Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

Thomson scattering in strong external fields

In the present paper we shall investigate relativistic Thomson scattering in two external fields. A free classical electron will be embedded in a strong, constant and homogeneous magnetic field and in a powerful electromagnetic field. Both fields will be considered in the Redmond configuration, in which case the electromagnetic wave is circularly polarized and propagates in the direction of the homogeneous magnetic field. The electron will be allowed to have arbitrary initial conditions and the electromagnetic wave will be switched on either suddenly or adiabatically. We shall present the exact solution of the Lorentz equation of motion in the above external field configuration and we shall evaluate the spectrum and cross sections of the scattered radiation. In particular, we shall consider scattering close to resonance and we shall compare our results with the findings of earlier work.     

Anomalous temperature dependence of a dielectric relaxation rate

A polypropylene film containing 2,4,6-triiodophenol had, at 8 K, a dielectric absorption peak at 13.5 Hz. The peak moved to 22 Hz at 20 K, back to 15.5 Hz at 48 K, then rapidly to higher frequency with further increase in temperature. This probably results from a change in regime as the thermal phonon wavelengths become comparable to the size of the molecules.     

Birefringence and dielectric relaxation decay transients and anisotropic rotational diffusion of macromolecules in a strong external electric field

The decay transient response of polar and polarizable rigid bodies (macromolecules) diluted in a nonpolar solvent after a sudden switch-off of a strong external dc field is evaluated in the context of the anisotropic noninertial rotational diffusion model. On solving the differential-recurrence equations for the statistical moments (expectation values of Wigner's D functions), the decay transients of the birefringence and dielectric relaxation are obtained. The solutions (valid for arbitrary strengths of an external electric field) are given in a closed form suitable for comparison with experiment and Brownian dynamics simulations.     

Generalized Sturmians applied to atoms in strong external fields

The generalized Sturmian approach to quantum mechanical many‐body problems is described. The method allows correlated solutions to the many‐particle Schrödinger equation to be obtained directly, without the use of the self‐consistent‐field approximation. As an illustrative example, spectra and polarizabilities are calculated for atoms and ions in the 2‐electron and 3‐electron isoelectronic series under the influence of very strong external electric fields.     

Structure formation and dynamics of water in strong external electric fields

We have performed molecular dynamics computer simulations of water in homogeneous external electric fields which were varied in a wide range of field strengths. The dielectric response is found to be linear up to fields E₀≈0.01 V/Å from where dielectric saturation effects become important. At fields of E₀≈3 V/Å a phase transition into an ordered, ice-like structure is observed, which is stabilized through hydrogen-bonds. With an increasing external electric field, the frequency spectrum of the water dynamics shows a remarkable red shift of the intramolecular modes and a blue shift of the librational motions, where the frequency varies quadratically with the field strength. A simple analytical model is discussed which reproduces the observed behavior.     

Anomalous relaxation of a twisted cell under an external magnetic field: The nearly homogeneous relaxation

We report experimental and theoretical investigations of the dynamic behaviour of a π/2 twisted NLC layer in a magnetic field. When a magnetic field H is applied in the layer plane at a suitable angle β with respect to the easy axis on the first surface, the relaxation towards the equilibrium texture occurs through a slow decay of unstable textures. Depending on the values of H and β, the relaxation of the system can be nearly homogeneous or strongly inhomogeneous. In this paper we restrict our attention to the case where the relaxation occurs in a nearly homogeneous way. The theoretical relaxation time τw of the unstable textures is found to depend strongly on the angle β and on the amplitude of the magnetic field. The experimental dependence of τw on H and β is found to be in good agreement with the theoretical predictions. The relaxation process is extremely sensitive to small dishomogeneities of the director easy alignment on the surfaces. From the measured relaxation we are able to estimate a spread of 0.3° on the surface easy axes at a planar anchored SiO surface.     

