Electrical potential profiles

FIG. 11 Schematic illustration of the electric potential profiles inside and outside a nanopore with lipid bilayer membranes separating the internal and external electrolyte solutions. The dotted line is a junction potential representation where the internal potential is shifted. 

FIG. 10 Schematic representation of the proposed surface model (a) the concentration and (b) the electrical potential profiles at the interface of the membrane and aqueous sample solution, x = 0 and 0 are the positions of ions in the planes of closest approach (outer Helmholtz planes) from the aqueous and membrane sides, respectively. (From Ref. 17.)... 

Other resolutions of the Poisson Nernst Planck equations (i.e. using various simplifying assumptions) have been proposed that couple the adsorption, desorption and permeation of ions through a membrane (e.g. [273,274]) as might be observed for a carrier-mediated transport. For example, for a symmetrical membrane (identical electrolyte on both sides of the membrane) and variation in the electrical potential profile given by i//m, /int can be estimated from ... 

Figure 7. Electrical potential profile near the membrane surface. The surface potential is mainly changed by taste substances.

The electrical potential profile for various electrolyte concentrations is plotted in Fig. 3, which shows that its magnitude decreases with increasing electrolyte concentration. The surface potential is more negative than for a uniform... 

In some previous calculations [16-18] of the interactions involving polyelectrolyte chains grafted to two surfaces, the charge of the polyelectrolyte chains was assumed to be constant and this fixed charge density was introduced into a one-dimensional Poisson-Boltzmann equation to calculate the electrical potential profile. All the above treatments involved a unidimensional model. 

Using the boundary conditions (2)-(4), (13), (14), and (16), the Poisson-Boltzmann equations (1) and (15) can be solved numerically to obtain the electrical potential profile. 

Figure 5.17. Electric potential profile yflz) auid field strength profile E(z) in the multilayer Stem model of Bohmer et al.21.

Specific adsorption of anions can give rise to unconventional temperature dependence of Tafel slopes on account of the temperature dependence of the ion adsorption and consequent changes of the structure and electric potential profile across the double layer where the transition state is established. 

C. Rose and S. G. Schulz. Electrical potential profile across rabbit ileum. J. Gen. Physiol. 57 641-662 (1971). 

Figures 16.7 and 16.8 show the electric potential profile for the conditions explained in the legends. The influence of Ad>° on the electric potential distribution is not very critical, but the values of j0 and X strongly affect the absolute values of A< but not its linear dependence with y.

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. ... 

Figure 23. (A) A schematic representation of a cross section of a two-dimensional electric dipole array. (B) Electrical potential profile across a two-dimensional dipole array of infinite dimension, where the dipole array is at the hydrocarbon/vacuum interface. (C) The same dipole array as in (B) except that the dipole array is at the hydrocarbon/aqueous interface in this case.

Fig. 2.6 (a) Schematic of the standard Weston cell and (b) hypothetical electric potential profile in the Weston cell. 

The specific surface o is defined as the area of one surface of the thylakoid membrane per total chlorophyll contained therein. By means of this quantity the specific volume of the membrane from its thickness or the average distance between the plane thylakoid membranes from specific volumes can be estimated. Such distances are required for the computation of the electrical potential profile across thylakoid stacks (If 2). The specific surface has not yet been measured but only inferred from indirect evidence. The value most frequently used is 1.5 m /yumol as estimated by Barber (3). 

The electric potential profile and the flow velocity profile for a particle with a soft permeable coating are qualitatively represented in Figure 10.9. The electrophoretic mobility comprises two terms The first term on the right-hand side of Equation 10.34 represents the contribution that is related to the potential /(x) across -d < x < 0. This term is sensitive to the ionic strength (through k and the / s). The second... 

FIGURE 10.9 Electric potential profile (—) and flow velocity profile (—) for a particle with a soft permeable coating. 

FIGURE 13.5 Top impermeable (a) and permeable (b) sphere models. Bottom schematic electric potential profiles for each case. 

C(X) = 10 M. The flow rate increases sharply with the particle size when the particle is smaller than 160 nm and a small plateau when the particle becomes larger. For macroscale cases, the variety of particle size only changes the locations of the boundaries but never changes the shape and maximum value of the electric potential profiles under the thin EDL assunption. However, for nanoscale, the particle size not only changes the maximum electric potential but also changes the profile shape, as shown in Fig. 19. This is why the current results disagree with the macroscale predictions. This result also suggests that fine porous media can be used to control electric fluids precisely. 

Fig. 4 Electrical Potential Profiles (a) Two-electrode system. In the absence of current, two equilibrium interfacial potentials exist, and the cell potential measured between the two electrodes is the difference between these equilibrium potentials. As shown the equilibrium potentials are the same (as would be the case if the same metal was used for both electrodes), and the cell potential would be zero. Upon passing current, overpotentials develop at both interfaces (one interfacial potential becomes greater, one smaller). The net change in measured cell potential is due to three sources the voltage drop in solution i Rs and two overpotentials rji and r]2- (b) Three-electrode system. The measured potential is between the working electrode and reference electrode. Since no substantial overpotential can be developed at the reference electrode, any change in measured potential upon passing current is due to two sources the overpotential at the working electrodesolution interface, and the solution drop i Rjj, where the uncorrected resistance Rjj is the solution resistance between the WE interface and RE interface...

Bipolar and other electrode configurations have more complex voltage and current patterns and will not be discussed here. I>urand [106] has reviewed solutions for electrical-potential profiles of various systems. 

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