations. This interaction potential, which decays as an inverse cube of the interparticle distance, belongs to the class of very soft long-ranged interactions. As a result, the investigated system exhibits certain universal properties that are also shared by other related soft-interacting particle systems (like, for instance, the one-component plasma and weakly screened Coulomb systems). These universalities are explored in this article to construct a simple and reliable description of the system thermodynamics. In particular, Helmholtz free energies of the fluid and solid phases are derived, from which the location of the fluid-solid coexistence is determined. The quasicrystalline approximation is applied to the description of collective modes in dipole fluids. Its simplification, previously validated on strongly coupled plasma fluids, is used to derive explicit analytic dispersion relations for the longitudinal and transverse wave modes, which compare satisfactory with those obtained from direct MD simulations in the long-wavelength regime. Sound velocities of the dipole fluids and solids are derived and analyzed.

Collective modes of two-dimensional classical Coulomb fluids

“…In a series of papers we have reported detailed investigation of thermodynamics and dynamics of several classical systems of soft-interacting particles in 2D, such as one-component plasma (characterized by logarithmic interaction between the particles), 29,30 Yukawa systems, 31 and dipole-like systems (with ∝ r −3 interaction). 32 Present work represents a logical continuation of these studies. The reported results complement those previously obtained and complete the story.…”

“…The standard QCA-based approaches are not very useful to describe the transverse dispersion relations in fluids, because damping effects are not included. 32,55 For example, in Figs. 1 and 2 clear disagreement between the QCA and MD spectra is observed at short wavelengths.…”

Onset of transverse (shear) waves in strongly-coupled Yukawa fluids

“…This approach has been shown to be rather useful in describing long-wavelength dispersion relations in various systems with sufficiently soft interactions in both three dimensions (3D) and two dimensions (2D). 24,25,37,38,41 Equation (1) does not include the term responsible for the kinetic effects [(q/a) 2 v 2 T , where v T = T /m is the thermal velocity scale], which is numerically small in the strongly coupled regime (where transverse waves can propagate).…”

“…Due to this damping, the peak structure of C t (q, ω) is lost and they become much broader. 24,74 In this case, an appropriate theoretical model taking into account competition between processes giving rise to mode propagation and damping is required.…”

“…One of the important topics in investigating stronglycoupled systems is related to collective dynamics and collective modes. [20][21][22][23][24][25] It is well known that a dense fluid, not too far from the fluid-solid phase transition, can sustain one longitudinal and two transverse modes. The existence of transverse modes in fluids is a consequence of the fact that its response to high-frequency short-wavelength perturbations is similar to that of a solid body.…”