Anomalous dielectric relaxation of water molecules at the surface of an aqueous micelle

Dielectric relaxation of aqueous solutions of micelles, proteins, and many complex systems shows an anomalous dispersion at frequencies intermediate between those corresponding to the rotational motion of bulk water and that of the organized assembly or macromolecule. The precise origin of this anomalous dispersion is not well-understood. In this work we employ large scale atomistic molecular dynamics simulations to investigate the dielectric relaxation (DR) of water molecules in an aqueous micellar solution of cesium pentadecafluorooctanoate. The simulations clearly show the presence of a slow component in the moment-moment time correlation function [PhiMW(t)] of water molecules, with a time constant of about 40 ps, in contrast to only 9 ps for bulk water. Interestingly, the orientational time correlation function [Cmu(t)] of individual water molecules at the surface exhibits a component with a time constant of about 19 ps. We show that these two time constants can be related by the well-known micro-macrorelations of statistical mechanics. In addition, the reorientation of surface water molecules exhibits a very slow component that decays with a time constant of about 500 ps. An analysis of hydrogen bond lifetime and of the rotational relaxation in the coordinate frame fixed on the micellar body seems to suggest that the 500 ps component owes its origin to the existence of an extended hydrogen bond network of water molecules at the surface. However, this ultraslow component is not found in the total moment-moment time correlation function of water molecules in the solution. The slow DR of hydration water is found to be well correlated with the slow solvation dynamics of cesium ions at the water-micelle interface.     

Non-markovian effects in dielectric relaxation

A generalized Nee—Zwanzig equation is proposed to describe both low and high frequency dielectric relaxation. It is shown that the inertial effect is closely related to the non-markovian character of the differential equation governing the time evolution of the dipole—dipole autocorrelation function. Comparison with experimental results is given.     

Anomalous strong exchange narrowing in excitonic systems

We investigate theoretically the phenomenon of exchange narrowing in the absorption spectrum of a chain of monomers, which are coupled via resonant dipole-dipole interaction. The individual (uncoupled) monomers exhibit a broad absorption line shape due to the coupling to an environment consisting of a continuum of vibrational modes. Upon increasing the interaction between the monomers, the absorption spectrum of the chain narrows. For a non-Markovian environment with a Lorentzian spectral density, we find a narrowing of the peak width [full width at half maximum (FWHM)] by a factor 1∕N, where N is the number of monomers. This is much stronger than the usual 1/√N narrowing. Furthermore, it turns out that for a Markovian environment no exchange narrowing at all occurs. The relation of different measures of the width (FWHM, standard deviation) is discussed.     

The effect of external orienting electric field on dielectric relaxation of segmented polyesters in dilute solution

A comparative study of dipole polarization relaxation in the absence and in the presence of an external orienting electric field was performed for linear segmented polyesters with alternating rigid (oxyfumaroylbis-4-oxybenzoates) and flexible (methylene-CH₂-, ethylene oxide-CH₂CH₂-O-, and dimethylsiloxane-Si(CH₃)₂-O-Si(CH₃)₂-) fragments in dilute solutions. Polyesters that do not display mesomorphic properties in the bulk show several regions of dielectric absorption with relaxation character. These regions are associated with the motions via the local mobility mechanisms of different polar fragments of the macromolecule. In solutions of polyesters that possess LC properties in the bulk, large-scale dipole polarization relaxation with long relaxation times and high activation energies was revealed along with local dielectric relaxation transitions. This process is associated with the cooperative motion of mesogenic fragments in their associates. In an external orienting electric field, the intensity of dielectric absorption usually increases for all types of dielectric transition; relaxation times and activation energies experience changes only for large-scale processes.     

Anomalous nuclear spin-lattice relaxation in copper small particles

Anomalously long nuclear spin-lattice relaxation time is expected in small metallic particles when the life time width of the conduction electron energy levels is smaller than their mean spacing. A new method for setting nuclear magnetization to zero is developed in order to measure the relaxation time in Cu small particles. The anomaly is observed in the relaxation of⁶³Cu in the particles with the diameters smaller than 100 A at temperatures below 0.5 K.     

Dipole-phonon coupling and dielectric relaxation

Equations of motion for the average polarisation are derived from a microscopic approach by use of the local density matrix. A specific form of the dipole-phonon coupling in the memory kernel is investigated and the necessary conditions for the generation of a non-Debye form of response examined. It is shown that these conditions can only be fulfilled by allowing for dipole-induced distortion with the lifetime of the “phonons” determined by the lifetime of the dipole correlation.     

