Electrical potential versus distance from

Figure 4. Schematic plots of electrical potential, counterion concentration, and co-ion concentration in the diffuse layer versus distance from a charged surface.

Figure 2. (a) The electric potential and (b) the average polarization of a water molecule between two surfaces with a= 5 x 10 4 C/m2, separated by a distance 2d = 40 A, as a function of the position from the middle distance. The average polarization of the water molecules from interface, mo, is calculated from eq 32a. A perturbation 6m = -0.2 D illustrates the effect of surface dipoles, (c, d) The interaction force calculated, at various electrolyte concentrations, from eqs 12a,b with the boundary conditions (19b) and (32a), versus the separation distance, compared to the DLVO predictions. A perturbation 6m = -0.2 D illustrates the effect of surface dipoles. 

Equation 3.7 points out that the variation in the electric field strength (-dy/dx) is related to the second power of the inverse of the thickness of the double layer times /, while Equation 3.8 shows that / decays exponentially with respect to distance (jc) from the surface (Fig. 3.23). A plot of ln( // (/0) versus x produces a straight line with slope k, which is the inverse of the double layer thickness. The assumption ij/0 < 25 mV is not applicable to all soil minerals or all soils. Commonly, clay minerals possess more than 25 mV in surface electrical potential, depending on ionic strength. The purpose of the assumption was to demonstrate the generally expected behavior of charged surfaces. 

Fig. 2. A graph of the radial electric field and potential versus the distance from the plasma column axis in centimeters. The shaded region is the Debye sheath. The electron temperature is 5 eV, m+ is 20 amu, and the radius of the discharge tube is 2.4 cm. The electron temperature is approximately that for neon at 0.2 Torr. ...

FIGURE 1.7. The energy of the available sites versus the distance x from the metallic electrode under the influence of the image force potential and the applied electric field. 

Teissie and coworkers detected rapid lateral movement of protons on a phospholipid monolayer-water interface by a number of measurements fluorescence from a pH indicator dye near the membrane surface, electrical surface conductance, and surface potentiaL These investigators found that the conduction of protons along the surface is considerably faster than proton conduction in the bulk phase (2 to 3 min versus 40 min for a comparable distance in their measurement setup). This novel conduction mechanism is proton-specific, as confirmed by a radioactive electrode measurement as well as by replacement with deuterated water. It is a consequence of cooperativity between neighboring phospholipid molecules the conduction mechanism disappears when phospholipid molecules are not in contact with each other. 

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