Thermodynamic Properties of O-Donor Polyelectrolytes: Determination

Article pubs.acs.org/jced

Thermodynamic Properties of O‑Donor Polyelectrolytes: Determination of the Acid−Base and Complexing Parameters in Different Ionic Media at Different Temperatures Clemente Bretti, Rosalia Maria Cigala,* Francesco Crea, Concetta De Stefano, Giuseppe Gattuso, Anna Irto, Gabriele Lando, Demetrio Milea, and Silvio Sammartano Dipartimento di Scienze Chimiche, Biologiche, Farmaceutiche ed Ambientali, Università di Messina, Viale F. Stagno d’Alcontres, 31, I-98166 Messina (Vill. S. Agata), Italy S Supporting Information *

ABSTRACT: A potentiometric study on the acid−base properties and formation of complexes with alkali metals (i.e., Na+ and K+) of some poly(methyl vinyl ether-co-maleic) acids, namely, Gantrez AN169 (2000 kDa), S95 (220 kDa), and S97 (1200 kDa), was carried out under different experimental conditions consisting of the ionic medium, ionic strength, and temperature. Owing to the possible formation of micelles, the critical micelle concentration of Gantrez AN169 was determined by means of different techniques in pure water and at T = 298.15 K. The diprotic-like model was used for the elaboration of the experimental protonation data, and the best model was obtained by assuming that a monomeric unit consists of two methyl vinyl ether-co-maleic acid residues. Moreover, the protonation data of two poly(acrylic comaleic acids), PCA 3 kDa and 70 kDa (published in a previous paper), under different experimental conditions were reanalyzed. The trend in the protonation constants of polyelectrolytes in different ionic media is (C2H5)4N+ ≫ K+ > Na+. The variation of the protonation and complex formation constants with the ionic strength was interpreted in terms of both the variation of the activity coefficients and the formation of Na+- and K+-polymer complexes.

1. INTRODUCTION Gantrez (GTZ) copolymers belong to an important class of ligands such as those of the poly(carboxylic acid)s at high molecular weight. The GTZ copolymers, in the solid state, are a white hygroscopic powder, but in solution, they are a viscous liquid. They have some important characteristics, for example, high chelating power, excellent dispersion and antisoil redeposition properties, and good stability in hard water. Owing to these important characteristics, GTZ copolymers are widely used in several applications: in cosmetics (toothpastes, mouthwashes, dermal gels, etc.), medical products (denture adhesive bases, controlled release coatings, enteric coatings, ostomy adhesives, and dermal patches), and industrial products (bioadhesive materials, color dispersants, emulsion stabilizers, film-forming agents, and viscosity-increasing agents).1,2 From a scientific point of view, because of the presence of several carboxylic groups in their polymeric chain, the GTZ can be considered to be a good model molecule for the study of more complex natural macromolecules, such as natural organic matter, richer in carboxylic groups, which acts as a binding site for organic and inorganic cations over a wide pH range. In light of this, high-molecular-weight polyelectrolytes have been studied as model molecules for more complicated natural macromolecules, such as humic and fulvic acids, both for the acid−base properties and for the interacting ability toward almost all organic and inorganic cations.3−15 These properties depend on numerous factors, such as the molecular weight, distance between © 2017 American Chemical Society

carboxylic groups, and structure (for example, in terms of cross-linking). As is well known, there was found to be a slight enhancement in the basicity with increasing molecular weight and the consequent increase in the stability of alkali and alkaline earth metal complexes.3,4,7,11,12,15 It is possible to find the Gantrez copolymer in the form of acid or anhydride; in particular, the ligands studied were Gantrez S95 and Gantrez S97 (acid form) and Gantrez AN169 (anhydride form). GTZ S95 and S97 are copolymers of methyl vinyl ether and maleic acid, and they are distinguished by their molecular weight; the first is 220 kDa, and GTZ S97 is 1200 kDa. GTZ AN169 contains alternating units of methyl vinyl ether and maleic anhydride, which in aqueous solution hydrolyze to the acid form; its molecular weight is 2000 kDa. Given the great usefulness of these copolymers, both from scientific and practical points of view, it is important to understand their acid−base properties and how they can be influenced by the variation of the molecular weight or even their ability to bind alkali and alkaline earth metal cations. Considering the structure of these polymers, when dissolved in water they form sticky and jelly solutions, increasing the polymer concentration. This behavior is probably due to the formation of Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 30, 2017 Accepted: April 26, 2017 Published: May 8, 2017 2676

DOI: 10.1021/acs.jced.7b00101 J. Chem. Eng. Data 2017, 62, 2676−2688

Journal of Chemical & Engineering Data

Article

micelles in the solution, consequently influencing their acid− base properties. For this reason, the determination of the critical micelle concentration (CMC) is fundamental prior to studying the protonation of these ligands. In the literature, many papers report the determination of the CMC with many analytical techniques, such as cyclic voltammetry, light scattering, conductivity measurements, and dielectric constant determinations.16−20 Following the indication reported in these papers,16−20 here the CMC value of GTZ AN169 was determined by light scattering, conductivity, surface tension, and DOSY NMR measurements. In the past, the acid−base and thermodynamic properties of different classes of polyelectrolytes of very different molecular weights were studied by this group.3−15 Studying the aqueous thermodynamic properties of polyelectrolytes, different approaches can be used to model the behavior of these molecules as a function of pH, dissociation degree, ionic strength, and so forth. The most frequently used models are the Henderson− Hasselbalch and Högfeldt approaches,21−23 each of them with advantages and disadvantages in terms of difficulty of elaboration of the experimental data and of information obtained. Recently, our group introduced a new simplified approach called the diprotic-like model12,13,24 that allows a polyelectrolyte to be treated, from acid−base and complexing points of view, like a simple low-molecular-weight ligand, taking into account the minimum number of protonation sites necessary to extensively depict the system. The protonation constants of the three copolymers were determined in NaCl, KCl, and (C2H5)4NI aqueous solutions at 0.15 ≤ I/mol dm−3 ≤ 1.7 and at T = 291.15, 298.15, and 318.15 K for GTZ AN169 and GTZ S95; in the case of GTZ S97, the protonation constants were determined in NaCl at 0.10 ≤ I/mol dm−3 ≤ 0.96 and T = 298.15 K. Literature data on two polyacrylic comaleic acids (PCA 3 kDa and 70 kDa)15 were reanalyzed following this approach. From the analysis of the experimental data of GTZ (220, 1200, and 2000 kDa), it was possible to observe a trend in the protonation constants in different ionic media: (C2H5)4N+ ≫ K+ > Na+. This trend is significant because it enables us to estimate the different strengths of the interaction of the copolymers with Na+ and K+. (C2H5)4N+ was considered to be a noninteracting medium toward O-donor ligands.9,10,25−27 Furthermore, as already evidenced in previous studies,7,11,12,15 a regular variation in the behavior of the copolymers was investigated with respect to the molecular weight. In fact, the protonation constants of GTZ AN169 are slightly higher than the corresponding values for GTZ S95 and GTZ S97. At the same time, for the PCA polymers the protonation constants of the 70 kDa polymer are higher than the values of the 3 kDa polymer.15

In the case of (C2H5)4NI salts, the solutions were prepared after recrystallization from methanol and vacuum dried before use. More details of the chemicals are reported in Table 1. Table 1. Chemicals chemicals

symbol

purity

Gantrez AN169 Gantrez S95 Gantrez S97 sodium chloride

GTZ AN169 GTZ S95 GTZ S97 NaCl

>99.5%

potassium chloride

KCl

>99.5%

tetraethylammonium iodide hydrochloric acid

(C2H5)4NI

98%a

HCl

std. solution p.a.

sodium hydroxide

NaOH

std. solution p.a.

potassium hydroxide

KOH

std. solution p.a.

tetaethylammonium hydroxide potassium hydrogen phthalate sodium carbonate

(C2H5)4NOH KHPHTH

electrochemical grade ≥99.5%

Na2CO3

≥99.5%

methanol anhydrous

CH3OH

99.8%

a

supplier Ashland Ashland Ashland SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich

Used after recrystallization from methanol. See section 2.1.

