Relaxation equations for the magnetic moment of a system of coupled spins

Redfield's equation [4] for the spin-density matrix is used to derive the macroscopic relaxation equations for the magnetic moment of a system of three nuclear spins coupled by dipole-dipole interaction. The relaxation is due to the Brownian rotation of the molecule in which the spin nuclei are randomly placed. The relaxation problem is solved for a system of spins at the vertices of an isosceles triangle; four exponentials are involved. A formula is derived for the number of relaxation equations governing the magnetic moment in the case of an arbitrary number of interacting spins.     

Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

The cumulant expansion is used to derive two formally different master equations for a two-level molecular system interacting with a bath, starting wit The two master equations reduce to the same form in the markovian limit for the bath (where its correlation time is much shorter than the relaxation pr A detailed comparison is made between the predictions of the two approaches which enables us to understand their range of validity and limitations. We apply the formalism to the vibrational relaxation and dephasing of a molecular impurity in a solid matrix and obtain a closed expression for the vib In contrast to the simple stochastic approaches we predict that the line shape in the non-markovian limit contains information regarding the interactio However, the fluctuations in the mean interaction energy of the two-level system with the bath, if correlated with the frequency modulation, result in     

General criteria for assessing the accuracy of approximate wave functions and their densities

Master equations for propagators in quantum open systems and their spectral resolutions are derived. The Zwanzig partitioning scheme along the superoperator algebra are used to derive equations of motion for partitioned operators in a Liouville space. The reservoir influence on the dynamical evolution of operators is shown to lead explicitly to dissipative effects arising from memory terms in the evolution equations of such operators. It is also shown that spectral representations may be written in a self-consistent analytic way by means of the self-energy fields for transition energies of the system by taking into account the lack of the complete knowledge about the reservoir. A kinematic fluid interpretation of the resultant equations is given and an explicit form of the “collision” superoperator is obtained. Finally, a simple example to illustrate the determination of self-energy fields for the system–reservoir interaction corrections is given. © 1995 John Wiley & Sons, Inc.     

Relaxation times of an electrolytic cell subject to an external electric field: role of ambipolar and free diffusion phenomena

We evaluate the relaxation times for an electrolytic cell subject to a step-like external voltage, in the case in which the mobility of negative ions is different from that of positive ions. The electrodes of the cell, in the shape of a slab, are supposed to be perfectly blocking. The theoretical analysis is performed by assuming that the applied voltage is so small that the fundamental equations of the problem can be linearized. In this framework, the eigenvalues equations defining all relaxation times of the problem are deduced. In the numerical analysis, we solve the complete set of equations describing the time evolution of the system under the action of the external voltage. Two relaxation processes, connected with the ambipolar and free diffusion phenomena, are sufficient to describe the dynamics of the system, when the diffusion coefficients are of the same order of magnitude.     

The Stage of Ultrafast Relaxation in Micellar Surfactant Solutions

The Becker–Döring kinetic equations are employed to describe the stage of ultrafast relaxation in micellar surfactant solutions, which ends in the establishment of a quasi-equilibrium distribution in the premicellar region of aggregate sizes. This is performed by analyzing the spectrum of the eigenvalues of the matrix of kinetic coefficients of the linearized Becker–Döring difference equations, which describes the complete multistage relaxation in a micellar system. The first value of the spectrum ordered as an ascending series is equal to zero (infinite relaxation time), thereby corresponding to the law of conservation of the surfactant quantity. The second value is very small; it differs from the series of subsequent values by several orders of magnitude and determines the time of slow relaxation. The other eigenvalues describe the processes of fast relaxation and comprise the contributions from the relaxation processes in both micellar and premicellar regions of aggregate sizes. In the latter region of the spectrum, the contribution of the ultrafast relaxation can be numerically distinguished. The obtained result is confirmed by the analysis of the spectrum of relaxation times of premicellar aggregates, which are considered as a closed system. It is also shown that the spectrum of ultrafast relaxation times is mainly determined by the first diagonal elements of the matrix of the linearized Becker–Döring equations and can be described analytically.     

Applicability of the method of kinetic equations for describing nuclear quadrupole resonance in molecular crystals

The applicability of the method of kinetic equations for describing nuclear quadrupole resonance (NQR) in molecular crystals is demonstrated for the case in which the relaxation processes are produced by torsional vibrations of the molecules. The Bloch system of equations for NQR spins I=3/2 situated in an axisymmetric electrical field and expressions for spin-lattice relaxation times were obtained.     

Dielectric spectroscopy of monatomic alcohols

The frequency dependences of permittivity ?(f) and dielectric loss tanδ(f) of monatomic alcohols are measured in range of frequencies f from 0.025 to 1000 kHz. Dielectric relaxation is observed in the investigated frequency range. Empirical correlation equations describing the relationships between the dielectric characteristics and physicochemical properties of monatomic alcohols are obtained.     

