Gibbs-Bogolyubov inequality and transport properties for strongly coupled Yukawa fluids

Excess entropy and Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s_{ex} can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s_{ex}≲-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s_{ex}≃-1.

Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms

It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.

Determination of viscosity in shear-induced melting two-dimensional dusty plasmas using Green-Kubo relation

Langevin dynamical simulations of shear-induced melting two-dimensional (2D) dusty plasmas are performed to study the determination of the shear viscosity of this system. It is found that the viscosity calculated from the Green-Kubo relation, after removing the drift motion, well agrees with the viscosity definition, i.e., the ratio of the shear stress to the shear rate in the sheared region, even the shear rate is magnified ten times higher than that in experiments. The behaviors of shear stress and its autocorrelation function of shear-induced melting 2D dusty plasmas are compared with those of uniform liquids at the same temperatures, leading to the conclusion that the Green-Kubo relation is still applicable to determine the viscosity for shear-induced melting dusty plasmas.

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed, and other characteristics of the collective modes are determined using exclusively the static structure factor calculated from various theoretical approaches including the hypernetted chain approximation. A good quantitative agreement with molecular dynamics simulation data is achieved.

Multidimensional Chebyshev interpolation for warm and hot dense matter

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

Temperature relaxation in dense plasmas

We present a model to calculate temperature-relaxation rates in dense plasmas. The electron-ion interaction potential and the thermodynamic data of interest are provided by an average-atom model. This approach allows the study of the temperature relaxation in a two-temperature electron-ion system.

Modified Enskog kinetic theory for strongly coupled plasmas

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.

Resistivity saturation in warm dense matter

Electrical resistivity is shown to saturate in solid-density aluminum in the warm dense matter regime. Calculations are done using the average-atom model SCAALP and the finite-temperature Ziman-Evans formula for electrical resistivity. The mean free path is estimated using the Drude law. This mean free path is shown to present a minimum of the order of the interatomic spacing.

Numerical simulations of thermal conductivity in dissipative two-dimensional Yukawa systems

Numerical data on the heat transfer constants in two-dimensional Yukawa systems were obtained. Numerical study of the thermal conductivity and diffusivity was carried out for the equilibrium systems with parameters close to conditions of laboratory experiments with dusty plasma. For calculations of heat transfer constants the Green-Kubo formulas were used. The influence of dissipation (friction) on the heat transfer processes in nonideal systems was investigated. The approximation of the coefficient of thermal conductivity is proposed. Comparison of the obtained results to the existing experimental and numerical data is discussed.

Viscoelastic response of Yukawa liquids

The viscoelastic properties of strongly coupled Yukawa liquids are characterized by computing the complex shear viscosity η(ω) . This is done using three methods of molecular-dynamics simulation: equilibrium, nonequilibrium, and Langevin dynamics, all with a mutually repulsive Yukawa interparticle potential. A change from viscous to elastic response is observed with increasing frequency, as well as a decrease of the magnitude of the viscosity with increasing frequency. The Langevin simulation reveals that the dependence of the complex viscosity on the friction has a different character for hot and cool liquids. At ω=0 , we find that as friction increases, the viscosity diminishes at high temperature but increases at low temperature. In addition to finding its frequency dependence, we also derive the wave-number (length-scale) dependence of the shear viscosity.

X-ray Thomson scattering in warm dense matter at low frequencies

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the "plasmon-pole"-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.

Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.

Shear viscosity of strongly coupled Yukawa liquids

We present molecular-dynamics calculations of the shear viscosity of three-dimensional strongly coupled Yukawa liquids which are frequently used as a model system of complex plasmas. The results obtained using two independent nonequilibrium simulation methods are critically compared with each other and with earlier published data for a wide range of plasma coupling (Gamma) and screening (kappa) parameters. The non-Newtonian behavior of the liquid, manifested as a decrease of the shear viscosity with increasing shear rate (shear thinning), and the validity of the Stokes-Einstein relation at high coupling strength are also demonstrated.

Shear viscosity and shear thinning in two-dimensional Yukawa liquids

A two-dimensional Yukawa liquid is studied using two different nonequilibrium molecular dynamics simulation methods. Shear viscosity values in the limit of small shear rates are reported for a wide range of Coulomb coupling parameter and screening lengths. At high shear rates it is demonstrated that this liquid exhibits shear thinning; i.e., the viscosity eta diminishes with increasing shear rate. It is expected that two-dimensional dusty plasmas will exhibit this effect.

Equilibrium properties and phase diagram of two-dimensional Yukawa systems

Properties of two-dimensional strongly coupled Yukawa systems are explored through molecular dynamics simulations. An effective coupling coefficient gamma* for the liquid phase is introduced on the basis of the constancy of the first peak amplitude of the pair-correlation functions. Thermodynamic quantities are calculated from the pair-correlation function. The solid-liquid transition of the system is investigated through the analysis of the bond-angular order parameter. The static structure function satisfies consistency relation, attesting to the reliability of the computational method. The response is shown to be governed by the correlational part of the inverse compressibility. An analysis of the velocity autocorrelation demonstrates that this latter also exhibits a universal behavior.

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.

Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approach

The variational modified hypernetted chain approach as proposed by J. Stat. Phys. 42, 437 (1986)] is used to describe strongly coupled Yukawa fluids. The integral equations of interest can be solved using the spherical harmonic oscillator wave functions as a seed. Comparisons are done with simulation results for equation of state and transport coefficients over the entire fluid domain for a wide range of the system parameters.

Equation of state and transport coefficients for dense plasmas

We hereby present a model to describe the thermodynamic and transport properties of dense plasmas. The electronic and ionic structures are determined self-consistently using finite-temperature density functional theory and Gibbs-Bogolyubov inequality. The main thermodynamic quantities, i.e., internal energy, pressure, entropy, and sound speed, are obtained by numerical differentiation of the plasma total Helmholtz free energy. Electronic electrical and thermal conductivities are calculated from the Ziman approach. Ionic transport coefficients are estimated using those of hard-sphere system and the Rosenfeld semiempirical "universal" correspondence between excess entropy and dimensionless transport coefficients of dense fluids. Numerical results and comparisons with experiments are presented and discussed.

Thermal conductivity of strongly coupled Yukawa liquids

The thermal conductivity of strongly coupled Yukawa liquids, being relevant to dusty plasmas, is calculated from nonequilibrium molecular dynamics simulations. The calculations cover a wide range of plasma coupling (Gamma) and screening (kappa) parameters and yield data which are generally in good agreement with the results of recent independent calculations. An improved analytical formula, relating the thermal conductivity to the reduced temperature and to the screening length, is proposed.