Potentiometric Titration Curves Research Articles

The titration of clay minerals: II. Structure-based model and implications for clay reactivity

The potentiometric titration and CEC data presented in part I are modeled in this paper, part II. Two models are compared: the two p K, three complexation sites plus exchange sites nonelectrostatic model developed by Baeyens and Bradbury and a model based on the MUSIC approach developed by Hiemstra and Van Riemsdijk. Both morphological and structural information is used to develop this new model. Morphological information is taken from the literature, while structural information is taken from the literature and constrained by supporting FTIR experiments. The Baeyens and Bradbury model is found to reproduce the general tendency of the titration curve, whereas the model based on the Hiemstra and Van Riemsdijk MUSIC approach provides a better fit to the experimental data. The former uses only 3 edge reaction sites, whereas the latter uses at least 27 edge reaction sites. Five main reactive sites are sufficient to fit the MUSIC model curve, but the model allows us to derive the properties of 22 other reactive sites. Logically, the greater the number of sites, the better the fit. Nevertheless, fewer adjustable parameters are necessary for the Hiemstra and Van Riemsdijk MUSIC model than for the Baeyens and Bradbury model, thanks to structural and morphological constraints. The precision of the potentiometric titration curve is insufficient to verify that the properties of the 27 sites given by the MUSIC model are effective. Thus, we coupled some properties of clay minerals, such as dissolution, to the modeled acid–base properties of these sites to assess our model. We then questioned the ability of simplified models such as the Baeyens and Bradbury model to predict the interactions between clay minerals and solutions in natural environments. In addition, we derived the cation exchange selectivity coefficients for CaCl + ionic pairs and H + from our CEC data and gave an estimate for the CaOH + selectivity coefficient.

Base−Acid Equilibria in Polyelectrolyte Systems: From Weak Polyelectrolytes to Interpolyelectrolyte Complexes and Multilayered Polyelectrolyte Shells

We have measured potentiometric titration curves of the weak polyelectrolytes, PAH1 and PAA, interpolyelectrolyte complexes PAH−PAA, PDADMAC−PAA, and PAH−PAA, prepared by mixing of the polyelectrolyte solutions, and multilayered microcapsules made by layer-by-layer adsorption of the same pairs of oppositely charged polyelectrolytes onto CaCO3 microspheres(PAH/PAA)5, (PDADMAC/PAA)5, and (PAH/PSS)5. The data were analyzed within the frame of an Ising model taking into account the nearest-neighbor interaction between proton binding sites. The anticooperative character of proton binding with PAH (cooperativity parameter q = 0.13) was shown to become a highly cooperative process in the interpolyelectrolyte complex PAH−PSS and multilayered microcapsules (PAH/PSS)5, q ≈ 2−3. The cooperativity of the process is increased also for complexes PDADMAC−PAA and PAH−PAA and for multilayered shells (PDADMAC/PAA)5 and (PAH/PAA)5; however, the cooperativity parameter q remains below unity for the PDADMAC−PAA system or a li...

Metal Ion Complexes Containing Nucleobases and Some Zwitterionic Buffers

Potentiometric equilibrium measurements have been performed at (25.0 ± 0.1) °C and ionic strength I = 0.1 mol·dm-3 (KNO3) for the interaction of guanine (2-amino-6-oxypurine), thymine (2,4-dihydroxy-5-methylpyrimidine), adenine (6-aminopurine), uracil (2,4-dioxypyrimidine), hypoxanthine (6-oxypurine), and Cu(II), Ni(II), Co(II), Mn(II), Zn(II), Ca(II), and Mg(II) with the biologically important secondary ligands glycine (aminoethanoic acid), bicine [N,N-bis(2-hydroxyethyl)glycine], tricine [N,N,N-tris(hydroxymethyl)methylglycine], and ADA [N-(2-acetamido)-3-iminodiacetic acid] in a 1:1:1 ratio. The experimental conditions were selected such that self-association of the nucleobases and their complexes was negligibly small; that is, the monomeric normal and protonated complexes were studied. The formation of various 1:1:1 mixed ligand complexes was inferred from the potentiometric titration curves. Initial estimates of the formation constants of the resulting species and the acid dissociation constants of guanine, thymine, adenine, uracil, hypoxanthine, and the secondary ligands glycine, bicine, tricine, and ADA have been refined with the SUPERQUAD computer program. Confirmation of the formation of ternary complexes of the type Cu(II) + NB + Z in solution has been carried out using differential pulse polarography (DPP), square wave voltammetry (SWV), cyclic voltammetry (CV), and UV−visible spectroscopic measurements.

