Self-correlation Function Research Articles

Dynamics of inherent structure in supercooled liquids near kinetic glass transition.

We present a description of the dynamics of a supercooled binary Lennard-Jones liquid in term of the potential landscape of the system. The slowing down of the dynamics in supercooled liquids near the kinetic glass transition is related to the existence of basins in the potential landscape. The inherent structures that are the local potential minima in the configuration space obtained by a quench process are employed to represent the configurations of the basins. We present time correlation functions of the inherent structure, both the self and the coherent part, as a function of wave vector. We also calculated the mean-square displacement, and the non-Gaussian parameter of the van Hove self-correlation function. Compared with the dynamics of original configurations, the short-time relaxation has almost been eliminated by the quench process. However, the long-time alpha relaxations remain essentially the same. We conclude that the long-time alpha relaxation is the result of cross-basin transition in the potential landscape in the configuration space.

Quasielastic nuclear forward scattering as a background-free probe of slow glass dynamics in confined geometries

The microscopic dynamics of dibutylphthalate/ferrocene in nanoporous silica matrices with pore sizes of 25, 50, 75, and 200 A, respectively, has been investigated in a temperature range between 70 and 200 K by nuclear resonant scattering of synchrotron radiation. The decay of the coherently forward scattered signal is enhanced owing to the diffusive motion of resonant nuclei on the timescale of the nuclear resonance lifetime. This enhancement contains information about the self-correlation function for a fixed wave vector k = 7.3 A-1. In the viscous regime and for 25 A pores the diffusional dynamics is clearly slowed down when compared to the bulk material.

Molecular diffusion in monolayer and submonolayer nitrogen

The orientational and translational motions in a monolayer fluid of physisorbed molecular nitrogen are treated using molecular dynamics simulations. Dynamical response functions and several approximations to the coefficient of translational diffusion are determined for adsorption on the basal plane surface of graphite and on a fictitious uncorrugated graphite surface. The rotational diffusion constants in the plastic crystal and in the fluid phase are calculated. The possibility of observing these phenomena with quasielastic scattering experiments is discussed. The wave vector range is determined where the ballistic approximation to the translational molecular self-correlation function is accurate.

Neutron scattering and the glass transition in polymers – present status and future opportunities

We present results obtained by the exploration of molecular motions by neutron scattering and outline future opportunities resulting from methodological progress in high-resolution neutron spectroscopy. Starting on methododical grounds, we will commence with possible future developments in neutron spin echo spectroscopy (NSE), the prime technique for the observation of molecular processes in the nanosecond domain. After describing the scope of neutron scattering for experiments on glass-forming materials, we will present measurements of the self-correlation function, which include the β-relaxation in polyisobutylene, and address the problem of the heterogeneity of the α-process. Thereafter, we deal with different aspects of the pair correlation function, starting from coherent scattering experiments on polybutadiene, where the choice of the momentum transfer is selective for the observation of the α- or β-relaxation. Then, we emphasize results on the structural relaxation obtained for the different polymers at the first structure factor peak. Finally, by example, we will address the capability of neutron scattering, to deal with motions in polymer blends, where by judicious labeling the dynamics of the different components can be observed separately.

Dynamics in a supercooled molecular liquid: theory and simulations.

We report extensive simulations of liquid supercooled states for a simple three-site molecular model, introduced by Lewis and Wahnström [Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of orthoterphenyl. The large system size and the long simulation length allow us to calculate very precisely (in a large q-vector range) self-correlation and collective correlation functions, providing a clean and simple reference model for theoretical descriptions of molecular liquids in supercooled states. The time and wave-vector dependence of the site-site correlation functions are compared (neglecting the molecular constraints) with detailed ideal mode-coupling theory predictions. Except for the wave-vector region where the dynamics are controlled by the center of mass (around 9 nm(-1)), the theoretical predictions compare very well with the simulation data.

