Polyelectrolyte dynamics coefficients

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 ... 

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. 

First of all, the comparison of the PB-theory and experiment shown in Fig. 8 proceeds virtually without adjustable parameters. The osmotic coefficient (j) is solely determined by the charge parameter polyelectrolyte concentration. The latter parameter determines the cell radius R0 (see the discussion in Sect. 2.1) Figure 8 summarizes the results. It shows the osmotic coefficient of an aqueous PPP-1 solution as a function of counterion concentration as predicted by Poisson-Boltzmann theory, the DHHC correlation-corrected treatment from Sect. 2.2, Molecular Dynamics simulations [29, 59] and experiment [58]. 

Chen, W. J., D. P. Lin, and 1. P. Hsu (1998). Contrihution of electrostatic interaction to the dynamic stability coefficient for coagulation-flocculation kinetics of beta-iron oxy-hydroxides in polyelectrolyte solutions. J. Chem. Eng. Japan. 31, 5, 722-733. 

Liao, Q., Dobrynin, A.V., and Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions Osmotic coefficient and counterion condensation. Macromolecules, 2003, 36, No. 9, p. 3399-3410. 

Since the experimentally determined osmotic coefficient appears to be smaller even than the molecular dynamics results, this indicates effects to be relevant that go beyond the model used for simulation. Most obvious candidates for this are the neglect of additional chemical interactions between the ions and the polyelectrolyte as well as solvation effects, i.e., interactions between the ions or the polyelectrolyte with the water molecules from the solution. It is for instance demonstrated in Ref. 46 that the osmotic coefficient also depends on whether one uses chlorine or iodine counterions. While one could certainly account for the different radii of these ions when computing the distance of closest approach entering the PB equation, the implications of the different hydration energies is much less obvious to incorporate and in principle requires very expensive all-atom simulations. 

Abstract Aqueous solutions of star-like polyelectrolytes (PEs) exhibit distinctive features that originate from the topological complexity of branched macromolecules. In a salt-free solution of branched PEs, mobile counterions preferentially localize in the intramolecular volume of branched macroions. Counterion localization manifests itself in a dramatic reduction of the osmotic coefficient in solutions of branched polyions as compared with those of linear PEs. The intramolecular osmotic pressure, created by entrapped counterions, imposes stretched conformations of branches and this leads to dramatic intramolecular conformational transitions upon variations in environmental conditions. In this chapter, we overview the theory of conformations and stimuli-induced conformational transitions in star-like PEs in aqueous solutions and compare these to the data from experiments and Monte Carlo and molecular dynamics simulations. 

Table 1 Simulated diflnision coefficients and dielectric crmstant of water confined within a polyelectrolyte mixture that corresponds to an experimental PEM [160]. Three parallel simulations were performed for system (i), which has the slowest dynamics of water, and two for systems (ii) and (iii). In the parallel runs, only the random seeds in building the initial structures were different. Experimental data based on PSS/PDADMA PEMs...

Fujita and coworkers [79] smdied fluorescently labeled polyoxyethylene chains and found a good correlation between the concentration dependence of the friction coefficient evaluated from the anisotropy measurements and from the macroscopic viscosity. Fujita developed the fi ee-volume theory which describes reasonably well the concentration dependence of in the whole concentration region, [80] but it does not enable prediction of the parameters at a molecular level. Hyde et al. [81] used the Fujita theory for fairly successful interpretation of the experimental data. An interesting paper has been published by Viovy and Moimerie [82]. The authors studied concentrated solutions of anthracene-labeled polystyrene in toluene. They found good correlation of the local dynamics with the viscosity in the range of high concentrations and made one very important observation the local dynamics are unaffected by the overlap of the polymer chains that occurs at concentrations higher than c (concentration of the first overlap—see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions ). 

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-... 

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