TY  - JOUR
AU  - Ezzati, Rohollah
AU  - Azizi, Maryam
PY  - 2026
DA  - 2026/09/28
TI  - The Pseudo-Second-Order Model in Adsorption Kinetics: Why a Good Fit Does Not Prove a Two-Site Chemisorption Mechanism
JO  - Environmental Adsorption Research
T2  - Environmental Adsorption Research
JF  - Environmental Adsorption Research
VL  - 1
IS  - 1
SP  - 4
EP  - 14
DO  - 10.62762/EAR.2026.643297
UR  - https://www.icck.org/article/abs/EAR.2026.643297
KW  - pseudo-second-order model
KW  - adsorption kinetics
KW  - chemisorption mechanism
KW  - Langmuir kinetics
KW  - intraparticle diffusion
KW  - statistical rate theory
AB  - The pseudo-second-order (PSO) model, popularized by Ho and McKay's work on divalent metal sorption onto peat, is routinely misinterpreted as proof of a two-site chemisorption mechanism. This article provides a rigorous, multi-faceted refutation of that inference. It demonstrates that a PSO fit offers no mechanistic proof through three converging lines of evidence. First, the PSO rate law is mathematically non-unique: it emerges as a limiting case from Langmuir kinetics, intraparticle diffusion, and statistical rate theory. Most critically, the two-site Coleman mechanism itself yields a mixed-order rate equation in which pure PSO appears only under restrictive conditions; a formal reductio ad absurdum further reveals that interpreting PSO as a two-site signature contradicts its own short-time behavior. Second, the linearized fitting method suffers from spurious correlation and statistical bias. Third, the independent-site collision required by the mechanism is physically implausible for solid adsorbents. The routine practice of inferring a chemisorption pathway from a PSO fit must be replaced by independent experimental validation.
SN  - pending
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Ezzati2026The,
  author = {Rohollah Ezzati and Maryam Azizi},
  title = {The Pseudo-Second-Order Model in Adsorption Kinetics: Why a Good Fit Does Not Prove a Two-Site Chemisorption Mechanism},
  journal = {Environmental Adsorption Research},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {4-14},
  doi = {10.62762/EAR.2026.643297},
  url = {https://www.icck.org/article/abs/EAR.2026.643297},
  abstract = {The pseudo-second-order (PSO) model, popularized by Ho and McKay's work on divalent metal sorption onto peat, is routinely misinterpreted as proof of a two-site chemisorption mechanism. This article provides a rigorous, multi-faceted refutation of that inference. It demonstrates that a PSO fit offers no mechanistic proof through three converging lines of evidence. First, the PSO rate law is mathematically non-unique: it emerges as a limiting case from Langmuir kinetics, intraparticle diffusion, and statistical rate theory. Most critically, the two-site Coleman mechanism itself yields a mixed-order rate equation in which pure PSO appears only under restrictive conditions; a formal reductio ad absurdum further reveals that interpreting PSO as a two-site signature contradicts its own short-time behavior. Second, the linearized fitting method suffers from spurious correlation and statistical bias. Third, the independent-site collision required by the mechanism is physically implausible for solid adsorbents. The routine practice of inferring a chemisorption pathway from a PSO fit must be replaced by independent experimental validation.},
  keywords = {pseudo-second-order model, adsorption kinetics, chemisorption mechanism, Langmuir kinetics, intraparticle diffusion, statistical rate theory},
  issn = {pending},
  publisher = {Institute of Central Computation and Knowledge}
}