Polarizable Particles Research Articles

A phenomenological model for chains and bands in dipolar suspensions

We introduce a phenomenological model for the dipolar interaction of polarizable particles under an external field, where the relative radial and rotational components of a particle pair interaction can be tuned. We show that the relative strengths of these two components govern the microstructure and dynamics of a suspension of such particles. Notably, dominant radial interactions give rise to the formation of zigzag band patterns, which were previously only thought to occur in systems where hydrodynamic interactions dominate. Through this phenomenological model, we show that dipolar interactions can be used to access an array of patterns in suspensions of polarizable particles, from chains to bands, which would dramatically affect suspension shear rheology, for instance.

Scalar QED Model for Polarizable Particles in Thermal Equilibrium or in Hyperbolic Motion in Vacuum

We consider a scalar QED (quantum electrodynamics) model for the frictional force and the momentum fluctuations of a polarizable particle in thermal equilibrium with radiation or in hyperbolic motion in a vacuum. In the former case the loss of particle kinetic energy due to the frictional force is compensated by the increase in kinetic energy associated with the momentum diffusion, resulting in the Planck distribution when it is assumed that the average kinetic energy satisfies the equipartition theorem. For hyperbolic motion in vacuum the frictional force and the momentum diffusion are similarly consistent with an equilibrium with a Planckian distribution at the temperature T=ℏa/2πkBc. The quantum fluctuations of the momentum imply that it is only the average acceleration a that is constant when the particle is subject to a constant applied force.

Surface Scattering Expansion of the Casimir–Polder Interaction for Magneto-Dielectric Bodies: Convergence Properties for Insulators, Conductors, and Semiconductors

Fluctuation-induced forces are a hallmark of the interplay between fluctuations and geometry. We recently proved the existence of a multi-parametric family of exact representations of Casimir and Casimir–Polder interactions between bodies of arbitrary shape and material composition, admitting a multiple scattering expansion (MSE) as a sequence of inter-body and intra-body multiple wave scatterings. The approach requires no knowledge of the scattering amplitude (T-matrix) of the bodies. In this paper, we investigate the convergence properties of the MSE for the Casimir–Polder interaction of a polarizable particle with a macroscopic body. We consider representative materials from different classes, such as insulators, conductors, and semiconductors. Using a sphere and a cylinder as benchmarks, we demonstrate that the MSE can be used to efficiently and accurately compute the Casimir–Polder interaction for bodies with smooth surfaces.

Optimal positioning and distribution of magnetorheological damper

During seismic events, devices are used to disperse energy in buildings, reducing structural damage and preventing collapse. One such device is the magnetically polarizable particle damper, consisting of a hydraulic cylinder filled with magnetically responsive particles in fluid. Recent research optimized damper placement and distribution using detailed mathematical modeling and mode shapes covering over 95% of the building's mass. Researchers identified critical damper positions by correlating these models with maximum force functions in the equations of motion. The study proposed a positioning strategy to reduce costs associated with damper installation in typical building practices. The number of dampers required varied with applied loads: 20kN, 30kN, 90kN, and up to 200kN. For instance, under 20kN and 30kN loads, optimal distribution included assigning 8 dampers to the ground, first, second floors, decreasing to 4 on floors three and four, and 2 on the fifth floor, totaling 14 and 20 dampers, respectively. Optimization values for these loads were calculated at 17.71. Dealing with a 90kN load required 44 dampers, distributed as 8 on lower levels, 4 on the third floor, and 8 each on floors four and five. Remarkably, while 20kN and 30kN damper counts reduced, 24 were added for 90kN, yielding an optimization score of 45.84. For a 200kN load, 17 dampers were strategically allocated, with specific placements adjusted per floor, achieving an efficiency score of 49.616. This underscores the effectiveness of the chosen damper arrangement in bolstering structural resilience against seismic forces.

Semi-continuous dielectrophoretic separation at high throughput using printed circuit boards

Particle separation is an essential part of many processes. One mechanism to separate particles according to size, shape, or material properties is dielectrophoresis (DEP). DEP arises when a polarizable particle is immersed in an inhomogeneous electric field. DEP can attract microparticles toward the local field maxima or repulse them from these locations. In biotechnology and microfluidic devices, this is a well-described and established method to separate (bio-)particles. Increasing the throughput of DEP separators while maintaining their selectivity is a field of current research. In this study, we investigate two approaches to increase the overall throughput of an electrode-based DEP separator that uses selective trapping of particles. We studied how particle concentration affects the separation process by using two differently-sized graphite particles. We showed that concentrations up to 800 mg/L can be processed without decreasing the collection rate depending on the particle size. As a second approach to increase the throughput, parallelization in combination with two four-way valves, relays, and stepper motors was presented and successfully tested to continuously separate conducting from non-conducting particles. By demonstrating possible concentrations and enabling a semi-continuous process, this study brings the low-cost DEP setup based on printed circuit boards one step closer to real-world applications. The principle for semi-continuous processing is also applicable for other DEP devices that use trapping DEP.

