Fumed silica suspensions in low molecular weight solvents are used in many photonic and microelectronic applications. The rheology of these thixotropic systems plays a major role in the effectiveness of their usage. In this study, we use dynamic rheological measurements to examine the particle–particle and particle–solvent interactions of fumed silica with hydrophilic and hydrophobic surface groups dispersed in both polar and nonpolar solvents, polypropylene glycol and mineral oil, respectively. We find the mineral oil-based suspensions to have a frequency-independent elastic modulus (G′) for all solids concentration, whereas the polypropylene glycol-based systems exhibit a ‘‘sol–gel’’ transition to a frequency-independent G′ at high concentrations. The results are explained in terms of different solvent particle mechanisms present in the two systems. The behavior of the mineral oil suspensions are dominated by particle–particle interactions through hydrogen bonds, resulting in a gel structure. The polypropylene glycol systems, on the other hand, are dominated by the interactions of the polar solvent with the fumed silica thereby preventing the formation of a 3D gel network. Static light-scattering experiments are used to probe the microstructure of both suspensions. We find the presence of a gel-like network in mineral oil but not in polypropylene glycol, corroborating the rheological results. In addition, both rheology and light-scattering data for the mineral oil suspensions are consistent with the prediction of a diffusion-limited cluster–cluster aggregation model.

We develop a general formalism for including nonelectrostatic interactions, such as excluded volume interactions, in the Poisson−Boltzmann (PB) equation. The resulting theory can be applied to any boundary condition and is as easy to numerically implement as the original PB equation. As a specific example, we combine the PB equation with the Boublik−Mansoori−Carnahan−Starling equation of state to model charged hard-sphere systems. This theory is applied to a charged sphere immersed in a salt solution, and the electric field and ion distribution about the sphere are computed.

The McMillan−Mayer theory of multicomponent solutions is utilized to formulate a statistical-thermodynamic description of surfactant solution behavior from which quantitative predictions of micelle formation, micellar size distribution, and micellar solution phase separation can be made. Specifically, a model is constructed for the Gibbs free energy of the micellar solution, which is divided into ideal and excess contributions. The advantage of this approach is that it enables a systematic analysis of various models of intermicellar interactions. In this paper, we focus on micelles of nonionic surfactants which exhibit both repulsive and attractive interactions. The repulsive interactions are described using excluded-volume considerations, while the attractive ones are modeled using a mean-field description. Utilizing this statistical-thermodynamic framework, expressions for the chemical potentials of each of the solution components are obtained and used, along with the principle of multiple chemical equilibrium, to calculate the micellar size distribution and its moments. An analysis of the effect of excluded-volume interactions on the monomer and micelle concentrations and on the weight-average aggregation number of micelles which exhibit one-dimensional (cylindrical) growth indicates that these steric interactions promote micelle formation and growth. Interestingly, in the limit of extensive cylindrical micellar growth, we recover the well-known expressions for the micellar size distribution and its moments corresponding to the popular phenomenological “ladder model”, with modified “ladder model” parameters which are explicit functions of the excluded-volume parameters. In addition, quantitative predictions of the critical micellar concentration, the polydispersity of the micellar size distribution, and phase separation characteristics are presented and found to compare favorably with available experimental data for aqueous micellar solutions of alkyl poly(ethylene oxide) nonionic surfactants.

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