Adsorption on nanoparticles with surface defects: mean field and energy level approaches.

In this work two theoretical approximations, the so-called theoretical approach of energy levels and an extension of the modified mean field approach (TAEL and MMFA, respectively) are applied to the study of surface decoration of modified nanostructures like crystalline nanoparticles. The surface of the nanoparticles is modified by the irreversible random deposition of defects consisting in isolated atoms. Such deposition is carried out until a certain surface density is reached, leaving the rest of the sites available for a second species to adsorb. Through the formulation of the integral equation, the theoretical approaches permit obtaining the adsorption isotherms and the compressibility of the adlayer. The main difference between the two approaches is the degree of details considered in their mathematical formulations: TAEL takes in account all the energy levels meanwhile MMFA only an average. The degree of precision and usefulness of both theories were evaluated in comparison with Monte Carlo simulations in the grand canonical assembly. Several cases were studied: attractive and repulsive lateral interactions and different fraction of defects. The effects of the nanoscale were considered for different types and sizes of nanoparticles. By calculating an integral error, we are able to affirm that TAEL reproduces all the properties of the analyzed quantities from the reference simulated curves. On the other hand, the MMFA performance is good only for a certain limited range of the parameters, however the strength is in the mathematical simplicity compared to TAEL.