Charged Spheres Research Articles

Tailoring the optical properties of holey Si thin films

Abstract Si thin films with holes are composite materials with interesting optical properties that can be fabricated and modified by state-of-the-art Si process technologies. Adjusting the volumetric air fraction of these films allows control over their effective refractive indices. This work demonstrates a novel scalable method that combines charged sphere colloidal lithography (CSCL) and dry etching to pattern spatially disordered nanoholes in Si thin films. The method can also be adapted to dielectric materials other than silicon. We show controlled tuning of the effective refractive index by lateral dry-etching of the holes. Utilizing this process, a progressive widening of the average hole diameter was obtained, expanding from initial diameters of 60 nm and 100 nm to dimensions reaching 118 nm and 168 nm, respectively. Consequently, the refractive index of the holey films decreased to approximately 2.1 determined via ellipsometry and Bruggeman's model in the near-infrared (NIR) - mid-infrared (MIR) range, in contrast to the unstructured Si refractive index of 3.42. The systematic optical modification was also observed in the reflection spectra of the fabricated films using Fourier-transform infrared spectroscopy (FTIR). Dielectric holey thin films can be attractive for potential applications in MIR photonic devices such as filters and waveguides.

Exploring the viability of charged spheres admitting non-metricity and matter source

This research paper investigates the impact of non-metricity and matter source on the geometry of charged spheres in the presence of anisotropic matter configuration. We use a specific model of extended symmetric teleparallel theory to minimize the complexity of the field equations. Moreover, the feasible non-singular solutions are used to examine the interior composition of the charged spheres. The Darmois junction conditions are used to determine the unknown constants in the metric coefficients. We explore some significant properties in the interior of compact stars under consideration to check their viable existence in this modified framework. The equilibrium state of the charged spheres is discussed using the Tolman–Oppenheimer–Volkoff equation and stability is analyzed by sound speed and Herrera cracking approach. We find that the charged spheres in this theoretical framework are physically viable and stable.

General isotropic charged fluid spheres within the matter coupling gravity formalism

In this paper, we proposed a new mathematical model of charged isotropic compact relativistic object in the f(R,T) gravity. In the f(R,T) framework, the gravitational action involves the trace of the energy–momentum tensor T and the Ricci scalar R. We choose a specific f(R,T) framework such that f(R,T)=R+2χT, in which χ represents the coupling parameter, which is responsible for measuring the deviation from the standard Einstein’s general theory of relativity (GR). A short overview of the modified f(R,T) gravity theory is presented and the field equations are formulated in this novel modified gravity. It is shown that for a specific limit of the coupling parameter, the standard GR can be restored from the considered f(R,T) model. We modeled, mathematically, a specific charged compact star XTEJ1739−217 (M=1.51M⨀, R=10.9 km), within the f(R,T) extended gravity theory framework by taking benefit from the well studied Heintzmann IIa ansatz [H. Heintzmann, Z. Physik 228, 489–493 (1969)]. To examine the reliability and physical plausibility of Our model, different physical characteristics such as the energy density and pressure, electric field, energy conditions, stability analysis via Herrara cracking technique and the adiabatic index, equilibrium conditions under different forces, mass–radius relationship, compactness and surface red-shift are studied carefully, which are essential for confirming the model’s physical feasibility. The mathematically established results are more accurately represented by graphical illustrations for the various chosen values of the coupling parameter χ. In this study, we also compared our findings with the standard GR results and the observational facts, and we inferred that for nonzero values of the coupling parameter, χ, our results in f(R,T) framework are closely related to the observational facts in comparison with the standard GR. We conclude that our presented model is well consistent with all the requirements and viably modeled the compact star XTEJ1739−217.

