Chapter 4
The equations for Gouy-Stern-Grahame model are as follows:[16L [17]
σs+σi+σd=0 [4.1]
ψs~ψi=- [4.2]
εb
Vi-Vd=2-^- [4-3]
εd
σd = -sign(σd){2^T^ς0[exp(-zi.e^∕^T)-l]}ιz2 [4.4]
i
b and d: thickness of compact layer and diffuse layer.
σs, σ∣ and σd: charge density of solid surface, Stern layer and diffuse layer.
ψs, ψ∣ and ψd: potential of solid surface, IHP and OHP.
εb and εd: permittivity in compact layer and diffuse layer.
z∣: valency of ion species.
ε: permittivity of bulk solution.
C∕°: concentration of ion species i in the bulk.
Gouy-Stern-Grahame model can be simplified if making assumptions are
made.
1) The shear surface coincides with the Outer Helmholtz Plane (OHP), thus
zeta potential ζ = ψd.
2) The charge of solids surface and Stern layer are combined into net
surface charge, σo = σs + σ,.
Ill
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