Electric Polarizability Tensor Research Articles

Lower Bounds to the Q Factor of Electrically Small Resonators Through Quasistatic Modal Expansion

The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of devices including antennas, metamaterials, and nanoresonators, and have been featured in seminal papers in the past decades. Here, we determine the lower bounds of Q factors of small-size plasmonic and high-permittivity dielectric resonators, which are characterized by quasi-electrostatic and quasi-magnetostatic natural modes, respectively. We expand the induced current density field in the resonator in terms of these modes, leading to closed-form analytical expressions for the electric and magnetic polarizability tensors, whose largest eigenvalue is directly linked to the minimum Q factor. Our results allow also to determine in closed form the corresponding optimal current density field. In particular, when the resonator exhibits two orthogonal reflection symmetries the minimum Q factor can be simply obtained from the Q factors of the single current modes with non-vanishing dipole moments aligned along the major axis of the resonator. Overall, our results open exciting opportunities in the context of nano-optics and metamaterials, facilitating the analysis and design of optimally shaped resonators for enhanced and tailored light-matter interactions.

An ON-OFF Magneto-Optical Probe of Anisotropic Biofluid Crystals: A β-Hematin Case Study.

We have designed, developed and evaluated an innovative portable magneto-optical detector (MOD) in which a light beam with variable polarization passes through a fluid sample immersed in a variable magnetic field. The light intensity is measured downstream along the forward scattering direction. The field is turned on and off through the in-and-out motion of nearby permanent magnets. As a result, for sufficiently magnetically and optically anisotropic samples, the optical absorption is sensitive to changes in the light polarization. Both detection and characterization applications are therefore available. For instance, both the degree of malaria infection can be measured and hemozoin crystalline properties can be studied. We present experimental results for synthetic hemozoin, and describe them in terms of the basic physics and chemistry underlying the correlations of the directions of the external magnetic field and the light beam polarization. We connect this work to a commercialized product for malaria detection and compare it to other magneto-optical instruments and methods. We conduct tests of absorption parameters, the electric polarizability tensor, and we discuss the connection to magnetic and electric dipole moments.

Universal interrelation between measures of particle and polymer size.

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration Rg, hydrodynamic radius Rh, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor αE and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between αE, C, and Rg for nanoparticles and polymers of general shape and the corresponding properties η, Rh, and Rg using a hydrodynamic-electrostatic property interrelation.

ZENO: Software for calculating hydrodynamic, electrical, and shape properties of polymer and particle suspensions

The ZENO software tool computes material, solution,and suspension properties for a specified particle shape or molecular structure using path-integral and Monte Carlo methods. These properties include: capacitance, electric polarizability tensor, intrinsic conductivity, volume, gyrationtensor, hydrodynamic radius, intrinsic viscosity, friction coefficient, diffusion coefficient, sedimentation coefficient, and related quantities.

Detecting Chirality in Molecules by Linearly Polarized Laser Fields.

A new scheme for enantiomer differentiation of chiral molecules using a pair of linearly polarized intense ultrashort laser pulses with skewed mutual polarization is presented. The technique relies on the fact that the off-diagonal anisotropic contributions to the electric polarizability tensor for two enantiomers have different signs. Exploiting this property, we are able to excite a coherent unidirectional rotation of two enantiomers with a π phase difference in the molecular electric dipole moment. The approach is robust and suitable for relatively high temperatures of molecular samples, making it applicable for selective chiral analysis of mixtures, and to chiral molecules with low barriers between enantiomers. As an illustration, we present nanosecond laser-driven dynamics of a tetratomic nonrigid chiral molecule with short-lived chirality. The ultrafast time scale of the proposed technique is well suited to study parity violation in molecular systems in short-lived chiral states.

