Polymers in Transport

According to the Scher-MontroU model, the dispersive current transient (Fig. 5b) can be analyzed in a double-log plot of log(i) vs log(/). The slope should be —(1 — ct) for t < and —(1 + a) for t > with a sum of the two slopes equal to 2, as shown in Figure 5c. For many years the Scher-MontroU model has been the standard model to use in analyzing dispersive charge transport in polymers. 

More detailed theoretical approaches which have merit are the configurational entropy model of Gibbs et al. [65, 66] and dynamic bond percolation (DBP) theory [67], a microscopic model specifically adapted by Ratner and co-workers to describe long-range ion transport in polymer electrolytes. 

Charge transfer kinetics for electronically conducting polymer formation, 583 Charge transport in polymers, 567 Chemical breakdown model for passivity, 236... 

Electric-field-driven transport in media made of hydrophilic polymers with nanometer-size pores is of much current interest for applications in separation processes. Recent advances in the synthesis of novel media, in experimental methods to study electrophoresis, and in theoretical methodology to study electrophoretic transport lead to the possibility for improvement of our understanding of the fundamentals of macromolecular transport in gels and gel-like media and to the development of new materials and applications for electric-field-driven macromolecular transport. Specific conclusions concerning electrodiffusive transport in polymer hydrogels include the following. 

Another quasi-thermodynamical model of ion transport in polymers is based on the concept of minimum configurational entropy required for rearrangement of the polymer, giving practically identical o—T and D — T dependences as the preceding model. 

For a classical diffusion process, Fickian is often the term used to describe the kinetics of transport. In polymer-penetrant systems where the diffusion is concentration-dependent, the term Fickian warrants clarification. The result of a sorption experiment is usually presented on a normalized time scale, i.e., by plotting M,/M versus tll2/L. This is called the reduced sorption curve. The features of the Fickian sorption process, based on Crank s extensive mathematical analysis of Eq. (3) with various functional dependencies of D(c0, are discussed in detail by Crank [5], The major characteristics are... 

CR Robert, PA Buri, NA Peppas. Effect of degree of crosslinking of water transport in polymer microparticles. J Appl Polym Sci 30 301-307, 1985. 

U. Pasaogullari, C. Y. Wang, and K. S. Chen. Two-phase transport in polymer electrolyte fuel cells with bilayer cathode gas diffusion media. Journal of the Electrochemical Society 152 (2005) A1574-A1582. 

These materials are introduced in Chapter 5 and only brief mention of them is necessary here. It is important to appreciate that polymer electrolytes, which consist of salts, e.g. Nal, dissolved in solid cation coordinating polymers, e.g. (CH2CH20) , conduct by quite a different mechanism from crystalline or glass electrolytes. Ion transport in polymers relies on the dynamics of the framework (i.e. the polymer chains) in contrast to hopping within a rigid framework. Intense efforts are being made to make use of these materials as electrolytes in all solid state lithium batteries for both microelectronic medical and vehicle traction applications. 

The interaction of poly(ethylene oxide) and other polar polymers with metal salts has been known for many years (Bailey and Koleska, 1976). Fenton, Parker and Wright (1973) reported that alkali metal salts form crystalline complexes with poly(ethylene oxide) and a few years later, Wright (1975) reported that these materials exhibit significant ionic conductivity. Armand, Chabagno and Duclot (1978, 1979) recognised the potential of these materials in electro-chemical devices and this prompted them to perform more detailed electrical characterisation. These reports kindled research on the fundamentals of ion transport in polymers and detailed studies of the applications of polymer-salt complexes in a wide variety of devices. 

The electrolyte concentration is very important when it comes to discussing mechanisms of ion transport. Molar conductivity-concentration data show conductivity behaviour characteristic of ion association, even at very low salt concentrations (0.01 mol dm ). Vibrational spectra show that by increasing the salt concentration, there is a change in the environment of the ions due to coulomb interactions. In fact, many polymer electrolyte systems are studied at concentrations greatly in excess of 1.0 mol dm (corresponding to ether oxygen to cation ratios of less than 20 1) and charge transport in such systems may have more in common with that of molten salt hydrates or coulomb fluids. However, it is unlikely that any of the models discussed here will offer a unique description of ion transport in a dynamic polymer electrolyte host. Models which have been used or developed to describe ion transport in polymer electrolytes are outlined below. 

Table 6.1. Methods for the measurement of transport in polymer electrolytes...

The different techniques which have been applied to determine transport in polymer electrolytes are listed in Table 6.1. For a fully dissociated salt all the techniques yield the same values of t (small differences may arise due to second order effects such as long range ion interactions or solvent movement which may influence the different techniques in different ways). In the case of associated electrolytes, any of the techniques within one of the three groups will respond similarly, but the values obtained from different groups will, in general, be different. Space does not permit a detailed discussion of each technique, this is available elsewhere (see Bruce and Vincent (1989) and the references cited therein). However, we will consider one technique from each group to illustrate the differences. A solid polymer electrolyte containing an associated uni-univalent salt is assumed. 

The concept of electric transport in polymers due to the availability of polymeric materials with characteristics similar to those of metals is certainly fascinating and, indeed, many studies have been directed towards the preparation and the characterisation of these new electroactive conductors. The final goal is their use as new components for the realisation of electronic and electrochemical devices with exotic designs and diverse applications. 

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... 

Modeling Transport in Polymer-Electrolyte Fuel Cells... 

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