Chemistry Reference
In-Depth Information
difficulties. This is because the attainment of the final equilibrium interfacial con-
centration of surfactant may be slow, and most common experimental methods such
as the du Nouy ring, the Wilhelmy plate, and the drop and bubble procedures are
dynamic and rely on an increasing interfacial area during the measurement. Such
methods, then, will usually produce results larger than the true equilibrium value.
At equilibrium, the interfacial tension in a system will be uniform. However, in
the dynamic environment of an emulsion system, nonuniformities will arise as a
result of particle deformations in which new surface area will be produced by devia-
tion of the droplet from a perfectly spherical shape. Since the diffusion of new sur-
factant molecules to the interface to lower the interfacial tension will require a finite
amount of time, interfacial tension gradients will develop, leading to the presence
of surface elastic response. If sufficient differences in local interfacial tensions
develop, a rapid spreading of surfactant molecules into regions of higher tension
will occur. Concurrent with the movement of surfactant into regions of high
s
i
,
underlying layers of liquid associated with the surfactant may be dragged along.
Surface elasticity in the sense under consideration cannot exist in a system of
pure liquid phases. In a system containing surfactant molecules, gradients in inter-
facial tension can arise as a result of the formation of new area, as mentioned above,
or because of the loss of interfacial area. In the former case, the time lag between
the formation of new interface and the diffusion of surfactant to that interface will
produce an interfacial tension that is higher than equilibrium. The local value of the
surface excess
i
will fall and the value of
s
i
will approach that of the pure system.
The net effect will be a tendency for the interface to contract, providing a ''healing''
effect to reduce the chance of droplet coalescence. In the case of loss of inter-
facial area, there will be a time lag from the point of compression of the interfacial
film until the excess surfactant molecules can desorb and diffuse away from the
interface.
In addition to the Marangoni effect, surface elasticity is affected by the Gibbs
effect, which is concerned with changes in the physical condition of the liquid
lamella as two drops approach and begin to touch in the process of flocculation
and coalescence. Not only do interfacial tension gradients occur in the film as a
result of the finite time required for the adsorption of surfactant molecules at
newly formed interface, but the film will have a limit to which it can be stretched
before the lamellar interfacial tension increases to the point where the stabilizing
effect of the film is lost. The coefficient of elasticity E for an interfacial film
under such conditions was given by Gibbs as
¼
ds
i
d
A
1
þ d
ln
s
i
=d
ln C
h
ðs
i
=
E
¼
2A
4RT
C
Þ
ð
9
:
6
Þ
þ
2
ds
i
=
dC
where A is the interfacial area occupied by a given quantity of surfactant of con-
centration C and h is the thickness of the adsorbed film. Calculations using Eq. (9.6)
indicate that in a 0.1 M solution of surfactant with a lamellar thickness of 100 nm,
the Gibbs coefficient of elasticity will be on the order of 100 mN/m. An extension
of the film of 1%, therefore, will result in an increase in the interfacial tension of
