Dynamic Scaling Theory Research Articles

Scaled phase separation in a critical nonionic surfactant solution

The time evolution of phase separation in a critical mixture of non-ionic surfactant, pentaethylene glycol n-decylether and water, was investigated by the time-resolved small-angle light scattering in the spinodal region focusing to the scaling concept. The scaled behavior of the wave number and the intensity corresponding to the spinodal ring and of the scattering function are examined in relation to recent theoretical work. Good agreement was obtained with the dynamic scaling theory.

Spin-dynamics study of the dynamic critical behavior of the three-dimensional classical Heisenberg ferromagnet.

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L body-centered-cubic classical Heisenberg ferromagnet with L\ensuremath{\le}40 in the vicinity of the critical point ${\mathit{T}}_{\mathit{c}}$. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins by a fourth-order predictor-corrector method with initial spin configurations generated by Monte Carlo methods. The space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms were calculated to determine the neutron-scattering functions. We developed a dynamic finite-size scaling theory for the neutron-scattering function at ${\mathit{T}}_{\mathit{c}}$ and used it to extract the dynamic critical exponent z. Within our resolution limit, the value of z was estimated to be 2.478(28), in excellent agreement with the dynamic scaling prediction, and dynamic scaling was found to be valid for momentum transfer q up to 0.4\ensuremath{\pi} in the (1,0,0) direction.

Thermodynamic velocity and dispersion of first sound in liquid helium near the lambda transition

We extend the functional form of thermodynamic velocity of first sound in liquidhelium near λ transition, at different pressures, by using the heat capacity (as proposed by Chase[l], Pippard[2] and G. Ahlers[3]) to reach the hydrodynamic region ( t=T−T λ> 10 mK). For heat capacity we use both descriptions, logarithmic and power-law. These results are compared with experimental data obtained in resonant cavities for 20 μK <t< 1 mK and frequencies w, less than 7.5 KHz. In adition, these results are used to calculate the critical dispersion in the phenomenological theory of Ferrell and Bhattacharjee[4], based on dynamic scale theory. A strikingly good agreement with experimental results is found.

Basic aspects regarding irregular metal surfaces and their application in electrochemistry

The topography and other properties related to disordered metal surfaces play an important role in deposition, corrosion and growth phenomena. Metal surfaces resulting from columnar or dendritic metal deposits can be taken as models of anisotropic and isotropic strong surface disorder, respectively. The topography of rough columnar surfaces can be determined by scanning tunneling microscopy at different scales and described by means of the dynamic scaling theory. Roughness relaxation kinetics can be followed by electrochemical techniques and interpreted through a coalescence-type mechanism. Typical examples of electrochemical reactions at this type of electrodes are presented. The study of the electrochemical formation of 3D or 2D metal dendrites provides basic information about the development of either diffusion limiting aggregation-type or dense radial patterns and the design and working condition ranges. In this case, the influence of convection and, particularly, that of the relative contribution of migration and diffusion on determining the topography of the object has been established. A generalized model based upon a Monte Carlo simulation has accounted for the experimental results

Spinodal Decomposition of the Three-Component Microemulsion System: Aot/Water/Decane

ABSTRACTWe have performed a series of spinodal decomposition measurements of a three-component microemulsion system made of a surfactant AOT, water, and decane. The measurements were made by a temperature jump from a one-phase droplet microemulsion to a two-phase droplet microemulsion along the critical iso-volume fraction line (10%) using the time resolved light scattering intensity technique. All three stages of the evolution were studied. The typical scattering intensity distribution is in good agreement with recent dynamic scaling theories.

Critical and Gaussian conductivity fluctuations in YBa2Cu3O7- delta.

