Collective motion in liquids

Entropy of strongly coupled Yukawa fluids

The entropy of strongly coupled Yukawa fluids is discussed from several perspectives. First, it is demonstrated that a vibrational paradigm of atomic dynamics in dense fluids can be used to obtain a simple and accurate estimate of the entropy without any adjustable parameters. Second, it is explained why a quasiuniversal value of the excess entropy of simple fluids at the freezing point should be expected, and it is demonstrated that a remaining very weak dependence of the freezing point entropy on the screening parameter in the Yukawa fluid can be described by a simple linear function. Third, a scaling of the excess entropy with the freezing temperature is examined, a modified form of the Rosenfeld-Tarazona scaling is put forward, and some consequences are briefly discussed. Fourth, the location of the Frenkel line on the phase diagram of Yukawa systems is discussed in terms of the excess entropy and compared with some predictions made in the literature. Fifth, the excess entropy scaling of the transport coefficients (self-diffusion, viscosity, and thermal conductivity) is reexamined using the contemporary datasets for the transport properties of Yukawa fluids. The results could be of particular interest in the context of complex (dusty) plasmas, colloidal suspensions, electrolytes, and other related systems with soft pairwise interactions.

Viscoelastic relaxation and topological fluctuations in glass-forming liquids

A method for characterizing the topological fluctuations in liquids is proposed. This approach exploits the concept of the weighted gyration tensor of a collection of particles and permits the definition of a local configurational unit (LCU). The first principal axis of the gyration tensor serves as the director of the LCU, which can be tracked and analyzed by molecular dynamics simulations. Analysis of moderately supercooled Kob-Andersen mixtures suggests that orientational relaxation of the LCU closely follows viscoelastic relaxation and exhibits a two-stage behavior. The slow relaxing component of the LCU corresponds to the structural, Maxwellian mechanical relaxation. Additionally, it is found that the mean curvature of the LCUs is approximately zero at the Maxwell relaxation time with the Gaussian curvature being negative. This observation implies that structural relaxation occurs when the configurationally stable and destabilized regions interpenetrate each other in a bicontinuous manner. Finally, the mean and Gaussian curvatures of the LCUs can serve as reduced variables for the shear stress correlation, providing a compelling proof of the close connection between viscoelastic relaxation and topological fluctuations in glass-forming liquids.

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density-density and hydrostatic pressure-pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. These results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

Multiphonon scattering formula of dynamic structure factors for classical Debye solids

A semianalytic formula of the dynamic structure factor S(k,ω) for classical Debye solids over the entire wave-number (k) and frequency (ω) range is constructed by taking into account multiphonon thermal diffuse scattering up to infinite order. The formula adopts Gaussian approximations to the spatial and time decay of the multiphonon part of the displacement correlation function. Numerical illustrations for isotropic polycrystals reveal that, as k increases, sharp peaks due to one-phonon normal scattering in the hydrodynamic regime (k→0) are replaced by diffuse spectra consisting of umklapp scattering and multiphonon continuum; approach toward the ideal-gas spectra in the large-k limit is proven from analytic properties of the multiphonon term. When k coincides with a Bragg reflection point, total thermal diffuse scattering S_{TDS}(k,ω) exhibits a 1/ω divergence as ω→0, which in turn gives rise to a logarithmic enhancement of the corresponding static structure factor S_{TDS}(k). Overall accuracy of the theory is confirmed through the exact zeroth-order frequency-moment sum rule between S_{TDS}(k,ω) and S_{TDS}(k); agreement with the second-order sum rule is shown to be satisfactory except for the vicinity of the Debye cutoff region.

