Relaxation Processes In Liquids Research Articles

Non-equilibrium Onsager–Machlup theory

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or ‘piecewise’) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein–Uhlenbeck stochastic process (which is globally stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager–Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager–Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the non-equilibrium self-consistent generalised Langevin equation (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model.

Dynamics of relaxation processes in liquids: Analysis of oscillation and orientation spectra

Based on the spectra of molecular (Rayleigh) scattering of light, we investigate relaxation dynamics in the molecules of para-, meta-, and ortho-xylenes which are confined in a container and heated from room through critical temperature Tc. We experimentally elucidate the successive transitions from hindered to absolutely-free rotations at temperatures up to a pre-critical temperature T*(<Tc) and then from individual to collective motions (macroscopic vibrations) of the molecules at higher temperatures above T⁎ up to Tc. Close to Tc, the inner field anisotropy is the same along three axes of inertia of the ellipsoid, and the depolarization degree is universal and independent of the specific nature of xylene isomers. A marked deviation from the Rayleigh's theory is also found in the spectral intensity of scattering light.

Relaxation processes in liquids: Variations on a theme by Stokes and Einstein

We investigate numerically the temperature and density dependence of the Stokes-Einstein ratio, Dη∕T, and of two commonly-used variants thereof, Dτ and Dτ∕T, where D is a diffusivity, η the shear viscosity, and τ a structural relaxation time. We consider a family of atomic binary mixtures with systematically-softened repulsive interactions, and the Lewis-Wahnström model of ortho-terphenyl (OTP). The three quantities grow significantly as the temperature decreases in the supercooled regime, a well-known phenomenon. At higher temperatures, Dτ exhibits negative violations of Stokes-Einstein behavior, i.e., decrease upon cooling, for the atomic systems, though not for OTP. We consider two choices for the relaxation time, one based on the decay of the self-intermediate scattering function, and the other on the integral of the stress autocorrelation function. The instantaneous shear modulus exhibits appreciable temperature dependence for the two classes of systems investigated here. Our results suggest that commonly-invoked assumptions, such as τ ∼ η and τ ∼ η∕T, should be critically evaluated across a wide spectrum of systems and thermodynamic conditions. We find the Stokes-Einstein ratio, Dη∕T, to be constant across a broad range of temperatures and densities for the two classes of systems investigated here.

Polymer–polymorphoid nature of relaxation processes in liquid and vitreous SiO2

AbstractOn the basis of the concept of polymer–polymorphoid structure of glass and glass‐forming liquid the experimental data are analyzed which are connected with structural and relaxation processes in condensed SiO2. It is shown that all relaxation processes in liquid and vitreous silica have a uniform physical‐chemical nature – interconversion of structure fragments (polymorphoids) of the various crystal polymorphic modifications that do not have translational symmetry (long‐range order), copolymerized to a greater or lesser extent, accordingly, in vitreous or liquid state. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A quantum statistical estimation of the amount of energy dissipated by molecular relaxation processes in liquids

The physical conditions concerning the far-infrared (FIR) absorption process in molecular liquids are discussed. It is shown that the well-known first-order perturbational treatment of the fluctuation-dissipation theorem (FDT) cannot be justified within quantum statistics. The basic physical concepts concerning the derivation and validity of the generalized FDT as revealed in an earlier article are discussed. It is shown that dissipation of irradiation energy is mainly due to the coupling V of the molecular system with the thermal bath, as proposed by van Vliet. The following cases are treated: (i) The coupling V leads to a time-dependent density operator. It turns out that nonvanishing dissipation is due to dynamical fluctuations of the density operator. (ii) The operator m(t) which represents the coupling of the system with an external field obeys, for V ≠ 0, a non-Markovian equation of motion. The irradiation energy dissipation is a direct consequence of memory effects concerning m(t). The “anomalous” temperature dependence of the FIR absorption bands of CH3CN is presented and explained by means of the generalized FDT.

Collective dynamics in liquid aluminum near the melting temperature: Theory and computer simulation

The microscopic collective dynamics of liquid aluminum near the melting temperature has been studied using two independent methods: first, using a theoretical approach developed in terms of the Zwanzig-Mori formalism and based on Bogolyubov’s idea of reduced description of relaxation processes in liquids; second, using molecular dynamics simulation. The X-ray inelastic scattering spectra obtained with the theoretical approach and computer simulation are compared with experimental data. The high-frequency acoustic excitations that appear on microscopic spatial scales in liquid aluminum are found to be mainly caused by two-, three-, and four-particle interactions.

