Diffusiophoresis in suspensions of highly charged soft particles

Diffusiophoresis phenomenon of aoft particles suspended in binary electrolyte solutions is explored theoretically in this study based on the spherical cell model, focusing on the chemiphoresis component in absence of diffusion potential. Both the electrostatic and hydrodynamic aspects of the boundary confinement, or steric effect, due to the presence of neighboring particles are examined extensively under various electrokinetic conditions. Significant local extrema are found in mobility profiles expressed as functions of the Debye length in general, synchronized with the strength of the motion-inducing double layer polarization. Moreover, a seemingly peculiar phenomenon is observed that the soft particles may move faster in more concentrated suspensions. The competition between the simultaneous enhancement of the motion-inducing electric driving force and the motion-retarding hydrodynamic drag force from the boundary confinement effect of the neighboring particles is found to be responsible for it. The above findings are also demonstrated experimentally in a very recent study on the diffusiophoretic motion of soft particles through porous collagen hydrogels. The results presented here are useful in various practical applications of soft particles like drug delivery.     

Diffusiophoresis of a cylindrical colloidal particle oriented parallel to an electrolyte concentration gradient field

We derive the general expression for the diffusiophoretic mobility of a cylindrical particle oriented parallel to an applied electrolyte concentration gradient field in a symmetrical electrolyte solution. From the general mobility expression as combined with an approximate analytic expression with negligible error for the electric potential distribution around a cylinder, an accurate analytic mobility expression is obtained, which is applicable for arbitrary values of the particle zeta potential and the electrical double layer thickness. It is also found that the low zeta potential approximation is an excellent approximation for low-to-moderate values of the particle zeta potential.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

Study on Electric Double Layer of a Cylindrical Particle with Functional Theoretical Approach

A new method, i.e. the iterative method in functional theory, was introduced to solve analytically the nonlinear Poisson-Boltzmann （PB） equation under general potential ψ condition for the electric double layer of a charged cylindrical colloid particle in a symmetrical electrolyte solution. The iterative solutions of ψ are expressed as functions of the distance from the axis of the particle with solution parameters： the concentration of ions c, the aggregation number of ions in a unit length m, the dielectric constant e, the system temperature T and so on. The relative errors show that generally only the first and the second iterative solutions can give accuracy higher than 97%. From the second iterative solution the radius and the surface potential of a cylinder have been defined and the corresponding values have been estimated with the solution parameters, Furthermore, the charge density, the activity coefficient of ions and the osmotic coefficient of solvent were also discussed,     

Start‐up of electrophoresis of an arbitrarily oriented dielectric cylinder

An analytical study is presented for the transient electrophoretic response of a circular cylindrical particle to the step application of an electric field. The electric double layer adjacent to the particle surface is thin but finite compared with the radius of the particle. The time‐evolving electroosmotic velocity at the outer boundary of the double layer is utilized as a slip condition so that the transient momentum conservation equation for the bulk fluid flow is solved. Explicit formulas for the unsteady electrophoretic velocity of the particle are obtained for both axially and transversely applied electric fields, and can be linearly superimposed for an arbitrarily‐oriented applied field. If the cylindrical particle is neutrally buoyant in the suspending fluid, the transient electrophoretic velocity is independent of the orientation of the particle relative to the applied electric field and will be in the direction of the applied field. If the particle is different in density from the fluid, then the direction of electrophoresis will not coincide with that of the applied field until the steady state is attained. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.     

On the Role of Heterogeneous Nanopore Junction in Osmotic Power Generation

Osmotic power generated by mixing ionic solutions of different concentration is an underutilized clean energy resource that satisfy potentially the ever‐growing energy demand. For decades, substantial efforts are made to enhance the power density. Toward this goal, we once developed a heterogeneous nanoporous membrane comprising of heterojunctions between negatively charged mesoporous carbon and positively charged macroporous alumina to harvest electric power from salinity difference and achieved outstanding performance (J. Am. Chem. Soc. 2014 , 136, 12265). The heterogeneous nanopore junction effectively suppresses ion concentration polarization (ICP) at low concentration end, and consequently promotes the overall power density. However, to date, a systematic understanding of the role of the heterogeneous nanopore junction in osmotic energy conversion remains urgent and largely unexplored. Herein, we provide an in‐depth theoretical investigation on this issue with special emphasis on several influential factors, such as the ionic concentration, the surface charge density, and the geometry of heterogeneous part. To balance the suppression of ICP and maintenance of charge selectivity, we find that these influential factors in the heterogeneous part should be restricted to a specific range. These findings provide direct guidance for design and optimization of high‐performance nanofluidic power sources.     

Accounting for the Adsorption of Anions When Interpreting the Mechanism of Electrodeposition of Metals from Complex Electrolytes: The Reaction Order by the Electrochemically Active Ion

The relationship between the current and the bulk concentration of complex ions during concurrent specific adsorption of an electrochemically active complex ion and a complexing ligand is considered. The effect of parameters that characterize adsorption of such ions and the structure of the electrical double layer on this relationship is analyzed.__________Translated from Elektrokhimiya, Vol. 41, No. 7, 2005, pp. 817–822.Original Russian Text Copyright © 2005 by Rogozhnikov.     

