Stability constants: comparative study of fitting methods. Determination of second-order complexation constants by (23)Na and (7)Li NMR chemical shift titration

NMR chemical shift titration has been widely used as a method for the determination of stability constants. Systems involving metal-ligand complexation have been investigated using a number of methodologies. There are significant differences in the values reported for stability constants obtained by different experimental methods, such as calorimetry and ion selective electrode (ISE) titrations; nor has NMR chemical shift titration always yielded consistent results. Different researchers have obtained different results for the same system with results differing by as much as an order of magnitude. The chemical shift data are generally plotted against the concentration ratio of the metal and ligand for a set of solutions. A nonlinear least squares fitting method using an analytical solution of the cubic equation for the equilibrium concentration of the free ligand is used in this study and compared with methods used in the literature. Second-order association constants for the LiClO(4):12-crown-4 system in acetonitrile and the NaClO(4):12-crown-4 system in methanol are reported. Formation of both 1:1 and 1:2 metal-ligand complexes are considered. The LiClO(4):12-crown-4 acetonitrile system had been investigated previously by NMR titration but only 1:1 complexation was considered in that study. This study provides convincing evidence that both 1:1 and 1:2 complexes are important, at least, in the lithium system. A Monte Carlo investigation of the propagation of errors from the chemical shifts to the stability constants shows that the choice of data analysis methods may, in part, contribute to discrepancies and that the nonlinear nature of the model can dramatically affect the error limits on the stability constants.     

Target transform fitting in a voltammetric study of metal complexation

In this work target transform fitting (TTF) is proposed as a hard-model based data analysis method to analyze differential pulse polarograms recorded in a successive metal complexation system. In such cases, equations for both complexation equilibria and shape of the differential pulse polarogram for individual species are available. Utilizing TTF to fit these models in separate stages, stability constants and E_1/2 values of species were estimated. In the first stage, E_1/2 values of all species were acquired using the shape-equation of voltamograms and projection of a test vector into the row space of data matrix. In the second stage, using equations derived from relationships among species’ concentrations in complexation equilibria and a non-linear parameter fitting algorithm, the optimum values of overall formation constants were estimated. Finally, rank annihilation (RA) method was employed for calculation of diffusion coefficients. In spite of the fact that proposed method is a hard-model based approach, obtained results show that analysis can be performed correctly even in presence of unknown species. The reliability of the method was tested analyzing simulated data and also polarograms obtained from Cd(II) and 1, 10-phenanthroline complexation system. This experimental system yields three successive complexes which are relatively inert from electrochemical point of view. The results were in a good agreement with reported results in the literature.     

A novel methodology for evaluation of formation constants of complexes: example of lanthanide-Arsenazo III complexes

A novel method is proposed for the computation of formation constants of complexes. It makes use essentially of the data from the first stages of the titration and is based on the Taylor expansion of the concentration of the ligand as a function of the titrant concentration. The applicability of the methodology is examplified by the computation of the complexation constants of lanthanides (Ln) by 3,6-bis[(2-arsonophenyl)azo]-4,5-dihydroxy-2,7-naphtalenedisulphonic acid disodium salt (Arsenazo III). Arsenazo III is known to form stable complexes with a large variety of ions. The spectrophotometric study of these complexes in the visible domain is facilitated by the presence of chromophore groups in the ligand. In the present work, spectral deconvolution was used to improve the accuracy in the determination of formation constants of complexes between Arsenazo III and lanthanides. It turns out that all the 11 lanthanides studied here form the same type of complexes with this ligand. For each of them, the three formation constants correspond, respectively, to Ln to Ar ratios 1:1, 1:2 and 2:2. Their approximate values are in the ranges: K₁₁=10⁵; K₁₂=10¹⁰; K₂₂=10¹⁵. Accurate values are given in the text. The results are compared with those obtained with the classical iteration method which makes use of the whole titration curve. The two techniques give satisfactorily convergent results. The new methodology might be useful in the treatment of the competition of two ligands for the complexation of the same lanthanide, where the first stages of the titration of only one of the complexants is experimentally available.     