Flexible bent rod model with a saturating induced dipole moment to study the electric linear dichroism of DNA fragments

In the present work we make a theoretical study of the steady state electric linear dichroism of DNA fragments in aqueous solution. The here developed theoretical approach considers a flexible bent rod model with a saturating induced dipole moment. The electric polarizability tensor of bent DNA fragments is calculated considering a phenomenological model which theoretical and experimental backgroung is presented here. The model has into account the electric polarizability longitudinal and transversal to the macroion. Molecular flexibility is described using an elastic potential. We consider DNA fragments originally bent with bending fluctuations around an average bending angle. The induced dipole moment is supposed constant once the electric field strength grows up at critical value. To calculate the reduced electric linear dichroism we determine the optical factor considering the basis of the bent DNA perpendicular to the molecular axis. The orientational distribution function has into account the anisotropic electric properties and the molecule flexibility. We applied the present theoretical background to fit electric dichroism experimental data of DNA fragments reported in the bibliography in a wide range of molecular weight and electric field. From these fits, values of DNA physical properties are estimated. We compare and discuss the results here obtained with the theoretical and experimental data presented by other authors. The original contributions of this work are: the inclusion of the transversal electric polarizability saturating with the electric field, the description of the electric properties with an electric polarizability tensor dependant on the bending angle and the use of an arc model originally bent.

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry.

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient σ in the conductive and insulating particle limits, which are required to estimate σ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications.

Stored energies in electric and magnetic current densities for small antennas

Electric and magnetic currents are essential to describe electromagnetic-stored energy, and the associated antenna Q and the partial directivity to antenna Q-ratio, D / Q , for arbitrarily shaped structures. The upper bound of previous D / Q results for antennas modelled by electric currents is accurate enough to be predictive. This motivates us to develop the analysis required to determine upper and/or lower bounds for electromagnetic problems that include magnetic model currents. Here we derive new expressions for the stored energies, which are used to determine antenna Q bounds and D / Q bounds for the combination of electric and magnetic currents, in the limit of electrically small antennas. In this investigation, we show both new analytical results and we illustrate numerical realizations of them. We show that the lower bound of antenna Q is inversely proportional to the largest eigenvalue of certain combinations of the electric and magnetic polarizability tensors. These results are an extension of the electric only currents, which come as a special case. The proposed method to determine the minimum Q -value which is based on the new expressions for the stored energies, also yields a family of current-density minimizers for optimal electric and magnetic currents that can lend insight into antenna designs.

Shape characteristics of equilibrium and non-equilibrium fractal clusters

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other between the viscosity and hydrodynamic radii, as potential measures of shape anisotropy. We also find a strong correlation between anisotropy and effective fractal dimension. These observations should provide new practical methods for quantifying the nature of particle clustering in diverse contexts.

Potential for the measurement of the tensor electric and magnetic polarizabilities of the deuteron in storage-ring experiments with polarized beams

The measurement of the tensor electric and magnetic polarizabilities of the deuteron is of great interest, especially in connection with the possibilities of COSY and GSI. These polarizabilities can be measured in storage rings by the frozen spin method providing a disappearance of g – 2 precession. This method will be used in the planned deuteron electric-dipole-moment experiment in storage rings. The tensor electric polarizability of the deuteron significantly influences the buildup of the vertical polarization in the above experiment. The spin interactions depending on the electric dipole moment, the tensor electric polarizability, and main systematical errors caused by field misalignments have very different symmetries. For the considered experimental conditions, the sensitivity to the deuteron EDM of 1 × 10−29 e·cm corresponds to measuring both tensor polarizabilities with an accuracy δαT ≈ δβT ≈ 5 × 10−42 cm3. This conservative estimate can be improved by excluding the systematical error caused by the field instability which is negligible for the measurement of the tensor polarizabilities. In order to determine the tensor magnetic polarizability, the horizontal components of the polarization vector should be measured.

