Theoretical Study of Phase Transition Behaviour in Mixed Biopolymer + Surfactant Interfacial Layers Using the Self-Consistent-Field Approach - Food Colloids: Self-Assembly and Material Science - page 251

The sudden change in the amount of adsorbed surfactant with increas-
ing surfactant bulk concentration is reminiscence of a first-order phase tran-
sition. The existence of a genuine first-order phase transition in any system
implies the presence of metastable states. As mentioned in the previous
section, our numerical scheme should be able to detect such metastable solu-
tions. We have investigated this proposition, by feeding into our SCF calcu-
lations a variety of starting guesses for our initial profiles. Indeed, at and
close to the threshold value for c s , we have found that the SCF calculations
do converge onto a second solution, different from the one shown by the
solid lines in Figures 1 and 2. As one might expect for a metastable state, for
each surfactant bulk concentration the value of the free energy associated
with this secondary solution is greater than the corresponding original solution.
The volume fractions of surfactant and polymer segments in direct contact
with the solid surface, for the second solution, are indicated by the dashed lines
in Figures 1 and 2. It is clear that these metastable solutions form the
continuation of the stable parts of the curves, for the low- and high-coverage
surfactant phases, below and above the threshold value of c s ¼ 0.0265,
respectively.
The existence of a first-order phase transition can further be corroborated
by studying the way in which the difference between the free energy of the
high- and the low-coverage surfactant phase varies with bulk surfactant con-
centration. This is illustrated in Figure 3, where we present the result of the
free energy difference, calculated once again from SCF theory. The graph
clearly shows that, at surfactant bulk concentrations below the transition point,
the high-coverage surfactant phase has a higher free energy and therefore
constitutes the metastable state. At the transition concentration, the graph
passes through zero, indicating that free energies of the two solutions are
Figure 3 The difference in the free energy ( D F) per interfacial area between the
surfactant phases of high- and low-surface coverage. At the transition point,
the two phases have identical free energy per unit area ( D F ¼ 0)