Thermodynamics of Hierarchical Aggregation in Pigment Dispersions.

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.

Enthalpy and Entropy of Scission in Wormlike Micelles.

The free scission energy is the thermodynamic parameter that governs the contour length of wormlike micelles (WLMs). It is the contour length and the propensity to coil and entangle that determine the viscoelastic properties of this commercially important substance class. The free scission energy Δ Fsc and the associated change in enthalpy Δ Hsc and entropy Δ Ssc on scission have been determined for a mixed anionic/zwitterionic surfactant system (sodium laureth sulfate and cocamidopropyl betaine) at various salt concentrations (3-5 wt % NaCl). Both enthalpy Δ Hsc and entropy Δ Ssc changes decrease linearly with increasing NaCl concentration. At NaCl concentrations above 4 wt %, Δ Ssc even adopts negative values. The term TΔ Ssc decreases more rapidly than Δ Hsc around room temperature and causes the observed elongation of WLMs upon addition of NaCl. It is suggested that Δ Ssc is initially positive due to fewer bound counterions per surfactant molecule at end caps compared to the intact, cylindrical parts before scission, leading to a net release of ions upon scission. Negative values of Δ Ssc are attributed to hydrophobic hydration occurring at the end caps at high salt concentrations. 23Na NMR measurements indicate the presence of immobilized ions, supporting a previously proposed ion-cloud model based on neutron scattering results.

Structural Emergence in Particle Dispersions.

Particle dispersions, such as pigment-based inks, comprise weakly bound, milled nanoparticles. The properties of these pigments depend on both their chemical composition and a rather complex structural hierarchy which emerges from these dispersions. The emergence of structure under semidilute conditions is related to the structure of the dilute particles, the particle spacing (mesh size), processing history, and the interaction potential. Kinetic simulations could predict such emergence using these input parameters. In this paper, organic pigments are studied as an example of the importance of emergent structure to predict properties such as brilliance and opacity. Organic pigments are used to impart color to commercial inks, plastics, coatings, and cosmetics. In many cases, dilute pigments are mass fractal structures consisting of aggregated nanoparticles held together by weak van der Waals forces. In water, surfactant is added to create a pigment dispersion (an ink). The final properties of a pigment emerge from a complex interplay between aggregation and dispersion of aggregates as a function of concentration. Samples of the organic pigment yellow 14, PY14, were milled to four primary particle sizes to study the effect on structural emergence. The interaction between surfactant-stabilized PY14 aggregates in an aqueous medium was quantified by the second virial coefficient, A2, which reflects long-range interactions. The degree of aggregation is associated with short-range attractive interactions between primary particles. In this series of pigments, the degree of aggregation increases dramatically with reduction in primary particle size. Concurrently, the second-order virial coefficient, A2, increases reflecting stronger long-range repulsive interactions with particle size. Structural emergence can be understood through the percolation concentration and the filler mesh size. A2 is translated into a repulsive interaction potential for use in dissipative particle dynamics simulations to enable predictive modeling. This description of the interactions between dispersed pigment aggregates allows for a more scientific and predictive approach to understand structural emergence.