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.     

Influence of the anisotropic polarizability on the anomalous dielectric relaxation spectra

The nonlinear dielectric response due to the application of a strong dc bias electric field superimposed on a weak ac electric field is considered in the context of the anomalous diffusion (subdiffusion). A perturbation procedure is used to derive analytical expressions for the first three harmonic components of the electric polarization of an assembly of both polar and anisotropically polarizable symmetric-top molecules. To accomplish that, an infinite hierarchy of multiterm (21) differential-recurrence equations of noninteger order for the moments is established and solved for the stationary regime. The results so obtained are illustrated in the form of Argand diagrams and three-dimensional relaxation spectra for the complex nonlinear dielectric increment extracted from the first harmonic component of the electric susceptibility. These plots show the role and importance played by the fractional exponent and the parameter P measuring the influence of the dipole moment over the permanent one.     

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.     

Determination of the nonlinear dielectric increment in the Cole-Davidson model

The problem of the nonlinear dielectric relaxation of complex liquids is tackled in the context of the Cole-Davidson [J. Chem. Phys. 19, 1484 (1951)] model. By using an appropriate time derivative of noninteger order, an infinite hierarchy of differential-recurrence relations for the moments (expectation values of the Legendre polynomials) is obtained. The solution is established for the stationary regime of an ensemble of polar and symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The results for the first three nonlinear harmonic components of the electric susceptibility are analytically established and illustrated with the help of Argand diagrams for the nonlinear dielectric increment and three-dimensional dispersion and absorption spectra for the second and the third harmonic components as a function of the anomalous exponent beta相似文献   

Nuclear spin relaxation of sodium cations in bacteriophage Pf1 solutions

The nuclear magnetic resonance (NMR) spectra for the I=3/2 23Na cation dissolved into filamentous bacteriophage Pf1 solutions display line splittings and relaxation times consistent with an interaction between the 23Na nuclear quadrupole moment and the electric field gradient produced by the negatively charged Pf1 particles. The 23Na NMR line splittings and relaxation rates corresponding to magnetization recovery and single, double, and triple quantum coherence decays are measured in Pf1 solutions and compared to theoretical values. The deviation of the observed dc spectral density J0 from the equal first harmonic J(omega0) and second harmonic J(2omega0) values as J(omega0)=J(2omega0) not equal to J0 in these solutions suggests that ion migration in the electric field gradient of the Pf1 particles produces an anisotropic relaxation mechanism. Correlation functions and thus spectral densities for this process are calculated from solutions to the Fokker-Planck equation for radial motion in an electric potential and used to estimate measured relaxation rates. Appropriate electric potentials are generated from the solutions to the Poisson-Boltzmann equation for a charged Pf1 particle in aqueous phase, functions that lead to theoretical estimates of NMR line splittings consistent with experimental observations.     

Advantage of Fractional Calculus Based Hybrid‐Theoretical‐Computational‐Experimental Approach for Alternating Current Voltammetry

The dynamic electrochemical behavior of electroactive species is believed to be represented better by the fractional calculus, because it can consider the history of mass‐transfers of that species near the electrode surface. The elucidation of mathematical fundamentals of fractional calculus has been recently introduced for batteries, supercapacitors and a few voltammetry studies. The working equations for faradaic fundamental and second‐harmonic (SHac) components of alternating current (ac) for ac voltammetry of an electrochemically reversible redox reaction on an electrode of macroscopic diameter have been derived here by using generalized formulae of the fractional calculus. A computation code is written in Python language with a matrix based algorithm developed based on latest, accurate, efficient and stable Grunwald‐Letnikov‐Improved fractional‐order differentiation equation. That computational code is used to find the concealed faradaic fundamental, SHac components of the total current and other double‐layer parameters of experimentally recorded voltammograms of ruthenium(III/II) redox reaction on gold‐disc electrode by a common electrochemical workstation without having inbuilt Fourier transformation features. The amplitude of the computed faradaic current concealed in the experimental data gets enhanced through this hybrid theoretical‐computational‐experimental approach and thus it keeps scope of application and further improvement in electroanalysis.     

Surface enhanced second harmonic generation from macrocycle, catenane, and rotaxane thin films: experiments and theory

Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

The electric birefringence of polyelectrolytes: an electrokinetic approach

We discuss the Kerr constant of a polyelectrolyte solution in the dilute regime. We show that the birefringence induced in a suspension of nonspherical polyelectrolytes by an external electric field probes the electrokinetic properties of the suspension. This is because the Kerr constant is directly connected to the electric torque exerted on the particles, and therefore contains information on the induced dipole, similarly to the other electrokinetic techniques. The article is a guideline for the development of an electrokinetic theory of the electric birefringence of polyelectrolytes. We compare two different methods to derive the Kerr constant of the polyelectrolyte solution. The first method uses an expression for the electric torque which is obtained through electrostatics, and yields a Kerr constant which has the same frequency dependence as the anisotropy of the real part of the polarizability of the dressed particle (that is, of the particle plus surrounding ions). The second method assigns an effective value of the induced electric dipole per particle by using the theory of the dielectric enhancement, and gives a Kerr constant proportional to the anisotropy of the real part of the dielectric constant of the suspension. The two methods give a considerably different frequency dependence of the Kerr constant: we suggest that the expression obtained by the second method is more capable of correctly describing the main features of the experimental results obtained with polyelectrolytes having small shape anisotropy.     

