Conduction in solid electrolytes

The ionic conductivity is generally seen with an amorphous polymer. The ion diffusion in a polymer electrolyte is assisted by the local motion of the polymer chain. Therefore, the polymer chain must be flexible at the application temperature. This is conventionally achieved by choosing a polymer with a glass transition temperature (Tg) below the temperature being used or by blending it with another polymer and/or additives. At the same time, it needs to have sufficient mechanical stability for such an application. However, there are some vitreous solid electrolytes which are used above Tg in which ion diffusion is decoupled from the motion of the matrix polymer. The cation migration with segmental mobility of the polymer chain is shown in Fig. 11.2.  

In parallel with the Williams-Landel-Ferry (WLF) equation, the Vogel-Tamman-Fulcher (VTF) equation is used to express the temperature dependency of conductivity  

A great deal of research has been performed on polymer electrolytes using PEO, but the problem with PEO is its crystallinity. Crystalline polymers, or crystalline regions in semicrystalline polymers, do not allow ions to move freely. Therefore, attempts have been made to modify the polymer by forming copolymers, forming blends, blending with inert fillers, or by using heteropolymer and so on. There is another series of polymers, which are usually called proton conductors. 

Advancement in this field was propelled by continuous improvement in properties coupled with demands from various technological applications. Some of the developments will be discussed here. 

When Nafion was discovered in 1962, it was considered to be a solid polymer electrolyte due to the presence of a sulfonic acid group attached to the perfluorinated chain (Fig. 11.3). It is not a true solid proton conductor as ion transport occurs via a quasi-liquid phase as in other polyelectrolytes. In 

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We begin our discussion by characterizing the electrical conduction in solid electrolytes. These are solids with predominantly ionic transference, at least over a certain range of their component activities. This means that the electronic transference number, defined as... 

Activation energy for 0 conduction in solid electrolyte, J/mole... 

It can be observed from Equation (1.27) that the average ionic transference number indicates on the m/deviation of the electrochemical cell (1.20) from the thermodynamic cm/at the presence of electronic conductivity in solid electrolytes. 

Consequently, the proposed model allows the necessary information regarding the electrolyte-metal electrode interface and about the character of the electronic conductivity in solid electrolytes to be obtained. To an extent, this is additionally reflected by the broad range of theoretical studies currently published in the scientific media and is inconsistent with some of the research outcomes relative to both physical chemistry of phenomena on the electrolyte-electrode interfaces and their structures. Partially, this is due to relative simplifications of the models, which do not take into account multidimensional effects, convective transport within interfaces, and thermal diffusion owing to the temperature gradients. An opportunity may exist in the further development of a number of the specific mathematical and numerical models of solid electrolyte gas sensors matched to their specific applications however, this must be balanced with the resistance of sensor manufacturers to carry out numerous numbers of tests for verification and validation of these models in addition to the technological improvements. 

Mott N F and M J Littleton 1938. Conduction in Polar Crystals. I. Electrolytic Conduction in Solid Salts. Transactions of the Faraday Society 34 485-499. 

This relationship makes it possible to calculate the maximum ionic conductivity of solid electrolytes. Assuming that the mobile ions are moving with thermal velocity v without resting and oscillating at any lattice site, this results in a jump frequency... 

Another way of looking at high ionic conductivities of solid electrolytes is to consider the activation enthalpy as illustrated in Fig. 8. Generally, the activation enthalpy is strongly correlated with the room-temperature ionic conductivity the higher the room-temperature ionic conductivity, the lower the activation enthalpy. The straight lines in the Arrhenius... 

Traditionally, the chemical stability of the electrode/electrolyte interface and its electronic properties have not been given as much consideration as structural aspects of solid electrolytes, in spite of the fact that the proper operation of a battery often depends more on the interface than on the solid electrolyte. Because of the high ionic conductivity in the electrolyte and the high electronic conductivity in the electrode, the voltage falls completely within a very narrow region at the electrolyte/electrode interface. 

Detailed information about the conductivity of solid electrolytes can be found elsewhere.2,3,6 8,10,11 As shown in Fig. 3.1, the temperature dependence of the ionic conductivity o can, in general, be described by the semiempirical equation ... 

AgsSBr, /3-AgsSI, and a-AgsSI are cationic conductors due to the structural disorder of the cation sublattices. AgsSI (see Fig. 5) has been discussed for use in solid-electrolyte cells (209,371, 374,414-416) because of its high silver ionic conductivity at rather low temperatures (see Section II,D,1). The practical use seems to be limited, however, by an electronic part of the conductivity that is not negligible (370), and by the instability of the material with respect to loss of iodine (415). 

In solid electrolyte fuel cells, the challenge is to engineer a large number of catalyst sites into the interface that are electrically and ionically connected to the electrode and the electrolyte, respectively, and that is efficiently exposed to the reactant gases. In most successful solid electrolyte fuel cells, a high-performance interface requires the use of an electrode which, in the zone near the catalyst, has mixed conductivity (i.e. it conducts both electrons and ions). Otherwise, some part of the electrolyte has to be contained in the pores of electrode [1]. 

The conductivity of solid salts and oxides was first investigated by M. Faraday in 1833. It was not yet known at that time that the nature of conduction in solid salts is different from that in metals. A number of fundamental studies were performed between 1914 and 1927 by Carl Tubandt in Germany and from 1923 onward by Abram Ioffe and co-workers in Russia. These studies demonstrated that a mechanism of ionic migration in the lattice over macroscopic distances is involved. It was shown that during current flow in such a solid electrolyte, electrochemical changes obeying Faraday s laws occur at the metal-electrolyte interface. 

