AcidâBase Properties and Alkali and Alkaline Earth Metal Complex

Article pubs.acs.org/IECR

Acid−Base Properties and Alkali and Alkaline Earth Metal Complex Formation in Aqueous Solution of Diethylenetriamine‑N,N,N′,N″,N″‑pentakis(methylenephosphonic acid) Obtained by an Efficient Synthetic Procedure Rosalia Maria Cigala,† Massimiliano Cordaro,† Francesco Crea,† Concetta De Stefano,† Veronica Fracassetti,‡ Marco Marchesi,‡ Demetrio Milea,† and Silvio Sammartano*,† †

Dipartimento di Scienze Chimiche, Università di Messina, Viale F. Stagno d’Alcontres, 31, I-98166 Messina, Italy Giovanni Bozzetto S.p.A., Via Provinciale, 12, I-24040 Filago (BG), Italy

‡

S Supporting Information *

ABSTRACT: Diethylenetriamine-N,N,N′,N″,N″-pentakis(methylenephosphonic acid) (DTPMPA) is used in a wide range of industrial applications, mainly because of its binding ability toward several metal cations. Because of difficulties in its synthesis and purification, very little reliable data have been reported in the literature about the coordination chemistry of this ligand in aqueous solution. For these reasons, in this article, we report an efficient procedure for the synthesis and purification of DTPMPA. The pure product obtained was used to determine its acid−base properties in different aqueous ionic media, namely, (C2H5)4NI(aq), NaCl(aq), and KCl(aq), at 288.15 ≤ T/K ≤ 318.15 [only T = 298.15 K for KCl(aq)] by potentiometry (H+ ionselective electrode, glass electrode) and at different ionic strengths (0 < I/mol L−1 ≤ 1.0). Measurements performed in alkali metal chlorides were also interpreted in terms of weak complex formation between DTPMPA and Na+ and K+, and further measurements were also performed in NaCl(aq) at T = 298.15 K and different ionic strengths (0 < I/mol L−1 ≤ 1.0) in the presence of Mg2+ or Ca2+, to determine the stability constants of species formed by DTPMPA and these cations. The protonation and complex-formation constants obtained at different ionic strengths and temperatures were modeled by different equations, providing all of the thermodynamic data necessary to define the solution behavior and the chemical speciation of DTPMPA under a wide number of variable conditions, such as those encountered in the very different industrial applications in which this chelating agent is used and those involving many natural fluids.

1. INTRODUCTION The number of applications of phosphonates and their metal complexes is very broad, ranging from the industrial and technological fields (including nanomaterials) to medicine (see, e.g., refs 1 and 2). This is true mainly for several reasons, such as (i) a strong structural relationship to natural compounds, together with a high stability and low toxicity; (ii) the ease of attaching the phosphonate group to organic moieties (favoring the synthesis of many diverse ligands); and (iii) the coordinating ability of phosphonic derivatives toward several metal cations.2 Among the most common organophosphonates, diethylenetriamine-N,N,N′,N″,N″-pentakis(methylenephosphonic acid), DTPMPA (Chart 1), is becom-

ing a preferred chelant in many applications in which strong metal chelation is desired (see, e.g., refs 3−14), owing to the frequent absence of precipitation of some of its complexes over a wide pH range. As an example, DTPMPA appears to be very promising in the replacement of classical chelants such as ethylenediaminetetraacetic acid (EDTA) in hair-coloring products, where the chelation of metal cations such as Cu2+ controls and prevents Fenton-chemistry-induced radical formation, thereby reducing damage to hair fibers.15,16 As phosphonates resist biodegradation, chemical speciation calculations based on numerical equilibrium data are of extreme importance for many applications, including environmental science, waste management, agriculture, scale inhibition, magnetic resonance imaging, and radiopharmaceutical behavior in blood plasma.17 Unfortunately, although a great number of high-/sufficient-quality stability data are available in the main databases for several phosphonates under various conditions, this is not the case for DTPMPA.17−20 For example, for the database of the U.S. National Institute of Standards and

