Phase Behavior of Magnetic Nanocolloids of Different Sizes Suspended in an Apolar Solvent

Abstract

We employ classical density functional theory (DFT) to investigate the phase behavior and composition of binary mixtures; each compound consists of hard spheres of different sizes with superimposed dispersion attraction. In addition to the dispersion attraction, molecules of one component carry an additional three-dimensional magnetic "spin" where the orientation-dependent spin-spin interaction is accounted for by the Heisenberg model. We are treating the excess free energy using a modified mean-field approximation (second virial coefficient) for the orientation-dependent pair correlation function. Depending on the concentration of the magnetic particles, the strength of the spin-spin coupling, and the size ratio of the particles, the model predicts the formation of ordered (polar) phases in addition to the more conventional gas and isotropic liquid phases. Key features of our model are a particle-size dependent shift of the gas-liquid critical point (critical temperature and density) and a change in the width of the phase diagram. In the near-critical region, the latter can be analyzed quantitativly in terms of an effective critical exponent β that may differ from the classical critical exponent [Formula: see text]; the classical value is attained in the immediate vicinity of the critical point as it must. The deviation between β and β can be linked to nontrivial composition effects along the phase boundaries.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. II. The interplay between molecular packing and orientational order

“…First, we verified by a procedure described in detail in Ref. 36 that over the temperature range accessible through the above protocol, solutions of Eq. (4.9) can be described by…”