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<σ/2 is calculated in this approximation by considering the saturation limit when all the ions are associated to form dimers and steric hindrance prevents polymerization. The results are in good agreement with Monte Carlo simulations for dipolar dumbbells and compare favorably with the solutions to the MSA and the HNC approximation using the site–site Ornstein–Zernike equation.