Electrophoresis of hydrophilic/hydrophobic rigid colloid with effects of relaxation and ion size

This article deals with a semi‐analytical study on the electrophoresis of charged spherical rigid colloid by considering the effects of relaxation and ion size. The particle surface is taken to be either hydrophilic or hydrophobic in nature. In order to consider the ion size effect we have invoked the Carnahan and Starling model (J. Chem. Phys. 1969, 51, 635‐636). The mathematical model is based on Stokes equation for fluid flow, modified Boltzmann equation for spatial distribution of ionic species and Poisson equation for electric potential. We adopt a linear perturbation technique under a weak electric field assumption. An iterative numerical technique in employed to solve the coupled set of perturbed equations. We have validated the numerically obtained electrophoretic mobility with the corresponding analytical solution derived under low potential limit. Going beyond the widely employed Debye‐Hückel linearization, we have presented the results for a wide range of surface charge density, electrolyte concentration, and slip length to Debye length ratio. We have also identified several interesting features including occurrence of local maxima and minima in the mobility for critical choice of pertinent parameters.     

Analytical analysis of anisotropic thermophoresis of a charged spheroidal colloid in aqueous media for extremely thin EDL cases

Thermophoresis of charged spheroids has been widely applied in biology and medical science. In this work, we report an analysis of the anisotropic thermophoresis of diluted spheroidal colloids in aqueous media for extremely thin EDL cases. Under the boundary layer approximation, we formulate the thermophoretic velocity, the thermophoretic force, and the thermodiffusion coefficient of a randomly dispersed spheroid. The parametric studies show that under the aforementioned conditions, the thermophoresis is anisotropic and its thermodiffusion coefficient should be considered as a vector, D _T. The thermodiffusion coefficient values and directions of D _T are strongly related to the aspect ratio and the angle θ between the externally applied temperature gradient and the particle's axis of revolution: The increasing aspect ratio enlarges the thermodiffusion coefficient value D_T of prolate (oblate) spheroids to a constant value when θ < 60° (θ > 45°), and it reduces D_T of prolate (oblate) spheroids to a constant value when θ > 60° (θ < 45°). The thermodiffusion coefficient direction of both prolate and oblate spheroids deviates slightly from −∇T_∞ for a small aspect ratio, and such deviation becomes serious for a large aspect ratio.     

Exact solutions of the rigid rotor in the electric field

We first present a new constraint condition on the confluent Heun function H_C(α, β, γ, δ, η;z) (β, γ ≥ 0, z ∈ [0, 1]) and then illustrate how to solve the rigid rotor in the electric field. We find its exact solutions unsolved previously through solving the Wronskian determinant. The present results compared with those by the perturbation methods are found to have a big difference for a large parameter a. We also present 2D and 3D probability density distributions by choosing different angular momentum quantum numbers l. We observe that the original eigenvalues with degeneracy (2 l + 1) are split into the (l + 1) state with approximate eigenvalues l(l + 1) for small a but large l.     

Range of Validity of a Simplified Model for Diffuse Charge Dynamics

The modelling of electrochemical processes often requires the solution of the Poisson‐Nernst‐Planck (PNP) equations. In complex geometries, such as porous electrodes, that is challenging due to the presence of disparate length scales, ranging from the Debye screening length (～nm) to the device length scale (～cm). To overcome this difficulty, one often assumes that the electric double layer (EDL) is at quasi‐equilibrium to construct a simplified model that accounts for ion diffusion in the electro‐neutral bulk of the electrolyte while replacing the EDLs with appropriate boundary conditions. Various researchers have demonstrated that such an approach is valid in the asymptotic limit of a thin EDL and moderate electrode potentials. In this note, we explore the range of validity of this approximation by considering a one‐dimensional electrolytic cell with blocking electrodes subjected to a step change and time‐periodic alternations in the electrodes’ potentials by calculating the errors associated with the approximate approach as functions of the EDL thickness and electric field frequency and intensity. Additionally, we delineate numerical instabilities associated with the numerical solutions of the bulk equations with the nonlinear boundary condition peculiar to this problem.     

Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

The water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.     

Numerical simulation of droplet coalescence behavior in gas phase under the coupling of electric field and flow field

The coalescence behavior of droplets in an electric field belongs to the important research contents of electrohydrodynamics. Based on the phase field method of the Cahn–Hilliard equation, the electric field and the flow field are coupled to establish the numerical model of twin droplet coalescence in a coupled field. The effects of flow rate, electric field strength, droplet diameter, and interfacial tension on the coalescence behavior of droplets during the coalescence process were investigated. The results show that the dynamic behavior of the droplets is divided into coalescence, after coalescence rupture, and no coalescence under the coupling of electric field and flow field. The proper increase of the electric field strength will accelerate the coalescence of the droplets, and the high electric field strength causes the droplets to burst after coalescence. Excessive flow rates make droplets less prone to coalescence. Under the coupling field, the larger the droplet interface tension, the smaller the droplet diameter, the smaller the flow rate, and the shorter the droplet coalescence time. The results provide a theoretical basis for the application of electrostatic coalescence in gas–liquid separation technology.     

