Ion transfer resistance

Ion transfer resistance, caused by the slowness of the transport of charge-determining ions across the (solid-liquid) Interface. This leads to a finite exchange current density and an Ion transfer resistance 6 given by... 

Figure 3.31. Randles circuit, consisting of a pure capacitance C. an ion transfer resistance 0 and a diflusion impedance all counted per unit area.

Much attention has been paid to a variety of inorganic solid electrolytes (Li7P3Sn [18] etc.) and its application to all-solid-state lithium-ion batteries. Since the transference number of the inorganic solid electrolyte is almost unity, the lithium-ion conductivity of the solid electrolyte is almost comparable to that of organic liquid electrolyte. However, in spite of the presence of highly lithium-ion conductive solid electrolytes, the all-solid-state batteries had not provided sufficient power densities until recendy. One of the critical reasons for the limited power density was due to the large lithium-ion transfer resistance at the interface between cathode and solid electrolyte. 

When the dilute stream becomes progressively depleted in ions, the increase in mass transfer resistance at the water-resin boundary... 

From an analysis of data for polypyrrole, Albery and Mount concluded that the high-frequency semicircle was indeed due to the electron-transfer resistance.203 We have confirmed this using a polystyrene sulfonate-doped polypyrrole with known ion and electron-transport resistances.145 The charge-transfer resistance was found to decrease exponentially with increasing potential, in parallel with the decreasing electronic resistance. The slope of 60 mV/decade indicates a Nemstian response at low doping levels. 

Very often, the electrode-solution interface can be represented by an equivalent circuit, as shown in Fig. 5.10, where Rs denotes the ohmic resistance of the electrolyte solution, Cdl, the double layer capacitance, Rct the charge (or electron) transfer resistance that exists if a redox probe is present in the electrolyte solution, and Zw the Warburg impedance arising from the diffusion of redox probe ions from the bulk electrolyte to the electrode interface. Note that both Rs and Zw represent bulk properties and are not expected to be affected by an immunocomplex structure on an electrode surface. On the other hand, Cdl and Rct depend on the dielectric and insulating properties of the electrode-electrolyte solution interface. For example, for an electrode surface immobilized with an immunocomplex, the double layer capacitance would consist of a constant capacitance of the bare electrode (Cbare) and a variable capacitance arising from the immunocomplex structure (Cimmun), expressed as in Eq. (4). 

There will always be a charge transfer resistance (R i) associated with the ion exchange across the interface. Where there are very small Debye lengths in each phase (compared with the size of an ion) the exchange current I o can be evaluated from the relationship... 

The mass transfer resistance of chloride ion in feed and stripping solution may be neglected. 

A significant feature of physical adsorption is that the rate of the phenomenon is generally too high and consequently, the overall rate is controlled by mass (or heat transfer) resistance, rather than by the intrinsic sorption kinetics (Ruthven, 1984). Thus, sorption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

The equivalent circuit corresponding to this interface is shown in Fig. 6.1b. The charge-transfer resistances for the exchange of sodium and chloride ions are very low, but the charge-transfer resistance for the polyanion is infinitely high. There is no direct sensing application for this type of interface. However, it is relevant for the entire electrochemical cell and to many practical potentiometric measurements. Thus if we want to measure the activity of an ion with the ion-selective electrode it must be placed in the same compartment as the reference electrode. Otherwise, the Donnan potential across the membrane will appear in the cell voltage and will distort the overall result. 

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