Uniform Surface Charge Density Research Articles

Analytical solution of the Sommerfeld–Page equation

The Sommerfeld–Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. It is a delay differential equation, and almost no exact solution of this equation was known until recently. However, progress has been made, and an analytical solution was recently found for an almost identical delay differential equation, which arose in the context of the mathematical modeling of the COVID-19 epidemics. Inspired by this research, we offer a pedagogical exposition of how one can find an analytical solution of the Sommerfeld–Page equation.

A unified model for mechanical deformations of single stranded DNA-microbeam biosensors considering surface charge effects

A unified energy model for mechanical deformation of the microbeam included by single stranded DNA (ssDNA) adsorption considering the surface charge density on substrate is investigated. First, a free energy model is established to quantify the deflection and axial displacement of the microbeam, the ion concentration in the solution, as well as the electric potential distribution inside and outside the ssDNA film with a uniform surface charge density. Then, the governing equations and corresponding boundary conditions are obtained by minimizing the free energy with three types of variational variables. And, the relationship of the electric potential difference between the two sides of the ssDNA film and the deformation of microcantilever and simply support beam are determined in different solutions (1: 1, 1: 2, 1: 3). Moreover, the numerical solutions of the electric potential distribution inside and outside the ssDNA film are investigated by using the finite difference method and Newton's iteration method. The results suggest that the nonlinear model for electric potential distribution should be used under higher surface charge density. By fitting and comparing the present predictions with Arroyo-Hernandez's experimental data, the effectiveness of the model is verified. The study shows that the surface charge density can modulate the magnitude and direction of ssDNA-microbeam deformation, which also indicates that there exists a critical surface charge density, causing the failure of ssDNA-microbeam detection. These conclusions are helpful for designing the efficient biosensors based on DNA-microbeam.

A spherical version of Feynman’s static field momentum example

The Feynman demonstration that electromagnetic field momentum is real—even for static fields—can be made more pedagogically useful by simplifying its geometry. Instead of Feynman’s disk with charged balls on its surface, this article uses the geometry of a hollow non-conducting sphere with uniform surface charge density. With only methods available in a typical upper-division electrodynamics course, the initial field angular momentum and the final mechanical angular momentum can then be calculated in closed form and shown to be equal.

Dynamic Electrophoresis of a Hydrophobic and Dielectric Fluid Droplet.

Dynamic electrophoresis is the foundation for electroacoustical measurements, in which the electroacoustical signals may be used to analyze the size and electrostatic charge of colloidal entities by means of the results for dynamic electrophoretic mobility. Thus, the electrophoresis under an alternating electric field is the key foundation for electroacoustic theory. In this article, we develop a tractable analytical theory for the dynamic electrophoresis of hydrophobic and dielectric fluid droplets possessing uniform surface charge density. The tiny fluid droplets possess charged mobile surfaces and have found widespread applications in our day-to-day life. For dielectric fluid droplets (e.g., oil-water emulsions), the tangential electric stress at the interface is nonzero, which significantly affects its electrohydrodynamics under an oscillatory electric field, which has, however, a negligible impact on the electrophoretic motion of conducting droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid droplets often show hydrophobicity when they are immersed in an aqueous medium, and the impact of the electric field on hydrophobic surfaces remains a research frontier in the chemical discipline. Whereas a number of approximate expressions for electrophoretic mobility have been derived for the conducting droplet, none of them are applicable to such generic hydrophobic fluid droplets with dielectric permittivity that is significantly lower than or comparable to that of an aqueous medium. In this work, within the Debye-Hückel electrostatic framework, we elaborate an original analytical expression of dynamic electrophoretic mobility for this generic dielectric fluid droplet with a hydrophobic surface considering that the droplet retains its spherical shape during its oscillatory motion. We further derived a set of simplified expressions for dynamic electrophoretic mobility deduced under several limiting cases. The results are further illustrated, indicating the impact of pertinent parameters.