Relation of the force constant of a bond to the electric field at a nucleus

The change in the electric field at a nucleus in a molecule due to bond stretch is related to the force constant of the stretched bond. The validity of this relationship using approximate wave functions at the SCF and MP2 levels of theory is tested for the diatomic molecules H₂, HF, CO, and N₂. The effect of basis set variation on H₂ is also investigated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1664–1667, 1997     

Mass transfer of a neutral solute in polyelectrolyte grafted soft nanochannel with porous wall

A soft nanochannel involves a soft interface that contains a polyelectrolyte layer (PEL) sandwiched between a rigid surface and a bulk electrolyte solution. Mass transfer of a neutral solute in a combined electroosmotic and pressure driven flow through a polyelectrolyte grafted charged nanochannel with porous wall is presented in this work. Assuming the PEL as fixed charged layer and PEL-electrolyte interface as a semi-penetrable membrane, analytical solutions were obtained for potential distributions (for small wall potential). Velocity profiles were also derived in the same domains, for both inside and outside the PEL. Convective-diffusive species balance equation was semi-analytically solved inside the PEL. Expression of length averaged Sherwood number was also obtained and effects of different parameters, namely, drag parameter (α), Debye parameter , and PEL thickness were studied in detail. The variation of permeate concentration and permeation flux across the porous wall was obtained.     

New concept in focusing field-flow fractionation and thin layer isopycnic focusing: Coupling of primary electric field with secondary gravitational force

A new concept of isopycnic focusing exploiting the simultaneous action of coupled electric and gravitational fields is described. Experimental implementation of this concept is demonstrated under conditions of focusing field-flow fractionation and of newly proposed thin layer isopycnic focusing. Both methods are aimed for particle separations. Although the demonstration was performed by using model cross-linked polymer and latex particles, the most important field of potential applications is intended for analytical and preparative separations of biological particles.     

Influence of the electric field on a particle in a space with a disclination

We consider a quantum particle in a space with a linear topological defect, i.e., disclination. The effect of the uniform electric field in this space, on the particle, is shown to cause a translation of the wave function. In addition, the electric field is not found to be affected by the defect. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A core-shell nanoparticle approach to photoreversible fluorescence modulation of a hydrophobic dye in aqueous media

Amphiphilic core-shell nanoparticles containing spiropyran moieties have been prepared in aqueous media. The nanoparticles consist of hydrophilic and biocompatible poly(ethyleneimine) (PEI) chain segments, which serve as the shell, and a hydrophobic copolymer of methyl methacrylate (MMA), a spiropyran-linked methacrylate, and a cross-linker, which forms the core of the nanoparticles. A hydrophobic fluorescent dye based on the nitrobenzoxadiazolyl (NBD) group was introduced into the nanoparticles to form NBD-nanoparticle complexes in water. The nanoparticles not only greatly enhance the fluorescence emission of the hydrophobic dye NBD in aqueous media, probably by accommodating the dye molecules in the interface between the hydrophilic shells and the hydrophobic cores, but also modulate the fluorescence of the dye through intraparticle energy transfer. This biocompatible and photoresponsive nanoparticle complex may find applications in biological areas such as biological diagnosis, imaging, and detection. In addition, this nanoparticle approach will open up possibilities for the fluorescence modulation of other hydrophobic fluorophores in aqueous media.     

Forces at the nuclei of a molecule in the presence of non-uniform electric field

The interaction Hamiltonian within the Bloch gauge for the potentials of the electric field has been used to define electric multipole moment operators. Perturbation theory has been applied to evaluate the induced electronic moments and electric field at the nuclei in the presence of spatially non-uniform electric fields of high intensity. Multipole nuclear electric shielding tensors have been defined to describe the contributions arising from a non-homogeneous electric field. These quantities are useful to rationalize linear and non-linear responses of a molecule in the presence of intense external electric perturbations.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Experimental study of isopycnic focusing generated by coupled electric and gravitational field forces: Use in thin layer focusing and focusing field-flow fractionation

Various operational parameters affecting the formation of the density gradient generated by the electric field action on a binary pseudo-continuous carrier liquid composed of charged colloidal silica particles suspended in water and the isopycnic focusing of sample particles were investigated under conditions of static thin layer focusing and dynamic focusing field-flow fractionation. The properties and the behavior of the density gradient forming carrier liquid were studied. The experimental results are compared with theoretical predictions and discussed with respect to potential applications of the proposed concept not only for separation purposes but also for studies of interparticle interactions.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Local order and shape of a polymer chain in an external electric field

A solution of polymer chains in the presence of an external electric field is considered. Dipole-like interactions between polymer chain segment-vectors and the electric field are assumed to be proportional to the cosine of the angle between the segment-vector and the direction of the electric field. Parameters characterizing the shape of the chain (i.e., the chain end-to-end distance and cross-section per chain), and parameters describing the local order at the segmental and chain level (i.e., moments of the first and second Legendre polynomials 〈P₁〉 and 〈P₂〉 are calculated. The optical anisotropy and the molecular shape change induced by the external electric field are discussed.     

