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 248

w a s , not explicitly shown in Equation (1), specifying the adsorption energies for
each type of segment.
The next step in the calculation involves the evaluation of the probability of
each possible configuration that can be taken up by different polymer species
under the influence of the fields c a (z). This in turn provides us with a new set of
density profiles, generally different from the starting solution. Due to the very
large number of configurations available to a macromolecule, at first such a
numeration seems like an unfeasible task. However, by using the Scheutjens-
Fleer scheme, 16 such a calculation can be carried out very efficiently. The newly
obtained density profiles are then fed back into Equation (1), and the whole
process is repeated until convergence is obtained. The resulting self-consistent
solutions can be shown to be a local minimum of the free energy, and they are
stable against any small concentration fluctuations about the calculated pro-
files. 16 They may not, however, correspond to the global minimum. That is, the
method does not preclude the calculation of metastable solutions. In fact, it is
precisely this feature of the procedure that the current work seeks to exploit.
A more detailed account of the method and its implementation can be found
in a number of studies 17-22 where SCF calculations have been applied success-
fully to a variety of problems involving food biopolymers.
16.2.2 The Mixture Model
In the model adopted here, both biopolymer and surfactant are represented as
chains consisting of hydrophobic and hydrophilic monomers of equal size. The
presence of both types of monomer is essential to capture the amphiphilic
nature of the molecules. The biopolymer is a diblock copolymer consisting of
100 hydrophobic and 100 hydrophilic segments. To ensure a fixed amount of
polymer at the interface we assume that the last hydrophobic segment of each
chain is anchored onto the solid surface. The much smaller surfactant mole-
cules consist of two hydrophobic and two hydrophilic monomers; as discussed
before, they are free to adsorb or desorb from the surface.
The degree of hydrophobicity of the monomers is specified through their
interactions with the solvent molecules. For simplicity, and to keep the number
of parameters in the model small, we shall assume that the hydrophobic
segments of both biopolymer and surfactant molecules have the same unfav-
ourable interaction with the solvent. This is specified by setting the values of the
appropriate Flory-Huggins w parameters to 1 (in units of kT). As for hydro-
philic segments, the solvent is assumed to be athermal (i.e., w ¼ 0). Both sets of
hydrophobic monomers have a strong affinity for the surface, with adsorption
energies of 1 kT and 3 kT per monomer, for the polymer and surfactant
molecules, respectively.
An important feature of the model studied is the strong degree of incom-
patibility between the macromolecules and the low-molecular-weight surfact-
ants. Thus, the competition to occupy the interface is influenced by factors
beyond simple geometric considerations. Note that, while the actual number of