Solution to the Glarum model with a finite relaxation rate

The one-dimensional version of the Glarum model of target relaxation by diffusing defects is generalized by considering a finite relaxation rate upon an encounter defect-target. This eliminates the difficulties associated with the instantaneous relaxation of the targets initially occupied by a defect. The diffusion and relaxation processes are described in terms of the master equation for a continuous-time random walk. An exact solution valid for all times and relaxation rates is obtained by the use of the van Kampen-Oppenheim method. The transition from exponential relaxation at short times to fractional exponential behaviour at long times is described in detail.     

Stress relaxation in an Zr<Subscript>52.5</Subscript>Ti<Subscript>5</Subscript>Cu<Subscript>17.9</Subscript>Ni<Subscript>14.6</Subscript>Al<Subscript>10</Subscript> bulk metallic glass

The isothermal relaxation of stresses in a bulk metallic glass is measured at temperatures below the glass transition point. The kinetic law of relaxation is determined. It is argued that the stress relaxation in the temperature range covered is due to the irreversible structural relaxation oriented by an external stress and characterized by a distribution of activation energies.     

Relaxation of strains in fibrillar porous carbon dioxide saturated media near their critical point

The isothermal relaxation of strains in deformed fibrillar porous layers saturated with subcritical or supercritical carbon dioxide has been studied at different temperatures by full-field speckle correlometry. The relaxation of strains is produced by the porous layer—fluid transition of a system from one equilibrium thermodynamic state to another due to a jump-like change in pressure. It has been established that the relaxation time attains a maximum near a critical point and rapidly decreases with increasing deviation of the system temperature from its critical value. The mechanisms of hydrodynamic relaxation in the density of a fluid layer and viscoelastic relaxation in a porous matrix are discussed. It is shown that the experimentally observed slow relaxation of a system is due to the viscoelastic relaxation of a porous fluid saturated layer at equal fluid densities inside and outside the layer.     

Relationship between structural and stress relaxation in a block-copolymer melt

The relationship between structural relaxation on molecular length scales and macroscopic stress relaxation was explored in a disordered block-copolymer melt. Experiments show that the structural relaxation time, measured by x-ray photon correlation spectroscopy is larger than the terminal stress relaxation time, measured by rheology, by factors as large as 100. We demonstrate that the structural relaxation data are dominated by the diffusion of intact micelles while the stress relaxation data are dominated by contributions due to disordered concentration fluctuations.     

Broadband dielectric dispersion in ferroelectric P(VDF-TrFE) copolymer films

Ferroelectric polyvinylidenefluoride-trifluoroethylene copolymer films with different thicknesses are prepared by a solvent-cast technique, by spin coating, and by a horizontal Langmuir–Blodgett technique respectively. The frequency dependent dielectric permittivity of these films is investigated with varying sample thickness and varying temperature in the ferroelectric as well as in the paraelectric phase. A dielectric relaxation according to a Vogel–Tamman–Fulcher law of the relaxation times is found in all samples. However, the relaxation times extracted from the dielectric permittivity in the frequency range are not consistent with the relaxation times determined from the temperature range. An explanation for this behavior is given by a temperature dependent distribution of relaxation times. Additionally, in thin samples a second relaxation with a weak anomalous temperature dependence, i.e. an increasing relaxation time with increasing temperature, is observed at high frequencies. Detailed investigations show that this behavior can be attributed to an electrode effect.     

Relaxation kinetics of the long-range order parameter in a non-uniform system studied by the phase field method using the free energy obtained by the cluster variation method

The order-order relaxation process of the long-range order parameter in the non-uniform L1 0 ordered phase is investigated by the hybridized calculation using the phase field method (PFM) and the cluster variation method (CVM). The resultant kinetics are composed of three processes sufficiently differing in the relaxation rates. The first and second processes correspond to antisite ordering-disordering relaxation within the ordered domain and relaxation due to a wetting-antiwetting of the antiphase boundary respectively. The third process is due to a coarsening of the ordered domain and its relaxation rate is fairly slow compared with the relaxation rates of the first and second processes; this is consistent with experimental observation. It is noted that the present result of relaxation kinetics involving the three processes is obtained only by the hybridized calculation using the PFM and CVM.     

