Logarithmic Relaxation Research Articles

Magnetic relaxation in disordered exchange interacting systems with random anisotropy

The magnetic relaxation of the disordered exchange interacting random anisotropy systems is investigated based on the Monte Carlo method. Similar to the dipolar interacting systems [M. Ulrich, J. García-Otero, J. Rivas, A. Bunde, Phys. Rev. B 67 (2003) 024416], the logarithmic relaxation rate decays by a universal power law, W ( t ) = A t − n . The exponent n increases monotonically with the decreasing temperature as well as the increasing exchange interaction. Depending on the value of n , short-range ferromagnetic correlations (or spin-glass-like behaviour) and superferromagnetic order are suggested.

Experimental evidence of logarithmic relaxation in single-particle dynamics of hydrated protein molecules

We observe a logarithmic-like decay of the intermediate scattering function (ISF) of the hydrogen atoms in the protein molecule in the time interval from 10 ps to 1 ns. We analyze the ISF, FH(Q,t), in terms of an asymptotic expression proposed by mode coupling theory (MCT). The result clearly shows that this logarithmic stretching of the β-relaxation range is real, substantiating the prediction of the molecular dynamics (MD) simulation results that used the formula proposed by MCT for the analysis of ISF.

Robust room temperature persistent photoconductivity in polycrystalline indium oxide films

We have investigated the effects of UV irradiation on the electrical and optical properties of polycrystalline In2O3 films. We found that UV illumination at a peak wavelength of 365 nm leads to a sharp drop in resistance and increase in carrier concentration. This highly conductive state persists for a timescale of hours in air at room temperature after illumination. We observe distinct changes in the optical absorption spectra and the associated change in carrier concentration, which is consistent with a Burstein–Moss shift of ∼0.1 eV. The relaxation rate of this persistent conducting state depends strongly on temperature. We find that the conductance relaxation in an oxygen-free environment can be described by a stretched exponential while the behavior of the samples in air is better described by a logarithmic relaxation, both of which may be associated with glassy behavior.

Improved Interpretation of Nuclear Magnetic Resonance T1 and T2 Distributions for Permeability Prediction: Simulation of Diffusion Coupling for a Fractal Cluster of Pores

NMR relaxometry is a powerful tool for inferring porosity and permeability data. In practice, measured magnetization decay curves are inverted for relaxation time distributions. Subsequently, one presumes a linear relationship between the pore radius distribution and the T1 and T2 distribution, for longitudinal and transverse magnetization, respectively. The fundamental equations used are based on a pore model, in which pores are assumed to be isolated from each other with respect to the NMR process and have smooth walls. The present study is based on a geometrical pore space model with connected pores and structured pore walls. The physical processes of surface relaxation, irreversible dephasing of magnetic spins and diffusive proton exchange between pores, are described by a system of differential equations. The solution yields a set of exponential functions representing the relaxation time distribution. We describe the difference between the distributions obtained for diffusion coupling and for isolated pores. With diffusion coupling on, the spectral width of the T1 distribution is strongly reduced, which indicates that the influence of large and small radii according to the T1-pore radius relationship is mixed to some extent. For a fractal pore space structure, where large pores are surrounded by adjacent minor pores, the T1 distribution does not resolve these substructures. Nevertheless, permeability values calculated from the logarithmic mean relaxation time T1,LM are quite the same for diffusion coupling and for isolated pores. The T2 distribution for diffusion coupling is little constricted and gives a better resolution of the pore wall structures than the corresponding T1 distribution. The permeability values from T2 distributions agree with the values from longitudinal magnetization, provided that we use a corrected relaxation time T2,corr, accounting for the dependence of the surface relaxivity ρ2 on pore radius. The study shows that radius distributions calculated from a T1 and from a T2 distribution differ from one another and both present an altered image of the true pore radius distribution. In practice, this has no serious influence on estimating permeability of medium- to high-permeability sandstones with the currently applied methods. The presented methodology of calculating the NMR response of pore space models with diffusion coupling may facilitate understanding porosity-permeability relationships of different rock types such as carbonate rocks with micro-porosity.

Investigation of polyamorphism in compressed B2O3 glass by the direct measurement of the density

Precise measurements of the relative volume change of vitreous B2O3 have been performed by the strain-gauge technique at hydrostatic pressures up to 9 GPa. The features of the strain-gauge technique are analyzed and the specificity of the measurements of “relaxed” and “unrelaxed” bulk moduli is discussed. Smeared anomalies of compressibility (at P > 0.5 GPa and P > 5 GPa) and logarithmic relaxation of the glass density are observed. A significant (by several times!) difference has been revealed between the relaxed bulk modulus of glass obtained from the volume measurements and the unrelaxed modulus estimated from the Brillouin spectroscopic data. The measurements of the relative volume change under compression together with the previous structure investigations and computer simulation results reveal the basic features of the phase transitions in B2O3 glass. Both direct and reverse transitions are smeared in pressure. The residual densification in glass is not associated with change in the short-range order.

