# Evaluating the DLVO Model for Non-Aqueous Colloidal Suspensions

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Application of DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory for suspensions utilizing non-aqueous suspension mediums has been tested. Prediction of suspension stability using DLVO theory requires the calculation of the attractive and repulsive forces between the suspended colloids and that the only significant stabilization mechanism present is electrostatic stabilization which was tested. The van der Waals attractive potential was calculated for 12 different colloids in 11 suspending mediums in accord with Lifshitz’s treatment and a new approximation proposing that the material bandgap energy can be used to approximate the Hamaker constant was developed. This treatment requires the complete knowledge of the permittivity as a function of frequency for all the components in the respective suspension. The permittivity data was simplified using a damped oscillator model described by Ninham and Parsegian. All permittivity data was compiled from the literature. Microwave data was tabulated by NIST, infrared parameters were determined from FTIR data, and the ultraviolet/visual parameters were determined via Cauchy plots or estimated by the bandgap. Using the bandgap to approximate the ultraviolet/visual parameters proved to be more accurate than other approximations when compared to the accepted values. It was found that the non-oxide and non-stoichiometric colloids tested had the largest associated van der Waals attractive force. The van der Waals potential calculated for oxide particles was found to follow a direct relationship with the ionic character of the bonding. Repulsive forces were calculated for 12 different colloids in 11 suspending mediums. The calculated repulsive potential generated is a function of both the magnitude of charge generated on each colloid (ζ-potential) and the size of the interacting double-layers. ζ-potential was measured for each suspension using a microelectrophoretic technique and the double-layer thickness was calculated. It was demonstrated that as the polarity of the suspending medium increased, the thickness of the double-layer also increased. A large double-layer thickness was found to directly correlate to the suspension stability. A large double-layer thickness results in a decreased slope of the charge degradation from the colloidal surface to the bulk suspension. This coupled with a large magnitude of surface charge increases the probability of dispersion. Through viscosity measurements, the stability mechanism of each suspension was determined by comparison of the viscosity at a shear rate of 1.0s-1 with the shear thinning exponent. It was determined that, of the suspension mediums tested, heptane, octanoic acid, and poly(ethylene xiv glycol) introduce non-electrostatic stabilization mechanisms significant enough to invalidate the DLVO predictions for suspensions made using those mediums. Consistent with DLVO theory, the total interaction potential was calculated by summation of the repulsive and attractive potentials of each suspension (84 suspensions total) as a function of separation distance. Based upon the results of the summation, the suspension stability can be predicted. 64 of the 84 suspensions were determined to be unstable as the colloids agglomerated in the primary minimum, 11 suspensions were determined to be weakly flocculated, and nine suspensions were found to be stable. Viscosity was used to determine the critical value for the thermal energy barrier and to test the DLVO predictions. The critical value of the thermal energy barrier was found to be 2.0 x 10-6J/m2. Therefore, for suspensions calculated to have a thermal energy barrier less than the critical value, the Brownian motion of the colloids in suspension at 298K were enough to overcome it, resulting in agglomeration at the primary minimum. For suspensions with a thermal barrier larger than 2.0 x 10-6J/m2, the interacting colloids moved into the secondary energy minimum. All suspensions tested in which the thermal energy barrier was less than 2.0 x 10-6J/m2 had a specific viscosity at a shear rate of 1.0s-1 greater than the cut-off viscosity for stability. If the colloids moved into the secondary minimum, the resulting suspension was characterized as either being weakly flocculated or stable. Weakly flocculated suspensions had an equilibrium separation distance of colloids less than 40nm resulting in a viscosity at a shear rate of 1.0s-1 larger than the determined specific viscosity cutoff (1.1x 104), but a shear thinning exponent greater than 1.0. Stable suspensions were defined by the colloids as having an equilibrium separation distance greater than 40nm, resulting in viscosity values at a shear rate of 1.0s-1 smaller than that of the determined cut-off viscosity value.