Ultrasonic spectroscopy of pure cyclic compounds

Ultrasonic studies of the group of halogens of benzene and particularly dependence of acoustic parameters on the structure of organic liquids, demonstrate some interesting regularities in the group of these compounds in gas and liquid states. In this paper results for five cyclic liquids: bromo-, chloro-, fluoro- and jodobenzene are discussed and compared to benzene. Vibrational relaxation was observed in all the compounds. The studies reported here as well as other experimental for great number of compounds support the conclusion that almost all vibrational relaxation processes in liquids can be described using a single relaxation time. It also seems that all vibrational degrees of freedom of the molecule take part in this vibrational process. It seems that differences in transition probabilities between molecules studied could be caused by additional attraction between of molecules having a significant dipole moments.

Standards for molecular dynamics modelling and simulation of relaxation

An attempt is made to formulate a set of requirements for simulation and modelling of relaxation in dense media. Each requirement is illustrated by examples of numerical simulation of particles with different types of interaction given by soft-sphere, Lennard–Jones, embedded atom method or Coulomb potential. The approaches developed are expected to be universal for some classes of relaxation processes in liquids, fluids, crystals and plasmas.

Relaxation time scales in collective dynamics of liquid alkali metals.

In this paper the investigation of the dynamical processes of liquid alkali metals is executed by analyzing the time scales of relaxation processes in liquids. The obtained theoretical dynamic structure factor S(k,omega) for the case of liquid lithium is found to be in excellent agreement with the recently received inelastic x-ray scattering data. The comparison and interrelation with other theories are given here. Finally, an important part of this paper is the confirmation of the scale uniformity of the dynamic processes in liquid alkali metals predicted by some previous molecular dynamic simulation studies.

Diffusion time-scale invariance, randomization processes, and memory effects in Lennard-Jones liquids.

We report the results of calculation of diffusion coefficients for Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation processes in liquids. The results were compared with the molecular dynamics data for the Lennard-Jones system and a good agreement of our theory with these data over a wide range of densities and temperatures was obtained. By calculations of the non-Markovity parameter we have numerically estimated statistical memory effects of diffusion in detail.

New evidence for the idea of timescale invariance of relaxation processes in simpleliquids: the case of molten sodium

The idea of the timescale invariance of relaxation processes in liquids (Yulmetyevet al 2001 Phys. Rev. E 64 057101; 2002 JETP Lett. 76 147) is used to analyse theshort-wave collective excitation in liquid sodium, as recently measured by meansof very-high-energy-resolution inelastic x-ray scattering (Scopigno et al 2002Phys. Rev. E 65 031205). The dynamic structure factor, S(Q, ω),calculated on the basis of this idea is in very good agreement with theexperimental data in the wavevector range from 1.5 to 14.6 nm−1,where pronounced collective excitations exist. The frequencydependence of the non-Markovity parameter ϵi (Q, ω)(i = 1, 2, 3, 4)allows us to reveal the alternation of the amplification and thedecay of non-Markovity effects for the observed region of wavevectorQ.

A second-order Kubo response theory-centroid approach to vibrational energy relaxation for single-mode excitations

We consider an approach for describing vibrational energy relaxation processes in liquids for solutes excited to states which are dominated by single-mode excitations. The method utilizes the fact that adding a suitable linear term to the solute intramolecular potential, creates excitations in the first excited state of a chosen vibrational mode. The fully quantum energy decay rate of the vibrational excitation can then be derived using quadratic response theory, which expresses the decay rate as the decay of a second-order Kubo transformed correlation function. This correlation function can be exactly related to a path integral centroid second-order correlation function, which can be evaluated approximately by centroid molecular dynamics. The abilities and limitations of the approach are discussed. It is shown that the method should work best when only a single vibrational state is occupied prior to excitation. Practical matters require also that the relaxation is in the pico-second regime or shorter. In contrast to the usual golden rule approach, the present method incorporates quantum effects and does not require explicit evaluation of vibrational coupling elements or Fourier transforms. It also incorporates the intramolecular vibrational coupling, whereby intramolecular relaxation can be monitored explicitly. The approach is tested on asymmetric stretch excited OClO(aq), using a classical bath, and gives results which are in good accord with earlier findings. The theory also points in the direction of how to improve the so-called classical approach to vibrational energy relaxation, where energy is put directly into the mode subsequently undergoing relaxation.

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.

A new application of the nonlinear dielectric method for studying relaxation processes in liquids

The measurement setup for studying changes of electric permittivity induced in liquids by a strong electric field nonlinear dielectric effect, (NDE) is presented. The construction is based on the idea of frequency modulation of an LC generator (with an inductance L and a capacitance C in resonant circuit), proposed by Malecki [J. Chem. Soc. Faraday Trans. II 72, 104 (1976)]. The strong electric field is applied in the form of rectangular pulses (typically 1–4 ms). The setup enables measurements in a broad range of frequencies (80 kHz–12 MHz) and contains a new calibrating system, minimizing the influence of systematic error on the measured NDE values. We also indicate menthol as a standard, reference liquid in NDE studies. New applications of the NDE technique for studying relaxation processes in critical solution are also presented. They are based on the time resolved analysis of NDE decay after switching off the strong electric field.

