Bond integral short-range

Physical adsorption (physisorption) occurs when an adsorptive comes into contact with a solid surface (the sorbent) [1]. These interactions are unspecific and similar to the forces that lead to the non-ideal behavior of a gas (condensation, van der Waals interactions). They include all interactive and repulsive forces (e.g., London dispersion forces and short range intermolecular repulsion) that cannot be ascribed to localized bonding. In analogy to the attractive forces in real gases, physical adsorption may be understood as an increase of concentration at the gas-solid or gas-liquid interface imder the influence of integrated van der Waals forces. Various specific interactions (e.g., dipole-induced interactions) exist when either the sorbate or the sorbent are polar, but these interactions are usually also summarized under physisorption unless a directed chemical bond is formed. 

The short-range contribution h il 2) is defined graphically as the subsum of all cluster integrals in a graphical 4>-bond-/o-bond representation of h(l 2) such that points 1 and 2 are connected by a path of /o-bonds, where foil 2) represents the function — 1. One can define in a like manner, or equivalently, by an OZ equation... 

The last term is the short-range repulsion. The two first ones give the covalent energy. For resonance integrals varying as 1// , the equihbrium bond length is equal to ... 

One approach of this category is to solve the integral equations using the Percus-Yevick closure for the system of adhesive hard sphere (AHS) mixtures (17-22). An adhesive hard sphere is a hard sphere that has attractive sites at surface. The attractive interaction on these attractive sites is infinitely strong and infinitesimally short ranged. The Percus-Yevick closime yields an analytical solution for such systems. The adhesive attraction, which resembles the chemical bonding, is used to build up chains by employing the proper connectivity constraints. 

Early approaches include the works of Eck and Dronskowski [22,23], who in their aixCCAD software integrated bond valence terms to derive fictional extra charges, while the interaction is essentially treated as a Coulomb interaction. Shin et al. [24] suggested a bond valence mismatch term in combination with standard Coulombic, short-range repulsion and angle bending terms to describe, e.g., the ferroelectric transition in PbTiOs... 

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