Two-dimensional Yukawa Liquids Research Articles

Bulk moduli of two-dimensional Yukawa solids and liquids obtained from periodic compressions

Langevin dynamical simulations are performed to determine the bulk modulus in two-dimensional (2D) dusty plasmas from uniform periodic radial compressions. The bulk modulus is calculated directly from its physical definition of the ratio of the internal pressure/stress to the volume strain. Under various conditions, the bulk moduli obtained agree with the previous theoretical derivations from completely different approaches. It is found that the bulk moduli of 2D Yukawa solids and liquids are almost independent of the system temperature and the external compressional frequency.

Origin of viscosity at individual particle level in Yukawa liquids

The transition of the viscosity $\ensuremath{\eta}$ from a collisional gas through a minimum value to a correlated liquid is investigated using computer simulations with the Green-Kubo relation. It is discovered that, as the temperature varies, the transition of $\ensuremath{\eta}$ is well described by the unity ratio of the instantaneous transverse sound speed ${C}_{T}$ to the average particle speed ${\overline{v}}_{p}$. While ${C}_{T}/{\overline{v}}_{p}<1, \ensuremath{\eta}$ increases with the temperature, since in this regime the viscosity is dominated by the gaslike individual dynamics. However, when ${C}_{T}/{\overline{v}}_{p}>1$ where the cooperative dynamics dominates, the fundamental origin of viscosity of liquids is found to be just losing or gaining neighbors for individual particles, so that the viscosity of a typical liquid reasonably decreases with the temperature. Our results reveal that the viscosity transition point of ${C}_{T}/{\overline{v}}_{p}=1$ is just $\ensuremath{\approx}20$ times the corresponding melting point for both two-dimensional and three-dimensional Yukawa liquids with various screening parameters, which probably can be used as a new criterion to distinguish the strong and weak couplings in plasma physics.

Effect of particle mass inhomogeneity on the two-dimensional Rayleigh–Bénard system of Yukawa liquids: A molecular dynamics study

The effect of particle mass inhomogeneity on the evolution of macroscale fluid flow in the Rayleigh–Bénard system of two-dimensional Yukawa liquids is studied using “first principles” classical molecular dynamics simulations. We find that Rayleigh–Bénard convection cells (RBCCs) formed in the quasi-steady-state become unstable at later times as a result of introducing a small fraction (≤2% of the total particles) of particle mass inhomogeneity in a Yukawa system made up of point particles of uniform charges. The unstable RBCCs, after passing through several intermediate states, give rise to a unidirectional shear flow in the direction perpendicular to the external gravity. Depending on the fraction and phase space of the particle mass inhomogeneity introduced in the system, the unidirectional shear flow further evolves to give shearless parallel flow. We use single or dual particle mass distributions of various forms, such as Gaussian distribution, Dirac-delta distribution, or a combination of both, around different mean values in order to introduce particle mass inhomogeneity. The role of system size on the emergence of various intermediate fluid flow states is also investigated. Furthermore, by introducing an inhomogeneity in charge commensurate with mass inhomogeneity, we demonstrate the robustness of our findings. Finally, for the case of decreasing correlation strength and for otherwise identical parameters, it is shown that the particle mass inhomogeneity fails to generate shear flows from RBCCs in 2D Yukawa liquids.

Structure and thermodynamics of two-dimensional Yukawa liquids.

The thermodynamic and structural properties of two-dimensional dense Yukawa liquids are studied with molecular dynamics simulations. The "exact" thermodynamic properties are simultaneously employed in an advanced scheme for the determination of an equation of state that shows an unprecedented level of accuracy for the internal energy, pressure, and isothermal compressibility. The "exact" structural properties are utilized to formulate a novel empirical correction to the hypernetted-chain approach that leads to a very high accuracy level in terms of static correlations and thermodynamics.

