Generalisation of Langmuir's theory of adsorption

While studying trace elements in sediments, I became involved in researching their partitioning between the water column and the sediments (Kd), their speciation in the solid phase (referred to as particulate speciation by Tessier in his 1979 article), and the processes of adsorption.

There are various adsorption isotherms, but they can all be generalized by considering localized adsorption sites that exhibit a Langmuirian isotherm. All of these sites have the Boltzmann distribution of adsorption energies. In my opinion, there is no better approach than the generalized Langmuirian isotherm model for describing adsorption. Unfortunately, this concept has very few proponents.

This generalized approach is not only important for studying adsorption but also for mineral dissolution, reaction kinetics, investigating the interactions of plant exudates with minerals in the soil, understanding the transport of trace elements by rivers worldwide, studying the interactions between phytoplankton and trace elements (uptake), and comprehending interface chemistry.

Here are some of the best articles I have come across on the topic of adsorption processes.

1. Anandaraj, B., Eswaramoorthi, S., Rajesh, T.P., Aravind, J., Suresh Babu, P., 2018. Chromium(VI) adsorption by Codium tomentosum: evidence for adsorption by porous media from sigmoidal dose–response curve. Int. J. Environ. Sci. Technol. 15, 2595–2606. https://doi.org/10.1007/s13762-017-1488-7
2. Avnir, D., Jaroniec, M., 1989. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials. Langmuir 5, 1431–1433. https://doi.org/10.1021/la00090a032
3. Bertin, E., Droz, M., Grégoire, G., 2006. Boltzmann and hydrodynamic description for self-propelled particles. Phys. Rev. E 74, 022101. https://doi.org/10.1103/PhysRevE.74.022101
4. Bourg, A.C.M., 1987. Trace metal adsorption modelling and particle-water interactions in estuarine environments. Continental Shelf Research 7, 1319–1332. https://doi.org/10.1016/0278-4343(87)90036-7
5. Burhan, M., Shahzad, M.W., Ng, K.C., 2018. Energy distribution function based universal adsorption isotherm model for all types of isotherm. International Journal of Low-Carbon Technologies 13, 292–297. https://doi.org/10.1093/ijlct/cty031
6. Cerofolini, G.F., Rudziński, W., 1997. Chapter 1. Theoretical principles of single- and mixed-gas adsorption equilibria on heterogeneous solid surfaces, in: Studies in Surface Science and Catalysis. Elsevier, pp. 1–103. https://doi.org/10.1016/S0167-2991(97)80064-X
7. Czepirski, L, Balys, MR & Czepirska, EK 2000, ?Some generalization of Langmuir adsorption isotherm?, Internet Journal of Chemistry, vol.3, pp. 1-27.
8. Delgado, M., Arean, C., 2018. Non-linear enthalpy-entropy correlation for nitrogen adsorption in zeolites. Molecules 23, 2978. https://doi.org/10.3390/molecules23112978
9. Emons, H., Wittstock, G., 1996. Analytical in situ characterization of chemical reactivities at interfaces in aqueous systems. Marine Chemistry 53, 17–23. https://doi.org/10.1016/0304-4203(96)00009-6
10. Hochella, M.F., 2002. There’s plenty of room at the bottom: nanoscience in geochemistry. Geochimica et Cosmochimica Acta 66, 735–743. https://doi.org/10.1016/S0016-7037(01)00868-7
11. Jaroniec, M, Marczewski, A.W., 1984. Relationships defining dependence between adsorption parameters of Dubinin-Astakhov and generalized Langmuir equations. Journal of Colloid and Interface Science 101, 280–281. https://doi.org/10.1016/0021-9797(84)90030-4
12. Jaroniec, M., 1975. Adsorption on heterogeneous surfaces: The exponential equation for the overall adsorption isotherm. Surface Science 50, 553–564. https://doi.org/10.1016/0039-6028(75)90044-8
13. Jaroniec, M., Marczewski, A.W., 1984. Adsorption from solutions of nonelectrolytes on heterogeneous solid surfaces: A four-parameter equation for the excess adsorption isotherm. Monatsh Chem 115, 541–550. https://doi.org/10.1007/BF00799161
