Self-Assembled Structures of Amphiphilic Ionic Block Copolymers: Theory, Self-Consistent Field Modeling and Experiment - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 89

Although at low salt concentrations the structural parameters of quasi-neutral
micelles formed by copolymers with an annealing PE block are close to those of
micelles formed by non-ionic block copolymers, the CMC for the former is signifi-
cantly larger than that for the latter. Indeed, the degree of ionization of the annealing
PE blocks in the unimer state of copolymer,

α b , is significantly larger than that of
the copolymers incorporated in micelles. Hence, the association of copolymers into
micelles is accompanied by an additional free energy penalty (recombination of sig-
nificant fraction of counterions with the acidic groups of the annealing PE blocks).
As a result, the CMC increases as a function of N A and

α b according to the equation:

4 / 11 N 1 / 11
A

v 2 / 11
A

2 / 3 6 / 11

ln CMC quasi − neutral ≈− γ ( N B / ϕ ) + γ ( N B / ϕ ) − N A ln ( 1 − α b )

= ln CMC neutral − N A ln ( 1 − α b ) . (103)

Here, the first two terms specify the CMC for equivalent uncharged (neutral) block
copolymer with lengths of blocks, N A and N B :

11 N 1 / 11
A

v 2 / 11
A

2 / 3 6 / 11 4 /

ln CMC neutral ≈− γ ( N B / ϕ ) + γ ( N B / ϕ ) , (104)

and we have neglected the N A ( term in the free energy of the coronae of the

quasi-neutral micelles as well as the contribution due to intramolecular repulsive
interactions and the stretching of the block A in unimers.
Equation ( 103 ) demonstrates that the CMC for quasi-neutral micelles is a
strongly increasing function of

1 − α )

α b , i.e., it is strongly affected by the value of

2 / 3 , quasi-neutral micelles do not
form at any copolymer concentration in the solution.

the bulk pH. When − N A ln ( 1 − α b ) ≥ γ ( N B / ϕ )

7.1.2 Charged Micelles

α b c p , the difference between
the pH in the bulk solution and inside the micellar corona is negligible. At a given
solution pH,

In the opposite limit of high salt concentration, Φ ion

α b is specified according to ( 98 ), and the monomer units of blocks
A in the micellar corona approach their maximal at given pH degree of ionization,
α ≈ α b . The corona is indistinguishable from that formed by quenched PE chains
with a degree of ionization

α b in the salt-dominated regime. The evolution of the
structural parameters of the micelles follows the same trends as described above: the
aggregation number increases and the coronal dimensions decrease upon an increase
in the salt concentration according to ( 87 )and( 89 ), respectively. An increase in α b

(an increase in the pH) enhances repulsive interactions in the corona and thus leads
to a progressive decrease in the aggregation number and an increase in the coronal
dimensions.