Another aspect that has been studied is the influence of polyelectrolyte chain
length on PEM formation. Short polymer chains have a tendency to form polyelectrolyte complexes in solution rather than form PEMs. An explanation for this
phenomenon is that the number of charged groups on a polyelectrolyte determines
the number of counterions that can be released. At a certain chain length the entropy
gain due to counterion release is approximately the same as the entropy of free
chains or polyelectrolyte complexes in solution [34].
The complex formation between two weakly charged polyelectrolytes depends
on the pH of the system. At both low and high pH one of the polyelectrolytes is
uncharged (see Fig. 2) and no polyelectrolyte complex formation will occur.
A complication is that the charge density also depends on charged objects in their
vicinity: weakly charged polyelectrolytes are able to mutually influence their
dissociation behaviour [30, 35–39]. This feature will later be discussed in more
detail (see Sect. 2.1.1 on pH during light scattering titrations).
At low ionic strength and when the pH is fixed, three different growth regimes
are observed for PEM formation [30]. At low and high pH, when one of the
polyelectrolytes is fully charged and the other one is very weakly charged, multilayer
formation may occur due to interactions other than electrostatic interactions. For
instance, it is known that PAA forms hydrogen bonds at low pH [40]. This regime is
similar to the first regime of PEM formation for strong polyelectrolytes with low
charge densities. The second regime is observed at a pH where one polymer is
almost fully charged and the other polymer is becoming charged. At this pH range,
exponentially growing PEMs are often observed and thick PEMs are found [30].
In the third regime, thin linearly growing PEMs are found. Here the pH equals the
average pK of the two polyelectrolytes. This point at pH ¼
1
2 ðpK anion þ pK cation Þ is
called the isoprotic point and is indicated in Fig. 2. This regime is the most favourable
for PEM formation [2, 30, 31].
The growth behaviour of PEMs can be controlled by mixing a weakly and a
strongly charged polymer with the same charge (to form one layer). Two growth
regimes are found using this procedure, namely initial exponential growth and later,
from a certain number of layers on, linear growth. The growth rate in the linear
regime is smaller than the growth rate of the exponentially growing regime. The
proposed explanation for this phenomenon is that the number of chains diffusing in
and out of the PEM during each cycle becomes constant [29].
A transition from exponential to linear growth was also observed during multilayer formation of two weakly charged polyelectrolytes [41, 42]. The observation
of the exponential-to-linear transition resulted in a new model, the three-zone
model, which is no longer based on diffusion of polyelectrolytes into and out of
the PEM. The behaviour of the PEM in the first zone, the zone in closest contact to
the substrate, is mainly determined by the properties of the surface. Above a certain
number of layers the third zone is found, in which the multilayer grows exponentially. From a certain layer number on, the film undergoes a restructuring of the
bottom layers of the third zone. The zone in which this restructuring occurs is
referred to as the second zone. This zone hinders the diffusion process of polyelectrolytes within the film and the film starts growing linearly [41]. Diffusion of high
Relaxation Phenomena During Polyelectrolyte Complex Formation
145
length on PEM formation. Short polymer chains have a tendency to form polyelectrolyte complexes in solution rather than form PEMs. An explanation for this
phenomenon is that the number of charged groups on a polyelectrolyte determines
the number of counterions that can be released. At a certain chain length the entropy
gain due to counterion release is approximately the same as the entropy of free
chains or polyelectrolyte complexes in solution [34].
The complex formation between two weakly charged polyelectrolytes depends
on the pH of the system. At both low and high pH one of the polyelectrolytes is
uncharged (see Fig. 2) and no polyelectrolyte complex formation will occur.
A complication is that the charge density also depends on charged objects in their
vicinity: weakly charged polyelectrolytes are able to mutually influence their
dissociation behaviour [30, 35–39]. This feature will later be discussed in more
detail (see Sect. 2.1.1 on pH during light scattering titrations).
At low ionic strength and when the pH is fixed, three different growth regimes
are observed for PEM formation [30]. At low and high pH, when one of the
polyelectrolytes is fully charged and the other one is very weakly charged, multilayer
formation may occur due to interactions other than electrostatic interactions. For
instance, it is known that PAA forms hydrogen bonds at low pH [40]. This regime is
similar to the first regime of PEM formation for strong polyelectrolytes with low
charge densities. The second regime is observed at a pH where one polymer is
almost fully charged and the other polymer is becoming charged. At this pH range,
exponentially growing PEMs are often observed and thick PEMs are found [30].
In the third regime, thin linearly growing PEMs are found. Here the pH equals the
average pK of the two polyelectrolytes. This point at pH ¼
1
2 ðpK anion þ pK cation Þ is
called the isoprotic point and is indicated in Fig. 2. This regime is the most favourable
for PEM formation [2, 30, 31].
The growth behaviour of PEMs can be controlled by mixing a weakly and a
strongly charged polymer with the same charge (to form one layer). Two growth
regimes are found using this procedure, namely initial exponential growth and later,
from a certain number of layers on, linear growth. The growth rate in the linear
regime is smaller than the growth rate of the exponentially growing regime. The
proposed explanation for this phenomenon is that the number of chains diffusing in
and out of the PEM during each cycle becomes constant [29].
A transition from exponential to linear growth was also observed during multilayer formation of two weakly charged polyelectrolytes [41, 42]. The observation
of the exponential-to-linear transition resulted in a new model, the three-zone
model, which is no longer based on diffusion of polyelectrolytes into and out of
the PEM. The behaviour of the PEM in the first zone, the zone in closest contact to
the substrate, is mainly determined by the properties of the surface. Above a certain
number of layers the third zone is found, in which the multilayer grows exponentially. From a certain layer number on, the film undergoes a restructuring of the
bottom layers of the third zone. The zone in which this restructuring occurs is
referred to as the second zone. This zone hinders the diffusion process of polyelectrolytes within the film and the film starts growing linearly [41]. Diffusion of high
Relaxation Phenomena During Polyelectrolyte Complex Formation
145