Self-Assembled Structures of Amphiphilic Ionic Block Copolymers: Theory, Self-Consistent Field Modeling and Experiment - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 106

In Fig. 10 d we show that the CMC depends exponentially on the length N B of
the core-forming block. The slope of this dependence is proportional to the

χ BS ,
and is well documented in the surfactant literature. We note that the dependence
of the CMC on the length of the core block (Fig. 10 d ) is much stronger than that
of the corona (Fig. 10 b ). In passing, we note that the SCF theory assumes that the
chains in the bulk are ideal and are fully surrounded by the solvent. The method
thus ignores the possibility that the core-forming block of unimers is collapsed. In
such a state, the unimer also avoids most contacts with the solvent and we conclude
that the SF-SCF approach overestimates the free energy of unimers. Collapse of the
hydrophobic block of unimer would increase CMC according to ( 31 ), ( 37 ).

9.3 Micelles with Quenched Polyelectrolyte Corona

For block copolymers comprising ionic hydrophilic blocks one has, in addition to
the parameters discussed in the previous section, several new parameters that influ-
ence the micelle characteristics. Here, we focus on how these new parameters, i.e.,
the charge density in the corona and the ionic strength influence the micelle charac-
teristics. In this section we therefore focus on a given molecular composition and we
opt for a symmetric case, A 200 B 200 , and fixed the values for the excluded-volume in-
teractions parameters: 0.

Hence, we choose for the scenario that the ions have similar excluded-volume inter-
actions with the polymer segments as the solvent. Note that in practice ions might
have some specific affinity for either the core or the coronal blocks, and this situation
could be also addressed in frames of the SF-SCF model.
In Fig. 11 we show an example of the relevant radial distributions for an equi-
librium micelle composed of a symmetric ionic/non-ionic diblock copolymer with a

χ BS = χ NaB = χ ClB = χ AB = 1 . 5and χ AS = χ NaS = χ ClS =

a

b

1

0 0.001

0.006

B

X 2

ϕ Ψ

0.8

−0.01 0.0005

0.004

Ψ

ϕ

Na +

q/e

−0.02 0 0.002

q

0.4

Cl −

[V]

X 1

0

−0.03 −0.0005

0.2

0 40

20 60

r

80 100

A

0

−0.04 −0.001

0 20 40 60 80 100 100

0 20 40 60 80

r

r

Fig. 11 ( a ) Radial volume fraction profiles for apolar block B and charged coronal block A with

α = e ). Inset shows radial

distributions for the two markers and for the 1:1 electrolyte for which the bulk concentration is
Φ

0 . 2 (every fifth segment along the coronal block has a negative charge −

= 0 . 001. ( b ) Corresponding radial electrostatic potential profile Ψ ( r ) ( left ordinate ) in volts s

and the dimensionless radial charge density q ( r ) / e ( right ordinate )