Thin Liquid Films - Surface and Colloid Chemistry: Principles and Applications - page 166

To this value one needs to add 60 Å (=10 −10 m) for the two films of oriented soap
molecules, giving a total of 660 Å. The experimental value is 700 Å. The thick-
ness decreases on the addition of electrolytes, as is also suggested by Equation 8.2.
For instance, the value of h ilm is 120 Å in the case of 0.1 M-NaCl. The addition
of a small amount of certain nonionic surface-active agents (e.g., n -lauryl alcohol,
n -decyl glycerol ether, laurylethanolamide, laurylsufanoylamide) to anionic deter-
gent solutions has been found to stabilize the foam. It was suggested that the mode
of packing is analogous to the palisade layers of the micelles and the surface layers
of the foam lamellae.
Measurements have been carried out on the excess tensions, equilibrium thicknesses,
and compositions of aqueous foam films stabilized by either n -decyl methyl sulfoxide
or n -decyl trimethyl ammonium-decyl sulfate, and containing inorganic electrolytes.
It was recognized at a very early stage (Marangoni, 1871; Gibbs, 1878; Birdi,
2002, 2007) that the stability of a liquid film must be greatest if the surface pressure
strongly resists deforming forces. In case the area of the film is extended by a shock
(or vibration), then the change in surface pressure, Π, is given as

Π = −[d Π/dA] [A2 − A1] (8.3)

where A1 and A2 are, respectively, the available areas per molecule of the foam-
stabilizing agent in the original and in the extended parts of the surface. This can
be written as

Π = − A1 [d Π/dA] [A2/A1 − 1] (8.4)

= − A1 [d Π/dA] [j − 1] (8.5)

= Cs −1 [j − 1] (8.6)

where j is the area extension factor. The term (−A[d Π/dA]) is the surface compress-
ibility modulus of the monolayer. For a large restoring pressure Π, this modulus
should be large. In the extended region, the local reduction of the surface pressure to
(Π-Π) results in a spreading of molecules from the adjacent parts of the monolayer
to the extended region. The tension of TLFs can be measured by applying pressure
and measuring the radius of curvature. Then, using the Laplace equation, the tension
can be estimated.
It has been shown (Friberg, 2003; Birdi, 2002, 2008) that there exists a correla-
tion between foam stability and the elasticity [ E ] of the film (i.e., the monolayer). In
order for E to be large, surface excess must be large. Maximum foam stability has
been reported in systems with fatty acid and alcohol concentrations well below the
minimum in γ. Similar conclusions have been observed with n -C 12 H 25 SO 4 Na [SDS]
+ n -C 12 H 25 OH systems that give minimum in γ versus concentration with maximum
foam at the minimum point (Chattoraj and Birdi, 1984). Because of mixed mono-
layer formation it has been found that SDS + C 12 H 25 OH (and some other additives)
make liquid-crystalline structures at the surface. This leads to a stable foam (and liq-