A molecular approach to quantum fluids based on a generalized Ornstein–Zernike integral equation

In this paper, we present an Ornstein–Zernike-type integral equation applicable to quantum fluids. This integral equation was obtained by averaging fully imaginary-time-dependent reference interaction site model integral equation for the quantum fluids over imaginary time. The resulting integral equation is a scalar integral equation for linear response correlation function. The self-correlation function in the integral equation was determined in a self-consistent manner with the aid of Feynman’s variational perturbation method. Our theoretical treatment is an extension of the theory for an excess electron in the classical solvents [J. Chem. Phys. 81, 1975 (1984)] to that for the fully quantum fluids. Numerical calculations have been performed for the fluid helium-4 assuming Boltzmann statistics. The calculated pair correlation functions are in good agreement with path integral molecular dynamics results. The experimental static structure factors are well described by our theory. It was found that the calculated excess quantum kinetic energy decreases slowly with raising temperature; even at high temperature the quantum effect on the kinetic energy cannot be neglected.

Density fluctuation spectra of expanded liquid [formula omitted]Rb at different temperatures

Density fluctuation spectra in expanded liquid 85 Rb measured at 1373 and 1873 K have been successfully explained using the microscopic theory of density fluctuations in a monatomic liquid. The self-diffusion coefficient occurring in the intermediate self-correlation function which is inextricably linked with the collective dynamics of the system, turns out to be frequency dependent and such a consideration also leads to the reproduction of the observed peak in dynamical structure factor near 4–5 ps −1 .

Molecular-dynamics study of the diffusion coefficient on a crystal surface

We use molecular-dynamics simulation to study the migration of an individual atom on the surface (010) of a (12-6) Lennard-Jones bcc crystal. Although the Lennard-Jones potential does not describe quantitatively all crystalline features, it can give us several clues on its thermodynamical behavior. We calculate the displacement self-correlation function and the residence time for a particle deposited on the crystal surface. We show that an anomaly occurs on these quantities which can be a signature of a premelting process.

Magnetism in Ferromagnetic Spin-1/2 Ising Multilayers

In this work, we study the magnetization profiles of ferromagnetic multilayers consisting of two materials in a sandwich structure (ABA), with ferromagnetic coupling between the films, using an effective field theory with a probability distribution technique that accounts for the self-correlation function. Different exchange interaction terms at the interface are investigated. We present also results on the effect of both the exchange interaction constant in material B and the surface exchange interaction constant on the whole system.

Experimental observations of non-Gaussian behavior and stringlike cooperative dynamics in concentrated quasi-two-dimensional colloidal liquids

We report, from direct observation of particle trajectories as a function of time, the presence of stringlike cooperative motion in a quasi-two-dimensional liquid. We have used digital video microscopy to study the equilibrium dynamics of suspensions of sterically stabilized uncharged poly(methylmethacrylate) spheres confined in a thin glass cell. Our experiments reveal the existence, in semidilute and dense liquid states, of a transition in the qualitative dynamical behavior of the system. At short times particles undergo unhindered Brownian motion, at intermediate times they undergo uncorrelated binary collisions, and at long times these one-particle self-diffusive modes are coupled to collective longitudinal acoustic modes of the fluid, the signature of which is local fluctuating domains of enhanced particle mobility. We study the properties of these domains by examining the density dependence of the van Hove self-correlation function and its deviation from Gaussian behavior. We observe that periods of non-Gaussian behavior correlate precisely with the timing of events involved in the relaxation of "caged" particles and their nearest neighbors. In contrast with relaxation processes in supercooled liquids, the lifetime of dynamical heterogeneities in a dissipative colloidal suspension is found to shift towards shorter time scales with increasing particle density. During time periods for which a quasi-two-dimensional system follows Gaussian behavior, we observe that, as predicted by Cichocki and Felderhof [J. Phys. Condens. Matter 6, 7287 (1994)], the time dependence of the evolution of the effective diffusion coefficient from its short time to its long time value has the form (ln t)/t. This last finding is true for all observed particle densities. To our knowledge, these results are the first experimental verification of the existence of microscopic cooperativity and the predicted temporal evolution of the diffusion coefficient for Brownian motion in concentrated quasi-two-dimensional liquids.

