Solution of the associative MSA for the patchy colloidal model with dipole-dipole interaction

An analytical solution of the associative mean spherical approximation (AMSA) for the hard-sphere multi-patch colloidal model with dipole–dipole interaction is derived. The solution is obtained using the Baxter factorization method following the scheme developed by Blum and co-workers to treat nonspherical interactions. This solution is used to build two more approximations: the exponential approximation (EXPA) and the reference AMSA. To access the accuracy of the theoretical predictions we have generated a set of exact computer simulation data for the water-like model with four tetrahedrally arranged patches and compare them against the corresponding theoretical results for the structure, excess internal energy and dielectric constant. Predictions of the reference AMSA are in a good agreement with Monte Carlo predictions. EXPA and AMSA appear to be less accurate with the accuracy of the AMSA similar to that of the regular MSA for the hard-sphere dipolar fluid. Possible extensions of the theory are briefly outlined.