Biomedical Engineering Reference
In-Depth Information
Loop
Bridge
Figure 4.10
Transient network of flowers connected by bridges. Adapted from Semenov et al. (1995) © 1995
American Chemical Society.
close to the brush edge and, by interpenetration of the chains, become similar to the
conformation of a semi-dilute solution. The distance of interpenetration is of the order of
the correlation length of the semi-dilute solution. When brushes are made of telechelic
polymers, each telechelic chain is a dense, highly stretched brush, and can be considered
as two half-chains. However, the possibility of bridge formation in telechelic brushes
gives rise to an additional attraction.
In the micellar structure, the same mechanism of interaction takes place: the coronas of
the two micelles are deformed in the overlapping region, to an extent that depends on the
distance between their centres, and if the aggregation number is assumed to be constant, a
large energy of attraction is derived by analogy with the planar surfaces.
The attractive free energy
Δ
F attract between two
flowers depends on the number of
bridges in the
'
cone of contact
'
. This is much larger than k B T, and is estimated in the
model to vary as
F attract ~ N 0 ~ N agg 0 : 3 k B T
D
;
ð
4
:
17
Þ
where N 0 is the number of bridges between micelles. This large attractive energy leads to
a second virial coef
cient which is negative, meaning that the system phase separates into
a
'
liquid of micelles
'
while the second phase is a correspondingly very dilute solution of
micelles. The
phase are those of a transient gel
network or a physical gel, since micelles are connected by multiple bridges, but the
chains can also disentangle from one micelle and stick to another one.
The important factor which controls the rheology of the solutions is the monomer
concentration c m . At a concentration c min the distance between neighbouring micelles
corresponds to the minimum of the attraction energy. When the monomer concentration
c m is large enough (c m >c min ), a micellar gel can form. Under compression or under shear,
the free energy is increased because the distance between micelles is changed.
Three regimes can be analysed: non-compressed micelles for c m < c min , weakly com-
pressed for c m ~ c min and strongly compressed micelles for c m >> c min . For each regime
flow properties of the
'
liquid of micelles
'
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