Transverse current and generalized shear viscosity in liquid rubidium

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Wave vector dependent damping of THz collective modes in a liquid metal

Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.

Density functional study of structure and dynamics in liquid antimony and Sbn clusters

Density functional/molecular dynamics simulations have been performed on liquid antimony (588 atoms and six temperatures between 600 K and 1300 K) and on neutral Sb clusters with up to 14 atoms. We study structural patterns (coordination numbers, bond angles, and ring patterns, structure factors, pair distribution functions) and dynamical properties (vibration frequencies, diffusion constants, power spectra, dynamical structure factors, viscosity) and compare with available experimental results and with the results of our previous simulations on Bi. Three short covalent bonds characteristic of pnictogens are common in the clusters, and higher temperatures lead in the liquid to broader bond angle distributions, larger total cavity volumes, and weaker correlations between neighboring bond lengths. There are clear similarities between the properties of Sb and Bi aggregates.

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t^{-3/2} long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t^{-5/2} decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t^{-2} decay.

Decoupled length scales for diffusivity and viscosity in glass-forming liquids

The growth of the characteristic length scales both for diffusion and viscosity is investigated by molecular dynamics utilizing the finite-size effect in a binary Lennard-Jones mixture. For those quantities relevant to the diffusion process (e.g., the hydrodynamic value and the spatial correlation function), a strong system-size dependence is found. In contrast, it is weak or absent for the shear relaxation process. Correlation lengths are estimated from the decay of the spatial correlation functions. We find the length scale for viscosity decouples from the one of diffusivity, featured by a saturated length even in high supercooling. This temperature-independent behavior of the length scale is reminiscent of the unapparent structure change upon supercooling, implying the manifestation of configuration entropy. Whereas for the diffusion process, it is manifested by relaxation dynamics and dynamic heterogeneity. The Stokes-Einstein relation is found to break down at the temperature where the decoupling of these lengths happens.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Viscoelasticity of 2D liquids quantified in a dusty plasma experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wave-number-dependent viscosity η(k), which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, η(k) is computed from the transverse current autocorrelation function, which is found by tracking random particle motion. The transverse current autocorrelation function exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.

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.

Single-random-valley approximation in vibration-transit theory of liquid dynamics

The first goal of vibration-transit theory is to be able to calculate from a tractable partition function and without adjustable parameters the thermodynamic properties of the elemental monatomic liquids. The key hypothesis is that the random class of potential energy valleys dominates the statistical mechanics of the liquid at temperatures above melting T approximately greater than Tm and that these valleys are macroscopically uniform in the thermodynamic limit. This allows us to use a single random valley to calculate the vibrational contribution to liquid properties, exactly in the thermodynamic limit, and as an approximation at finite number of particles N . This approximation is tested here for liquid Na with a physically realistic potential based on electronic structure theory. Steepest descent quenches were made from the molecular dynamics equilibrium liquid (N=500) at temperatures from 0.90Tm to 3.31Tm, and six potential parameters were calculated for each structure, namely, the potential energy and five principal moments of the vibrational frequency distribution. The results show temperature-independent means and small standard deviations for all potential parameters, consistent with random valley uniformity at N-->infinity, and with finite- N broadening at N=500. The expected error in the single random valley approximation for Na at N=500 and T approximately greater than Tm is 0.1% for the entropy and 0.5% for the internal energy, negligible in the current development of liquid dynamics theory. In related quench studies of recent years, the common finding of nearly temperature-independent means of structural potential energy properties at T approximately greater than Tm suggests that the single random valley approximation might also apply to systems more complicated than the elemental liquids.

Mode-coupling theory of the fifth-order Raman spectrum of an atomic liquid

A fully microscopic molecular hydrodynamic theory for the two-dimensional (fifth-order) Raman spectrum of an atomic liquid (Xe) is presented. The spectrum is obtained from a simple mode-coupling theory by projecting the dynamics onto bilinear pairs of fluctuating density variables. Good agreement is obtained in comparison with recently reported molecular dynamics simulation results. The microscopic theory provides an understanding of the timescales and molecular motions that govern the two-dimensional signal. Predictions are made for the behavior of the spectrum as a function of temperature and density. The theory shows that novel signatures in the two-dimensional Raman spectrum of supercritical and supercooled liquids are expected.