Integral equation theory applied to atomic force microscopy reveals the number density distribution of colloidal particles on a solid substrate

Abstract Colloidal probe atomic force microscopy (CP-AFM) can measure the force curve between the colloidal probe and the substrate in a colloidal disperse system. The force curve reflects the layer structure of the colloidal particles formed at the solid-liquid interface on the substrate. However, the relationship between the force curve and the layer structure is not simple. Recently, we developed a new method to calculate the number density distribution of colloidal particles on the substrate from the CP-AFM force curve with reasonable accuracy (Journal of Molecular Liquids, 294, 111584 [2019]). This new method assumes that the probe-particle pair potential and the substrate-particle pair potential are the same, but it does not restrict the shape of the potentials. In this study, we applied this method to experimental force curves measured by CP-AFM. The calculated number density distributions were compared with the results of other methods. The results of the new method were closer to the results calculated from the substrate ζ potential than the results of our previous method, which assumes that the probe-particle pair potential is the hard wall potential. We succeeded in obtaining substrate-particle pair potentials from experimental CP-AFM force curves.