Potential energy-distance curves

Fig. 6. Van der Waals potential energy-distance curve showing regions of operation of contact, noncontact, and intermittent contact or tapping-mode afm...

Fig. 20.17 Potential energy-distance curves for a cathodic reaction showing how the potential energy barrier is lowered by when E < p,z.c. The barrier is assumed to be symmetrical so that /S => yi, where 5 is the distance of the O.H.P. from the surface of the electrode. Full curve—no field across double layer dashed curve-potential diflcrence is E and is negative...

FIGURE 14.1 Potential energy-distance curves for reactants and products in a chemical reaction. 

FIGURE 14.2 Potential energy-distance curves for two reactions of the same type. 

When the potential energy-distance curves for the reactants and products are symmetric and have the same slope, we have a = a = 0.5. 

FIGURE 14.3 Schematic potential energy-distance curves of reactants in (1) a normal, (2) a barrierless, (3) an activationless reaction, and (4) potential energy-distance curve for the products. 

The principle of this method is that the initial slope (time = zero) of the optical density-time curve is proportional to the rate of flocculation. This initial slope increases with increasing electrolyte concentration until it reaches a limiting value. The stability ratio W is defined as reciprocal ratio of the limiting initial slope to the initial slope measured at lower electrolyte concentration. A log W-log electrolyte concentration plot shows a sharp inflection at the critical coagulation concentration (W = 1), which is a measure of the stability to added electrolyte. Reerink and Overbeek (12) have shown that the value of W is determined mainly by the height of the primary repulsion maximum in the potential energy-distance curve. 

A different (second) approach may be adopted. The main point in this new approach is that the value of P will be shown to depend on the relative slopes of the potential energy-distance curves representing the energies of the particles (rather than... 

Interesting possibilities arise in these potential energy-distance curves if they are not drawn in the extreme simplification of straight lines (see Fig. 9.33), but with the natural curvature that potential energy-distance relations have. Thus, Fig. 9.33 shows the simplified situation where, from the formula given above for P it can be seen that with approximately equal slopes of the potential energy curves near the intersection point, equal slopes of the value of P will be about one-half, as is often observed. 

Fig. 9.33. Potential-energy-distance curves for (a) a typical electrode reaction, (b) an activationless electrode reaction, and (c) a barrierless electrode reaction. (Reprinted from J. O M. Bockris and S. U. M. Khan, Surface Electrochemistry, Plenum, 1993, p, 278.)...

One equation that does express the shape of the potential-energy-distance curve for the interaction of two particles is the Morse equation24 ... 

Figure 3. Diagram of a potential energy-distance curve to illustrate the condition for defining the critical coagulation concentration...

FIGURE 4.32 Schematic form of the total potential energy-distance curves. 

Fig. 7. Schematic potential energy-distance curves for ionic transitions when film is present on metal surface.

Figure 10.21 (a)-(c) Potential energy-distance curves for different situations. For reference to curve numbers (1)-(5) in (c) see discussion of figure in main text. Adapted from Israelachivili (1985), with permission from Academic Press, Elsevier... 

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