Decay Of Density Fluctuations Research Articles

Structural relaxation dynamics of colloidal nanotrimers.

By Molecular Dynamics simulation, we investigate the dynamics of isotropic fluids of colloidal nanotrimers whose interactions are described by varying the strength of attractive and repulsive terms of the Mie potential. To provide a consistent comparison between the systems described by different force fields, we determine the phase diagram and critical points of each system, characterize the morphology of high-density liquid phases at the same reduced temperature and density, and finally investigate their long-time relaxation dynamics. In particular, we detect an especially complex dynamics that reveals the existence of slow and fast nanotrimers and the resulting occurrence of non-Gaussianity, which develops at intermediate timescales. Deviations from Gaussianity are temporary and vanish within the timescales of the system's density fluctuations decay, when a Fickian-like diffusion regime is eventually observed.

Collective Motions and Mechanical Response of a Bulk of Single-Chain Nano-Particles Synthesized by Click-Chemistry.

We investigate the effect of intra-molecular cross-links on the properties of polymer bulks. To do this, we apply a combination of thermal, rheological, diffraction, and neutron spin echo experiments covering the inter-molecular as well as the intermediate length scales to melts of single-chain nano-particles (SCNPs) obtained through ‘click’ chemistry. The comparison with the results obtained in a bulk of the corresponding linear precursor chains (prior to intra-molecular reaction) and in a bulk of SCNPs obtained through azide photodecomposition process shows that internal cross-links do not influence the average inter-molecular distances in the melt, but have a profound impact at intermediate length scales. This manifests in the structure, through the emergence of heterogeneities at nanometric scale, and also in the dynamics, leading to a more complex relaxation behavior including processes that allow relaxation of the internal domains. The influence of the nature of the internal bonds is reflected in the structural relaxation that is slowed down if bulky cross-linking agents are used. We also found that any residual amount of cross-links is critical for the rheological behavior, which can vary from an almost entanglement-free polymer bulk to a gel. The presence of such inter-molecular cross-links additionally hinders the decay of density fluctuations at intermediate length scales.

Propagating density fluctuations in hydrodynamics and beyond

Density fluctuations in simple liquids are analysed in the context of three different and widely used formalisms, whose equivalence in the hydrodynamic limit is shown. We, furthermore, address the issue of the dispersion of the propagating modes outside the hydrodynamics, by comparing three different definitions of the generalized sound velocity. The first definition is standard in statistical mechanics. It relates the sound velocity to the imaginary part of the complex conjugate poles of the so-called intermediate scattering function. Other definitions, frequently used in the literature, identify the characteristic frequencies of the inelastic excitations with the maxima of the inelastic features of the dynamic structure factor, or with the maxima of the current function. The behaviour of these three quantities in the hydrodynamic limit is discussed. Deviations from hydrodynamic dispersion law are also considered with particular emphasis given to the analysis of different sound propagation regimes related to different density fluctuations decay channels.

Heating of the Solar Wind by Ion Acoustic Waves

Abstract Calculations are made of the energy supplied to the solar wind by the rapid decay of density fluctuations, identified as ion acoustic waves. It is shown that this process supplies an appreciable fraction, perhaps nearly all, of the observed heating of the solar wind. This process may be an important step in the conversion of magnetic turbulence to particle energy.

Inverse Ising inference, hyperuniformity, and absorbing states in the Manna model

Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying short-ranged repulsion and long-ranged attraction. As the model approaches the critical point the interaction becomes purely repulsive, decaying as $r^{-\alpha}$ and we conjecture the exact value $\alpha=1/2$, suggesting density fluctuations decay as $r^{-3/2}$. We present a simple Gaussian field theory for the long distance behaviour of critical absorbing states and discuss implications for the Manna universality class.

Dynamics on next-neighbour distances in liquid and undercooled gallium

Density fluctuations of liquid and 20 K undercooled gallium have been studied by neutron spectroscopy. The decay of density fluctuations has been recorded at the structure factor maximum over a wide temperature range up to twice the melting temperature. The amplitude of the scattering function falls off with rising temperature in a nonlinear way with a changing slope around . The derived generalized longitudinal viscosity shows an upturn with decreasing temperature in the same temperature range. This increase in viscosity can be understood that liquid gallium transforms from a more fluid liquid metal to a more viscous liquid metal in that temperature range upon cooling. The change in the amplitude shows a remarkable agreement with results from liquid aluminium, lead and rubidium. This study suggests a universal crossover in dynamics of liquid monatomic metals, despite the many peculiar properties of gallium.

Power law relationship between diffusion coefficients in multi-component glass forming liquids.

The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.

Dynamical heterogeneities: from glasses to gels

One of the challenges in soft and condensed matter over the last few years has beenunderstanding the phenomena of glass and jamming transitions. A recent advance inthe field is the idea that the dynamical heterogeneities play here the same roleas the critical fluctuations in ordinary critical phenomena. This is due to thefact that the decay of density fluctuations in glasses and jammed systems takesplace thanks to the dynamically correlated motions of groups of particles. In thispaper, after a brief review of the properties of the dynamical heterogeneities inglasses we analyze the cases of chemical and colloidal gels, which are still intenselydebated.

