measurements. Relaxation dynamics at different time scales have been studied by
Spruijt et al. [43] on 1:1 PAA/PDMAEMA complexes with different chain lengths,
the same polymers that were used to study the binodal compositions [13] (see
Sect. 1 on the kinetics of polyelectrolyte complex formation). By studying the
storage and loss moduli of these complexes as a function of frequency at different
salt concentrations, curves having the familiar shape of a viscoelastic fluid
(e.g., polymer melt or concentrated polymer solution) were obtained. In these
curves, the storage and loss modulus cross at some typical frequency. At high salt
concentrations, liquid-like behaviour is observed in the experimental frequency
window; here, the deformations relax faster than they are typically applied. Softsolid behaviour is observed at low salt concentrations; relaxation of the
deformations occurs slower than they are typically applied. Interestingly, the salt
concentration influences the absolute values of the moduli, but not the shape of the
curves, which means that the rheological data can be superimposed using two saltdependent shift-factors: the apparent relaxation time t c and the modulus G c . Similar
behaviour is found in polymer melts as function of temperature; here, the procedure
of shifting the data in order to make them coincide is known as “time–temperature
superposition”. Hence, the polyelectrolyte complexes possess the property of
“time–salt superposition”. This finding suggests that the dynamics of electrostatic
complexes is simple in nature. By choosing the shift factors in such a way that the
rescaled frequency equals 1, the apparent relaxation time of polyelectrolyte
complexes as function of the salt concentration and ionic strength can be estimated.
A decrease in salt concentration results in a slightly more than exponential
increase in relaxation time. The two longest polymers show an even stronger
increase in relaxation time at low salt concentration. For common polymers, the
divergence of the relaxation time at low temperatures indicates the glass transition
of the system. Polyelectrolyte complexes at low salt also undergo a glass transition
(see Fig. 4) and become kinetically quenched.
1.4 Entropy, Enthalpy and Free Energy
It has also been observed that certain systems show different growth behaviour as
function of the temperature [45, 46]. Exponentially growing multilayers are more
sensitive to changes in temperature than linearly growing systems. To gain more
insight into this phenomenon, Laugel et al. [47] performed isothermic titration
calorimetry (ITC) to study the entropy (D f S) and enthalpy (D f H) of polyelectrolyte
complex formation. They made an important discovery: the sign of the enthalpy
correlates with the growth behaviour of PEMs. A negative D f H, indicating an
exothermic process, is found in cases of linear growth. Addition of salt results in
a D f H of around zero (slightly negative or positive). Endothermic processes (positive D f H) are observed for systems that typically show exponential growth,
e.g., polyelectrolyte complex formation of two weakly charged polyelectrolytes
above an ionic strength of 150 mM. Similar results were obtained by means of
148
S. Lindhoud and M.A. Cohen Stuart
Spruijt et al. [43] on 1:1 PAA/PDMAEMA complexes with different chain lengths,
the same polymers that were used to study the binodal compositions [13] (see
Sect. 1 on the kinetics of polyelectrolyte complex formation). By studying the
storage and loss moduli of these complexes as a function of frequency at different
salt concentrations, curves having the familiar shape of a viscoelastic fluid
(e.g., polymer melt or concentrated polymer solution) were obtained. In these
curves, the storage and loss modulus cross at some typical frequency. At high salt
concentrations, liquid-like behaviour is observed in the experimental frequency
window; here, the deformations relax faster than they are typically applied. Softsolid behaviour is observed at low salt concentrations; relaxation of the
deformations occurs slower than they are typically applied. Interestingly, the salt
concentration influences the absolute values of the moduli, but not the shape of the
curves, which means that the rheological data can be superimposed using two saltdependent shift-factors: the apparent relaxation time t c and the modulus G c . Similar
behaviour is found in polymer melts as function of temperature; here, the procedure
of shifting the data in order to make them coincide is known as “time–temperature
superposition”. Hence, the polyelectrolyte complexes possess the property of
“time–salt superposition”. This finding suggests that the dynamics of electrostatic
complexes is simple in nature. By choosing the shift factors in such a way that the
rescaled frequency equals 1, the apparent relaxation time of polyelectrolyte
complexes as function of the salt concentration and ionic strength can be estimated.
A decrease in salt concentration results in a slightly more than exponential
increase in relaxation time. The two longest polymers show an even stronger
increase in relaxation time at low salt concentration. For common polymers, the
divergence of the relaxation time at low temperatures indicates the glass transition
of the system. Polyelectrolyte complexes at low salt also undergo a glass transition
(see Fig. 4) and become kinetically quenched.
1.4 Entropy, Enthalpy and Free Energy
It has also been observed that certain systems show different growth behaviour as
function of the temperature [45, 46]. Exponentially growing multilayers are more
sensitive to changes in temperature than linearly growing systems. To gain more
insight into this phenomenon, Laugel et al. [47] performed isothermic titration
calorimetry (ITC) to study the entropy (D f S) and enthalpy (D f H) of polyelectrolyte
complex formation. They made an important discovery: the sign of the enthalpy
correlates with the growth behaviour of PEMs. A negative D f H, indicating an
exothermic process, is found in cases of linear growth. Addition of salt results in
a D f H of around zero (slightly negative or positive). Endothermic processes (positive D f H) are observed for systems that typically show exponential growth,
e.g., polyelectrolyte complex formation of two weakly charged polyelectrolytes
above an ionic strength of 150 mM. Similar results were obtained by means of
148
S. Lindhoud and M.A. Cohen Stuart