Frequency dependence, polyelectrolyte

Although several experimental studies [22, 62, 63] have been reported on p, G, and the compliance of polyelectrolyte solutions, systematic investigations on the frequency dependence is still lacking. 

Dilute polyelectrolyte solutions, such as solutions of tobacco mosaic virus (TMV) in water and other solvents, are known to exhibit interesting dynamic properties, such as a plateau in viscosity against concentration curve at very low concentration [196]. It also shows a shear thinning at a shear strain rate which is inverse of the relaxation time obtained from the Cole-Cole plot of frequency dependence of the shear modulus, G(co). 

A simple theory of the concentration dependence of viscosity has recently been developed by using the mode coupling theory expression of viscosity [197]. The slow variables chosen are the center of mass density and the charge density. The final expressions have essentially the same form as discussed in Section X the structure factors now involve the intermolecular correlations among the polyelectrolyte rods. Numerical calculation shows that the theory can explain the plateau in the concentration dependence of the viscosity, if one takes into account the anisotropy in the motion of the rod-like polymers. The problem, however, is far from complete. We are also not aware of any study of the frequency-dependent properties. Work on this problem is under progress [198]. 

The electrical properties of polyelectrolyte complexes are more closely related to those of biologically produced solids. The extremely high relative dielectric constants at low frequencies and the dispersion properties of salt-containing polyelectrolyte complexes have not been reported for other synthetic polymers. Neutral polyelectrolyte complexes immersed in dilute salt solution undergo marked changes in alternating current capacitance and resistance upon small variations in the electrolyte concentration. In addition, their frequency-dependence is governed by the nature of the microions. As shown in... 

We have not taken into consideration electrophoretic motion of polyions [35,39], However, we have already obtained characteristic features of the electric properties of polyelectrolytes in aqueous solution. Electric polarizability components originating from the fluctuations of condensed counterions show smaller concentration and salt dependence, while those due to a diffuse ion atmosphere, by contrast, a larger dependence. Anisotropy of the electrical polarizability Aa is positive without invoking an enhancement of the longitudinal component by the solvent flow. Simulation on the frequency dependence of the electrical polarizability is in progress to study how the... 

After the very early work by Michaels et al., the next frequency-dependent permittivity spectra of solid polyelectrolyte materials were only pubhshed in 2001 by Durstock and Rubner, who studied PEM prepared by the layer-by-layer technique [27]. The investigated PEM were made of the polycation poly(allylamine hydrochloride) (PAH) and the polyanions PAA or PSS. The authors investigated very systematically the influences of parameters like pH, temperature, salt content, and RH (wet and dry PEM) on the real and imaginary part of the permittivity. 

The above results permit to present a model for the kinetics of counter-ion site binding. This model rests primarily (1) on the similarity which has been found for the frequency dependence of the absorptions due to site binding and to ion-pair formation and (2) on Manning s theory [16] for counter-ion condensation in polyelectrolyte solutions. In this model, site binding between a counter-ion C and a part P of the polyion writes ... 

The time dependence of the stress relaxation modulus in semidilute unentangled solution is sketched in Fig. 8.10. Experimental verification of Rouse dynamics for frequencies smaller than 1/r was shown in Fig. 8.5, for a semidilute unentangled polyelectrolyte solution. 

The colloid particle or polyelectrolyte molecule may possess a permanent dipole moment. Considerable influence of this moment on the magnitude and the sign of the electro-optical effect is expected in the range of particle rotation. Discrimination between the induced and the rotational relaxation of the particles can be reached, however, since the electro-optical response to a sinusoidal electric field is the sum of a time-independent term adc and a term a2rjJ that is sensitive to the particle rotation [24,45]. The critical frequency of the alrjJ relaxation depends on the rotational diffusion coefficient Dr of the particle, while the critical frequency of relaxation of the time-independent term adc depends on the translational diffusion coefficient of the ions moving on the particle surface. 

From an analysis of the a dependence on the field frequency v (dispersion curve) for different colloids, it has been shown that the orientation of particles in the kHz range originates solely from their induced dipole moments [2,3,51]. It is generally accepted now that the induced dipole moment of a colloid particle in this region is mainly due to movement of ions in the diffuse part of the particle electrical double layer [51-54], What is the origin of the effect observed in a suspension containing polyelectrolyte molecules ... 

The results in Fig. 22 show that the RH-dependent spectra of a given PEC, can, indeed, be superimposed to a master curve. The agreement between the curves is excellent in all parts of the spectra except at low frequencies, where electrode polarization effects dominate however, these do not describe material properties. We can therefore claim that for the presented polyelectrolyte materials there is a time-humidity superposition-principle (THSP) in analogy to the well-established TTSP. Moreover, the special case of Summerfield-type scaling is fulhUed. The same holds true for other investigated PEC compositions not presented here. 

Because the configurations of the chains which predominantly contain the trans and gauche conformations of short parts formed by four C atoms (in sp hybridization) fit fairly well to the tetrahedral lattice (see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions, Fig. 3), to a first approximation they assumed that the basic motion of the fluorophore can be described as a jump-like rotation on the tetrahedral lattice with one characteristic time, p (which depends on the characteristic jump frequency and the conformation structure of the chain), in the form [100, 101] ... 

---