DLVO Interaction Energies for Hollow Particles: The Filling Matters

A thorough knowledge of the interaction energy between a hollow particle (HP) and a surface or between two HPs is critical to the optimization of HP-based products and assessing the environmental risks of HPs and HP-associated pollutants. The van der Waals (vdW) energy between a HP and a surface is often calculated by subtracting the vdW energies of the inner and outer HP geometries. In this study, we show that this subtraction method is only valid when the interior and exterior fluids are the same, for example, for water-filled HPs (WHPs) dispersed in an aqueous solution. Expressions were developed to calculate the vdW energies for HPs whose interiors were filled with air (AHPs). The vdW energies were then calculated between a planar surface and a spherical or cylindrical WHP and AHP, and between WHPs or AHPs. The vdW attraction between a surface and a WHP was decreased at large separation distances compared to solid particles, and this reduced the depth of the secondary minimum. In contrast, the vdW attraction for AHPs and a surface was significantly reduced at all separation distances, and even became repulsive for thin shells, and this inhibited both primary and secondary minimum interactions. The vdW attraction between WHPs decreased with increasing shell thicknesses, and this reduced aggregation in both primary and secondary minima. In contrast, aggregation of AHPs was increased in both minima with decreasing shell thicknesses because of an increase in vdW attraction. Our theoretical calculations show the evolution of vdW and total interaction energies for HPs with different interior fluids and shell thicknesses. These results help explain various experimental observations such as inhibited attachment and favorable aggregation for AHPs (e.g., carbon nanotubes) and favorable bubble coalescence.