Stored electrostatic energy of a uniformly charged annulus

We show that a method that makes clever use of the axial symmetry of the model considerably simplifies the calculation of the electrostatic Coulomb self-energy of an annulus with uniform surface charge density. Differently from a disk, the case of an annulus represents a rather challenging geometry with no obvious solution for the calculation. The final result obtained for the electrostatic Coulomb self-energy of a uniformly charged annulus is expressed in compact form as a function of the ratio of the inner radius relative to the outer radius and involves special standard functions such as the complete elliptic integrals of the first and second kind.

Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density.

The present article deals with the theoretical study on electrophoresis of hydrophobic and dielectric spherical fluid droplets possessing uniform surface charge density. Unlike the ideally polarizable liquid droplet bearing constant surface ζ-potential, the tangential component of the Maxwell stress is nonzero for dielectric fluid droplets with uniform surface charge density. We consider the continuity of the tangential component of total stress (sum of the hydrodynamic and Maxwell stresses) and jump in dielectric displacement along the droplet-to-electrolyte interface. The typical situation is considered here for which the interfacial tension of the fluid droplet is sufficiently high so that the droplet retains its spherical shape during its motion. The present theory can be applied to nanoemulsions, hydrophobic oil droplets, gas bubbles, droplets of immiscible liquid suspended in aqueous medium, etc. Based on weak field and low charge assumptions and neglecting the Marangoni effect, the resultant electrokinetic equations are solved using linear perturbation analysis to derive the closed form expression for electrophoretic mobility applicable for the entire range of Debye-Hückel parameter. We further deduced an alternate approximate expression for electrophoretic mobility without involving exponential integrals. Besides, we have derived analytical results for mobility pertaining to various limiting cases. The results are further illustrated to show the impact of pertinent parameters on the overall electrophoretic mobility.

Calculation of the Coulomb Self-Energy of a Spherical Surface with Uniform Surface Charge Density Using the Fourier Transform Method

Undergraduate students in upper levels of physics or engineering programs learn the theory of Fourier series and integral transform method from mathematics courses. Nevertheless, they rarely see the application of such a method to solving problems in calculus-based physics courses that deal with topics such as electrostatics or magnetism. In this work, we illustrate the utility of the Fourier transform method by considering and solving via such a technique a representative problem that arises in electrostatics. The chosen case study is that of a spherical surface with uniform surface charge density and the calculation of its electrostatic Coulomb self-energy. By solving this problem by using the Fourier transform technique we also draw attention to the pedagogical aspects of the treatment. In particular, we stress the point that the Fourier transform method should be treated at more depth in calculus-based physics courses for undergraduate students.

Electrostatic interaction between two spheroidal particles at large separations

Asymptotic expressions for the electrostatic interaction energy between two weakly charged spheroidal particles (prolate and oblate) with uniform surface potential or surface charge density at large separations in an electrolyte solution are derived on the basis of the linear superposition approximation. The electrostatic interaction between two spheroids is found to be the screened Coulomb interaction between two hypothetical point particles with orientation-dependent charges. Explicit interaction energy equations, which are expressed in terms of spheroidal wave functions, are given for four particular configurations of two similar spheroids, that is, side-to-side prolates, end-to-end prolates, side-to-side oblates, and end-to-end oblates. Comparison is also made with results obtained using Derjaguin’s approximation. Electrostatic interaction between two spheroids • Asymptotic expressions for the electrostatic interaction energy between two spheroidal particles are derived. • Constant surface potential and charge density cases are considered. • Side-to-side prolates, end-to-end prolates, side-to-side oblates, and end-to-end oblates are considered.

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Obtaining the interaction energy between two uniformly charged hemispherical surfaces in compact analytical form seems to be an impossible task to achieve under arbitrary conditions. However, we show in this work that one can obtain the interaction energy between two identical hemispherical surfaces with uniform surface charge density for the special condition of them touching each other along the ‘equator’. The mathematical solution method that we apply is remarkable in that the bulk of the treatment is analytic with the only drawback of having to rely on knowledge of certain special functions and their properties.

Results for the electrostatic potential of a uniformly charged hemispherical surface

We study the form of the electrostatic potential created by a hemispherical surface with uniform surface charge density. We specifically consider a “northern” hemispherical surface and try to obtain analytical expressions for the electrostatic potential at an arbitrary point in space. Some compact analytical results are obtained for special cases and an interesting mathematical integral formula is derived as a by-product of the approach. The results suggest that a general expression for the electrostatic potential at an arbitrary point in space, if possible, would be very hard to obtain in compact analytical form.