Mechanism of metals’ electrodeposition from complex electrolytes allowing for the anions’ adsorption: Effect of the position of ligands and complex ions in the compact layer on the reaction orders

Effect of the relative position in the compact layer of specifically adsorbed electroactive complex ion and complexing ligand on the magnitude of current is considered. Effect of parameters that characterize the adsorption of such ions and the electrical double layer structure on the dependence of current on the solution composition and effective reaction orders is analyzed.     

Modeling of specific adsorption of ions at electrodes during the passing from a mixed solution of constant ionic strength to a binary solution

Electrocapillary curves in the mc NaNO₃ + (1 ? m)c NaF mixed solutions are calculated in terms of the Alekseev-Popov-Kolotyrkin model. The analysis of limiting case m = 1 shows that in a NaNO₃ binary solution the model predicts quadratic dependence of the NO ₃ ^? anion adsorption energy on the potential, which contradicts to experimental data. A modification of the model is suggested, which allowed removing this contradiction.     

Study on the Radius of an Electrical Spherical Micelle： Functional Theoretical Approach

For the purpose of eliminating restriction, the Poisson-Bokzmann (PB) equation, which represents the potential of the electrical double layer of spherical miceUes, can be solved analytically only under the lower potential condition, a kind of iterative method in functional analysis theory has been used. The radius of the spherical particle can be obtained from the diagram of the second iterative solution of the potential versus the distance from the center of the particle. The influences of the concentration of the ions, the charge number of ions, the aggregation number of the particle, the dielectric constant of solvent and the temperature of system on the radius also have been studied.     

Salient features of the electrical double layer structure on mechanically renewed gold-silver electrodes in aqueous solutions of a surface-inactive electrolyte

The behavior of electrodes, which are made of binary Au-Ag alloys (Ag content 1–15 at %) and renewed by mechanical cutting in aqueous solutions of sodium fluoride, is studied with the aid of cyclic voltammetry and impedance methods. It is established that, in the region of potentials corresponding to ideal polarizability, the differential capacitance of the electrical double layer rapidly changes with time elapsed after the renewal of the surface of the electrodes. The change in the capacitance is brought about by the exit of silver atoms into a surface layer. The implication is that silver is the surface-active component in these alloys. The rate of the surface segregation of silver atoms depends on the electrode potential. The segregation rate substantially increases upon going into the region that corresponds to positive charges of the silver electrode surface and to the beginning of adsorption of atomic oxygen on the electrode. Based on phenomenological models, a method for processing capacitance curves is realized, which links experimentally observed time effects to variations that occur in the surface composition, and assumptions concerning the mechanism of relaxation processes that are responsible for the observed time effects are put forth. Explicit data on the effect, which is exerted by mechanical renewal on the composition of the surface layer of Au-Ag alloys at different distances from the interface with a vacuum, are obtained with the aid of an x-ray photoelectron spectroscopy method. It is established that the surface layer (～0.5 nm) is enriched by silver atoms as compared with the alloy’s bulk.     

Study of the Electrical Double Layer of a Spherical Micelle: Functional Theoretical Approach

The electrical double layer theory is the base of the colloid stability theory (DLVO theory), and the PB eq. is a key to the study of the layer1,2. For a spherical particle, the PB eq. is (1) where and are the dielectric constant of the medium, the valence of ions, the elementary charge, the concentration of ions far away from the particle, the Boltzmann's constant and the temperature of the system, respectively. Since this eq. is a second order nonlinear differential one, only the anal…     

Specific Features of the Initial Stages of Oxidation of a Silver Electrode in Weakly Acidified Solutions of Sodium Fluoride

The behavior of a silver electrode, which is renewed in situ by mechanical cutting, in weakly acidified sodium fluoride solutions is studied with the aid of an impedance method and a method of cyclic voltammetry. The application of said procedures makes it possible to record time effects, which reflect the processes of electrochemical adsorption of oxygen at the interface between the silver electrode and the solution, in the potential region extending from −0.7 to 0.2 V (SCE). Approximate calculations of the effect of potential and the time of the electrode’s exposure (after its renewal) in contact with the electrolyte at given values of potential on the amount of adsorbed oxygen are performed on the basis of an analysis of the obtained experimental data. A comparison of the obtained results with the literature data makes it possible to put forth a substantiated opinion as to the reasons for the substantial difference in the intervals of potentials of ideal polarizability of the silver electrode/solution of a surface-inactive electrolyte system, which are presented in works of various authors.__________Translated from Elektrokhimiya, Vol. 41, No. 7, 2005, pp. 857–865.Original Russian Text Copyright © 2005 by Safonov, Choba, Oshkin.     

