Electrostatic potential energy curve

Rg. 4,131. Angular electrostatic potential-energy curves for rotation of HgO near the ion (ion dipole contribution not... 

FIGURE 5.5. (fl) Because of some strong ion adsorption at the surface, the actual electrostatic potential-energy curve may show a break at the Stern layer (b) additional specific adsorption processes may further alter the curve shape to produce a more rapid dropoff in charge density (curve 1) or even charge reversal (curve 2). 

Figure 13.1 Schematic illustration of the electrostatic potential energy curve.

Let us now consider the same species of molecule situated in a particular solvent and dissociated into a pair of ions. The potential-energy curve will be similar but will have a much shallower minimum, as in Fig. 86, because in a medium of high dielectric constant the electrostatic attraction is much weaker. Let the dissociation energy in solution be denoted by D, in contrast to the larger Dvac, the value in a vacuum. 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

An initial, ultrafast pump pulse promotes IBr to the potential energy curve Vj, where the electrostatic nuclear and electronic forces within the incipient excited IBr molecule act to force the I and Br atoms apart. contains a minimum, however, so as the atoms begin to separate the molecule remains trapped in the excited state unless it can cross over onto the repulsive potential VJ, which intersects the bound curve at an extended... 

Figure 6.3. Schematic potential energy curve describing the interactions between colloidal particles. The overall potential is a sum of an electrostatic repulsive term which arises due to any charged groups on the surface of the particle and the attractive van der Waals term.

Figure 2.3 The potential-energy curve for Li+ + F ionic bond formation according to quantum mechanics (solid line) or classical electrostatics (dotted line).

Figure 2.4 Components of the Li-F potential-energy curve E R) = E (R) + E(NL>(R), showing the localized natural-Lewis-structure model energy E(L> (circles, left-hand scale) and delocalized non-Lewis correction ,(NL) (squares, right-hand scale). The classical electrostatic estimate E (dotted line) is shown for comparison.

Figure 2.13 The potential-energy curve for collinear Li+-F-Li ion-dipole interaction, comparing quantal (solid) and classical electrostatic (dotted) values.

What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

Figure 13.7 Example of potential energy curves for separate VB Hamiltonians and the curve for the lowest energy eigenvalue when the separate Hamiltonians are coupled by an off-diagonal term in a 2x2 Hamiltonian matrix. Note that the difference between the minima for and 7/22 is the term r2 in the example given in the text only if all non-bonded and electrostatic interactions are identical in the two VB representations, and thus the quotes around the label...

To apply these ideas to coagulation phenomena, we must consider what happens to these distributions of potential when two similar surfaces approach one another (Section 11.7). To study coagulation phenomena, we need to compare the electrostatic effects of particle approach with the van der Waals effects discussed in the last chapter. This is done in terms of potential energy curves as discussed in Section 10.2. As we move through the chapter, our interest shifts from potential (volts) to potential energy (joules). It is important to keep track of the difference between the two as the development progresses. 

At the equilibrium distance r, the electrostatic attraction terms balance the repulsion terms. This equilibrium distance is identified as the bond length of the molecule and the curve is known as the potential energy diagram. If no attractive interaction is possible, then no bond formation is predicted and the potential energy curve shows no minimum. 

Figure 12. Diagram illustrating the form of the potential energy curve for two particles with adsorbed layers interacting in the absence of electrostatic repulsion ...

FIG. 12 Potential energy curves for the hectorite-water-hectorite system. The top panel represents the traditional DLVO approach (electrostatic + van der Waals (unretarded) interactions). The bottom panel represents an extended DLVO approach (electrostatic+van der Waals fynretarded) + Lewis acid-base interactions). The experimentally determined ccc 100molc/m3 [61]. 

If the stability of particles at relatively high concentrations of free polymer arises from the presence of a repulsive maximum in the potential energy curve, then it follows that any stability that is imparted by free polymer must be of a kinetic type. Depletion stabilization thus corresponds to thermodynamic metastability. In this regard, it obviously resembles electrostatic stabilization rather than steric stabilization, which usually corresponds to thermodynamic stability. 

---