Chart 1. DTPMPA Structure

Received: Revised: Accepted: Published: © 2014 American Chemical Society

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Technology (NIST), some published data for this ligand “do not meet criteria for critical selection”,19 and a technical report by the International Union of Pure and Applied Chemistry (IUPAC) considers most data as “doubtful”,17 owing to the difficulties with the ligand’s synthesis and purification. The analysis performed in that work revealed “only 60−75% DTPPH (DTPMPA) content” for several samples, although “at the same time, the element analysis data for the same white powder samples was well consistent with the chemical composition of DTPPH, which was not surprising taking into account that the impurities are a mixture of the underphosphorylated derivative and ‘free’ H3PO3/H3PO4”.17 Owing to the presence of considerable amounts of impurities with significant acid−base and coordination properties, the accuracy of the protonation and complex-formation constants obtained using these “impure” products is low, resulting in unreliable speciation models and low modeling ability for systems containing DTPMPA. For this reason, we decided to start a new systematic study of the aqueous chemistry of this ligand, based on measurements performed on a product of sufficient purity to obtain reliable thermodynamic data. In this article, we report an efficient procedure for DTPMPA synthesis and purification, based on a U.S. patent held by Monsanto.21 The pure product obtained, commercialized by the company where some of us work (Giovanni Bozzetto S.p.A., Filago, Italy), was therefore used to determine, by potentiometry (H+ ion-selective electrode, glass electrode), the acid−base properties of DTPMPA in different aqueous ionic media, namely, (C2H5)4NI(aq), NaCl(aq), and KCl(aq), at 288.15 ≤ T/K ≤ 318.15 [only T = 298.15 K for KCl(aq)] and at different ionic strengths (0 < I/mol L −1 ≤ 1.0). Measurements performed in alkali metal chlorides were also interpreted in terms of weak complex formation between DTPMPA and Na+ and K+, whereas complex formation with Mg2+ and Ca2+ was investigated by performing further potentiometric measurements in NaCl(aq) at T = 298.15 K and different ionic strengths (0 < I/mol L−1 ≤ 1.0). The protonation and complex-formation constants determined at different ionic strengths and temperatures were modeled by an extended Debye−Hückel equation, providing all of the thermodynamic data necessary to define accurately the solution behavior and the chemical speciation of DTPMPA under a wide number of variable conditions, such as those encountered in the very different industrial applications in which this chelating agent is used and those involving many natural fluids.

see, e.g., Fluka product no. 36818). Various solvents with different polarities were used in this phase, such as methanol, ethanol, tetrahydrofuran, and ethyl acetate. However, experimental evidence during various attempts led to the final, proposed purification procedure, which consists of the direct addition, dropwise, of glacial acetic acid to the dilute aqueous solution of DTPMPA coming from the synthesis, with the further advantage of avoiding the addition of HCl to stabilize the solution. The crystals obtained were then filtered, dried, and characterized as described in section 2.3. 2.2. Chemicals. DTPMPA solutions were prepared from the purified and characterized product, and the concentrations were also checked alkalimetrically. Stock aqueous solutions were quite easily prepared at ligand (i.e., DTPMPA) concentrations up to cL ≈ 0.013 mol L−1, although the actual solubility of the ligand was not determined analytically. Aqueous solutions of alkali and alkaline earth metal chlorides were prepared by weighing pure salts dried in an oven at T = 383.15 K. (C2H5)4NI was previously purified by recrystallization from methanol. Stock solutions of magnesium and calcium chlorides were previously standardized against EDTA standard solutions.22 Hydrochloric acid and tetraethylammonium, sodium, and potassium hydroxide solutions were prepared by diluting the concentrated ampules. Acid and base solutions were then standardized against sodium carbonate and potassium hydrogen phthalate, respectively, previously dried in an oven at T = 383.15 K for 2 h. Hydroxide solutions were preserved from atmospheric CO2 by means of soda lime traps. All solutions were prepared with analytical-grade water (R = 18 MΩ cm−1) using grade A glassware. All chemicals were of the highest available purity and were purchased from Sigma-Aldrich (Milan, Italy). 2.3. Apparatus and Procedure. Elemental analyses were performed for chlorides, water content (Karl Fischer), and total nitrogen (NTOT, digestion in a Kjeldhal DK6 Heating Digester, VELP Scientifica, Milan, Italy) on a Mettler Toledo DL53 tritrator; for total phosphorus (PTOT) by the molybdate method on an HP8453 UV−vis spectrophotometer; and for total carbon (CTOT) on a Carlo Erba total carbon monitor (model 480). The acetic acid contents of the samples were determined by high-performance liquid chromatography (HPLC) on an Agilent 1100 Series instrument equipped with a diode array detector. DSC thermograms were recorded on a DSC Q100 calorimeter (TA Instruments); IR spectra were recorded on a Thermo-Nicolet Nexus FT-IR spectrophotometer; and NMR spectra of the synthesized and commercial products were recorded on Bruker AMX 400 MHz and Varian Inova 500 MHz spectrometers, respectively. Potentiometric measurements were carried out in thermostated cells at the desired temperatures [288.15 ≤ T/K ≤ 318.15; only T = 298.15 K for KCl(aq) and for the determination of Mg 2+ and Ca 2+ complexes] by two operators using two different setups, to minimize systematic errors and to check the repeatability of the systems. The first setup consisted of a model 713 Metrohm potentiometer, equipped with a half-cell glass electrode (Ross type 8101, from Thermo-Orion) and a double-junction reference electrode (type 900200, from Thermo-Orion), and a model 765 Metrohm motorized buret. The apparatus was connected to a PC, and automatic titrations were performed using a suitable homemade computer program to control titrant delivery and data acquisition and to check for emf stability. The second setup consisted of a Metrohm model 809 Titrando apparatus equipped with a combination glass electrode (Ross