Entropy of simple fluids with repulsive interactions near freezing

Among different thermodynamic properties of liquids, the entropy is one of the hardest quantities to estimate. Therefore, the development of models allowing accurate estimations of the entropy for different mechanisms of interatomic interactions represents an important problem. Here, we propose a method for estimating the excess entropy of simple liquids not too far from the liquid-solid phase transition. The method represents a variant of cell theory, which particularly emphasizes relations between liquid state thermodynamics and collective modes properties. The method is applied to calculate the excess entropy of inverse-power-law fluids with ∝r^-n repulsive interactions. The covered range of potential softness is extremely wide, including the very soft Coulomb (n = 1) case, much steeper n = 6 and n = 12 cases, and the opposite hard-sphere interaction limit (n = ∞). An overall reasonably good agreement between the method's outcome and existing "exact" results is documented at sufficiently high fluid densities. Its applicability condition can be conveniently formulated in terms of the excess entropy itself. The method is also applied to the Lennard-Jones potential but demonstrates considerably lower accuracy in this case. Our results should be relevant to a broad range of liquid systems that can be described with isotropic repulsive interactions, including liquid metals, macromolecular systems, globular proteins, and colloidal suspensions.

Sound Velocities of Generalized Lennard-Jones (n - 6) Fluids Near Freezing

In a recent paper [S. Khrapak, Molecules 25, 3498 (2020)], the longitudinal and transverse sound velocities of a conventional Lennard-Jones system at the liquid-solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid-solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft-sphere and hard-sphere models at the fluid-solid phase transition. This implies that attraction does not considerably affect the magnitude of the sound velocities at the fluid-solid phase transition. This paper provides further evidence to this by examining the generalized Lennard-Jones (n - 6) fluids with n ranging from 12 to 7 and demonstrating that the steepness of the repulsive term has only a minor effect on the magnitude of the sound velocities. Nevertheless, these minor trends are identified and discussed.

Universal G' ∼ L-3 Law for the Low-Frequency Shear Modulus of Confined Liquids

Liquids confined to sub-millimeter scales have remained poorly understood. One of the most striking effects is the large elasticity revealed using good wetting conditions, which grows upon further decreasing the confinement length, L. These systems display a low-frequency shear modulus in the order of 1-10³ Pa, contrary to our everyday experience of liquids as bodies with a zero low-frequency shear modulus. While early experimental evidence of this effect was met with skepticism and abandoned, further experimental results and, most recently, a new atomistic theoretical framework have confirmed that liquids indeed possess a finite low-frequency shear modulus G', which scales with the inverse cubic power of confinement length L. We show that this law is universal and valid for a wide range of materials (liquid water, glycerol, ionic liquids, non-entangled polymer liquids, isotropic liquids crystals). Open questions and potential applications in microfluidics mechanochemistry, energy, and other fields are highlighted.

Dispersion relations of Yukawa fluids at weak and moderate coupling

In this paper we compare different theoretical approaches to describe the dispersion of collective modes in Yukawa fluids when the interparticle coupling is relatively weak, so that the kinetic and potential contributions to the dispersion relation compete with each other. A thorough comparison with the results from molecular dynamics simulation allows us to conclude that, in the investigated regime, the best description is provided by the sum of the generalized excess bulk modulus and the Bohm-Gross kinetic term.

Explaining the low-frequency shear elasticity of confined liquids

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01 to 0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerging framework shows that applying confinement to a liquid can effectively suppress the low-frequency modes that are responsible for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The theory successfully predicts the scaling law [Formula: see text] for the low-frequency shear modulus of liquids as a function of the confinement length L, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales.

Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the "exact" values obtained from their relations to excess energy and pressure. Some consequences, in particular in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients, are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.

Observation of High-Frequency Transverse Phonons in Metallic Glasses

Using inelastic neutron scattering and molecular dynamics simulations on a model Zr-Cu-Al metallic glass, we show that transverse phonons persist well into the high-frequency regime, and can be detected at large momentum transfer. Furthermore, the apparent peak width of the transverse phonons was found to follow the static structure factor. The one-to-one correspondence, which was demonstrated for both Zr-Cu-Al metallic glass and a three-dimensional Lennard-Jones model glass, suggests a universal correlation between the phonon dynamics and the underlying disordered structure. This remarkable correlation, not found for longitudinal phonons, underscores the key role that transverse phonons hold for understanding the structure-dynamics relationship in disordered materials.