Electrorheological Kelvin-Helmholtz instability of a fluid sheet

The present work deals with the gravitational stability of an electrified Maxwellian fluid sheet shearing under the influence of a vertical periodic electric field. The field produces surface charges on the interfaces of the fluid sheet. Due to the rather complicated nature of the problem a mathematical simplification is considered where the weak effects of viscoelastic fluids are taken into account. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations with damping terms and having complex coefficients. Stability criteria are discussed through the assumption of symmetric and anti-symmetric deformations. The disappearance of surface charges from the interfaces obeys a certain relation derived in the marginal state. Furthermore, the case dealing with general deformation is discussed through marginal state analysis. The stability behavior in resonant and nonresonant cases are studied. In addition, the stability picture in the case of absence of the field frequency is studied. The numerical examination for stability showed that the relaxation time ratio plays a destabilizing influence in the case of anti-symmetric deformation or in the general deformation. The stabilizing effect for the relaxation time ratio is saved in the case of general deformation in the presence of the field frequency. In the later case the viscosity, the velocity, and the thickness parameter play a stabilizing influence. A dual role is readied for these parameters in the absence of the field frequency or in the anti-symmetric deformation. The field frequency still plays a destabilizing role in both cases.     

Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

The problem of electroviscoelastic Kelvin-Helmholtz waves of Maxwellian fluids under the influence of a vertical periodic electric field is studied in the absence of surface charges. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming semi-infinite dielectric fluids. Due to the streaming flow and the influence of a periodic force, a mathematical simplification is considered. The weak viscoelastic effects are taken into account so that their contributions are demonstrated in the boundary conditions. The approximate equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations of damping terms having complex coefficients. Symmetric or antisymmetric deformation that relaxes the coupled Mathieu equations and yields a single Mathieu equation is considered. Stability criteria are discussed and numerical estimation shows that the increase in the sheet thickness plays a destabilizing effect in the presence or in the absence of the field frequency as well as the field intensity. In the absence of the field frequency the velocity ratio between the upper fluid velocity and the sheet velocity has a destabilizing influence, while that between the velocity of the lower fluid and the velocity of the sheet has a stabilizing influence. Moreover, the viscosity ratios have a damping influence while the elasticity ratios have a destabilizing influence. Furthermore, a range of general deformations of the surface deflections is studied. Moreover, the stability behavior for the resonance cases is studied and discussed. The coupled Mathieu equations are analyzed by the multiple scale method. The numerical examination for stability yields some changes in the stability behavior. The fluid sheet thickness plays a stabilizing role in the presence of a constant field while the damping role is observed for the resonance case. Similar results are found for both the stratified velocities and the stratified relaxation times. The dual role of the stratified viscosities is observed in the presence or the absence of the field frequency. Copyright 2000 Academic Press.     

The nuclear magnetic resonance relaxation data analysis in solids: general R1/R1(ρ) equations and the model-free approach

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.     

The validity of the “few-level” approximation in gaseous relaxation phenomena

The Bloch equations including damping are formulated for a molecular system excited by incident radiation. In contrast with a previous treatment the present formalism gives an intuitively satisfactory form of relaxation terms. A three-level system irradiated by a single oscillating field is specifically considered, and using this manifold as a model for a two-level system immersed in a heat bath, the problem of “embedding” a pair of levels connected by radiation within a multi-level manifold is treated. A brief discussion of transient solutions to the Bloch equations is included.     

Studies about the influence of self-organization of colloidal magnetic nanoparticles on the magnetic Néel relaxation time

The monodomain magnetic nanoparticle-based colloids are mainly used in biomedical applications. In this type of colloids, there is a tendency of agglomeration even in the absence of external magnetic field. So, the Néel magnetic relaxation time of the system is affected by that tendency. In this paper, we propose a model to study how the nanoparticle tendency to agglomerate in the nanofluid affects the Néel relaxation time of the system. For simulating the self-organization of colloidal nanoparticles, we apply a Monte Carlo method, and the Néel magnetic relaxation time is assessed through the adaptation and solution of Coffey equations in oblique magnetic field, adapted to the local magnetic field on a nanoparticle.     

Molecular dynamics of an epoxy resin modified with an epoxidized poly(styrene-butadiene) linear block copolymer during cure and microphase separation processes

Molecular dynamics of diglycidyl ether of bisphenol A (DGEBA) epoxy resin modified with an epoxidized poly(styrene-b-butadiene) (SepB) linear block copolymer has been monitored during cure and microphase separation process by dielectric relaxation spectroscopy (DRS) for wide frequency and temperature ranges. Different primary and secondary relaxation processes have been analyzed for neat components and ternary mixture. Relaxational behaviour has been modelled with Havriliak-Negami, Vogel-Fulcher-Tammann and Arrhenius equations and fitting parameters and their evolution have been obtained. The retention of the epoxidized poly(butadiene) (PepB) block in the epoxy-rich phase during all the polymerization process, previously detected by our group with atomic force and transmission electron microscopies, has been confirmed by dielectric relaxation spectroscopy. The evolution of molecular dynamics during the polymerization process of the epoxy resin in the ternary system indicates a change in the trend of the main relaxation at times that agree with phase separation detected by rheology.     

