Nikita P. Kryuchkov

Practical thermodynamics of Yukawa systems at strong coupling

Simple practical approach to estimate thermodynamic properties of strongly coupled Yukawa systems, in both fluid and solid phases, is presented. The accuracy of the approach is tested by extensive comparison with direct computer simulation results (for fluids and solids) and the recently proposed shortest-graph method (for solids). Possible applications to other systems of softly repulsive particles are briefly discussed.

Thermodynamics of two-dimensional Yukawa systems across coupling regimes

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-Hückel) 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.

Pair correlations in classical crystals: The shortest-graph method.

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.

Interpolation method for pair correlations in classical crystals

Effects of anharmonicity on the pair correlation function of classical crystals are studied. The recently proposed shortest-graph approach using the Gaussian representation of the individual correlation peaks (the peak width is determined by the length of the shortest graph connecting a given pair of particles) is further improved, to account for anharmonic corrections due to finite temperatures and hard-sphere-like interactions. Two major effects are identified, leading to a modification of the correlation peaks at large or short distances: (i) the peaks at large distances, well described by Gaussians, should be calculated from the finite-temperature phonon spectra; (ii) at short distances, the correlation peaks deviate significantly from the Gaussian form due to the lattice discreteness. We propose the analytical interpolation method, based on the shortest-graph approach, which includes both effects. By employing the molecular dynamics simulations, the accuracy of the method is verified for three- and two-dimensional crystals with the Yukawa, inverse-power-law, and pseudo-hard-sphere pair interactions. The capabilities of the method are demonstrated by calculating the phase diagram of a three-dimensional Yukawa system.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 μm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 μm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.

Bizarre behavior of heat capacity in crystals due to interplay between two types of anharmonicities

The heat capacity of classical crystals is determined by the Dulong-Petit value CV ≃ D (where D is the spatial dimension) for softly interacting particles and has the gas-like value CV ≃ D/2 in the hard-sphere limit, while deviations are governed by the effects of anharmonicity. Soft- and hard-sphere interactions, which are associated with the enthalpy and entropy of crystals, are specifically anharmonic owing to violation of a linear relation between particle displacements and corresponding restoring forces. Here, we show that the interplay between these two types of anharmonicities unexpectedly induces two possible types of heat capacity anomalies. We studied thermodynamics, pair correlations, and collective excitations in 2D and 3D crystals of particles with a limited range of soft repulsions to prove the effect of interplay between the enthalpy and entropy types of anharmonicities. The observed anomalies are triggered by the density of the crystal, changing the interaction regime in the zero-temperature limit, and can provide about 10% excess of the heat capacity above the Dulong-Petit value. Our results facilitate understanding effects of complex anharmonicity in molecular and complex crystals and demonstrate the possibility of new effects due to the interplay between different types of anharmonicities.

The structure and spectral properties of two-dimensional dipole systems

A molecular dynamics simulation of two-dimensional dipole systems was performed. The influence of particles dipole moment (PDM) on structures and spectral properties of the systems was analyzed. It was found that increase of PDM leads to qualitative changes in systems structure and spectrum. There is a critical ratio between temperature and PDM at which the system is polymerized. It was also shown that the spectral properties of the system are extremely sensitive to PDM.

Collective modes of two-dimensional classical Coulomb fluids

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.