A lattice model on the entropic origin of repulsive potential between interacting ions

We present a lattice model for the origin of the repulsive potential between two interacting particles. The model posits that the vanishing probability of finding two ions confined to a unit volume in a hypothetical lattice, as the interatomic distance which circumscribes the volume of the interacting particles approaches the incompressible size of these particles, decreases the entropy of the system. The derivative equation from the chemical potential expresses the lattice energy in terms of known physical constants. The lattice energy thus calculated show good agreement with the Born-Haber lattice energy. From this new model it is shown that the inverse power-law repulsive potential, aixx→aom, and hard sphere repulsive potential,aixm→∞m, where x is the distance between the two interacting particles, ai the length of the compressible cell, ao the diameter of an incompressible ion core, and m the Born exponent, are both limiting cases of the entropic repulsion. For interacting ions, and by extension fermions, there will be a resultant entropic potential that prevents the formation of fermionic condensates of classically interacting particles. [Display omitted]