In chemistry, catalytic resonance theory was developed to describe the kinetics of reaction acceleration using dynamic catalyst surfaces. Catalytic reactions occurring on surfaces that undergo variation in surface binding energy and/or entropy exhibit overall increase in reaction rate when the surface binding energy frequencies are comparable to the natural frequencies of the surface reaction, adsorption, and desorption.
History
Catalytic resonance theory is constructed on the Sabatier principle of catalysis developed by French chemistry Paul Sabatier. In the limit of maximum catalytic performance, the surface of a catalyst is neither too strong nor too weak. Strong binding results in an overall catalytic reaction rate limitation due to product desorption, while weak binding catalysts are limited in the rate of surface chemistry. Optimal catalyst performance is depicted as a 'volcano' peak using a descriptor of the chemical reaction defining different catalytic materials. Experimental evidence of the Sabatier principle was first demonstrated by Balandin in 1960.
The concept of catalytic resonance was proposed on dynamic interpretation of the Sabatier volcano reaction plot. As described, extension of either side of the volcano plot above the peak defines the timescales of the two rate-limiting phenomena such as surface reaction(s) or desorption. For binding energy oscillation amplitudes that extend across the volcano peak, the amplitude endpoints intersect the transiently accessible faster timescales of independent reaction phenomena. At the conditions of sufficiently fast binding energy oscillation, the transient binding energy variation frequency matches the natural frequencies of the reaction and the rate of overall reaction achieves turnover frequencies greatly in excess of the volcano plot peak.
Theory
The basis of catalytic resonance theory utilizes the transient behavior of adsorption, surface reactions, and desorption as surface binding energy and surface transition states oscillate with time. The binding energy of a single species, i, is described via a temporal functional including square or sinusoidal waves of frequency, fi, and amplitude, dUi:
Other surface chemical species, j, are related to the oscillating species, i, by the constant linear parameter, gamma γi-j:
The two surface species also share the common enthalpy of adsorption, delta δi-j. Specification of the oscillation frequency and amplitude of species i and relating γi-j and δi-j for all other surface species j permits determination of all chemical surface species adsorption enthalpy with time. The transition state energy of a surface reaction between any two species i and j is predicted by the linear scaling relationship of the Bell–Evans–Polanyi principle which relates to the surface reaction enthalpy, ΔHi-j, to the transition state energy, Ea, by parameters α and β with the following relationship:
The oscillating surface and transition state energies of chemical species alter the kinetic rate constants associated with surface reaction, adsorption, and desorption. The surface reaction rate constant of species i converting to surface species j includes the dynamic activation energy:
The resulting surface chemistry kinetics are then described via a surface reaction rate expression containing dynamic kinetic parameters responding to the oscillation in surface binding energy:
,
with k reactions with dynamic activation energy. The desorption rate constant also varies with oscillating surface binding energy by:
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Implementation of dynamic surface binding energy of a reversible A-to-B reaction on a heterogeneous catalyst in a continuous flow stirred tank reactor operating at 1% conversion of A produces a sinusoidal binding energy in species B as shown. In the transition between surface binding energy amplitude endpoints, the instantaneous reaction rate (i.e., turnover frequency) oscillates over an order of magnitude as a limit cycle solution.