Robert T. Beyer’s contributions in ultrasonics.

Robert T. Beyer was a major contributor to our understanding of ultrasonic relaxation processes in liquids and solids during the heyday of that field. One could argue that this period ran roughly from the time of his major review article in 1951 [J. J. Markham, R. T. Beyer, and R. B. Lindsay, Rev. Mod. Phys. 23, 353–411 (1951)] until his monograph in 1969 [R. T. Beyer and S. V. Letcher, Physical Ultrasonics (Academic, New York, 1969)]. He adopted and extended new measurement techniques of ultrasonic attenuation and used them to advance our understanding of relaxation processes in liquified gases, in water and aqueous solutions, in organic liquids and organic single crystals, and in liquid metals.

The spectrum of the non-Markovity parameter for relaxation processes in liquids

A general theory of the spectrum of the non-Markovity parameter is introduced for the detailed analysis of non-Markovian peculiarities of relaxation processes in liquids. The numerical calculations have been carried out for vibrational, dielectrical and structural relaxation. It is shown that the non-Markovian time effects play the main role in the kinetics of the relaxation processes in liquids.

Temperature-jump method for characterization of structural fluctuations and irreversible relaxation processes in liquids and glasses.

Enthalpy relaxations of propylene glycol and glycerol were followed in the time domain at 160 and 182 K, respectively, in the glass-transition region with use of an adiabatic calorimeter. The relaxation processes were analyzed and fitted with a stretched-exponential function with nonexponentiality parameter \ensuremath{\beta}. Specification of the temperature jump prior to the relaxation measurement, (\ensuremath{\Delta}T${)}_{\mathit{j}}$, was found to be indispensable for the characterization of the relaxation processes in the nonlinear-response regime and the value of \ensuremath{\beta} was studied as a function of (\ensuremath{\Delta}T${)}_{\mathit{j}}$. The value of \ensuremath{\beta} depends on both the sign and magnitude of (\ensuremath{\Delta}T${)}_{\mathit{j}}$, indicating a characteristic difference between the rates of creation and annihilation of structurally ordered regions in liquids. However, the values of \ensuremath{\beta} extrapolated from the positive and negative sides of (\ensuremath{\Delta}T${)}_{\mathit{j}}$ to zero degree Kelvin agree with each other (0.62\ifmmode\pm\else\textpm\fi{}0.02 for propylene glycol and 0.65\ifmmode\pm\else\textpm\fi{}0.02 for glycerol, respectively), and are in excellent agreement with results obtained by heat-capacity spectroscopy. This is an experimental verification that the enthalpy-relaxational observation in time domain is equivalent to that in frequency domain only for (\ensuremath{\Delta}T${)}_{\mathit{j}}$=0 K.

Physical criterion of the degree of non-Markovity of relaxation processes in liquids

The microscopic parameter characterizing the degree of non-Markovity of irreversible processes is introduced. It is shown that the structure relaxation process in liquids is essentially non-Markovian in a wide range of wave vectors excluding the region near the first maximum of the static structure factor.

Short time relaxation processes in liquids from viscosity and light scattering studies in molten KCl 2BiCl3

Brillouin scattering, viscosity, and calorimetric studies of the congruently melting glass-forming compound KCl⋅2BiCl3 have been made to clarify and extend a pattern of relaxation behavior seen over wide temperature ranges in a recent study of the simple ionic liquid system KNO3 +Ca(NO3)2. Viscosity data for the two systems covering nearly four orders of magnitude superimpose when scaled by the glass temperature Tg ratio, and comparable parallels are seen in the hypersonic absorption behavior. Sound velocity and absorption data are consistent with single relaxation time kinetics at high temperature in accordance with findings for the KNO3 +Ca(NO3)2 system. In each system high temperature Arrhenius behavior breaks down when τ&amp;gt;10−11s. It is shown in the present system that this is forced by the approach of the system to a thermodynamic limit where liquid and crystalline entropy contents would equalize: the limit falls only 26 K below Tg. A relationship to the behavior of argon is considered.

Relaxation processes in liquid and supercooled toluene by light scattering experiments

We report detailed light scattering experiments in toluene comprising measurements of shifts and linewidths of polarized (VV) and depolarized (VH) spectra in the temperature range from 30°C to the glass transition T g = - 156°C. The values of the longitudinal sound velocity and attenuation are analysed in association with the existing ultrasonic data. We find that both types of measurement support the prevalence of a vibrational relaxation process at high temperatures and a viscous one (structural+shear viscosity) at low temperatures. Viscous processes are analysed in the framework of current viscoelastic models. Transverse light scattering data do not agree with the corresponding quantities usually found in ultrasonic shear wave experiments. Although longitudinal properties look similar to those obtained in ultrasonic experiments, we find unusual features in the compressional component.