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Analysis of nonlinear reactions in modulated molecular beam surface experiments
Author(s) -
Olander D. R.,
Ullman Alan
Publication year - 1976
Publication title -
international journal of chemical kinetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.341
H-Index - 68
eISSN - 1097-4601
pISSN - 0538-8066
DOI - 10.1002/kin.550080416
Subject(s) - nonlinear system , chemistry , desorption , adsorption , representation (politics) , fourier transform , beam (structure) , molecular beam , kinetic energy , surface (topology) , biological system , thermodynamics , statistical physics , molecule , mathematical analysis , classical mechanics , mathematics , optics , physics , quantum mechanics , geometry , organic chemistry , politics , political science , law , biology
An approximate method of analyzing nonlinear reaction models in modulated molecular beam surface kinetic studies is developed. The exact method for treating nonlinear surface mechanisms is tedious and almost always requires computer analysis. The proposed approximate method is a simple extension of the Fourier expansion technique valid for linear surface reactions; it quickly provides analytical expressions for the phase lag and amplitude of the reaction product for any type of nonlinear surface mechanism, which greatly facilitates comparison of theory and experiment. The approximate and exact methods are compared for a number of prototypical adsorption–desorption reactions which include coverage‐dependent adsorption and desorption kinetics of order greater than unity. Except for certain extreme forms of coverage‐dependent adsorption, the approximate method provides a good representation of the exact solution. The errors increase as the nonlinearities become stronger. Fortunately, when the discrepancy between the two methods is substantial, the reaction product signal is so highly demodulated that reliable experimental data usually cannot be obtained in these regions anyway.