Extracting the Oscillatory Component and Defining a Mean Amplitude of Thermokinetic Oscillations in the H/Pd System

Abstract

Self-sustained oscillations may help in the research of catalytic reactions. But analysis of the resulting nonlinear time series may be complicated, not least due to the lack of a definite baseline. A mathematical method to transform such irregular time series into a more useful form that oscillates around the zero line has been proposed, which preserves both the frequency and the key topological aspects of the originals in the process. To this end, the mean value theorem for integrals has been applied in constructing a base curve for nonequilibrium, periodic thermokinetic oscillations, q(t), recorded microcalorimetrically in two experiments, respectively, with oscillatory sorptions of H2 and D2 in Pd. Once the mean values are so calculated for each period of q(t), they are subjected to cubic spline interpolation to form a new nonoscillatory curve, h(t). The latter can be used as an essential baseline for the oscillatory component of the original thermokinetic time series. Crucially, the areas under both q(t) and h(t) are supposed to be strictly identical. This being confirmed, the pointwise subtraction q(t) – h(t) yields another oscillatory time series g(t), considered to be the oscillatory component extracted from the original thermokinetic data. Subsequently, the method has been applied to a further group of nine microcalorimetric time series q(t) representing thermokinetic oscillations in the H/Pd system. Using the so-constructed g(t) curves (i.e., extracted oscillatory components), a new parameter, the mean amplitude, has been defined and used for correlating the observed gradation of intensities (i.e., amplitudes) of thermokinetic oscillations with a range of experimental conditions applied. The mean amplitude turns out to be a linear function of the first ionization potential of noble gases, admixed intentionally to H2 before its contacting Pd.