Identification of time scales of the violation of the Stokes–Einstein relation in Yukawa liquids

We investigate the origin of the violation of the Stokes–Einstein (SE) relation in two-dimensional Yukawa liquids. Using comprehensive molecular dynamics simulations, we identify the time scales supporting the violation of the SE relation D∝(η/T)−1, where D is the self-diffusion coefficient and η is the shear viscosity. We first compute the self-intermediate scattering function Fs(k,t), the non-Gaussian parameter α2, and the autocorrelation function of the shear stress Cη(t). The time scales obtained from these functions include the structural relaxation time τα, the peak time of the non-Gaussian parameter τα2, and the shear stress relaxation time τη. We find that τη is coupled with D for all temperatures indicating the SE preservation; however, τα and τα2 are decoupled with D at low temperatures indicating the SE violation. Surprisingly, we find that the origins of this violation are related to the non-exponential behavior of the autocorrelation function of the shear stress and non-Gaussian behavior of the distribution function of particle displacements. These results confirm dynamic heterogeneity that occurs in two-dimensional Yukawa liquids that reflect the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.

Negative entropy-production rate in Rayleigh-Bénard convection in two-dimensional Yukawa liquids.

The steady-state fluctuation theorem (SSFT) gives the relative probability of occurrence of events violating the second law of thermodynamics in a system with a small number of degrees of freedom. Using two-dimensional complex plasma as a working medium, wherein particle level observation of instantaneous velocities and positions has become experimentally possible, we perform "first-principles" molecular-dynamics simulations using the Yukawa potential in the presence of external gravity and an external temperature gradient leading to the onset and formation of Rayleigh-Bénard convection cells. In such a far-from-equilibrium steady state, the SSFT is put to the test. It is demonstrated that the SSFT is satisfied without any additional fit parameter for observation time τ, comparable to or greater than the relevant microscopic timescale associated with the system under observation.

Fickian yet non-Gaussian diffusion in two-dimensional Yukawa liquids.

We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self-van Hove correlation function G_{s}(r,t) and the self-intermediate scattering function F_{s}(k,t), and we compare these functions with those obtained from mean-squared displacement (MSD) using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for G_{s}(r,t) and F_{s}(k,t) at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate timescales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase when the temperature of the liquid decreases. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.

Dynamics and transport of magnetized two-dimensional Yukawa liquids

Laboratory dusty plasma typically refers to a collection of micron-sized solid dust particles immersed in the plasma environment, as a result, these dust particles are negatively charged to thousands of elementary charges. Due to the electrical shielding provided by free electrons and ions, the interaction between these dust particles can be modeled as the Yukawa potential. These dust particles are strongly coupled due to their high charges, so that they exhibit collective behaviors of solids and liquids. Magnetic fields are often experimentally introduced in the modulation of dusty plasmas, and later the equivalent “magnetized” dusty plasma experiment is performed, so that magnetized Yukawa systems can be experimentally achieved now. Here, we review a series of results of collective behaviors and different transport processes of magnetized two-dimensional (2D) Yukawa liquids from Langevin dynamical simulations. From the obtained spectra of the simulation results, the vibrational density of states has only one dominant peak frequency, which can be analytically expressed as a function of the cyclotron and plasma frequencies, suggesting that the cyclotron motion of dust particles has been coupled with their thermal motion. It is also found that the statistics of particle motion with a strong magnetic field tend to deviate from the classical Maxwellian distribution. When the ratio of the cyclotron and plasma frequencies for dust particles is around the order of unity, the motion of dust particles tends to be superdiffusive. As the magnetic field increases, the shear viscosity increases with the magnetic field when the Yukawa liquid is cold; however, when the Yukawa liquid is hot, the variation trend of shear viscosity is reversed. It is also found that the structural relaxation time and the diffusion coefficient can be described as a power law relationship with two distinct values of the exponent at low and high temperatures, respectively.

Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state.

Langevin dynamical simulations of two-dimensional (2D) Yukawa liquids are performed to investigate the shear modulus of 2D solid dusty plasmas. Using the known transverse sound speeds, we obtain a theoretical expression of the shear modulus of 2D Yukawa crystals as a function of the screening parameter κ, which can be used as the candidate of their shear modulus. The shear relaxation modulus G(t) of 2D Yukawa liquids is calculated from the shear stress autocorrelation function, consisting of the kinetic, potential, and cross portions. Due to their viscoelasticity, 2D Yukawa liquids exhibit the typical elastic property when the time duration is much less than the Maxwell relaxation time. As a result, the infinite frequency shear modulus G_{∞}, i.e., the shear relaxation modulus G(t) when t=0, of a 2D Yukawa liquid should be related to the shear modulus of the corresponding quenched 2D Yukawa solid (with the same κ value), with all particles suddenly frozen at their locations of the liquid state. It is found that the potential portion of the infinite frequency shear modulus for 2D Yukawa liquids at any temperature well agrees with the shear modulus of 2D Yukawa crystals with the same κ obtained from the transverse sound speeds. Thus, we find that the shear modulus of 2D Yukawa solids can be obtained from the motion of individual particles of the corresponding Yukawa liquids using their viscoelastic property.

