(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Ensuring the purity of edible oils is essential for human health, especially given the widespread use of oils in modern diets. Oil impurities, often in the form of nanoscale particles, necessitate advanced analytical techniques, confirmed by a theoretical model, for detection. In this study, a nanoquantum model based on Klein-Gordon and energy-momentum quantum equations beside perturbation theory is developed to theoretically explain how such impurities affect the spectral properties of pure oils. The model predicts that the impurities affect the wave number and length through the medium-field potential and the collision energy resulting from the free vibration. The intensity is also affected by these parameters in addition to the effects of the internal magnetic field along with the friction through the exponential term. This means that the effects of impurities on the intensity should be relatively larger than the wave number and length because of the existence of additional parameters and the enhancing effect of the exponential term. Experimental studies were carried out using UV-VIS and FTIR techniques on pure olive oil mixed with corn, sunflower, and soybean oils. The findings indicated a considerable decrease in the intensity of olive oil when increasing the amount of mixture associated with very slight changes in the number and length of waves. The results of the absorption and transmittance of three bean oil samples consisting of different impurities indicated that the effects of impurities on the intensity are more significant compared to the number and length of the waves, which is consistent with the theoretical findings. The theoretical model also shows that the inner shell electron energies remain largely unaffected by impurities, resulting in spectral convergence at high wave numbers (short wavelengths). In contrast, outer shell energies vary significantly due to environmental perturbations, causing spectral divergence at low wave numbers (long wavelengths). These theoretical predictions are validated using experimental data obtained by Fourier transform infrared (FTIR) and ultraviolet-visible (UV-vis) spectroscopy on various oil samples, including olive and sesame oils. The strong agreement between theoretical expectations and experimental observations confirm the effectiveness of the model in detecting oil purity.