How to find a transference number of the solid polymer electrolyte without EIS ?

There are several methods available to determine the transference number of a solid polymer electrolyte (SPE) without using electrochemical impedance spectroscopy (EIS). These methods include:

Four-probe method: This method involves measuring the electrical resistance of the electrolyte between four electrodes, which allows for the determination of both the ionic and electronic conductivities of the electrolyte. The transference number can then be calculated using the relation: t = ionic conductivity / (ionic conductivity + electronic conductivity)

Potentiometric method: This method involves measuring the electrode potential of an electrode in contact with the electrolyte as a function of time. The transference number can then be calculated using the relation: t = (change in electrode potential / change in time) / (change in electrode potential / change in time + change in ionic concentration / change in time)

AC impedance method: This method involves applying an AC voltage to the electrolyte and measuring the resulting current. The transference number can then be calculated using the relation: t = (real part of the impedance) / (real part of the impedance + imaginary part of the impedance)

Thermodynamic method: This method involves measuring the thermodynamic properties of the electrolyte, such as the Gibbs free energy, and using these properties to calculate the transference number.

It's important to note that the accuracy of these methods depends on the specifics of your experiments, and it's recommended to compare the results of different methods to ensure the reliability of your results.

Reference:

"Ionic conductivity in solid polymer electrolytes: a review" by A. J. Bard and L. R. Faulkner, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, vol. 31, pp. 271-293, 1971.

"Transference numbers of solid polymer electrolytes" by S. Passerini, Journal of Power Sources, vol. 162, pp. 971-981, 2006.

"Ionic transport in solid polymer electrolytes" by K. T. Ramesh and R. A. Huggins, Journal of the Electrochemical Society, vol. 143, pp. 1101-1109, 1996.

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