Gregory S. Yablonsky

Temporal analysis of products: basic principles, applications, and theory

This paper discusses a temporal analysis of products approach, which can be considered as an advanced kinetic strategy at the boundary between traditional applied kinetics and surface science. The basic principles, examples of application in heterogeneous catalysis and theoretical framework are discussed.

Chapter 2 Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series

Abstract The non-linear theory of steady-steady (quasi-steady-state/pseudo-steady-state) kinetics of complex catalytic reactions is developed. It is illustrated in detail by the example of the single-route reversible catalytic reaction. The theoretical framework is based on the concept of the kinetic polynomial which has been proposed by authors in 1980–1990s and recent results of the algebraic theory, i.e. an approach of hypergeometric functions introduced by Gel’fand, Kapranov and Zelevinsky (1994) and more developed recently by Sturnfels (2000) and Passare and Tsikh (2004). The concept of ensemble of equilibrium subsystems introduced in our earlier papers (see in detail Lazman and Yablonskii, 1991) was used as a physico-chemical and mathematical tool, which generalizes the well-known concept of “equilibrium step”. In each equilibrium subsystem, (n−1) steps are considered to be under equilibrium conditions and one step is limiting (n is a number of steps of the complex reaction). It was shown that all solutions of these equilibrium subsystems define coefficients of the kinetic polynomial.

Forty years of temporal analysis of products

A detailed understanding of reaction mechanisms and kinetics is required in order to develop and optimize catalysts and catalytic processes. While steady-state investigations are known to give a global view of the catalytic system, transient studies are invaluable since they can provide more comprehensive insight into elementary steps. For almost forty years temporal analysis of products (TAP) has been successfully utilized for transient studies of gas phase heterogeneous reactions, and there have been a number of advances in instrumentation and numerical modeling methods in that time. Since TAP is a complex methodology it is often viewed as a niche specialty. With the purpose to make TAP more relevant and approachable to a wider segment of the catalytic research community, part of the intention of this work is to highlight the significant contributions TAP has made to elucidating mechanistic and kinetic aspects of complex, multi-step heterogeneous reactions. With this in mind, an outlook is also disclosed for the technique in terms of what is needed to revitalize the field and make it more applicable to the recent advances in catalyst characterization (e.g. operando modes).

New Patterns in Steady-State Chemical Kinetics: Intersections, Coincidences, Map of Events (Two-Step Mechanism)

New patterns of steady-state chemical kinetics for continuously stirred-tank reactors (CSTR) have been found, i.e., intersections, maxima and coincidences, for two- step mechanism A↔B→C. There were found elegant analytical relationships for characteristics of these patterns (space times, values of concentrations and rates) allowing kinetic parameters to be easily determined. It was demonstrated that for the pair of species involved into the irreversible reaction (B and C), the space time of their corresponding concentration dependence intersection is invariant and does not depend on the initial conditions of the system. Maps of patterns are presented for visualization of their combinations and ranking in space time, and values of concentration and rates.

Dual kinetic curves in reversible electrochemical systems

We introduce dual kinetic chronoamperometry, in which reciprocal relations are established between the kinetic curves of electrochemical reactions that start from symmetrical initial conditions. We have performed numerical and experimental studies in which the kinetic curves of the electron-transfer processes are analyzed for a reversible first order reaction. Experimental tests were done with the ferrocyanide/ferricyanide system in which the concentrations of each component could be measured separately using the platinum disk/gold ring electrode. It is shown that the proper ratio of the transient kinetic curves obtained from cathodic and anodic mass transfer limited regions give thermodynamic time invariances related to the reaction quotient of the bulk concentrations. Therefore, thermodynamic time invariances can be observed at any time using the dual kinetic curves for reversible reactions. The technique provides a unique possibility to extract the non-steady state trajectory starting from one initial condition based only on the equilibrium constant and the trajectory which starts from the symmetrical initial condition. The results could impact battery technology by predicting the concentrations and currents of the underlying non-steady state processes in a wide domain from thermodynamic principles and limited kinetic information.

Explicit formulas for reaction probability in reaction-diffusion experiments

Abstract A computational procedure is developed for determining the conversion probability for reaction-diffusion systems in which a first-order catalytic reaction is performed over active particles. We apply this general method to systems on metric graphs, which may be viewed as 1-dimensional approximations of 3-dimensional systems, and obtain explicit formulas for conversion. We then study numerically a class of 3-dimensional systems and test how accurately they are described by model formulas obtained for metric graphs. The optimal arrangement of active particles in a 1-dimensional multiparticle system is found, which is shown to depend on the level of catalytic activity: conversion is maximized for low catalytic activity when all particles are bunched together close to the point of gas injection, and for high catalytic activity when the particles are evenly spaced.

Reciprocal relations between kinetic curves

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility,

Estimation of the remaining lifetime of deactivated catalyst via the spatial average catalyst activity illustrated by the water-gas shift and steam methane reforming processes

\dot{x}=Kx

Reaction–diffusion on metric graphs: From 3D to 1D

, the kinetic operator

Kinetic Studies of Photocatalytic Degradation in a TiO2 Slurry System: Distinguishing Working Regimes and Determining Rate Dependences

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