Polyelectrolytes, linear intrinsic viscosities

The highly nonlinear concentration dependence evident in Figure 1.9 makes determination of the intrinsic viscosity by extrapolation of tjsp/c data via Eqs. (1.24) and (1.25) impossible. Cohen and Priel [1990] report observing that linear concentration dependence is observed at concentrations substantially below Cmax. allowing determination of [ ]. Theoretical analysis [Nishida et al., 2001, 2002] suggests that the dominant contribution responsible for the appearance of the peak in the / sp/c versus c plots comes from the intermolecular electrostatic repulsions between polyions. Based on this idea, Nishida et al. [2002] propose a method to determine the intrinsic viscosity of polyelectrolyte solutions at very low ionic strength, by assuming additivity in the contributions of intra- and intermolecular interactions that is. 

Still the coil expansion and the intrinsic viscosity depend on the salt concentration, even for a linear curve progression. For this reason, intrinsic viscosities of polyelectrolytes should be always accompanied by the salt concentration that they were determined at. This is extremely important for the [/j]-M-relationships described in chapter 6. As one can see in Fig. 6.11 theses relationships change for the same polymer, depending on the salt concentration at which the intrinsic viscosity was determined. 

Fig. 5.23. Fuoss plot of the reciprocal reduced viscosity l/rjred a function of the square root of the concentration for the sodium pectinate samples from Fig. 5.18 with different concentrations of sodium chloride.The intersection with the Y-axis is not the reciprocal intrinsic viscosity, the Fuoss plot is rather an empirical method to linearize the reduced viscosity data from polyelectrolytes...

Both the proportionality constant K and the exponent a depend on the polymer-solvent system. For linear polymers in configurations approximating random coils, 0.5 < a < 1.0. For compact polymers, such as latex particles, the exponent can approach 0, while for extended chains, such as polyelectrolytes in pure water, the exponent can approach 2. Once the proportionality constant and exponent have been determined for a given polymer-solvent system (as by calibration against osmotically measured molecular weights), intrinsic viscosity provides a convenient way to estimate molecular weight. 

The linear relation between the reduced viscosity and concentration upon isoionic dilution has been experimentally verified [163-167]. For high salt concentration where x k is fairly constant upon dilution of the polyelectrolyte component, similar to the case of isoionic dilution. Thus there is no maximum and the data may be easily extrapolated to zero concentration in order to determine the intrinsic viscosity. 

Plots of the reduced and inherent viscosities are linear with concentration, at least at low concentrations, in accord with Equations 5.16 and 5.17, and have a common intercept, the intrinsic viscosity (Figure 5.4). Exceptions occur with polyelectrolytes, where the degree of ionization and, therefore, the chemical nature of the polymer changes with concentration. 

The linear regression coefficients (R ) for equations were determined. Parameters obtained by fitting the data in Fedors model are presented in Table 20.3 [44]. In our previous study we observed that the higher the DS, then the higher the intrinsic viscosity ([n]) at the same temperature, and [q] was also dependent on the properties of the solvent [44]. The polymer concentration parameter (Cni) in the Fedors correlation depends on solvent quality and molecular interaction, which shows that DMAc is a strong solvent for SPEEK (Table 20.2). The values of parameter B in the Fouss-Strauss correlation also depends on the polyelectrolyte-solvent interaction this again indicates strong interaction between SPEEK and DMAc. 

It was found earlier by experiment and theory that the viscosity intrinsic of polyelectrolyte solutions is nearly linear with the reciprocal square root of the ionic strength over a certain range, such as... 

Some of the relevant questions primarily motivated by scientific interest are the following. How is the size of a polyelectrolyte affected by molecular weight, intrinsic stiffness, solvent quality, or ionic strength Which observables are well characterized by coarse-grained quantities such as a linear charge density, and which depend on chemical details How are dynamic quantities like viscosity or electrophoretic mobility related to static properties of poly electrolytes ... 

---