Self-Assembled Structures of Amphiphilic Ionic Block Copolymers: Theory, Self-Consistent Field Modeling and Experiment - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 72

Fig. 2 Self-assembled block-copolymers aggregates of different morphologies: spherical ( i = 3),

cylindrical ( i 1). Hydrophobic blocks B and polyelectrolyte blocks A form the

core and the corona of the micelle, respectively

= 2), lamellar ( i =

The polymorphism of non-ionic block copolymer aggregates was theoretically
analyzed by Zhulina and Rubinstein [ 50 ] , and here we briefly summarize the main
results.
The morphology of a block copolymer aggregate is specified by index i .We
distinguish between spherical ( i

1) mor-
phologies (see Fig. 2 ) . The latter describes lamellae, vesicles, discs, etc. Edge effects
for nonspherical aggregates ( i

= 3), cylindrical ( i = 2 ) , and planar ( i =

= 1 , 2) can be incorporated on the level of correction

terms.
The condition of constant core density ϕ imposes a relation between the core

radius, R core , and the interfacial area per chain, s ( R core ) , in an aggregate of mor-

phology i as:

iN B

s = s ( R core )= i = 1 , 2 , 3 . (38)

ϕ R core

The latter determines the excess interfacial free energy per chain as:

F ( i )

interface (

R core )
k B T

= γ s ( R core ) , i = 1 , 2 , 3 . (39)

The elastic free energy of a stretched block B in the core of an aggregate with
morphology i yields:

F ( i )

b i R core
N B

R core )
k B T

(

core

= , (40)

where:

⎧
⎨

2

π / 8 , i = 1

2

b i = π / 16 , i = 2

3 .

(41)

⎩

2

3 π / 80 , i =

The values of the numerical coefficients in ( 41 ) account for the nonuniform and
nonequal extension of the core blocks in micelles of different morphologies. They
were first calculated by Semenov [ 59 ] for a dense micellar core, ϕ =

1, within