Neutron spin echo study of low-Tc ferrofluid

We studied the diffusion of single domain particles of Mn0.3Zn0.7(Fe2O4) (Rp≈100Å) stabilized by oleic acid in dodecane near the transition temperature Tc of particles from superparamagnetic to paramagnetic state. The structure of the ferrofluid has been studied by small angle neutron scattering. We found a strong density fluctuation near Tc≈20°C and H=0, induced by critical spin diffusion. In addition, we studied this system using neutron spin echo (NSE) inelastic scattering. The temperature variation of the self-correlation function GS(T,q,t)=exp[−q2D(t/τ)β(T)] at momentum transfer q=0.07Å−1 in the time interval t=0.5–40ns reveals strong influence of magnetic fluctuations on the mobility: these fluctuations decrease the diffusion rate D and induce stretched relaxation (β≈0.6) at T<Tc≈16°C. Above Tc, Stokes diffusion dominates (β≈1)

Investigating one-dimensional diffusion by quasielastic neutron scattering: a theoretical approach.

Scattering functions and full widths at half maximum for quasielastic neutron scattering (QENS) are calculated for diffusion in systems of one-dimensional channels. The self-correlation function for diffusion in isotropically oriented channels is given and it is found that this function diverges at the origin. The calculations are carried out for both normal and single-file diffusion and the influence of the ballistic phase is investigated. It is found that the ballistic phase influences the scattering functions very strongly for large diffusion coefficients. QENS data from the literature are analyzed with respect to this influence. The influence of three different resolution functions (triangular, Gaussian, and Lorentzian) is considered.

Nanostructured precipitates: Experimental versus exact theoretical saxs profiles

Small Angle X-Ray Scattering is one of the few techniques suitable for the determination of the grain size distribution of nanostructured materials. A theoretical development has allowed us to determine the spatial self-correlation function of such systems and thus the scattering profile associated with the grain size distribution in the SAXS spectra without supposing any specific shape in the precipitates and taking into account their impingement. It has been tested in the primary crystallization of the amorphous Fe 73.5Cu 1Nb 3Si 17.5B 5 giving excellent agreement with the experimental data.

Heterogeneous Diffusion in Highly Supercooled Liquids

The diffusivity of tagged particles is demonstrated to be very heterogeneous on time scales comparable to or shorter than the $\alpha$ relaxation time $\tau_{\alpha}$ ($\cong$ the stress relaxation time) in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Einstein-Stokes value. The van Hove self-correlation function $G_s(r,t)$ is shown to have a long distance tail which can be scaled in terms of $r/t^{1/2}$ for $t \ls 3\tau_{\alpha}$. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure ($\sim 3 \tau_{\alpha}$).

Aging in a simple model of a structural glass

We consider a simple model of a structural glass, represented by a lattice gas with kinetic constraints in contact with a particle reservoir. Quench below the glass transition is represented by the jump of the chemical potential above a threshold. After a quench, the density approaches the critical density where the diffusion coefficient of the particles vanishes following a power law in time. In this regime, the two-time self-correlation functions exhibit aging. The behavior of the model can be understood in terms of simple mean-field arguments.

Elastic scattering under simultaneous excitation of x-ray standing waves in multilayers

We have measured the structure factor of diffuse scattering and amorphous scattering in a W/Si multilayer under simultaneous excitation of x-ray standing waves. The tuning of the nodes and antinodes to the location of the W and Si sublayers or to the respective interfaces increases the selective sensitivity to the structure of the respective sublayer or interface. The dynamically broadened first multilayer Bragg peak is modeled by the Darwin theory of dynamic diffraction, which allows for the exact determination of the standing wave phase. The decay of diffuse intensity, as measured in a grazing incidence geometry at different standing wave phase shifts, indicates that the height–height self-correlation function is of the same form for both types of interfaces, W/Si and Si/W. The amorphous peaks of the Si sublayer can only be observed if the angles of incidence and exit are optimized to suppress the scattering from the otherwise dominating W layers. The peak positions are the same as for bulk amorphous silicon.