On a Study of Photoionization of Atoms and Ions from Endohedral Anions

We study the relationship between the results of two qualitatively different semi-empirical models for photoionization cross sections, σnℓ, of neutral atoms (A) and their cations (A+) centrally encapsulated inside a fullerene anion, CNq, where q represents the negative excess charge on the shell. One of the semi-empirical models, broadly employed in previous studies, assumes a uniform excess negative charge distribution over the entire fullerene cage, by analogy with a charged metallic sphere. The other model, presented here, considers the quantum states of the excess electrons on the shell, determined by specific n and ℓ values of their quantum numbers. Remarkably, both models yield similar photoionization cross sections for the encapsulated species. Consequently, we find that the photoionization of the encapsulated atoms or cations inside the CNq anion is influenced only slightly by the quantum states of the excess electrons on the fullerene cage. Furthermore, we demonstrate that the influence decreases even further as the size of the fullerene cage increases. All this holds true at least under the assumption that the encapsulated atom or cation is compact, i.e., its electron density remains primarily within itself rather than being drawn into the fullerene shell. This remarkable finding results from Hartree–Fock calculations combined with a popular modeling of the fullerene shell which is simulated by an attractive spherical annular potential.

Dumbbell Impurities in 2D Crystals of Repulsive Colloidal Spheres Trap Dislocations.

Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle differences in the dumbbell length determine whether it induces a local distortion of the lattice or traps a dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes toward controlling material properties and understanding fundamental questions in phase transitions through particle-bound dislocations.

Finite Nuclear Size Effect on the Relativistic Hyperfine Splittings of 2s and 2p Excited States of Hydrogen-like Atoms

Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact knowledge is thus of prior relevance. In this work, we analytically investigate the relativistic effects on the hyperfine splittings of hydrogen-like atoms, including finite-size effects of the nucleis’ structure. We start from exact solutions of Dirac’s equation using different nuclear models, where the nucleus is approximated by (i) a point charge (Coulomb potential), (ii) a homogeneously charged full sphere, and (iii) a homogeneously charged spherical shell. Equivalent modelling has been done for the distribution of the nuclear magnetic moment. For the 1s ground state and 2s excited state of the one-electron systems H1, H2, H3, and He+3, the calculated finite-size related hyperfine shifts are quite similar for the different structure models and in excellent agreement with those estimated by comparing QED and experiment. This holds also in a simplified approach where relativistic wave functions from a Coulomb potential combined with spherical-shell distributed nuclear magnetic moments promises an improved treatment without the need for an explicit solution of Dirac’s equation within the nuclear core. Larger differences between different nuclear structure models are found in the case of the anisotropic 2p3/2 orbitals of hydrogen, rendering these excited states as promising reference systems for exploring the proton structure.

Creating High Yield Stress Particle-Laden Oil/Water Interfaces Using Charge Bidispersity.

Interfacial engineering has been increasingly used to stabilize Pickering emulsions in commercial products and biomedical applications. Pickering emulsion stabilization is aided by interfacial viscoelasticity; however, typically the primary means of stabilization are steric hindrances between high surface concentration shells of particles around the drops. In this work, the concept of creating large interfacial viscoelastic yield stresses with low particle surface concentrations (<50%) using bidisperse charged particle systems is tested to evaluate their potential efficacy in emulsion stabilization. To explore this hypothesis, interfacial rheology and visualization experiments are conducted at o/w interfaces using positively charged amidine, negatively charged carboxylate, and negatively charged sulfate-coated latex spheres and compared to a model based on interparticle forces. Bidisperse particle systems have been observed to create more networked structures than monodisperse systems. For surface concentrations of <50%, bidisperse interfaces created measurable viscoelastic moduli ∼1 order of magnitude larger than monodisperse interfaces. Furthermore, these interfaces have measurable yield stresses on the order of 10-4 Pa·m when monodisperse systems have none. Bidispersity impacts surface viscoelasticity primarily by increasing the overall magnitude of attraction between particles at the interface and not due to changes in the microstructure. The developed model predicts the relative surface fraction that creates the largest moduli and shows good agreement with the experimental data. The results demonstrate the ability to create large viscoelastic moduli for small surface fractions of particles, which may enable stabilization using fewer particles in future applications.

Torque about electrostatically charged spheres makes them more attractive.

