Conformations and Solution Properties of Star-Branched Polyelectrolytes - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 40

of an annealing
PE star might become so low that a star macroion releases a noticeable fraction
of its counterions into the surrounding solution. As a result, the increase in local
pH promotes ionization of the branches. The released counterions become more
strongly attracted to the macroion and eventually condense back into its interior.
Therefore, under low salt conditions, an annealing branched macroion stays at the
threshold of ion release, Q

At low salt concentration, however, the degree of ionization α

pN = pN =

= α R / l B . The ion localization condition, α

l B , together with the intrastar osmotic balance condition, R =

2 N ,setthe
scaling dependence for the star size in this so-called annealing charged regime [ 28 ]:

1 /

R / a α

a 2 N
l B p

R =

(50)

The crossover between ( 49 )and( 50 ) specifies the boundary between the

a 2 l B b N 2

≈

annealing osmotic and the annealing charged regimes as α Φ

ion

a 2 l B K a N 2

/

c bH +

1.
Remarkably, in both annealing charged and annealing osmotic regimes, ( 49 )and
( 50 ) predict a decrease in the star size as a function of the number of branches p .
The reason for this is a decrease in the average degree of ionization of the arms upon
an increase in the intramolecular density of the monomers. However, the strong
dependence, R

Φ ion

p − 1 , predicted by ( 49 )and( 50 ) is hardly observable in real or
numerical experiments because of a corresponding increase of the non-electrostatic
(excluded-volume) intramolecular repulsion.
Various scaling regimes of quenched and annealing PE star polymers are summa-
rized in the diagram of states given in Fig. 17 . For an annealing star, in addition to
the annealing osmotic and annealing charged regimes (where the star size R is given
by ( 49 )and( 50 ), respectively), one finds the regime of a charged star ( 13 ), the salt-
dominated regime ( 47 ), and the regime of a neutral star ( 3 ). The latter is specified
in Fig. 17 for theta-solvent conditions,

∼

0. Remarkably, in the charged annealing
regime, the size R of a star polymer does not exhibit a power law dependence on
Φ ion . This might explain why, in contrast to planar brushes, the spherically curved
weak PE colloidal brushes do not demonstrate a distinct increase in R upon an in-
crease in

υ =

Φ ion [ 45 ]. Note that, in a planar geometry, the scaling theory predicts a
salt-induced increase in brush thickness, H

1 / 3
ion

for both the annealing osmotic
and the annealing charged regimes [ 126 ] . Whereas the general theoretical trends
predicted for the annealing planar and quasi-planar brushes were confirmed in a
number of experimental studies [ 45 , 127 - 133 ] , a comprehensive test of annealing
star-like spherical brushes remains a challenging problem. The width of the osmotic
annealing regime is rather limited (see diagram in Fig. 17 ) , and a proper choice of
the relevant parameters ( p , N , and pH) is of crucial importance for detecting the
R

∼ Φ ,

∼ Φ ion dependence, ( 49 ).
The coupling between the ionization of an annealing polyion and its confor-
mation is expected for other branched macroions as well. Recently, this effect
was unambiguously demonstrated for thermoresponsive spherical star-like micelles
of diblock copolymers with a polybasic (PDMAEMA) corona [ 134 ] . Due to the