Influence of hydrodynamic coupling on the electric linear dichroism of DNA fragments

In the present work, we study the effect of translational-rotational hydrodynamic coupling on the stationary electric linear dichroism of DNA fragments. The theoretical resolution of the problem has, so far, been dealt with analytic methods valid only in the limit of low electric fields. In this work, we apply numerical methods that allow us to study the problem and also consider electric fields of arbitrary strength. We use the bent rod molecules model to describe DNA fragments with physical properties characterized by their electric charge, electric polarizability tensor, rotational diffusion tensor, and translation-rotation coupling diffusion tensor. The necessary orientational distribution function to calculate electric dichroism is obtained by solving the Fokker-Planck equation through the finite difference method. We analyze the different contributions due to electric polarizability and translational-rotational coupling to the electric dichroism.

Electric dichroism transients of aqueous solutions of DNA

In this work we develop a theory of reduced electric linear dichroism transients of DNAfragments in aqueous solution. The DNA fragments are modelled as rigid ‘bent-rod molecules’(BRM) with the following physical parameters: electric charge, electric polarizabilitytensors and hydrodynamical ones, and the average transition probability tensor permolecule. In order to study the growth and decay of electric dichroism transients, theorientational distribution function of the molecules is needed. This function is obtained bysolving the time-dependent Fokker–Planck equation in the presence of a low electric fieldE, using a perturbation method and the Fourier method with time-dependent coefficients. Inour calculations the origin of the coordinate system is the mass centre of the BRM. Withrespect to this centre, the electric dipole moment of the molecule is zero. The developedtheory adequately explains the experimental results. We show that the theoretical approachused in this work is equivalent to the one applied in the Brownian dynamics simulationwork performed by Porschke and co-workers. We also analyse the effect of a possibleelectric dipole moment on the transients of the reduced electric linear dichroism in DNAbent fragments.

Measurement of the tensor electric polarizability of a deuteron in storage rings

When an electric field of resonant frequency acts on a deuteron beam in a storage ring, the tensor electric polarizability stimulates buildup of the vertical polarization of the beam (the Baryshevsky effect). This effect allows high-precision measurement of the tensor electric polarizability of the deuteron, which contains important information about spin-dependent nuclear forces. The general formulas describing the Baryshevsky effect are derived. It is shown that doubling of the resonant frequency leads to dramatic enhancement of the effect.

Tensor electric polarizability of the deuteron in storage-ring experiments

The tensor electric polarizability of the deuteron gives important information about spin-dependent nuclear forces. If a resonant horizontal electric field acts on a deuteron beam circulating into a storage ring, the tensor electric polarizability stimulates the buildup of the vertical polarization of the deuteron (the Baryshevsky effect). General formulas describing this effect have been derived. Calculated formulas agree with the earlier obtained results. The problem of the influence of tensor electric polarizability on spin dynamics in such a deuteron electric-dipole-moment experiment in storage rings has been investigated. Doubling the resonant frequency used in this experiment dramatically amplifies the Baryshevsky effect and provides the opportunity to make high-precision measurements of the deuteron's tensor electric polarizability.

Electromagnetic wave scattering by many small particles

Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a "smart" material by embedding many small particles in a given region is formulated.

Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects.

The problem of calculating the electric polarizability tensor alpha(e) of objects of arbitrary shape has been reformulated in terms of path integration and implemented computationally. The method simultaneously yields the electrostatic capacity C and the equilibrium charge density. These functionals of particle shape are important in many materials science applications, including the conductivity and viscosity of filled materials and suspensions. The method has been validated through comparison with exact results (for the sphere, the circular disk, touching spheres, and tori), it has been found that 10(6) trajectories yield an accuracy of about four and three significant figures for C and alpha(e), respectively. The method is fast: For simple objects, 10(6) trajectories require about 1 min on a PC. It is also versatile: Switching from one object to another is easy. Predictions have also been made for regular polygons, polyhedra, and right circular cylinders, since these shapes are important in applications and since numerical calculations of high stated accuracy are available. Finally, the path-integration method has been applied to estimate transport properties of both linear flexible polymers (random walk chains of spheres) and lattice model dendrimer molecules. This requires probing of an ensemble of objects. For linear chains, the distribution function of C and of the trace (alpha(e)), are found to be universal in a size coordinate reduced by the chain radius of gyration. For dendrimers, these distribution functions become increasingly sharp with generation number. It has been found that C and alpha(e) provide important information about the distribution of molecular size and shape and that they are important for estimating the Stokes friction and intrinsic viscosity of macromolecules.

