Mechanisms of Ionic Motion

The importance of polymer segmental motion in ion transport has already been referred to. Although classical Arrhenius 

The form of the VTF equation normally used to fit the thermal dependence of the ionic conductivity is  

Tq is a reference temperature which can be identified with, and although the constant B is not related to any simple activation process, it has dimensions of energy. This form of the equation is derived by assuming an electrolyte to be fully dissociated in the solvent, so it can be related to the diffusion coefficient through the Stokes-Einstein equation. It suggests that thermal motion above Tq contributes to relaxation and transport processes and that 

The WLF approach is a general extension of the VTF treatment to characterize relaxation processes in amorphous systems. Any temperature-dependent mechanical relaxation process, R, can be expressed in terms of a universal scaling law  

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. 

The importance of polymer segmental motion in ion transport has already been referred to. Although classical Arrhenius theory remains the best approach for describing ion motion in solid electrolytes, in polymer electrolytes the typical curvature of the log a vs. 1/T plot is usually described in terms of Tg-based laws such as the Vogel-Tamman-Fulcher (VTF) [61] and Williams-Landel-Ferry (WLF) [62] equations. These approaches and other more sophisticated descriptions of ion motion in a polymer matrix have been extensively reviewed [6, 8, 63]. 

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Schottky, W. Uber den Mechanismus der lonenbewegung in festen Elektrolyten. [The mechanism of ionic motion in solid electrolytes,] Z. Phys. Chem. B29, 335-355 (1935). 

Inside the bulk of the electrolyte, mass transport is mainly because of migration, a mechanism of ionic motion caused by the presence of an applied electric field. In the electrochemical cell the potential drop creates an electric field that is much more intense in the regions near the surface of the electrodes, but is sufficiently intense in the bulk of the electrolyte to promote the migration of the ions to the border of the diffusion layers. 

FIGURE 25.3 Schematic representation of ionic motion by (a) a vacancy mechanism and (b) an interstitial mechanism. (From Smart and Moore, 1996, Fig. 5.4, with permission from Routledge/Taylor Francis Group.)... 

FIGURE 5.4 Schematic representation of ionic motion by (a) a vacancy mechanism and (b) an interstitial mechanism. 

Basilevsky et al. [1982] proposed a mechanism of ionic polymerization in crystalline formaldehyde that was based on Semenov s assumption [Semenov, 1960] that solid-state chain reactions are possible only when the products of each chain step prepare a configuration of reactants that is suitable for the next step. Monomer crystals for which low-temperature polymerization has been observed fulfill this condition. In the initial equilibrium state the monomer molecules are located in lattice sites and the creation of a chemical bond requires surmounting a high barrier. However, upon creation of the primary cation (protonated formaldehyde), the active center shifts toward another monomer, and the barrier for addition of the next link diminishes. Likewise, subsequent polymerization steps involve motion of the cationic end of the polymer toward a neighboring monomer, which results in a low barrier to formation of the next C-0 bond. Since the covalent bond lengths in the polymer are much shorter than the van der Waals distances of the monomer crystal, this polymerization process cannot take place in a strictly linear fashion. It is believed that this difference is made up at least in part by rotation of each CH20 link as it is incorporated into the chain. 

A third type of ionic conduction occurs in polymer electrolytes, such as polyethylene oxide. The mechanism of ionic conduction in polymer electrolytes is not entirely understood. However, it is believed to involve rapid polymer segmental motion which creates regions of an elastomeric nature. These elastomeric regions have relaxation times similar to liquids, and, thus, allow a higher ionic mobility than would be concluded from the polymer s macroscopic properties [2]. 

H3O+ mobility is very large compared with typical ionic mobilities in solids ( < io cm s ), higher by two orders of magnitude than the H3O+ mobility in water, and indeed almost comparable to electron mobilities in metals and elemental semiconductors like germanium (lo-io cm s ). We shall return to consider the mechanism of proton motion in more detail when discussing electrical properties for the present let us give some attention to the structure of the ion states themselves. 

Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

When particles or large molecules make contact with water or an aqueous solution, the polarity of the solvent promotes the formation of an electrically charged interface. The accumulation of charge can result from at least three mechanisms (a) ionization of acid and/or base groups on the particle s surface (b) the adsorption of anions, cations, ampholytes, and/or protons and (c) dissolution of ion-pairs that are discrete subunits of the crystalline particle, such as calcium-oxalate and calcium-phosphate complexes that are building blocks of kidney stone and bone crystal, respectively. The electric charging of the surface also influences how other solutes, ions, and water molecules are attracted to that surface. These interactions and the random thermal motion of ionic and polar solvent molecules establishes a diffuse part of what is termed the electric double layer, with the surface being the other part of this double layer. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

Microwave radiation, as all radiation of an electromagnetic nature, consists of two components, i.e. magnetic and electric field components (Fig. 1.3). The electric field component is responsible for dielectric heating mechanism since it can cause molecular motion either by migration of ionic species (conduction mechanism) or rotation of dipolar species (dipolar polarization mechanism). In a microwave field, the electric field component oscillates very quickly (at 2.45 GHz the field oscillates 4.9 x 109 times per second), and the strong agitation, provided by cyclic reorientation of molecules, can result in an... 

Non-ionic polymer gel, swollen with dielectric solvent, can be extremely deformed as is the case for non-ionic polymer plasticised with non-ionic plasticiser. Instead of the charge-injected solvent drag as a mechanism of the gel actuation, the principle is based on local asymmetrical charge distribution at the surface of the gel18. The mechanism can also be applied to non-ionic elastomers in which the motion of the polymer chain is relatively free. In spite of their many difficulties for practical actuators, polyelectrolyte gels and related materials are the most interesting electroactive polymer materials. 

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