Chemistry Reference
In-Depth Information
SDS, R-Na, and NaCl, for example, the Gibbs equation [2.40] may be written as
(Adamson and Gast, 1997; Birdi, 1989; Chattoraj and Birdi, 1984):
−dγ = Γ
RNa
dμ
RNa
+ Γ
NaCl
dμ
NaCl
(4.10)
Further,
μ
RNa
= μ
R
+ μ
Na
(4.11)
μ
NaCl
= μ
Na
+ μ
Cl
(4.12)
It can be easily seen that the following will be valid:
Γ
NaCl
= Γ
Cl
(4.13)
and
Γ
RNa
= Γ
R
(4.14)
It is also seen that following equation will be valid for this system:
-dγ = Γ
RNa
dμ
RNa
+ Γ dμ
Na
+ Γ dμ
Cl
(4.15)
This is the form of the Gibbs equation for an aqueous solution containing three
different ionic species (e.g., R, Na, Cl). Thus, the more general form for solutions
containing i number of ionic species would be
−dγ = Σ Γ
i
dμ
i
(4.16)
In the case of charged films, the interface will acquire
surface charge
. The surface
charge may be positive or negative, depending on the cationic or anionic nature
of the lipid or polymer ions. This would lead to the corresponding
surface poten-
tial
, ψ, also having a positive or negative charge (Chattoraj and Birdi, 1984; Birdi,
1989). The interfacial phase must be electroneutral, which can only be possible if
the inorganic counterions also are preferentially adsorbed in the interfacial phase
(Figure 4.8).
The surface phase can be described by the Helmholtz double-layer theory
(Figure 4.8.) If a negatively charged lipid molecule, R-Na
+
, is adsorbed at the inter-
face AA′, the interface will be negatively charged (air-water or oil-water). According
to the Helmholtz model for the double layer, Na
+
on the interfacial phase will be
arranged in a plane BB′ toward the aqueous phase. The distance between the two
planes, AA′ and BB′, is given by Ù. The charge densities are equal in magnitude but
with opposite signs, Γ (charge per unit surface area), in the two planes. The (negative)
charge density of the plane AA′ is related to the surface potential (negative), ψ
o
, at
the Helmholtz charged plane:
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