Analytical-grade water (R = 18 MΩ cm) and grade A glassware were used for the preparation of all of the solutions. Soda lime traps were employed to preserve the solutions from atmospheric CO2. 2.2. Potentiometric Apparatus and Procedures. The measurements were carried out by the potentiometric technique at T = (291.15, 298.15, and 318.15) ± 0.01 K in NaCl, KCl, and (C2H5)4NI at different ionic strengths. In order to minimize systematic errors and to check the repeatability of the systems, the measurements were also carried out by two operators using two different apparatuses. More details on the apparatuses and procedures are reported in a previous paper.14 All of the potentiometric titrations were carried out under magnetic stirring and bubbling purified presaturated N2 through the solutions in order to exclude O2 and CO2, and 25 cm3 of solutions containing GTZ (S95, S97, or AN169), an amount of strong acid, and an ionic medium (to obtain the pre-established ionic strength) were titrated with standard NaOH (or KOH or (C2H5)4NOH) solutions. The determination of the electrode potential (E0) and acidic junction potential (Ej = ja[H+]) was carried out by titrating strong acid solution with standard alkaline solutions under the same experimental conditions of the systems investigated. The pH scale used was the free proton concentration scale, where pH ≡ −log[H+]. 2.3. Working Equations and Computer Programs. Nonlinear least-squares computer program ESAB2M was used for the refinement of all of the parameters of the acid−base titration (E0, pKw, liquid junction potential coefficient, ja, analytical concentration of ligands). The BSTAC and STACO computer programs were used for the calculation of protonation and complex formation constants; these programs can deal with measurements at different ionic strengths.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The Gantrez S97 and AN169 solutions were prepared by weighing the powders (from Ashland) whereas the Gantrez S95 solutions were prepared by dilution from a solution at 35%. All of the ligand solutions were prepared without further purification. The ligand concentration was determined by acidimetric titrat ions. Alkali (NaO H, KOH, and (C2H5)4NOH) and ionic medium (NaCl and KCl) solutions were prepared and standardized (for the first) following the procedures already employed and reported in previous papers.10,14,15 2677



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DOSY NMR spectroscopy is usually an excellent tool for the structural characterization of polymers because the signal decays exponentially when phenomena of self-diffusion of the individual molecules was observed. The diffusion coefficient is related to the properties of each molecule, such as the size, mass, and charge, as well as its surrounding environment, such as solution, temperature, and aggregation states. The DOSY NMR measurements were performed at T = 298.15 K in D2O with a Varian 500 MHz instrument equipped with a pulse-field gradient probe. The HDO residual solvent peak (δ = 4.65 ppm) was used as an internal standard. Diffusion-ordered NMR spectroscopy studies were performed using a DgcsteSL pulse sequence,30 optimizing experimental parameters according to the sample under investigation. Diffusion gradients were progressively incremented over 30 steps, varying the gradient strength from 1.8 to 50.0 G/cm. Sixteen transients were collected for each increment, with a diffusion-gradient length of 3 ms and diffusion delays of 300 ms. The Gantrez AN 169 solutions were prepared by the dissolution of the polymer in D2O at different concentrations ranging from 0.0015 to 0.0147 mol dm−3, with a known amount of hydrochloric acid (0.0034 mol dm−3). The experimental diffusion coefficient (D) collected under those conditions shows a decreasing trend increasing the Gantrez concentration. The CMC was determined by a linear fitting of the diffusion coefficient versus the inverse of the Gantrez AN 169 concentration; two slopes were obtained and the CMC values were calculated at the intersection point of these two lines, resulting in 0.00454 mol dm−3. The light-scattering measurements were carried out with a fluoromax-4 spectrofluorometer by Horiba Jobin-Yvon equipped with a Peltier Sample Cooler (model F-3004) controlled by a Peltier thermoelectric temperature controller (model LFI-3751, 5 A - 40 W). The instrument was controlled by FluorEssence 2.1 software by Horiba Jobin-Yvon. The Gantrez AN 169 solutions were prepared by the direct dissolution of the polymer at different concentrations ranging from 0.001 to 0.030 mol dm−3 in pure water; the scans were recorded at T = 298.15 K in the range of 200 ≤ λ/nm ≤600 with a scan rate of 2 nm s−1 and an integration time of 0.2 s. The scattering intensity of the different Gantrez solutions was plotted against the concentration, and also in this case the CMC was calculated as in the case of the DOSY NMR data. The CMC value was found to be 0.00650 mol dm−3. Conductivity measurements were carried out by means of a WTW InoLab Cond 7310 conductimeter in a thermostated room at T = 298.15 K under magnetic stirring. Solutions of GTZ AN169 were prepared in pure water in the concentration range of 0.0005−0.030 mol dm−3 and following the procedures already reported for the other techniques. Also in this case the conductivity values of the different Gantrez solutions were plotted against the concentration, and the CMC value was found to be 0.00754 mol dm−3. With regard to the surface tension measurements, these were carried out by means of the stalagmometric method, one of the most common methods used for the surface tension determination. For each GTZ AN169 solution, prepared as for the other techniques, the drops of liquid that leaked out of the glass capillary of the stalagmometer were weighted, and the surface tension was calculated at each GTZ AN169 concentration. The plot of the surface tension values vs GTZ AN169 concentration gave a CMC value of 0.00653 mol dm−3.

For the systems investigated at different ionic strengths and temperatures in different ionic media, the ES2WC program28 was used to calculate the stability constants of the Na+-, K+polymer complexes and to model altogether the dependence of the protonation constants on both the ionic strength and temperature. For GTZ S97 (system investigated only in NaCl at T = 298.15 K), the dependence of the stability constants on ionic strength was fitted by means of the LIANA computer program. Further details on all of the software used are reported in De Stefano et al.29 When we study the acid−base properties of polyelectrolytes to determine the protonation constants, it is necessary to use models21−23 that take into account the dependence of log KH on the dissociation degree of the polyelectrolyte, α: α=

[L] [L] = [HL] + [L] [L]T

(1)

The elaboration of the experimental data by using these models is often not simple, especially in the dissociation degree ranges of α < 0.1 and α > 0.9, where the variation of the protonation constants for carboxylic polyelectrolytes is more than 2.5 units. Instead in many cases, for 0.1 ≤ α ≤ 0.9, the acid−base behavior of these macromolecules should be independent of α. This suggested us to propose a simple approach called the diproticlike model12,13,24 to study the acid−base properties of polyelectrolytes. Taking into account this approach, a highmolecular-weight polyelectrolyte can be considered to be a simple low-molecular-weight ligand with a given number of dicarboxylic units. Initially, this approach was applied to simple high-molecular-weight polyelectrolytes such as polyacrylates and polymethacrylates whose monomeric units contain only two carboxylic groups. For this reason, by applying the diprotic-like model, only two protonation constants (KH1 and KH2) independent of the dissociation degree (α) were taken into account. If this approach is applied to other classes of polyelectrolytes, then it is necessary to estimate the minimum number of protonation sites sufficient to depict the acid−base behavior of the polyelectrolytes with a negligible loss of precision.12,13,24 For these studies, the best model was obtained by assuming that a monomeric unit consisted of two methyl vinyl ether-co-maleic acid residues; therefore, four carboxylic groups were considered and four protonation constants were determined. On the basis of these assumptions, the protonation constants of the ligands are given according to the overall (βHr) and stepwise (KHr) equilibria: rH+ + Ln − = Hr L(r − n)

(2)

H+ + H(r − 1)L((r − 1) −n) = Hr L(r − n)

(3)

The complex formation constants (βpqr) of the ligands with the cations of the supporting electrolyte are expressed by q M+ + r H+ + Ln − = MqHr L(q + r − n)

(4)

3. RESULTS AND DISCUSSION 3.1. Critical Micelle Concentration. The determination of the critical micelle concentration (CMC) was performed by means of DOSY NMR, light scattering experiments, and surface tension and conductivity measurements. 2678



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Figure 1. CMC value calculated at T = 298.15 K by means of different experimental techniques. (A) Light scattering, (B) surface tension, (C) DOSY NMR, and (D) conductivity.