Cork biomass as biosorbent for Cu(II), Zn(II) and Ni(II)

The removal of Cu(II), Zn(II) and Ni(II) from solutions using biosorption in cork powder is described. The adsorption isotherms were determined, along with the effect of different variables, such as the solid–liquid ratio, temperature and pH on the removal efficiency of the metals. The potentiometric titration curve of the cork biomass was determined and some zeta-potential studies were carried out. The effect of the pre-treatment by Fisher esterification on the biosorption properties of cork is also presented. It was concluded that the adsorption of the heavy metals was favoured by an increase in pH. The degree of heavy metal removal is directly related to the concentration of cork biomass, and the maximum sorption capacity of cork biomass for Cu(II), Zn(II) and Ni(II) was 0.63, 0.76 and 0.34 meq./g, respectively. It is shown that ion exchange plays a more important role in the sorption of Cu(II) and Ni(II) on cork biomass than in the sorption of Zn(II). The pre-treatment by Fisher esterification confirmed the important role of the carboxylic groups in binding of Cu(II) and Ni(II) and showed that they are the only binding sites for Zn(II).

Theoretical Description of the Kinetics of Proton Adsorption at the Oxide/Electrolyte Interface Based on the Statistical Rate Theory of Interfacial Transport and the 1pK Model of Surface Charging

A new approach describing ion adsorption kinetics on metal oxide surfaces from electrolyte solution is presented. It was assumed that the diffusion of ions to the oxide surface is fast, and the kinetics of ion adsorption is controlled by the transition of ions from the bulk to the adsorbed state. The transition rate is considered in terms of the statistical rate theory (SRT) of interfacial transport. To simplify the theoretical considerations, the simple Gouy−Chapman model of the electric double layer is applied together with the 1pK protonation model. The above theoretical approach was used to analyze the rate of proton adsorption. Additionally, that kinetic model was applied to study the hysteresis of potentiometric titration curves and the heat of proton adsorption (i.e., difference in the measured quantity at a given pH from acid and base titration). According to the SRT approach, the rate of hydrogen ion adsorption strongly depends on pH, which has a significant influence on numerically simulated titration curves and the heat of proton adsorption.

Points of Zero Charge and Potentiometric Titrations

Based on the various categories of surface charge and the definitions of points of zero charge proposed by Sposito (1984, 1998), the determination of the adsorbed proton charge (σH) and the point of zero net charge (PZNPC) of insoluble oxides and layer silicates in aqueous solution was examined in detail using potentiometric titration experiments. The confusion, various interpretations and difficulties associated with points of zero charge, including the point of zero net proton charge (PZNPC), the point of zero net charge (PZNC) and the point of zero charge (PZC), were discussed and clarified. The importance of comparing potentiometric titration curves for pure insoluble oxides in the presence and absence of specific adsorption and of layer silicates with a permanent negative charge was emphasized. The dependency of expressions of points of zero charge on the model assumed and the weakness of the method of potentiometric titrations widely used for the determination of points of zero charge were discussed.

