Energies of Interactions

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

Our discussion of solids and alloys is mainly confined to the Ising model and to systems that are isomorphic to it. This model considers a periodic lattice of N sites of any given symmetry in which a spin variable. S j = 1 is associated with each site and interactions between sites are confined only to those between nearest neighbours. The total potential energy of interaction... 

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... 

Direct ligand-protein interactions. Van der Waals and Coulomb energy of interaction of atoms of ligand with atoms on protein. 

In the reaction field method, a sphere is constructed around the molecule with a radius equal to the cutoff distance. The interaction with molecules that are within the sphere is calculated explicitly. To this is added the energy of interaction with the medium beyond the sphere, which is rnodelled as a homogeneous medium of dielectric constant g (Figure 6.23). The electrostatic field due to the surrounding dielectric is given by ... 

The resultant corrections to the SCF picture are therefore quite large when measured in kcal/mole. For example, the differences AE between the true (state-of-the-art quantum chemical calculation) energies of interaction among the four electrons in Be and the SCF mean-field estimates of these interactions are given in the table shown below in eV (recall that 1 eV = 23.06 kcal/mole). 

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 effect of polarity in enhancing the energy of interaction has been discussed by Kiselev and his associates who distinguish between non-specific adsorption, where only dispersion and repulsive forces are involved 4>d and and specific adsorption, where coulombic contributions (some or all of (p, [Pg.11]

To obtain isolated polymer chains, a solvent must be present. The solvent might be selectively excluded or imbibed by the coil, depending on the free energy of interaction, and thereby perturb the coil dimensions. 

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. 

The total potential energy of adsorption interaction may be subdivided into parts representing contributions of the different types of interactions between adsorbed molecules and adsorbents. Adopting the terminology of Barrer (3), the total energy of interaction is the sum of contributions... 

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...

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

This dispersion interaction must be added to the dipole-dipole interactions between molecules, such as HCl, NH3 and H2O which have a permanent dipole, fi. The magnitude of die dipole moment depends on tire differences in electronegativity of the atoms in the molecule. Here again, the energy of interaction varies as (orientation effect). 

Energy of Interaction of the Solute Molecule with the Stationary Phase... 

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