Stochastic approaches: modeling the probability of encounters between H2-molecules and metallic atomic clusters in a cubic box

MAXIMILIANO RIDDICK; ENRIQUE E. ÁLVAREZ; REQUEJO, FÉLIX G.; LEANDRO ANDRINI

arXiv

Cornell University

Año: 2023

2331-8422

In recent years the advance of chemical synthesis has made it possible toobtain extquotedblleft nakedextquotedblright clusters of differenttransition metals. It is well known that cluster experiments allow studying thefundamental reactive behavior of catalytic materials in an environment thatavoids the complications present in extended solid-phase research. Inphysicochemical terms, the question that arises is the chemical reduction ofmetallic clusters could be affected by the presence of H2 molecules,that is, by the probability of encounter that these small metal atomicagglomerates can have with these reducing species. Therefore, we consider thestochastic movement of N molecules of hydrogen in a cubic box containing Mmetallic atomic clusters in a confined region of the box. We use a Wienerprocess to simulate the stochastic process, with σ given by theMaxwell-Boltzmann relationships, which enabled us to obtain an analyticalexpression for the probability density function. This expression is an exactexpression, obtained under an original proposal outlined in this work,extit{i.e.} obtained from considerations of extit{mathematical rebounds}.On this basis, we obtained the probability of encounter for three differentvolumes, 0.13, 0.23 and 0.43 m3, at threedifferent temperatures in each case, 293, 373 and 473 K, for 101≤N≤1010, comparing the results with those obtainedconsidering the distribution of the position as a Truncated NormalDistribution. Finally, we observe that the probability is significantlyaffected by the number N of molecules and by the size of the box, not by thetemperature.