The lower CMC value determined by DOSY NMR can be due to the measurements carried out on GTZ AN169 solutions containing HCl (0.0034 mol dm−3). From the CMC values obtained from the different techniques, a mean value was calculated and was found to be CMC (GTZ AN169) = 6.28 ± 1.25 mmol dm−3, taking into account the four techniques, or CMC (GTZ AN169) = 6.83 ± 0.59 mmol dm−3 if the DOSY NMR value was neglected. Figure 1 shows the four different diagrams obtained from the different techniques, plotting the instrumental signal vs GTZ AN169 concentration at T = 298.15 K. The effect of temperature on the CMC value of GTZ AN169 was also evaluated by means of light-scattering measurements carried out on solutions at a concentration 0.001 to 0.010 mol dm−3 by following the criteria reported above for the same technique. The temperature was varied between 288.15 ≤ T/K ≤ 318.15 with an increment of 278.15 K; the temperature was controlled by a Peltier sample cooler (model F-3004) controlled by Peltier thermoelectric temperature controller model LFI3751 (5 A - 40 W). Figure 2 reports the mean scattering-intensity values and the corresponding error obtained by taking into account the different GTZ AN169 solutions measured at each temperature at a given concentration. The mean values of the scattering intensity vs concentration (mol dm−3) increase up to ∼0.006 mol dm−3 and then decrease; the two parts of the graph were fitted by a linear fitting, and the intersection of the straight lines occurs at a concentration of 0.00578 mol dm−3. This concentration can be assumed to be a mean CMC value of GTZ AN169 that is valid in the temperature range of 288.15 ≤ T/K ≤ 318.15. Taking into account the fairly similar behavior in the aqueous solution of the GTZ polymers investigated here, the mean CMC value calculated for GTZ AN169 was assumed to be a reference

Figure 2. Average light-scattering intensity calculated in the temperature range of 288.15 ≤ T/K ≤ 318.15 vs the GTZ AN169 concentration.

value also for GTZ S95 and GTZ S97, and all of the investigated solutions were prepared at lower concentrations. 3.2. Protonation Constants. GTZ AN169 (2000 kDa) and GTZ S95 (220 kDa) ligands were studied potentiometrically at different temperatures (291.15, 298.15, and 318.15 K), ionic strengths, and ionic media, namely, NaCl, KCl, and (C2H5)4NI. GTZ S97 (1200 kDa) was studied only in NaCl at T = 298.15 K. The protonation constants are reported in Tables 2−4. By using the diprotic-like model (see also section 2.3), four protonation constants are sufficient to fit the experimental data with a very small difference between these and the calculated ones, independent of the experimental conditions (ionic strength, 2679



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Table 2. Experimental Stepwise Protonation Constantsa of Gantrez AN169 at Different Ionic Media, Ionic Strengths, and Temperatures on the Molar Concentration Scale Tb

Ic

log KH1

log KH2

log KH3

log KH4

291.15

0.158 0.478 0.962 1.684 0.151 0.480 0.960 1.662 0.158 0.482 0.974 1.682

8.033 ± 0.005d 7.676 ± 0.004 7.478 ± 0.003 7.314 ± 0.006 8.034 ± 0.005 7.683 ± 0.004 7.459 ± 0.004 7.341 ± 0.003 8.120 ± 0.005 7.773 ± 0.005 7.517 ± 0.003 7.298 ± 0.006

6.680 ± 0.008d 6.331 ± 0.005 6.142 ± 0.005 6.024 ± 0.008 6.741 ± 0.007 6.341 ± 0.005 6.144 ± 0.005 6.032 ± 0.004 6.838 ± 0.007 6.463 ± 0.006 6.213 ± 0.003 6.077 ± 0.007

4.064 ± 0.009d 3.824 ± 0.006 3.732 ± 0.006 3.730 ± 0.011 4.012 ± 0.009 3.776 ± 0.006 3.692 ± 0.006 3.684 ± 0.005 4.018 ± 0.009 3.750 ± 0.008 3.615 ± 0.004 3.621 ± 0.008

3.307 ± 0.008d 3.120 ± 0.007 3.079 ± 0.007 3.124 ± 0.012 3.325 ± 0.008 3.102 ± 0.006 3.040 ± 0.006 3.056 ± 0.006 3.244 ± 0.007 3.074 ± 0.007 3.008 ± 0.004 3.022 ± 0.007

0.156 0.502 0.718 0.989 0.156 0.499 0.740 0.991 0.151 0.507 0.720 0.996

8.200 ± 0.008 7.771 ± 0.014 7.781 ± 0.005 7.873 ± 0.028 8.202 ± 0.007 7.775 ± 0.012 7.789 ± 0.004 7.871 ± 0.026 8.272 ± 0.008 7.771 ± 0.018 7.825 ± 0.005 7.854 ± 0.031

6.710 ± 0.010 6.297 ± 0.013 6.305 ± 0.007 6.321 ± 0.025 6.787 ± 0.010 6.330 ± 0.010 6.316 ± 0.005 6.349 ± 0.022 6.868 ± 0.010 6.400 ± 0.014 6.371 ± 0.007 6.410 ± 0.024

4.060 ± 0.020 3.831 ± 0.015 3.795 ± 0.009 3.768 ± 0.027 4.092 ± 0.013 3.808 ± 0.015 3.754 ± 0.006 3.738 ± 0.026 4.010 ± 0.010 3.733 ± 0.017 3.675 ± 0.009 3.650 ± 0.025

3.270 ± 0.010 3.123 ± 0.017 3.096 ± 0.008 3.087 ± 0.024 3.334 ± 0.009 3.098 ± 0.015 3.052 ± 0.006 3.057 ± 0.022 3.248 ± 0.008 3.021 ± 0.012 2.974 ± 0.007 2.970 ± 0.019

0.104 0.293 0.583 0.862 0.110 0.292 0.578 0.890 0.106 0.294 0.580 0.873

10.212 ± 0.011 9.830 ± 0.010 9.790 ± 0.020 9.810 ± 0.020 10.149 ± 0.011 9.910 ± 0.030 9.740 ± 0.020 9.710 ± 0.030 10.026 ± 0.022 9.730 ± 0.020 9.800 ± 0.030 9.590 ± 0.030

7.941 ± 0.024 7.700 ± 0.020 7.690 ± 0.030 7.760 ± 0.030 7.934 ± 0.020 7.740 ± 0.040 7.670 ± 0.030 7.710 ± 0.030 7.944 ± 0.017 7.760 ± 0.030 7.810 ± 0.040 7.790 ± 0.050

4.383 ± 0.015 4.250 ± 0.030 4.210 ± 0.030 4.210 ± 0.030 4.339 ± 0.012 4.230 ± 0.050 4.190 ± 0.030 4.220 ± 0.040 4.242 ± 0.009 4.150 ± 0.030 4.100 ± 0.040 4.120 ± 0.050

3.547 ± 0.014 3.480 ± 0.020 3.500 ± 0.020 3.470 ± 0.030 3.516 ± 0.011 3.450 ± 0.040 3.460 ± 0.030 3.510 ± 0.030 3.443 ± 0.006 3.390 ± 0.020 3.370 ± 0.030 3.420 ± 0.030

NaCl

298.15

318.15

KCl 291.15

298.15

318.15

(C2H5)4NI 291.15

298.15

318.15

a

Refers to eq 3. bIn K, standard uncertainties, u(T) = 0.01 K. cIn mol·dm−3, standard uncertainties, u(I) = 0.001 mol·dm−3. d±Standard deviation.

GTZ anions with the Na+ cation are stronger than those with K+, as already observed for other classes of inorganic (phosphate, pyrophosphate, and tripolyphosphate) and organic (lowmolecular-weight polycarboxylic ligands, glutathione, and so forth) ligands.10,25,26,31−33 Generally, the protonation constants of polyelectrolytes with high molecular weight are dependent on the molecular weight and N (number of monomeric units in the polymer chain). In several previous works,3−5,7,11,12,15 we reported that an increase in log N gives an increase in the binding ability of polyelectrolytes owing to the higher charges available to interact with a cation such as H+. From a comparison among the protonation constants of the three polymers, namely, GTZ polymers, investigated here, we do not observe a similar trend, as can be seen in Figure 4, where the experimental protonation constant values of GTZ AN169, S95, and S97 in NaCl at different ionic strengths and T = 298.15 K are reported; this can be explained by taking into account that there is not a large difference in the molecular weight of these copolymers,

ionic medium, and temperature) taken into account for the ligand. As an example, Figure 3 reports a comparison between the experimental and calculated pH values of GTZ AN169 vs cm−3 of NaOH added during a titration (cGTZ AN169 = 0.0025 mol dm−3 in NaCl(aq) at I = 0.50 mol dm−3 and T = 298.15 K). In this case, the maximum ΔpH value observed was 0.04 pH unit, in correspondence with the inflection points; similar evidence was also observed for all the other titrations. Data of the poly(acrylic comaleic) acids, PCA, (MW = 3 and 70 kDa) in NaCl and (C2H5)4NI at different ionic strengths have already been published by this group.15 They were reanalysed by using the same approach (i.e., the diprotic-like model), and the new values are reported in Tables 5 and 6 for PCA 3 kDa and 70 kDa, respectively. The protonation constant of the Gantrez polymers investigated in different ionic media follows the trend (C2H5)4N+ ≫ K+ > Na+ (see as an example Figure S1 in the Supporting Information), indicating that the interactions of the 2680