Interpolyelectrolyte Reactions in Solutions of Polycarboxybetaines

The utility of different polycarboxybetaines (PCB) as positively charged components of polyelectrolyte complexes was elucidated by potentiometry, turbidimetry, and fluorescence spectroscopy. PCB practically did not quench the fluorescence of either pyrenyl-tagged poly(methacrylic acid) or ethidium bromide intercalated in DNA. This indicates small, if any, interaction of PCB with the above polyanions due to formation of stable ion pairs between carboxylic and quaternary amino groups positioned in each repeated unit of PCB chains. Potentiometric titration curves of PCB solutions practically coincided with the curve of distilled water in the studied pH range 2−11. Addition of sodium poly(styrenesulfonate) (PSS) did not result in phase separation or noticeable change of the titration curve of PCB at pH > 7, whereas at pH < 7 phase separation occurred and the titration curve of the mixture significantly changed, being in close proximity with the curve of poly(acrylic acid). The pH value corresponding to the “c...

Cation-Exchange Properties of CrPO4

Alkali metal ion exchange (Li+, Na+ and K+) on chromium phosphate (CrPO4) was studied potentiometrically as a function of temperature and metal ion concentration. The shift in the potentiometric titration curves corresponding to the exchange of alkali metal cations increased with increasing pH and concentration of the metal ions, while the opposite results were obtained by increasing the temperature of the system. The affinity of the exchanger for alkali metal ions was also found to be in the order Li+ &gt; Na+ &gt; K+. The data were employed to evaluate the apparent deprotonation constants of CrPO4 and the corresponding thermodynamic parameters ΔH0, ΔS0 and ΔG0.

Synthesis and characterization of goethite and goethite–hematite composite: experimental study and literature survey

Aging of synthetic goethite at 140 °C overnight leads to a composite material in which hematite is detectable by Mössbauer spectroscopy, but X-ray diffraction does not reveal any hematite peaks. The pristine point of zero charge (PZC) of synthetic goethite was found at pH 9.4 as the common intersection point of potentiometric titration curves at different ionic strengths and the isoelectric point (IEP). For the goethite–hematite composite, the common intersection point (pH 9.4), and the IEP (pH 8.8) do not match. The electrokinetic potential of goethite at ionic strengths up to 1 mol dm −3 was determined. Unlike metal oxides, for which the electrokinetic potential is reversed to positive over the entire pH range at sufficiently high ionic strength, the IEP of goethite is rather insensitive to the ionic strength. A literature survey of published PZC/IEP values of iron oxides and hydroxides indicated that the average PZC/IEP does not depend on the degree of hydration (oxide or hydroxide). Our material showed a higher PZC and IEP than most published results. The present results confirm the allegation that electroacoustic measurements produce a higher IEP than the average IEP obtained by means of classical electrokinetic methods.

Use of linear regression for the processing of curves of differential potentiometric titration of a binary mixture of heterovalent ions using precipitation reactions

A method is proposed for the computer processing of curves of differential potentiometric titration of a binary mixture of heterovalent ions using precipitation reactions. The method is based on the transformation of the titration curve to piecewise linear characteristics, whose parameters (within the accuracy of the least-squares method) determine the sequence of the equivalence points and solubility products of the resulting precipitates. The computational algorithm is implemented as a Turbo-Pascal program DIFTITR. The method is applied to the titration of Ag(I)–Cd(II), Hg(II)–Te(IV), and Cd(II)–Te(IV) mixtures by a sodium diethyldithiocarbamate solution with membrane sulfide and glassy carbon indicator electrodes. For 4 to 11 mg of the analyte in 50 mL of the solution, RSD varies from 1 to 9%.

Low-Dentate Reagents as Titrants in Complexometry: Titration Curves in the Formation of a Mixture of Complexes

Approximate equations were derived that allow one to predict the number and heights of jumps in the potentiometric titration curves recorded for the formation of a mixture of complexes differing in coordination saturation. Criteria were proposed for the selection of promising titrants, namely, low-dentate reagents that give the only jump in the titration curve of a stepwise complexation reaction. The theoretical predictions were supported by computer experiments and by potentiometric titrations of model solutions.

