139 research outputs found

    Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

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    In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 50915100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, μ. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or μ, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed

    Development of a score for prediction of occult malignancy in stroke patients (occult-5 score).

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    BACKGROUND AND PURPOSE Malignancy associated acute ischemic stroke (AIS) requires specific diagnostic work-up, treatment and prevention to improve outcome. This study aimed to develop a biomarker-based score for prediction of occult malignancy in AIS patients. METHODS Single-center cross-sectional study including consecutive AIS patients treated between July 2017 and November 2018. Patients with active malignancy at presentation, or diagnosed within 1 year thereafter and patients free of malignancy, were included and malignancy associated biomarkers were assessed. LASSO analyses of logistic regression were performed to determine biomarkers predictive of active malignancy. Predictors were derived from a predictive model for active malignancy. A comparison between known and unknown (=occult) malignancies when the index stroke occurred was used to eliminate variables not associated with occult malignancy. A predictive score (OCCULT-5 score) for occult malignancy was developed based on the remaining variables. RESULTS From 1001 AIS patients, 61 (6%) presented an active malignancy. Thirty-nine (64%) were known and 22 (36%) occult. Five variables were included in the final OCCULT-5 score: age ≥ 77 years, embolic stroke of undetermined source, multi-territorial infarcts, D-dimer levels ≥ 820 µ/gL, and female sex. A score of ≥ 3 predicted an underlying occult malignancy with a sensitivity of 64%, specificity of 73%, positive likelihood ratio of 2.35 and a negative likelihood ratio of 0.50. CONCLUSIONS The OCCULT-5 score might be useful to identify patients with occult malignancy. It may thus contribute to a more effective and timely treatment and thus lead to a positive impact on overall outcome

    Electrochemical methods for speciation of trace elements in marine waters. Dynamic aspects

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    The contribution of electrochemical methods to the knowledge of dynamic speciation of toxic trace elements in marine waters is critically reviewed. Due to the importance of dynamic considerations in the interpretation of the electrochemical signal, the principles and recent developments of kinetic features in the interconversion of metal complex species will be presented. As dynamic electrochemical methods, only stripping techniques (anodic stripping voltammetry and stripping chronopotentiometry) will be used because they are the most important for the determination of trace elements. Competitive ligand ex- change-adsorptive cathodic stripping voltammetry, which should be considered an equilibrium technique rather than a dynamic method, will be also discussed because the complexing parameters may be affected by some kinetic limitations if equilibrium before analysis is not attained and/or the flux of the adsorbed complex is in fluenced by the lability of the natural complexes in the water sample. For a correct data interpretation and system characterization the comparison of results obtained from different techniques seems essential in the articulation of a serious discussion of their meaning

    Elemental Composition of Natural Nanoparticles and Fine Colloids in European Forest Stream Waters and Their Role as Phosphorus Carriers

