Fast diffusion coefficient, polyelectrolyte

We have identified three diffusion coefficients. These are the self-translational diffusion coefficient D, cooperative diffusion coefficient Dc, and the coupled diffussion coefficient fly. fl is the cooperative diffusion coefficient in the absence of any electrostatic coupling between polyelectrolyte and other ions in the system, fly is the cooperative diffusion coefficient accounting for the coupling between various ions. For neutral polymers, fly and Dc are identical. Furthermore, we identify fly as the fast diffusion coefficient as measured in dynamic light scattering experiments. The fourth diffusion coefficient is the slow diffusion coefficient fl discussed in the Introduction. A satisfactory theory of flj is not yet available. 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

Thus in salt-free semidilute solutions, the fast diffusion coefficient is expected to be independent of both N and c, although the polyelectrolyte concentration is higher than the overlap concentration. This remarkable result is in agreement with experimental data [31, 33, 34] discussed in the Introduction. Upon addition of salt, Df decreases from this value as given by the above formulas. 

The hght scattering data [24—34] of polyelectrolyte solutions are characteristic of two diffusion coefficients Df (fast) and Dj (slow). D/ for a solution with a given Cj increases with monomer concentration c and above a certain concentration c, Df is independent [31, 33, 34] of both c and M. 

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.

The fast effective diffusion coefficient Dlcll is plotted as a function of polyelectrolyte concentration and it increases as C increases. From the logarithm plot a power law is deduced >feff varies as C045 0 05. 

The presence of a slow diffusion seems to be characteristic for most polyelectrolyte solutions. The slow mode was first detected by Schurr et al. [218] for poly(L-lysine) upon variation of salt concentration. A sudden drop of the diffusion coefficient was observed as the salt concentration was decreased below some critical value. Since then, this transition is called ordinary-extraordinary transition , the fast diffusion being referred to as ordinary and the slow diffusion as extraordinary . Drifford and Dalbiez [219] later gave an empirical expression which describes the relation between this critical salt concentration... 

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. 

---