because of the positive potential of the polycations. The measured increase in pH
indicates that the former effect dominates. At the other extreme of the titration curve,
when a negatively charged macromolecule is introduced into a solution of positively
charged macromolecules (F
À
¼ 0), the opposite effect is seen. Proton release
dominates and the bulk pH decreases.
In the intermediate regime, in the region where polyelectrolyte complex micelles
are present in the system, the increasing and decreasing extremes are connected by
a curve that crosses the initial pH value. The slope of the curve is steepest at F
À
micelle ,
which is also the “isoelectric point” of the complex. Here, the number of positive
charges and negative charges at this composition are the same. Depending on the
potential, the negatively charged groups deprotonate, and the positively charged
groups protonate. The net effect depends on the differences between the pH and the
pK values of the charged groups of the macromolecules. For two isolated oppositely
charged species, the effect is exactly symmetric for pH values halfway between the
two pKs. In that case, the extra protonation of the positive species cancels
deprotonation of the negative species and the pH will stay the same. Hence, for a
symmetric system, at pH ¼
1
2 ðpK anion þ pK cation Þ, one would expect the pH to be
the same at F
À
¼ 0, F
À
¼ 0.5, and F
À
¼ 1. At pH values that are not the average
of the pKs of the system, the pH curve of a titration experiment can be totally
different, but in all cases at F
À
micelle the slope of the curve is the steepest because the
buffering capacity of the system, which comes from free, uncomplexed polyelectrolyte, has a minimum in this point.
2.1.2 Polyelectrolyte Complex Micelles with Protein Molecules
In the previous section, the polyelectrolyte complex micelle formation of anionic
diblock copolymers and cationic homopolymers was discussed. A simple way to
obtain micelles filled with protein molecules is to replace the cationic homopolymer
with positively charged protein molecules. Harada and Kataoka were the first to
apply this procedure [64]. They formed protein-filled micelles by mixing lysozyme
and poly(ethylene glycol)–poly(aspartic acid) block copolymers.
Polyelectrolyte complex micelles consisting of protein molecules and diblock
copolymers only, contain thousands of protein molecules. One would expect that
when used as nanoreactors, not all the protein molecules would be accessible to
the substrate molecules. A way to down-regulate the number of protein molecules
inside the polyelectrolyte complex micelles is by diluting them with like-charged
homopolymers. Using this procedure it was found that an excess of homopolymer
leads to the formation of stable micelles with protein molecules in the core [62].
Protein-filled micelles consisting of like-charged diblock copolymers together
with protein molecules and homopolymers of opposite charge were unstable
because of macroscopic complex formation between the homopolymer and protein molecules [1].
By making use of three components, the way the components are mixed may
become important. Two different systems, one for incorporating negatively charged
Relaxation Phenomena During Polyelectrolyte Complex Formation
155
indicates that the former effect dominates. At the other extreme of the titration curve,
when a negatively charged macromolecule is introduced into a solution of positively
charged macromolecules (F
À
¼ 0), the opposite effect is seen. Proton release
dominates and the bulk pH decreases.
In the intermediate regime, in the region where polyelectrolyte complex micelles
are present in the system, the increasing and decreasing extremes are connected by
a curve that crosses the initial pH value. The slope of the curve is steepest at F
À
micelle ,
which is also the “isoelectric point” of the complex. Here, the number of positive
charges and negative charges at this composition are the same. Depending on the
potential, the negatively charged groups deprotonate, and the positively charged
groups protonate. The net effect depends on the differences between the pH and the
pK values of the charged groups of the macromolecules. For two isolated oppositely
charged species, the effect is exactly symmetric for pH values halfway between the
two pKs. In that case, the extra protonation of the positive species cancels
deprotonation of the negative species and the pH will stay the same. Hence, for a
symmetric system, at pH ¼
1
2 ðpK anion þ pK cation Þ, one would expect the pH to be
the same at F
À
¼ 0, F
À
¼ 0.5, and F
À
¼ 1. At pH values that are not the average
of the pKs of the system, the pH curve of a titration experiment can be totally
different, but in all cases at F
À
micelle the slope of the curve is the steepest because the
buffering capacity of the system, which comes from free, uncomplexed polyelectrolyte, has a minimum in this point.
2.1.2 Polyelectrolyte Complex Micelles with Protein Molecules
In the previous section, the polyelectrolyte complex micelle formation of anionic
diblock copolymers and cationic homopolymers was discussed. A simple way to
obtain micelles filled with protein molecules is to replace the cationic homopolymer
with positively charged protein molecules. Harada and Kataoka were the first to
apply this procedure [64]. They formed protein-filled micelles by mixing lysozyme
and poly(ethylene glycol)–poly(aspartic acid) block copolymers.
Polyelectrolyte complex micelles consisting of protein molecules and diblock
copolymers only, contain thousands of protein molecules. One would expect that
when used as nanoreactors, not all the protein molecules would be accessible to
the substrate molecules. A way to down-regulate the number of protein molecules
inside the polyelectrolyte complex micelles is by diluting them with like-charged
homopolymers. Using this procedure it was found that an excess of homopolymer
leads to the formation of stable micelles with protein molecules in the core [62].
Protein-filled micelles consisting of like-charged diblock copolymers together
with protein molecules and homopolymers of opposite charge were unstable
because of macroscopic complex formation between the homopolymer and protein molecules [1].
By making use of three components, the way the components are mixed may
become important. Two different systems, one for incorporating negatively charged
Relaxation Phenomena During Polyelectrolyte Complex Formation
155