Investigating Theoretical Frameworks: Comprehending the Relationship between σ, n, and μ in MnO₂ Dispersed Films

Solid polymer electrolytes (SPEs) made from a polymer-salt matrix show great potential for use in various applications, such as batteries, fuel cells, supercapacitors, solar cells, and electrochromic devices. Research on various theoretical and experimental aspects of these SPEs is highly pursued worldwide. However, due to the lack of direct experimental techniques for the measurement of the number of charge carriers (n) and their mobility (μ), reports on their correlation with conductivity (σ) and their exact theoretical justification are rare in literature studies. This paper is an attempt toward the search for the well-established theoretical formulation for n and μ that can justify the experimental results. In a previous attempt, it could only be demonstrated that the available theoretical bases show different values, but we could not come to any concrete conclusion. This research involves the use of three theoretical models, namely, the Rice and Roth model, the Trukhan model, and the Schutt and Gerdes model. The purpose of this study is to analyze the varying conductivity levels by calculating the concentration and mobility of charge carriers. To obtain the required parameters, impedance spectroscopy data were used. The Trukhan model was used to determine the precise value of the diffusion coefficient. By utilizing the dielectric tangent loss, the concentration of charge carriers and ion mobility were calculated. The Schutt and Gerdes (S&G) model was also used; this model is based on the dielectric constant and the relaxation frequency, which were derived from the EIS data. Finally, the Rice and Roth model was also employed, which is known for the ion transport in "super" ionic conductors. This was employed on the temperature-dependent impedance data for three different compositions of the films. A correlation is established between n and μ with σ using all three models. However, the Trukhan model is the most suitable for explaining the behavior of our system.