Dependence of DNA steady-state electric birefringence on field strength

Abstract A major task in our work has been to calculate the dependence of DNA steady-state electric birefringence on field strength for a ‘hinged bent rod’ (HBR) composed of two rod-like arms of length L with a restoring force proportional to the angle of bending at the hinge. The system is considered to have a permanent dipole moment due to asymmetric charge distribution with respect to its centre of diffusion. The electric and optical polarizability tensors of HBR macroions are also calculated. To calculate the electric birefringence, the statistical averages of the differential optical polarizability per molecule in the directions parallel and perpendicular to the applied electric field are made over all conformations as well as over all spatial orientations and all the velocities in the presence of the electric field. Using this approach, numerical calculations are carried out to achieve a fitting of electric birefringence experimental curves versus the square of the electric field for the sonicated and fractioned DNA and restriction enzyme fragments of DNA. It is shown that the HBR macroion presents a reversal of the birefringence sign at low electric fields for certain chain lengths, electric polarizability and stiffness constant values, in agreement with the experimental results obtained for DNA. It is observed that the HBR model adequately represents DNA elastic properties.

Structures and Electronic Properties of SinC5-n Clusters in Electric Fields

We obtained the structures of silicon-carbon clusters SinC5-n and Si5C5 by first-principles supercell calculations using the local density approximation and the pseudopotential plane wave method. The ground-state atomic geometries of SinC5-n agreed well with previous studies by ab initio Hartree-Fock calculations. The ground-state structure of Si5C5 is a distorted monocyclic geometry resembling a stable C10 structure. We calculated the electric polarizability tensors of SinC5-n clusters by applying a low electric field. We found an abrupt drop in the average polarizability when n increases from 2 to 3, reflecting the structural change from one to two dimensions. We manipulated Si2C3 and Si3C2 clusters theoretically with a high electric field. Linear (Si2C3) and plane (Si3C2) clusters bend in the direction of the field. Field-induced distortion is interpreted using the electronegativity of Si and C atoms. The present simulation enabled us to emphasize the electronegativity of atoms in mixed clusters as a crucial factor in controlling and designing the structures of clusters using high electric fields.

The polarizability of the deuteron

The scalar and tensor polarizabilities of the deuteron are calculated using the recently developed effective field theory that describes nucleon-nucleon interactions. Leading and next-to-leading order contributions in the perturbative expansion predict a scalar electric polarizability of α e0 = 0.595 fm 3. The tensor electric polarizability receives contributions starting at next-to-leading order from the exchange of a single potential pion and is found to be α e2 = −0.062 fm 3. We compute the leading contributions to the scalar and tensor magnetic polarizabilities, finding β m0 = 0.067 fm 3 and β m2 = 0.195 fm 3.

Static polarizabilities of single-wall carbon nanotubes.

The static electric polarizability tensor of single-wall carbon nanotubes is calculated within the random-phase approximation using a simple tight-binding model and a classical correction to include local fields. We find that the polarizability for constant fields parallel to the cylindrical axis is highly dependent on the details of the tube`s electronic structure. In contrast, the polarizability for fields perpendicular to the axis only depends on the tube radius. The relative magnitudes of these two quantities suggests that under the application of a randomly oriented electric field, nanotubes acquire dipole moments pointing mainly along their axes, with the size of the dipole inversely proportional to the square of the minimum direct band gap.