Abstract
Mathematically, complex chemical reactions can be simplified by “model reduction,” that is, the rigorous way of approximating and representing a complex model in simplified form. Furthermore, to reduce the dimension of the reaction mechanism, there are different available model reduction techniques (MRT). Without losing the essential information of the system, we have reduced the higher-dimension manifold to low-dimension manifold using spectral quasi equilibrium manifold (SQEM). Near the equilibrium point for different values of rate constant, the solution trajectories of reacting species are examined. The possible approaches to their solution and key problems are based on the Horiuti’s rules and their slow invariants. The characteristic properties of nodes and trees of reaction mechanisms are addressed with the graph theory. The impact of the rate coefficient over the equilibrium of the system has been measured. The numerical approximations have been measured using SQEM with MATLAB and the model is analyzed graphically.
Similar content being viewed by others
References
Constales D, Yablonsky GS, Dhooge DR, Thybout JW, Marin GB (2016) Advanced data analysis and modelling in chemical engineering. Elsevier, Amsterdam
Gorban AN, Karlin IV (2003) Method of invariant manifold for chemical kinetics. Chem Eng Sci 58:4751–4768
Gorban AN, Shahzad M (2011) The Michaelis–Menten–Stueckelberg theorem. Entropy 13:966
Kooshkbaghi M, Frouzakis CE, Boulouchos K, Karlin IV (2016) Spectral quasi-equilibrium manifold for chemical kinetics. J Phys Chem A 120:3406–4313
Maas U (1996) Simplifying chemical kinetics using intrinsic low-dimensional manifolds. In: Gas phase chemical reaction systems. Springer, Berlin, Heidelberg, pp 334–342
Shahzad M, Sultan F (2018) Complex reactions and dynamics: advanced chemical kinetics. InTech, Rijeka. https://doi.org/10.5772/intechopen.70502
Shahzad M, Rehman S, Bibi R, Wahab HA, Abdullah S, Ahmed S (2015a) Measuring the complex behavior of the SO2 oxidation reaction. Comput Ecol Softw 5:254–260
Shahzad M, Sajid M, Gulistan M, Arif H (2015b) Initially approximated quasi equilibrium manifold. J Chem Soc Pak 37:1–7
Shahzad M, Sultan F, Haq I (2016a) Computing the low dimension manifold in dissipative dynamical systems. Nucleus 53:107–113
Shahzad M, Sultan F, Wahab A, Faizullah F, Ur Rehman G (2016b) Slow manifolds in chemical kinetics. J Chem Soc Pak 38(5)
Shahzad M, Sultan F, Ali M, Khan WA, Irfan M (2019a) Slow invariant manifold assessments in multi-route reaction mechanism. J Mol Liq 284:265–270
Shahzad M, Sultan F, Shah SIA, Ali M, Khan HA, Khan WA (2019b) Physical assessments on chemically reacting species and reduction schemes for the approximation of invariant manifolds. J Mol Liq 285:237–243. https://doi.org/10.1016/j.molliq.2019.03.031
Shahzad M, Sultan F, Haq I, Ali M, Khan WA (2019c) C-matrix and invariants in chemical kinetics: a mathematical concept. Pramana J Phys. https://doi.org/10.1007/s12043-019-1723-5
Shahzad M, Shah SIA, Ali M, Sultan F (2020a) The C-matrix augmentation in a multi-route reaction mechanism. J Appl Nanosci. https://doi.org/10.1007/s13204-020-01497-6
Shahzad M, Sultan F, Ali M, Khan WA, Mustafa S (2020b) Modeling multi-route reaction mechanism for surfaces: a mathematical and computational approach. Appl Nanosci. https://doi.org/10.1007/s13204-020-01275-4
Sultan F, Shahzad M, Ali M, Khan WA (2019a) The reaction routes comparison with respect to slow invariant manifold and equilibrium points. AIP Adv 9:015212. https://doi.org/10.1063/1.5050265
Sultan F, Khan WA, Shahzad M, Ali M, Shah SIA (2019b) Activation energy characteristics of chemically reacting species in multi-route complex reaction mechanism. Indian J Phys. https://doi.org/10.1007/s12648-019-01624-2
Sultan F, Ali M, Shahzad M, Khan M (2020) Multi-route reaction mechanism and steady-state flow: a MATLAB-based analysis. Appl Nanosci. https://doi.org/10.1007/s13204-020-01410-1
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sultan, F., Ali, M., Mustafa, S. et al. The impact of the rate coefficient over the reaction mechanism. Appl Nanosci 10, 5375–5381 (2020). https://doi.org/10.1007/s13204-020-01501-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13204-020-01501-z