Complexation Constants of Lanthanide Ions with Poly(Methacrylic Acid) and its Copolymers

Complexation of some lanthanide ions with poly(methacrylic acid) and its copolymers was studied by potentiometric titration. Poly [methacrylic acid-co-oligo(ethylene oxide)methacrylate] and poly(methacrylic acid-co-acrylamide) formed tris-carboxylate coordinate lanthanide complexes with large overall complexation constants, while poly-(methacrylic acid)s and copolymer with higher content of the methacrylic acid residue formed bis-coordinate ones. It was concluded that the comonomer residues in the copolymer chains decreased the steric hindrance for the complexation and/or acted as co-coordinating groups of the carboxylic group to lanthanide ions. Very large positive and favorable entropy changes were observed for the complexation with poly(methacrylic acid) and its copolymers. This contribution of thermodynamic parameters to the complexation was contrary to that for the analogous monomeric methacrylic acid complex and is assumed to be induced by dehydration of the polymers through the lanthanide ion complexation.     

Kinetics of bacterial potentiometric titrations: the effect of equilibration time on buffering capacity of Pantoea agglomerans suspensions

Several recent studies have made use of continuous acid-base titration data to describe the surface chemistry of bacterial cells as a basis for accurately modelling metal adsorption to bacteria and other biomaterials of potential industrial importance. These studies do not share a common protocol; rather they titrate in different pH ranges and they use different stability criteria to define equilibration time during titration. In the present study we investigate the kinetics of bacterial titrations and test the effect they have on the derivation of functional group concentrations and acidity constants. We titrated suspensions of Pantoea agglomerans by varying the equilibration time between successive titrant additions until stability of 0.1 or 0.001 mV s(-1) was attained. We show that under longer equilibration times, titration results are less reproducible and suspensions exhibit marginally higher buffering. Fluorescence images suggest that cell lysis is not responsible for these effects. Rather, high DOC values and titration reversibility hysterisis after long equilibration times suggest that variability in buffering is due to the presence of bacterial exudates, as demonstrated by titrating supernatants separated from suspensions of different equilibration times. It is recommended that an optimal equilibration time is always determined with variable stability control and preliminary reversibility titration experiments.     

Development of algorithms for automated spectrophotometric titrations

A versatile method for evaluation of equilibrium constants from automated spectrophotometric titrations is described. General algorithms were derived for normalized titration curves of reactions having various stoichiometric ratios. Normalization of data involve converting it from absorption versus time to product formed (0 to 1) versus equivalents of titrant added. Relevance of derived algorithms was assessed by the quality of their fit to real data. The demonstration system chosen for this investigation was the 1:3 complexation reaction of Fe(II) and 1,10-phenantroline (o-Phen). Titrations were performed at three distinct infusion rates under controlled pH of 5.0 and at 25.0 °C, with sets produced using both Fe(II) and o-Phen as the titrant. Direct fitting of titration curves yielded values for overall equilibrium constants. Furthermore, resulting curves revealed reproducible initial deviation, consistent with step-wise reaction, when titrating Fe(II) with o-Phen. No unusual deviations were evident anywhere in the titration curves when Fe(II) was the titrant. Overall, our approach facilitates adoption of automated titrimetry and data analysis methodologies for the determination of stoichiometries and equilibrium constants of many UV/Vis active reactions.     

Precise dipolar coupling constant distribution analysis in proton multiple-quantum NMR of elastomers

In this work we present an improved approach for the analysis of (1)H double-quantum nuclear magnetic resonance build-up data, mainly for the determination of residual dipolar coupling constants and distributions thereof in polymer gels and elastomers, yielding information on crosslink density and potential spatial inhomogeneities. We introduce a new generic build-up function, for use as component fitting function in linear superpositions, or as kernel function in fast Tikhonov regularization (ftikreg). As opposed to the previously used inverted Gaussian build-up function based on a second-moment approximation, this method yields faithful coupling constant distributions, as limitations on the fitting limit are now lifted. A robust method for the proper estimation of the error parameter used for the regularization is established, and the approach is demonstrated for different inhomogeneous elastomers with coupling constant distributions.     

镧系金属离子Ln3+定量构效关系的神经网络研究

以Ln³⁺离子的半径、电负性、4f电子排布周期因子q(本文自定义)以及基态L值等为参数,使用函数连接型神经网络(FLN)对Ln³⁺离子的EDTA等络合常数lgK、水化能ΔH、水解常数pK₁及氢氧化物溶解度pK_m分别进行非线性关联和预测,获得了非常好的结果.与对应的线性模型比较表明,神经网络关联效果是较理想的.     