We report on systematic conductivity fluctuation measurements on three different samples of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. We show, using the temperature derivative of the resistivity and the logarithmic derivative of the conductivity with respect to temperature, that the transition is a two-step process. In the normal phase, contributions from Gaussian and critical fluctuations are clearly evidenced. Far from ${\mathit{T}}_{\mathit{c}}$, the Gaussian exponents indicate that a fractal topology might be adequate to describe the space dimensionality of the fluctuation spectrum. Closer to ${\mathit{T}}_{\mathit{c}}$ we observe a crossover to a three-dimensional (3D) homogeneous Gaussian regime. Still closer to ${\mathit{T}}_{\mathit{c}}$ we unambiguously identify the exponent ${\ensuremath{\lambda}}_{\mathrm{cr}}$\ensuremath{\sim}0.33, predicted by the simplest full dynamic scaling theory of critical superconducting fluctuations. The obtained exponent is consistent with a 3D, two-component, order parameter. Near the zero-resistance state, the temperature dependence of our data is rather consistent with power-law behavior, suggesting the occurrence of a phase-transition phenomenon related to the percolation granular network.

Measurements of dynamic scaling from epitaxial growth front: Fe film on Fe(001).

Dynamic scaling behavior has been observed during the growth of Fe films on Fe(001) using high-resolution low-energy electron diffraction technique. The interface width grows with time according to the power law w∼t β , with β=0.22±0.02. Time-invariant self-affine behavior on the short-range scale has also been observed with the roughness exponent α=0.79±0.05. The time-invariant characteristic agrees with the recent prediction based on the dynamic scaling theory. From the measured growth exponents, we suggest that the growth of Fe film is more consistent with a conservative growth process

Dynamic scaling behavior of spinodal decomposition in a critical mixture of 2,5-hexanediol and benzene

Time-resolved light scattering was used to study the time evolution of phase separation in a critical mixture of 2,5-hexanediol and benzene in the spinodal region. The early stage behavior of spinodal decomposition where the linearized theory of Cahn–Hillard is valid has been observed. The wave number and the interdiffusion coefficient characteristic of the early stage were well described by three-dimensional Ising model values, and the symmetric law of critical point universality was ascertained. A shoulder was observed at the higher scattering angle region in the structure factor and its wave number dependence was well expressed by the Porod law in the later stage of spinodal decomposition. The scaled behavior of the scattering function relating to the time evolution of phase separation was examined. The present result is in good agreement with the recent dynamic scaling theory.

Ultrasonic Absorption Coefficient and Propagation Velocity in Critical Benzonitrile-Isooctane Mixture

Measurements of the absorption coefficient and propagation velocity of ultrasonic waves in critical benzonitrile and isooctane mixture are reported for the frequency range of 5-25 MHz and temperatures ΔT = Τ Τcfrom 0.15 to 20 K. The analysis of the experimental results is based on dynamic scaling theory leading to good agreement with the theoretical predictions, especially in the reduced frequency range 1 < ω < 100. The adiabatic coupling constant g is calculated and compared to the experimental value.

Dynamic critical behavior of the random-exchange Ising system Fe0.9Zn0.1F2 determined via Mössbauer spectroscopy.

We have made M\"ossbauer-effect-spectroscopy (MES) measurements of the dynamical broadening of the M\"ossbauer lines above ${\mathit{T}}_{\mathit{N}}$ for a high-quality single crystal of ${\mathrm{Fe}}_{0.9}$${\mathrm{Zn}}_{0.1}$${\mathrm{F}}_{2}$ with an inhomogeneity-induced N\'eel-temperature (${\mathit{T}}_{\mathit{N}}$) broadening of less than 25 mK. In the reduced-temperature range 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$t (==T/${\mathit{T}}_{\mathit{N}}$-1)${10}^{\mathrm{\ensuremath{-}}2}$, we find that the excess linewidth diverges as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathit{w}}$ with w=0.79(7). On the assumption of a single divergent relaxation time, this measurement of w implies a dynamical exponent z=2.18(10) via dynamic-scaling theory. Our value for z involves an asymptotic approach to ${\mathit{T}}_{\mathit{N}}$, which is an order of magnitude closer than previous MES and neutron-spin-echo measurements and agrees with the renormalization-group prediction z\ensuremath{\approxeq}2.11 for the d=3 random-exchange Ising model. The result does not agree with the predictions of conventional van Hove theory, z=1.97, or the results of previous, fundamentally less asymptotic, measurements.

Bose glass-vortex-glass phase transition and dynamics scaling for high-Tc Nd2-xCexCuO4 thin films.