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    "This is the peer reviewed version of the following article: Gottselig, N., W. Amelung, J. W. Kirchner, R. Bol, W. Eugster, S. J. Granger, C. Hernández-Crespo, et al. 2017. Elemental Composition of Natural Nanoparticles and Fine Colloids in European Forest Stream Waters and Their Role as Phosphorus Carriers. Global Biogeochemical Cycles 31 (10). American Geophysical Union (AGU): 1592 1607. doi:10.1002/2017gb005657, which has been published in final form at https://doi.org/10.1002/2017GB005657. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] Biogeochemical cycling of elements largely occurs in dissolved state, but many elements may also be bound to natural nanoparticles (NNP, 1-100 nm) and fine colloids (100-450 nm). We examined the hypothesis that the size and composition of stream water NNP and colloids vary systematically across Europe. To test this hypothesis, 96 stream water samples were simultaneously collected in 26 forested headwater catchments along two transects across Europe. Three size fractions (similar to 1-20 nm, >20-60 nm, and >60 nm) of NNP and fine colloids were identified with Field Flow Fractionation coupled to inductively coupled plasma mass spectrometry and an organic carbon detector. The results showed that NNP and fine colloids constituted between 2 +/- 5% (Si) and 53 +/- 21% (Fe; mean +/- SD) of total element concentrations, indicating a substantial contribution of particles to element transport in these European streams, especially for P and Fe. The particulate contents of Fe, Al, and organic C were correlated to their total element concentrations, but those of particulate Si, Mn, P, and Ca were not. The fine colloidal fractions >60 nm were dominated by clay minerals across all sites. The resulting element patterns of NNP <60 nm changed from North to South Europe from Fe-to Ca-dominated particles, along with associated changes in acidity, forest type, and dominant lithology.The authors gratefully acknowledge the assistance of the following people in locating suitable sampling sites, contacting site operators, performing the sampling, and providing data: A. Avila Castells (Autonomous University of Barcelona), R. Batalla (University of Lleida), P. Blomkvist (Swedish University of Agricultural Sciences), H. Bogena (Julich Research Center), A.K. Boulet (University of Aveiro), D. Estany (University of Lleida), F. Garnier (French National Institute of Agricultural Research), H.J. Hendricks-Franssen (Research Center Julich), L. JacksonBlake (James Hutton Institute, NIVA), T. Laurila (Finnish Meteorological Institute), A. Lindroth (Lund University), M.M. Monerris (Universitat Politecnica de Valencia), M. Ottosson Lofvenius (Swedish University of Agricultural Sciences), I. Taberman (Swedish University of Agricultural Sciences), F. Wendland (Research Center Julich), T. Zetterberg (Swedish University of Agricultural Sciences and The Swedish Environmental Research Institute, IVL) and further unnamed contributors. The Swedish Infrastructure for Ecosystem Science (SITES) and the Swedish Integrated Monitoring, the latter financed by the Swedish Environmental Protection Agency, and ICOS Sweden have supported sampling and provided data for the Swedish sites. J.J.K. gratefully acknowledges the support from CESAM (UID/AMB/50017/2013), funded by the FCT/MCTES (PIDDAC) with cofunding by FEDER through COMPETE. N.G. gratefully acknowledges all those who contributed to organizing and implementing the continental sampling. The raw data can be found at http://hdl.handle.net/2128/14937. This project was partly funded by the German Research Foundation (DFG KL2495/1-1).Gottselig, N.; Amelung, W.; Kirchner, J.; Bol, R.; Eugster, W.; Granger, S.; Hernández Crespo, C.... (2017). Elemental Composition of Natural Nanoparticles and Fine Colloids in European Forest Stream Waters and Their Role as Phosphorus Carriers. Global Biogeochemical Cycles. 