In the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework of the past 60 years, colloidal interaction between similarly charged particles has been claimed to be simply repulsive, and an attraction such as the van der Waals interaction is attached to the Coulombic repulsion. Statistical-thermodynamic considerations show that the electrostatic Helmholtz free energy Δ
Fel is generally not equal to the electrostatic Gibbs free energy Δ
Gel for simple ionic solutions, and the difference Δ
Gel–Δ
Fel (corresponding to the electrostatic osmotic pressure
pel) becomes larger with increasing charge number. Thus, it is expected that Δ
Gel–Δ
Fel be large for highly charged macroions. In the DLVO framework, however, Δ
Gel=Δ
Fel was postulated. Sogami showed that a mean field approach reproduced repulsion at the level of Δ
Fel but resulted in (repulsion and) attraction at the level of Δ
Gel. Overbeek’s critique of Sogami theory is shown to be in error. If this criticism were correct, then not only the Sogami theory but also the Debye-Hückel theory would be wrong. The attraction is thus confirmed to exist not only for multi-valent but also mono-valent counterions.
(Communicated by Hiroo INOKUCHI, M.J.A.)
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