This paper reports the measurements of resistivities near the superconductor-insulator transition for high-${\mathit{T}}_{\mathit{c}}$ oxide superconductor ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ single-crystal thin films. The transition was tuned by magnetic fields and/or introducing disorder. The results of the resistivities are analyzed in line with dynamical scaling theory. The product of the dynamical exponent (${\mathit{z}}_{\mathit{B}}$) and the exponent for the correlation length (${\ensuremath{\nu}}_{\mathit{B}}$) is extracted. This value is consistent with that expected by the scaling theory. Our results provide the first evidence of the Bose-glass--vortex-glass phase transition in high-${\mathit{T}}_{\mathit{c}}$ ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ single-crystal thin films.

Viscoelasticity of crosslinked gels.

The damping characteristics of a crosslinked polymer are determined by its viscoelastic properties. Yet the loss mechanisms of networks have not been fully understood. It is shown that insight into network behavior can be gained from studies of how viscoelasticity evolves during the curing process. In addition, the peculiar viscoelasticity of the incipient gel (the polymer exactly at the gel point) is shown to offer unique damping characteristics. Experimental studies on an epoxy system show that the evolution of structure prior to the gel point follows the predictions of percolation and that the divergence of the bulk viscosity and the power law behavior of the dynamic shear moduli, G’∼G‘∼ωΔ, at the gel point follow the predictions of a dynamic scaling theory. A new superposition principle (time-cure superposition) holds for the linear viscoelastic responses at different extents of reaction in the critical regime both before and after the gel point. From the master curve beyond the gel point, the divergence of the inverse equilibrium modulus and the terminal relaxation time are shown to obey the theoretical predictions as well. In addition, an intriguing relationship exists between the relaxation time spectra of a network at the gel point and in the fully cured state. Measurements of the dynamic shear moduli of several epoxy and siloxane networks, with equilibrium moduli varying by four orders of magnitude, show G‘∼ωΩ at all extents of reaction past the gel point, where the network viscoelastic exponent Ω remains at the incipient gel value Δ. This surprising correspondence suggests that chemical networks possess some remnant of the fractal structure of the incipient gel. [Work supported by the U.S. DOE under Contract No. DE-AC-04-76DP00789.]

Critical behavior of the ultrasonic attenuation and velocity and shear viscosity for the binary mixture of carbon tetrachloride and coconut oil

Measurements of the ultrasonic velocity and absorption at the critical concentration were made as a function of temperature and frequency for the binary mixture of carbon tetrachloride and coconut oil. In addition, viscosity measurements were made. Ultrasonic absorption at 5, 7, 10, 15, 21, 25, 30, and 35 MHz above Tc is analyzed by the dynamic scaling theory of Ferrell and Bhattacharjee [Phys. Rev. A 31, 1788 (1985)]. The values of αc/f2 vs f−1.06 show a good agreement with the theory. Also, the experimental values of α/αc for carbon tetrachloride and coconut oil are compared to the scaling function F(ω*). The temperature and frequency dependence of the velocity are also determined. The coefficient of viscosity of the critical mixture shows a different temperature dependence from that of the pure components.

Asymptotics of random walk displacement in a percolation system under threshold

Long-time fluctuation-induced asymptotics for the mean square displacement of a random walk on a percolation system below the percolation threshold is investigated. A Flory-like estimate is constructed. It yields the same stretched-exponential law as the dynamic scaling theory. The contribution of linear clusters is proved to determine the long-time asymptotical relaxation

Aggregation Kinetics in Electro-Rheological Fluids

We study the aggregation kinetics of Electro-Rheological Fluid particles which interact through dipoles induced by an external electric field and experience negligible thermal motion. For a system in d-dimensions, our theoretical calculations show that the average cluster size s av increases with time t as s av ∝ t d /( d +3) . This result shows good agreement with experiments in 3 dimensions, and with computer simulations in 2 dimensions. It also shows good qualitative agreement with the dynamic scaling theory of the cluster-cluster aggregation model.

Scaling theory applied to far-infrared absorption by metal-insulator composite materials.