31(10):1592-1607. https://doi.org/10.1002/2017GB005657S159216073110Baken, S., Moens, C., van der Grift, B., & Smolders, E. (2016). Phosphate binding by natural iron-rich colloids in streams. Water Research, 98, 326-333. doi:10.1016/j.watres.2016.04.032Baken, S., Regelink, I. C., Comans, R. N. J., Smolders, E., & Koopmans, G. F. (2016). Iron-rich colloids as carriers of phosphorus in streams: A field-flow fractionation study. Water Research, 99, 83-90. doi:10.1016/j.watres.2016.04.060Benedetti, M. F., Van Riemsdijk, W. H., Koopal, L. K., Kinniburgh, D. G., Gooddy, D. C., & Milne, C. J. (1996). Metal ion binding by natural organic matter: From the model to the field. Geochimica et Cosmochimica Acta, 60(14), 2503-2513. doi:10.1016/0016-7037(96)00113-5Binkley, D., Ice, G. G., Kaye, J., & Williams, C. A. (2004). NITROGEN AND PHOSPHORUS CONCENTRATIONS IN FOREST STREAMS OF THE UNITED STATES. Journal of the American Water Resources Association, 40(5), 1277-1291. doi:10.1111/j.1752-1688.2004.tb01586.xBishop, K., Buffam, I., Erlandsson, M., Fölster, J., Laudon, H., Seibert, J., & Temnerud, J. (2008). Aqua Incognita: the unknown headwaters. Hydrological Processes, 22(8), 1239-1242. doi:10.1002/hyp.7049Bol, R., Julich, D., Brödlin, D., Siemens, J., Kaiser, K., Dippold, M. A., … Hagedorn, F. (2016). Dissolved and colloidal phosphorus fluxes in forest ecosystems-an almost blind spot in ecosystem research. Journal of Plant Nutrition and Soil Science, 179(4), 425-438. doi:10.1002/jpln.201600079Buffle, J., & Leppard, G. G. (1995). Characterization of Aquatic Colloids and Macromolecules. 2. Key Role of Physical Structures on Analytical Results. Environmental Science & Technology, 29(9), 2176-2184. doi:10.1021/es00009a005Celi, L., & Barberis, E. (s. f.). Abiotic stabilization of organic phosphorus in the environment. Organic phosphorus in the environment, 113-132. doi:10.1079/9780851998220.0113Dahlqvist, R., Benedetti, M. F., Andersson, K., Turner, D., Larsson, T., Stolpe, B., & Ingri, J. (2004). Association of calcium with colloidal particles and speciation of calcium in the Kalix and Amazon rivers. Geochimica et Cosmochimica Acta, 68(20), 4059-4075. doi:10.1016/j.gca.2004.04.007Darch, T., Blackwell, M. S. A., Hawkins, J. M. B., Haygarth, P. M., & Chadwick, D. (2014). A Meta-Analysis of Organic and Inorganic Phosphorus in Organic Fertilizers, Soils, and Water: Implications for Water Quality. Critical Reviews in Environmental Science and Technology, 44(19), 2172-2202. doi:10.1080/10643389.2013.790752Dynesius, M., & Nilsson, C. (1994). Fragmentation and Flow Regulation of River Systems in the Northern Third of the World. Science, 266(5186), 753-762. doi:10.1126/science.266.5186.753Erickson, H. P. (2009). Size and Shape of Protein Molecules at the Nanometer Level Determined by Sedimentation, Gel Filtration, and Electron Microscopy. Biological Procedures Online, 11(1), 32-51. doi:10.1007/s12575-009-9008-xEspinosa, M., Turner, B. L., & Haygarth, P. M. (1999). Preconcentration and Separation of Trace Phosphorus Compounds in Soil Leachate. Journal of Environmental Quality, 28(5), 1497-1504. doi:10.2134/jeq1999.00472425002800050015xFernández-Martínez, M., Vicca, S., Janssens, I. A., Sardans, J., Luyssaert, S., Campioli, M., … Peñuelas, J. (2014). Nutrient availability as the key regulator of global forest carbon balance. Nature Climate Change, 4(6), 471-476. doi:10.1038/nclimate2177Giddings, J., Yang, F., & Myers, M. (1976). Flow-field-flow fractionation: a versatile new separation method. Science, 193(4259), 1244-1245. doi:10.1126/science.959835Gimbert, L. J., Andrew, K. N., Haygarth, P. M., & Worsfold, P. J. (2003). Environmental applications of flow field-flow fractionation (FIFFF). TrAC Trends in Analytical Chemistry, 22(9), 615-633. doi:10.1016/s0165-9936(03)01103-8Gottselig, N., Bol, R., Nischwitz, V., Vereecken, H., Amelung, W., & Klumpp, E. (2014). Distribution of Phosphorus-Containing Fine Colloids and Nanoparticles in Stream Water of a Forest Catchment. Vadose Zone Journal, 13(7), vzj2014.01.0005. doi:10.2136/vzj2014.01.0005Gottselig, N., Nischwitz, V., Meyn, T., Amelung, W., Bol, R., Halle, C., … Klumpp, E. (2017). Phosphorus Binding to Nanoparticles and Colloids in Forest Stream Waters. Vadose Zone Journal, 16(3), vzj2016.07.0064. doi:10.2136/vzj2016.07.0064Hagedorn , A. G. 2006 EG-Sicherheitsdatenblatt (Gemäß 2001/58/EG)Hart, B. T., Douglas, G. B., Beckett, R., Van Put, A., & Van Grieken, R. E. (1993). Characterization of colloidal and particulate matter transported by the magela creek system, Northern Australia. Hydrological Processes, 7(1), 105-118. doi:10.1002/hyp.3360070111Hassellöv, M., Lyvén, B., Haraldsson, C., & Sirinawin, W. (1999). Determination of Continuous Size and Trace Element Distribution of Colloidal Material in Natural Water by On-Line Coupling of Flow Field-Flow Fractionation with ICPMS. Analytical Chemistry, 71(16), 3497-3502. doi:10.1021/ac981455yHassellov, M., & von der Kammer, F. (2008). Iron Oxides