Nearly incompressible fluids: Decay of solar wind density fluctuations

The evolution of density fluctuations throughout the solar wind is investigated as the basis of a newly developed theory of nearly incompressible hydrodynamics for an inhomogeneous flow. The model is explored using two‐dimensional numerical simulations. The lowest‐order density fluctuations (absent in the original homogeneous nearly incompressible theory) obey a passive scalar evolution equation with an additional source term that results from coupling to the large‐scale inhomogeneous mean density gradient. The importance of this source term is explored, and we estimate analytically an upper bound for the maximum possible effect of a source term for nearly incompressible flows with an inhomogeneous background (static and spherically symmetric). For typical solar wind parameters, we show that this effect is rather weak beyond 0.1 AU and that the density fluctuations can be described sufficiently accurately as a pure passive scalar. Our simulations identify the sensitive dependence of density fluctuation evolution on typical initial length‐scale ratio of scalar (density) and velocity fields, an effect known from the theory of passive scalar decay and experimentally measured in grid‐generated turbulence. It has long been thought that the variance in the density fluctuations (δρ)2 should decay in the manner analogous to the mean background density, implying that with heliocentric distance (δρ)2 ∝ R−4 throughout the heliosphere. Analysis of plasma data obtained by the Voyager spacecraft by Bellamy et al. (2005) showed that the density fluctuations decay much more slowly than R−4 and the decay rate exhibits a flattening between 20–30 AU and a possible rise afterward. A possible mechanism to reduce the decay rate within 30 AU was suggested to be turbulence driven by stream‐stream interactions followed by more dominant pickup ion interactions beyond 30 AU. Here we show that the variance in the density fluctuations as described by the inhomogeneous nearly incompressible theory evolves essentially independently of the mean density background with a decay rate that reduces and possibly levels off with increasing heliocentric distance.

Temperature dependent next-neighbour dynamics of liquid lead

The temperature dependence of the density correlation function at next-neighbourdistances has been investigated for the liquid metal lead. This correlation function is asensitive parameter for changes in the local environment and its Fourier transform wasmeasured in a coherent inelastic neutron scattering experiment. The zero-frequencyamplitude related to the long time decay of density fluctuations decreases in a nonlinearway and indicates a change in dynamics above the melting point. The derived generalizedlongitudinal viscosity shows a decrease near this temperature range. From theseobservations we suppose that solidification sets in on a microscopic level distinct above themelting point.

On the anomalous behaviour of microscopic diffusion of liquid water

We propose here a new interpretation of recent quasi-elastic neutron scattering (QENS)measurements on water. A line-shape analysis based on a stretched exponential ansatz forthe time decay of density fluctuations enabled us to observe an anomalous dependence onthe exchanged momentum of relevant relaxation parameters. We discuss this effect andrelate it to an a priori uncorrelated anomaly, previously evidenced by diffractionmeasurements.

High-frequency dynamics of liquid and supercritical water

The dynamic structure factor S(Q,omega) of water has been determined by high-resolution inelastic x-ray scattering (IXS) in a momentum (Q) and energy (E) transfer range extending from 2 to 4 nm{-1} and from +/-40meV . IXS spectra have been recorded along an isobaric path (400bar) in a temperature (T) interval ranging from ambient up to supercritical (T>647K) conditions. The experimental data have been described in the frame of the generalized hydrodynamic theory, utilizing a model based on the memory function approach. This model allows identifying the active relaxation processes which affect the time decay of density fluctuations, as well as a direct determination of the Q , T , and density (rho) dependencies of the involved transport parameters. The experimental spectra are well described by considering three different relaxation processes: the thermal, the structural, and the instantaneous one. On approaching supercritical conditions, we observe that the microscopic mechanism responsible for the structural relaxation is no longer related to the making and breaking of intermolecular bonds, but to binary intermolecular collisions.

Temperature dependence of the de Gennes narrowing in liquid rubidium

The temperature dependence of the density correlation function at next neighbor distances has been investigated for the liquid metal rubidium. This correlation function is a sensitive parameter for changes in the local structure and its Fourier transform was measured in a coherent inelastic neutron scattering experiment. The zero frequency amplitude related to the long time decay of density fluctuations decreases in a nonlinear way and indicates a change in dynamics around $1.5{T}_{\mathrm{melt}}$. The derived generalized longitudinal viscosity shows a decrease near this temperature. These observations are in agreement with the supposition that solidlike units may melt at this temperature.

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.

