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

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.

Figure 1

Thermal component of the reduced excess energy, $u_{\mathrm{th}}$, of a strongly coupled IPL3 system in two dimensions versus the coupling parameter $\mathrm{\Gamma }$. Circles correspond to the results of MD simulations performed in this work. Triangles are the results by Golden et al. [54, 55]. The curve is the analytical fit of Eq. (9).

Figure 2

Longitudinal and transverse wave dispersion relations in color-coded format as obtained from Eq. (22) for $\mathrm{\Gamma }=56$ (a)–(c) and $\mathrm{\Gamma }=28$ (d)–(f). Top panel [(a), (d)] corresponds to the longitudinal mode, bottom panel [(b), (e)] to the transverse mode. Circles and $\top$ and $\perp$ symbols correspond to the frequencies ${\omega }_0$ and ${\omega }_0\pm \alpha$ values, respectively, obtained by applying a fitting function (23) for every fixed value of dimensionless wave vector $q=ka$. White dashed lines correspond to the acoustic asymptotes $\omega =C_{\mathrm{L}}k$ and $\omega =C_{\mathrm{T}}k$, where $C_L$ and $C_{\mathrm{T}}$ are the longitudinal and transverse sound velocities. For detailed discussion about the sound velocities in the IPL3 fluid, see Sec. 5. The dotted red lines correspond to the short-wavelength kinetic asymptote $\omega \simeq ck$, with $c=\sqrt{2}{v}_{\mathrm{T}}$ (see the text). The insets (c) and (f) show the long-wavelength portions of the dispersion relations. Here the red (blue) circles correspond to the longitudinal (transverse) dispersion relations as obtained from MD simulations. The red and blue solid curves display calculations using QCA approach of Eqs. (D3) and (D4) with the RDFs obtained from MD simulations. The dashed black curves correspond to simple analytical expressions of Eqs. (19) and (20).

Figure 3

Anharmonic corrections to the reduced excess energy of the IPL3 crystal in two dimensions versus the inverse coupling parameter $1/\mathrm{\Gamma }$. Symbols represent the results from our MD simulation, the solid curve is a fit of Eq. (24).

Figure 4

Example of the radial distribution function $g\left(r\right)$ for the IPL3 crystalline lattice at $\mathrm{\Gamma }=92.8$. The symbols correspond to the MD simulation results, the solid curve is obtained using the IM approach. The inset demonstrates BvK phonon dispersion curves for the IPL3 triangular lattice.

Figure 5

The reduced excess energy, $u_{\mathrm{ex}}$, of a weakly to moderately coupled IPL3 system in two dimensions versus the coupling parameter $\mathrm{\Gamma }$. Circles correspond to the results of MD simulations performed in this work, the green line corresponds to the weak coupling asymptote [Eq. (12)] the orange line corresponds to the strong coupling asymptote of Eq. (10), and the red curve is the fit of Eq. (B1) appropriate for the moderately coupled regime.