An evaluation of voltammetric titration procedures for the determination of trace metal complexation in natural waters by use of computers simulation

The impact of random analytical errors on the determination of metal complexation parameters of natural waters by metal titration procedures based on cathodic stripping (CSV) or anodic stripping (ASV) voltammetry is investigated by means of computer simulation. The results indicate that random analytical errors are of overriding importance in establishing the range of ligand concentrations and conditional stability constants that can be accurately determined by these techniques. Simulations incorporating realistic estimates of random analytical error show that only stability constants lying within a relatively narrow range, typically three orders of magnitude, can be determined accurately by the ASV procedure. The CSV procedure suffers from the same limitations, but is potentially more flexible in that the available detection window can be moved (but not widened) by adjustments to the method. Both techniques are capable of accurately determining ligand concentrations provided that the corresponding stability constant, K′, is greater than a threshold value which corresponds to the lower end of the available detection window for the stability constant. Realistically attainable improvements in analytical precision did not greatly improve the performance of either technique. Two graphical treatments for the evaluation of metal complexation parameters from titration data are compared: the Scatchard and Van den Berg/Ruzic plots. Simulations indicate that at least for the single-ligand model of complexation, the Van den Berg/Ruzic method is superior. The importance of the simulation results with respect to determining metal complexation parameters in natural waters is discussed. This study illustrates the value of computer simulation when complex, time-consuming analytical techniques are applied and the need for rigorous analysis of errors in producing data of environmental relevance.     

Deep Learning Insights into Lanthanides Complexation Chemistry

Modern structure–property models are widely used in chemistry; however, in many cases, they are still a kind of a “black box” where there is no clear path from molecule structure to target property. Here we present an example of deep learning usage not only to build a model but also to determine key structural fragments of ligands influencing metal complexation. We have a series of chemically similar lanthanide ions, and we have collected data on complexes’ stability, built models, predicting stability constants and decoded the models to obtain key fragments responsible for complexation efficiency. The results are in good correlation with the experimental ones, as well as modern theories of complexation. It was shown that the main influence on the constants had a mutual location of the binding centers.     

Effect of temperature on the acid-base properties of the alumina surface: microcalorimetry and acid-base titration experiments

Sorption reactions on natural or synthetic materials that can attenuate the migration of pollutants in the geosphere could be affected by temperature variations. Nevertheless, most of the theoretical models describing sorption reactions are at 25 degrees C. To check these models at different temperatures, experimental data such as the enthalpies of sorption are thus required. Highly sensitive microcalorimeters can now be used to determine the heat effects accompanying the sorption of radionuclides on oxide-water interfaces, but enthalpies of sorption cannot be extracted from microcalorimetric data without a clear knowledge of the thermodynamics of protonation and deprotonation of the oxide surface. However, the values reported in the literature show large discrepancies and one must conclude that, amazingly, this fundamental problem of proton binding is not yet resolved. We have thus undertaken to measure by titration microcalorimetry the heat effects accompanying proton exchange at the alumina-water interface at 25 degrees C. Based on (i) the surface sites speciation provided by a surface complexation model (built from acid-base titrations at 25 degrees C) and (ii) results of the microcalorimetric experiments, calculations have been made to extract the enthalpic variations associated respectively to first and second deprotonation of the alumina surface. Values obtained are deltaH1 = 80+/-10 kJ mol(-1) and deltaH2 = 5+/-3 kJ mol(-1). In a second step, these enthalpy values were used to calculate the alumina surface acidity constants at 50 degrees C via the van't Hoff equation. Then a theoretical titration curve at 50 degrees C was calculated and compared to the experimental alumina surface titration curve. Good agreement between the predicted acid-base titration curve and the experimental one was observed.     

Development of a fitting model suitable for the isothermal titration calorimetric curve of DNA with cationic ligands

A novel curve fitting model was developed for the isothermal titration calorimetry (ITC) of a cationic ligand binding to DNA. The ligand binding often generates a DNA conformational change from an elongated random coil into a compact collapsed form that is referred to as "DNA condensation". The ligand binding can be classified into two regimes having different binding constants Ki, i.e., the binding to an elongated DNA chain with a binding constant K1 and with K2 that occurred during the conformational transition. The two-variable curve fitting models are usually bound by a strict regulation on the difference in the values of the binding constants K1 > K2. For the DNA condensation, however, the relationships for K1 and K2 are still unclear. The novel curve fitting model developed in this study takes into account this uncertainty on the relationship of the binding constants and is highly flexible for the two-variable binding constant system.     

