Chemical ion association and dipolar dumbbells in the mean spherical approximation

The sticky electrolyte model (SEM) is solved analytically in the mean spherical approximation (MSA) for binding between oppositely charged ions of a symmetrical electrolyte at a distance L=σ/4 and σ/5, where σ is the atomic diameter, extending earlier analytic studies for L=σ, σ/2, and σ/3. The excess energy of a fluid of dipolar dumbbells of elongation L