Electromagnetic Casimir–Polder Interaction for a Conducting Cone

Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals.

Recent Developments in the Methods and Applications of Electrostatic Theory.

ConspectusThe review improves our understanding of how electrostatic interactions in the electrolyte, gas phase, and on surfaces can drive the fragmentation and assembly of particles. This is achieved through the overview of our advanced theoretical and computational modeling toolbox suitable for interpretation of experimental observations and discovery of novel, tunable assemblies and architectures. In the past decade, we have produced a significant, fundamental body of work on the development of comprehensive theories based on a rigorous mathematical foundation. These solutions are capable of accurate predictions of electrostatic interactions between dielectric particles of arbitrary size, anisotropy, composition, and charge, interacting in solvents, ionized medium, and on surfaces. We have applied the developed electrostatic approaches to describe physical and chemical phenomena in dusty plasma and planetary environments, in Coulomb fission and electrospray ionization processes, and in soft matter, including a counterintuitive but widespread attraction between like-charged particles.Despite its long history, the search for accurate methods to provide a deeper understanding of electrostatic interactions remains a subject of significant interest, as manifested by a constant stream of theoretical and experimental publications. While major international effort in this area has focused predominantly on the computational modeling of biocatalytic and biochemical performance, we have expanded the boundaries of accuracy, generality, and applicability of underlying theories. Simple solvation models, often used in calculating the electrostatic component of molecular solvation energy and polarization effects of solvent, rarely go beyond the induced dipole approximation because of computational costs. These approximations are generally adequate at larger separation distances; however, as particles approach the touching point, more advanced charged-induced multipolar descriptions of the electrostatic interactions are required to describe accurately a collective behavior of polarizable neutral and charged particles. At short separations, the electrostatic forces involving polarizable dielectric and conducting particles become nonadditive which necessitates further developments of quantitatively accurate many-body approaches. In applications, the electrostatic response of materials is commonly controlled by externally applied electric fields, an additional complex many-body problem that we have addressed most recently, both theoretically and numerically.This review reports on the most significant results and conclusions underpinning these recent advances in electrostatic theory and its applications. We first discuss the limitations of classical approaches to interpreting electrostatic phenomena in electrolytes and complex plasmas, leading to an extended analytical theory suitable for accurate estimation of the electrostatic forces in a dilute solution of a strong electrolyte. We then introduce the concept and numerical realization of many-body electrostatic theory focusing on its performance in selected experimental cases. These experiments underpin, among other applications, electrostatic self-assembly of two-dimensional lattice structures, melting of ionic colloidal crystals in an external electric field, and coalescence of charged clusters.

On the radiative and multiple reflection corrections of the van der Waals force between two particles/atoms: dipolar contribution

We present a theoretical formalism based on fluctuational electrodynamics and the Maxwell-stress tensor for describing the impact of radiative and multiple reflections corrections on the van der Waals force between two nanoscale spherical particles and a pair of atoms in the dipolar approximation. Particularly, we examine the van der Waals forces for two metallic particles whose dielectric constant is represented by the Drude model, for two dielectric particles in which their material response has phononic resonances, and for two atoms with dynamic polarizabilities containing a single resonant frequency. For the metallic particles, in relation to the case in which the aforementioned effects are omitted, the van der Waals force is unchanged by the radiative corrections of the polarizabilities, whereas the mechanism of multiple reflections perturbs force about a few percentage points when the spheres nearly touch each other. In contrast to the the metallic case, the radiative corrections of the polarizabilities of the dielectric particles modify peculiarly the van der Waals force in comparison to the case where such corrections are neglected; there is a critical interparticle separation that divides two regimes: when the interparticle separation is smaller (larger) than this critical distance the force with radiative corrections is smaller (greater) than that without these corrections. Moreover, the van der Waals force is practically unchanged when effect of multiple reflections is taken into account. For the atomic case, the deviation of the van der Waals force due to multiple reflections is about a few percentage points when the interatomic separation corresponds to twice the van der Waals radius, and this deviation can reach about seventeen percent at a separation of 2.5 times the atomic radius. This work might have implications concerning the fine-tuning between theoretical and experimental outcomes of the van der Waals forces.