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Table 3. Experimental Stepwise Protonation Constantsa of the Gantrez S95 at Different Ionic Media, Ionic Strengths, and Temperatures on the Molar Concentration Scale Tb

Ic

log KH1

log KH2

log KH3

log KH4

291.15

0.148 0.510 1.001 1.738 0.162 0.484 0.990 1.685 0.150 0.162 0.491 0.993 1.687

8.08 ± 0.03d 7.65 ± 0.03 7.40 ± 0.03 7.18 ± 0.03 8.45 ± 0.01 7.69 ± 0.03 7.42 ± 0.03 7.22 ± 0.01 8.08 ± 0.02 8.46 ± 0.01 7.72 ± 0.03 7.44 ± 0.03 7.14 ± 0.01

6.28 ± 0.03d 5.94 ± 0.03 5.73 ± 0.02 5.53 ± 0.02 6.59 ± 0.02 5.99 ± 0.03 5.76 ± 0.02 5.57 ± 0.01 6.28 ± 0.03 6.66 ± 0.02 6.05 ± 0.03 5.82 ± 0.03 5.55 ± 0.01

4.23 ± 0.02d 4.04 ± 0.02 3.93 ± 0.02 3.85 ± 0.02 4.37 ± 0.03 4.02 ± 0.02 3.91 ± 0.02 3.79 ± 0.01 4.17 ± 0.04 4.33 ± 0.03 3.96 ± 0.01 3.85 ± 0.02 3.72 ± 0.01

3.31 ± 0.02d 3.21 ± 0.02 3.15 ± 0.02 3.10 ± 0.02 3.28 ± 0.03 3.20 ± 0.01 3.13 ± 0.01 3.09 ± 0.01 3.24 ± 0.04 3.21 ± 0.03 3.15 ± 0.02 3.09 ± 0.01 3.03 ± 0.02

0.146 0.507 0.945 1.740 0.148 0.507 0.948 1.684 1.689 0.145 0.497 0.997 1.701

8.60 ± 0.04 8.22 ± 0.04 8.04 ± 0.03 7.91 ± 0.03 8.61 ± 0.04 8.22 ± 0.03 8.05 ± 0.03 8.06 ± 0.01 7.91 ± 0.01 8.64 ± 0.04 8.24 ± 0.04 8.03 ± 0.03 7.82 ± 0.01

6.70 ± 0.02 6.37 ± 0.02 6.19 ± 0.02 6.01 ± 0.01 6.72 ± 0.02 6.39 ± 0.02 6.21 ± 0.01 6.11 ± 0.02 6.03 ± 0.02 6.78 ± 0.02 6.44 ± 0.02 6.23 ± 0.02 5.99 ± 0.02

4.59 ± 0.02 4.35 ± 0.02 4.21 ± 0.01 4.04 ± 0.01 4.56 ± 0.02 4.32 ± 0.02 4.18 ± 0.01 4.03 ± 0.02 3.99 ± 0.02 4.49 ± 0.02 4.24 ± 0.02 4.08 ± 0.01 3.93 ± 0.02

3.49 ± 0.02 3.33 ± 0.02 3.21 ± 0.01 3.04 ± 0.01 3.47 ± 0.02 3.31 ± 0.02 3.19 ± 0.01 3.02 ± 0.02 3.03 ± 0.02 3.42 ± 0.02 3.26 ± 0.01 3.12 ± 0.01 2.98 ± 0.02

0.099 0.299 0.590 0.902 0.101 0.292 0.601 0.870 0.895 0.101 0.292 0.597 0.881 0.905

10.14 ± 0.02 9.87 ± 0.02 9.76 ± 0.02 9.74 ± 0.02 10.09 ± 0.01 9.83 ± 0.04 9.70 ± 0.01 9.72 ± 0.03 9.68 ± 0.02 9.96 ± 0.02 9.55 ± 0.03 9.55 ± 0.01 9.53 ± 0.04 9.53 ± 0.01

7.35 ± 0.03 7.16 ± 0.03 7.10 ± 0.03 7.11 ± 0.02 7.35 ± 0.03 7.22 ± 0.05 7.10 ± 0.02 7.22 ± 0.05 7.11 ± 0.02 7.36 ± 0.02 7.12 ± 0.05 7.09 ± 0.02 7.11 ± 0.07 7.10 ± 0.03

4.64 ± 0.02 4.52 ± 0.02 4.48 ± 0.02 4.50 ± 0.02 4.60 ± 0.02 4.52 ± 0.06 4.44 ± 0.02 4.48 ± 0.05 4.45 ± 0.02 4.50 ± 0.02 4.34 ± 0.06 4.33 ± 0.02 4.36 ± 0.08 4.34 ± 0.02

3.59 ± 0.03 3.54 ± 0.02 3.53 ± 0.02 3.55 ± 0.01 3.56 ± 0.02 3.62 ± 0.06 3.50 ± 0.02 3.49 ± 0.05 3.52 ± 0.01 3.49 ± 0.02 3.39 ± 0.05 3.42 ± 0.01 3.38 ± 0.07 3.44 ± 0.01

NaCl

298.15

318.15

KCl 291.15

298.15

318.15

(C2H5)4NI 291.15

298.15

318.15

a

Refers to eq 3. bIn K, standard uncertainties, u(T) = 0.01 K. cIn mol·dm−3, standard uncertainties, u(I) = 0.001 mol·dm−3. d±Standard deviation.

Table 4. Experimental Stepwise Protonation Constantsa of the Gantrez S97 in NaCl at Different Ionic Strengths and T = 298.15 K on the Molar Concentration Scale

a

Ib

log KH1

0.100 0.154 0.155 0.235 0.476 0.717 0.960

8.318 ± 0.006 7.963 ± 0.004 8.181 ± 0.009 7.980 ± 0.01 7.730 ± 0.01 7.533 ± 0.004 7.286 ± 0.008

log KH2 c

6.852 ± 0.008 6.591 ± 0.006 6.589 ± 0.010 6.510 ± 0.020 6.290 ± 0.010 6.121 ± 0.006 5.974 ± 0.010

log KH3 c

4.300 ± 0.010 4.145 ± 0.006 4.100 ± 0.020 4.050 ± 0.020 3.860 ± 0.020 3.807 ± 0.008 3.740 ± 0.010

log KH4 c

3.300 ± 0.010c 3.370 ± 0.006 3.340 ± 0.020 3.250 ± 0.020 3.170 ± 0.010 3.130 ± 0.008 3.170 ± 0.010

Refers to eq 3. bIn mol·dm−3, standard uncertainties, u(I) = 0.001 mol·dm−3. c±Standard deviation.

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where log βH0 is the overall protonation constant at infinite dilution z* = Σ(charge)react 2 − Σ(charge)prod 2

(6)

C and D are the ionic strength dependence parameters. In many cases, in interacting ionic media (NaCl, KCl, etc.) the C parameter is sufficient to model the variation of the protonation constants with the ionic strength, whereas noninteracting media such as tetraalkylammonium salts require the use of the C and D parameters. For the systems investigated at different temperatures, the ES2WC program was used to model the dependence of the protonation constants on both the ionic strength and temperature by means of the following equation log β = log β H0 + Figure 3. Experimental (□) and theoretic (−) titration curves of Gantrez AN169. Experimental condition: cGTZ AN169 = 0.0025 mol dm−3 in NaCl(aq) at I = 0.50 mol dm−3 and T = 298.15 K.

