Binodal compositions of polyelectrolyte complexes as a function of the ionic
strength have been studied by Spruijt et al. [13]. They used fluorescently
labelled polyacrylic acid (PAA) and poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA) with different chain lengths. The dilute and dense polymeric
phases were separated. The dense phase was weighed and dried and weighed
again to determine the amount of water. The composition of the dilute phase was
measured using a densiometer; the concentration of fluorescently labelled PAA
was determined using UV–visible spectrometry. A phase diagram could be
constructed. It was found that the water content of the complex is independent
of the polymer chain length, far from the critical salt concentration, and that it
increases upon increasing the ionic strength.
The first theory of polyelectrolyte complex formation was proposed by Voorn
and Overbeek [14, 15]. This mean field model was used to describe the binodal
compositions, the water content and the critical salt concentration as a function of
the polymer chain length. This theoretical description uses the Debye–H€ uckel
approximation; the approximations within the derivation of the electrostatic interaction free energy are therefore only valid at low charge densities. The correlation
effects at high concentrations of salt and monomeric units are neglected, and ion
pairing effects such as counterion condensation are not taken into account. Despite
these limitations, the experimental results could be described reasonably well [13].
Over the years, the theory of polyelectrolyte complex formation has been further
developed. The theory of Voorn and Overbeek was later extended by Nakajima and
Sato, who included an interaction parameter w to account for additional interactions
such as hydrophobicity [16]. Correlation effects within the dense complex phase
were included in the theory by Castelnovo and Joanny, which enables prediction of
a critical salt concentration [17]. Kramarenko and Khokhlov included specific ionpairing energies, but their theory ignores the formation of ion pairs between
polyelectrolytes and monovalent counterions; hence, they do not present a salt
dependence of the complex formation [18]. Heterogenous cell models can be
used to describe experimental data on polyelectrolyte complex formation. These
models take the spatial structure of the complex into account [19]. In Sect. 3 on
protein–protein complexation we discuss how such a model can be used to describe
experimental data.
1.1 Strongly and Weakly Charged Polyelectrolytes
The previous section described how the relaxation rate of polyelectrolyte complex
formation may depend on the nature of the charges on the polyelectrolytes. The
polyelectrolytes in Fig. 1 are strongly charged polyelectrolytes, i.e., their charge is
independent of the pH of the system. However, there are many polyelectrolytes that
are weak (e.g., with carbonyl or amine groups), many of natural origin, and their
number of charges is dependent on the pH of the system. Figure 2 shows the charge
of these weakly charged polyelectrolytes as function of the pH schematically.
142
S. Lindhoud and M.A. Cohen Stuart
strength have been studied by Spruijt et al. [13]. They used fluorescently
labelled polyacrylic acid (PAA) and poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA) with different chain lengths. The dilute and dense polymeric
phases were separated. The dense phase was weighed and dried and weighed
again to determine the amount of water. The composition of the dilute phase was
measured using a densiometer; the concentration of fluorescently labelled PAA
was determined using UV–visible spectrometry. A phase diagram could be
constructed. It was found that the water content of the complex is independent
of the polymer chain length, far from the critical salt concentration, and that it
increases upon increasing the ionic strength.
The first theory of polyelectrolyte complex formation was proposed by Voorn
and Overbeek [14, 15]. This mean field model was used to describe the binodal
compositions, the water content and the critical salt concentration as a function of
the polymer chain length. This theoretical description uses the Debye–H€ uckel
approximation; the approximations within the derivation of the electrostatic interaction free energy are therefore only valid at low charge densities. The correlation
effects at high concentrations of salt and monomeric units are neglected, and ion
pairing effects such as counterion condensation are not taken into account. Despite
these limitations, the experimental results could be described reasonably well [13].
Over the years, the theory of polyelectrolyte complex formation has been further
developed. The theory of Voorn and Overbeek was later extended by Nakajima and
Sato, who included an interaction parameter w to account for additional interactions
such as hydrophobicity [16]. Correlation effects within the dense complex phase
were included in the theory by Castelnovo and Joanny, which enables prediction of
a critical salt concentration [17]. Kramarenko and Khokhlov included specific ionpairing energies, but their theory ignores the formation of ion pairs between
polyelectrolytes and monovalent counterions; hence, they do not present a salt
dependence of the complex formation [18]. Heterogenous cell models can be
used to describe experimental data on polyelectrolyte complex formation. These
models take the spatial structure of the complex into account [19]. In Sect. 3 on
protein–protein complexation we discuss how such a model can be used to describe
experimental data.
1.1 Strongly and Weakly Charged Polyelectrolytes
The previous section described how the relaxation rate of polyelectrolyte complex
formation may depend on the nature of the charges on the polyelectrolytes. The
polyelectrolytes in Fig. 1 are strongly charged polyelectrolytes, i.e., their charge is
independent of the pH of the system. However, there are many polyelectrolytes that
are weak (e.g., with carbonyl or amine groups), many of natural origin, and their
number of charges is dependent on the pH of the system. Figure 2 shows the charge
of these weakly charged polyelectrolytes as function of the pH schematically.
142
S. Lindhoud and M.A. Cohen Stuart