Quantum friction in the presence of a perfectly conducting plate

A neutral but polarizable particle at rest near a perfectly conducting plate feels a force normal to the surface of the plate, which tends to pull the particle towards the plate. This is the well-known Casimir-Polder force, which has long been theoretically proposed and experimentally observed. In this paper, we explore the transverse frictional force on an atom moving uniformly parallel to a perfectly conducting plate. Although many theoretical predictions can be found for the quantum friction on a particle moving above an imperfect surface, the extreme situation with a perfectly conducting plate seems to have been largely unaddressed by the theoretical community. We investigate this ideal case as a natural extension of our previous work on quantum vacuum friction, and conclude that there does exist a quantum frictional force on an atom moving above a perfectly conducting plate, which we will abbreviate by PCQF. Like quantum vacuum friction, PCQF arises from the interaction between the particle and the surrounding blackbody radiation. But, the behavior of PCQF differs from the quantum vacuum friction in that the vacuum fields are modified by the perfectly conducting plate. Very interestingly, the distance dependence, the temperature dependence, and even the sign of the frictional force can depend on the polarization state of the atom. For an isotropic atom with a static polarizability, the resultant frictional force is found to be negative definite and therefore remains a true drag. Just above the surface of the plate, the magnitude of the frictional force is twice that of the quantum vacuum friction in the absence of the plate.

Epsilon-near-zero (ENZ)-based optomechanics

Optomechanics deals with the control and applications of mechanical effects of light that stems from the redistribution of photon momenta in light scattering. As an example, light-induced levitation of an infinitesimally small dipolar particle is expected in front of epsilon-near-zero (ENZ) metamaterials. However, a theoretical understanding of these effects on single-material and multi-material larger particles is still lacking. Here, we investigate, analytically and numerically, optical forces on polarizable particles with size ranging from 20 nm to a 1 μm in proximity of ENZ metamaterials. We look at the general features of the repulsive-attractive optomechanics from the nano to the microscale exploiting different theoretical methods (dipole approximation, finite elements calculations, transition (T-)matrix). We discuss the role of realistic layered materials, as our ENZ substrate, on optical forces and analyze the influence of composition and shape by studying a range of complex particles (dielectric, core-shell, plasmonic ellipsoids). Physical insights into the results are discussed and future research directions are forecasted. Our results provide possibilities in exploiting engineered materials and surfaces for the manipulation and tailoring of light-induced forces in optomechanics.

Sign inversion in the lateral van der Waals force between an anisotropic particle and a plane with a hemispherical protuberance: an exact calculation

We investigate the lateral van der Waals (vdW) force between an anisotropic polarizable particle and a perfectly conducting plane with a hemispherical protuberance with radius R. We predict, via an exact calculation, a sign inversion in the lateral vdW force, in the sense that, instead of pointing to the protuberance, in certain situations this force points to the opposite direction. In the literature, predictions of sign inversions in the lateral vdW force were based on perturbative solutions, valid when the height of the protuberance is very small when compared to the distance z 0 between the particle and the plane. Here, taking into account exact formulas, we investigate how such nontrivial geometric effect depends on the ratio , and how the particle orientation and anisotropy affect this sign inversion.

Mechanisms of like-charge attraction in three-body systems

The physics of like-charge attraction in three-body systems has been investigated via a polarizable-ion model. It was found that like-charge attraction is possible for two configurations of a collinear binary system with regular interparticle spacings. For the mirror-symmetric configuration ABA, the dominant mechanism of like-charge attraction between the type-B particle and each type-A particle is the polarization of each type-A particle by the type-B particle. For the mirror-asymmetric configuration AAB, the dominant mechanism of like-charge attraction between the type-B particle and the pair of type-A particles is either the polarization of the pair of type-A particles by the type-B particle, or vice versa. For either configuration, the occurrence of like-charge attraction is conditional upon the presence of dissimilarities in net charge or polarizable volume between the two types of particles, as in the case of a two-particle system. The findings point to a new direction for manipulating interactions of polarizable particles at the micro- or nano-scale.

Kinetics of isotropic to string-like phase switching in electrorheological fluids of nanocubes.