+ (C + C′ΔT )I + (D + D′ΔT )I1.5

z*0.51I 0.5 + CI + DI1.5 1 + 1.5I 0.5

(7)

where log β is the overall protonation constant at infinite dilution calculated by taking into account the Na+ or K+ interaction with the ligand. ∂log β0/∂T is the temperature gradient of the protonation constant, ΔT is the temperature difference (T − 298.15) K, and z* is the same as in eq 6. C and D are the ionic strength dependence parameters, and C′ and D′ are the temperature gradients of these parameters. Table 7 reports the parameters for the dependence of the protonation constants of GTZ polymers on the ionic strength, the temperature gradient of the protonation constants, and the parameters for the dependence of C and D on temperature (C′ and D′). Similar calculations were carried out on the PCA copolymers, and Table 8 reports the protonation constants at infinite dilution at T = 298.15 K, the parameters for their dependence on the ionic strength in NaCl and (C2H5)4NI aqueous solutions, and for PCA 3 kDa, the temperature gradient of the first two protonation constants. The knowledge of the temperature gradient allowed us to estimate ΔH/kJ mol−1 values for the protonation steps of GTZ AN169, GTZ S95, and PCA 3 kDa (Tables 7 and 8, respectively). 3.4. Na+-, K+-Polymer Complexes. If the variation of the protonation constants with the ionic strength is explained in terms of the formation of complexes between the anion of the ligand and the cation of the supporting electrolyte, then it is necessary to consider the following points. First, we have to find a baseline supporting electrolyte whose cation does not interact H0

whereas in the case of the PCA copolymers, the different is about 1.8 orders of magnitude. Consequently, we observe the net difference log KH PCA 70 kDa > log KH PCA 3 kDa. Figure 5 reports the distribution of the protonated species of GTZ AN169 at I = 0.15 mol dm−3 and in the three ionic media studied; a significant shift at high pH values is observed in (C2H5)4NI(aq) owing to the noninteracting nature of the medium, whereas almost overlapping curves are observed in NaCl and KCl because of the fairly similar interacting ability toward the ligands. 3.3. Dependence of the Stability Constants on Ionic Strength and Temperature. The dependence of the protonation constants on ionic strength can be interpreted by means of two different approaches: the first one that considers the variation in log KiH with the ionic strength in terms of activity coefficient variation and the second one that takes into account the possible formation of Na+-, K+-polymer species between the anion of the ligand and the cation of the supporting electrolyte. In the first case, using a simple Debye−Hückel type equation, the dependence of the protonation constants on ionic strength can be modeled by the following equation log β H = log β H0 −

∂log β 0 z*I 0.5 ΔT − ∂T 2 + 3I 0.5

(5)

Table 5. Overall Experimental Protonation Constantsa of the PCA 3 kDab at Different Ionic Strengths and T = 298.15 K on the Molar Concentration Scale Ic NaCl 0.05 0.10 0.25 0.50 1.00 (C2H5)4NI 0.10 0.25 0.50 a

log KH1

log βH2

log βH3

log βH4

7.059 ± 0.006d 6.849 ± 0.004 6.629 ± 0.006 6.420 ± 0.009 6.24 ± 0.01

12.708 ± 0.009d 12.204 ± 0.006 11.76 ± 0.01 11.35 ± 0.02 11.03 ± 0.02

17.46 ± 0.01d 16.739 ± 0.007 16.11 ± 0.01 15.58 ± 0.02 15.16 ± 0.03

21.20 ± 0.02d 20.21 ± 0.01 19.47 ± 0.03 18.82 ± 0.05 18.35 ± 0.07

7.139 ± 0.008 7.056 ± 0.008 7.101 ± 0.007

12.62 ± 0.01 12.45 ± 0.01 12.52 ± 0.01

17.14 ± 0.01 16.90 ± 0.01 17.02 ± 0.02

20.59 ± 0.02 20.29 ± 0.02 20.54 ± 0.04

Refers to eq 2. bReanalysis of literature data.15 cIn mol·dm−3, standard uncertainties, u(I) = 0.01 mol·dm−3. d±Standard deviation. 2682



Article

Table 6. Overall Experimental Protonation Constantsa of the PCA 70 kDab at Different Ionic Strengths and T = 298.15 K on the Molar Concentration Scale Ic NaCl 0.05 0.10 0.50 1.00 (C2H5)4NI 0.10 0.25 0.50 a

log KH1

log βH2

log βH3

log βH4

7.106 ± 0.006d 6.912 ± 0.006 6.61 ± 0.01 6.51 ± 0.01

12.910 ± 0.008d 12.457 ± 0.008 11.67 ± 0.02 11.44 ± 0.02

17.83 ± 0.01d 17.15 ± 0.01 15.99 ± 0.03 15.66 ± 0.03

21.65 ± 0.02d 20.78 ± 0.02 19.35 ± 0.06 18.95 ± 0.07

7.499 ± 0.008 7.404 ± 0.006 7.352 ± 0.006

13.42 ± 0.01 13.19 ± 0.01 13.105 ± 0.008

18.23 ± 0.02 17.88 ± 0.01 17.79 ± 0.01

21.92 ± 0.02 21.47 ± 0.02 21.40 ± 0.01

Refers to eq 2. bReanalysis of the literature data.15 cIn mol·dm−3, standard uncertainties, u(I) = 0.01 mol·dm−3. d±Standard deviation.

discussed this problem and found a simple model based on the assumptions that for I ≤ 1 mol dm−3 it is possible to obtain Na+ or K+ complex formation constants from the difference between protonation constants in (C2H5)4NI and NaCl or KCl using data in tetraethylammonium salt as the baseline by means of a suitable computer program to make appropriate calculations (ES2WC). Moreover, the assumptions imply that activity coefficients of free species do not depend on the background electrolyte but are dependent only on the charge (I ≤ 1 mol dm−3). For the ligands investigated here, the difference among values in NaCl, KCl, and (C2H5)4NI is quite sharp and accounts for the very different interacting abilities of Na+, K+, and (C2H5)4N+ toward the ligands; this behavior is a consequence of the very different nature of the three cations. Sodium and potassium cations are considered to be structure-promoting ions (water molecules assume the structure of pure water), whereas tetraalkylammonium cations are structure-breaking ions. (More details are reported in refs 27 and 36.) Taking into account the assumptions reported here for the formation and calculation of metal complexes, it was possible to calculate the complex formation constants of the GTZ-Na+ and -K+ species by means of the ES2WC computer program. Applying eq 7, we calculated the complex formation constants at infinite dilution together with their dependence on the ionic strength and temperature. Tables 9 and 10 report the complex formation constants for GTZ AN169 and GTZ S95, respectively, the temperature gradient for the formation constants for both the Na+ and K+ complexes, and the C and D parameters for their dependence on the ionic strength. In the same tables, the C′ and D′ values, namely, the parameters that account for the dependence of the C and D parameters on the temperature, are also given. Similar calculations were carried out on the GTZ S97 ligand investigated only in NaCl aqueous solution at T = 298.15 K (Table 11). + Generally, these ion pairs have KM (M+ = Na+ or K+) values of 2 3 26,27 As observed from the data reported in Tables 9 ∼10 −10 . and 10, for the GTZ-Na+ and GTZ-K+ complexes we have values + of KM ≈ 104, so they cannot be considered to be weak

Figure 4. Experimental protonation constants of the different Gantrez ligands vs ionic strength in NaCl(aq) at T = 298.15 K. Legend: (□) GTZ AN169, (○) GTZ S95, and (Δ) GTZ S97.

+

Figure 5. Distribution diagram of the protonation species of Gantrez AN 169 in three different ionic media: (−) NaCl(aq), (---) KCl(aq), and (···) (C2H5)4NI(aq). Experimental condition: cGTZ AN169 = 0.003 mol dm−3, I = 0.50 mol dm−3, and T = 298.15 K.

complexes. The higher KM values calculated for the GTZ-Na+ and GTZ-K+ complexes, with respect to M+/low molecular weight O-donor complexes, can be explained in terms of the higher available charge of the polyanions to interact with the metal ions.3,9,10,15 The experimental protonation constants of GTZ AN169 and GTZ S95 at different ionic strengths in different ionic media and at different temperatures, are reported as Supporting Information in Tables SI1 and SI2, respectively, on the molal

with the carboxylic anion. Second, we must choose a simple model for the ionic strength dependence that is valid for both protonation constants and complex formation constants. With regard to this point, in some previous papers27,28,34,35 we 2683



