Electrical double layer frequency potential

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

The electrical double-layer structure at Ga/DMF, In(Ga)/DMF, and Tl(Ga)/DMF interfaces upon the addition of various amounts of NaC104 as a surface-inactive electrolyte has been investigated by differential capacitance, as well as by the streaming electrode method.358 The capacitance of all the systems was found to be independent of the ac frequency, v. The potential of the diffuse layer minimum was independent of... 

The principle behind this investigation is electrochromism or Stark-effect spectroscopy. The electronic transition energy of the adsorbed chromophore is perturbed by the electric field at the electric double layer. This is due to interactions of the molecular dipole moment, in the ground and excited states, with the interfacial electric field induced by the applied potential. The change in transition frequency Av, is related to the change in the interfacial electric field, AE, according to the following ... 

At frequencies below 63 Hz, the double-layer capacitance began to dominate the overall impedance of the membrane electrode. The electric potential profile of a bilayer membrane consists of a hydrocarbon core layer and an electrical double layer (49). The dipolar potential, which originates from the lipid bilayer head-group zone and the incorporated protein, partially controls transmembrane ion transport. The model equivalent circuit presented here accounts for the response as a function of frequency of both the hydrocarbon core layer and the double layer at the membrane-water interface. The value of Cdl from the best curve fit for the membrane-coated electrode is lower than that for the bare PtO interface. For the membrane-coated electrode, the model gives a polarization resistance, of 80 kfl compared with 5 kfl for the bare PtO electrode. Formation of the lipid membrane creates a dipolar potential at the interface that results in higher Rdl. The incorporated rhodopsin may also extend the double layer, which makes the layer more diffuse and, therefore, decreases C. ... 

PDEIS is a new technique based on fast measurements of the interfacial impedance with the virtual instruments [3] that benefits from the efficient synchronization of direct hardware control and data processing in the real-time data acquisition and control [4], The built-in EEC fitting engine of the virtual spectrometer divided the total electrochemical response into its constituents those result from different processes. Thus, just in the electrochemical experiment, we come from the mountains of raw data to the characteristics of the constituent processes - the potential dependencies of the electric double layer capacitance, charge transfer resistance, impedance of diffusion, adsorption, etc. The power of this approach results from different frequency and potential dependencies of the constituent responses. Because of the uniqueness of each UPD system and complex electrochemical response dependence on the frequency and electrode potential, the transition from the PDEIS spectrum (Nyquist or Bode plot expanded to the 3D plot... 

Coalescence frequency J depends on dimensionless parameters k, p, Sa, Sr, t, y, a. The parameter k characterizes relative sizes of interacting drops p is the viscosity ratio of drops and ambient liquid Sa and Sr are the forces of molecular attraction and electrostatic repulsion of drops r is the relative thickness of electric double layer, which depends, in particular, on concentration of electrolyte in ambient liquid y is the electromagnetic retardation of molecular interaction a is relative potential of surfaces of interacting drops. Let us estimate the values of these parameters. For hydrosols, the Hamaker constant is F 10 ° J. For viscosity and density of external liquid take m /s, 10 kg/m. ... 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

We shall restrict our consideration here to the simplest electrochemical case the electrical double layer, which is not complicated by charge transfer or by specific adsorption. At first glance it would seem that, if there is no change in mass and nothing happens in the bulk of the solution in which the electrode is immersed, the EQCM response should be zero. However, essentially all measurements show that in the double-layer region the frequency of the EQCM depends on potential. The effect is rather small—a few Hz for crystals with fundamental frequencies of 5-10 MHz. 

When a metal is in contact with an electrolyte solution, a dc potential occurs which is the result of two processes. These are (1) the passage of metallic ions into solution from the metal, and (2) the recombination of metal ions in the solution with free electrons in the metal to form metal atoms. After a metal electrode is introduced into an electrolyte, equilibrium is eventually established and a constant electrode potential is established (for constant environmental conditions). At equilibrium, a dipole layer of charge (electrical double layer) exists at the metal-electrolyte interface. There is a surface layer of charge near the metal electrode and a layer of charge of opposite sign associated with the surrounding solution. Although diffuse, this dipole layer produces an effective electrical capacitance (Cp) which accounts for the low-frequency behavior of the electrode polarization impedance as discussed in Chapters 2, 3, and 4. 