Quantum dynamics of a discontinuously kicked charged particle in harmonic,symmetric double,or triple wells

The quantum dynamics of a charged particle in a harmonic trap in the presence of discontinuous reversals of a homogeneous or an inhomogeneous electric field is studied. The dynamics reveals classically expected patterns in harmonic wells. In a symmetric double‐well potential, the discontinuously switched low intensity homogeneous electric field does not appear to assist tunneling, whereas an inhomogeneous electric field is found to assist the process. Resonance like enhancement is noticed at a critical reversal frequency. Dynamics in a triple well is also analyzed under similar conditions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Molecules under external electric field: On the changes in the electronic structure and validity limits of the theoretical predictions

A detailed analysis of the electronic structure of the ground and first excited spin state of three diatomic molecules ( and ) under static applied electric field is performed at CCSD(T), DFT, MRCI and MRCI(Q) levels of theory. Our findings have revealed that by boosting the applied field one induces changes in the occupation numbers of molecular orbitals, giving rise to changes in the equilibrium geometry and in the HOMO–LUMO energy gap. Specifically, singlet to triplet spin transition can be induced by increasing the applied electric field beyond a critical value. Accordingly, affecting the accuracy of the widely used expression of energy expanded in Taylor series with respect to the applied electric field. © 2018 Wiley Periodicals, Inc.     

固溶体内电场调控增强Bi24O31ClxBr10-x体相电荷流动和光催化活性

光催化是一种在能源和环境领域有着重要应用前景的绿色技术,在光照射下可将有机污染物彻底降解为二氧化碳和水,但因缺乏精确调控电荷流动的方法,导致大多数光催化剂活性不高.因此,促进光生电荷的高效分离一直是光催化研究的重要方向.目前多数电荷分离调控研究集中于表面修饰、表面缺陷设计、异质结构建等表面电荷分离改善策略,而对于体相电荷分离调控研究相对较少.卤氧化铋固溶体光催化材料由于独特的层状晶体结构、可调节的带隙结构和优化的电荷分离效率,近年来受到广泛关注.目前对固溶体的体相电荷分离机理尚不清楚.内电场作为一种新的增强光催化反应活性的有效调控途径,通过定向促进体相电荷的分离和转移,使光生载流子快速参与氧化还原反应.然而,通过调控内电场来增强卤氧化铋固溶体光催化活性的报道较少,且缺乏从理论和实验的角度对固溶体内电场大小以及电荷分离机理的分析.本文构建了具有相同形貌和晶体结构的Bi₂₄O₃₁Cl_xBr_10-x固溶体光催化剂,并考察了其催化性能.密度泛函理论计算、开尔文探针力显微镜(KPFM)和Zeta电位测试结果表明,通过改变卤素类型和比例可增加晶体结构单元的不对称性,从而调节[Bi₂₄O₃₁]和[X]层之间的电势差,增强光催化材料的内电场强度,促进体相电荷分离和转移效率,进而提高酚类有机污染物的降解活性.光电化学测试发现,相较于Bi₂₄O₃₁Cl₁₀和Bi₂₄O₃₁Br₁₀,Bi₂₄O₃₁Cl₄Br₆固溶体体相电荷分离效率显著提高,表面和界面上的电荷转移效率以及载流子密度增加.Bi₂₄O₃₁Cl₄Br₆的载流子密度分别是Bi₂₄O₃₁Cl₁₀和Bi₂₄O₃₁Br₁₀的33.1倍和4.7倍,Bi₂₄O₃₁Cl₄Br₆固溶体降解双酚A活性分别是Bi₂₄O₃₁Cl₁₀和Bi₂₄O₃₁Br₁₀的6.21倍和2.71倍.此外,其它酚类的降解实验也证明了光催化活性和内电场强度以及电荷分离效率成正相关.综上所述,本文从内电场的角度揭示了固溶体策略对光催化性能增强的内在机理,这些发现将进一步加深对体相电荷运动行为的理解,为设计高活性光催化剂提供一条新的途径.     

电场作用下离子型稀土矿浸矿溶浸液渗流特性研究

根据多孔介质中电动渗流效应,在离子型稀土矿浸出过程中,提出了利用电场强化浸矿溶浸液渗流能力的方法,通过机制分析和电动渗流试验,探讨了电场作用对溶浸液的渗流特性的影响。结果表明:电场作用可以有效地强化矿床孔隙中浸矿溶浸液渗流能力,强化效果与电场强度、矿床渗透率和溶浸液流体性质等因素有关;相同流体压力梯度下,电场作用下矿床中溶浸液电动渗流随电场强度增大而增加变快;矿床渗透率越高,电场作用对溶浸液渗流特性的影响越明显;浸矿溶浸液浓度越高,孔隙中溶浸液的电动渗流效应越明显。