Mean electric potential

Instead of an exact calculation, Gouy and Chapman have assumed that (4) can be approximated by combining the Poisson equation with a Boltzmann factor which contains the mean electrical potential existing in the interface. (This approximation will be rederived below). From this approach the distribution of the potential across the interface can be calculated as the function of a and from (2) we get a differential capacitance Cqc- It has been shown by Grahame that Cqc fits very well the measurements in the case of low ionic concentrations [11]. For higher concentrations another capacitance in series, Q, had to be introduced. It is called the inner layer capacitance and it was first considered by Stern [1,2]. Then the experimental capacitance Cexp is analyzed according to ... 

The history of PB theory can be traced back to the Gouy-Chapmann theory and Debye-Huchel theory in the early of 1900s (e.g., see Camie and Torrie, 1984). These two theories represent special simplified forms of the PB theory Gouy-Chapmann theory is a one-dimensional simplification for electric double-layer, while the Debye-Huchel theory is a special solution for spherical symmetric system. The PB equation can be derived based on the Poisson equation with a self-consistent mean electric potential tj/ and a Boltzmann distribution for the ions... 

PB equation is based on the mean-field approximation, where ions are treated as continuous fluid-like particles moving independendy in a mean electric potential. The theory ignores the discrete ion properties such as ion size, ion-ion correlation and ion fluctuations. Fail to consider these properties can cause inaccurate predictions for RNA folding, especially in the presence of multivalent ions which are prone to ion correlation due to the strong, long-range Coulomb interactions. For example, PB cannot predict the experimentally observed attractive force between DNA helices in multivalent ion solutions. 

In a mean field theory, the forces acting on each ion because of all the other species in the system can be described by a potential Ui, which can be separated into an electrical part due to the interaction between the charge additional term A Wj, which accounts for all the other interactions between the ion and the rest of the system, not included in ip,... 

The Helmholtz free energy F consists of an electric part Fel and an osmotic part F°sm. In Appendix A of reference [13], the electric part Fel is represented generally as a functional of the mean electric potential (x) as follows ... 

The lower graph of Figure 6.14 represents the behavior of the mean electric potential 4>(x) in the plate configuration at which the potential V6P takes its minimum (2Dj = d = 17.7 nm). The surface potential of all plates is taken to be Os = -4.0. The potential V/ takes a minimum at dl = 17.7 nm, similar to the case of /), = I)r The value d = 17.7 nm is the same as dmiu of Figure 6.9. In this sense, the solution of the many-plate problem does not really introduce any new physics beyond the two-plate problem, and we will not consider it further when we calculate the Gibbs free... 

For some purposes the mean electric potentials at position Tj Is required provided there is an ion o fixed at r. We shall call it Bringing the... 

An expansion in powers of 1 /c is a standard approach for deriving relativistic correction terms. Taking into account electron (s) and nuclear spins (1), and indicating explicitly an external electric potential by means of the field (F = —V0, or —— dAjdt if time dependent), an expansion up to order 1/c of the Dirac Hamiltonian including the... 

Hence, in Eq. (36), which sign, positive or negative, should be chosen depends on the adsorption state of ionic species in the Helmholtz layer if any kind of specific adsorption is neglected or such adsorption is not so intense, the positive sign can be adopted because there is no inversion of the signs of the electric potentials, as depicted in Fig. 23. This means that the sign of the potential difference in the Helmholtz layer is the same as that of the potential difference in the diffuse layer, i.e.,... 

As shown in Fig. 24, the mechanism of the instability is elucidated as follows At the portion where dissolution is accidentally accelerated and is accompanied by an increase in the concentration of dissolved metal ions, pit formation proceeds. If the specific adsorption is strong, the electric potential at the OHP of the recessed part decreases. Because of the local equilibrium of reaction, the fluctuation of the electrochemical potential must be kept at zero. As a result, the concentration component of the fluctuation must increase to compensate for the decrease in the potential component. This means that local dissolution is promoted more at the recessed portion. Thus these processes form a kind of positive feedback cycle. After several cycles, pits develop on the surface macroscopically through initial fluctuations. 

