Mechanics of nanoparticle adhesion — A continuum approach

10J. TomasFigure 1. Characteristic spherical particle contact deformation. (a) Approach and (b) elastic contactdeformation (titania, primary particles d = 20–300 nm, surface diameter d S = 200 nm, median particlediameter d 50,3 = 610 nm, specific surface area A S,m = 12 m²/g, solid density ρ s = 3870 kg/m 3 , surfacemoisture X W = 0.4%, temperature θ = 20°C) [148]. Pressure and compression are defined aspositive but tension and extension are negative. The origin of this diagram (h K = 0) is equivalent tothe characteristic adhesion separation for direct contact (atomic center to center distance), and canbe estimated for a molecular force equilibrium a = a 0 = a F=0 . After approaching from an infinite distance–∞ to this minimum separation a F=0 the sphere–sphere contact without any contact deformationis formed by the attractive adhesion force F H0 (the so-called “jump in”). Then the contact maybe loaded F H0 – Y and, as a response, is elastically deformed with an approximate circular contactarea due to the curve marked with Hertz (panel b). The tensile contribution of principal stresses accordingto Huber [42] at the perimeter of contact circle is neglected for the elliptic pressure distribution,drawn below panel b.