Electroacoustics — Ultrasound passing through a colloidal dispersion forces the colloidal particles to move back and forth, which leads to a displacement of the double layer around the particles with respect to their centers, and thus induces small electric dipoles. The sum of these dipoles creates a macroscopic AC voltage with the frequency of the sound waves. The latter is called the Colloid Vibration Potential (CVP) [i]. The reverse effect is called Electrokinetic Sonic Amplitude (ESA) effect [ii]. See also Debye effect. 

The electrochemical double layer offers the exceptional possibility of investigating the Stark effect at very high electric fields. Some important progress has been made in the theoretical treatment of the problem. Experimental data of potential effects upon the frequency and/or the intensity of vibrational modes must discriminate between the pure electric field effect and the secondary effect of potential on the coverage and, consequently, on the lateral interactions. 

When voltage U2 is applied at the transducer, a sound wave propagates into the colloid. If the densities of the dispersed and continuous phases differ, relative motion between the colloidal particles and their double layer will result. The combined relative motion will generate an electric field, which is detected as voltage Ui between the electrodes. The measured signals are proportional to the high-frequency electrophoretic mobility As derived by Babchin et al. (28), the frequency-dependent electrophoretic mobility, ix a)), for the case of low potentials, can be expressed by... 

This figure compares with an electrical barrier of 0.28 eV estimated from the point charge model. These values would coincide for a = 0.34. Hence the theory based on the Verwey-Overbeek potential is consistent with experiment. From (4) and (5) the experimental plot of In v versus AF should yield a straight line with the so-called Liley slope. Inserting the numerical values, we find that this slope, with a = 0.34, corresponds to a tenfold increase in frequency of MEPP for each 15.0 mV depolarization. The most recent experimental value on the rat muscle preparation was 12.5 mV, and Liley reported about 16 mV. We can thus conclude that a discussion of the approach of a synaptic vesicle to a presynaptic membrane, which is based on the Verwey-Overbeek theory of the interaction of two double layers, gives reasonable quantitative agreement with the available data on the dependence of V of MEPP on depolarization of the presynaptic membrane. 

Te and Cu monolayers on gold, as well as Ag and Bi monolayers on platinum were obtained by cathodic underpotential deposition and investigated in situ by the potentiodynamic electrochemical impedance spectroseopy (PDEIS). PDEIS gives the graphical representation of the real and imaginary interfacial impedance dependencies on ac frequency and electrode potential in real-time in the potential scan. The built-in analyzer of the virtual spectrometer decomposes the total electrochemical response into the responses of the constituents of the equivalent electric circuits (EEC). Dependencies of EEC parameters on potential, especially the variation of capacitance and pseudocapacitance of the double layer, appeared to be very sensitive indicators of the interfacial dynamics. 

Oscillations may exert a strong effect on adsorption processes in the frictional contact. Adsorption of particles on the electrode with a certain potential is known [23] to occur at a finite speed. Under low oscillation frequencies the adsorption manages to follow the potential and participate in the variation of the interfacial layer structure. At high frequencies the adsorption mechanism does not work, giving place to electrostatic charging of the layer as a condenser, i.e. the generation of the double electric layer (DEL). A mechanical model of the interfacial DEL has been elaborated by Shepenkov [24]. It follows from the model that, if a periodic mechanical force acts on the double layer from the side of the liquid or electrode, the electrode potential will vary periodically with the same excitation frequency. 

The factor (1 in Eq. (2) measures the tangential electric field at the particle siuface. It is this component which generates the electrophoretic or electroacoustic motion. For a fixed frequency, it can be seen from Eq. (4) that (1 +J) depends on the permittivity of the particles and on die function X - Kg/K a, where Ks is the surface conductance of the double layer X measures the enhanced conductivity due to the charge at the particle surface. It is usually small unless the zeta potential is very high, so for most emulsions with large ka, X has a negligible effect. The ratio fp/f is also small for oil-in-water emulsions. Equation (4) can then be reduced to/= 0.5 and hence the dynamic mobility becomes ... 

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