Energy of interaction between

No more than one particle may occupy a cell, and only nearest-neighbour cells that are both occupied mteract with energy -c. Otherwise the energy of interactions between cells is zero. The total energy for a given set of occupation numbers ] = (n, of the cells is then... 

The parameter J.j is a measure of the energy of interaction between sites and j while h is an external potential or field common to the whole system. The tenn ll, 4s a generalized work temi (i.e. -pV, p N, VB M, etc), so is a kind of generalized enthalpy. If the interactions J are zero for all but nearest-neighbour sites, there is a single nonzero value for J, and then... 

The two-center two-electron repulsion integrals ( AV Arr) represents the energy of interaction between the charge distributions at atom Aand at atom B. Classically, they are equal to the sum over all interactions between the multipole moments of the two charge contributions, where the subscripts I and m specify the order and orientation of the multipole. MNDO uses the classical model in calculating these two-center two-electron interactions. 

The energy of interaction between a pair of solvent molecules, a pair of solute molecules, and a solvent-solute pair must be the same so that the criterion that = 0 is met. Such a mixing process is said to be athermal. The solvent and solute molecules must be the same size so that the criterion... 

Adsorption Forces. Coulomb s law allows calculations of the electrostatic potential resulting from a charge distribution, and of the potential energy of interaction between different charge distributions. Various elaborate computations are possible to calculate the potential energy of interaction between point charges, distributed charges, etc. See reference 2 for a detailed introduction. 

Dispersive Interactions. For pairs of nonpolar polymers, the intermolecular forces are primarily of the dispersive type, and in such cases the energy of interaction between unlike segments is expected to be closely approximated by the geometric mean of the energies of interaction between the two like pairs (98). In this case, the Flory-Huggins interaction energy between this polymer pair can be expressed in terms of the solubiUty parameters 5 of the pure components. 

Surface Coating. A dense surface coating (encapsulation) that contains no occluded solvent decreases interparticle attraction provided that the coating has a Hamaker constant intermediate between the particle and the Hquid. This is called semisteric stabilization (ST). The energy of interaction between coated spheres is as follows (26) ... 

Fig. 1. Potential energies of interaction between two coUoidal particles as a function of their surface-surface separation, for electrical double layers due...

It is evident that many solutions fall between these limiting categories, with both energetic and entropic effects contributing to solution non-ideality. For example, if the energy of interaction between unlike species in a solution is highly favored over like-like interactions, it is obvious that these interactions will be preferred, a fact which in itself will lead to non-randomness of the packing in the solution. 

Electrostatic potential (Section 1.10) The energy of interaction between a point positive charge and the charge field of a molecule. 

This simple expression can be used to obtain only a semi-quantitative idea of the effect of an alloying element because the assumptions of randomness and a constant pairwise energy of interaction between atoms are only approximations to the truth in most systems. 

The relative strengths of different ionic bonds can be estimated from Coulomb s law, which gives the electrical energy of interaction between a cation and anion in contact with one another ... 

The configuration of the polymer molecule must depend also on its environment. In a good solvent, where the energy of interaction between a polymer element and a solvent molecule adjacent to it exceeds the mean of the energies of interaction between the polymer-polymer and solvent-solvent pairs, the molecule will tend to expand further so as to reduce the frequency of contacts between pairs of polymer elements. In a poor solvent, on the other hand, where the energy of interaction is unfavorable (endothermic), smaller configurations in which polymer-polymer contacts occur more frequently will be favored. 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

It was found in later work that it is precisely the idea of ionic hydration that is able to explain the physical nature of electrolytic dissociation. The energy of interaction between the solvent molecules and the ions that are formed is high enough to break up the lattices of ionophors or the chemical bonds in ionogens (for more details, see Section 7.2). The significance of ionic hydration for the dissociation of electrolytes had first been pointed out by Ivan A. Kablukov in 1891. 

Let J,o be the dipole moment of a solvent molecule and Tq its radius. The electrostatic energy of interaction between the ion and hj solvent molecules in the primary shell when computed per mole of ions can be written as... 

Underpotential Deposition of Metal Atoms Because of the energy of interaction between a foreign substrate and the adsorbed metal atoms formed by discharge, cathodic discharge of a limited amount of metal ions producing adatoms is possible at potentials more positive than the equilibrium potential of the particular system, and also more positive than the potential of steady metal deposition. 

Thus the stability of a colloid is a function of the energy of interaction between the particles. The conventional strategies for the preparation of small precious metal... 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

---