Equation of state of ionized monolayers

Abstract

The equation of state of soluble ionized monolayers is discussed and it is concluded that the equation takes the Davies form π = k T A − A 0 + 8 ε N C ( k T ) 3 10 3 π e 2 ( cosh ⁡ e ψ 0 2 k T − 1 ) , irrespective of the presence or absence of foreign neutral salt, provided that Gouy-Chapman's electrical double-layer model applies. The equation is derived by three independent methods; the first is that of the integration of Gibbs' equation, the second is that of an extension of the theory of Derjaquin, Verwey, and Overbeek, and the last is that of an extension of the osmotic pressure theory of Pockels. The question as to whether counterions in diffuse layers contribute to surface pressure and, if they do, whether the contribution is allowed for in the Davies equation is answered as follows: (1) The counterions do contribute to the surface pressure; and (2) the contribution is completely allowed for in this equation, more specifically, in its second term, which is the free energy of electrical double layers.