as Geochemical Nanovectors for Metal Transport in Soil-River Systems. Elements, 4(6), 401-406. doi:10.2113/gselements.4.6.401Hens, M., & Merckx, R. (2001). Functional Characterization of Colloidal Phosphorus Species in the Soil Solution of Sandy Soils. Environmental Science & Technology, 35(3), 493-500. doi:10.1021/es0013576Hill, D. M., & Aplin, A. C. (2001). Role of colloids and fine particles in the transport of metals in rivers draining carbonate and silicate terrains. Limnology and Oceanography, 46(2), 331-344. doi:10.4319/lo.2001.46.2.0331Jarvie, H. P., Neal, C., Rowland, A. P., Neal, M., Morris, P. N., Lead, J. R., … Hockenhull, K. (2012). Role of riverine colloids in macronutrient and metal partitioning and transport, along an upland–lowland land-use continuum, under low-flow conditions. Science of The Total Environment, 434, 171-185. doi:10.1016/j.scitotenv.2011.11.061Jiang, X., Bol, R., Nischwitz, V., Siebers, N., Willbold, S., Vereecken, H., … Klumpp, E. (2015). Phosphorus Containing Water Dispersible Nanoparticles in Arable Soil. Journal of Environmental Quality, 44(6), 1772-1781. doi:10.2134/jeq2015.02.0085Kögel-Knabner, I., & Amelung, W. (2014). Dynamics, Chemistry, and Preservation of Organic Matter in Soils. Treatise on Geochemistry, 157-215. doi:10.1016/b978-0-08-095975-7.01012-3Krám, P., Hruška, J., & Shanley, J. B. (2012). Streamwater chemistry in three contrasting monolithologic Czech catchments. Applied Geochemistry, 27(9), 1854-1863. doi:10.1016/j.apgeochem.2012.02.020Lyvén, B., Hassellöv, M., Turner, D. R., Haraldsson, C., & Andersson, K. (2003). Competition between iron- and carbon-based colloidal carriers for trace metals in a freshwater assessed using flow field-flow fractionation coupled to ICPMS. Geochimica et Cosmochimica Acta, 67(20), 3791-3802. doi:10.1016/s0016-7037(03)00087-5Marschner, B., & Kalbitz, K. (2003). Controls of bioavailability and biodegradability of dissolved organic matter in soils. Geoderma, 113(3-4), 211-235. doi:10.1016/s0016-7061(02)00362-2Martin, J.-M., Dai, M.-H., & Cauwet, G. (1995). Significance of colloids in the biogeochemical cycling of organic carbon and trace metals in the Venice Lagoon (Italy). Limnology and Oceanography, 40(1), 119-131. doi:10.4319/lo.1995.40.1.0119Mattsson, T., Kortelainen, P., Laubel, A., Evans, D., Pujo-Pay, M., Räike, A., & Conan, P. (2009). Export of dissolved organic matter in relation to land use along a European climatic gradient. Science of The Total Environment, 407(6), 1967-1976. doi:10.1016/j.scitotenv.2008.11.014Missong, A., Bol, R., Willbold, S., Siemens, J., & Klumpp, E. (2016). Phosphorus forms in forest soil colloids as revealed by liquid-state31P-NMR. Journal of Plant Nutrition and Soil Science, 179(2), 159-167. doi:10.1002/jpln.201500119Montalvo, D., Degryse, F., & McLaughlin, M. J. (2015). Natural Colloidal P and Its Contribution to Plant P Uptake. Environmental Science & Technology, 49(6), 3427-3434. doi:10.1021/es504643fNeubauer, E., Köhler, S. J., von der Kammer, F., Laudon, H., & Hofmann, T. (2013). Effect of pH and Stream Order on Iron and Arsenic Speciation in Boreal Catchments. Environmental Science & Technology, 47(13), 7120-7128. doi:10.1021/es401193jNeubauer, E., v.d. Kammer, F., & Hofmann, T. (2011). Influence of carrier solution ionic strength and injected sample load on retention and recovery of natural nanoparticles using Flow Field-Flow Fractionation. Journal of Chromatography A, 1218(38), 6763-6773. doi:10.1016/j.chroma.2011.07.010Nischwitz, V., & Goenaga-Infante, H. (2012). Improved sample preparation and quality control for the characterisation of titanium dioxide nanoparticles in sunscreens using flow field flow fractionation on-line with inductively coupled plasma mass spectrometry. Journal of Analytical Atomic Spectrometry, 27(7), 1084. doi:10.1039/c2ja10387gRan, Y., Fu, J. ., Sheng, G. ., Beckett, R., & Hart, B. . (2000). Fractionation and composition of colloidal and suspended particulate materials in rivers. Chemosphere, 41(1-2), 33-43. doi:10.1016/s0045-6535(99)00387-2Regelink, I. C., Koopmans, G. F., van der Salm, C., Weng, L., & van Riemsdijk, W. H. (2013). Characterization of Colloidal Phosphorus Species in Drainage Waters from a Clay Soil Using Asymmetric Flow Field-Flow Fractionation. Journal of Environmental Quality, 42(2), 464-473. doi:10.2134/jeq2012.0322Regelink, I. C., Voegelin, A., Weng, L., Koopmans, G. F., & Comans, R. N. J. (2014). Characterization of Colloidal Fe from