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Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations have been performed to investigate in detail collective modes spectra of two-dimensional Coulomb fluids in a wide range of coupling. The obtained dispersion relations are compared with theoretical approaches based on quasi-crystalline approximation, also known as the quasi-localized charge approximation, in the plasma-related context. An overall satisfactory agreement between theory and simulations is documented for the longitudinal mode at moderate coupling and in the long-wavelength domain at strong coupling. For the transverse mode, satisfactory agreement in the long-wavelength domain is only reached at very strong coupling, when the cutoff wave-number below which shear waves cannot propagate becomes small. The dependence of the cutoff wave-number for shear waves on the coupling parameter is obtained. [ABSTRACT FROM AUTHOR]

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-Hüuckel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous states to strongly coupled fluid and crystalline states. Important thermodynamic quantities, such as internal energy and pressure, are obtained and accurate physically motivated fits are proposed. This allows us to put forward simple practical expressions to describe thermodynamic properties of two-dimensional Yukawa systems. For crystals, in addition to numerical simulations, the recently developed shortest-graph interpolation method is applied to describe pair correlations and hence thermodynamic properties. It is shown that the finite-temperature effects can be accounted for by using simple correction of peaks in the pair correlation function. The corresponding correction coefficients are evaluated using MD simulation. The relevance of the obtained results in the context of colloidal systems, complex (dusty) plasmas, and ions absorbed to interfaces in electrolytes is pointed out. [ABSTRACT FROM AUTHOR]

The shortest-graph method is applied to calculate the pair correlation functions of crystals. The method is based on the representation of individual correlation peaks by the Gaussian functions, summed along the shortest graph connecting the two given points. The analytical expressions for the Gaussian parameters are derived for two- and three-dimensional crystals. The obtained results are compared with the pair correlation functions deduced from the molecular dynamics simulations of Yukawa, inverse-power law, Weeks-Chandler-Andersen, and Lennard-Jones crystals. By calculating the Helmholtz free energy, it is shown that the method is particularly accurate for soft interparticle interactions and for low temperatures, i.e., when the anharmonicity effects are insignificant. The accuracy of the method is further demonstrated by deriving the solid-solid transition line for Yukawa crystals, and the compressibility for inverse-power law crystals. [ABSTRACT FROM AUTHOR]

A new method for approximate calculation of the pair correlation function g(r) is proposed for crystalline systems of identical particles with isotropic interactions. The main idea of the method is to account for the relative delocalization of each node in g(r) by using only the shortest lattice graph between the given points, thus neglecting smaller contributions from other (non-shortest) graphs. By employing the Lennard-Jones and Yukawa crystalline systems as representative examples, it is shown that the proposed approach yields very good agreement with the results of molecular dynamics simulations up to the melting line. The approach can be useful in approximating the structure of simple crystals (in particular, of crystalline colloids and plasma crystals), and can also be generalized for systems with anisotropic interactions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]