Relationship between relaxation time and diffusion of magnetized two-dimensional Yukawa liquids

Structural relaxation and self-diffusion of magnetized two-dimensional (2D) Yukawa liquids are investigated using Langevin dynamical simulations. The structural relaxation time τα is obtained from the self-intermediate scattering function, while the self-diffusion coefficient D is calculated from the mean-squared displacement. It is discovered that, for the magnetized 2D Yukawa liquids with the coupling parameter of Γ, the relationship between τα and D can be expressed as D ∝ (1/ταΓ)ξ with two distinct values of the exponent ξ at low and high temperatures, respectively. At low temperatures, the exponent ξ decreases with the applied magnetic field, which is attributed to the dynamical heterogeneity caused by the magnetic field. At high temperatures, it is found that both D and ταΓ obey the Arrhenius behaviors, reasonably leading to the discovered D ∝ (1/ταΓ)ξ relationship.

Equations of state and diagrams of two-dimensional liquid dusty plasmas

Recently, the pressure of two-dimensional (2D) Yukawa liquids has been calculated from the simulations of isochores [Feng et al., J. Phys. D: Appl. Phys. 49, 235203 (2016)], which is applicable to 2D dusty plasmas. Thus, the equation of state for 2D strongly coupled liquid dusty plasmas is obtained. Isobars and isotherms of 2D liquid dusty plasmas are derived from this equation of state. For 2D liquid dusty plasmas, the surface corresponding to this equation of state has also been obtained in the 3D space of the pressure, the temperature, and the screening parameter which is related to the volume in the equilibrium state.

Pressure of two-dimensional Yukawa liquids

A simple analytic expression for the pressure of a two-dimensional Yukawa liquid is found by fitting results from a molecular dynamics simulation. The results verify that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of the Wigner–Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytic expression, with its empirically determined coefficients, is plotted as isochores, or curves of constant area. These results should be applicable to monolayer dusty plasmas.

Effect of Dipole‐Dipole Interaction on the Compressional Oscillations in Two‐Dimensional Yukawa liquids

AbstractThe paper presents the study of oscillations in the two‐dimensional Yukawa liquids where the interparticle interaction potential in addition to the Yukawa term has the dipole‐dipole interaction term. The frequency of longitudinal oscillations was studied using the Fourier transform of the velocity autocorrelation function. It was found that in the two‐dimensional Yukawa liquids the longitudinal oscillation frequency of particles becomes sensitive to variations in the coupling parameter if even weak additional dipole‐dipole interaction between particles exists. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical experiment of thermal conductivity in two-dimensional Yukawa liquids

A newly improved homogenous nonequilibrium molecular dynamics simulation (HNEMDS) method, proposed by the Evans, has been used to compute the thermal conductivity of two-dimensional (2D) strongly coupled complex (dusty) plasma liquids (SCCDPLs), for the first time. The effects of equilibrium external field strength along with different system sizes and plasma states (Γ, κ) on the thermal conductivity of SCCDPLs have been calculated using an enhanced HNEMDS method. A simple analytical temperature representation of Yukawa 2D thermal conductivity with appropriate normalized frequencies (plasma and Einstein) has also been calculated. The new HNEMDS algorithm shows that the present method provides more accurate results with fast convergence and small size effects over a wide range of plasma states. The presented thermal conductivity obtained from HNEMDS method is found to be in very good agreement with that obtained through the previously known numerical simulations and experimental results for 2D Yukawa liquids (SCCDPLs) and with the three-dimensional nonequilibrium molecular dynamics simulation (MDS) and equilibrium MDS calculations. It is shown that the HNEMDS algorithm is a powerful tool, making the calculations very efficient and can be used to predict the thermal conductivity in 2D Yukawa liquid systems.