Strain Stiffening And Soft Glassy Rheology In A Generalized Sliding Filament Model

Despite their enormous complexity and structural diversity, most biological materials show a remarkably similar viscoelastic phenomenology: nonlinear elasticity, power-law or logarithmic stress relaxation, and plastic length adaptation. Here we present a simple model based on Huxley's sliding filament model to demonstrate that such behavior can arise from generic structural properties, independent of the actual molecular constituents of the system. We compare the model predictions to data from active and passive microrheological experiments on epithelial cells and fibroblasts, smooth muscle tissue, and extracellular matrix protein networks.The material is represented by an uniaxial arrangement of infinitely stiff filaments crosslinked with parallel elastic elements that have a distribution of attachment angles. When the system is sheared or stretched, elements start to align, leading to strain stiffening due to a geometric recruitment of springs. The elastic elements have force-dependent average lifetimes described by energy traps with a broad distribution of energy trap depths. Broken links can reattach at random positions and attachment angles after unbinding. Such nanoscale structural rearrangements lead to viscous flow and plastic length adaptation on a macroscopic scale. Due to a broad distribution of energy trap depths, the system displays power law stress relaxation and soft glassy rheology.The model is capable of qualitatively reproducing experiments, and gives quantitative agreement for creep compliance, stress stiffening and plasticity in the case of cell microrheology. These results suggest that recruitment and dynamic unbinding of elastic elements are the common mechanism underlying the mechanical behavior of many complex biological materials from single cells to whole tissues.

Evidence for Two-Dimensional Spin-Glass Ordering in Submonolayer Fe Films on Cleaved InAs Surfaces

Magnetotransport measurements have been performed on two-dimensional electron gases formed at InAs(110) surfaces covered with a submonolayer of Fe. Hysteresis in the magnetoresistance, a difference in remanent magnetoresistance between zero-field-cooling procedures and field-cooling procedures, and logarithmic time-dependent relaxation after magnetic field sweep are clearly observed at 1.7 K for a coverage of 0.42 monolayer. These features are associated with spin-glass ordering in the Fe film.

The effect of a pulse magnetic field on the microwave properties of a YBCO thin filmstrip-line resonator

The effect of a single pulse magnetic field on the resonant frequency and quality factor of anYBa2Cu3O7−δ thin film strip-line resonator was studied at different temperatures and input power levels.It was shown that: (i) the induced magnetic flux and screening dc current, resulting fromthe pulse action, noticeably change both the resonant frequency and the quality factor; and(ii) relaxation of the trapped flux and induced current, caused by the flux creep process (atrather high temperatures), lead to a time evolution of these resonator characteristics.This relaxation proceeds in two stages: quick relaxation during the first 1–2 s (atT = 78 K) and long term (logarithmic) relaxation. The rate of long term relaxation increases withtemperature increase; on the other hand it does not depend on the input power level.

Pinning performance of (Nd0.33Eu0.2Gd0.47)Ba2Cu3Oy single crystal

We present data on the flux pinning performance of a twinned (Nd0.33Eu0.2Gd0.47)Ba2Cu3Oy single crystal with a strip-like surface structure, in the temperature range 65 K to 90 K. The critical current density Jc, the pinning force density F(=BJc), and the logarithmic dynamic relaxation rate Q were determined from the magnetic hysteresis loops (MHLs) measured by vibrating sample magnetometer up to 9 Tesla. At 65 K, the MHL featured a strong second peak with the top slightly depressed by twin plane channeling. This effect continuously decreased with increasing temperature but persisted up to 84 K. The second peak decreased faster with increasing temperature than the central one. None of the Jc(B) and F(B) dependences scaled, let alone in a narrow range of T. This fact, together with the multiple linear character of the Q(B) curve, indicated a strong effect of twin channeling on the crystal's pinning performance. No special effect due to the strip-like structure was recognized.

