A new DLVO-R theory: Surface roughness and nanoparticle stability

Conventional theory of surface forces and nanoparticle aggregation assumed particles had smooth surfaces. But real particles have a degree of surface roughness, typically characterized by root mean square roughness, σ. A theory of surface forces can account for the impact of surface roughness chiefly in two distinct ways. Firstly, shorter distances between asperities, which means that short-range noncontact interactions are amplified, be it attractive or repulsive. Secondly, asperities in contact introduce a repulsive contact force. We present simple analytical formulas for these effects. The contact force is determined by the elastic modulus of materials and the average radius r of asperity tips. Contact repulsion exceeds noncontact forces to form a repulsive barrier when surfaces are separated by a distance less than 3-5 σ m. Consequently, the general effect of surface roughness is to impede aggregation or adhesion of nanoparticles. The theory has been tested with measurements of surface forces of titania and hafnia surfaces using atomic force microscopy. Repulsive forces are found even in the case of minimal surface roughness with σ only 0.5-1 nm.