Theory of asymmetric electrochemical stochastic diffusion

Strict analysis of electrochemical strochastic diffusion due to asymmetric Brownian motion of electric charge in an equilibrium electrochemical ac circuit containing double electric layer capacitance and noisy Faradaic resistance is carried out. Cumulant analogs (for 3rd and 5th order correlations) of the Einstein formula are obtained. It is proved that equilibrium asymmetric (nongauss) stochastic diffusion is in agreement with the central limiting theorem of the probability theory. The Hurst exponent was found in the case of the nongauss components of the process of equilibrium stochastic diffusion. Apart from electrochemistry, the performed stochastic analysis of equilibrium electrochemical nongauss diffusion is also of general theoretical interest, including its application in the stochastic theory of asymmetric anomalous transport and strict theory of fluctuations at large deviations from equilibrium.     

Acoustic second harmonic generation from rough surfaces under shear excitation in liquids

Emission of compressional acoustic waves at the second harmonic frequency (second harmonic generation, SHG) is possible from rough surfaces undergoing oscillatory shear in liquids. This nonlinear response is a consequence of the inertial term in the Navier-Stokes equation. On a corrugated surface, the streamlines of the sheared liquid are not strictly parallel to the surface, leading to variation of pressure along the streamlines and a concomitant Bernoulli pressure. Being quadratic in speed, the Bernoulli pressure contains a static term and a term at the second harmonic frequency, 2omega. Pressure fluctuations at 2omega generate compressional waves.     

Real-time time-dependent density functional theory approach for frequency-dependent nonlinear optical response in photonic molecules

We present ab initio calculations of frequency-dependent linear and nonlinear optical responses based on real-time time-dependent density functional theory for arbitrary photonic molecules. This approach is based on an extension of an approach previously implemented for a linear response using the electronic structure program SIESTA. Instead of calculating excited quantum states, which can be a bottleneck in frequency-space calculations, the response of large molecular systems to time-varying electric fields is calculated in real time. This method is based on the finite field approach generalized to the dynamic case. To speed the nonlinear calculations, our approach uses Gaussian enveloped quasimonochromatic external fields. We thereby obtain the frequency-dependent second harmonic generation beta(-2omega;omega,omega), the dc nonlinear rectification beta(0;-omega,omega), and the electro-optic effect beta(-omega;omega,0). The method is applied to nanoscale photonic nonlinear optical molecules, including p-nitroaniline and the FTC chromophore, i.e., 2-[3-Cyano-4-(2-{5-[2-(4-diethylamino-phenyl)-vinyl]-thiophen-2-yl}-vinyl)-5,5-dimethyl-5H-furan-2-ylidene]-malononitrile, and yields results in good agreement with experiment.     

Anomalous diffusion governed by a fractional diffusion equation and the electrical response of an electrolytic cell

The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and negative ions have the same mobility and that the electric potential profile across the sample satisfies the Poisson's equation. The results cover a rich variety of scenarios, including the ones connected to anomalous diffusion.     

Influence of subdiffusive motion on spin relaxation and spin effects in radical pairs

Specific features of spin relaxation and the kinetics of spin effect generation in radical pairs (RPs) undergoing subdiffusive relative motion are studied in detail. Two types of processes are analyzed: (1) spin relaxation in biradicals, resulting from anomalously slow subdiffuisive reorientation (with the correlation function P(t) approximately (wt)(-alpha), where 0 < alpha < 1) and (2) spin effect generation in subdiffusion-assisted RP recombination. Analysis is made with the use of the non-Markovian stochastic Liouville equation (SLE) derived within the continuous time random walk approach. The SLE predicts anomalous (very slow and nonexponential) spin relaxation in biradicals which results in some peculiarities of the spectrum of the system. In RP recombination, the subdiffusive relative motion shows itself in slow dependence of the reaction yield Y(r)() on reactivity and parameters of the RP spin Hamiltonian and anomalous electron spin polarization of escaped radicals. The spectrum of the reaction yield detected magnetic resonance, that is, the Y(r)() dependence on the frequency omega of microwave field, is found to be strongly non-Lorenzian with the width determined by the field strength omega(1) and very broad wings depending on alpha. Analysis shows that the majority of interesting, specific features of the observables in both systems are controlled only by the parameter alpha.     

