Thermodynamics of Hierarchical Aggregation in Pigment Dispersions.

Abstract

Many commercially and industrially important materials aggregate to form nanoscale mass-fractal structures. Unlike hard aggregates such as fumed silica, aqueous pigment-based inks consist of weakly bound nanoparticles stabilized by a surfactant. These soft aggregates can easily break apart and re-form balancing mixing energy and the reduction in surface energy with clustering or aggregation. Rapid thermal motion of small elemental crystallites leads to dense clusters or primary particles. The larger primary particles have slower thermal motion and aggregate into ramified mass fractals to form a dual-level hierarchical structure. It is proposed that the hierarchical structure relies on subtle and competitive equilibria between the different hierarchical structural levels. A new hierarchical thermodynamics model by Vogtt is used. Pigment yellow 14 and pigment blue 15:3 as surfactant-stabilized aqueous dispersions were employed to explore the thermodynamics of nanoparticle hierarchical equilibria. It was demonstrated that reversible nanoparticle aggregation can be described solely by the change in free energy of dissociation and the change in free energy of mixing in the context of a subunit being removed from a cluster. The hierarchical thermodynamics is dominated by the solubility of the dispersing surfactant. At the cloud point for the surfactant, primary particles approach the size of an elemental particle and the degree of aggregation becomes very large. The results indicate that subtle and reproducible control over pigment hierarchical structure and size is possible through thermal equilibration, manipulation of the surfactant properties, and elemental crystallite size.