Article

Table 7. Overall Protonation Constants at Infinite Dilution for GTZ AN169, GTZ S95, and GTZ S97 at T = 298.15 K and Parameters for the Dependence on Ionic Strength and Temperature Gradientsa log βH0b

species GTZ AN169 HL H2L H3L H4L GTZ S95 HL H2L H3L H4L GTZ S97 HL H2L H3L H4L a

∂ log β/∂t

10.78 ± 0.03c 19.24 ± 0.05 23.91 ± 0.06 27.54 ± 0.06

0.002 ± 0.005c 0.009 ± 0.008 0.008 ± 0.009 0.005 ± 0.010

10.84 ± 0.04 18.77 ± 0.06 23.76 ± 0.07 27.45 ± 0.08

−0.006 ± 0.003 −0.006 ± 0.005 −0.011 ± 0.006 −0.014 ± 0.006

10.63 ± 0.03 19.31 ± 0.05 23.98 ± 0.07 27.57 ± 0.09

C

C′

D

D′

1.32 ± 0.04c 2.34 ± 0.07 3.06 ± 0.08 3.46 ± 0.09

−0.01 ± 0.02c −0.02 ± 0.04 −0.03 ± 0.05 −0.03 ± 0.06

−0.80 ± 0.04c −1.40 ± 0.07 −1.80 ± 0.08 −2.00 ± 0.09

0.003 ± 0.013c 0.005 ± 0.023 0.007 ± 0.029 0.008 ± 0.033

1.24 ± 0.18 2.19 ± 0.32 2.87 ± 0.43 3.26 ± 0.50

−0.005 ± 0.015 −0.009 ± 0.026 −0.012 ± 0.035 −0.014 ± 0.041

−0.87 ± 0.11 −1.52 ± 0.20 −1.95 ± 0.26 −2.17 ± 0.29

0.004 ± 0.009 0.006 ± 0.016 0.008 ± 0.021 0.009 ± 0.024

0.51 ± 0.05 0.91 ± 0.09 1.22 ± 0.12 1.42 ± 0.13

−0.60 ± 0.05 −1.05 ± 0.09 −1.35 ± 0.12 −1.50 ± 0.13

Equation 7. bRefers to rH+ + Ln− = HrL(r−n). c±Standard deviation.

Table 8. Overall Protonation Constants at Infinite Dilution for PCA 3 and 70 kDa at T = 298.15 K and Parameters for the Dependence on Ionic Strength and Temperature Gradientsa NaCl species PCA 3 kDa HL H2L H3L H4L PCA 70 kDa HL H2L H3L H4L a

(C2H5)4NI

log βH0b

∂ log β/∂t

C

C

D

7.77 ± 0.02c 13.83 ± 0.05 18.77 ± 0.08 22.41 ± 0.11

0.0020 ± 0.0002b 0.0021 ± 0.0002

0.10 ± 0.04c 0.02 ± 0.10 0.02 ± 0.15 −0.02 ± 0.20

1.9 ± 0.2b 3.0 ± 0.4 3.7 ± 0.4 4.2 ± 0.4

−0.6 ± 0.3c −1.0 ± 0.6 −1.3 ± 0.7 −1.4 ± 0.8

0.30 ± 0.06 0.2 ± 0.1 0.1 ± 0.2 −0.1 ± 0.2

2.4 ± 0.3 3.9 ± 0.5 4.6 ± 0.6 4.8 ± 0.6

−0.6 ± 0.3 −1.0 ± 0.6 −1.3 ± 0.7 −1.4 ± 0.8

7.84 ± 0.06 14.10 ± 0.08 19.24 ± 0.13 23.12 ± 0.19

Equation 7. bRefers to rH+ + Ln− = HrL(r−n). c±Standard deviation.

Table 9. Complex Formation Constants at Infinite Dilution for the GTZ AN169-Na+ and -K+ Ion Pairs at T = 298.15 K and Corresponding Parameters for the Dependence on Ionic Strength and Temperature Gradientsa Na+ species ML MHL MH2L MH3L M2L a

log β

K+ ∂ log β/∂t

0b

4.78 ± 0.11 13.80 ± 0.05 20.45 ± 0.06 24.22 ± 0.08 6.26 ± 0.06 c

−0.007 ± 0.013 0.003 ± 0.009 0.010 ± 0.010 0.006 ± 0.011 0.003 ± 0.009

log β0b c

∂ log β/∂t

4.62 ± 0.12 13.72 ± 0.06 20.53 ± 0.07 24.36 ± 0.10 5.95 ± 0.09 c

0.001 ± 0.012 0.006 ± 0.009 0.012 ± 0.010 0.008 ± 0.012 0.004 ± 0.010

C c

1.32 ± 0.04 2.34 ± 0.07 3.06 ± 0.08 3.46 ± 0.09 2.34 ± 0.07

C′ c

−0.01 ± 0.02 −0.02 ± 0.04 −0.03 ± 0.05 −0.03 ± 0.06 −0.02 ± 0.04

D c

−0.80 ± 0.04 −1.40 ± 0.07 −1.80 ± 0.08 −2.00 ± 0.09 −1.40 ± 0.09

D′ c

0.003 ± 0.013c 0.005 ± 0.023 0.007 ± 0.029 0.008 ± 0.033 0.005 ± 0.023

Equation 7. bRefers to qM+ + rH+ + Ln− = MqHrL(q+r−n). c±Standard deviation.

Table 10. Complex Formation Constants at Infinite Dilution for the GTZ S95-Na+ and -K+ Ion Pairs at T = 298.15 K and Corresponding Parameters for the Dependence on Ionic Strength and Temperature Gradientsa Na+ species ML MHL MH2L MH3L M2L a

log β

0b

4.64 ± 0.14c 13.79 ± 0.07 20.14 ± 0.08 24.08 ± 0.09 6.33 ± 0.08

K+ ∂ log β/∂t

−0.019 ± 0.012c −0.014 ± 0.005 −0.011 ± 0.006 −0.013 ± 0.008 −0.015 ± 0.006

log β

0b

3.73 ± 0.09c 13.02 ± 0.07 19.67 ± 0.08 23.92 ± 0.10 4.73 ± 0.10

∂ log β/∂t

C

C′

D

D′

−0.012 ± 0.007c −0.011 ± 0.006 −0.009 ± 0.007 −0.012 ± 0.008 −0.010 ± 0.009

1.24 ± 0.19c 2.19 ± 0.35 2.87 ± 0.46 3.26 ± 0.54 2.19 ± 0.35

−0.005 ± 0.015c −0.009 ± 0.026 −0.012 ± 0.035 −0.014 ± 0.041 −0.009 ± 0.026

−0.87 ± 0.12c −1.52 ± 0.22 −1.95 ± 0.28 −2.17 ± 0.31 −1.52 ± 0.22

0.004 ± 0.009c 0.006 ± 0.016 0.008 ± 0.021 0.009 ± 0.024 0.006 ± 0.016

Equation 7. bRefers to qM+ + rH+ + Ln− = MqHrL(q+r−n). c±Standard deviation.

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Table 11. Complex Formation Constants at Infinite Dilution of the GTZ S97-Na+ Ion Pairs at T = 298.15 K and Corresponding Parameters for the Dependence on Ionic Strengtha species

log Β0b

C

D

NaL NaHL NaH2L NaH3L Na2L

3.9 ± 0.3c 13.60 ± 0.02 20.08 ± 0.04 23.90 ± 0.08 6.23 ± 0.05

0.51 ± 0.05c 0.91 ± 0.09 1.22 ± 0.12 1.42 ± 0.13 0.91 ± 0.09

−0.60 ± 0.05c −1.05 ± 0.09 −1.35 ± 0.12 −1.50 ± 0.13 −1.05 ± 0.09

Equation 5. bRefers to qM+ + rH+ + Ln− = MqHrL(q+r−n). c±Standard deviation. a

concentration scale. The conversion from the molar concentration scale to the molal scale was made following a procedure reported in previous papers.37,38 The same speciation model for complexation was obtained for each GTZ polymer and was independent of the alkali metals. + Also, the log βM values are very similar, as are the protonation constants. Table 12 reports the PCA-Na+ complex formation constants for the two acrylic comaleic polymers (3 and 70 kDa) and the

Figure 6. Distribution diagram of the complexes of Gantrez AN169 with Na+ (−) and K+ (---). Experimental condition: cGTZ AN169 = 0.003 mol dm−3, cM = 0.15 mol dm−3, and T = 298.15 K. Legend: (1) MH3L, (2) MH2L, (3) MHL, (4) ML, and (5) M2L (charges omitted for simplicity).