Applying an electric field to polarizable colloidal particles, whose permittivity differs from that of the dispersing medium, generates induced dipoles that promote the formation of string-like clusters and ultimately alter the fluid mechanical and rheological properties. Complex systems of this kind, whose electric-field-induced rheology can be manipulated between that of viscous and elastic materials, are referred to as electrorheological fluids. By using dynamic Monte Carlo simulations, we investigate the dynamics of self-assembly of dielectric nanocubes upon application of an electric field. Switching the field on induces in-particle dipoles and, at sufficiently large field intensity, leads to string-like clusters of variable length across a spectrum of volume fractions. The kinetics of switching from the isotropic to the string-like state suggests the existence of two mechanisms, the first related to the nucleation of chains and the second to the competition between further merging and separation. We characterize the transient unsteady state by following the chain length distribution and analyzing the probability of the transition of nanocubes from one chain to another over time. Additionally, we employ passive microrheology to gain insight into the effect of the electric field on the viscoelastic response of our model fluid. Not only do we observe that it becomes more viscoelastic in the presence of the field but also that its viscoelasticity assumes an anisotropic signature, with both viscous and elastic moduli in planes perpendicular to the external field being larger than those along it.

Multimodal antireflective coatings for perfecting anomalous reflection from arbitrary periodic structures

Metasurfaces possess vast wave-manipulation capabilities, including reflection and refraction of a plane wave into non-standard directions. This requires meticulously-designed sub-wavelength meta-atoms in each period of the metasurface which guarantee unitary coupling to the desired Floquet-Bloch mode or, equivalently, suppression of the coupling to other modes. Herein, we propose an entirely different scheme to achieve such suppression, alleviating the need to devise and realize such dense scrupulously-engineered polarizable particles. Extending the concept of anti-reflective coatings to enable simultaneous manipulation of multiple modes, we show theoretically and experimentally that a simple superstrate consisting of only several uniform dielectric layers can be modularly applied to \textit{aribtrary} periodic structures to yield perfect anomalous reflection. This multimodal anti-reflective coating (MARC), designed based on an analytical model, presents a conceptually and practically simpler paradigm for wave-control across a wide range of physical branches, from electromagnetics and acoustics to seismics and beyond.

Dipoles in blackbody radiation: momentum fluctuations, decoherence, and drag force

An expression is derived for the momentum diffusion constant due to photon scattering of a small polarizable particle in blackbody radiation, and is shown to be related to the long-wavelength collisional decoherence rate for such a particle in a thermal environment. We show how this diffusion constant appears in the steady-state photon emission rate of two dipoles induced by blackbody radiation. We consider in addition the Einstein–Hopf drag force on a small polarizable particle moving in a blackbody field, and derive its relativistic form from the Lorentz transformation of forces. We obtain an expression for the rate of change of the field energy density associated with changes in the particles’ kinetic energies and relate it to the Kompaneets equation for the case of Compton scattering by thermalized electrons.

Two bridge-particle-mediated RET between chiral molecules.

The problem of resonance energy transfer between a pair of chiral molecules mediated by two electrically polarizable bridging particles is solved using molecular quantum electrodynamics theory. In this framework, a single virtual photon propagates between any two-coupled entities and is responsible for the conveyance of excitation energy from the emitter to the absorber. Electric dipole and quadrupole, and magnetic dipole couplings linear in the Maxwell fields are employed for donor and acceptor, while each mediator scatters two virtual photons and responds quadratically to the electric displacement field via its electric dipole polarizability. This enables fourth-order diagrammatic perturbation theory to be used to compute the probability amplitude for the process. Individual multipole moment contributions to the Fermi golden rule rate are then extracted for oriented and isotropic systems. Discriminatory transfer rates arise when either the donor or the acceptor are electric-magnetic dipole and the other has a pure multipole moment, or when both are chiral, with mixed electric dipole-quadrupole contributions vanishing in the fluid phase. The bridge-mediated transfer rate is found to be a maximum for a collinear geometry. Moreover, a multi-level model of the mediator is necessary for energy migration. Asymptotically limiting rates for arbitrary and collinear geometries are also obtained for one center purely electric dipolar and the other purely quadrupolar, or both donor and absorber purely quadrupolar. Understanding is gained of radiationless and radiative transfer mechanisms between chiral moieties in a dielectric medium.

Dielectrophoresis-Based Universal Membrane Antifouling Strategy toward Colloidal Foulants

