Electrochemical Studies of the Benzoate Adsorption on Au (111) Electrode

Cyclic voltammetry (CV), differential capacity (DC), and charge densitymeasurements have been employed to study the benzoate (BZ) adsorption at the Au(111)electrode surface. Thermodynamic analysis of charge density (_M) data has beenperformed to describe the properties of the adsorbed benzoate ion. The Gibbsexcess , Gibbs energy of adsorption G, and the number of electrons flowingto the interface per adsorbed benzoate ion at a constant potential (electrosorptionvalency) and at a constant bulk concentration of the benzoate (reciprocal of theEsin—Markov coefficient) have been determined. The results demonstrate thatalthough benzoate adsorption starts at negative charge densities, it takes placepredominantly at a positively charged surface. At the most positive potentials,the surface concentration of benzoate attains a limiting value of about 7.3×10^–10mol-cm^–2, which is independent of the bulk benzoate concentration. This valueis consistent with packing density corresponding to a closed-packed monolayerof vertically adsorbed benzoate molecules. At negative charge densities, benzoateassumes a flat (-bonded) surface coordination. The surface coordination ofbenzoate changes, by moving from a negatively to positively charged surface.At the negatively charged surface, the electrosorption bond is quite polar. Thepolarity of the chemisorption bond is significantly reduced due either to a chargetransfer or a screening of the charge on the anion by the charge on the metal.     

Interaction of Dissimilar Plane Parallel Double Layers at Arbitrary Potential

The elliptic integrals related to the interaction between two dissimilar parallel plates (the potentials on two plates have the opposite sign) are expanded in the series for the smaller surface potential y₀ (or ¦y _d ¦) and the smaller integration constant C as well as the larger surface potential and the larger integration constant, respectively. The number of series terms required to obtain the interaction with six significant digits is not more than 5 when the surface potential is less than or equal to 20 if the series being fit for smaller y₀ and C is combined with the series being fit for larger y₀ and C. The approximate expressions with different precision can be obtained by retaining different number of series terms. The results of Devereux O. F. and de Bruyn P. L. are discovered to be incorrect when absolute value of the surface potential is very large or the integration constant is very large or very small.     

Approximate analytical expressions for the electrical potential in a cavity containing salt-free medium

The electrical potential in a closed surface such as a cavity containing counterions only is derived for the cases of constant surface potential and constant surface charge density. The results obtained have applications in, for example, microemulsion-related systems in which ionic surfactants are introduced to maintain the stability of a dispersion and electroosmotic flow-related analysis. An analytical expression for the electrical potential is derived for a planar slit, and the methodology used is modified to derive approximate analytical expressions for spherical and cylindrical cavities. The higher the surface potential, the better the performance of these expressions. For the case where the surface potential is above ca. 50 mV, the performance of the approximate analytical expressions can further be improved by multiplying a correction function.     

Electrokinetic Properties of the Methylated Surface of Quartz Capillaries

The surface charge and electrokinetic potential of quartz capillaries with hydrophobized (methylated) surface are measured. It is shown that, during the flow of an electrolyte solution through the capillary, the potential lowers with time due to formation of gas bubbles on the surface screening the surface charge. In a certain period of time, drastic jump of the potential to its initial value is observed, which is interpreted as a detachment of bubbles by the flowing solution. The formation of bubbles is provoked by the roughness of the methylated surface with asperities of up to 20 nm in height. The profiles of the methylated surface were obtained by the atomic force microscopy. An addition of a nonionic surfactant hydrophilizing the hydrophobic surface to the electrolyte solution lowers the -potential, which could be caused by the suppression of the slip effect. Estimations made on the basis of an earlier developed theory lead to the values of slip coefficient that are close to those measured for micron-sized hydrophobic capillaries.     

Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles

The optical response of colloidal particles depends on a variety of properties of the cluster, e.g., shape, size, size distribution and particle material. Since particles often are charged, also the surface charge may be a parameter which influences their optical properties. In this paper the effect of a surface charge on optical properties of spherical colloidal particles is studied and its magnitude is estimated by extended computations for silver clusters with surface plasmon in aqueous suspension. Two models are presented and discussed. The first model is based on the electrodynamic solution by Bohren and Hunt (Can. J. Phys. 55, 1930 (1977)), where a surface conductivity _S for a free surface charge yield an additional contribution _S to the dielectric constant of the particle material. In the second model, the surface charge contributes to the number density of free electrons in the cluster. Both models lead to a shift of the cluster plasmon peak, while an increase of the plasmon halfwidth could not be derived. The effect is quite small and limited on very small clusters.PACS 61.46+w 73.20.Mf 78.20.Dj     

Surface electric field manipulation of the adsorption kinetics and biocatalytic properties of cytochrome c on a 3D macroporous Au electrode

Upon adsorbing on a solid-state substrate, water-soluble proteins are prone to denaturation and deterioration of their functions due to the conformation change. The surface electric field of a conductive substrate is one of the important factors that influence the character of adsorbed proteins. In this work, a 3D macroporous gold electrode has been prepared and served as the working electrode to study the influence of surface electric field on the adsorption kinetics and conformation of the adsorbed cytochrome c (cyt-c) with the help of electrochemical, in situ electrochemical IR spectroscopic, atomic force microscopic, and contact angle measurements. The external electric field creates excess surface charge which can manipulate the adsorption rate of proteins on the substrate by the enhanced electrostatic interactions between the electrode and protein patches by coupling with complementary charges. The amount of immobilized cyt-c with electrochemical activity on the 3D macroporous gold electrode showed a minimum at potential of zero charge (PZC) and it increased with increasing net excess surface charge. Higher electric field could influence the conformation and the corresponding properties such as direct electrochemistry, bioactivity, and surface character of the adsorbed cyt-c molecules. However, high external electric field leads to damage of the protein secondary structure. This study provides fundamentals for the fabrication of biomolecular devices, biosensors, and biofuel cells through electrostatic interactions. Figure Two cases are illustrated for the protein immobilized on electrode surfaces: a retention of protein structure under moderate excess surface charge, b denaturation and conformation change of proteins adsorbed at high excess surface charge, e.g., due to the higher external electric field.     

Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts

A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fraction 1 for a1 (where is the Debye–Hückel parameter and a is the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditions 1 and a1are both satisfied.     

Colloidal stability of sulfonated polystyrene model colloids. Correlation with electrokinetic data

In this work we describe the colloid stability of functionalized latexes: two sulfonated polystyrene model colloids with the same particle size and different surface charge densities. The critical coagulation concentration (ccc) was determined in the presence of two electrolytes (11 and 22), being around 0.75 M and 0.075 M, respectively. By the DLVO theory the electrokinetic and colloid stability data were correlated to calculate the Hamaker constant at both experimental conditions. By comparing the experimental and theoretical values of the Hamaker constant, it is possible to get more information about the colloidal stabilization mechanism of functionalized latexes. In the case of sulfonated latexes, the electrostatic and seric contributions occur, with different influence for each latex depending of their surface electric charge.     

The rotational barrier of an enaminonitrile. Charge and energy redistribution during rotation about the C-N bond

Ab initio quantum mechanical techniques were used together with PROAIM electron density partitioning and CHELPG electrostatic potential analysis to examine the charge density distribution of model enaminonitrile1 in its planar ground state and in its two rotational transition states. The barrier to rotation about the C-N bond was calculated to be 15.4 and 15.6 kcal/mole for the two rotational transition states at the HF/6-31G^** level of theory, and was found to originate from a redistribution of electronic kinetic energy between the amino group and the rest of the molecule in a manner similar to that found for formamide and sulfonamide. Similarly, the C-N bond length and amino group electron population were found to depend upon the C-N torsional angle. Electrostatically derived atomic point charges were also examined at each stationary point using the CHELPG program. CHELPG electrostatic potential results were found to represent the traditional external viewpoint of the charge density consistent with a resonance model, while the results from PROAIM calculations were found to describe the underlying charge density and kinetic energy density redistribution responsible for the rotational barrier.     

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 ?₀ 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 ?₀ and ξ potentials are increased.     