A model for transits in dynamic response theory

The first goal of vibration-transit (V-T) theory was to construct a tractable approximate Hamiltonian from which the equilibrium thermodynamic properties of monatomic liquids can be calculated. The Hamiltonian for vibrations in an infinitely extended harmonic random valley, together with the universal multiplicity of such valleys, gives an accurate first-principles account of the measured thermodynamic properties of the elemental liquids at melt. In the present paper, V-T theory is extended to nonequilibrium properties, through an application to the dynamic structure factor S(q,omega). It was previously shown that the vibrational contribution alone accurately accounts for the Brillouin peak dispersion curve for liquid sodium, as compared both with molecular-dynamics (MD) calculations and inelastic x-ray scattering data. Here it is argued that the major effects of transits will be to disrupt correlations within the normal-mode vibrational motion and to provide an additional source of inelastic scattering. We construct a parametrized model for these effects and show that it is capable of fitting MD results for S(q,omega) in liquid sodium. A small discrepancy between model and MD at large q is attributed to multimode vibrational scattering. In comparison, mode coupling theory formulates S(q,omega) in terms of processes through which density fluctuations decay. While mode coupling theory is also capable of modeling S(q,omega) very well, V-T theory is the more universal since it expresses all statistical averages, thermodynamic functions, and time correlation functions alike, in terms of the same motional constituents, vibrations and transits.

Dynamics of dense, charge-stabilized suspensions of colloidal silica studied by correlation spectroscopy with coherent X-rays

The dynamics of concentrated, charge-stabilized colloidal silica suspensions was studied over a wide range of wave-vectors. The short-time diffusion coefficient, D(Q), was measured for concentrated suspensions up to their solidification points by photon correlation spectroscopy with coherent X-rays and compared to free particle diffusion D0, studied by Dynamic Light Scattering (DLS) in the dilute case. Small angle X-ray scattering (SAXS) was used to determine the static structure factor S(Q). D0/D(Q) peaks for Q values corresponding to the maximum of the static structure factor showing that the mostly likely density fluctuations decay the slowest. The data allow one to estimate the diffusion coefficient D(Q) in the Q → 0 and Q → ∞ limits. Thus, hydrodynamic functions can be derived free from any modeling of the static or dynamic properties. The effects of hydrodynamic interactions on the diffusion coefficient in charge-stabilized suspensions are presented for volume fractions 0.075 < Φ < 0.28.

Structure and structure relaxation

A discrete-dynamics model, which is specified solely in terms of a system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are identical with the ones obtained from the mode-coupling theory for ideal liquid–glass transitions. The decay of density fluctuations outside the transient regime is shown to be given by a superposition of Debye processes. The concept of structural relaxation is given a precise meaning. It is proven that the long-time part of the mode-coupling theory solutions is structural relaxation, while the transient motion merely determines an overall time scale for the glassy dynamics.

Coulomb drag in compressible quantum Hall states

We consider the Coulomb drag between two layers of two-dimensional electronic gases subject to a strong magnetic field. We first focus on the case in which the electronic density is such that the Landau level filling fraction $\nu$ in each layer is at, or close to, $\nu=1/2$. Discussing the coupling between the layers in purely electronic terms, we show that the unique dependence of the longitudinal conductivity on wave-vector, observed in surface acoustic waves experiments, leads to a very slow decay of density fluctuations. Consequently, it has a crucial effect on the Coulomb drag, as manifested in the transresistivity $\rho_D$. We find that the transresistivity is very large compared to its typical values at zero magnetic field, and that its temperature dependence is unique -- $\rho_D \propto T^{4/3}$. For filling factors at or close to $1/4$ and $3/4$ the transresistivity has the same $T$-dependence, and is larger than at $\nu = 1/2$. We calculate $\rho_D$ for the $\nu=3/2$ case and propose that it might shed light on the spin polarization of electrons at $\nu=3/2$. We compare our results to recent calculations of $\rho_D$ at $\nu=1/2$ where a composite fermion approach was used and a $T^{4/3}$-dependence was obtained. We conclude that what appears in the composite fermion language to be drag induced by Chern-Simons interaction is, physically, electronic Coulomb drag.

Coulomb drag in the quantum Hall ν= state: Role of disorder

We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being 1/2. We find $\rho_D$ to be very large, as compared to the zero magnetic field case. We attribute this enhancement to the slow decay of density fluctuations in a strong magnetic field. For a clean system, the linear $q$-dependence of the longitudinal conductivity, characteristic of the $\nu=1/2$ state, leads a unique temperature dependence---$\rd \propto T^{4/3}$. Within a semiclassical approximation, disorder leads to a decrease of the transresistivity as compared with the clean case, and a temperature dependence of $T^2\log T$ at low temperatures.

Dynamics of Polymer Chains

The generalized Rouse equation derived by Schweizers is applied to chains in the crossover region between Rouse-like behavior and reptation-like behavior. A self-consistent scheme takes into account the coupling of single can motion and the decay of density fluctuations in the polymer matrix. It will be shown that this model may be understood as a generalized bead-spring model, comprising beads with a frequency-dependent mobility and effective springs modified by their surroundings. The correlation functions of normal coordinates are investigated as a function of frequency, and strong qualitative deviations from the Rouse case with respect to the distribution of relaxation times are found