Frequency response analysis of nonsuperimposable systems using a pseudo-transfer function: Application to systems with coverage-dependent adsorption

• Published in: Chemical engineering science Vol. 41; no. 3; pp. 495 - 510
• Main Authors: Schwartz, Jeffrey P., Sawin, Herbert H., Hatton, T.Alan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1986
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/0009-2509(86)87031-2

The concept of a pseudo-transfer function is introduced to characterize the frequency response behaviour of nonsuperimposable systems, i.e. those described by nonlinear differential equations or by linear differential equations with time-dependent coefficients. The pseudo-transfer function shapes can be used to match experimentally measured frequency response data to the most probable system model and to identify model parameters. The concepts are illustrated using a model system of coverage-dependent adsorption of the reactant on a partially exposed sample, followed by surface diffusion of the reactant and first-order chemical reaction in a modulated reactive molecular beam scattering experiment. From an exact analysis of the example system, features of nonsuperimposable systems are inferred. Nonsuperimposable systems can cause both a cusp and an inflection at the first harmonic in the pseudo-transfer function. The cusp is distinguishable from that observed for a superimposable, parallel reaction mechanism in that its position depends on the chopping frequency and other experimentally controllable parameters. The inflection also depends on chopping frequency and is not observed in superimposable systems. Thus, the pseudo-transfer function can be a sensitive means for discriminating between entirely different mechanisms that lead to similar overall system behaviour.