Computation of the Madelung constant for hypercubic crystal structures in any dimension

A new method of computing the Madelung constants for hypercubic crystal structures in any dimension \(n\ge 2\) is given. It is shown for \(n\ge 3\) that the Madelung constant may be obtained in a simple, efficient and unambiguous way as the Hadamard finite part of the integral representation of the potential within the crystal which is divergent at any point charge location. Such a regularization method fails in the bidimensional case due to the logarithmic nature of singularities for the potential. In that case, a specific approach is proposed taking in account the scale invariance of the Poisson equation and the existence of a finite horizon for each point charge in the plane. Since a closed-form exact solution for the 2D electrostatic potential may be derived, one shows that the Madelung constant may be defined via an appropriate limit calculation as the mean value of potential energies of charges composing the unit cell.     

Role of coupling operators on open shell RHF equations

We have derived the expressions for the extremum condition of E, corresponding to any wave function. These expressions are given as a function of the spin orbitals. We have carried out the derivation considering the spin orbitals as vectors belonging to an orthonormal basis. The corresponding variational equations have been derived introducing the condition that the norm of the wave function is constant, as the only additional constraint.From the expression obtained for the first variation of the matrix elements of H, as a function of the spin orbitals, we have derived the RHF equations for a simple case.In the present procedure, the couplings between orbitals of different shells appear directly, being defined explicitly, and they may be taken as corresponding with the elements of a Hermitian matrix.The calculations that we have carried out show that the coupling operators defined in the paper give results which are variationally correct.     

Electrical Properties of Cylindrical Reverse Micelle

In this article, accurate analytic expressions of the surface charge density/surface potential and adsorption excesses for cylindrical reverse micelle in a solution of symmetric electrolyte are derived from the nonlinear cylindrical Poisson–Boltzmann equation. These expressions are in good agreement with numerical values and Van Aken's results for cylindrical reverse micelle with high surface potentials and large κa.     

The role of carbon nanotubes on the capacitance of MnO<Subscript>2</Subscript>/CNTs

The electrochemical behavior of MnO₂/carbon nanotubes (CNTs) has been studied by using cyclic voltammetry, galvanostatic charge discharge measurement and electrochemical impedance spectroscopy in 0.5 M Na₂SO₄ solution. The loading mass of CNTs, the potential sweep rate as well as the frequency have been investigated in detail to make clear of their influence on capacitance, resistance, and relaxation time constant. The dependence of the voltammetric surface charge q* on different loading mass of CNTs and potential scan rate has been investigated. With the addition of CNTs, resistance and relaxation time constant of the material are reduced and the rate capability increased. In particular, CNTs is beneficial for the outer surface capacitance contribution of MnO₂. The outer surface capacitance contribution of MnO₂/CNTs (1: 1) can reach 67% total capacitance contribution.     

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.     

Effect of divalent cations on the adhesion rate of cellular surfaces with ionizable groups