Excitation spectra in fluids: How to analyze them properly

Although the understanding of excitation spectra in fluids is of great importance, it is still unclear how different methods of spectral analysis agree with each other and which of them is suitable in a wide range of parameters. Here, we show that the problem can be solved using a two-oscillator model to analyze total velocity current spectra, while other considered methods, including analysis of the spectral maxima and single mode analysis, yield rough results and become unsuitable at high temperatures and wavenumbers. To prove this, we perform molecular dynamics (MD) simulations and calculate excitation spectra in Lennard-Jones and inverse-power-law fluids at different temperatures, both in 3D and 2D cases. Then, we analyze relations between thermodynamic and dynamic features of fluids at (Frenkel) crossover from a liquid- to gas-like state and find that they agree with each other in the 3D case and strongly disagree in 2D systems due to enhanced anharmonicity effects. The results provide a significant advance in methods for detail analysis of collective fluid dynamics spanning fields from soft condensed matter to strongly coupled plasmas.

Onset of transverse (shear) waves in strongly-coupled Yukawa fluids

A simple practical approach to describe transverse (shear) waves in strongly-coupled Yukawa fluids is presented. Theoretical dispersion curves, based on hydrodynamic consideration, are shown to compare favorably with existing numerical results for plasma-related systems in the long-wavelength regime. The existence of a minimum wave number below which shear waves cannot propagate and its magnitude are properly accounted in the approach. The relevance of the approach beyond plasma-related Yukawa fluids is demonstrated by using experimental data on transverse excitations in liquid metals Fe, Cu, and Zn, obtained from inelastic x-ray scattering. Some potentially important relations, scalings, and quasi-universalities are discussed. The results should be interesting for a broad community in chemical physics, materials physics, physics of fluids and glassy state, complex (dusty) plasmas, and soft matter.

Thermodynamics and dynamics of two-dimensional systems with dipolelike repulsive interactions

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.

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.

Collective modes in simple melts: Transition from soft spheres to the hard sphere limit

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\,\gtrsim 20$$\end{document}n≳20. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.

Direct link between boson-peak modes and dielectric α-relaxation in glasses

We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting generalized Langevin equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, which we take from numerical evaluation of a marginally stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye ∼ω_{p}^{2} law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at T≲T_{g}. Good agreement is found for both the reactive (real) part of the response and for the α-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches. On the low-frequency side of the α peak, the fitting supports the presence of ∼ω_{p}^{4} modes at vanishing eigenfrequency as recently shown [E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.035501]. α-wing asymmetry and stretched-exponential behavior are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.

Note: Sound velocity of a soft sphere model near the fluid-solid phase transition

The quasilocalized charge approximation is applied to estimate the sound velocity of simple soft sphere fluid with the repulsive inverse-power-law interaction. The obtained results are discussed in the context of the sound velocity of the hard-sphere system and of liquid metals at the melting temperature.

Transition from hydrodynamic to viscoelastic propagation of sound in molten RbBr

Inelastic neutron scattering was applied to measure the acoustic-type excitations in the molten alkali halide rubidium bromide. For molten RbBr neutron scattering is mainly sensitive to the number density fluctuation spectrum and is not influenced by charge fluctuations. Utilizing a dedicated Brillouin scattering spectrometer, we focused on the small-wave-vector range. From inelastic excitations in the spectra a dispersion relation was obtained, which shows a large positive dispersion effect. This frequency enhancement is related to a viscoelastic response of the liquid at high frequencies. Towards small wave vectors we identify the transition to hydrodynamic behavior. This observation is supported by a transition of the sound velocity from a viscoelastic enhanced value to the adiabatic speed of sound for the acoustic-type excitations. Furthermore, the spectrum transforms into a line shape compatible with a prediction from hydrodynamics.

Nonexponential relaxation in a simple liquid metal

A hallmark of the changes in dynamics towards the glass transition is the stretched exponential structural relaxation. Quasielastic neutron scattering results on liquid rubidium demonstrate such a nonexponential relaxation process in a simple liquid metal above the melting point. The nonexponential decay is an indication of non-Markovian dynamics and points to the collective character of the relaxation process. Describing the relaxation dynamics by a two-step process, the long lasting part of the decay process is in remarkable quantitative agreement with predictions from mode coupling theory. The feedback mechanism of the slowing down process in the theoretical description suggests that this contribution is at the origin of the structural arrest. With rising temperature the intermediate scattering function transforms into a simple exponential decay at a temperature range which indicates the end of the highly viscous solidlike behavior in the liquid.

