Polyelectrolyte relaxation time

FIG. 2 Relaxation times of dynamic modes observed in polyelectrolyte solutions and mixtures over a broad range of experimental conditions 0 diffusion of low molecular weight salt diffusion of polyions or polyion segments in semidilute solutions 3 interaction mode in polyelectrolyte mixtures and diffusion of polyelectrolyte domains (clusters). The data are based mostly on the work on linear flexible polyelectrolytes. Relaxation times correspond to scattering at 90°. See text for more details. 

Nuclear Magnetic Resonance (NMR) Spectroscopy. Longitudinal and transverse relaxation times (Ti and T2) of 1H and 23Na in the water-polyelectrolytes systems were measured using a Nicolet FT-NMR, model NT-200WB. T2 was measured by the Meiboom-Gill variant of the Carr-Purcell method (5). However, in the case of very rapid relaxation, the free induction decay (FID) method was applied. The sample temperature was changed from 30 to —70°C with the assistance of the 1180 system. The accuracy of the temperature control was 0.5°C. 

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). 

Miles, M. J., Tanaka, K., and Keller, A. (1983). The behaviour of polyelectrolyte solutions in elongational flow the determination of conformadonal relaxation times (with an Appendix of an anomalous adsorption effect). Polymer 24 1081-1088. 

Note that if the polymer in dilute solution were highly extended with exponent i> > 2/3, the relaxation time in unentangled semidilute solutions would be predicted to decrease with increasing concentration. This is actually observed for semidilute unentangled solutions of charged poly-mers, called polyelectrolytes, which have u=lin dilute solutions because... 

III. LIGHT SCATTERING FROM POLYELECTROLYTE SOLUTIONS—MULTIMODAL SPECTRA OF RELAXATION TIMES... 

Figure 3 shows the correlation function and the corresponding spectrum of relaxation times for a solution of sodium poly(styrenesulfonate) (NaPSS) in 3.7 M NaCl. Two modes can be clearly recognized. The slower mode corresponds to the diffusion of polyions, which will be discussed in the next section. The faster mode corresponds to the diffusion of salt (NaCl). As expected for a diffusive process, the inverse relaxation time of this mode Tvf (the subscript vf refers to very fast ) is q2 dependent (Figure 4). The diffusion coefficient of the salt small ions was calculated from the slope of the dependence Tvf = Dwfq2 in Figure 4 as Dvf = (1.7 0.1) X 10 5 cm2s The scattering amplitude of the very fast mode varies proportionally with the salt concentration and is q independent as expected. Figure 5 shows the correlation function and the corresponding spectrum of relaxation times for a pure solution of NaCl in water (no polymer added). Only one diffusive mode is present with the diffusion coefficient matching relatively closely the value of Dvf obtained in polyelectrolyte solution.

Influence of Added Salt on the Slow Mode. As with NaCl and CaCl2, the system NaPSS/LaCl3 presents a pseudo splitting phenomenon between the two modes at a critical salt concentration [32], The amplitude of the slow mode becomes very low and undetectable. Only the fast component of the autocorrelation function is present. These results are analogous to many observations made on a lot of polyelectrolyte solutions and recall the pseudo-transition from extraordinary phase to ordinary phase [31,32,34,37,64]. At last, in the upper one-phase at Cs 0.5 M (D-point on Figure 15), a large scattered intensity is observed with only one relaxation time. The value of the effective coefficient diffusion is about 10 7 cm2/s. 

Both the disappearance of the slow relaxation time on a very long time-scale after preparation of solutions (from a few months to one year) and the nonreappearance of this mode when cycling between high and low salt concentrations indicate that the solution, at very low salt concentration, slowly tends to equilibrium. The thermodynamic equilibrium of salt-free polyelectrolyte solution is very difficult to obtain. Strong electrostatic repulsion dominates the solution, and some electrostatic domains or clusters stay present for a long time in the fresh solution. Only with an excess of external salt or with a very long time scale can the solution be in thermodynamic equilibrium. 

In Figure 2 are represented the electro-optical effect a, the electrophoretic mobility Ue, and the relaxation time r of the particle disorientation after the switching off of the electric field as a function of the initial polyelectrolyte concentration. One observes that the a and r variations correspond to the variation of f/e, i.e., the electrostatic attraction of the polyelectrolyte to the oppositely charged surface, which is the main driving force for the adsorption, governs the electro-optical behavior and stability of the suspension containing this polyelectrolyte. 

If c is greater than Cg. there will be a semidilute regime of entangled polyelectrolyte solution rheology. Here, the terminal relaxation time is predicted to be [Colby et al.. 

Since the chain conformation appears as unperturbed in the concentrated solutions, the coil sizes will not depend on the concentration any more. With further increase of concentrations, C 1, and eventually the electrostatic repulsion between charged monomers will be completely screened. In the end, the polyelectrolyte chain will behave like a charge-neutral polymer chain in highly concentrated solutions. Correspondingly, the coil sizes will increase in a sudden, leading to an increase of characteristic relaxation time as well as the intrinsic viscosity, and appearing as a gelation process, as demonstrated in Fig. 4.13 (Dobrynin and Rubinstein 2005). 

We have already mentioned several effects that are connected with the polymeric nature of the layer. It is evident tliat all the charge transport processes listed are affected by the physicochemical properties of the polymer. Therefore, we also must deal with the properties of the polymer layer if we wish to understand the electrochemical behavior of these systems. The elucidation of the stracture and properties of polymer (polyelectrolyte) layers as well as the changes in their morphology caused by the potential and potential-induced processes and by other parameters (e.g., temperature, electrolyte composition) set an entirely new task for electrochemists. Owing to the long relaxation times that are characteristic of polymeric systems, the equilibrium or steady-state situation is often not reached within the time allowed for the experiment. 

FIGURE 5.19 Spin-lattice relaxation time as a function of bilayer numbers for D O-saturated PEM films. (Adapted with permission from McCormick, M., Smith, R.N., Graf, R., Barrett, C.J., Reven, L., and Spiess, H.W., NMR studies of the effect of adsorbed water on polyelectrolyte multilayer films in the solid state. Macromolecules 36, 3616-3625, 2003. Copyright 2003 American Chemical Society.)... 

The equilibrium constant for this exchange was obtained by using Na NMR (15,16) to measure the change in the relaxation time of Na as a function of added [l-ArN2l. We assume that the total number of counterions in the condensed volume remains constant, i.e. one-to-one exchange of counterions. The assumption of one-to-one exchange is supported by the repeated observation that the fraction of counterions bound to a polyelectrolyte is unaffected by dilution or added electrolyte (1,6,12,13,11,18). 

Because the polyelectrolytes are typically flexible molecules, the boundaries between the layers in the film are somewhat fuzzy. The blurriness depends on the relaxation time of the polyelectrolyte complex formation. This, in turn, is determined by the molecular properties of the polyelectrolytes (i.e., charge density,... 

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