Spread Lipid Films on Liquid Surfaces (Langmuir–Blodgett Films) - Surface and Colloid Chemistry: Principles and Applications - page 84

0

A S B

FIGure 4.8 Double-layer model (schematic). (See text for details.)

ψ o = [4 π σ δ]/ D (4.17)

where D is the dielectric constant of the medium (aqueous). According to the
Helmholtz double-layer model, the potential ψ decreases sharply from its maximum
value, ψ o , to zero as δ becomes zero (Birdi, 1989, 1999). The variation of ψ is depicted
in Figure 4.9.
The Helmholtz model was found not to be able to give a satisfactory analysis of
measured data. Later, another theory of the diffuse double layer was proposed by
Gouy and Chapman. The interfacial region for a system with charged lipid, R-Na + ,
with NaCl, is shown in Figure 4.10.
As in the case of the Helmholtz model, the plane AA′ will be negative due to
the adsorbed R-species. Therefore, the Na + and Cl − ions will be distributed nonuni-
formly due to electrostatic forces. The concentrations of the ions near the surface can
be given by the Boltzmann distribution, at distance x from the plane AA′, as

C s Na+ = C Na+ [exp − (εψ/kT)] (4.18)

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Z = 1

C = 0.001

C = 0.004

C = 0.01

0

0 100

Distance

FIGure 4.9 Double-layer model (variation of ψ with distance).