Defect-diffusion models of dielectric relaxation

Dielectric relaxation due to defect-diffusion in liquids, as introduced by Glarum, is considered for the case that reorientation of a molecule at time t ? 0 may be due not only to the nearest defect at t = 0, but to any defect in the liquid. For one-dimensional diffusion one then obtains the empirical relaxation function introduced by Williams and Watts with β = 0.5, and for three-dimensional diffusion a result only slightly differing from that for a single relaxation time. It is concluded that a model of dielectric relaxation by diffusion of defects only leads to considerable deviations from a single relaxation time when the diffusion is restricted in some way.     

Low temperature dielectric relaxation spectroscopy

It has been found during the last 2$\text{1}\text{2}$ years that dielectric relaxations associated with many organic compounds could be observed by dissolving or dispersing them in hydrocarbon solvents or matrices and cooling them to 4.2 K. Such relaxations were nearly always attributable to conformational changes of independent solute or dopant molecules and could be used as a means of spectroscopic investigation. Two ways of using such data are outlined and the advantages and limitations are discussed using ROH, RSH and R₁R₂NH compounds as examples.     

Anomalous Kerr effect relaxation in an alternating field

Perturbation theory is used to derive the complex harmonic components (stationary regime) arising in Kerr effect relaxation for an assembly of nonelectrically interacting, polar, and polarizable symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The approach starts from a fractional kinetic equation written in configuration space and represents an extension of the Smoluchowski equation to fractional dynamics. This equation is solved in the context of a subdiffusive process characterized by an anomalous exponent alpha ranging from 0 to 1, the Brownian limit. By using a perturbation procedure restricted to the second order in the ac field strength, analytic expressions for the electric birefringence spectra representing the frequency dependence of the first (in omega) and the second (in 2omega) harmonic components are obtained. Various Cole-Cole-like diagrams are presented in order to illustrate the results so obtained and to emphasize the role played by the fractal parameter alpha in the anomalous diffusion collision process. A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a dilute polymer solution [poly(3-hexylthiophene)] appears to be quite satisfactory.     

Two-particle dynamics on an electrode in ac electric fields

The relative motion between pairs of negatively charged latex particles 9.7 microm in diameter and deposited on an electrode was measured by optical microscopy and image analysis. At an rms field of approximately 30 V cm(-1), the two particles moved toward each other at frequencies below 500 Hz, but they separated at 1000 Hz. In the cases of aggregation, there are several interesting characteristics. First, when the center-to-center separation of a pair was initially 6 particle radii or more apart, a transient 'incubation' period of tens of seconds was observed before the particles began to move toward each other. Second, the two particles never came into contact, rather at long times the pair maintained a stationary gap between them equal to approximately one-half the particle radius. This stationary gap between particles was also observed for the aggregation of clusters of three or more particles. Finally, the rate of approach for a pair of particles decreased as the frequency increased. Larger fields are required to move particles together in ac compared to dc fields; at 30 Hz the ac field must be 130 times greater than the dc field to achieve the same rate of approach. Taking advantage of the qualitative and quantitative differences of the cooperative motion of particles in dc vs. ac fields, one should be able to re-position particles by alternating between these two modes. We demonstrated that the same pair of particles can be brought together at low frequency (100 or 200 Hz) and then separated at high frequency (1000 Hz).     

Resonant non-linear spectroscopy in strong fields

A method is presented to describe multiple resonant non-linear spectra in the presence of strong laser fields. The Liouville equation for the density operator of the molecular system is transformed to a time-independent linear equation system. This can be easily solved rigorously by numerical methods or, after partitioning into a strong-field part and a perturbation, the solution can be obtained analytically by a novel perturbative approach. The results account for power broadening. Rabi splitting of signals, and power-induced extra resonances, the latter being related to the pure dephasing-induced resonances in the weak-field limit. The method can be applied to a large number of multiple resonant non-linear spectroscopies, especially CARS, CSRS, coherent Rayleigh scattering and sum- or difference-frequency generation.     

Coexistence of magnetization relaxation and dielectric relaxation in a single-chain magnet

A novel single-chain magnet, [MnIII3O(Meppz)3(EtOH)4(OAc)] (1), has been successfully synthesized from a secondary building block [MnIII3O(Meppz)3(EtOH)5Cl] (2) with an S = 1 ground state. SCM 1 exhibits both magnetization relaxation and dielectric relaxation properties.