Comparative study of the electrical double layer on liquid electrodes of mercury, gallium, and an In-Ga alloy in hexamethylphosphortriamide

The structure of the electrical double layer (EDL) on sp metals is studied by exploring it on liquid renewable electrodes of mercury, gallium, and an indium-gallium alloy containing 16.4 at % In. The study is performed in a solvent with a high donor number (DN), specifically, in hexamethylphosphoramide (HMPA, DN = 38.8). A very strong chemisorption interaction between the metal and HMPA is fixed on the Ga and In-Ga electrodes. It is shown that the energy of the metal-HMPA chemisorption interaction increases in the series Hg < In-Ga < Ga. The pattern revealed by the study is exactly the opposite to that previously observed on these very electrodes. The strong chemisorption interaction between the metal and HMPA does not lead to an increase in the capacitance of the inner part of the EDL and is at the same time characterized by a very large chemisorption jump of the solvent potential. The data obtained in HMPA show that, for sp metals in contact with a solvent whose DN is high enough, the effects of the metal-solvent chemisorption interaction may be commensurate with the effects previously observed on catalytically active metals. Such a result is an invincible proof, which requires no additional modeling notions, of the existence of a correlation between energies of the chemisorption interaction between a metal and a solvent and the solvent’s DN. This in turn is a convincing evidence that the specific interaction between a metal and a solvent has a donor-acceptor origin. The data obtained in HMPA make it possible to unite all the available results yielded by research into the EDL structure on the catalytically active and sp metals.     

On the asymmetry of thermodynamic fluctuations of the electrode potential

The asymmetry of thermodynamic fluctuations of the equilibrium electrode potential and the asymmetry of thermodynamic fluctuations of the electrical double layer charge is characterized quantitatively on the basis of third-order noise spectra.Translated from Elektrokhimiya, Vol. 41, No. 2, 2005, pp. 131–136.Original Russian Text Copyright © 2005 by Grafov.This revised version was published online in April 2005 with corrections to the article note and article title and cover date.     

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length： Functional Theoretical Approach

Introduction The electrostatic potentialΨis the most importantproperty for the electrical double layer( EDL) of acharged particle in an electrolyte solution[1—4]. Thispotential is characterized by the so-called Poisson-Bolt-zmann(PB) equation. The PB equation is a second-or-der nonlinear differential equation with a constant coef-ficient, except a flat-plate model, which cannot besolved analytically by the traditional method. To ourknowledge, apart from the numerical solution to thisequa…     

Effect of the electrical double layer on the behavior of molecules: Regio-and stereoselective electrochemical reduction of 2,4-pentadienol

An approach to studying the effect of the electrical double layer (EDL) on the behavior of molecules in the electrode vicinity is proposed. The approach consists of comparing the results of a “direct” electrolysis of a model substance (process P ¹) with the results of its electrolysis performed in the mode of a homogeneous catalytic endoergic electron transfer (process P ₂). Two EDL effects are discovered in the electrochemical reduction of deuterated 2,4-pentadienol (I): the predominant formation of positional isomer IVa ? (IVa ? IVb) (regioselective synthesis) and a drastic increase in the concentration of cis-isomers of both IVa and IVb compounds (stereoselective synthesis). Possible reasons for these effects are discussed. In particular, it is shown that the regioselectivity of electrosynthesis is due to the “effect of heredity” that initial molecule I and its ether and ester produce on the behavior of an intermediate pentadienyl anion (PDA). A hypothesis is considered for the nonequilibrium orientation of PDA near the electrode as a result of the superviscous state of the medium (heredity of orientation of the initial unsymmetrical molecule). A principle of EDL tomography based on electrolysis with gradual movement of the reaction layer from the electrode into the bulk solution under conditions of mixed P ₁₂ process is proposed.     

Electrophoretic motion of a soft spherical particle in a nanopore

Many biocolloids, biological cells and micro-organisms are soft particles, consisted with a rigid inner core covered by an ion-permeable porous membrane layer. The electrophoretic motion of a soft spherical nanoparticle in a nanopore filled with an electrolyte solution has been investigated using a continuum mathematical model. The model includes the Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes and Brinkman equations for the hydrodynamic fields outside and inside the porous membrane layer, respectively. The effects of the “softness” of the nanoparticle on its electrophoretic velocity along the axis of a nanopore are examined with changes in the ratio of the radius of the rigid core to the double layer thickness, the ratio of the thickness of the porous membrane layer to the radius of the rigid core, the friction coefficient of the porous membrane layer, the fixed charge inside the porous membrane layer of the particle and the ratio of the radius of the nanopore to that of the rigid core. The presence of the soft membrane layer significantly affects the particle electrophoretic mobility.     

A Procedure for Transforming Impedance Spectra for the Determination of Mechanism of Electrochemical Reactions

Transformation of impedance spectra into relaxation time spectra (RTS) is used for determining contributions of individual processes of the oxygen electroreduction reaction (OER) to the polarization resistance of the electrochemical cell. The transformation technique involves the solution of the convolution equation found with the aid of a modified Van Cittert iteration algorithm checked on model impedance spectra. The technique, when used to analyze impedance spectra of electrochemical cells air|Pt|YSZ|YSZ + Pt|air, shows that the conversion of a globular structure of the YSZ + Pt cermet layer to a columnar one is accompanied by a change of peak amplitudes in RTS. The revealed RTS dynamics when heated to 750°C is compared with peculiarities of individual processes in OER.     

Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi-quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near-surface region, for example if a substrate is solid like aforementioned cellulose.