Nanometer-ranged attraction induced by multivalent ions between similar and dissimilar surfaces probed using an atomic force microscope (AFM)

Direct force measurements between positively charged amidine latex (AL) and negatively charged sulfate latex (SL) particles are carried out using an atomic force microscope (AFM). Forces between three different pairs, namely AL–AL, AL–SL, and SL–SL, are measured in solutions containing multivalent cationic aliphatic hexamines (N6) and in simple monovalent KCl solutions. The classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) can rationalize the observed force profiles very well, provided the PB equation is solved for the appropriate asymmetric electrolyte and charge regulation effects are included in the analysis. However, the DLVO description is typically valid only at distances beyond several nanometers. At shorter distances, a short-ranged non-DLVO attraction is present, which can be modeled with an exponential force profile. In KCl solutions, the range of this attraction is around 0.3 nm. In N6 solutions, the range of this attraction is about 1.0 nm in the SL–SL system, 0.6 nm in the AL–SL system, and 0.3 nm in the AL–AL system