The strength of interparticle interactions in a granular system controls how a collection of insulating particles flow, cohere and fragment. Forces due to electrostatic charging, particularly in free-fall or low gravity environments, can dominate the static and dynamic interactions with important implications for understanding natural and industrial processes. Here we show that shaking of homogeneous, spherical particles can result in a non-uniform surface charge distribution. The measured dipole moment and torque for each particle are found to be strongly correlated. However, our model shows that to predict the torque and force requires one to consider the full surface charge distribution. This overlooked torque is not only significant, but would amplify attractive interactions through particle reorientation.

Understanding the role of negative charge in the scaffold of an artificial enzyme for CO2 hydrogenation on catalysis.

We have approached the construction of an artificial enzyme by employing a robust protein scaffold, lactococcal multidrug resistance regulator, LmrR, providing a structured secondary and outer coordination spheres around a molecular rhodium complex, [RhI(PEt2NglyPEt2)2]-. Previously, we demonstrated a 2-3 fold increase in activity for one Rh-LmrR construct by introducing positive charge in the secondary coordination sphere. In this study, a series of variants was made through site-directed mutagenesis where the negative charge is located in the secondary sphere or outer coordination sphere, with additional variants made with increasingly negative charge in the outer coordination sphere while keeping a positive charge in the secondary sphere. Placing a negative charge in the secondary or outer coordination sphere demonstrates decreased activity by a factor of two compared to the wild-type Rh-LmrR. Interestingly, addition of positive charge in the secondary sphere, with the negatively charged outer coordination sphere restores activity. Vibrational and NMR spectroscopy suggest minimal changes to the electronic density at the rhodium center, regardless of inclusion of a negative or positive charge in the secondary sphere, suggesting another mechanism is impacting catalytic activity, explored in the discussion.

Evolution of charged anisotropic spheres in Gauss–Bonnet gravity

Evolution of charged anisotropic spheres in Gauss–Bonnet gravity

Anisotropic generalization of charged isotropic spheres with double equation of state

We propose a technique to generate a new class of solutions for an anisotropic charged matter distribution. We show its viability as a model to describe an ultra-compact static spherically symmetric star where anisotropy may be a dominant factor. The solution extends some previously reported stellar solutions with or without charge or anisotropy. The interior matter distribution satisfies a double equation of state with two parameters. The parameters affect the gravitational behaviour of the model and the physical features, such as stability.

Two Methods Based on Integral Equation Approaches in Analyzing Polyelectrolyte Solutions: Macrophase Separation.

To understand the phase behaviors of polyelectrolyte solutions, we provide two analytical methods to formulate a molecular equation of state for a system of fully charged polyanions (PAs) and polycations (PCs) in a monomeric neutral component, based on integral equation theories. The mixture is treated in a primitive and restricted manner. The first method utilizes Blum's approach to charged hard spheres, incorporating the chain connectivity contribution by charged spheres via Stell's cavity function method. The second method employs Wertheim's multi-density Ornstein-Zernike treatment of charged hard spheres with Baxter's adhesive potential. The pressures derived from these methods are compared to available molecular dynamics simulations data for a solution of PAs and monomeric counterions as a limiting case. Two-phase equilibrium for the system is calculated using both methods to evaluate the relative strength of phase segregation that leads to complex coacervation. Additionally, the scaling exponents for a selected solution near its critical point are examined.

Surface Tension of Simple Molten Salts: Insight from a Charged Hard Sphere Model.

Surface tension of molten salts is rooted in many important phenomena in physical chemistry. We develop an analytical theory for the surface tension of molten salts, where the molten salt is described by a restricted primitive model electrolyte consisting of charged hard spheres, and surface tension is related to the formation of a cavity in the electrolyte. The integral equation theory is applied to the restricted primitive model electrolyte to derive an analytical formula of the cavity formation energy. The scaling relation of the cavity formation energy is further combined with morphological thermodynamics theory to determine the formula for surface tension. According to our formula, surface tension consists of a positive hard sphere contribution and a negative electrostatic contribution. Using the molar mass, interionic distance, density, and temperature as the input, our theory leads to a good prediction of surface tension of more than 16 molten salts at their melting point without introducing any adjustable parameters.

