Long-range electrostatic forces

Smith P E and v an Gunsteren W F1993. Methods for the Evaluation of Long Range Electrostatic Forces. In van Gunsteren W F, P K Weiner and A J Wilkinson (Editors). Computer Simulation ofBiomolecular Systems. Leiden, ESCOM. 

In this model, reaction is considered to occur preferentially at that position in the aromatic molecule to which the approach of the electrophile causes the smallest increase in zero energy. In molecules possessing polar or dipolar groups, long range electrostatic forces will initially be the most important. 

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. 

In simple systems such as nonpolar films wetting on surfaces, the van der Waals forces play a dominant role, but in more complex systems long-range electrostatic forces are also involved. 

P. E. Smith and W. F. van Gunsteren, Methods for the evaluation of long range electrostatic forces in computer simulation of molecular systems, in Computer Simulation of Biomolecular Systems, vol. 2, W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, eds., Escom, Leiden (1993), pp. 315. 

The function f(I) expresses the effect of long-range electrostatic forces between ions. It is a function of ionic strength, temperature and solvent properties. The empirical form chosen by Pitzer for f(I) is... 

While several investigators contributed substantially to the resolution of this problem, it was the classic work of Debye and Hiickel ( 1) which provided a simple yet adequate explanation of the effect on thermodynamic properties of the long-range electrostatic forces between ions in solution. The experimental work of that era tended to emphasize dilute solutions at room temperature. 

Subsequently major theoretical advances were made, principally by Mayer, in creating an adequate statistical mechanical theory in which both long-range electrostatic forces and short-range forces of whatever origin were properly considered. 

The theory proposed by Debye and Huckel dominated the study of aqueous electrolytes from around 1920 to near the end of the 1950 s. The Debye-Huckel theory was based on a model of electrolyte solutions in which the ions were treated as point charges (later as charged spheres), and the solvent was considered to be a homogeneous dielectric. Deviations from ideal behaviors were assumed to be due only to the long range electrostatic forces between ions. Refinements to include ion-ion pairing and ion... 

QM calculations provide an accurate way to treat strong, long-range electrostatic forces that dominate many solvation phenomena. The errors due to the use of the approximate eontinuum solvation models ean be small enough to allow the quantitative treatment of the solute behavior therefore, this approach is widely used also for evaluating solvent extraetion equilibria of organic molecules [56]. 

A theoretical analysis of the stability of such colloidal crystals of spherical latex particles has been carried out by Marcel ja et al (28.). They employ the Lindemann criterion that a crystal will be stable if the rms thermal displacement of the particles about their equilibrium positions is a small fraction f of the lattice spacing R. Comparison with Monte Carlo simulations shows that f is about 0.1 for "hard crystals, and 0.08 for "soft crystals stabilized by long-ranged electrostatic forces. This latter criterion translates into a critical ratio... 

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). 

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.

As we have already seen, the derivative of (1 - ) at the origin is finite in the case of a non-electrolyte, but infinite for an electrolyte. This behaviour of strong electrolytes is related to the long range electrostatic forces between the ions in the solution.J The statistical theory, in the form developed by Debye and Hiickel, leads to the following expression for the activity coefficient of an ion with a charge 2 , in a very dilute solution in which the ionic strength is I (cf. 27.38) ... 

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