Nanoparticle Delivered Anti-miR-141-3p for Stroke Therapy.

Ischemic stroke and factors modifying ischemic stroke responses, such as social isolation, contribute to long-term disability worldwide. Several studies demonstrated that the aberrant levels of microRNAs contribute to ischemic stroke injury. In prior studies, we established that miR-141-3p increases after ischemic stroke and post-stroke isolation. Herein, we explored two different anti-miR oligonucleotides; peptide nucleic acid (PNAs) and phosphorothioates (PS) for ischemic stroke therapy. We used US FDA approved biocompatible poly (lactic-co-glycolic acid) (PLGA)-based nanoparticle formulations for delivery. The PNA and PS anti-miRs were encapsulated in PLGA nanoparticles by double emulsion solvent evaporation technique. All the formulated nanoparticles showed uniform morphology, size, distribution, and surface charge density. Nanoparticles also exhibited a controlled nucleic acid release profile for 48 h. Further, we performed in vivo studies in the mouse model of ischemic stroke. Ischemic stroke was induced by transient (60 min) occlusion of middle cerebral artery occlusion followed by a reperfusion for 48 or 72 h. We assessed the blood-brain barrier permeability of PLGA NPs containing fluorophore (TAMRA) anti-miR probe after systemic delivery. Confocal imaging shows uptake of fluorophore tagged anti-miR in the brain parenchyma. Next, we evaluated the therapeutic efficacy after systemic delivery of nanoparticles containing PNA and PS anti-miR-141-3p in mice after stroke. Post-treatment differentially reduced both miR-141-3p levels in brain tissue and infarct injury. We noted PNA-based anti-miR showed superior efficacy compared to PS-based anti-miR. Herein, we successfully established that nanoparticles encapsulating PNA or PS-based anti-miRs-141-3p probes could be used as a potential treatment for ischemic stroke.

Electrostatic potential energy stored in a hemispherical surface with uniform surface charge distribution

We report an exact result for the electrostatic potential energy stored in a hemispherical surface with uniform surface charge density. This system lacks the spherical symmetry of a uniformly charged spherical surface or its solid sphere counterpart. Consequently, a hemispherical surface with all its charge uniformly spread on its surface represents an interesting case study in electrostatics. In this work we combine the fact that the body has axial symmetry with clever mathematical tools to obtain an outcome that is remarkably simple. The final exact expression obtained for the electrostatic potential energy stored in a hemispherical surface with uniform surface charge density answers a long-standing question. Though the bulk of the treatment is analytical, the accuracy of the findings can also be ascertained by using symbolic computation software or numerical recipes. Hence, the present analytical results can be compared to ones obtained with various powerful numerical methods which nowadays are routinely used to check the correctness of analytical and semi-analytical calculations.

Investigation of PLGA nanoparticles in conjunction with nuclear localization sequence for enhanced delivery of antimiR phosphorothioates in cancer cells in vitro

Numerous first generation phosphorothioates (PS) and their derivatives have shown promise targeting mRNA for therapeutic applications and also gained market approval for their use as a drug. However, PS have not been explored for targeting microRNAs (miRNAs or miRs). In particular, efficient delivery remains a critical cog in PS-based antimiR applications. In this study, we tested and characterized a series of poly-lactic-co-glycolic-acid (PLGA) polymers of different molecular weights that can encapsulate the optimum amount of antimiR-155 PS with uniform morphology and surface charge density. We found that nuclear localization sequence substantially increases loading of antimiR-155 PS in PLGA nanoparticles. Further, in a battery of cell culture studies, we confirmed that PLGA nanoparticles encapsulated nuclear localization sequence/antimiR-155 PS combination undergoes significant intracellular delivery and results in reduced expression of miR-155. In conclusion, we successfully demonstrate the feasibility and promise of optimized PLGA nanoparticles based PS delivery in combination with nuclear localization sequence for antimiRs based therapeutics.

