(572c) DLVO Theory Calculations for Spherical or Cubic Nanoparticles--Some Applications to CuPc Pigments

Even though the DLVO theory has been available for about 60 years, its use is often restrained by some calculation complexities, and the lack of reliable Hamaker constants. A new simple dimensionless group formulation of the key equation for the potential energy vs. interparticle distance is presented. Several key dimensionless groups are identified. The repulsive potential energy maximum is calculated analytically for spheres or cubes which are oriented with their faces parallel to each other, in terms of the dimensionless size Rs (sphere) or l (cube) and Hamaker constant A. The Hamaker constant was calculated with a novel combination of an ab initio and an empirical methodology. With the new formulation one can readily determine the interplay of A, Rs (or l), surface potential (taken to be to the zeta potential) and Debye length (related to the ionic strength) on the DLVO- predicted stability.

The predictions allow easy comparisons with experimental results of the colloidal stability of aqueous dispersions of copper phthalocyanine (CuPc). The comparisons reveal that electrostatic forces play a significant role in the dispersion stabilization. Moreover, as the particles come close together for possible coagulation, other forces start playing key roles in the stability.

The new DLVO equations predict that as Rs (or l) decreases, the dispersion should become less stable. Dispersions of cubes in most cases are predicted to be more stable than spheres of the same size (with 2Rs=l).