2. EXPERIMENTAL SECTION 2.1. Synthesis and Purification of DTPMPA. The synthesis was performed according to U.S. Patent 3,288,846.21 Generally, the synthesis is based on a Kabachnik−Fields reaction, involving an iminium ion as an intermediate. Iminium ion is also an intermediate in both the Mannich and Eschweiler−Clarke reactions, but in this case, the nucleophile is phosphorous acid in its acid tautomeric form. This is one of few cases where phosphorous acid can react efficiently even if it is not esterified, as typically found in the “classic” Kabachnik−Fields reaction. This is possible because of the high reactivity of formaldehyde and the strong acidity of the solution. The purification process of the synthesized DTPMPA was first empirically approached by adding different solvents to the bulk aqueous solution containing DTPMPA, initially stabilized with a high content of hydrochloric acid (usually, commercial solutions of 50% DTPMPA contain ∼15% HCl; 9545

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type 8102, from Thermo-Orion) controlled by Metrohm TiAMO 1.2 software. The estimated precision was the same for both setups, at ±0.15 mV and ±0.003 mL for the emf and titrant volume readings, respectively. All potentiometric titrations were carried out under magnetic stirring and bubbling of purified presaturated N2 through the solution, to exclude O2 and CO2. Titrand solutions were prepared by adding different amounts of DTPMPA (1.0 ≤ cL/mmol L−1 ≤ 8.0), hydrochloric acid (2.0 ≤ cH/mmol L−1 ≤ 10.0), and ionic medium to obtain pre-established ionic strength values (0.1 ≤ I/mol L−1 ≤ 1.0). For measurements performed for the determination of the stability constants of Mg2+ and Ca2+ complexes in NaCl(aq), different amounts of MgCl2(aq) and CaCl2(aq) (0.7 ≤ cM/ mmol L−1 ≤ 8.0) were also added to the titrand solutions prepared as described above, using different cL/cM ratios. Potentiometric measurements were carried out by titrating 25 or 50 mL of the titrand solutions with standard base solutions [(C2H5)4NOH, NaOH, and KOH for measurements in (C2H5)4NI(aq), NaCl(aq), and KCl(aq), respectively] up to pH ∼11.0. For each experiment, independent titrations of strong acid solutions with standard base were carried out under the same medium and ionic strength conditions as the systems to be investigated, with the aim of determining the electrode potential (E0) and the acidic junction potential (Ej = ja[H+]). In this way, the pH scale used was the free scale, pH ≡ −log10[H+], where [H+] is the free proton concentration (not activity). The reliability of the calibration in the alkaline pH range was checked by calculating the appropriate pKw values; for each titration, 80−100 data points were collected. 2.4. Calculations. The nonlinear least-squares computer program ESAB2M was used for the refinement of all parameters of the acid−base titration (E0, pKw, liquid junction potential coefficient ja, analytical concentrations of reagents). The BSTAC and STACO computer programs were used for the calculation of the protonation and complex-formation constants. Both programs can deal with measurements at different ionic strengths. The LIANA computer program was used to fit different functions. The ES4ECI program was used to draw the speciation diagrams and to calculate the species formation percentages. More details on the computer programs are given in ref 23. The ES2WC24 computer program was used in the calculation of formation constants of weak DTPMPA− alkaline cation complexes using conditional protonation constants in different ionic media. Details on the models used for the dependence on temperature and ionic strength are given in the following sections. Formation constants, concentrations, and ionic strengths are expressed in the molar (c, mol L−1) and molal (m, mol (kg of H2O)−1] concentration scales. Molar to molal conversions were made using appropriate density values. Protonation equilibria are expressed as Hi − 1L(z − i + 1) − + H+ = HiL(z − i) − K iH

(1)

Lz − + i H+ = HiL(z − i) − βi H

(2)

j Mm + + i H+ + Lz − = MjHiL(z − i − jm) − βji

with Mm+ = Na+, K+, Mg2+, or Ca2+. The charge z was used in defining various equilibria because a brief discussion of the correct definition of “fully deprotonated” form and the effective charge of the “free ligand” is necessary. It will follow in the next sections. The dependence of the protonation and complex-formation constants on ionic strength in various ionic media was taken into account by an extended-Debye−Hückel- (EDH-) type equation log K = log K 0 − z*DH + f (I )

(5)

where K is the formation constant, K0 is the formation constant at infinite dilution, and z* =

∑ (charges)2 reactants − ∑ (charges)2 products

(6)

DH is the Debye−Hückel term DH = AI1/2(1 + 1.5I1/2)−1

(7)

with A = 0.510 at T = 298.15 K in water. The generic function f(I) can be expressed in most cases as a polynomial function of I f (I ) = CI + DI 3/2

(8)

where C and D are empirical parameters. Sometimes, D can be neglected when I ≤ 1 mol L−1. In those cases, when constants are expressed in the molal concentration scale, eq 5 becomes the classical and widely used SIT (specific-ion interaction theory),25,26 where C is replaced by Δε Δε =