Dynamic scaling theory is used to obtain expressions for the far-infrared absorption coefficient \ensuremath{\alpha} of metal-insulator granular composite materials near the dc percolation threshold ${\mathit{p}}_{\mathit{c}}$ in the quasistatic limit. An anomalous frequency dependence is predicted near ${\mathit{p}}_{\mathit{c}}$ for 50-\AA{}-radius Au particles. The frequency dependence of \ensuremath{\alpha} obtained from an analysis of published data on Au blacks is inconsistent with the scaling theory for Drude Au particles in the three-dimensional limit, and the theoretical estimate of the magnitude of \ensuremath{\alpha} at \ensuremath{\omega}\ifmmode \tilde{}\else \~{}\fi{}=100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ is a factor of 7 too large.

Nature of thermodynamic fluctuations in the electrical conductivity of Y-Ba-Cu-O pellets and tapes containing silver

Results on the temperature dependence of the electrical resistivity of single-phase silver-doped Y-Ba-Cu-O pellets and tapes, prepared by a coprecipitation technique, are presented. The excess electrical conductivity nearT>T c is analyzed using Aslamzov-Larkin (AL) formulations. Silver addition in Y-Ba-Cu-O influences strongly the temperature range of both the 3D and 2D regions. The lower limit of the breakdown temperature of the mean-field region (x=−0.5) shifts toward higher temperatures as the concentration of Ag increases in Y-Ba-Cu-O. For samples with higher Ag contents, a third region with critical exponent 〈x〉=−0.28 is seen beyond the mean-field region. This possibly indicates the appearance of a fully critical 3D region, where dynamic scaling theory applies.

Critical behavior of the ultrasonic attenuation and velocity and shear viscosity for the binary mixture of nitrobenzene-n-hexane

Ultrasonic velocity and absorption as a function of temperature, concentration, and frequency (5–25 MHz) and shear viscosity as a function of concentration and temperature are reported for the binary mixture nitrobenzene-n-hexane in the homogeneous phase above Tc. For the observed absorption at critical concentration and critical temperature αc/f2 vs f−1.06 yields a straight line as predicted by the dynamic scaling theory of Ferrell and Bhattacharjee [Phys. Rev. A 24, 1643 (1981)]. Also, the critical amplitudes of the thermal expansion and specific heat have been calculated using the two-scale factor universality relation. The adiabatic coupling constant g is calculated and compared to the experimental value. In addition, the experimental values of α/αc (where α is the absorption at critical concentration above the critical temperature) for nitrobenzene-n-hexane are compared to the scaling function F(ω*) and show a good agreement with the theory. Finally, the velocity for the system at the critical concentration above the critical temperature appears to decrease linearly with increasing temperature.

Generation of superfluid vortex turbulence by high-amplitude second sound in4He

High-amplitude second sound in superfluid4He is used to generate vortex turbulence. By the use of a novel resonator designed to avoid nonlinear effects, a steady-state ac counterflow field is produced with amplitudes high enough to generate the turbulent state. The transition to the turbulent state shows hysteresis similar to that observed in dc superflow measurements. Critical velocities were measured as a function of both temperature and frequency. The frequency dependence agrees with the predictions of dynamic scaling theory, and the temperature dependence is the same as that observed in dc counterflow experiments.

Critical behavior of the ultrasonic attenuation and velocity and shear viscosity for the binary mixture of nitrobenzene‐n‐hexane

Ultrasonic velocity and absorption and shear viscosity as a function of temperature and frequency are reported for the binary mixture nitrobenzene‐n‐hexane in the homogeneous phase above Tc. The observed absorption αc/f2 vsf f−1.06 yields a straight line as predicted by the dynamic scaling theory of Ferrell and Bhattacharjee. The critical amplitudes of the thermal expansion and specific heat have been calculated using the two‐scale factor universality relation. The adiabatic coupling constant g is calculated and compared to the experimental value. The experimental values of α/αc for nitrobenzene‐n‐hexane are compared to the scaling function F(ω*) and show a good agreement with the theory. The velocity for the system at the critical concentration above the critical temperature appears to linearly decrease with increasing temperature.