1pK and 2pK Protonation Models in the Theoretical Description of Simple Ion Adsorption at the Oxide/Electrolyte Interface: The Analysis of Temperature Dependence of Potentiometric Titration Curves

Two models of oxide surface charging (1pK and 2pK) were used to describe the potentiometric titration curves measured by Blesa et al. ( J. Colloid Interface Sci. 101, 410 (1984)) at three temperatures and at three concentrations of electrolyte. Rudzinski et al. ( Langmuir 13, 483 (1997)) have applied the 2pK Triple Layer Model to analyze the above system earlier. Two calculation procedures based on the 1pK Basic Stern Model were developed to described Blesa's data. Since the experimental curves have the CIP (common intersection point) it was assumed that heat of electrolyte ion adsorption was equal to zero. We assumed two different values of the double layer innermost capacitance on both sides of PZC (point of zero charge), which was followed from asymmetry of surface charge curves relative to PZC. Moreover, it was necessary to take into consideration the dependence of capacitance on ionic strength and temperature. The quality of fit given by two models was comparable. Since the 1pK BSM is simpler than the 2pK TLM and includes not so many best-fit parameters it seems to be a better choice in this case. Discussion of the results obtained by other authors concerning the subject under consideration is also presented.

1pK and 2pK Protonation Models in the Theoretical Description of Simple Ion Adsorption at the Oxide/Electrolyte Interface: Studying of the Role of the Energetic Heterogeneity of Oxide Surfaces

Two theoretical approachesthe 2pK triple layer model and the 1pK basic Stern modeldescribing the charging process at oxide/electrolyte interfaces were applied to analyze the surface charge isotherms and the heats of proton adsorption. The presented analysis was carried out by accepting both the frequently employed model of an energetically homogeneous oxide surface and a more realistic model taking into account the energetic heterogeneity of the actual oxide surfaces. The developed theoretical expressions were applied to analyze experimental data sets reported for three adsorption systems: Al2O3/NaCl, TiO2/NaCl, and SiO2/NaCl. It was found that both the 2pK and the 1pK surface charging models could well describe potentiometric titration curves, and can represent the most characteristic features of the measured enthalpy of proton adsorption. In the case of the 1pK model, introducing the concept of surface energetic heterogeneity does not affect much the fit of the experimentally measured heats of proton adsorption. Best fits were obtained by applying the 2pK model taking into account the surface energetic heterogeneity. These best fits, however, were obtained at the expense of introducing more best-fit parameters. So, the general conclusion is that, for some adsorption systems, the use of the simpler 1pK model leads to a sufficiently accurate description of experimental data, whereas, for some other systems, the use of the 2pK model seems to be necessary.

Ponto de efeito salino nulo: determinação analítico-computacional a partir de dados de titulação potenciométrica

O ponto de efeito salino nulo (PESN) de amostras de solo é normalmente determinado por método gráfico e corresponde ao valor de pH referente ao ponto de interseção de curvas de titulação potenciométrica. Embora a elaboração dos gráficos em planilhas eletrônicas diminua a subjetividade existente no traçado manual, um tempo considerável é necessário quando a determinação do PESN envolve grande número de amostras. Este trabalho objetivou o desenvolvimento de um programa computacional para a determinação analítica do PESN de amostras de solo, com vistas em eliminar a subjetividade do método gráfico, proporcionar rapidez às determinações e permitir o conhecimento do grau de precisão dos valores calculados. Com o procedimento de cálculo desenvolvido, determinaram-se os valores de PESN a partir de resultados experimentais de titulação potenciométrica obtidos por outros autores. A comparação dos valores calculados pelo programa com os apresentados nos trabalhos consultados, os quais foram obtidos pelos autores por meio do método gráfico convencional, demonstrou ser o método analítico-computacional proposto bastante adequado para a determinação rápida e não-subjetiva do PESN de amostras de solo.