Second harmonic generation measurements in aligned samples of liquid crystals composed of bent-core molecules

The second-order susceptibility tensor of three liquid crystals composed of banana-shaped molecules has been fully determined. The measurements were carried out in single domain samples, aligned by means of an electric field parallel to the cell surface. Special care was taken with the appropriate determination of the index mismatch between the fundamental and second harmonic waves. This was achieved by using samples of different thickness. This parameter is very important for obtaining reliable values of the second order susceptibility tensor components, and is seldom directly measured. The suitability of the experimental procedure was checked by comparing the results obtained for the reference compound P-8-O-PIMB with previously reported measurements for this material. The d_ij coefficients obtained in this work are in the range 1-4 pm V^-1 and are compared with other values obtained in previous reports.     

中心对称双酞菁铥LB膜二次谐波产生特性

利用二次谐波产生(SHG)方法研究了中心对称分子稀土夹心双酞菁铥(TmPc₂) Langmuir-Blodgett (LB)膜二阶非线性光学特性, 测量了二次谐波强度随入射基频光入射角的关系, 并对其二阶非线性产生机制进行了讨论. 实验结果表明, TmPc₂分子LB膜具有较好的二次谐波信号, 二次谐波信号强度的最大值在基频光入射角为45°的地方, 其二阶非线性极化率χ⁽²⁾和分子超极化率β分别为1.152×10^-8和1.905×10^-30 esu. 通过测量样品二次谐波信号的偏振特性, 并与理论分析相比较, 得出其二阶非线性起源于电四极子作用机制.     

Kerr effect in solutions of carbosilane dendrimers with terminal mesogenic groups

First results of investigations of electro-optical properties of liquid crystalline (LC) dendrimers in solution are presented. Measurements of electric birefringence (Kerr effect) and dielectric polarization of first generation carbosilane dendrimers with different ester linked terminal mesogenic groups (cholesteryl, cyanobiphenylyl and 4-methoxyphenyl benzoate) have been carried out using dilute solutions in CCl4. The results show that the dielectric polarization is proportional to the second power of the electric field in accordance with Kerr law. The Kerr constants calculated are close to those of the low molar mass analogues of the corresponding mesogenic groups. Thus the electric birefringence of the LC dendrimer solutions is mainly determined by the electro-optical properties of their terminal mesogenic groups oriented in the electric field independently of the main chain.     

Dynamic Kerr effect responses in the terahertz range

Dynamic Kerr effect measurements provide a simple realization of a nonlinear experiment. We propose a field-off experiment where an electric field of one or several sinusoidal cycles with frequency omega is applied to a sample in thermal equilibrium. Afterwards, the evolution of the polarizability is measured. If such an experiment is performed in the terahertz range it might provide valuable information about the low-frequency dynamics in disordered systems. We treat these dynamics in terms of a Brownian oscillator model and calculate the Kerr effect response. It is shown that frequency-selective behavior can be expected. In the interesting case of underdamped vibrational motion we find that the frequency dependence of the phonon damping can be determined from the experiment. Also the behavior of overdamped relaxational modes is discussed. For typical glassy materials we estimate the magnitude of all relevant quantities, which we believe will be helpful in experimental realizations.     

Electric birefringence in solutions of cellulose carbanilate as a function of molecular weight

Electro-optical, dynamo-optical and hydrodynamic properties of solutions of some fractions of cellulose carbanilate (CC) in dioxan have been investigated. In a variable electric field, strong dispersion of the Kerr effect is observed, indicating the dipole-orientational mechanism of electrical birefringence and its relaxation. A comparison of relaxation times of fractions with their molecular weights and intrinsic viscosities indicates that the mechanism responsible for the Kerr effect is the rotation of the molecule as a whole in an electric field (a kinetically rigid molecule). The dependence of relaxation time on molecular weight (M) shows that, with increase in M, the conformation of the CC molecule changes from a slightly curved rod to a rigid Gaussian coil. The same conclusion may be drawn from a study on the dependence of the equilibrium value of the Kerr constant on M. In the Gaussian range (high M), the Kerr effect depends on the longitudinal (with respect to the chain) component of the dipole moment formed by the CO bonds in the glucoside ring. At low M, the transverse components of the monomer dipoles begin to play an important part in birefringence.     

Nonlinear Optical Response of a Polymer Electret with Incorporated Organic Chromophores

An analytical approach aimed at modeling the nonlinear optical (NLO) response of a polymer electret with incorporated organic dipole chromophores is extended to the dynamic case. The approach allows the effect of the locally anisotropic, polarizable, deformable polymer matrix on the chromophore NLO response to be accounted for. The method exploits the original cavity ansatz according to which the virtual cavity occupied by the chromophore in the polymer matrix is chosen to be conformal to the characteristic ellipsoid of the generalized permittivity tensor. Analytical expressions for the dynamic electric moments of dipole chromophores and macroscopic polarization of a polymer electret at fundamental and second harmonic frequencies are obtained by using a computational scheme based on two self‐consistency procedures. On the basis of the expressions for dynamic macroscopic polarization, the analytical formulas for linear, ${\chi _j^{i(1)} (\omega )}$ , and quadratic, ${\chi _{jk}^{i(2)} (2\omega )}$ , electric susceptibilities are obtained. The presented expressions establish the relationship between the molecular polarizabilities of chromophores and the macroscopic electrical properties of the polymer electret.