Quasi-Steady-State and Partial-Equilibrium Approximations in Chemical Kinetics: One Stage Beyond the Elimination of a Fast Variable

Abstract

<pre>Classical approximations in chemical kinetics, the quasi-steady-state approximation (QSSA) and the partial-equilibrium approximation (PEA), are used to reduce rate equations for the concentrations and the extents of the reaction steps, respectively. We make precise two conditions on the rate constants necessary and sufficient to eliminate a well-chosen variable in the vicinity of a steady state. The first condition expresses that dynamics admits a small characteristic time associated with a fast variable. The second condition ensures that the fast variable is a concentration for QSSA and an extent for PEA. Both approximations exploit the zeroth order of a singular perturbation method. Eliminating a fast variable does not mean that it has reached a steady state. The fast evolution is considered over and the slow evolution of the eliminated variable is governed by the slow variables. The evolution of the slow variables occurs on a slow manifold in the space of the concentrations or the extents. In some cases the dynamics of the slow variables can be associated with a reduced chemical scheme. QSSA and PEA are applied to three chemical schemes associated with linear and nonlinear dynamics. We find that QSSA cannot be identified with the elimination of a reactive intermediate. The nonlinearities of the rate equations induce a more complex behavior.</pre>

Thermodynamic Consistency and Kinetic Mechanism of a Complex Reaction Pathway by Analysis of Its Constituent Cyclic Networks

“…Kinetic analysis of chemical reaction networks typically involves solving the underlying system of differential equations to determine species concentrations. − Modeling of complex reaction networks is of particular interest in this domain and has been widely explored in previous works. − Several studies have used a combination of kinetic and thermodynamic approaches to quantify the overall rates of cyclic reaction systems. ,,,− …”