Calculation of liquidus in eutectic alkali halide mixtures using thermodynamic perturbation theory

A statistical-thermodynamic model that makes it possible to describe with good accuracy phase equilibria between melt and crystal in binary alkali halide mixtures with common cations and anions is proposed. This model is based on the thermodynamic perturbation theory, which takes into account the charge-dipole contribution to the interionic interaction of binary molten salts using a multicomponent mixture of charged hard spheres as a reference system. Specific expressions for chemical potentials, taking into account the charge-induced dipole interaction in the molten phase, are presented within the developed approach. Considering binary eutectic mixtures NaF–NaCl, CsF–CsCl, NaF–CsF, and NaCl–CsCl as an example, the liquidus curves obtained in two series of calculations are shown: with the equation of state and without it. The discrepancies between the calculated and experimental data on the position of eutectic equilibrium for most of the considered mixtures do not exceed about 10 percent on the temperature scale and 5 percent on the composition when using only the tabulated values of ionic radii and polarizabilities without any adjustment.

Scattering of a Bessel Pincer Light-Sheet Beam on a Charged Particle at Arbitrary Size.

Electromagnetic scattering is a routine tool for rapid, non-contact characterization of particle media. In previous work, the interaction targets of scattering intensity, scattering efficiency, and extinction efficiency of Bessel pincer light-sheet beams were all aimed at dielectric spheres. However, most particles in nature are charged. Considering the boundary condition on a charged sphere, the beam shape coefficients (BSCs) (pmn,qmn) of the charged spherical particle illuminated by a Bessel pincer light-sheet beam are obtained. The extinction, scattering, and absorption efficiencies are derived under the generalized Lorenz-Mie theory (GLMT) framework. This study reveals the significant differences in scattering characteristics of Bessel pincer light-sheet beams on a charged particle compared to traditional beams. The simulations show a few apparent differences in the far-field scattering intensity and efficiencies between charged and natural spheres under the influence of dimensionless size parameters. As dimensionless parameters increase, the difference between the charged and neutral spheres decreases. The effects of refractive index and beam parameters on scattering, extinction, and absorption coefficients are different but tend to converge with increasing dimensionless parameters. When applied to charged spheres with different refractive indices, the scattering, extinction, and absorption efficiencies of Bessel pincer light-sheet beams change with variations in surface charge. However, once the surface charge reaches saturation, these efficiencies become stable. This study is significant for understanding optical manipulation and super-resolution imaging in single-molecule microbiology.

Sedimentation of a Charged Soft Sphere within a Charged Spherical Cavity.

The sedimentation of a soft particle composed of an uncharged hard sphere core and a charged porous surface layer inside a concentric charged spherical cavity full of a symmetric electrolyte solution is analyzed in a quasi-steady state. By using a regular perturbation method with small fixed charge densities of the soft sphere and cavity wall, a set of linearized electrokinetic equations relevant to the fluid velocity field, electrical potential profile, and ionic electrochemical potential energy distributions are solved. A closed-form formula for the sedimentation velocity of the soft sphere is obtained as a function of the ratios of core-to-particle radii, particle-to-cavity radii, particle radius-to-Debye screening length, and particle radius-to-porous layer permeation length. The existence of the surface charge on the cavity wall increases the settling velocity of the charged soft sphere, principally because of the electroosmotic enhancement of fluid recirculation within the cavity induced by the sedimentation potential gradient. When the porous layer space charge and cavity wall surface charge have the same sign, the particle velocity is generally enhanced by the presence of the cavity. When these fixed charges have opposite signs, the particle velocity will be enhanced/reduced by the presence of the cavity if the wall surface charge density is sufficiently large/small relative to the porous layer space charge density in magnitude. The effect of the wall surface charge on the sedimentation of the soft sphere increases with decreases in the ratios of core-to-particle radii, particle-to-cavity radii, and particle radius-to-porous layer permeation length but is not a monotonic function of the ratio of particle radius-to-Debye length.