Evaluating alternative electrostatic potential models for polyacrylamide-co-acrylate in aqueous solution

The capabilities of three simplified analytical equations to accurately model electrostatic interactions during proton binding and release by linear anionic polyelectrolytes in aqueous solution were evaluated. The impermeable sphere (IS), Donnan (DN), and cylindrical (CY) electrostatic models were fit to experimental acid-base titration curves of linear polyacrylamide-co-acrylate having ionizable site densities ranging from ca. 10-35%. The titrations were conducted in 0.003-0.12M NaCl solutions and the sum of squared errors from modeled and experimental data was used as a comparative index of each model's capability. In addition, the relative size of each polyelectrolyte was estimated from its measured specific viscosity and then compared against the values obtained from the fitting procedure for the size parameter that each model contained. Although the IS and DN electrostatic models could be used to obtain reasonably good fits to each titration curve, the size parameter values obtained by each model were not reflective of the actual polyelectrolyte sizes, indicating that the models had limited physical meaning and that the size parameter was essentially just an additional fitting parameter in each model. In contrast, the CY model was not only more effective in its ability to fit the titration data but also provided a better physical representation of the polyelectrolyte size. Therefore, for polyelectrolytes that remain essentially linear or are only loosely coiled such that counter ions are free to travel throughout the polymer structure, we conclude that the CY model and its morphological representation of a cylindrical polyelectrolyte are more valid and realistic than the IS and DN models and their representation of polyelectrolytes as spheres.     

Modelling the adsorption of Cd(II), Cu(II), Ni(II), Pb(II), and Zn(II) onto Fithian illite

Illite samples from Fithian, IL were purified and saturated with Na(+) ions. The acid-base surface chemistry of the Na-saturated illite was studied by potentiometric titration experiments with 0.1, 0.01, and 0.001 M NaNO(3) solutions as the background electrolyte. Results showed that the titration curves obtained at different ionic strengths did not intersect in the studied pH range. The adsorption of Cd(II), Cu(II), Ni(II), Pb(II), and Zn(II) onto illite was investigated as a function of pH and ionic strength by batch adsorption experiments. Two distinct mechanisms of metal adsorption were found from the experimental results: nonspecific ion-exchange reactions at lower pH values on the basal surfaces and 'frayed edges' and specific adsorption at higher pH values on the mineral edges. Ionic strength had a greater effect on the ion-exchange reactions. The binding constants for the five heavy metals onto illite were determined using the least-square fitting computer program FITEQL. Linear free energy relationships were found between the surface binding constants and the first hydrolysis constants of the metals.     

Spectrophotometric study of complex formations between 1-(2-pyridylazo)-2-naphthol (PAN) and some metal ions in organic solvents and the determination of thermodynamic parameters

The complexation reactions between Ni(2+), Co(2+) and Zn(2+) metal ions with PAN in methanol (MeOH), acetonitrile (AN) and dimethyl sulfoxide (DMSO) were studied using a spectrophotometric method. The stability constants of the resulting complexes were determined from computer fitting absorbance mole-ratio data. The results revealed that the stability constants of complexes are varying in order of Ni(2+)相似文献   

Methods for determination of all binding parameters in systems with simultaneous borate and cyclodextrin complexation

Two novel methods for determination of binding constants in the systems with borate and cyclodextrin complexation were developed. The methods enable to determine all binding parameters in these systems and even the binding constants of interaction of a neutral analyte with a neutral cyclodextrin. The first method is based on nonlinear fitting of experimental data and further evaluation of fitting parameters. The second method requires a multiple regression. The methods provide identical results with low experimental error. Only one set of measurements is required for both methods. Thus the binding parameters can be mutually compared. The binding parameters for neutral analytes ((R,R)-(+)-hydrobenzoin and (S,S)-(-)-hydrobenzoin) and neutral cyclodextrin (heptakis(2,6-di-O-methyl)-β-cyclodextrin) were evaluated and the effect of individual types of interaction was revealed. The interaction of the analytes with cyclodextrin governs the chiral recognition, while the complexation of analyte with borate is responsible for electromigration. Very low values of the binding constants of mixed analyte-cyclodextrin-borate complexes indicate that this type of complexation has negligible effect on enantioseparation.     