Soils Using Field-Flow Fractionation and Fe K-Edge X-ray Absorption Spectroscopy. Environmental Science & Technology, 48(8), 4307-4316. doi:10.1021/es405330xRegelink, I. C., Weng, L., & van Riemsdijk, W. H. (2011). The contribution of organic and mineral colloidal nanoparticles to element transport in a podzol soil. Applied Geochemistry, 26, S241-S244. doi:10.1016/j.apgeochem.2011.03.114RICHARDSON, C. J. (1985). Mechanisms Controlling Phosphorus Retention Capacity in Freshwater Wetlands. Science, 228(4706), 1424-1427. doi:10.1126/science.228.4706.1424Roth , C. 2011 Sicherheitsdatenblatt Gemäß Verordnung (EG) Nr. 1907/2006 RepSchmitt, D., Taylor, H. E., Aiken, G. R., Roth, D. A., & Frimmel, F. H. (2002). Influence of Natural Organic Matter on the Adsorption of Metal Ions onto Clay Minerals. Environmental Science & Technology, 36(13), 2932-2938. doi:10.1021/es010271pSix, J., Elliott, E. T., & Paustian, K. (1999). Aggregate and Soil Organic Matter Dynamics under Conventional and No-Tillage Systems. Soil Science Society of America Journal, 63(5), 1350-1358. doi:10.2136/sssaj1999.6351350xStolpe, B., Guo, L., Shiller, A. M., & Hassellöv, M. (2010). Size and composition of colloidal organic matter and trace elements in the Mississippi River, Pearl River and the northern Gulf of Mexico, as characterized by flow field-flow fractionation. Marine Chemistry, 118(3-4), 119-128. doi:10.1016/j.marchem.2009.11.007Tipping, E., & Hurley, M. . (1992). A unifying model of cation binding by humic substances. Geochimica et Cosmochimica Acta, 56(10), 3627-3641. doi:10.1016/0016-7037(92)90158-fTombácz, E., Libor, Z., Illés, E., Majzik, A., & Klumpp, E. (2004). The role of reactive surface sites and complexation by humic acids in the interaction of clay mineral and iron oxide particles. Organic Geochemistry, 35(3), 257-267. doi:10.1016/j.orggeochem.2003.11.002Trostle, K. D., Ray Runyon, J., Pohlmann, M. A., Redfield, S. E., Pelletier, J., McIntosh, J., & Chorover, J. (2016). Colloids and organic matter complexation control trace metal concentration-discharge relationships in Marshall Gulch stream waters. Water Resources Research, 52(10), 7931-7944. doi:10.1002/2016wr019072U.S. Department of Agriculture 1993 Soil survey manual, chapter 3. Selected chemical propertiesVitousek, P. (1982). Nutrient Cycling and Nutrient Use Efficiency. The American Naturalist, 119(4), 553-572. doi:10.1086/283931Wells, M. L., & Goldberg, E. D. (1991). Occurrence of small colloids in sea water. Nature, 353(6342), 342-344. doi:10.1038/353342a0Wen, L.-S., Santschi, P., Gill, G., & Paternostro, C. (1999). Estuarine trace metal distributions in Galveston Bay: importance of colloidal forms in the speciation of the dissolved phase. Marine Chemistry, 63(3-4), 185-212. doi:10.1016/s0304-4203(98)00062-0Zirkler, D., Lang, F., & Kaupenjohann, M. (2012). «Lost in filtration»—The separation of soil colloids from larger particles. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 399, 35-40. doi:10.1016/j.colsurfa.2012.02.02

    Molecular dynamics simulation of humic substances

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    © 2014, Orsi. Humic substances (HS) are complex mixtures of natural organic material which are found almost everywhere in the environment, and particularly in soils, sediments, and natural water. HS play key roles in many processes of paramount importance, such as plant growth, carbon storage, and the fate of contaminants in the environment. While most of the research on HS has been traditionally carried out by conventional experimental approaches, over the past 20 years complementary investigations have emerged from the application of computer modeling and simulation techniques. This paper reviews the literature regarding computational studies of HS, with a specific focus on molecular dynamics simulations. Significant achievements, outstanding issues, and future prospects are summarized and discussed

    Computing steady-state metal flux at microorganism and bioanalogical sensor interfaces in multiligand systems. A reaction layer approximation and its comparison with the rigorous solution

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    In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 50915100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, μ. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or μ, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed
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