Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-SI thin films under varying relative humidity

Abstract

Polyethylene Glycol is known to have an irregular current characteristic under constant voltage and slowly varying relative humidity. In this study the current through a thin film of Gamma-isocyanatopropyltriethoxysilane added polyethylene glycol (PEG-Si), its hydrogenated, and hydrophobically modified forms is measured as a function of increasing relative humidity at equal time steps and analyzed for chaoticity. In previous studies it has been suggested that, after reaching a certain relative humidity level, a phase transition occurs from a semi crystalline state to a gel state. We propose that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended fluctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. The regime change signaled by the changing values of the maximal Lyapunov exponent occurs around a relative humidity of 70% consistent with the phase transition from semi crystalline state to gel state. Detrended fluctuation analysis has also been performed; this also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. Our study also confirms that the improvement in stability of the current through PEG-Si can be performed by hydrogenating and hydrophobically modifying PEG-Si.