Potentiometric titration of metal ions in ethanol

The potentiometric titrations of Zn2+, Cu2+ and 12 Ln3+ metal ions were obtained in ethanol to determine the titration constants (defined as the at which the [-OEt]/[Mx+]t ratios are 0.5, 1.5, and 2.5) and in two cases (La3+ and Zn2+) a complete speciation diagram. Several simple monobasic acids and aminium ions were also titrated to test the validity of experimental titration measurements and to establish new constants in this medium that will be useful for the preparation of buffers and standard solutions. The dependence of the titration constants on the concentration and type of metal ion and specific counterion effects is discussed. In selected cases, the titration profiles were analyzed using a commercially available fitting program to obtain information about the species present in solution, including La3+ for which a dimer model is proposed. The fitting provides the microscopic values for deprotonation of one to four metal-bound ethanol molecules. Kinetics for the La3+-catalyzed ethanolysis of paraoxon as a function of are presented and analyzed in terms of La3+ speciation as determined by the analysis of potentiometric titration curves. The stability constants for the formation of Zn2+ and Cu2+ complexes with 1,5,9-triazacyclododecane as determined by potentiometric titration are presented.     

Cationic lanthanide complexes of neutral tripodal N,O ligands: enthalpy versus entropy-driven podate formation in water

The cationic lanthanide complexes of two neutral tripodal N,O ligands, tpa (tris[(2-pyridyl)methyl]amine) and tpaam (tris[6-((2-N,N-diethylcarbamoyl)pyridyl)methyl]amine) are studied in water. The analysis of the proton lanthanide induced NMR shifts indicate that there is no abrupt structural change in the middle of the rare-earth series. Unexpectedly, the formation constant values of the lanthanide podates of tpaam and tpa in D2O at 298 K are similar, suggesting that the addition of the three amide groups to the ligand tpa does not lead to any increase in stability of the lanthanide complexes of tpaam in respect to tpa, even though the amide groups are coordinated to the metal in aqueous solution. The measurement of the enthalpy and entropy changes of the complexation reactions shows that the two similar ligands tpa and tpaam have different driving forces for lanthanide complexation. Indeed, the formation of tpa podates benefits from an exothermic enthalpy change associated with a small entropy change, whereas the complexation reaction with tpaam is clearly entropy-driven though opposed by a positive enthalpy change. The hydration states of the europium complexes were measured by luminescence and show the coordination of 4-5 water ligands in [Eu(tpa)]3+ whereas there are only 2 in [Eu(tpaam)]3+. Therefore the heptadentate ligand tpaam releases the translational entropy of more water molecules than does the tetradentate ligand tpa.     

Tetrad effect in the adsorption of the lanthanides on zeolite Y

The adsorption of the lanthanides (except for Pm) on the zeolite Y was investigated under various solution conditions of nitrate ion concentration ([NO(-)(3)]: 0.001-2 mol/dm(3)) and total lanthanide concentration (from 0.0001 to 0.001 mol/dm(3)). The solutions of the lanthanide nitrates were equilibrated with the zeolite samples at 296 K. The concentrations of lanthanides in the initial and equilibrium solutions were determined by means of spectrophotometrical method with Arsenazo III reagent and distribution constants K(d) of the lanthanides between aqueous and zeolite phases were calculated. The evident concave tetrad effect in the change of logK(d) values (nitrate concentrations 0.4-2 mol/dm(3)) within the lanthanide series was noticed and an attempt at its explanation through the comparison of covalence in LnO bonds existing in triple bond AlO(1/3Ln)Si triple bond species in the zeolite phase and in Ln(NO(3))(2+) complexes forming in the aqueous phase was presented. The weak convex tetrad effect for equilibrium nitrate concentrations 0.001-0.32 mol/dm(3), manifesting in the change of logK(d) values and in the alteration of logK (adsorption constants), is evidence of the complexation of the tripositive lanthanide ions by the oxygens originating both from water molecules and from the zeolite framework.