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Chapter 4

The equations for Gouy-Stern-Grahame model are as follows:[16L [17]

σsid=0                                               [4.1]

ψsi=-                                       [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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