Membrane fouling compromises the benefits of membrane technology, leading to its performance deterioration and incremental cost. Coupling with an electric field has been attractive but is limited by the electrical dependence of the electrophoresis (EP) mechanism and undesired faradic reactions. This study reports a universal dielectrophoresis-based (DEP) membrane antifouling strategy for electronegative, electropositive, and neutral colloidal foulants, which depends on the particle polarizability rather than its charge. The porous Ni@PVDF model electroconductive membrane was fabricated to construct a nonuniform electric field inducing DEP, while applying a low voltage avoided side electrochemical reactions. For electronegative SiO2(-) and electropositive Al2O3(+) particles with a lower relative permittivity than the medium water (78), the membrane permeability all remarkably increased by 90.1% under AC/DC (±1.0 V) fields. By contrast, serious membrane fouling occurred for the BaTiO3 colloids with a higher relative permittivity (∼2000). Notably, the permittivity of nearly all colloids in wastewater treatment is much less than that of water, which makes the dielectrophoresis-based antifouling strategy universal. The theoretical simulation systematically analyzed the forces on particles including DEP, EP, and others, indicating that the formed protected area on the membrane pore wall by DEP forces prevented the irreversible membrane blockage of colloids and facilitated loose cake layer formation for alleviating membrane fouling. In brief, this work reported a hopeful concept for dielectrophoresis-based membrane antifouling and verified its antifouling mechanism.

Signal-Based Methods in Dielectrophoresis for Cell and Particle Separation.

Separation and detection of cells and particles in a suspension are essential for various applications, including biomedical investigations and clinical diagnostics. Microfluidics realizes the miniaturization of analytical devices by controlling the motion of a small volume of fluids in microchannels and microchambers. Accordingly, microfluidic devices have been widely used in particle/cell manipulation processes. Different microfluidic methods for particle separation include dielectrophoretic, magnetic, optical, acoustic, hydrodynamic, and chemical techniques. Dielectrophoresis (DEP) is a method for manipulating polarizable particles’ trajectories in non-uniform electric fields using unique dielectric characteristics. It provides several advantages for dealing with neutral bioparticles owing to its sensitivity, selectivity, and noninvasive nature. This review provides a detailed study on the signal-based DEP methods that use the applied signal parameters, including frequency, amplitude, phase, and shape for cell/particle separation and manipulation. Rather than employing complex channels or time-consuming fabrication procedures, these methods realize sorting and detecting the cells/particles by modifying the signal parameters while using a relatively simple device. In addition, these methods can significantly impact clinical diagnostics by making low-cost and rapid separation possible. We conclude the review by discussing the technical and biological challenges of DEP techniques and providing future perspectives in this field.

The effect of inter-particle hydrodynamic and magnetic interactions in a magnetorheological fluid

A magnetorheological fluid, which consists of magnetic particles suspended in a viscous fluid, flows freely with well-dispersed particles in the absence of a magnetic field, but particle aggregation results in flow cessation when a field is applied. The mechanism of dynamical arrest is examined by analysing interactions between magnetic particles in a magnetic field subject to a shear flow. An isolated spherical magnetic particle undergoes a transition between a rotating state at low magnetic field and a static orientation at high magnetic field. The effect of interactions for spherical dipolar and polarisable particles with static orientation is examined for an unbounded dilute viscous suspension. There are magnetic interactions due to the magnetic field disturbance at one particle caused by the dipole moment of another, hydrodynamic interactions due to the antisymmetric force moment of a non-rotating particle in a shear flow, and a modification of the magnetic field due to the particle magnetic moment density. When there is a concentration variation, the torque balance condition results in a disturbance to the orientation of the particle magnetic moment. The net force and the drift velocity due to these disturbances is calculated, and the collective motion generated is equivalent to an anisotropic diffusion process. When the magnetic field is in the flow plane, the diffusion coefficients in the two directions perpendicular to the field direction are negative, implying that concentration fluctuations are unstable in these directions. This instability could initiate field-induced dynamical arrest in a magnetorheological fluid.

Determination of the average electro-thermophoretic force acting on a system of polarizable particles in an inhomogeneously heated fluid

The average force acting on the system of polarizing particles from the electric field in a non-uniformly heated dielectric liquid is determined. The case of pair interactions in the system is examined. To find the force acting on the particles, the interaction of two particles in a liquid is modelled in the presence of a given temperature gradient and the electric field strength far from the particles. The dependence of the particle permittivity on temperature is taken into account. The resulting expression for the force acting on two particles has such a power-law dependence on the distance between the particles, that allows to carry out the direct averaging procedure for a system of particles located in an infinite volume of liquid. When determining the average force, the probability density function of a continuous random variable is used, and the vector connecting the centers of particles plays the role of this variable. The differential equation for finding the probability density function is derived from two conditions. First, the pairs of particles are preserved in the space of all their possible configurations. Second, each pair of particles moves like a point with a speed equal to the speed of their relative motion. The resulting equation in the case under consideration has a set of solutions. Basing on the physical analysis of the problem, the choice of the probability density function is proposed, which allows one to determine the average electro-thermophoretic force acting in such a system with an accuracy up to the second degree of the volume concentration of particles.