∑ ε(p , q) (9)

p

The ε(p,q) parameter is the SIT interaction coefficient of the pth species (involved in the equilibrium represented by the formation constant K) with the qth component of opposite charge. Generally, the empirical parameters C and D can also be expressed as a function of both the charges (i.e., function of z*, eq 6) and the stoichiometric coefficients (p*) of species involved in the formation reaction27 C = c0p* + c1z*

(10a)

D = d0p* + d1z*

(10b)

where p* =

∑ (moles)reactants − ∑ (moles)products

(11)

and c0, c1, d0, and d1, are empirical parameters that are often independent of the kind of species involved in the equilibrium, but dependent only on the ionic medium and temperature.27 The dependence of the stability constants on temperature was taken into account by applying the van’t Hoff equation

or

log KT = log K θ + ΔH(1/θ − 1/T )/(R ln 10)

(12)

where log KT is the stability constant at a given ionic strength and temperature (in Kelvin), log Kθ is the corresponding value at the reference temperature (i.e., T = 298.15 K in our case), and R = 8.314472(15) J K−1 mol−1 when ΔH is expressed in J mol−1. The van’t Hoff equation is valid if the formation enthalpy changes are approximately constant in the considered temperature range. Because ΔH is considered to be a “well-

If not otherwise specified, the formation constants of alkali and alkaline earth species are expressed as j Mm + + HiL(z − i) − = MjHiL(z − i − jm) − Kji

(4)

(3)

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Figure 1. 31P NMR (161.92 MHz) spectrum of synthesized DTPMPA.

behaved function of T”,28 changes in ΔH can be taken into account using a Taylor’s series expansion, truncated after the second term if a small temperature range is considered ΔHT = ΔHθ + ΔCpθ(T − θ )

f (I )′ = C′I + ΔCp0p*(T − 298.15)/1000

where ΔC0p represents the heat capacity at T = 298.15 K and infinite dilution. These equations can be used to fit the dependence on ionic strength and temperature of the stability constants when they are expressed in either the molar or molal concentration scale. Refined parameters of these equations, however, have a chemicophysical meaning only in the latter case (especially regarding ΔH0 and ΔC0p, as the molal scale is independent of temperature). Nevertheless, parameters obtained in the molar scale have a more “practical” importance.

(13)

These ΔH values represent the formation enthalpy changes of the reaction considered at a fixed ionic strength value. However, they are, in turn, dependent on I ΔH = ΔH ° − z*DH′ + f (I )′

(14)

where DH′ = A′I1/2(1 + 1.5I1/2)−1

3. RESULTS AND DISCUSSION 3.1. Characterization of Pure DTPMPA. Once obtained, the final product from the synthesis appeared as a “microcrystalline” white powder that was not hygroscopic. It was then characterized by elemental analysis; differential scanning calorimetry (DSC); and IR (in KBr), 31P NMR, and 13C NMR spectroscopies (in D2O). Elemental analysis gave P = 25.7%, N = 6.9%, and C = 19.8%, compared to the theoretical values of P = 27.0%, N = 7.3%, and C = 18.9%. DSC measurements fixed the melting point of the product at T ≈ 410 K, whereas decomposition started at T ≈ 523 K. IR and 13 C NMR and 31P NMR spectra were also recorded and are reported in the Supporting Information. The analysis of all results is consistent with a DTPMPA purity of 94.6%. However, apart from the “simple” percentage, the most important aspect that must be emphasized is that the remaining part is represented by 4.9% acetic acid (the precipitating agent) and 0.5% chloride, as desired. In fact, for the reasons already stated in the Introduction, no other byproducts (minor phosphonates or free phosphates) are present, as can be simply appreciated by a quick comparison of the 13C and 31P NMR spectra of the synthesized DTPMPA and that of the commercial product. (31P NMR spectra are shown in Figures 1 and 2 for the synthesized

(15)

with A′ = RT 2 ln 10(∂A /∂T )

(16)

equal to 1.5 at T = 298.15 K. Equations 5−16 can be combined to obtain a single equation for the dependence of the stability constants on both the ionic strength and temperature in a given medium log K = log K 0 − z*AI1/2(1 + 1.5I1/2)−1 + f (I ) + (1/298.15 − 1/T )(R ln 10)−1[ΔH ° − z*A′ I1/2(1 + 1.5I1/2)−1 + f (I )′]

(17)

with A = 0.51 + [0.0856(T − 298.15) + 3.8510−3 (T − 298.15)2 ]/1000

(18)

f (I ) = (c0p* + c1z*)I + d1z*I 3/2

(19)

A′ = 1.5 + 0.024(T − 298.15)

(20)

(21)

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Figure 2. 31P NMR (202.40 MHz) spectrum of commercial DTPMPA.