1pK and 2pK Protonation Models in the Theoretical Description of Simple Ion Adsorption at the Oxide/Electrolyte Interface: A Comparative Study of the Predicted and Observed Enthalpic Effects Accompanying Adsorption of Simple Ions

There is developed a quantitative theoretical description of enthalpies of surface protonation of the (hydr)oxide/electrolyte solution interface assuming the lpKcharging mechanism. The predictions obtained by adopting the1pK basic Stern model (BSM) of the interface are compared with the experimental data (potentiometric titration curves and heats of proton adsorption) and with the results obtained recently by adopting the 2pK triple-layer model (TLM) of the interface. It is found that the 1pK BSM gives similar results to the 2pK TLM, but in some cases the latter appears to be more flexible than the 1pK BSM. The conditions for existence of the common intersection point were consistently applied in the calculations to reduce the number of parameters used. The obtained values of heats of proton adsorption are compared with the values available in the literature. The found heats are exothermic and range between +17 kJ/mol (silica) and +46 kJ/mol (alumina) in the case of 1pK BSM. The calculated values of the proton adsorption entropy (TAS) are almost constant for the investigated systems and equal to +3 kJ/mol. This means that enthalpic effects play a main part in the process of proton adsorption on metal (hydr)oxides and silica.

Characterization and Differentiation of Chemical Heterogeneity in Humic Substances by Continuous Intrinsic Proton Affinity Distribution

The chemical heterogeneity of proton binding on humic substances was studied via continuous intrinsic proton affinity distributions calculated using the condensation approximation from the master curves for two soil fulvic acids (FAs), one soil humic acid (HA) and one fulvic acid obtained from weathered coal. The master curves, i.e. plots of θT,H (the overall protonation degree) versus Hs (the proton concentration in the diffuse double layer), were obtained from potentiometric titration curves at three ionic strengths. The value of Hs was calculated using an electrical double-layer model in which the humic substances were considered as rigid impermeable spheres. For all four samples, the proton affinity distributions were characterized by a few peaks with peak positions in the range 4–5.5. The similarities and differences between the samples studied were discussed.

CATIONITES BASED ON CALIX[4]RESORCINARENE DERIVATIVES

Novel network polymers possessing cation-exchange properties have been synthesized by the catalytic resol polycondensation of calix[4]resorcinarene derivatives with formaldehyde or with furfural and formaldehyde. The ion-exchange capacities of the polymers with respect to Na+, Me4N+, Et4N+, Bu4N+cations have been determined. It is shown that the potentiometric titration curves of the polymers are similar to the titration curve of the resorcinol-formaldehyde resin, but they are shifted toward lower pH values and have inflections. The formation enthalpies of calix[4]resorcinarene derivatives and their salts with Na+, Me4N+have been calculated by the MNDO/PM3 method. The heat of the reaction simulating the interaction of the polymers with NaOH and Me4NOH has been determined. It is found out that the inflections of the potentiometric titration curves of the cationites appear when appreciable differences in the changes of the enthalpies of modeling reaction stages are observed.

Potentiometric Titration of Triazolethiols and Tetrazolethiols with Iodine in Alkaline Medium

The iodimetric determination of triazolethiols and tetrazolethiols in alkaline medium is presented. The volumetric titration with potentiometric end-point detection was applied. The range of determination, in which the error is lower than 1%, is 20-2 000 μmol for 1H-1,2,4-triazole-3-thiol (1), 25-1 000 μmol for 3-phenyl-1H-1,2,4-triazole-5-thiol (2), 25-500 μmol for 4-methyl-5-(trifluoromethyl)-4H-1,2,4-triazole-3-thiol (3), 50-500 μmol for 3-amino-1H-1,2,4-triazole-5-thiol (4), 10-1 000 μmol for sodium (5-mercapto-1H-tetrazol-1-yl)acetate (5), 125-500 μmol for 1-phenyl-1H-tetrazole-5-thiol (6) and 50-1 000 μmol for 1-(4-hydroxyphenyl)-1H-tetrazole-5-thiol (7). The relative standard deviation for all determinations was below 1%. The shape of potentiometric titration curve of 6 and 7 is noteworthy at higher concentrations of sodium hydroxide and depends on the type of the indicator electrode (platinum, gold). An introduction of iodine results in a strong potential drop. Some systems do not follow the Nernst equation.

