Molecular interactions Born repulsive forces

As already mentioned the present treatment attempts to clarify the connection between the sticking probability and the mutual forces of interaction between particles. The van der Waals attraction and Born repulsion forces are included in the calculation of the rate of collisions between two electrically neutral aerosol particles. The overall interaction potential between two particles is calculated through the integration of the inter-molecular potential, modeled as the Lennard-Jones 6-12 potential, under the assumption of pairwise additivity. The expression for the overall interaction potential in terms of the Hamaker constant and the molecular diameter can be found in Appendix 1. The motion of a particle can no longer be assumed to be... 

DLVO theory explained major principles of coagulation of hydrosols by electrolytes and brought to common grounds all previous observations (primarily of qualitative nature) that related to individual cases and often seemed to be contradictory. In years that followed further extensions of DLVO theory that took into account the possibility of reversible particle aggregation were developed. At very small distances between particles in addition to the usual long-range interaction, molecular attraction and electrostatic repulsion, one must account for other factors that play role at a direct particle contact. The formation of peculiarly structured hydration layers in the vicinity of solid surface, the appearance of elastic forces that are responsible for the Born repulsion between surface atoms at the point of contact, the repulsion between the adsorbed surfactant molecules in contact zone between two particles, all represent the so-called non-DLVO stability factors . This means that more or less deep primary minimum remains finite. 

The Born model is only a rough approximation. Improvements of the method take into account a local permittivity e and effective ionic radii fl= a -I- 5 , where Si is the distance between an ion and an adjacent solvent dipole. More elaborate models include in the calculation the energy of formation of a spherical cavity in the pure solvent into which an ion and its solvation shells can be transferred from the vacuum. Further interactions that can be taken into account result from ion-quadrupole, ion-induced dipole, dipole-dipole, dispersion, and repulsion forces. For nonaqueous electrolyte solutions most of the molecular and structural data needed for this calculation of the solvation energy are unknown, and ab initio calculations have not so far been very successful. Actual information on ion solvation in nonaqueous solutions is based almost exclusively on semiempirical methods and/or the extrathermodynamic assumptions quoted in Section II.C. 

The derivative -dAa h)/dh = is the force per unit cross-sectional area, also known as Derjaguin s disjoining pressure [4,5], Within the context of this definition, both Ao(/t) and W(fi) are positive in the case of a repulsion and negative in the case of an attraction. Molecular attraction forces prevail at long distances, while repulsive forces prevail at very short distances (the so-called Born repulsion). The principal theory that describes the interactions in a thin film is the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which focuses on the analysis of the competitive contribution of molecular (dispersion) attractive forces and electrostatic repulsion to the interaction between surfaces separated by a liquid film. 

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