Unexpectedly Large Decay Lengths of Double-Layer Forces in Solutions of Symmetric, Multivalent Electrolytes

Double-layer forces acting between micron-sized silica particles are measured with the atomic force microscope in solutions of symmetric, multivalent electrolytes. In particular, the 2:2 electrolytes, CuSO₄ and MgSO₄, and the 3:3 electrolyte LaFe(CN)₆ were investigated. For the multivalent electrolytes, the measured decay lengths are substantially larger than the ones expected on the basis of simple Debye-Hückel (DH) theory. These deviations can be explained quantitatively by the formation of neutral ion pairs. The measured surface charge density decreases in magnitude with increasing valence. Both effects are caused by ion-ion correlations, which are not included in the classical DH theory. However, this theory remains applicable, provided one considers the formation of ion pairs in solution and an effective surface charge density. This effective charge is substantially smaller in magnitude than the one of the bare surface. This reduction results from adsorption of counterions, which becomes stronger with increasing valence. These observations reveal that DH theory is applicable even in the presence of multivalent ions, provided the effective parameters are chosen appropriately.