Intermolecular potentials short-range repulsion

In actuality, molecules in a gas interact via long-ranged attractions and short-range repulsive forces. An interaction potential energy function is used to describe these forces as a function of intermolecular distance and orientation. This section introduces two commonly used interaction potential energy functions. 

Fig. 12.1. Schematic illustration of a van der Waals potential as a function of the intermolecular bond distance R measured from the atom X to the center-of-mass of the diatom, I2 in the present case. The orientation angle 7 and the intramolecular I2 bond distance are fixed. The potential parameters governing the long-range attractive and the short-range repulsive branches, namely A, a, and C, depend, in principle, on r and 7.

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

Interpreting bulk properties qualitatively on the basis of microscopic properties requires only consideration of the long-range attractive forces and short-range repulsive forces between molecules it is not necessary to take into account the details of molecular shapes. We have already shown one kind of potential that describes these intermolecular forces, the Lennard-Jones 6-12 potential used in Section 9.7 to obtain corrections to the ideal gas law. In Section 10.2, we discuss a variety of intermolecular forces, most of which are derived from electrostatic (Coulomb) interactions, but which are expressed as a hierarchy of approximations to exact electrostatic calculations for these complex systems. 

We consider first the Maier-Saupe theory and its variants. In its original formulation, this theory assumed that orientational order in nematic liquid crystals arises from long-range dispersion forces that are weakly anisotropic. However, it has been pointed out that the form of the Maier-Saupe potential is equivalent to one in which there are both long-range attractive and short-range repulsive contributions to the intermolecular potential. The general form of this potential is... 

For expUcit results we need, however, to adopt specific models. One such model is that of rebound reactions. Here one assumes tiiat reaction only occurs on close collisions when the reactants are subject to the short-range repulsive part of the intermolecular potential. The rearrangement thus takes place at close quarters and the newly formed products recede under the influence of the short-range repulsion. Hence, the net deflection is that typical of hard-sphere scattering. 

These rules are simple and immediately intuitive, once the electrical characterization of a molecule in terms of its point-like multipoles is accepted. The underlying physical assumption is that the electrostatic interaction is the dominant attractive component of the intermolecular potential determining the angular shape of the dimer, while short-range forces are assumed to provide a repulsive uniform background balancing attraction at the VdW minimum. Monomer size enters the model through rule 7, which corrects for deviation from uniform repulsion when steric interactions occur below the sum of the respective VdW radii.10... 

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