The adhesion rate of cells under charge regulation onto a rotating disc with constant potential is investigated theoretically in this paper. In particular, the effect of the presence of divalent carions in the suspension medium on adhesion rate of cells is discussed. By using sheep leucocytes as an illustrative example, it is shown that the presence of divalent cations in the suspension medium has the effect of decreasing the adhesion rate of cells. At a fixed level of ionic strength, the adhesion rate decreases with the increase of the concentration of divalent cations in the suspension medium for the various values of Peclet number andAd parameter given in this paper. For a fixed concentration of cations, the adhesion rate increases with the increase of ionic strength. At high ionic strength, the effect of increasing the concentration of cations on decreasing the adhesion rate of cells is not as high as that at low ionic strength. Applying the concept of Donnan potential, it is found that the magnitude of the electrostatic force between an ion-penetrable cell membrane and a solid surface is much smaller than that for the ion-impenetrable cell membrane.Nomenclature a cell radius (cm) - A Hamaker's constant (erg) - Ad A/kT - C dimensionless cell concentration - D cell diffusion coefficient (cm²/s) - e magnitude of electron charge (statcoul) - F dimensionless interaction force between cell and rotating disc pernkT - h minimum separation distance between cell surface and disc surface (cm) - H dimensionless separation distance between cell surface and disc surfaceh/a - [H ⁺] _r hydrogen ion concentration in the suspension medium (mole dm^–3) - [H ⁺] _s hydrogen ion concentration on the cell surface (mole dm^–3) - Boltzmann's constant (erg K^–1) - K _a dissociation equilibrium constant for acid groups on cell surface (mole dm^–3) - K _b dissociation equilibrium constant for base groups on cell surface (mole dm^–3) - n ionic strength in the suspension medium (ions cm^–3 - Pe Peclet number - q valence of cations - Sa the reciprocal of acidic density on the cell surface (cm²/group) - S _b the reciprocal of basic density on the cell surface (cm²/group) - Sh Sherwood number - T absolute temperature (K) - the fraction of cationic electrolyte in the suspension medium, 01 - reciprocal of Debye length, (cm^–1) - fluid kinematic viscosity (cm²/s) - ×a - l distance between two plate surfaces in Derjuguin's model (cm) - dimensionless total interaction energy between cell surface and disc surface - _vdw dimensionless unretarded van der Waals potential between cell surface and disc surface - _DL dimensionless double-layer interaction potential between cell surface and disc surface - dimensionless electrostatic potential between cell surface and disc surface - rotating speed of the disc (rad/s)     

Surface dissociation constants for solid oxide/aqueous solution systems

Summary An equation for the surface potential ₀ was used to define the surface dissociation constant of surface hydroxyls at a solid oxide/aqueous solution interface.Using the measurements of the surface charge, the Gouy-Chapman theory and crystallo-chemical data for oxides, the calculations of the surface dissociation constants have been carried out. The values of the acidic surface dissociation constants (in minus logarithmic scale) fall in range 8.7±0.8 at ionic strength 1 M and in the range 7.2±0.7 at 10^–3 M KNO₃ These constants exceed by 2 to 5 orders of magnitude the dissociation constants of M(OH) _naq species in solution.With 1 table     

Second-order Impedance in Electrode Kinetics

The kinetics of electrode reactions with a rather severe influence of the EDL structure is studied by nonlinear second-order impedance spectroscopy. Polarization impedance spectra and potential dependences of a nonlinear impedance are obtained for the reaction of electroreduction of the ferricyanide anion on the cadmium and bismuth electrodes in surface-inactive supporting NaF and Na₂SO₄ electrolytes. The results of measurements for the reaction Eu³⁺ + e Eu²⁺ on the bismuth and mercury electrodes are presented. It is shown that such important parameters of EDL as the potential of zero charge and the second derivative of potential with respect to the charge of the electrode surface can be determined directly from experimental curves even under conditions of occurrence of a faradaic process.     

Potentiometric Titrations of Rutile Suspensions to 250°C

A stirred hydrogen electrode concentration cell was used to conduct potentiometric titrations of rutile suspensions from 25 to 250°C in NaCl and tetramethylammonium chloride media (0.03 to 1.1m). Hydrothermal pretreatment of the rutile improved titration reproducibility, decreased titration hysteresis, and facilitated determination of the point of zero net proton charge (pHznpc). These pHznpc values are 5.4, 5.1, 4.7, 4.4, 4.3 (±0.2 pH units), and 4.2 (±0.3 pH units) at 25, 50, 100, 150, 200, and 250°C, respectively. The difference between these pHznpc values and pK_w(the neutral pH of water) is rather constant between 25 and 250°C (−1.45 ± 0.2). This constancy is useful for predictive purposes and, more fundamentally, may reflect similarities between the hydration behavior of surface hydroxyl groups and water. A three-layer, 1pKa surface complexation model with three adjustable parameters (two capacitance values and one counterion binding constant) adequately described all titration data. The most apparent trend in these data for pH values greater than the pHznpc was the increase in proton release (negative surface charge) with increasing temperature. This reflects more efficient screening by Na⁺relative to Cl⁻. Replacing Na⁺with the larger tetramethylammonium cation for some conditions resulted in decreased proton release due to the less efficient screening of negative surface charge by this larger cation.