Magnetic and electronic irreversibility and relaxation in Eu1−xLaxB6 (x=0.15 and 0.18)

We have investigated the magnetic and electronic transport properties of Eu1−xLaxB6 (x=0.15 and 0.18). Temperature-dependent magnetization of Eu1−xLaxB6 (x=0.15 and 0.18) exhibited antiferromagneticlike ground state with transition temperature Tm≈5K and thermal hysteresis below Tm between field-cooled and zero-field-cooled modes with the magnetic field of H=0.1kOe. Time dependent isothermal remnant magnetization MIRM of Eu1−xLaxB6 (x=0.15 and 0.18) was found to follow logarithmic magnetic relaxation behavior M(t)=M0−M1log(t). The temperature-dependent resistivity ρ(T) shows anomalous increase at low temperatures below T⩽20K, suppressed by magnetic field, which can be explained by magnetic polaron picture. Interestingly, field dependent electrical resistivity ρ(H) for Eu1−xLaxB6 (x=0.15 and 0.18) showed irreversibility between increasing and decreasing field. The relaxation of ρ(H→0) was found to follow the general stretched exponential form, ρ(t)=A+Bexp(−t∕τ)γ.

Logarithmic relaxation in radiation-amorphized zircon

We study relaxation under pressure of a radiation-amorphized material. The volume of zircon, $\mathrm{Zr}\mathrm{Si}{\mathrm{O}}_{4}$, amorphized by natural radiation over geologic times, was measured under high pressure using the precise strain-gauge technique. The volume shows logarithmic relaxation as a function of time. We compare the measured relaxation with the logarithmic relaxation of other different systems, and discuss the commonality of behavior in these systems in terms of local relaxation events that relax stress on a microscopic scale. We propose that logarithmic relaxation arises as the result of the elastic feed-forward interaction mechanism between local relaxation events.

Unusual magnetism ofEr0.75Dy0.25Al2

dc magnetization, ac magnetic susceptibility, magnetic relaxation, electrical resistivity and x-ray powder-diffraction studies of ${\mathrm{Er}}_{0.75}{\mathrm{Dy}}_{0.25}{\mathrm{Al}}_{2}$ compound have been carried out in the temperature range of $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The compound orders ferromagnetically at $\ensuremath{\sim}25\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, followed by another transition at $\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This transition at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is marked by a significant hysteresis in low applied fields in zero-field-cooled and field-cooled magnetization data. The saturation magnetic moment is $8.24{\ensuremath{\mu}}_{B}∕{\mathrm{R}}^{3+}$ at $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in a $70\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ field, indicating the presence of strong crystalline electric fields. A signature of weak glassy behavior is observed below $25\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in frequency dependent ac magnetic susceptibility measurements. This observation is attributed to competing single-ion anisotropies of ${\mathrm{Dy}}^{3+}$ and ${\mathrm{Er}}^{3+}$ ions that are statistically distributed in the lattice, thus creating large positional entropy. The paramagnetic phase of this compound includes a narrow region of Griffiths-phase-like behavior, signified by the presence of short-range ferromagnetic correlations. A long-time logarithmic relaxation of magnetization has been observed in the ferromagnetically ordered state. The electrical resistivity shows a slope change near $25\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and also a drop at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The electrical resistivity in the ferromagnetic state follows ${T}^{2}$ law, indicating the dominant role of magnon scattering. The magnetoresistance is $\ensuremath{\sim}13%$ at $25\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in a $30\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ field. The role of quadrupolar interactions and magnetoelastic coupling in producing a possible structural distortion at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ has been considered and x-ray-diffraction studies were carried out down to $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. No structural change has been detected at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and hence the quadrupolar coupling between the rare-earth ions via the lattice should be weak, whereas direct higher-order Coulombic interactions may prevail.

Unraveling the equilibrium chain exchange kinetics of polymeric micelles using small-angle neutron scattering – architectural and topological effects

In this paper, we present a study of micellar structures formed by poly(styrene)-poly(butadiene) (PS10-PB10; the numbers indicate the molecular weight in kg mol−1) diblock copolymers and PB10-PS20-PB10 triblock copolymers in different n-alkane solvents. Particular emphasis is placed on the dynamic properties of these micelles under equilibrium which are studied using a novel time-resolved small-angle neutron scattering technique. The results show that the structures of the micelles are very similar for both the diblock and triblock copolymers, which allows a direct comparison of the dynamic properties. A novel logarithmic relaxation is found for both the triblock and the diblock micelles which is not consistent with theoretical expectations. However, for the diblock micelles, the relaxation kinetics seem to approach the rate and the single exponential decay predicted by Halperin & Alexander [Macromolecules, (1989), 22, 2403–2412] when the micellar cores are strongly swollen with solvent. For the triblock micelles a logarithmic relaxation is found for all cases as an effect of additional topological knots present even in highly swollen micellar cores. This behavior is assigned to an increased coupling of chain motion within the dense confined core – an effect which seems to vanish in diblock micelles when the core is sufficiently swollen.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