and commercial DTPMPA, respectively, and both 13C NMR spectra are reported in the Supporting Information.) 3.2. DTPMPA Protonation in (C2H5)4NI(aq), NaCl(aq), and KCl(aq) at Different Ionic Strengths and Temperatures. DTPMPA, in its fully deprotonated form, should be a deca-anion, DTPMP10−. Nevertheless, a preliminary analysis of the experimental data and a careful examination of the available literature information on the acid−base properties of this ligand (e.g., protonation constants in the NIST database19) showed that, under the experimental conditions reported above, the first proton is very strongly bound to the ligand even at high pH values. This suggests considering it as a nona-protic acid, namely, H9(HDTPMP), in all subsequent calculations. This means that the monoprotonated HDTPMP9− species is considered in this work as the free ligand, indicated as L9−. On this basis, seven protonation constants were determined under all of the investigated conditions, whose overall (Tables 1S−3S, Supporting Information) and stepwise (Tables 4S−6S, Supporting Information) values are reported for (C2H5)4NI(aq), NaCl(aq), and KCl(aq) at different ionic strengths and temperatures [only one temperature for KCl(aq)]. The acid− base behavior of DTPMPA is fairly dependent on the ionic medium, as well as the ionic strength and temperature. This is better evidenced in Figures 3 and 4, where, as examples, the dependences of the fourth and second protonation constants, respectively, on ionic strength are reported in different media (Figure 3) and at different temperatures (Figure 4). The curves in the same figures represent the fittings of various constants to eq 17 (see next paragraph). These changes, of course, result in different distributions of various protonated species of DTPMPA, as shown in Figures 5−7, where several distribution diagrams of the protonated species of DTPMPA, obtained under different conditions, are compared. Figure 5 better evidences the influence of the ionic medium, because

Figure 3. Dependence of the fourth protonation constant (log βH4 ) of DTPMPA on the square root of ionic strength (in mol L−1) at T = 298.15 K in different media. Squares, (C2H5)4NI(aq); circles, NaCl(aq); triangles, KCl(aq).

three diagrams obtained at the same ionic strength and temperature (i.e., I = 1.0 mol L−1 and T = 298.15 K) for the three investigated media are plotted together. As can be noted, whereas the formation percentages of various species vary only slightly, the formation pH values are systematically shifted toward more acidic ranges going from (C2H5)4NI(aq) to NaCl(aq) and, finally, KCl(aq). A similar effect is observed (Figure 6) for increasing ionic strength [i.e., from 0.1 to 0.5 mol L−1 in NaCl(aq) at T = 298.15]. Quite differently, Figure 7 [i.e., I = 1.0 mol L−1 in NaCl(aq), T = 288.15 and 318.15 K] shows that changes in temperature do not result in systematic shifts of the protonated species toward more acidic or basic pH ranges, but they determine significant changes in the formation percentages of some species. 9548



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Figure 4. Dependence of the second protonation constant (log βH2 ) of DTPMPA on the square root of ionic strength (in mol L−1) in NaCl(aq) at different temperatures. Squares, T = 288.15 K; circles, T = 298.15 K; upward-pointing triangles, T = 310.15 K; downwardpointing triangles, T = 318.15 K.

Figure 7. Speciation diagrams of DTPMPA vs pH in NaCl(aq) at I = 1.0 mol L−1 and different temperatures: T = 288.15 K (solid lines) and T = 318.15 K (dashed lines). cL = 0.002 mol L−1. Values in the figure represent the number of protons bound to the ligand (as L9−); for example, the curves labeled 3 refer to H3L6− species.

modeled by the EDH and SIT equations (in the molar or molal concentration scales, respectively), whereas the van’t Hoff equation is used for the dependence on temperature. The combination of these models results in eq 17, which was applied here to the overall protonation constants of DTPMPA reported in Tables 1S−3S (Supporting Information). Refined parameters of this equation are reported in Table 7S (Supporting Information) for all of the overall protonation constants (always in the molar scale). This table is divided into three subsections: The first part reports the overall protonation constants at infinite dilution and T = 298.15 K and the z* and p* parameters for each constant, valid under all conditions; the second part reports the parameters (c0, c1, d1) for the dependence of log βiH on ionic strength in the three investigated media, valid for all constants; and the third part reports the formation enthalpy changes at infinite dilution and T = 298.15 K and the C′ parameters for their dependence on medium and ionic strength. As a footnote, the same table also reports a unique refined ΔC0p value, namely, ΔC0p = 183 ± 11 kJ K−1 mol−1, for all of the analyzed data. In fact, according to basic thermodynamics, heat capacities are different for different equilibria and are also dependent the conditions of the system, such as the ionic medium, ionic strength, and temperature. However, the variation of ΔCp values in limited ranges of temperature and ionic strength is usually of the same order of magnitude as the experimental error. Moreover, in the case of protonation equilibria, the heat capacities are usually a function of the protonation step.29 That is why the refinement of different ΔCp values is meaningless under the experimental conditions of this work, and it was preferred to determine only one ΔCp value, multiplied for p* in eq 21, where p* is equivalent to the protonation step if the overall reaction is considered. The goodness of various fits can also be appreciated by the very good agreement between the overall protonation constants determined experimentally under the investigated conditions (Tables 1S−3S, Supporting Information) and those calculated by the proposed equations (by means of parameters in Table 7S, Supporting Information), reported in Tables 8S−10S (Supporting Information) and plotted in Figure 8 against their corresponding experimental values (calculated stepwise con-

