Spectroscopic analysis of residual radicals of gamma sterilized UHMWPE with fractional order differential operators

The purpose of this research was to evaluate the Grunwald-Letnikov definition of fractional order derivatives for determining the fractional derivative of ESR signals from UHMWPE free radicals using the fitted Gaussian distribution method. Specifically, the study focused on analyzing two long-lasting oxygen-induced residual radicals di- or tri-enyls with a carbon center radical (R1) and the oxygen-containing radical (R2). The impact of the derivative order on ESR spectral parameters, such as the Landé g-factor and peak-to-peak separation, was analyzed, and new spectral parameters were established for both radicals. The samples were measured in an ESR tube using ESR power saturation techniques at room temperature. Following the measurements, the fitted Gaussian distribution of the ESR signals was used to determine the fractional derivative using the Grunwald-Letnikov definition. Two estimators (I and II) were developed for both radicals, and their values were found to be 9.19 and 4.27 for Radical R1 and 11.51 and 2060.62 for Radical R2. Our results showed that the fractional derivative approach provided accurate and reliable estimations for the radicals. This method can be easily implemented for various ESR signals and can be useful in many applications, including materials science and biomedical research. The accuracy and reliability of our estimators were confirmed by comparing them with the results obtained from the conventional method. Our findings have important implications for materials science and biomedical research, where ESR signals are widely used. This method can help researchers to obtain more accurate and reliable estimations of radicals, which can ultimately lead to more accurate and reliable conclusions in their studies. Additional research is required to assess the effectiveness of this approach on various ESR signals and to investigate its potential use in other fields of study.