Self-Assembled Structures of Amphiphilic Ionic Block Copolymers: Theory, Self-Consistent Field Modeling and Experiment - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 69

where:

R core = (

1 / 3

pN B / ϕ ) (23)

is the radius of micellar core, R corona is the outmost radius of the corona, and
H corona = R core is its thickness. The excess free energy of the core-corona

interface is given by:

R corona −

N B
ϕ

2 / 3

k B T = γ s = γ

p − 1 / 3 F interface ( p ) / , (24)

where:

s = p = ( R core /

2 / 3 p − 1 / 3

N B / ϕ ) (25)

is the area of the core-corona interface per chain.
Finally, the conformational entropy contribution of stretching in the radial direc-
tion of the core-forming block B scales as:

k B T =

R core / F core ( p ) / N B . (26)

3.1.1 Starlike Spherical Non-ionic Micelles

For strongly asymmetric copolymers, N A

N B , the structure of a micelle is con-
trolled by the balance of the coronal free energy, F corona , and the excess free energy
of the core-corona interface, F interface .
The minimization of the free energy with respect to p results in the equilibrium
aggregation number:

4 / 5 ln R corona
R core

− 6 / 5

p eq = γ

6 / 5

( N B / ϕ ) . (27)

Here, R corona = N A p ( 1 − ν ) / 2 v 2ν − 1

is the external radius of the corona, and ν is the

A

Flory exponent for the coronal block A ( ν ≈ 3 / 5and ν = 1 / 2 under good and theta-

solvent conditions, respectively).
With the accuracy of the logarithmic factors, the corona and the core radii are
given by:

5 N B
ϕ

2 ( 1 − ν ) / 5

R corona = N A v 2ν − 1

3 ( 1 − ν ) /

γ (28)

A

and:

5 N B
ϕ

3 / 5

R core = γ

2 /

(29)

respectively.