Figure 5. Speciation diagrams of DTPMPA vs pH in (C2H5)4NI(aq) (solid lines), NaCl(aq) (dashed lines), and KCl(aq) (dotted lines) at I = 1.0 mol L−1 and T = 298.15 K (cL = 0.002 mol L−1). Values in the figure represent the numbers of protons bound to the ligand (as L9−); for example, curves labeled 3 refer to H3L6− species.

Figure 6. Speciation diagrams of DTPMPA vs pH in KCl(aq) at T = 298.15 K and different ionic strengths: I = 0.1 mol L−1 (solid lines) and I = 0.5 mol L−1 (dashed lines). cL = 0.002 mol L−1. Values in the figure represent the number of protons bound to the ligand (as L9−); for example, the curves labeled 3 refer to H3L6− species.

3.3. Modeling the Dependence of DTPMPA Protonation Constants on Ionic Medium, Ionic Strength, and Temperature. As discussed above, the dependence of a stability constant on the medium and ionic strength can be 9549



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lowering of the protonation constants in one ionic medium with respect to another (assumed as noninteracting or very weakly interacting) can be interpreted in terms of the formation of an ion pair or weak complex between the ligand (and/or its differently protonated species) and the ions of the supporting electrolyte.33 In general, the lower the apparent protonation constant value, the higher the strength of interactions with other components in solution. As observed in various tables reported in the Supporting Information for this work or, better, in Figure 3, the protonation constants of DTPMPA in tetraethylammonium iodide are higher than those determined in alkali metal chlorides, and this is due to the fact that, in general, tetraalkylammonium cations are very weakly interacting with O-donor ligands, so that they are usually considered as “noninteracting” media for these compounds and are used as “baselines” for the determination of weak complexes with other cations.33 Starting from this last assumption, the stability constants of weak Na+ and K+ complexes formed by DTPMPA can be obtained from a comparison between its protonation constants in (C2H5)4NI(aq) and the analogous values in NaCl(aq) or KCl(aq), minimizing the differences between the average number of protons bound to DTPMPA, p,̅ in various ionic media.24,27,34 This number can be expressed as

Figure 8. Calculated (by eqs 17−21) vs experimental overall protonation constants of DTPMPA in various ionic media, at different ionic strengths and temperatures.

stants are reported in Tables 11S−13S, Supporting Information). From this graph, one obtains the expression log βi H = 0.02 + 0.9994 log βi H ,calc ,exp

with a correlation coefficient of R2 = 0.999. Finally, another consideration is necessary when interpreting the parameters reported in Table 7S (Supporting Information): It has already been stated that the use of the molar scale is practical, even though it is temperature-dependent. As a direct consequence, all of the parameters that take into account a temperature dependence (e.g., enthalpy changes and heat capacities) cannot be rigorously expressed in this scale. This is why temperature-independent concentration scales (such as molality and mole fraction) are preferred in these cases, because, only in these circumstances, do these parameters have their real chemicophysical significance. Therefore, ΔH and ΔCp reported in Table 7S (Supporting Information) are not the actual protonation enthalpies and heat capacities, although they maintain their practical importance. Their real values are those obtained from the fits of the protonation constants converted to the molal scale (reported in the Supporting Information in Tables 14S−19S, together with the corresponding refined parameters of eqs 17−21 in Table 20S; overall and stepwise protonation constants calculated by these equations in the molal scale are reported in Tables 21S−26S). The thermodynamic parameters correctly calculated in the molal scale at infinite dilution for all of the overall protonation equilibria of DTPMPA are reported in Table 27S (Supporting Information). Interestingly, from this table, it clearly emerges that the protonation of DTPMPA is an entropy-driven process and, at least for higher steps, it is endothermic (only the first three steps are slightly exothermic). 3.4. Formation of Weak Alkali Metal Complexes. The aforementioned influence of the ionic medium on the acid− base properties of a ligand, including DTPMPA, can be explained in different ways. One of the most common is to interpret it in terms of changes in the activity coefficients of both the proton and the ligand in solution, by means of widely used models and theories, such as the already-described EDH and SIT equations, or the Pitzer model. A detailed description of these models can be found, for example, in refs 26 and 30, and refs 31 and 32 provide some examples of applications to protonation data. Alternatively, at a given ionic strength, the

p̅ * =

∑ iβi H *[H+]i 1 + ∑ βi H *[H+]i

(22)

where the asterisks indicate the apparent parameters in NaCl(aq) or KCl(aq), that is, the parameters calculated without considering the formation of alkali metal complexes. If their formation is taken into account, p̅ can also be expressed as p̅ =