This can be accomplished by applying an electrical potential in the external circuit in such a manner that an emf occurs in opposition to that of the galvanic cell. The opposing emf is varied by means of a potentiometer until the current flow from the cell is essentially zero. Under these conditions, the cell may very well approach reversibility. This is readily tested by changing the direction of the current and allowing an infinitesimally small current flow in the opposite direction. If the cell is reversible, the cell reaction will proceed in the reverse direction with the same efficiency as in the forward direction. For a reversible reaction... 

When a solid material has been placed in an electrolytic solution a certain electrical potential may be built up at the contact surface however, this single potential cannot be measured in the absolute sense, nor can an electrical current be forced through the electrode without the aid of a second electrode. Therefore, electrometry in an electrolyte always requires two electrodes, the poles or terminals of the electroanalytical cell, and can be carried out by means of either non-faradaic or faradaic methods. 

Again, the consideration of the electrical potential in the electrolyte, and especially the consideration of the difference of potential in electrolyte and electrode, involve the consideration of quantities of which we have no apparent means of physical measurement, while the difference of potential in pieces of metal of the same kind attached to the electrodes is exactly one of the things which we can and do measure. 

Potential differences at the interface between two immiscible electrolyte solutions (ITIES) are typical Galvani potential differences and cannot be measured directly. However, their existence follows from the properties of the electrical double layer at the ITIES (Section 4.5.3) and from the kinetics of charge transfer across the ITIES (Section 5.3.2). By means of potential differences at the ITIES or at the aqueous electrolyte-solid electrolyte phase boundary (Eq. 3.1.23), the phenomena occurring at the membranes of ion-selective electrodes (Section 6.3) can be explained. 

Electrochemical interfaces are sometimes referred to as electrified interfaces, meaning that potential differences, charge densities, dipole moments, and electric currents occur. It is obviously important to have a precise definition of the electrostatic potential of a phase. There are two different concepts. The outer or Volta potential ij)a of the phase a is the work required to bring a unit point charge from infinity to a point just outside the surface of the phase. By just outside we mean a position very close to the surface, but so fax away that the image interaction with the phase can be ignored in practice, that means a distance of about 10 5 — 10 3 cm from the surface. Obviously, the outer potential i/ a U a measurable quantity. 

Data collection and communication in the nervous system occurs by means of graded potentials, action potentials, and synaptic coupling of neurons. These electrical potentials may be recorded and analyzed at two different levels depending... 

When the sunlight strikes the semiconductor material, an electrical potential is created by dislodging electrons due to the impact of the photons. Sunlight is made of photons that contain different amounts of photon-energy at different frequencies. The semiconductor material cannot readily be matched to convert all types efficiently. This means that some photons will not be converted at all because they have too little photon energy and some photons will only have a part of their energy converted to electricity because they have too much photon energy. 

Fluorescence is also a powerful tool for investigating the structure and dynamics of matter or living systems at a molecular or supramolecular level. Polymers, solutions of surfactants, solid surfaces, biological membranes, proteins, nucleic acids and living cells are well-known examples of systems in which estimates of local parameters such as polarity, fluidity, order, molecular mobility and electrical potential is possible by means of fluorescent molecules playing the role of probes. The latter can be intrinsic or introduced on purpose. The high sensitivity of fluo-rimetric methods in conjunction with the specificity of the response of probes to their microenvironment contribute towards the success of this approach. Another factor is the ability of probes to provide information on dynamics of fast phenomena and/or the structural parameters of the system under study. 

A cell potential of 0 V means that the cell has no electric potential, and no electrons will flow. You know that you can generate electricity by connecting a zinc electrode and a copper electrode that have been inserted into a lemon. However, you cannot generate electricity by connecting two copper electrodes that have been inserted into the lemon. The two copper electrodes are the same and are in contact with the same electrolyte. There is no potential difference between the two electrodes. 

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