Relaxation time and elasticity during polymerization with DER 332

To complement a study of the dielectric relaxation time’s relation with the velocity of propagation of hypersound wave in a polymerizing liquid [K. Venkateshan and G. P. Johari J. Chem. Phys.125, 014907 (2006)], we report results of an analogous study by using the same diglycidylether of bisphenol-A that had been used for measuring the velocity. The data show that the logarithmic relaxation time increases linearly with the square of the velocity of propagation of transverse hypersound wave.

Logarithmic relaxation due to minimization of interactions in the Burridge-Knopoff model

The time evolution of macroscopic quantities describing the relaxation of complex systems often contains a domain with logarithmic time dependence. This logarithmic behavior at the macroscopic level is often associated with strongly interacting elements at the microscopic level, whose interactions depend significantly on their history. In this paper we show that stress relaxation in the Burridge-Knopoff (BK) model of multicontact friction behaves logarithmically, when the model is in, or close to, the solitary state where the elements move independently. For this regime we present an automaton that allows us to follow the decay of stress relaxation over the entire range where it behaves logarithmically in time. We show that our model can be mapped onto a system of noninteracting elements subject to a uniform distribution of forces, for which logarithmic stress relaxation is derived analytically.

Logarithmic relaxation in a kinetically constrained model

We present Monte Carlo simulations on a coarse-grained model for relaxation in binary mixtures. The liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting, respectively, unexcited and excited local states in a mobility field. Change in local mobility (spin flip) is permitted according to kinetic constraints determined by the mobilities of neighboring cells. We introduce two types of cells ("fast" and "slow") with very different rates for spin flip. Fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in dynamic correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on polymer blends.

Equilibrium Chain Exchange Kinetics of Diblock Copolymer Micelles: Tuning and Logarithmic Relaxation

A systematic study of the equilibrium chain exchange kinetics of a tunable model system for starlike polymeric micelles is presented. The micelles are formed by well-defined highly asymmetrical poly(ethylene−propylene)−poly(ethylene oxide) (PEP−PEO) diblock copolymers. Mixtures of N,N-dimethylformamide (DMF) and water are used as selective solvents for PEO. With respect to PEP this solvent mixture allows the interfacial tension, γ, to be tuned over a wide range. The equilibrium chain exchange between these micelles has been investigated using a novel time-resolved small-angle neutron scattering (TR-SANS) technique. The results show that the exchange kinetics is effectively frozen for large interfacial tensions but can be readily tuned to accessible time scales (minutes to hours) by lowering γ. Independent of temperature and concentration, the corresponding relaxation functions show an extremely broad and heterogeneous logarithmical decay over several decades in time. We explicitly show that such broad relaxation cannot be explained by polydispersity or a classical distribution of activation energies. Instead, the logarithmic time dependence points toward a complex relaxation picture where the chains are slowed down due to mutual topological and geometrical interactions. We propose that the behavior stems from constrained core dynamics and correlations between the expulsion probability of a chain and its conformation.

Surface Wave Assisted Self-Assembly of Multidomain Magnetic Structures

An ensemble of magnetic microparticles at the liquid surface displays novel snakelike self-assembled structures induced by an alternating magnetic field. We demonstrate that these structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. The segments of the "snake" exhibit long-range antiferromagnetic ordering, while each segment is composed of ferromagnetically aligned chains of microparticles. The structures exhibit magnetic hysteretic behavior with respect to an external in-plane magnetic field and logarithmic relaxation of the remanent magnetic moment.

Universal time relaxation behavior of the exchange bias in ferromagnetic/antiferromagnetic bilayers

The resilience of the exchange bias (Hex) in ferromagnet/antiferromagnet bilayers is generally studied in terms of repeated hysteresis loop cycling or by protracted annealing under reversed field (training and long-term relaxation, respectively). In this paper we report measurements of training and relaxation in NiFe films coupled with polycrystalline FeMn and epitaxial α-Fe2O3. We show that Hex suppressed both by training and relaxation was partially recovered as soon as a field cycling for consecutive hysteresis loop measurement was stopped or the magnetization of the ferromagnet was switched back to the biased direction. In both cases we can model the observed logarithmic time relaxation behavior, and its film thickness and temperature dependence, in terms of a thermally activated reversal of the antiferromagnetic domain configuration to reduce the total magnetic energy.