Biopolymers are expected to replace synthetic polymers in the quest for cost-effective, environment friendly, and pollution free technology. We report here a study on gelatin films with different concentrations of lithium perchlorate, which may be a candidate for electrolyte material in solid polymer batteries. Morphology studies and impedance spectroscopy both are done on the same set of samples. We study the microstructure of the film by SEM and try to see if a correlation between impedance spectroscopy results and features of gel morphology can be identified. A network structure is revealed in the SEM images where details of the network parameters appear to depend on the salt fraction. Analysis of the impedance measurements is done using a physically meaningful model based on material properties instead of the usual equivalent circuit formalism, where circuit elements are difficult to interpret. We find that anomalous diffusion of charge carriers plays an important role; this is incorporated through a fractional calculus approach.

The purpose of the present work is to study the fractal behaviour of prime Indian stock exchanges, namely Bombay Stock Exchange Sensitivity Index (BSE Sensex) and National Stock Exchange (NSE). To analyze the monofractality of these indices we have used Higuchi method and Katz method separately. By applying Mutifractal Detrended Fluctuation Analysis (MFDFA) technique we have calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for the present indices. We have deduced Hölder exponents as well as singularity spectra for BSE and NSE. It has been observed that both the stock exchanges are possessing self-similarity at different small ranges separately and inhomogeneously. By comparing the multifractal behaviour of the BSE and NSE indices, we have found that the second one exhibits a richer multifractal feature than the first one.

In this article, we report a study on ion conduction in gelatin films with different concentrations of glycerol as a plasticizer; these films might be a candidate for electrolyte materials in solid polymer batteries. The ion conductivity was appreciable, showing a maximum of about 9.14 3 10 23 S/m at room temperature without the addition of any ionic salt. Analysis of the impedance measurements was done with a model based on material properties instead of the usual equivalent circuit formalism, where circuit elements are difficult to interpret. Generalized calculus was used to model the anomalous diffusion in the system.

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