“…So, the conventional LS estimations of fitting parameters lose their optimal statistical properties and should be replaced by the robust analogs. To overcome these complications, in this work we have applied a recently proposed procedure which is based on the application of robust Huber's M-estimations and fuzzy sets theory [36][37][38][39][40]. Fig.…”
“…So, the conventional LS estimations of fitting parameters lose their optimal statistical properties and should be replaced by the robust analogs. To overcome these complications, in this work we have applied a recently proposed procedure which is based on the application of robust Huber's M-estimations and fuzzy sets theory [36][37][38][39][40]. Fig.…”
“…As was shown earlier (Figure 3), the application of the linearized Langmuir equation gives unreliable estimations of t Q and b, and hypothesis about the insignificance of the cooperativity effects cannot be accepted. This conclusion is corroborated by the fact that for the model of polydentate binding with Z = 1, the minimal value of c t Q -= 0.10 mmol g -1 ; log b 1 (2) = 2.4 (s = 0.5); log b 2 (2) = 6.38 (s = 0.05) [a more complicated procedure described in Lucho et al (2007) gives the following estimates: t Q -= 0.11 mmol g -1 ; log b 1 (2) = 2.3; log b 2 (2) = 6.39.…”
Section: Adsorption Of Small Probes By Hybrid Silica-organic Materialsmentioning
confidence: 83%
“…The fitting parameters are determined through the approximation of the composition-property dependencies by a quantitative physicochemical analysis (Zaitsev et al 1991;Magosso et al 2006;Lucho et al 2007). The criterion to be minimized is (9) where N is the total number of experimental points, weighed discrepancy…”
Section: Calculation Of Equilibrium Constants and Effective Sorption mentioning
ABSTRACT:The property of non-ideality (cooperativity effects, energetic heterogeneity of binding centres) is often observed at probing surfaces by small ionic or molecular probes. A procedure based on the model of polydentate binding is recommended as a tool for detection and quantitative characterization of these effects. This procedure allows one to find objective estimations of effective sorption capacities and constants of adsorption equilibria. In this study, adsorption of small probes by two hybrid silica-organic materials has been studied. Ormosil with immobilized n-propylamine was probed with H + ions, and in addition, CoCl 2 adsorption from solutions of ethanol by silica chemically modified with 3-n-propyltrimethoxysilane-1-methylimidazolium chloride was also investigated. In both cases, the model of bidentate binding properly fitted the experimental data. This made it possible to determine the quantitative characteristics of adsorption equilibria and to arrive at conclusions on the cooperativity effects. Negative cooperativity effects are significant in adsorption of H + ions, while strong positive cooperativity affects CoCl 2 binding.
“…The program has allowed to calculate the constants of adsorption equilibria and to estimate the degrees of formation of different species on the surface [56][57][58]. The parameters for fitting obtained for each material are presented in Table 2.…”
This work describes a highly controlled post-grafting of mono and dicationic 4,4'-bipyridine alkoxysilane derivatives (Bipy(+) and Bipy(2+)) onto the surface of an ordered mesoporous silica, SBA-15. The materials obtained are designated as SBA-15/Bipy(+)Cl(-) and SBA-15/Bipy(2+)Cl(2)(-), both possessing chloride as counter ion. The regular arrangement of uniform pores of this inorganic matrix is likely to ensure good accessibility to the active centers (electron acceptors) attached to the surface. The materials are excellent adsorbents due to the ability of the functional groups to retain copper chlorides on their surfaces as anionic complexes (CuCl(2+n)(n-)) in ethanol. From the adsorption, results it was possible to probe the functional surface monolayer of the materials, which present a highly homogenous distribution of functional groups inside the ordered SBA-15 channels, with an exchange efficiency of 93% for SBA-15/Bipy(+)Cl(-) and 94% for SBA-15/Bipy(2+)Cl(2)(-). Both adsorbent materials are potentially useful in the pre-concentration and further analysis of Cu(II) present in trace amounts in ethanol, extensively used as an automotive fuel in Brazil.
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