Monte Carlo study of micellar solutions with a mixture of mono- and trivalent counterions

Monte Carlo results are presented for a micellar solution where the macroio ns and small ions are modeled as charged hard spheres embedded in a continu ous dielectric. The macroions are charged with 12 negative charges, and the counterions are mono- and/or trivalent cations. The ratio of the diameters of the macroions and counterions is 2.0 nm:0.2 nm. The results for the exc ess internal energy and osmotic coefficient are presented for three differe nt macroion concentrations, c,, in addition to the structural;information. For c(m) = 0.0005 M and c(m) = 0.001 M the osmotic coefficient presented as a function of the composition parameter x(3) exhibits a small maximum arou nd x(3) = 0.25, while the excess energy is a monotonic function of this par ameter. At a higher concentration of macroions, c, = 0.02 M, both the osmot ic coefficient and excess internal energy decrease monotonically with incre asing value of x(3). Changes in the structure of the solution, brought abou t by substitution of monovalent counterions with trivalent ones, are reflec ted in the shape of the macroion-macroion pair-distribution function. The e ffect of the interaction range was also studied; for this purpose the parti cles were allowed to interact via the screened Coulomb potential. It is int eresting that even for a potential of much shorter range than the original Coulomb potential, i.e., for the screening parameter kappa equal to 0.5 nm( -1), we observe a clustering of equally charged macroions in solution.