Specific features of proton NMR relaxation of hydrocarbons and water in the pore space of silicates

The relaxation of the proton magnetization of water and hydrocarbons in a model medium of glass beads and quartz sand is studied by the NMR method. The spectrum of relaxation times of fluids is one-component in the model environment and three-component in quartz sand. The surface relaxivities measured in the model medium are used to determine the pore size distribution in quartz sand. Estimates of the specific surface area of sand based on the relaxation data are consistent with the values measured by the sorption method. The EPR method is used to determine the chemical nature of the active paramagnetic centers responsible for the surface relaxation of the proton magnetization. Differences in the relaxation behavior of aqueous and hydrocarbon fluids are interpreted within the framework of a simple model of surface relaxation.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Dielectric relaxation spectrum of water studied by the site—site generalized Langevin/modified mode-coupling theory

The dielectric relaxation spectrum of water is calculated from the site-site generalized Langevin/modified mode-coupling theory. The main part of the relaxation follows the Debye-type function, and a small deviation from the Debye relaxation is found on the high-frequency side. This tendency is consistent with recent experiments, although the absolute relaxation time does not agree with the experimental value quantitatively. The time development of the longitudinal polarization function resembles the dielectric part of the memory function, and we consider that this is because the dielectric friction dominates the collective reorientation of the dipole moment of water. We performed calculations with different dielectric constants using the reference interaction-site model integral equation, and found that the large gap between the time scales of the dielectric relaxation and the longitudinal polarization relaxation causes the Debye-type dielectric relaxation in our theory when the dielectric friction is dominant in the friction on the collective reorientation of the dipole moment. Namely, the longitudinal polarization relaxation is fast enough to be considered as a white noise to the dielectric relaxation process, so that the relaxation becomes a Markov process. The large gap between the two relaxation times originates from a large local field correction owing to the large dielectric constant of water. It is also suggested that the deviation from the Debye relaxation at the high-frequency side is the manifestation of the slow memory caused by the long-time part of the longitudinal polarization relaxation in the low-wavenumber region.     

Cross-correlated relaxation for the measurement of angles between tensorial interactions

Theory,experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zero- and double-quantum coherences in liquid state NMR are presented. The relative size of the interaction depends on the projection angle between the two tensorial interactions. The tensorial interaction can be either a dipolar interaction or a chemical shift anisotropy relaxation mechanism (CSA). Effects of additional sources of relaxation on the cross-correlated relaxation rates are analyzed. Also, an easy-to-use formalism is given to manipulate different cross-correlated relaxation interactions. The application addresses measurement of the backbone angle psi in a protein by measuring dipole((15)N-(1)H)-dipole((13)C(alpha)-(1)H(alpha)) and CSA((15)N)-dipole((13)C(alpha)-(1)H(alpha)) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos(2)θ-1 dependence of one cross-correlated relaxation rate can be overcome by measuring additional cross-correlated relaxation rates. The use of cross-correlated relaxation rates is demonstrated in structure calculations.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

(110)-GaAs量子阱中光生载流子对电子自旋弛豫的影响

我们实验研究了(110)-GaAs量子阱中光生载流子对电子自旋弛豫的影响。通过测量量子阱的荧光寿命和光学吸收计算,我们能得到不同泵浦光功率下的带间吸收所产生的空穴浓度;相对应地,通过双色磁光科尔旋转技术,我们测量了该GaAs量子阱中电子自旋的动力学过程。结合两者,我们得到了电子自旋弛豫速率与空穴浓度的关系。实验结果表明电子自旋弛豫速率与空穴浓度呈线性依赖关系,验证了BirAronov-Pikus机制主导该体系的电子自旋弛豫。     

Density matrix formalism for anelastic relaxation

A density matrix formalism is developed for anelastic (mechanical) relaxation in crystalline materials with point defects characterized by elastic dipoles. The time-dependent approach to equilibrium of the strain response under the action of a constant applied stress is deduced. The formalism parallels the one used in nuclear magnetic relaxation. The anelastic relaxation time is determined as a function of the parameters occurring in the defect hopping term in the Hamiltonian. This term is responsible for the dissipation of the anelastic ‘potential’ energy into the host lattice. In a lengthy concluding section, the following aspects are discussed point by point: the advantages of the formalism presented, its scope and special cases; the physical implications of the expression obtained for the relaxation time; the similarities and differences between magnetic relaxation and anelastic relaxation, etc.     