A first principles simulation study of fluctuations of hydrogen bonds and vibrational frequencies of water at liquid-vapor interface

We present a theoretical study of the structure and dynamics of water-vapor interface by means of ab initio molecular dynamics simulations. The inhomogeneous density, hydrogen bond and orientational profiles, voids and vibrational frequency distributions are investigated. We have also studied various dynamical properties of the interface such as diffusion, orientational relaxation, hydrogen bond dynamics and vibrational frequency fluctuations. The diffusion and orientational relaxation of water molecules are found to be faster at the interface which can be correlated with the voids present in the system. The hydrogen bond dynamics, however, is found to be slightly slower at the interface than that in bulk water. The correlations of hydrogen bond relaxation with the dynamics of vibrational frequency fluctuations are also discussed.     

Collisional relaxation times in a three-level maser

We derive the Bloch equations for a three-level system, introducing phenomenological relaxation rates. Microscopic expressions are developed for these rates in the case of a gas of molecular absorbes for which relaxation is due to collisions with other molecules. Assuming that the colliding species move on classical paths and interact through long-range dipole terms, we can derive simple formulae for all the rates. A notable prediction is that certain off-diagonal rates are non-zero, though smaller than the diagonal terms. The physical significance of the results is briefly discussed.     

Dielectric analysis of sheep erythrocyte ghost. Examination of applicability of dielectric mixture equations

The purpose of this study is to confirm the applicability of dielectric mixture equations in dielectric analysis of biological cell suspensions. Two dielectric mixture equations, the Pauly-Schwan (P-S) equation and the Hanai-Asami-Koizumi (H-A-K) equation were tested using sheep erythrocyte ghosts whose internal solution is identical with the external solution. Dielectric measurements were carried out for the ghost suspensions over a frequency range 10 kHz to 100 MHz; a single dielectric relaxation was found between 100 kHz and 10 MHz. From the dielectric relaxation, the conductivity and permittivity of the ghost interior and the capacitance of the cell membrane were calculated following the P-S and H-A-K equations. When the H-A-K equation was employed (and as expected from the property of the ghosts), the estimated internal conductivity was in good agreement with the external conductivity at volume fractions up to about 0.7. With the P-S equation, on the other hand, the same results as above were obtained but only at low volume fractions below about 0.3. In addition, the H-A-K equation provided a better simulation for the observed relaxation curves than did the P-S equation, especially at high volume fractions. It is, therefore, concluded that the H-A-K equation is applicable to a wider range of volume fraction than is the P-S equation.     

Langevin-Bloch equations for a spin bath

We derive the Bloch equations for a two-level system coupled to a spin bath of infinitely many two-level atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of "motional narrowing" of spectral line. The theoretical results are discussed in the light of absorption-emission experiments on single quantum dots.     

Hydrodynamic correlation functions for molten salts

Abstract

The linearized hydrodynamic equations for a binary ionic fluid, with specific reference to a dissociated molten salt, are used to evaluate correlation functions of local fluctuation variables and the corresponding response functions. Previous results for the instantaneous correlation functions are extended and connected with thermodynamic fluctuation theory. Different dynamical behaviours, depending on the relative magnitude of the relaxation frequency for charge fluctuations and the sound wave frequency, are demonstrated. When 4πσ/? > ck, charge fluctuations are uncoupled from mass fluctuations, the latter being isomorphous to those of a one-component neutral fluid. Kubo relations for the transport coefficients are derived in this regime. When 4πσ/? < ck, the behaviour of the ionic fluid becomes isomorphous to that of a neutral mixture, with electrical conduction playing a role analogous to interdiffusion and contributing, in particular, to the damping of sound waves. An interpolation formula between these two limiting behaviours of the relaxation frequencies is also derived. The consequences of these results for the light scattering spectrum of an ionic fluid are briefly discussed     

Anomalous dielectric relaxation in strong ac external fields

Dielectric relaxation of complex polar fluids is considered in the context of the anomalous diffusion characterized by a fractional parameter alpha < or = 1 (subdiffusion). An infinite hierarchy of three-term differential-recurrence equations governing the time evolution of the electric polarization is established by following a purely phenomenological procedure. The matrix-continued fraction method is used to derive the exact numerical solution of the stationary regime for an assembly of nonelectrically interacting, polar symmetric-top molecules in presence of a strong ac electric field. The results so obtained are valid to any order in the field strength parameter gamma1, thus extending previous theories applicable to fields of very small amplitudes only. This is illustrated by Cole-Cole diagrams and three-dimensional relaxation spectra for the first- and third-harmonic components of the electric polarization as a function of alpha, gamma1, and the angular frequency.