∑ iβji[M+]j [H+]i 1 + ∑ βji[M+]j [H+]i

(23)

which also includes the protonation constants determined in the noninteracting medium (C2H5)4NI(aq) (β0i ≡ βHi ). Because eqs 22 and 23 must give the same results under given conditions, from the minimization of the function U=

∑ (p ̅

− p ̅ *)2

it is possible to calculate the formation constants of the weak sodium and potassium complexes (further details are given in refs 24, 27, and 34). This procedure was performed in this work using the ES2WC24 program for the determination of the stability constants of various NajHiL and KjHiL species at different ionic strengths and temperatures (only for NajHiL complexes). Among the tested models, that accepted takes into account, for both Na+ and K+ under all of the investigated conditions, the formation of seven mononuclear and two dinuclear species, namely, ML8−, MHL7−, MH2L6−, MH3L5−, MH4L4−, MH5L3−, and MH6L2−, plus M2L7− and M2HL6−. The corresponding stability constants are reported in Table 28S (Supporting Information) at I = 0 mol L−1 and T = 298.15 K, together with the refined parameters for their dependence on ionic strength by eq 17. The availability of the protonation constants at different temperatures in both (C2H5)4NI(aq) and NaCl(aq) also allowed, in the case of NajHiL species, the determination of their temperature-dependence parameters, according to the second part of eq 17. Refined ΔH0 values (always in the molar scale and, therefore, taking into account 9550



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comprehensive, systematic study of DTPMPA speciation in aqueous solutions could not neglect a study on the complexes formed by this ligand with both Mg2+ and Ca2+. Therefore, some measurements were also performed in this work in NaCl(aq) at T = 298.15 K and different ionic strengths (0 < I/ mol L−1 ≤ 1.0) in the presence of Mg2+ or Ca2+. The analysis of the experimental data evidenced the formation of six mononuclear and two dinuclear species, namely, ML7−, MHL6−, MH2L5−, MH3L4−, MH4L3−, and MH5L2−, plus M2L5− and M2H2L3−. The stability constants of the metal− ligand complexes, at all investigated ionic strengths, are reported in Table 29S (Supporting Information). The confirmation of the existence of these metal−ligand complexes could be obtained by simply comparing the titration curves for the protonation of the DTPMPA at a given concentration with the same curves when the metal ion (i.e., Na+, K+ or Mg2+, Ca2+, in our case) is also present. Another possible confirmation can be obtained from a comparison with species of similar complexones reported in the literature.17−20 Both of these cations form quite stable species with DTPMPA, with comparable strengths that are higher, as expected, than those of Na+ and K+ species, with no marked differences (within the experimental errors) between those of Mg2+ and Ca2+. The importance of these species can be better appreciated from Figure 10, where, as an example, the speciation diagram of Ca2+ in the presence of DTPMPA is reported as a function of pH at T = 298.15 K and infinite dilution.

the considerations described before), according to the same equilibria reported in Table 28S (Supporting Information), are −0.9, −96.8, 44.4, 69.8, 66.6, 81.6, 52.0, −60.4, and 91.4 kJ mol−1 for ML8−, MHL7−, MH2L6−, MH3L5−, MH4L4−, MH5L3−, MH6L2−, M2L7−, and M2HL6−, respectively, with 95% confidence intervals between ±0.2 and ±0.4. Concerning the C′ parameters (eq 21), the results gave C′ = ( −0.19 ± 0.10) − (4.24 ± 0.06)z*

where the refined ΔC0p value was ΔC0p = 118 ± 8 kJ K−1 mol−1 (p* = 1 for all equilibria considered in Table 28S, Supporting Information). The formation constants reported in Table 28S (Supporting Information) also show that these species are quite stable (considering the general order of magnitude for this kind of complexes33). The log K values of NajHiL species are higher than those for the analogous KjHiL species, as expected from the greater lowering of the apparent protonation constants in NaCl(aq) than in KCl(aq) (always referred to those in tetraethylammonium iodide, the baseline; see, e.g., Figure 3). Furthermore, as usually happens for series of complexes formed by different cations with ligands undergoing many protonation steps (see, e.g., the case of phytate ion35,36), the stability of Na+/DTPMPA and K+/DTPMPA species is a regular function of the number of protons bound to the ligand, as shown in Figure 9 for the log K values of the mononuclear NaHiL and KHiL species at I = 0 mol L−1 and T = 298.15 K.

Figure 9. Dependence of the stability (as log K1i; see eq 3) of the mononuclear NaHiL (squares) and KHiL (circles) species on the number of protons (i) bound to DTPMPA at I = 0 mol L−1 and T = 298.15 K.

Figure 10. Speciation diagram of Ca2+ in the presence of DTPMPA at infinite dilution and T = 298.15 K (cL = 0.0025 mol L−1, cCa = 0.0045 mol L−1). Species: 1, CaH5L2−; 2, CaH4L3−; 3, CaH3L4−; 4, CaH2L5−; 5, CaHL6−; 6, CaL7−; 7, Ca2H2L3−; 8, Ca2L5−.