Diffusiophoresis of a Charged Soft Sphere in a Charged Spherical Cavity

The quasi-steady diffusiophoresis of a soft particle composed of an uncharged hard sphere core and a uniformly charged porous surface layer in a concentric charged spherical cavity full of a symmetric electrolyte solution with a concentration gradient is analyzed. By using a regular perturbation method with small fixed charge densities of the soft particle and cavity wall, the linearized electrokinetic equations relevant to the fluid velocity field, electric potential profile, and ionic concentration distributions are solved. A closed-form formula for the diffusiophoretic (electrophoretic and chemiphoretic) velocity of the soft particle is obtained as a function of the ratios of the core-to-particle radii, particle-to-cavity radii, particle radius to the Debye screening length, and particle radius to the permeation length in the porous layer. In typical cases, the confining charged cavity wall significantly influences the diffusiophoresis of the soft particle. The fluid flow caused by the diffusioosmosis (electroosmosis and chemiosmosis) along the cavity wall can considerably change the diffusiophoretic velocity of the particle and even reverse its direction. In general, the diffusiophoretic velocity decreases with increasing core-to-particle radius ratios, particle-to-cavity radius ratios, and the ratio of the particle radius to the permeation length in the porous layer, but increases with increasing ratios of the particle radius to the Debye length.

Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects

AbstractWe summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non‐additive contact distances, including frequency‐dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six‐component seawater model.

Supramolecular trapping of a cationic all-metal σ-aromatic {Bi4} ring

Aromaticity in organic molecules is well defined, but its role in metal-only rings remains controversial. Here we introduce a supramolecular stabilization approach of a cationic {Bi4} rhomboid within the symmetric charge sphere of two bowl-shaped dianionic calix[4]pyrrolato indinates. Crystallographic and spectroscopic characterization, quantum chemical analysis and magnetically induced ring currents indicate σ-aromaticity in the formally tetracationic 16-valence electron [Bi4]4+ ring. Computational screening for other p-block elements identifies the planar rhomboid as the globally preferred structure for 16-valence electron four-atomic clusters. The aromatic [Bi4]4+ is isoelectronic to the [Al4]4−, a motif previously observed as antiaromatic in Li3[Al4]− in the gas phase. Thus, subtle factors such as charge isotropy seem to decide over aromaticity or antiaromaticity, advising for caution in debates based on the Hückel model—a concept valid for second-row elements but less deterministic for the heavier congeners.

Sequestration of Pb(II) using channel-like porous spheres of carboxylated graphene oxide-incorporated cellulose acetate@iminodiacetic acid: optimization and mechanism study

The adsorption property of the costless green cellulose acetate (CA) was boosted by the dual modifications: inner modification by incorporating carboxylated graphene oxide (COOH-GO) into the CA spheres and outer modification by the surface modification of the COOH-GO@CA spheres by iminodiacetic acid (IDA) for removing Pb(II). The adsorption experiments of the Pb(II) proceeded in a batch mode to evaluate the adsorption property of the COOH-GO@CA@IDA spheres. The maximal Pb(II) adsorption capacity attained 613.30 mg/g within 90 min at pH = 5. The removal of Pb(II) reached its equilibrium within 20 min, and the removal % was almost 100% after 30 min at the low Pb(II) concentration. The Pb(II) adsorption mechanism was proposed according to the kinetics and isotherms studies; in addition, the zeta potential (ZP) measurements and X-ray Photoelectron Spectroscopy (XPS) analysis defined the adsorption pathways. By comparing the XPS spectra of the authentic and used COOH-GO@CA@IDA, it was deduced that the contributed chemical adsorption pathways are Lewis acid–base, precipitation, and complexation. The zeta potential (ZP) measurements demonstrated the electrostatic interaction participation in adsorbing the cationic Pb(II) species onto the negatively charged spheres (ZP = 14.2 mV at pH = 5). The unique channel-like pores of the COOH-GO@CA@IDA spheres suggested the pore-filling mechanism of Pb(II). The promising adsorption results and the superb recyclability character of COOH-GO@CA@IDA enable it to extend of the bench scale to the industrial scale.