Mean field approach applied to surface deposition on a modified electrode

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.

Theoretical approach to energy levels applied to modified surfaces

The main objective of this work is to present a new theoretical basis to describe surface deposition on a modified electrode surface. The surface is modified via the irreversible deposition of fixed particles or impurities that can block a fraction of the adsorption sites. An electroactive species was allowed to adsorb to the accessible sites and transfer electric charge. Energetics interactions between the electroactive particles and impurities were considered. The theoretical approach of energy levels (TAEL) was presented, through the integral equation formalism, where for its formulation the binomial distribution of energy levels and the standard Langmuir isotherm were considered. Adsorption isotherms and the compressibility of the adsorption layer were compared with Monte Carlo simulations and the recently published modified mean field approach (MMFA). Various conditions were studied: attractive and repulsive lateral interactions, and different quantities of impurities in one- and two-dimensional lattices. The performance of the theoretical approximations was analyzed by calculating an integral error.