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Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case)
The “conservatively perturbed equilibrium” (CPE) technique for a complex chemical system is computationally analyzed in a batch reactor considering different linear mechanisms with three and four species. Contrary to traditional chemical relaxation procedures, in CPE experiments only some initial co...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597328/ https://www.ncbi.nlm.nih.gov/pubmed/33286929 http://dx.doi.org/10.3390/e22101160 |
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author | Xi, Yiming Liu, Xinquan Constales, Denis Yablonsky, Gregory S. |
author_facet | Xi, Yiming Liu, Xinquan Constales, Denis Yablonsky, Gregory S. |
author_sort | Xi, Yiming |
collection | PubMed |
description | The “conservatively perturbed equilibrium” (CPE) technique for a complex chemical system is computationally analyzed in a batch reactor considering different linear mechanisms with three and four species. Contrary to traditional chemical relaxation procedures, in CPE experiments only some initial concentrations are modified; other conditions, including the total amount of chemical elements and temperature are kept unchanged. Generally, for “unperturbed” species with initial concentrations equal to their corresponding equilibrium concentrations, unavoidable extreme values are observed during relaxation to the equilibrium. If the unperturbed species is involved in one step only, this extremum is a momentary equilibrium of the step; if the unperturbed species is involved in more reactions, the extremum is not a momentary equilibrium. The acyclic mechanism with four species may exhibit two extrema and an inflection point, which corresponds to an extremum of the rate of the species change. These facts provide essential information about the detailed mechanism of the complex reaction. |
format | Online Article Text |
id | pubmed-7597328 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75973282020-11-09 Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) Xi, Yiming Liu, Xinquan Constales, Denis Yablonsky, Gregory S. Entropy (Basel) Article The “conservatively perturbed equilibrium” (CPE) technique for a complex chemical system is computationally analyzed in a batch reactor considering different linear mechanisms with three and four species. Contrary to traditional chemical relaxation procedures, in CPE experiments only some initial concentrations are modified; other conditions, including the total amount of chemical elements and temperature are kept unchanged. Generally, for “unperturbed” species with initial concentrations equal to their corresponding equilibrium concentrations, unavoidable extreme values are observed during relaxation to the equilibrium. If the unperturbed species is involved in one step only, this extremum is a momentary equilibrium of the step; if the unperturbed species is involved in more reactions, the extremum is not a momentary equilibrium. The acyclic mechanism with four species may exhibit two extrema and an inflection point, which corresponds to an extremum of the rate of the species change. These facts provide essential information about the detailed mechanism of the complex reaction. MDPI 2020-10-15 /pmc/articles/PMC7597328/ /pubmed/33286929 http://dx.doi.org/10.3390/e22101160 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Xi, Yiming Liu, Xinquan Constales, Denis Yablonsky, Gregory S. Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title | Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title_full | Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title_fullStr | Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title_full_unstemmed | Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title_short | Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case) |
title_sort | perturbed and unperturbed: analyzing the conservatively perturbed equilibrium (linear case) |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597328/ https://www.ncbi.nlm.nih.gov/pubmed/33286929 http://dx.doi.org/10.3390/e22101160 |
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