Slow Dynamics in Liquid Metals as Seen by QENS

The quasielastic dynamics in liquid metals has been investigated by neutron scattering extensively during the past years. Precise measurements of the self-particle dynamics and the coherent quasielastic response provided conclusive evidence that the relaxation dynamics is governed by at least two processes. These two time scales in the correlation functions appear as two dynamical processes in their associated memory functions. One process shows a fast decay and is related to stochastic binary collisions. The second slow process stems from a non-linear coupling of slow collective modes. These slow density fluctuations arise mainly from the dynamics around the structure factor maximum. A rigorous treatment of these effects can be accomplished by mode coupling theory. A few selective experiments from monatomic metals are presented to demonstrate the influence of slow effects on the dynamics. Experiments and MD-simulations show a surprising good agreement with predictions of mode coupling theory on a quantitative level. The slow decay process appears to be related to structural arrest in the supercooled state and might indicate a link to the solidification process, starting deep in the liquid state. Accurate quasielastic neutron scattering experiments are still and will remain a fundamental pillar for elucidating the complex dynamics in the liquid state of metals.

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.

Efficient measurement of linear susceptibilities in molecular simulations: application to aging supercooled liquids

We propose a novel method to measure time-dependent linear susceptibilities in molecular simulations, which does not require the use of nonequilibrium simulations, subtraction techniques, or fluctuation-dissipation theorems. The main idea is an exact reformulation of linearly perturbed quantities in terms of observables accessible in a single unperturbed trajectory. We apply these ideas to supercooled liquids in a nonequilibrium aging regime. We show that previous work had underestimated deviations from fluctuation-dissipation relations in the case of a Lennard-Jones system, while our results for silica are in qualitative disagreement with earlier results.

State dependent particle dynamics in liquid alkali metals

This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.

de Gennes slowing in a liquid metal revisited: a neutron spin-echo study

In liquids the decay of density fluctuations shows a slowing down at the structure factor maximum, which is well known as de Gennes narrowing. Molecular dynamics simulations of the liquid metal rubidium and mode coupling theory suggested that this process can be described by a two-step relaxation function. We have probed these predictions with inelastic neutron scattering using the spin-echo technique to measure the dynamics directly in the time domain. The dynamics of liquid rubidium was investigated near the melting point at times beyond the fast contribution. The resulting intermediate-scattering function is in remarkable agreement with predicted values from the mode coupling calculations.

Microscopic self-dynamics in liquid hydrogen and in its mixtures with deuterium

We have measured the dynamic structure factor of liquid parahydrogen, pure and mixed with deuterium, in various thermodynamic conditions using incoherent inelastic neutron scattering. The experiments were carried out on TOSCA-II, a new time-of-flight, inverse-geometry, crystal-analyzer spectrometer. After an accurate data reduction, the high-energy parts of the neutron spectra recorded in backward scattering were studied through the modified Young and Koppel model, from which the mean kinetic energy values for a hydrogen molecule were estimated. In addition the low-energy parts of the neutron spectra recorded in forward scattering were analyzed in the framework of the Gaussian approximation and fitted through a Levesque-Verlet model for the velocity autocorrelation function. Thus various physical quantities are determined and compared with accurate path integral Monte Carlo simulations. Despite the excellent quality of these fits, the velocity autocorrelation functions derived from the forward-scattering data appear totally unable to properly describe the backward-scattering ones. These findings prove an unquestionable breakdown of the Gaussian approximation in semiquantum liquids. The present results appear of great interest and suggest further investigation on the limits of the widely used Gaussian approximation.

Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium

The realization of the idea of time-scale invariance for relaxation processes in liquids has been performed by the memory functions formalism. The best agreement with experimental data for the dynamic structure factor S(k,omega) of liquid cesium near melting point in the range of wave vectors (0.4 A(-1) < or = k < or = 2.55 A(-1)) is found with the assumption of concurrence of relaxation scales for memory functions of third and fourth orders. Spatial dispersion of the first four points in the spectrum of the statistical parameter of non-Markovity epsilon(i)(k,omega) at i=1,2,3,4 has allowed us to reveal the non-Markov nature of collective excitations in liquid cesium, connected with long-range memory effect.