Chemistry Reference
In-Depth Information
In what follows we describe a theoretical study to investigate the phase
behaviour of surfactant + biopolymer layers based on the well-known self-
consistent-field (SCF) approach.
16
This method is chosen here as it accounts for
all the possible configurations that the polymer chains can take at the interface.
Also, unlike most previous theoretical studies, the current work focuses on
situations where the mixed surfactants and biopolymers exhibit some degree of
unfavourable unlike interactions. The origins of such interactions are briefly
discussed below.
16.2 Methodology and Model
16.2.1 Self-Consistent-Field Calculations
In SCF theories, the quantities of interest are a set of density profiles,
f
i
(z),
representing the variation of the concentration of each kind of monomer
a
,
belonging to chains of type i, with distance z away from a planar interface. The
interface is assumed to be placed at z
¼
0 and for the purpose of the current
study this is taken to be a solid-liquid interface. The calculations implement an
iterative procedure, which results in the set of concentration profiles that
minimize the free energy of the system. It is this set of profiles which is assumed
to dominate the thermodynamic behaviour of the surface layer. The approxi-
mation is well justified for dense interfacial layers, such as the ones in this study,
where the fluctuations about the most probable profile are generally small.
16
The calculations begin by first choosing a rough starting estimate of the most
probable density profiles. Using these initial concentrations, a set of auxiliary
fields,
c
a
(z), is calculated. These fields represent the sum of interactions that
each kind of monomer feels due to the presence of the neighbouring segments
and the solvent molecules. For a segment of type
a
, at a distance z from the
interface, the field is related to the density profiles by
c
a
ð
z
Þ¼
c
hd
ð
z
Þþ
X
i
:
X
w
ab
f
i
ð
z
Þ
F
i
ð
1
Þ
b
In Equation (1), the bulk concentration of monomers of type
b
, belonging to
species i, is given by F
i
. For any species only present at the interface, of course,
the corresponding value of F
i
is set to zero. The set of parameters
w
ab
defines
the strength of interaction between different monomer kinds (
a
and
b
). From
Equation (1), it is noticed that all the interactions are assumed to be short range
and local. Fields
c
a
(z) also contain a hard-core potential term,
c
hd
(z), that
enforces the incompressibility condition
X
X
f
i
ð
z
Þ¼
X
i
X
F
i
;
ð
2
Þ
i
a
a
which needs to be satisfied at each point z. The value of
c
hd
(z) is the same for all
segments, irrespective of their type.
16
For monomers also in contact with the
solid surface, i.e., at position z
¼
0, there are additional interaction parameters,
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