The polyelectrolyte slow mode

The transition to independence from q is temperature dependent, being found at the Theta temperature (34.5 °C) but being absent at 52 °C. 

Star polymer solutions can exhibit a slow mode. Huber, et al. find that such a mode appears for a 467 kDa 12-arm polystyrene star in toluene at concentrations 50 g/1 3/[r/](50). The D/ of the fast mode did not depend on q -.D of the slow 

This section briefly considers the slow mode often seen in S q, t) of polyelectrolytes, especially at low ionic strength. The polyelectrolyte slow mode resembles the slow modes seen with some neutral polymers. While most of the remainder 

Sedlak used light scattering spectroscopy to study 50 and 710 kDa poly-styrenesulfonate, 3.3 kDa sodium polyacrylate, and 30 kDapolymethylacrylic acid. His spectrometer had a 200 mW argon-ion laser and full-dynamic-range multi-tau correlator. Unlike many DLS studies, this work incorporated absolute intensity measurements to determine the amplitude of each spectral mode. 

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Sedlak s results taken together unambiguously indicate that the polyelectrolyte slow mode in the systems he studied arises from long-lived equilibrium structures. The structures are much larger than a single polymer chain. The polymer concentration within a domain is larger than the concentration in the surrounding medium. 

Videomicroscopy of colloid suspensions finds that colloid particles in nondilute solutions form fast- and slow-moving clusters studies of Sedlak on the polymer slow mode indicate that random-coil polyelectrolytes also form slow and fast regions(12). Colloidal probes in colloid or polymer solutions both sometimes show re-entrance, in which the concentration dependences of D and rj differ, but only over a limited range of c. At large q and elevated c, the polymer slow mode sometimes becomes -independent, especially at low temperatures. A similar large- behavior does not appear to have been reported for spheres. 

The slow diffusion coefficient is measurable only at high enough polyelectrolyte concentrations. The value of c at which the slow mode appears is higher if Cj is higher. When the ratio X = c/cg is about 1, the onset of the slow mode and the crossover between the smaller Df for A, < 1 and higher Df for A > 1 occur. Dj depends [33] on c strongly. 

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

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]. 

Sedlak M. The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering the slow mode dilemma. J Chem Phys 1996 105 10123-10133. 

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

A bimodal decay is observed with the fresh solution and only a pseudo-monomodal correlation function is obtained with the old solution, which corresponds to the fast mode. Thus the time dependence of the contribution of the slow mode is an important phenomenon. Our results indicate that whatever these structures are, they must originate in the polyelectrolyte solution. The evolution of the slow mode with time seems to indicate that the fresh solution is not macroscopically in thermodynamic equilibrium with the presence of large clusters which disaggregate with time, indicating that a polyelectrolyte solution with a low external salt concentration (Cs/C 10 2) slowly tends to equilibrium in agreement with other observations [36,62,63], To quantify the evolution of the slow mode with the elapsed time from a fresh solution, we have measured the ratio of the amplitude of the autocorrelation function of the slow mode over the amplitude of the fast one AJAf. We observe a very slow decrease of this ratio as a function of time. Since the amplitude of the fast mode is time independent, the amplitude of the slow mode decreases to a value that is too small to be observed any longer. 

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. 

A final comment made was that although the observations in Reference [66] may have general vahdity for linear polyelectrolytes and some branched ones, more complex polyelectrolyte morphologies, such as dendiimers, may have different mechanisms at work that produce slow modes. 

Michel RC, Reed WF. New evidence of the nonequilibrium nature of the slow modes of diffusion in polyelectrolyte solutions. Biopolymers 2000 53 19-39. 

The present review mainly, but not exclusively, deals with linear flexible polyions and focuses on single chain properties such as the "electrostatic persistence length of intermolecular interactions of a mainly electrostatic nature, on static and dynamic properties at the dilute-semidilute cross-over regime and, only briefly, on the occurrence of unidentified polyelectrolyte structures, sometimes referred to as extraordinary phase , cluster , association or, according to its most striking phenomenology, slow mode . 

One of the most perplexing (and not yet understood) properties of polyelectrolyte dynamics is the fact that, at a certain ratio X. of polyion-concentration Cp (in mol monomer or mol charges, abbreviated monomol/l ) to added salt concentration c (mol/1), a slow mode is observed in dynamic light scattering with a concomitant drastic increase in scattering intensity. 

The value of this ratio X is only known approximately, as literature values vary from 1 < X < 5 for monovalent counterions. There is no question, however, that such a slow mode is observed for essentially all investigated polyelectrolytes and the phenomenon was attributed to the formation of an extraordinary phase (EO-phase). It is worth mentioning that there is some dispute as to whether the spectacular name is justified, i.e., whether this phase is a phase in the thermodynamic sense with the usually observed discontinuities for phase-transitions or not. We shall not participate in this speculative and partly semantic discussion but simply adopt the term extraordinary phase . 

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... 

The coupling theory described above is pertinent to only the fast mode where Df decreases with an increase in c. Furthermore, the counterion coupling theory (Muthukumar 1997) predicts that Df is independent of Cp in salt-free dilute and semidilute polyelectrolyte solutions, consistent with Figure 7.5a. The superfast mode mentioned above is not yet measurable in experiments with polyelectrolytes. The slow mode appearing for Cp/Cs > 1 may be attributed to temporary clustering of polyelectrolyte chains and its full understanding is yet to be reached. 

Sedlak M. On the possible role of nonelectrostatic interactions in the mechanism of the slow polyelectrolyte mode observed by dynamic light scattering. J Chem Phys 1994 101 10140-10144. 

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. 

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