Transport polyelectrolytes

Locke, BR Arce, P, Modeling Electrophoretic Transport of Polyelectrolytes in Beds of Non-porous Spheres, Separation Technology 3, 111, 1993. 

K Farng, K Nelson. Effects of polyelectrolytes on drug transport I Diffusion. J Pharm Sci 62 1435, 1973. 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

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 ... 

In the example above, a short-chain poly(ethylene glycol) was added to a rigid polyelectrolyte to plasticise the material and thereby increase polymer-solvent motion in the vicinity of mobile ions. This strategy has been widely explored as a means of improving ion transport in electrolytes. 

Thin-film ideal or Nemstian behavior is the starting point to explain the voltammetric behavior of polyelectrolyte-modified electrodes. This condition is fulfilled when (i) the timescale of the experiment is slower than the characteristic timescale for charge transport (fjD pp, with Ithe film thickness) in the film, that is all redox within the film are in electrochemical equibbrium at any time, (ii) the activity of redox sites is equal to their concentration and (iii) all couples have the same redox potential. For these conditions, anodic and cathodic current-potential waves are mirror images (zero peak splitting) and current is proportional to the scan rate [121]. Under this regime, there exists an analytical expression for the current-potential curve ... 

When the characteristic time for charge diffusion is lower than the experiment timescale, not all the redox sites in the film can be oxidized/reduced. From experiments performed under these conditions, an apparent diffusion coefficient for charge propagation, 13app> can be obtained. In early work choroamperometry and chronocoulometry were used to measure D pp for both electrostatically [131,225] and covalently bound ]132,133] redox couples. Laviron showed that similar information can be obtained from cyclic voltammetry experiments by recording the peak potential and current as a function of the potential scan rate [134, 135]. Electrochemical impedance spectroscopy (EIS) has also been employed to probe charge transport in polymer and polyelectrolyte-modified electrodes [71, 73,131,136-138]. The methods... 

One other design developed by Wang s group uses the same base sensor (GCE), which is coated with a layer of poly(4-vinylpyridine) (PVP). This cationic polyelectrolyte was one of the first polymers used to modify electrode surfaces [27]. Much research effort in this context has been directed to the characterization of the transport and electrostatic binding of multi-charged anions at PVP-coated electrodes. The ability of this polymer... 

In [104], the electrochemical reduction of N2O involving protons transported through a polyelectrolyte-coated porous glass wall was reported using zinc, lead, iron, and copper cathode. 

The electrostatic forces also play an important role in the conformation and structure of macromolecules such as polymers, polyelectrolytes, and proteins. The self-assembly of proteins from disks to virus is triggered by electrostatic interactions between neighboring subunits. In the case of polyelectrolytes (polymer molecules with charges) and charged colloids, transport behavior such as rheology is also affected significantly by charge effects, as we have already seen in Chapter 4. 

G. S. Manning, Limiting laws for equilibrium and transport properties of polyelectrolyte solutions, in Polyelectrolytes, E. S61dgny, M. Mandel, and U.P. Strauss, eds., D. Riedel, Dordrecht, the Netherlands, 1974, p. 9. 

These results have a natural explanation if we assume that contraction of polyelectrolyte networks in the course of the passage of the electric current is due to the electroosmotic transport of water. The phenomenon of electroosmosis can be described in the following way Suppose that the electric current passes through a finely porous medium with electrolytic solution inside the pores. In this case, the moving ions of electrolyte carry with them all molecules of water from the pores through which the current passes. 

To summarize, we have shown that proton transport and reaction with unionized amines is often a decisive factor in determining swelling rates in the hydrophobic amine gels we have studied. Simple explanations based on solvent diffusion and polymer relaxation, although useful for nonionic polymers, cannot account for swelling kinetic phenomena in initially dry polyelectrolyte gels. 

The influence of adsorption of polyelectrolytes on bimolecular phospholipid leaflets was studied. All polyelectrolytes studied were adsorbed on the surface of the film, as demonstrated by greatly increased drainage times. Only some of the polyelectrolytes investigated are able to decrease the d.c. resistance, notably a protein derived from ox erythrocyte ghosts and a Na-K polyphosphate. The combination of these latter substances proved particularly effective. It is concluded that the decrease of d.c. resistance is caused by adsorption and penetration of the polyelectrolytes into the membrane, resulting in the formation of pores or water channels, and not by the possibility of transport of charged macromolecules through the membrane. 

Polyphosphate was chosen as a polyelectrolyte in addition to the erythrocyte ghost protein, because van Steveninck demonstrated (17) that polyphosphate plays an important role in membrane transport in yeast cells. The results obtained with polyphosphate, especially on protein-covered membranes, indicate that the possibility of ionic transport is strongly enhanced. 

Figure 1 shows the results obtained by Francois and Skoulios (27) on the conductivity of various liquid crystalline phases in the binary systems water-sodium lauryl sulfate and water-potassium laurate at 50 °C. As might be expected, the water-continuous normal hexagonal phase has the highest conductivity among the liquid crystals while the lamellar phase with its bimolecular leaflets of surfactant has the lowest conductivity. Francois (28) has presented data on the conductivity of the hexagonal phases of other soaps. She has also discussed the mechanism of ion transport in the hexagonal phase and its similarity to ion transport in aqueous solutions of rodlike polyelectrolytes. 

Transport of salt and water into a capsule was considered in [3], Osmotic swelling of the capsule was assumed to be due to Donnan equilibrium between the salt solution outside the capsule and the interior solution which also contained polyelectrolyte molecules. The polyelectrolyte was unable to pass through the membrane which formed the wall of the capsule, but salt could pass freely. A model similar to that used for the clay membrane predicts two relaxation rates, only one of which was observed in experiments in which the salt concentration was varied in the external reservoir [4],... 

Refs. [i] Oosawa F (1971) Polyelectrolytes. Marcel Dekker, New York [ii] Rice SA, Nagasawa M, Moravetz H (1961) Polyelectrolyte solutions. Molecular Biol Int Ser, vol. 2. Academic Press, London [iii] Rydzewski R (1990) Continuum Mech Therm 2 77 [iv] Inzelt G (1994) Mechanism of charge transport in polymer-modified electrodes. In Bard AJ (ed) Elec-troanalytical chemistry, vol. 18. Marcel Dekker, New York, pp 90-241 [v] Inzelt G, Pineri M, Schultze IW, Vorotyntsev MA (2000) Electrochim Acta 45 2403... 

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