Synthesis of four derivatives of 3,6,10-tri(carboxymethyl)-3,6,10-triazadodecanedioic acid, the stabilities of their complexes with Ca(ii), Cu(ii), Zn(ii) and lanthanide(iii) and water-exchange investigations of Gd(iii) chelatesElectronic supplementary information (ESI) available: tables of pM values and relaxivities; potentiometric titration curves for TTDA-PY, TTDA-HP, TTDA-H1P and TTDA-H2P; species distribution curves, plots of temperature dependence of transverse electronic relaxation rates and plots of pH dependence

The protonation constants of four poly(aminocarboxylates), N′-pyridylmethyl (TTDA-PY), N′-2-hydroxypropyl (TTDA-HP), N′-2-hydroxy-1-phenylethyl (TTDA-H1P) and N′-2-hydroxy-2-phenylethyl (TTDA-H2P) derivatives of TTDA (3,6,10-tri(carboxymethyl)-3,6,10-triazadodecanedioic acid), and the stability constants of their complexes formed with Ca2+, Zn2+, Cu2+, La3+, Ce3+, Nd3+, Sm3+, Gd3+, Dy3+, Ho3+, Yb3+ and Lu3+ were determined by potentiometric methods at 25.0 ± 0.1 °C and 0.10 mol dm−3 ionic strength in Me4NNO3. The stability of the Gd(III) complexes follows the order TTDA-PY > TTDA-H2P ≊ TTDA-HP ≊ TTDA-H1P. The thermodynamic resistance of the gadolinium(III) complexes, at the plasma concentration used in clinical applications, towards demetallation in the presence of important components of blood plasma, such as Ca(II), Zn(II) and Cu(II), has been evaluated. The observed water proton relaxivity values of [Gd(TTDA-PY)]−, [Gd(TTDA-HP)]−, [Gd(TTDA-H1P)]− and [Gd(TTDA-H2P)]− became constant with respect to pH changes over the range of 4–10, 6–10, 6–10 and 6–10, respectively. 17O NMR shifts showed that the [Dy(TTDA-PY)]−, [Dy(TTDA-HP)]−, [Dy(TTDA-H1P)]− and [Dy(TTDA-H2P)]− complexes at pH 6.30 and 4.30 had 0.9 and 0.9; 2.2 and 3.4; 2.0 and 3.5; 1.8 and 3.0 inner-sphere water molecules, respectively. Water proton spin–lattice relaxation rates for gadolinium(III) complexes were also consistent with the number of inner-sphere water molecules. The EPR transverse electronic relaxation rate and 17O NMR transverse relaxation time were thoroughly investigated and the results obtained were compared with that previously reported for the other gadolinium(III) complex, [Gd(DTPA)(H2O)]2−. Short exchange lifetime values were obtained for the [Gd(TTDA)(H2O)]2−, [Gd(TTDA-PY)(H2O)]−, [Gd(TTDA-HP)(H2O)2]−, [Gd(TTDA-H1P)(H2O)2]− and [Gd(TTDA-H2P)(H2O)2]− complexes. Their water-exchange rates are about 24–45 times faster than that for the [Gd(DTPA)(H2O)]2− complex, which suggested that the longer backbone of the multidentate ligand may be pulled tightly into the first coordination sphere, resulting in high steric constraints at the water binding site.

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.