Table 12. Complex Formation Constants at Infinite Dilution for the PCA 3 kDa-Na+ and PCA 70 kDa-Na+ Ion Pairs at T = 298.15 K and Corresponding Parameters for the Dependence on Ionic Strengtha species PCA 3 kDa NaL NaHL NaH2L PCA 70 kDa NaL NaHL NaH2L

log β0b

For PCA 3 kDa and PCA 70 kDa, the literature data published in a previous paper15 were reanalyzed, as were the experimental data of the ligand investigated here, by means of the simple diprotic-like model. This allowed us to determine four different protonation steps for each ligand, independent of the molecular weight, ionic medium, and ionic strength, without a significant loss of precision with respect to the use of the most complicated Henderson−Hasselbach and Högfeldt models. By using the diprotic-like model, GTZ and PCA ligands were considered to be low-molecular-weight tetracarboxylic ligands, and the results obtained for the protonation constants confirm this assumption. In fact, the calculated stepwise protonation constants on the molar concentration scale reported in Tables SI3 and SI4 of the Supporting Information for GTZ AN169 and GTZ S95 can be compared with the protonation constants of the 1,2,3,4-benzenetetracarboxylic acid (BTC) at T = 298.15 K and I = 1.0 mol dm−3 in NaCl, KCl, and (C2H5)4NI aqueous solutions (Table 14).39 The protonation constants of BTC at T = 298.15 K and I = 1.0 mol dm−3 in NaCl, KCl, and (C2H5)4NI aqueous solutions are in very good agreement with those of the polyelectrolytes calculated by using the diprotic-like model; in particular, we observe that log K1H and log K2H of GTZ and PCA are significantly higher with respect to the same protonation constants of BTC. This, as already discussed in some previous works,3−5,7,11,12,15 is attributed to the high molecular weight and therefore the high available charge of the polyelectrolytes, whereas for log K1H and log K2H very similar values were obtained. As for BTC and also for the polyelectrolytes here studied, a significant medium effect on the protonation constants has been highlighted: log KH (C2H5)4NI ≫ log KH KCl > log KH NaCl. This was justified in terms of the difference in the activity coefficients of the species in the different supporting electrolytes because of the different interacting nature of their cations toward the polyelectrolyte anions. Taking into account some assumptions reported in the previous section, (C2H5)4NI was considered to be a non-

C 1.12 ± 0.05c

2.1 ± 0.1c 9.2 ± 0.1 14.2 ± 0.4

2.22 ± 0.12

2.3 ± 0.0.2c 9.4 ± 0.1 14.7 ± 0.3

1.58 ± 0.07c 2.54 ± 0.10 2.88 ± 0.15

Equation 5. bRefers to qM+ + rH+ + Ln− = MqHrL(q+r−n). c±Standard deviation. a

corresponding parameters for the dependence on the ionic strength at T = 298.15 K. Figure 6 reports the distribution diagram of the GTZ AN169 complexes with Na+ and K+ (CNa+or K+ = 0.15 mol dm−3); as for Figure 5, the curves of the KqLHr species reach similar formation percentages with respect to the ones in Na+, as a confirmation of the similar interacting ability of the ligands in these two ionic media. As said, the temperature gradients were calculated for both the protonation steps and the complexes; this allowed us to propose, other than ΔG/kJ mol−1, rough ΔH and TΔS values, as reported in Table 13. As can be seen, the entropic contribution is the driving force for both the protonation and Na+- and K+-polymer complex formation reactions.

4. CONCLUSIONS The acid−base properties of two different classes of O-donor polyelectrolytes of different molecular weights were determined by potentiometric titration in different ionic media (NaCl, KCl, and (C2H5)4NI) at different ionic strengths and temperatures (291.15 ≤ T/K ≤ 318.15). 2685


a

(±0.05−0.12)a −44.3 −78.9

(±0.3−0.5)a 3.5 3.6

PCA 3 kDa HL H2L

±Standard deviation range.

(±0.09−0.18)a −61.9 −107.1 −135.6 −156.6

(±5−10)a −10 −10 −19 −24

a

GTZ S95 HL H2L H3L H4L

(±0.07−0.14) −61.5 −109.8 −136.4 −157.1

ΔG/kJ mol

−1

(±5−12)a 3 15 14 8

a

ΔH/kJ mol

H+

GTZ AN169 HL H2L H3L H4L

species

−1

(±0.3−0.5)a 47.7 82.5

(±5−10)a 52 97 117 133

(±5−12) 65 125 150 166

a

TΔS/kJ mol

−1

ML MHL MH2L MH3L M2L

ML MHL MH2L MH3L M2L

species

(±8−20)a −32 −24 −19 −22 −26

(±2−8) −12 5 17 10 5

a

ΔH/kJ mol

−1

(±0.2−0.3)a −26.5 −78.7 −114.9 −137.4 −36.1

(±0.1−0.3) −27.3 −78.7 −116.7 −138.2 −35.7

a

−1

ΔG/kJ mol

Na+

(±8−20)a −6 55 96 115 11

(±2−8) 15 84 134 148 41

a

TΔS/kJ mol

−1

−1

(±10−15)a −20 −19 −15 −20 −17

(±3−8) 2 10 20 14 7

a

ΔH/kJ mol

Table 13. Thermodynamic Parameters for the H+-, Na+-, and K+-Polymer Species at Infinite Dilution on the Molar Concentration Scale

(±0.2−0.3)a −21.3 −74.3 −112.2 −136.5 −27.0

(±0.1−0.3) −26.4 −78.3 −117.1 −139.0 −34.0

a

ΔG/kJ mol−1

K+

(±10−15)a 1 56 97 116 10

(±3−8)a 28 88 138 153 41

TΔS/kJ mol−1

Journal of Chemical & Engineering Data Article

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Table 14. Literature Protonation Constants of BTC at T = 298.15 K and I = 1.0 mol dm−3 in Different Ionic Media and on the Molar Concentration Scale ionic medium

log KH1

log KH2

log KH3

log KH4

NaCl KCl (C2H5)4NI

5.76 5.73 6.68

4.78 4.66 5.47

3.88 3.83 4.34

3.37 3.06 3.33

(4) De Stefano, C.; Giuffrè, O.; Pettignano, A.; Sammartano, S. Thermodynamics of proton association of polyacrilates and polymethacrylates in NaCl(aq). J. Solution Chem. 2003, 32, 967−976. (5) De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Speciation of Organic Matter in Natural Waters-interaction of polyacrylates and polymethacrylates with major cation components of seawater. Mar. Chem. 2004, 86, 33−44. (6) De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Quantitative parameters for the sequestering capacity of polyacrilates towards alkaline earth metal ions. Talanta 2003, 61, 181−194. (7) De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Polyacrylates in aqueous solution. The Dependence of Protonation on Molecular Weight, Ionic Medium and Ionic Strength. React. Funct. Polym. 2003, 55, 9−20. (8) De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Polyacrylate protonation in various aqueous media at different temperatures and ionic strengths. J. Chem. Eng. Data 2000, 45, 876−881. (9) Daniele, P. G.; De Stefano, C.; Ginepro, M.; Sammartano, S. Salt effects on the protonation of polymetacrylate and Na+, K+, Ca2+ complex formation. Fluid Phase Equilib. 1999, 163, 127−137. (10) Crea, P.; De Robertis, A.; De Stefano, C.; Milea, D.; Sammartano, S. Modelling the dependence on medium and ionic strength of glutathione acid-base behavior in LiClaq, NaClaq, KClaq, CaCl2aq, (CH3)4NClaq and (C2H5)4NIaq. J. Chem. Eng. Data 2007, 52, 1028− 1036. (11) Crea, F.; Giacalone, A.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Modelling of natural synthetic polyelectrolyte interactions in natural waters by using SIT, Pitzer and Ion Pairing approaches. Mar. Chem. 2006, 99, 93−105. (12) Crea, F.; De Stefano, C.; Gianguzza, A.; Pettignano, A.; Piazzese, D.; Sammartano, S. Acid-base properties of synthetic and natural polyelectrolytes: experimental results and models for the dependence on different aqueous media. J. Chem. Eng. Data 2009, 54, 589−605. (13) Cigala, R. M.; Crea, F.; Sammartano, S. Mixing effects on the protonation of polyacrylate in LiCl/KCl aqueous solutions at different ionic strengths, I = 1 to 3.5 mol L−1, at T = 298.15 K. J. Mol. Liq. 2008, 143, 129−133. (14) Cigala, R. M.; Crea, F.; De Stefano, C.; Lando, G.; Milea, D.; Sammartano, S. Modeling the acid-base properties of glutathione in different ionic media, with particular reference to natural waters and biological fluids. Amino Acids 2012, 43, 629−648. (15) Bretti, C.; Crea, F.; Rey-Castro, C.; Sammartano, S. Interaction of acrylic-maleic copolymers with H+, Na+, Mg2+ and Ca2+: thermodynamic parameters and their dependence on medium. React. Funct. Polym. 2005, 65, 329−342. (16) Paillet, S.; Grassl, B.; Desbrières, J. Rapid and quantitative determination of critical micelle concentration by automatic continuous mixing and static light scattering. Anal. Chim. Acta 2009, 636, 236−241. (17) Mandal, A. B.; Nair, B. U. Cyclic voltammetric technique for the determination of the critical micelle concentration of surfactants, selfdiffusion coefficient of micelles, and partition coefficient of an electrochemical probe. J. Phys. Chem. 1991, 95, 9008−9013. (18) Khougaz, K.; Gao, Z.; Eisenberg, A. Determination of the Critical Micelle Concentration of Block Copolymer Micelles by Static Light Scattering. Macromolecules 1994, 27, 6341−6346. (19) Johnson, C. S., Jr Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications. Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203−256. (20) De Robertis, A.; De Stefano, C.; Sammartano, S.; Rigano, C. The determination of formation constants of weak complexes by potentiometric measurements: experimental procedures and calculation methods. Talanta 1987, 34, 933. (21) Katchalsky, A.; Spitnik, P. Potentiometric titrations of polymethacrylic acid. J. Polym. Sci. 1947, 2, 432−446. (22) Högfeldt, E.; Miyajima, T.; Marinsky, J. A.; Muhammed, M. Application of a Simple Three-Parameter Model to Titration Data for Some Linear Polyelectrolytes. Acta Chem. Scand. 1989, 43, 496−499.

