Continuum modelling for adhesion between paint surfaces
A mathematical model is proposed to describe the interaction between graphite, polyester and silica solid substrates whose surfaces are functionalized by hydroxyl group, carboxyl group and fluorine atoms. Assuming a relaxed form of these solid substrates, they are modelled as rectangular boxes, while the functional groups are modelled as boundary surfaces. Using the 6-12 Lennard-Jones potential together with a continuum approximation, the total van der Waals interaction energy is obtained as a function of the interfacial separation distance between two surfaces of the solid substrates. Here, the adhesion energy is the minimum energy calculated at the equilibrium separation distance. Our results reveal that among the substrates studied, graphite has the potential to be used as a base material in paints because of its strong adhesion when it is paired with either polyester or silica surfaces.