Particle surface impedance

Impedance of the Particle Surface. Electrochemical reactions, formation of a double layer, and adsorption aU contribute to the particle surface impedance. Adsorbed species can diffnse inside the bulk of active material in batteries, except for the case of metal anodes. Because of this, the impedance of the particle surface will involve a Warbnrg impedance element rather than a simple capacitor to represent adsorption (a model for metals can, however, nse a capacitor instead of Z ,). The Randles [1947] eqnivalent circuit in Figure 4.5.7 encompasses all these steps. Note that in batteries, active materials are not dissolved in the electrolyte bnt are... 

Figure 4.5.8. Equivalent circuit of particle surface impedance taking into account a passivating layer.

In order to evaluate specific electrochenucal characteristics, such as exchange current density io = R- Tin F Rct -S, estimation of the particles surface area S is necessary. Note that the experimental estimation of the surface boundary between electronically and ionically conductive media in a composite material consisting of multiple particles has not been successful to date. BET surface area estimation usually tends to severely overestimate this surface area. It correlates well with irreversible capacity loss during first intercalation (lijima et al. [1995]) but not with the surface impedance of materials (Aurbach et al. [2001]), which indicates that loosely electrically connected microparticles make a major contribution to BET surface area but not to the electrochemically active area. In order to estimate only the area that is electrically accessible and also to use the same value of S for both diffusion and surface kinetics, it is common to use a summary geometric area of the particles of the active material as an estimate for surface area. See further details in the bringing it aU together section. 

The anode of a Ni-Cd battery typically consists of a mix of Cd and CdO powders with the addition of a conductive additive (acetylene black). The impedance of the anode-particle surface is determined by the activated adsorption of OH anions first on the metal surface, with subsequent conversion into Cd(OH)2 and hydrated CdO layers (Duhirel et al. [1992])). Reaction products are also present in a partly dissolved Cd(OH)3" state. The activated adsorption mechanism of the anode reaction, as well as porous structure of the electrode, makes it appropriate to use for its analysis the equivalent circuit shown in Figure 4.5.14. It was shown by Xiong et al. [1996], by separate impedance measurements on the anode and cathode, that most of the impedance decrease during discharge is due to the anode, as the initial formation of a Cd(OH)Jrate limiting step of the reaction. The... 

Typically, the anode consists of small particles of hydride-building alloy held together by a binder and conductive additive (acetylene black) and pressed onto a Ni-foam current collector. The impedance of the particle surface is determined by the charge transfer resistance of hydrogen reduction, double layer capacitance, and the impedance of subsequent solid-state diffusion into the bulk of the particle. To take into account electronic resistance between the particles and ionic resistance of electrolyte in pores, as well as the impedance of the particle surface, we can use the transmission line model of Figure 4.5.9. Because particle shape is best approximated as a sphere, diffusion with spherical boundary conditions, as in Eq. (30) can be used for Za. 

Mixed-conducting lithium-ion-doped emeraldine polyaniline (PAni)-PEO blends have been developed in order to achieve optimal electronic-ionic conductivity balance in nano-tin composite anodes. They found that the SEI impedance of the composite anodes increases with a decrease in PEO content and is much lower in pressed than in cast electrodes. Nano-Sn, AlSi , and Li Sn powders were studied by EIS to determine the electrochemical kinetics and intrinsic resistance during initial lithium insertion-extraction. It was shown that the SEI formed on particle surfaces, together with particle pulverization are responsible for the high contact resistance. 

Fig. 12 Relative oxidation rates by OH radicals of condensed-phase cholestane vs gas-phase m-xylene in different organic-aerosol matrices, all of which include a high fraction of motor oil. Cholestane oxidation is independent of OA concentration or the presence of a substantial SOA coating consisting of up to half of the total particle mass. However, high relative humidity slows cholestane oxidation by an order of magnitude. This suggests that a thin film of water on oil can significantly retard cholestane oxidation, perhaps by excluding the cholestane from the particle surface the SOA, on the other hand, does not coat the particle surface but rather mixes with the oil and thus does not impede cholestane oxidation...

Alternatively, nonspherical potentials have also been used, where active spots are located on the particle surface [27], or many body interactions, such as a maximum number of neighbors attracted [28], or combination of both [29], Using these structural or energetic constraints, the formation of a dense phase is hindered, thus impeding crystallization and liquid-liquid crystallization. 

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