interacting medium, and the protonation constants determined there were used as baseline values for the calculation of the metal−ligand formation constants in NaCl and KCl. From the measurements carried out at different temperatures and ionic strengths and by means of the ES2WC program, the temperature gradients were calculated for both the protonation steps and the complexes; this allowed us to propose rough ΔH/ kJ mol−1 values for both the protonation and complex formation constants. As can be seen, the entropic contribution is the driving force of all of the reactions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00101. Experimental stepwise protonation constants of Gantrez AN169 at different ionic media, ionic strengths and temperatures on the molal concentration scale. Experimental stepwise protonation constants of Gantrez S95 at different ionic media, ionic strengths, and temperatures on the molal concentration scale. Calculated stepwise protonation constants of Gantrez AN169 at different ionic media, ionic strengths, and temperatures. Calculated stepwise protonation constants of Gantrez S95 at different ionic media, ionic strengths, and temperatures. Experimental protonation constants of Gantrez AN169 vs ionic strength. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +39-090-6765759. ORCID

Rosalia Maria Cigala: 0000-0003-2054-9191 Francesco Crea: 0000-0002-9143-9582 Giuseppe Gattuso: 0000-0003-4276-7384 Demetrio Milea: 0000-0003-1188-8837 Funding

We thank the University of Messina and Procter & Gamble Ltd. for financial support. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Authority, E. F. S. Scientific Opinion on the safety of “Methyl Vinyl Ether-Maleic Anhydride Copolymer” (chewing gum base ingredient) as a Novel Food ingredient. EFSA J. 2013, 11, 3423−3440. (2) Arbòs, P.; Wirth, M.; Arangoa, M. A.; Gabor, F.; Irache, J. M.; Gantrez, A. N. Gantrez® AN as a new polymer for the preparation of ligand-nanoparticle conjugates. J. Controlled Release 2002, 83, 321−330. (3) De Stefano, C.; Sammartano, S.; Gianguzza, A.; Piazzese, D. Speciation of polyelectrolytes in natural fluids. Protonation and interaction of polymetacrylates with major components of seawater. Talanta 2002, 58, 405−417. 2687



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(23) Hoegfeldt, E. A useful method for summarizing data in ion exchange. 4. Extension and application to weak acid and chelating resins. J. Phys. Chem. 1988, 92, 6475−6476. (24) Crea, F.; De Stefano, C.; Manfredi, G.; Sammartano, S. Sequestration of some biogenic amines and poly(allyl)amine by high molecular weight polycarboxylic ligands in aqueous solution. J. Mol. Liq. 2010, 151, 138−144. (25) De Stefano, C.; Foti, C.; Gianguzza, A. Ionic Strength Dependence of Formation Constants. Part XIX. The Effect of Tetramethylammonium, Sodium and Potassium Chlorides on the Protonation Constants of Pyrophosphate and Triphosphate at Different Temperatures. J. Chem. Res:(S) 1994, 464, 2639−2661. (26) De Robertis, A.; De Stefano, C.; Foti, C. Medium effects on the protonation of carboxylic acids at different temperatures. J. Chem. Eng. Data 1999, 44, 262−270. (27) Crea, F.; De Robertis, A.; Sammartano, S. Medium and alkyl chain effects on the protonation of dicarboxylates in NaCl(aq) and Et4NI(aq) at 25 °C. J. Solution Chem. 2004, 33, 499. (28) De Robertis, A.; De Stefano, C.; Sammartano, S.; Rigano, C. The determination of formation constants of weak complexes by potentiometric measurements: experimental procedures and calculation methods. Talanta 1987, 34, 933−938. (29) De Stefano, C.; Sammartano, S.; Mineo, P.; Rigano, C., Computer Tools for the Speciation of Natural Fluids. In Marine Chemistry - An Environmental Analytical Chemistry Approach, Gianguzza, A., Pelizzetti, E., Sammartano, S., Eds.; Kluwer Academic Publishers: Amsterdam, 1997; pp 71−83. (30) Pelta, M. D.; Barjat, H.; Morris, G. A.; Davis, A. L.; Hammond, S. J. Pulse sequences for high-resolution difusion-ordered spectroscopy (HR-DOSY). Magn. Reson. Chem. 1998, 36, 706. (31) Daniele, P. G.; De Robertis, A.; De Stefano, C.; Gianguzza, A.; Sammartano, S. Salts Effects on the Protonation of Ortho-Phosphate Between 10 and 50 °C, in Aqueous Solution. A Complex formation Model. J. Solution Chem. 1991, 20, 495−515. (32) De Stefano, C.; Foti, C.; Giuffrè, O.; Sammartano, S. Dependence on ionic strength of protonation enthalpies of polycarboxylic anions in NaCl aqueous solution. J. Chem. Eng. Data 2001, 46, 1417−1424. (33) Foti, C.; Sammartano, S.; Signorino, G. The Dependence on Ionic Strength of Protonation Constants of Carboxylic Acids in Aqueous Tetraethylammonium Iodide Solution, at Different Temperatures. Fluid Phase Equilib. 1998, 149, 91−101. (34) Daniele, P. G.; Foti, C.; Gianguzza, A.; Prenesti, E.; Sammartano, S. Weak alkali and alkaline earth metal complexes of low molecular weight ligands in aqueous solution. Coord. Chem. Rev. 2008, 252, 1093− 1107. (35) Daniele, P. G.; De Robertis, A.; De Stefano, C.; Sammartano, S.; Rigano, C. On the possibility of determining the thermodynamic parameters for the formation of weak complexes using a simple model for the dependence on ionic strength of activity coefficients: Na+, K+, and Ca2+ complexes of low molecular weight ligands in aqueous solution. J. Chem. Soc., Dalton Trans. 1985, 2353−2361. (36) Huyskens, P. L.; Luck, W. A. P. Intermolecular Forces. An Introduction to Modern Methods and Results; Zeegers-Huyskens, Ed.; Springer-Verlag: Berlin, 1991; p 368. (37) Bretti, C.; Cigala, R. M.; Crea, F.; De Stefano, C.; Lando, G.; Sammartano, S. Thermodynamics of Zn2+ 2-Mercaptopyridine-N-oxide and 2-Hydroxypyridine-N-oxide interactions: stability, solubility, activity coefficients and medium effects. J. Mol. Liq. 2015, 211, 876−884. (38) Crea, F.; De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Protonation of Carbonate in Aqueous Tetraalkylammonium Salts at 25°C. Talanta 2006, 68, 1102−1112. (39) De Robertis, A.; Foti, C.; Gianguzza, A. Studies on Polyfunctional O-ligands. Alkali and Alkaline Earth Metal Complexes of Butanetetracarboxylate in Aqueous Solution. Ann. Chim. (Rome) 1993, 83, 485− 497.

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Thermodynamic Properties of O-Donor Polyelectrolytes: Determination

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