In this case, one obtains the expressions Na +:

K+:

log K10i = 3.78 − 0.01i − 0.085i 2

These values were obtained from fits of the data reported in Table 29S (Supporting Information) for both Mg2+ and Ca2+ to eq 17, to model the dependence of these constants on ionic strength. Refined parameters for both cations are reported in Table 30S (Supporting Information) and can be used for the calculation of the formation constants of MgjHiL and CajHiL at T = 298.15 over the whole 0 < I/mol L−1 ≤ 1.0 range. Finally, as was the case for the Na+ and K+ complexes, the stability constants reported in Table 29S (Supporting Information) can also be modeled as functions of the number of protons bound to DTPMPA.

log K10i = 3.31 − 0.27i − 0.036i 2

with correlation coefficients of R2 = 0.996 and 0.999 for the Na+ and K+ complexes, respectively. 3.5. Formation of Alkaline Earth Metal Complexes. Together with Na+ and K+, Mg2+ and Ca2+ are main cations in several natural waters and biological fluids.30,37,38 Moreover, they are also important in technological/industrial fields, because they are responsible for the hardness of waters and for scale formation and they strongly affect the performances of all products containing chelating agents (detergents, hair colorants, and so on).3−16 For all of these reasons, a 9551



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4. FINAL REMARKS

ASSOCIATED CONTENT

S Supporting Information *

The main results obtained in this work can be briefly summarized as follows: An efficient procedure for the synthesis and purification of diethylenetriamine-N,N,N′,N″,N″-pentakis(methylenephosphonic acid), DTPMPA, has been reported. The synthesized product does not contain significant amounts of minor phosphonates or free phosphates that would be able to affect the solution behavior of DTPMPA. The availability of this pure product allowed the determination for the first time (to our knowledge) of reliable thermodynamic data on both the acid−base properties of DTPMPA and its binding ability toward Na+, K+, Mg2+, and Ca2+. The protonation and complexformation constants obtained in different ionic media at different ionic strengths and temperatures provided all of the thermodynamic data necessary to define the solution behavior and the chemical speciation of DTPMPA under a wide number of variable conditions. Finally, for the aforementioned uses of DTPMPA, it is also important to stress the fact that results reported here on its speciation, in particular in the presence of Mg2+ and Ca2+, are the first, mandatory step for a correct assessment of its sequestering ability toward these cations in real/industrial systems. In fact, because DTPMPA forms a wide number of species with different stabilities in a wide pH range, the evaluation from the simple analysis of its complex-formation constants is very difficult. Moreover, other competing reactions occur in these systems for both the metal cations and the ligand and cannot be neglected during the choice of a ligand as a sequestering agent of particular cations in multicomponent solutions such as many industrial formulations. To bypass these problems, for some years, this group has quantified the sequestering abilities of ligands through the calculation of the pL0.5, an empirical parameter that represents the analytical concentration ( cL = 10−pL0.5) of ligand necessary to sequester 50% of the metal in trace under given conditions of pH, ionic strength, supporting electrolyte, and temperature, even in the presence of interfering substances. A detailed description of this method can be found in refs 39 and 40. pL0.5 is easily obtained graphically from so-called sequestration diagrams, in which the fractions (x) of metal complexed by the ligand (L), determined under given conditions for different analytical concentrations of L (cL), are plotted as a function of pL (where pL ≡ −log cL). pL0.5 is the pL value at x = 0.5, which can also be calculated by fitting x/pL pairs to the equation

x=

Article

DSC scans and IR, 13C-NMR, and 31P-NMR spectra of the synthesized product; 13C-NMR and 31P-NMR spectra of the commercial product; experimental and calculated overall and stepwise protonation constants in the molar and molal concentration scales; parameters for the dependence of the overall protonation constants on T and I in the molar and molal concentration scales; thermodynamic protonation parameters at infinite dilution; stability constants of DTPMPA complexes with Na+, K+, Mg2+, and Ca2+; and parameters for their dependence on ionic strength. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.M.C., F.C., C.D.S., D.M., and S.S. thank Procter and Gamble Technical Centers Ltd. for financial support. REFERENCES

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1 1 + 10 pL − pL0.5

The higher the pL0.5, the higher the sequestering ability of the ligand. The application of this approach to DTPMPA showed that it is a quite good sequestering agent toward both Mg2+ and Ca2+, with no significant distinction between them. For example, in NaCl(aq) at I = 0.15 mol L−1, pL0.5 = 4.2 at pH 7.0, and pL0.5 = 5.6 at pH 9.0 for both Mg2+ and Ca2+. As a broader consideration, it is worth mentioning that these values can also be used to judge and compare the performances of various ligands under different conditions (pH in this case), on behalf of the “classical” conditional constants22 widely used in different application sectors. 9552



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