adsorbed. Apart from this phenomenon, high surface loads can be obtained
by adsorption of protein aggregates (e.g., casein micelles) rather than free
molecules; by formation of a gel layer at the interface (e.g., of gelatin at low
temperature); or by covalent intermolecular cross-linking (e.g., formation of
22 S 22 S 22 bonds between b-lactoglobulin molecules). Generally, lateral
interaction forces act between globular protein molecules in an adsorption
layer, and these forces markedly strengthen with time.
Reversibility of Adsorption. Apparently, the data in Figure 10.13
imply that the Gibbs equation (10.2) does not hold for the protein. As we
have seen, it is valid for the amphiphile. However, the slopes dP/d lncgiven
in the figure differ only by a factor 2 between the two surfactants, whereas
the values ofG?differ by two orders of magnitude. The explanation is not
fully clear. Application of the Gibbs equation to polymers is anyway
questionable, because it is generally not known what the relation is between
concentration (c) and activity (a) of the surfactant. Moreover, proteins and
other polymers are virtually always mixtures.
As indicated in Figure 10.13 by an arrow on theG–ccurve, it appears
as if lowering the solution concentration does not lead todesorptionof
protein, which would also defy the Gibbs equation. This observation is
based on washing experiments, where an O–W emulsion is diluted with
solvent and then concentrated again by centrifuging; repeating this a few
times may be expected to remove all protein, but it does not. This is mainly
because a very low value ofccan hardly be reached. Assume that after
dilution of the emulsion we would havec¼0,j¼0.01,d 32 ¼0.6mm, and
G?¼ 10 ^7 mol?m^2 ; the total concentration of protein in the emulsion then
is 0.01 mol?m^3. Consequently, only 0.3%of the adsorbed protein would
have to desorb to reach 3? 10 ^5 mol?m^3 in solution, which is roughly the
equilibrium concentration. A decrease inGby 0.3%cannot, of course, be
determined. It would take of the order of 50 washings to achieve significant
desorption. Moreover, desorption tends to be very slow. One reason is the
very large decrease of free energy per molecule upon adsorption, here about
60 timeskBT, which means that the activation free energy for desorption is
very large. Moreover, the concentration difference between the solution
adjacent to the interface and further away from it cannot be larger than
about 3? 10 ^5 mol?m^3 , and this would lead to very slow diffusion away
from the interface [cf. Section 10.4, Eq. (10.6)]. In other words, desorption
would be extremely slow.
Nevertheless, desorption can occur over fairly short time scales, e.g.,
15 min. It has been shown, for instance by using radio-labeled molecules,
that flexible large polymer molecules do exchange between bulk and
interface. Another indication is that two molecules of about equal surface