Non-newtonian flow for concentrated polymer systems

The modified Graessley theory with the three-dimensional Maxwell model can well explain some of the nonlinear viscoelastic behavior of concentrated polymer systems at least qualitatively with the assumption of a box-type relaxation spectrum for the equilibrium state.

The relaxation spectrum of concentrated polymer systems in shear flow is obtained by means of Graessley's theory. It is assumed that the characteristic time for the entanglement formation is the same order as that for its breakage and that the spectral density of the relaxation spectrum in the flow system is proportional to the number of entanglements between two molecules. The spectral density decreases approximately proportionally to 1/γ for relaxation times larger than 1/γ The non-Newtonian viscosity and other viscoelastic properties, such as the so-called stress overshoot and the stress relaxation, are calculated by using the obtained relaxation spectrum. Our theory explains very well the experimental results in many cases. Good agreement with experimental results is found if we assume that the so-called box-type relaxation spectrum in the equilibrium state has a finite gradient of the order of ?0.5 in the edge region of larger relaxation time on log-log plots.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA x DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

微波管中离子张弛振荡的混沌现象

微波管中离子张弛振荡引起的噪声对其工作性能有很大影响，已成为微波管领域研究的焦点之一.用包络方程描述电子束特性，用离散的宏粒子模型描述离子特性，在此基础上编写了一维粒子模拟程序，对行波管与速调管模拟，得到张弛振荡的时间序列；将振荡看作是一个复杂非线性动力学系统的响应，分析了离子张弛振荡时间序列的功率谱、重构相图及Lyapunov指数，指出离子张弛振荡具有混沌性质，为研究离子张弛振荡的控制与带有离子振荡噪声信号的处理提供了参考. 关键词： 张弛振荡 粒子模拟 微波管 混沌     

Measuring the longitudinal NMR relaxation rates of fast relaxing nuclei using a signal eliminating relaxation filter

A new experiment for selective determination of the relaxation rates of fast relaxing NMR signals is presented. The experiment is derived from the conventional inversion recovery experiment by substituting the 180 degrees inversion pulse of this experiment with a signal eliminating relaxation filter (SERF) consisting of three 180 degrees pulses separated by two variable delays, Delta1 and Delta2. The SERF experiment allows a selective suppression of signals with relaxation rates below a given limit while monitoring the relaxation of faster relaxing signals. The experiment was tested on a sample of 20% oxidized plastocyanin from Anabaena variabilis, where the fast exchange of an electron between the reduced (diamagnetic) and the oxidized (paramagnetic) form results in a series of average signals with widely different relaxation rates. To ensure an optimum extraction of information from the experimental data, the relaxation rates were obtained from the SERF experiment by a simultaneous analysis of all the FIDs of the experiment using a fast linear prediction model method developed previously. The reliability of the relaxation rates obtained from the SERF experiment was confirmed by a comparison of the rates with the corresponding rates obtained from a conventional inversion recovery experiment.     

Williams-watts dielectric relaxation: A fractal time stochastic process

Dielectric relaxation in amorphous materials is treated in a defect-diffusion model where relaxation occurs when a mobile defect, such as a vacancy, reaches a frozen-in dipole. The random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite. When there are many more defects than dipoles, the Williams-Watts decaying fractional exponential relaxation law is derived. The argument of the exponential is related to the number of distinct sites visited by the random walk of the defect. For the same reaction dynamics but with more traps than walkers, an algebraically decaying relaxation is found.