Viscosity of confined two-dimensional Yukawa liquids: A nonequilibrium method

We present a nonequilibrium method that allows one to determine the viscosity of two-dimensional dust clusters in an isotropic confinement. By applying a tangential external force to the outer parts of the cluster (e.g., with lasers), a sheared velocity profile is created. The decay of the angular velocity towards the center of the confinement potential is determined by a balance between internal (viscosity) and external friction (neutral gas damping). The viscosity can then be calculated from a fit of the measured velocity profile to a solution of the Navier-Stokes equation. Langevin dynamics simulations are used to demonstrate the feasibility of the method. We find good agreement of the measured viscosity with previous results for macroscopic Yukawa plasmas.

Kinetic origin of grain boundary migration, grain coalescence, and defect reduction in the crystallization of quenched two-dimensional Yukawa liquids.

The kinetic origin of grain boundary migration, grain coalescence, and defect reduction in the crystallization of quenched two-dimensional Yukawa liquids are numerically investigated. It is found that, in grain coalescence, stick-slip cracking the region in front of the grain boundary into smaller subgrains corotating with small angle, followed by healing, is the key for aligning lattice misorientation and inducing grain boundary stick-slip advance. Cracking is initiated from the weakly interlocked dislocation along its Burgers vector, which in turn causes dislocation motion along the crack. The cascaded scattering and recombination of two dislocations with 60^{∘} and 120^{∘} Burgers vector angle difference into two and one dislocations are the major processes for dislocation motion and reduction, respectively, in grain boundary migration. A rough grain boundary with large curvature easily supports the above process and induces high grain boundary mobility. Along a straight smooth grain boundary, the parallel Burgers vectors of the string of dislocations hinder defect reduction and induce coalescence stagnation.

Superdiffusion of two-dimensional Yukawa liquids due to a perpendicular magnetic field.

Stochastic transport of a two-dimensional (2D) dusty plasma liquid with a perpendicular magnetic field is studied. Superdiffusion is found to occur especially at higher magnetic fields with β of order unity. Here, β = ω(c)/ω(pd) is the ratio of the cyclotron and plasma frequencies for dust particles. The mean-square displacement MSD = 4D(α)t(α) is found to have an exponent α > 1, indicating superdiffusion, with α increasing monotonically to 1.1 as β increases to unity. The 2D Langevin molecular dynamics simulation used here also reveals that another indicator of random particle motion, the velocity autocorrelation function, has a dominant peak frequency ω(peak) that empirically obeys ω(peak)(2) = ω(c)(2) + ω(pd)(2)/4.

Effect of magnetic field on the velocity autocorrelation and the caging of particles in two-dimensional Yukawa liquids.

We investigate the effect of an external magnetic field on the velocity autocorrelation function and the "caging" of the particles in a two-dimensional strongly coupled Yukawa liquid, via numerical simulations. The influence of the coupling strength on the position of the dominant peak in the frequency spectrum of the velocity autocorrelation function confirms the onset of a joint effect of the magnetic field and strong correlations at high coupling. Our molecular dynamics simulations quantify the decorrelation of the particles' surroundings: the magnetic field is found to increase significantly the caging time, which reaches values well beyond the time scale of plasma oscillations. The observation of the increased caging time is in accordance with findings that the magnetic field decreases diffusion in similar systems.

Longitudinal viscosity of two-dimensional Yukawa liquids

The longitudinal viscosity η(l) is obtained for a two-dimensional (2D) liquid using a Green-Kubo method with a molecular dynamics simulation. The interparticle potential used has the Debye-Hückel or Yukawa form, which models a 2D dusty plasma. The longitudinal η(l) and shear η(s) viscosities are found to have values that match very closely, with only negligible differences for the entire range of temperatures that is considered. For a 2D Yukawa liquid, the bulk viscosity η(b) is determined to be either negligibly small or not a meaningful transport coefficient.

Higher Harmonic Generation in Strongly Coupled Magnetized Two-Dimensional Yukawa Liquids

The excitation spectra of 2-D strongly coupled (liquid-like) Yukawa systems under the influence of a magnetic field perpendicular to the plane are found to sustain additional high-frequency modes at multiples of magnetoplasmon. These modes are reminiscent of the well-known Bernstein modes but show a number of important differences due to the strong coupling of the particles.