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

The above two mechanisms may be regarded as isolated ion hops. Sometimes, especially in solid electrolytes, cooperative ion migration occurs. An example is shown in Fig. 2.1(c) for the so-called interstitialcy or knock-on mechanism. A Na" ion. A, in an interstitial site in the conduction plane of j -alumina (see later) cannot move unless it persuades one of the three surrounding Na ions, B, C or D, to move first. Ion A is shown moving in direction 1 and, at the same time, ion B hops out of its lattice site in either of the directions, 2 or 2. It is believed that interstitial Ag" ions in AgCl also migrate by an interstitialcy mechanism, rather than by a direct interstitial hop. 

The activation energy represents the ease of ion hopping, as already indicated above and shown in Fig. 2.5. It is related directly to the crystal structure and in particular, to the openness of the conduction pathways. Most ionic solids have densely packed crystal structures with narrow bottlenecks and without obvious well-defined conduction pathways. Consequently, the activation energies for ion hopping are large, usually 1 eV ( 96 kJ mole ) or greater and conductivity values are low. In solid electrolytes, by contrast, open conduction pathways exist and activation energies may be much lower, as low as 0.03 eV in Agl, 0.15 eV in /S-alumina and 0.90 eV in yttria-stabilised zirconia. 

Generally, in solid electrolytes, ionic conductivity is predominant (( = 1) only over a limited chemical potential. The electrolytic conductivity domain is an important factor limiting the application of solid electrolytes in electrochemical sensors. 

One of the most important aspects of point defects is that they make it possible for atoms or ions to move through the structure. If a crystal structure were perfect, it would be difficult to envisage how the movement of atoms, either diffusion through the lattice or ionic conductivity (ion transport under the influence of an external electric field) could take place. Setting up equations to describe either diffusion or conductivity in solids is a very similar process, and so we have chosen to concentrate here on conductivity, because many of the examples later in the chapter are of solid electrolytes. 

Much of the recent research in solid state chemistry is related to the ionic conductivity properties of solids, and new electrochemical cells and devices are being developed that contain solid, instead of liquid, electrolytes. Solid-state batteries are potentially useful because they can perform over a wide temperature range, they have a long shelf life, it is possible to make them very small, and they are spill-proof We use batteries all the time—to start cars, in toys, watches, cardiac pacemakers, and so on. Increasingly we need lightweight, small but powerful batteries for a variety of uses such as computer memory chips, laptop computers, and mobile phones. Once a primary battery has discharged, the reaction cannot be reversed and it has to be thrown away, so there is also interest in solid electrolytes in the production of secondary or storage batteries, which are reversible because once the chemical reaction has taken place the reactant concentrations can be... 

Analogs of the step 3 product were prepared by Rozhanskii et al. (1) and used in solid electrolytes and proton-conductive membranes. 

It is possible to make nonstoichiometric solids that have ionic conductivities as high as 0.1-1000 S m-1 (essentially the same as for liquid electrolytes) yet negligible electronic conductances. Such solid electrolytes are needed for high energy density electrical cells, fuel cells, and advanced batteries (Chapter 15), in which mass transport of ions between electrodes is necessary but internal leakage of electrons intended for the external circuit... 

A solid electrolyte is a material in which the electrolytic, or ionic, conductivity is much greater than the electronic conductivity (for solid electrolytes to be practically useful the ratio of electrolytic to electronic conductivities should be of the order of 100 or greater1,2). Solid electrolytes with conduction ions of 02 , H+, Li+, Na+, Ag+, F, Cl- have all been reported. Much attention has been devoted to oxygen-ion conducting solid electrolytes, many of which show appreciable oxygen-ion conductivities in the range of 200-1200°C. 

In both cases, ctj i depends on PO2- Figure 1.43 shows that eqn (1.167) is dominant in the pressure range I O2 > 10 atm and eqn (1.168) is dominant in the pressure range 02 < 10 atm. In the former case, CT , depends on temperature because ion mobility is temperature dependent. The relation between the ionic and electronic conductivity for solid electrolytes is shown schematically in Fig. 1.44. Since ionic conductivity originates from diffusion of ions in the solid phase, (Tio is closely related to the coefficient of self diffusion of ions ( X,o ) shown by the following equation... 

The second necessary condition for crystalline or vitreous solid to have high ionic conductivity is that the mobile ions have a high diffusion coefficient, i.e. it is indeed a fast ion conductor . Much attention has been given to developing models of ionic motion. The simple hopping models applied successfully in the case of defect transport are not appropriate because of the high density of mobile ions in solid electrolytes, and... 

Following the introduction of basic kinetic concepts, some common kinetic situations will be discussed. These will be referred to repeatedly in later chapters and include 1) diffusion, particularly chemical diffusion in different solids (metals, semiconductors, mixed conductors, ionic crystals), 2) electrical conduction in solids (giving special attention to inhomogeneous systems), 3) matter transport across phase boundaries, in particular in electrochemical systems (solid electrode/solicl electrolyte), and 4) relaxation of structure elements. 

A large body of literature has been accumulated over the last three decades concerning so-called fast ionic conductors. Fast ionic conductors have an ionic conductivity (Fig. 15-8) comparable to that of moderately concentrated aqueous ionic solutions (ca. 0.1-1 moll1). Fast ionic conduction is found in solid electrolytes and semiconducting crystals. Although known for quite some time, these materials became really interesting when solids were discovered which showed the unexpected high... 

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