A correlation-hole approach to the electric double layer with counter-ions only

ABSTRACTWe study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson–Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfil the contact-value theorem at all values of the coupling constant and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte Carlo simulations. The crossover to mean-field behaviour at large distance is studied in detail.

Poisson-Boltzmann model of electrolytes containing uniformly charged spherical nanoparticles.

Like-charged macromolecules typically repel each other in aqueous solutions that contain small mobile ions. The interaction tends to turn attractive if mobile ions with spatially extended charge distributions are added. Such systems can be modeled within the mean-field Poisson-Boltzmann formalism by explicitly accounting for charge-charge correlations within the spatially extended ions. We consider an aqueous solution that contains a mixture of spherical nanoparticles with uniform surface charge density and small mobile salt ions, sandwiched between two like-charged planar surfaces. We perform the minimization of an appropriate free energy functional, which leads to a non-linear integral-differential equation for the electrostatic potential that we solve numerically and compare with predictions from Monte Carlo simulations. Nanoparticles with uniform surface charge density are contrasted with nanoparticles that have all their charges relocated at the center. Our mean-field model predicts that only the former (especially when large and highly charged particles) but not the latter are able to mediate attractive interactions between like-charged planar surfaces. We also demonstrate that at high salt concentration attractive interactions between like-charged planar surfaces turn into repulsion.

Ions confined in spherical dielectric cavities modeled by a splitting field-theory.

The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ϕ0 and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ϕ0 and ξ potentials are increased.

Counter-ions at single charged wall: Sum rules

For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary condition for these sum rules is that the Coulomb fluid possesses good screening properties, i.e. the particle correlation functions or the averaged charge inhomogeneity, say close to a wall, exhibit a short-range (usually exponential) decay. In this work, we study equilibrium statistical mechanics of an electric double layer with counter-ions only, i.e. a globally neutral system of equally charged point-like particles in the vicinity of a plain hard wall carrying a fixed uniform surface charge density of opposite sign. At large distances from the wall, the one-body and two-body counter-ion densities go to zero slowly according to the inverse-power law. In spite of the absence of screening, all known sum rules are shown to hold for two exactly solvable cases of the present system: in the weak-coupling Poisson-Boltzmann limit (in any spatial dimension larger than one) and at a special free-fermion coupling constant in two dimensions. This fact indicates an extended validity of the sum rules and provides a consistency check for reasonable theoretical approaches.

Partition and Structure of Aqueous NaCl and CaCl2 Electrolytes in Carbon-Slit Electrodes

We report molecular dynamics simulation results obtained for aqueous NaCl and CaCl2 solutions used as electrolytes in model electric double layer capacitors. The electrodes are carbon-slit pores of widths 0.65, 0.7, 0.79, 0.9, 1.2, and 1.6 nm. The applied voltage is represented as a uniform surface charge density on the pore surfaces. Toward replicating experimentally relevant conditions, the surface charge densities span between 0 (neutral pore) and 15 μC/cm2 (both positive and negative). Charge localization on pore entrances is not considered. As the neutral pores are charged, we monitor the accumulation of the ions from the bulk (at ∼1.8 M ionic strength) to the pores. Our results show that the ionic concentration inside the pores increases as the surface charge density increases, as expected. More interestingly, the surface charge density at which the ions begin to penetrate the pores increases as the pore width decreases and as the ion size and the ion hydration strength increase. The pore width at w...

Nm-scale measurements of fast surface potential transients in an AlGaN/GaN high electron mobility transistor

Fast, bias-induced, surface potential transients (SPTs) and conductance transients (CTs) were simultaneously measured on an AlGaN/GaN high electron mobility transistor. SPTs measured near the drain-side gate edge and CTs have nearly the same shape and are well-fit with two exponentials having room-temperature time constants of 4.2 ms and 36 ms, likely indicating emission from two trap species. Kelvin probe force microscopy was used to measure SPTs. Electrostatic simulations of SPT amplitudes, which account for the measured probe/sample geometry, are consistent with a uniform trapped surface charge density of 7 × 1012 electrons/cm2 extending 200 nm from the drain-side gate edge.