Polyelectrolyte dynamics diffusion coefficients

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. 

Although the theory of polyelectrolyte dynamics reviewed here provides approximate crossover formulas for the experimentally measured diffusion coefficients, electrophoretic mobility, and viscosity, the validity of the formulas remains to be established. In spite of the success of one unifying conceptual framework to provide valid asymptotic results, in qualitative agreement with experimental facts, it is desirable to establish quantitative validity. This requires (a) gathering of experimental data on well-characterized polyelectrolyte solutions and (b) obtaining the relationships between the various transport coefficients. Such data are not currently available, and experiments of this type are out of fashion. In addition to these experimental challenges, there are many theoretical issues that need further elaboration. A few of these are the following ... 

It turned out that the dynamical behaviour of polyelectrolyte solutions is even more spectacular then theoretically anticipated. In the early 1970s mostly biopolymers such as DNA were studied and often two separate relaxations were observed which were then attributed to internal relaxations [197-202]. During the past twenty years numerous studies on synthetic polyelectrolytes (NaPSS, NaPMA, NaPAA, QPVP), proteins (BSA, PLL), polynucleotides (DNA, RNA) and charged polysaccharides (heparin, chondroitin-6-sulfate, proteoglycan hyal-onurate) have been performed. The dynamical behaviour of all these polymers exhibits common features which are attributed to the ionic character of the polyelectrolytes. So far, most studies have focused on the dependence of the apparent diffusion coefficient on polyelectrolyte concentration, salt concentra-... 

The problems involved in formulating a consistent theory of binding are illustrated when one measures the thermodynamic and dynamic properties of a limited number of polyelectrolytes with different counter-ions and then attempts to formulate a simple theory. For example, Gregor measured the selective uptake, self diffusion coefficients, electrical conductivity and electro-osmotic coefficients of a number of different ions in ion-exchange membrane and resin systems. The measurement of selective uptake is unequivocal and its correlation with binding is straightforward. Data on self-diffusion coefficients are complicated to interpret because the narrow pores of these insolu-bilized polyelectrolytes place steric and hydrodynamic restrictions upon the diffusive process. These can be overcome, at least in a semi-quantitative manner, by the use of appropriate correction terms [7]. The measurement of the electro-osmotic coefficient is simple and its interpretation is similarly straightforward. Data on electrical conductivity require interpretation because of the steric and hydrodynamic restraints of the pore nature of the system there is an electro-osmotic correction to the electrical conductivity. Table I tabulates normalized values for different counter-ions with... 

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