The main aim of this paper is to introduce a new class of Lommel matrix polynomials with the help of hypergeometric matrix function within complex analysis. We derive several properties such as an entire function, order, type, matrix recurrence relations, differential equation and integral representations for Lommel matrix polynomials and discuss its various special cases. Finally, we establish an entire function, order, type, explicit representation and several properties of modified Lommel matrix polynomials. There are also several unique examples of our comprehensive results constructed.

This study reports experimental analyses of adsorption thermodynamics using the polymeric adsorbent surface, polyethersulfone (PES), with different molar ratios of ZnO nanoparticles. Fourier transform infrared (FTIR), X-ray diffraction (XRD), and field emission scanning electron microscopy (FESEM) were performed to study the adsorbent structure and morphology. FTIR results showed that both PES and ZnO nanoparticles were successfully incorporated into the nanocomposite, while the XRD analysis showed that the crystal adsorbent characteristics did not change. FESEM of the ZnO exhibits the formation of aggregates in the form of small spherical grains, and the sizes were in the range of 45–65 nm. The effects of different parameters (contact time, pH, temperature, adsorbent dosage, and diazinon concentrations) were investigated to find the optimal conditions of the prepared adsorbents. The equilibrium data for diazinon adsorption onto PES and ZnO/PES were analyzed using the Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Jovanovic, and Flory-Huggins models. Based on the values of the correlation coefficient, Langmuir and pseudo-second-order were found to be the best-fitting model. In addition, adsorption at different temperatures (288.15–303.15 K) was used to determine thermodynamic parameters such as free energy, enthalpy, and entropy changes. Finally, these results allow designing different processing units for pollution removal.