Coarse-grained Hamiltonian and effective one component theory of colloidal suspensions

We develop a theory to trace out the solvent degrees of freedom from the grand partition function of colloid-solvent mixtures. Our approach to coarse-graining is based on density functional formalism of density profile and the grand thermodynamic potential of solvent. The solvent-induced interaction which is many-body in character is expressed in terms of two functionals; one that couples the solvent to the colloidal density distribution and the second represents the density-density correlation function of the solvent. The nature, strength, and range of the potential depend on these functionals and therefore on the thermodynamic state of the solvent. The solvent-induced contribution to free energy functional is also derived. A self-consistent procedure is developed to calculate the effective potential between colloidal particles, colloid-solvent, and colloid-colloid correlation functions. The theory is used to investigate both additive and nonadditive binary hard-sphere mixtures. Results are reported for the two systems for several values of packing fractions eta(b) and eta(s) and particles diameter ratio q = sigma(s)/sigma(b) where symbols b and s refer to colloid and solvent, respectively. Several interesting features are found: The short-range attractive part of the potential shows non-monotonic dependence on eta(b); when eta(b) is increased from zero, initially the potential becomes more attractive but beyond a certain value of eta(b) that depends on q, the attraction starts weakening. The repulsive peaks formed at R similar to (1 + 1/2 nq) where R is a distance between centers of colloidal particles expressed in units of sigma(b) and n is an integer, become stronger on increasing eta(b). These results show that many-body contribution to the effective potential depends in a subtle way on packing fractions eta(b), eta(s), size ratio q, and on nature of the interaction model and makes a non-negligible contribution to the coarse-grained Hamiltonian. (C) 2022 Elsevier B.V. All rights reserved.