Relaxation dynamics in dense binary colloidal mixtures: Brownian dynamics simulations

Brownian dynamics simulations have been carried out on a binary colloidal mixture of particles of two different diameters interacting via a Derjaguin-Landau-Verway-Overbeek potential. As the screening length is increased a transition from liquid to crystal (at a volume fraction $\ensuremath{\varphi}=0.2$) or a glassy state (at $\ensuremath{\varphi}=0.3$) is observed. Below a certain effective temperature ${T}^{\ensuremath{\star}}$, the temporal evolution of the mean-squared displacements shows a marked subdiffusive behavior at intermediate and long times. The supercooled liquid with $\ensuremath{\varphi}=0.3$ shows a staircase profile indicating strongly cooperative jump motion which is corroborated by the behavior of van Hove self-correlation functions and the non-Gaussian parameter. The van Hove distinct correlation function, in the $\ensuremath{\beta}$ relaxation regime, shows a factorization property in accordance with the mode-coupling theory predictions. The most interesting result is the observation of cooperative hop and subsequent hop-back motion at temperatures close to the glass transition.

Nonequilibrium properties of linear polar Kihara fluids from molecular dynamics. Results for models and for liquid acetonitrile

Molecular dynamics simulations for polar Kihara fluids are reported for linear models of different lengths at several dipole and quadrupole values and at three different thermodynamic states. Two of these states are close to the vapor–liquid equilibrium curve and the third one is at the same density as the first and at the same temperature as the second. Self-correlation functions and translational and orientational times are calculated and analyzed. Transport properties, diffusion, thermal conductivity, and shear viscosity are also reported and discussed in terms of multipolar forces. Correlation terms are used to calculate band broadening in different kinds of molecular spectra. Finally, it is shown how it is possible to discriminate between two models of acetonitrile that fit equilibrium properties equally well by using dynamic properties.

Comparative Analysis of Brightness and Lightness Functions

A study is reported of twelve chromatic functions and one achromatic function of brightness, and fourteen chromatic functions and one achromatic function of lightness with the aim of establishing the change in the exponent of the functions, a phenomenon considered as being related to: (a) the brightness or lightness response of a subject; (b) the influence of hue and saturation; (c) the level of the background surrounding the stimulus; (d) the Helmholtz - Kohlrausch effect. Different authors agree that these differences are produced by specific contributions of the tristimulus value Y and of chromaticity, the complexity of the problem arising from the fact that chromaticity would be expected to play a different role in each hue. They also agree that the Helmholtz - Kohlrausch effect is independent of the appearance of colour. We show that the variation due to hue and saturation does not prevent the lightness and brightness functions from showing a specific response that permits differentiation between them and other functions, for instance the saturation functions. Finally, we correlate chromatic and achromatic functions by means of the quadratic fluctuation function which allows us to define a self-correlation function. This mathematical analysis extends to all the samples without taking into account their variation in wavelength and purity. It shows the existence of a solid and stable coding system for luminance, a system that achieves stability through its instability, reflected in the variation of the exponent of the functions.

Deviation from Gaussian behavior in the self-correlation function of the proton motion in polybutadiene

In this article neutron-scattering experiments using the backscattering instrument IN13 on the glass-forming polymer polybutadiene are reported. As compared to other neutron spectrometers IN13 has a large range of wave vectors Q accessible. Therefore, a better statement can be made about the spatial extent of the observed motions. In order to obtain reliable results for the Q dependence a multiple scattering correction of the intensities has been performed. The Q dependence of the incoherent scattering from polybutadiene shows strong deviations from the Gaussian approximation at high Q. These deviations are interpreted under different microscopical model assumptions. Finally, a picture of a distribution of anharmonic potentials can give account for the observed deviation from Gaussian behavior in the incoherent intermediate scattering function at low temperatures. At higher temperatures the fast motion in these potentials is superimposed by a long-range diffusional motion. The latter may be extracted assuming a model for the fast motion. It shows certain characteristics of fractal diffusion but defies a simple scaling approach.