14. Jaroniec, M., Marczewski, A.W., 1984. Physical adsorption of gases on energetically heterogeneous solids I. GeneralizedLangmuir equation and its energy distribution. Monatsh Chem 115, 997–1012. https://doi.org/10.1007/BF00798768
15. Jaroniec, M., Marczewski, A.W., 1984. Physical adsorption of gases on energetically heterogeneous solids II. Theoretical extension of a generalizedLangmuir equation and its application for analysing adsorption data. Monatsh Chem 115, 1013–1038. https://doi.org/10.1007/BF00798769
16. Livi, K.J.T., Schaffer, B., Azzolini, D., Seabourne, C.R., Hardcastle, T.P., Scott, A.J., Hazen, R.M., Erlebacher, J.D., Brydson, R., Sverjensky, D.A., 2013. Atomic-Scale Surface Roughness of Rutile and Implications for Organic Molecule Adsorption. Langmuir 29, 6876–6883. https://doi.org/10.1021/la4005328
17. Marczewski, A.W., Dery?o-Marczewska, A., Jaroniec, M., 1989. A simplified integral equation for adsorption of gas mixtures on heterogeneous surfaces. Monatsh Chem 120, 225–230. https://doi.org/10.1007/BF00809278
18. Marczewski, A.W., Jaroniec, M., 1983. A new isotherm equation for single-solute adsorption from dilute solutions on energetically heterogeneous solids. Monatsh Chem 114, 711–715. https://doi.org/10.1007/BF01134184
19. Marczewski, A.W., Jaroniec, M., Dery?o-Marczewska, A., 1986. A new method for characterizing global adsorbent heterogeneity by using adsorption data. Materials Chemistry and Physics 14, 141–166. https://doi.org/10.1016/0254-0584(86)90078-7
20. Ng, K.C., Burhan, M., Shahzad, M.W., Ismail, A.B., 2017. A universal isotherm model to capture adsorption uptake and energy distribution of porous heterogeneous surface. Sci Rep 7, 10634. https://doi.org/10.1038/s41598-017-11156-6
21. Petkovska, M., Petkovska, L.T., 2003. Use of nonlinear frequency response for discriminating adsorption kinetics mechanisms resulting with bimodal characteristic functions. Adsorption 9, 133–142. https://doi.org/10.1023/A:1024241326422
22. pJougnot, D., Mendieta, A., Leroy, P., Maineult, A., 2019. Exploring the effect of the pore size distribution on the streaming potential generation in psaturated porous media, insight from pore network simulations. J. Geophys. Res. Solid Earth 124, 5315–5335. https://doi.org/10.1029/2018JB017240
23. Rudzinski, W., Lee, S.-L., Yan, C.-C.S., Panczyk, T., 2001. A Fractal Approach to Adsorption on Heterogeneous Solid Surfaces. 1. The Relationship between Geometric and Energetic Surface Heterogeneities. J. Phys. Chem. B 105, 10847–10856. https://doi.org/10.1021/jp011225e
24. Rudzinski, W., Panczyk, T., 2000. Kinetics of isothermal adsorption on energetically heterogeneous solid surfaces: a new theoretical description based on the statistical rate theory of interfacial transport. The Journal of Physical Chemistry B 104, 9149–9162. https://doi.org/10.1021/jp000045m
25. Ru?i?, I., 1996. Trace metal complexation at heterogeneous binding sites in aquatic systems. Marine Chemistry 53, 1–15. https://doi.org/10.1016/0304-4203(96)00008-4
26. Ru?i?, I., 1996. Trace metal complexation at heterogeneous binding sites in aquatic systems. Marine Chemistry 53, 1–15. https://doi.org/10.1016/0304-4203(96)00008-4
27. Sposito, G., 2004. The surface chemistry of natural particles. Oxford University Press, Oxford ; New York.
28. Vollhardt, D., Fainerman, V.B., 2010. Characterisation of phase transition in adsorbed monolayers at the air/water interface. Advances in Colloid and Interface Science 154, 1–19. https://doi.org/10.1016/j.cis.2010.01.003
29. Wang, Y., 2014. Nanogeochemistry: Nanostructures, emergent properties and their control on geochemical reactions and mass transfers. Chemical Geology 378–379, 1–23. https://doi.org/10.1016/j.chemgeo.2014.04.007
30. Zuniga-Hansen, N., Silbert, L.E., Calbi, M.M., 2018. Breakdown of kinetic compensation effect in physical desorption. Phys. Rev. E 98, 032128. https://doi.org/10.1103/PhysRevE.98.032128

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