Long-range potential forces

We consider first the Maier-Saupe tlieory and its variants. In its original foniiulation, tills tlieory assumed tliat orientational order in nematic liquid crystals arises from long-range dispersion forces which are weakly anisotropic [60, 61 and 62]. However, it has been pointed out [63] tliat tlie fonii of tlie Maier-Saupe potential is equivalent to one in... 

In Chapter 2 the curve of Fig. 7 was introduced, to show the mutual potential energy arising from short-range forces in contrast to that arising from long-range electrostatic forces. To account for the existence of molecules and molecular ions in solution, we need the same curve with the scale of ordinates reduced so as to be comparable with those of Fig. 

On the other hand, if we bring a proton up to the same nucleus, we will have a slightly different behavior. At first, the nucleus will repel the proton due to the long-range Coulomb force. Then, as we bring the proton very near to the surface, the same nuclear attraction will begin to overcome the repulsion. The nuclear attraction will increase until the proton is surrounded by nucleons as in the neutron case, but there will always be a net repulsion from the other protons. The repulsion decreases the overall attraction, and the proton potential energy well will not be... 

The second approach postulates a new chemical species and an equilibrium constant that relates the activity of the new species to the established species. The mechanism of nonspecific adsorption is believed to be due to long-range electrostatic forces on counterions near the charged Ti02 surface. The extent of nonspecific adsorption can be calculated once the electrical potential on the TiOz surface is known (Stone et al., 1993). 

This species is essentially an electron stabilised by the surrounding water molecules. It has been the subject of detailed theoretical studies(35), but can be considered as an electron in a spherical potential well consisting of solvent molecules. Specific short-range solvation effects are thought to be important as well as long-range polarization forces. 

Fig. 10. Standard Gibbs energy profile along the axis of an ion transfer across the liquid-liquid interface in the absence (1) and presence (2) of an additional potential barrier at the interface. The broken line represents the contribution of the long-range electrostatic forces the solid line corresponds to the sum of the long- and short-range contributions X2 Helmholtz planes in the aqueous and the organic solvent phases.

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