Ion Transport in an Electrolyte

Ion transport in an electrolyte is necessary for current flow. Because the ions carry charge, the net rate of ion transport through the electrolyte is directly proportional to the current flow  

The negative sign represents the fact that mass transport of j will occur in this mode in the direction of decreasing concentration of j. Here, Dj is the mass diffusivity coefQcient of j in the i direction and dCj/dxi is the concentration gradient of j in the i direction. 

F ure 5.2 Convection mass transfer results from net motion of fluid. 

By putting all the relevant modes together, we have the Nemst-Planck equation governing ion transport  

The mobility Uj of ion j in the electrolyte is an important parameter related to the diffusion coefficient Dj through the Nemst-Einstein relation [1]  

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To describe the mass transport in an electrolyte solution or in an ion-exchange membrane, three independent fluxes must be considered, that is, the fluxes of the cations the flux of anions, and the flux of the solvent [16]. The transport of ions is the result of an electrochemical potential gradient and the transport of the solvent through the membrane is a result of osmotic and electro-osmotic effects. 

The polymerized ionic liquid (IL) shows great promise for diverse applications. Some polymerization methods have already been oriented toward specific applications. Polymerized ILs are useful in polar environments or where there are ion species for transport in the matrix. Amphoteric polymers that contain no carrier ions are being considered for several porposes in polymer electrolytes. Zwitterionic liquids (ZBLs) were introduced in Chapter 20 as ILs in which component ions cannot move with the potential gradient. ZILs can provide ion conductive paths upon addition of salt to the matrix. It is therefore possible to realize selective ion transport in an IL matrix. If the resulting matrix can form solid film over a wide temperature range, many useful ionic devices can be realized. This chapter focuses on the preparation and characteristics of amphoteric IL polymers. 

For an electrochemical reaction, there are a number of barriers that must be overcome. These barriers concern the electric resistances of the circuit and ion transport in the electrolyte, activation energy of the reaction occurring on the surface of the electrodes, and effective surface area partially covered by the formed bubbles in the solution. The key factors are the activation energy of the reactions and the voltage distribution across the stack. As mentioned in Section 14.2.2.3, the reaction rate is linked to the current density, and the activation energy has a relationship with the electrode potential. 

Electrode for electrochemical oxidation reactions. In solid oxide fuel cells, hydrogen-containing fuels are oxidized by oxygen ions transported through an electrolyte to form water vapor or CO2 as the reaction products at this electrode. SOFC anodes may also act as fuel reforming catalysts when hydrocarbon-based fuels are supplied to the anodes. Electrode for electrochemical reduction reactions. In solid oxide fuel cells, oxygen in ambient air is reduced to oxygen ions at this electrode. 

Figure 7.4 shows an initial nonuniform distribution of element i in a medium of j. Atoms of species i diffuse from the region of high concentration to the region of low concentration and establish a more imiform concentration distribution of the species. Self-diffusion also takes place in a relatively pure crystalline solid material controlled by a process known as vacancy mechanism or the hopping process. The ion transport in crystalline electrolyte is controlled by this vacancy diffusion or hopping diffusion mechanism. In this... 

Further, it shall be noted that even though aU ions included in an electrolyte participate in the transport of the charge, they are not all necessarily included in the resulting redox reaction. 

In order to determine X+, X from measurements of the conductance of an electrolyte, it is necessary to know the fraction of the total current passed which is carried by each ion type. Such fractions are known as transport numbers, t. By definition, the sum of the transport numbers of all ion species in an electrolyte solution is unity. 

Transport numbers are intended to measure the fraction of the total ionic current carried by an ion in an electrolyte as it migrates under the influence of an applied electric field. In essence, transport numbers are an indication of the relative ability of an ion to carry charge. The classical way to measure transport numbers is to pass a current between two electrodes contained in separate compartments of a two-compartment cell These two compartments are separated by a barrier that only allows the passage of ions. After a known amount of charge has passed, the composition and/or mass of the electrolytes in the two compartments are analyzed. Erom these data the fraction of the charge transported by the cation and the anion can be calculated. Transport numbers obtained by this method are measured with respect to an external reference point (i.e., the separator), and, therefore, are often referred to as external transport numbers. Two variations of the above method, the Moving Boundary method [66] and the Eiittorff method [66-69], have been used to measure cation (tR+) and anion (tx ) transport numbers in ionic liquids, and these data are listed in Table 3.6-7. 

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 first key component of a membrane fuel cell is the membrane electrolyte. Its central role lies in the separation of the two electrodes and the transport of ionic species (e.g. hydroxyl ion, OH , in an AEM), between them. In general, quaternary ammonium groups are used as anion-exchange groups in these materials. However, due to their low stability in highly alkaline media [43,44], only a few membranes have been evaluated for use as solid polymer electrolytes in alkaline fuel cells. 

In addition to mass transport from the bulk of the electrolyte phase, electroactive material may also be supplied at the electrode surface by homogeneous or heterogeneous chemical reaction. For example, hydrogen ions required in an electrode process may be generated by the dissociation of a weak acid. As this is an uncommon mechanism so far as practical batteries are concerned (but not so for fuel cells), the theory of reaction overvoltage will not be further developed here. However, it may be noted that Tafel-like behaviour and the formation of limiting currents are possible in reaction controlled electrode processes. 

TRANSFERENCE NUMBER (Transport Number). Of a given ion in an electrolyte, the transference number is the fraction of total current... 

In electromembrane processes the anions move towards the anode where they are oxidized by releasing electrons to the electrode in an electrochemical reaction. Likewise, the positively charged cations move towards the cathode where they are reduced by receiving electrons from the electrode in an electrochemical reaction. Thus, the transport of ions in an electrolyte solution and ion-exchange membrane between electrodes results in a transport of electrical charges, that is, an electrical current which can be described by the same mathematical relation as the transport of electrons in a metallic conductor, that is, by Ohm s law that is given by ... 

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