Speciation models, conditional and intrinsic stability constants and EDH model parameters
The complete set of analytical results for the Zn(II)/ligand systems, including conditional stability constants (logβ) for the formation of hydrolysed Zn(II)–ligand complexes, of zinc hydroxide complexes and of Zn(II)–ligand complexes as well as acidity constants for citrate and DFOB at different ionic strength in NaCl and T = 298.1 K are reported in Table 1 and SI Table 2. Also shown are the values for the optimised parameter C and the intrinsic association constants (logβ0). SI Table 1 lists all the reactions included in the speciation models used to fit the potentiometric titrations and SI Fig. 2 shows single crystal X-ray structures for some of the proposed structures including ZnH2Cit2, Zn2Cit2(H2O)2 and ZnCit22− taken from the Cambridge Crystallographic Data Base. Figure 3 displays the experimentally determined conditional Zn(II)–ligand stability constants and the corresponding EDH model from this study. Also shown are logb values from the literature for [Zn(HCit)] and [Zn(Cit)]− for the Zn(II)/Cit system and [Zn(H2DFOB)]+, [Zn(HDFOB)] and [Zn(DFOB)]− for the Zn(II)/DFOB system. Examples of titration curves and manually fitted models along with the speciation model considered and the experimental conditions are included in the supporting information (see SI Figs. 3 and 4). Only models that fitted the experimental data with sigma values below 5 were considered. Examples of Hyperquad files showing titrations and model fits for Zn(II)/Cit and Zn(II)/DFOB systems and of Excel calculation files for the application of the EDH model to the Zn(II)/DFOB experimental data set, including error calculation for C and logβ0 are uploaded to the Zenodo repository (https://doi.org/10.5281/zenodo.4548162). Errors reported for measured logβ and calculated (modelled) logβ0 and C values have no detectable effect on subsequent speciation calculations. The errors reported on C are slightly larger than in comparable studies22, however, a sensitivity analysis on the two Zn(II)–ligand species with the largest relative error on C found that logβ0 remains within its error range even when logβ0 was recalculated for the maximum and minimum possible C values. The stability constant we report for specific Zn(II)–L complexes at specific ion strengths are in line with literature reports (Fig. 3). For example, the logβ for the formation of [Zn(Cit)]− in 0.15 mol dm−3 NaCl shows good agreement with the value reported by Cigala and co-workers in 0.15 mol dm−3 NaCl; 4.79 vs. 4.7126. We note, however, also significant variations within reported conditional logβ values as seen Fig. 3, with published values for the formation of [Zn(HCit)] and [Zn(Cit)]− in different 1:1 electrolytes differing over two orders of magnitudes. This highlights the analytical challenges associated with accurate and precise logβ determinations of low affinity metal–ligand complexes, in low ion strength solutions33.
Experimental Zn(II)–ligand conditional stability constants (logβ) for (a) citrate and (b) DFOB at 0.05, 0.15, 0.3, 0.5 and 1 mol dm−3 in NaCl solution (open circles) determined using potentiometric titrations. For each species, the Extended Debye-Hückel (EDH) model has been parameterised using the experimental data (see Table 1 for C and logβ0) and the corresponding model is shown as a solid line. Literature data is included in the figure for comparison (closed circles) from Cigala et al. (2015, NaNO3 and NaCl), Capone et al. (1986, KNO3), Daniele et al. (1988, KNO3), Field et al. (1975, KNO3), Matsushima et al. (1963, NaCl) and Li et al. 1959, NaCl) for the Zn–H–Cit system and from Schijf et al. (2015, NaClO4), Farkas et al. (1997, KCl) and Hernlem et al. (1996, KNO3) for the Zn-H-DFOB system. Note the large variability reported for the Zn–Cit system at 0.1 and 0.15 mol dm−3. We find good agreement with the data published by Sammartano and co-workers26,69.
The final speciation scheme with the best statistical fits and with chemically sensible species are given in Table 1. From the eight Zn-Cit species initially considered (SI Table 1), the inclusion of five species resulted in model fits with sigma values below 5. For the Zn(II)/Cit system, the dominant species are [Zn(Cit)]−, [Zn(HCit)], and [Zn2(Cit)2(OH)2]4−. We report also the presence of a [Zn(Cit)(OH)3]4− complex above pH 9 in significant amounts (> 20%) and we confirm the presence of [Zn(Cit)2]4− if citrate is present in large excess26,31. The presence of [Zn(Cit)]−, [Zn(HCit)] and [Zn(Cit)2]4− were confirmed in pH 6 solutions by mass spectrometry. To confirm the presence of [Zn(Cit)(OH)3]4−, further investigations are warranted. SI Fig. 5 shows the species distributions in the Zn(II)–Cit system with different Zn:L molar ratios (1:1, 1:2 and 1:10) and different concentrations (between 10–6 and 10–3 for Zn and 10–5 and 10–3 for citrate). We find that [Zn(Cit)]− dominates (i.e., formation relative to total Zn is above 50%) between pH 5 and 7.5, [Zn2(Cit)2(OH)2]4− dominates between pH 7.5 and 10 and [Zn(Cit)(OH)3]4− dominates at pH values above 10. We find the formation of [Zn(Cit)2]4− only at Zn:Cit molar ratio of 1:10 and [Zn] and [L] concentrations of 10–4 and 10–3 mol dm−3, respectively. The species [Zn(Cit)(OH)]2− and Zn(Cit)(OH))2]3− possibly form at higher pH but were excluded from the final model. We noted that for titrations of solutions with Zn:Cit molar ratios below 1:3, it was not possible to refine the stepwise stability constant (logK) for [Zn(Cit)2]4− to within ± 0.09 log units, indicating that it is an unstable species that forms at negligible concentrations. The stability constants for zinc complexation with citrate decrease with increasing ionic strength. Table 1 shows that the most significant change is seen between 0.05 and 0.15 mol dm−3 NaCl, where there is approximately a 0.5 to 1.5 log unit change. In dilute solutions, stability constants are sensitive to small increases in ionic strength because changes in the effective concentration (activity) of ions are large.
For the Zn(II)–DFOB system, all the stability constants measured during this study are in good agreement with those reported in the literature50,51,53. For example, the stability constant we report for [Zn(HDFOB)] in 0.5 mol dm−3 NaCl is 19.34. This is within ~ 0.5 log units of the stability constant reported by Schijf and co-workers in 0.7 mol dm−3 NaClO4 solutions53. The speciation scheme we report differs slightly from that predicted by Schijf based on a three-step model. Our model does not include the bidentate species [Zn(H3DFOB)]2+, the weakest and least stable Zn(II)–DFOB species. In Table 1, we report stability constants for hexadentate [Zn(DFOB)]− and [Zn(HDFOB)] and tetradentate [Zn(H2DFOB)]+. We observe that as the denticity of the complex increases, so does the strength of the stability constant. The stepwise stability constant (K) differs by approximately 2 log units between the formation of the three different DFOB:Zn:H species (7.75, 9.88, 11.67, see Table 1). DFOB complexation of Zn(II) shows the same pattern of ionic strength dependence as citrate, with the greatest decrease of logβ occurring between 0.05 and 0.15 mol dm−3 NaCl, the region of most importance to the rhizosphere.
The absolute decrease in [ZnL] and [Zn(HL)] stability constants between 0.05 and 0.15 mol dm−3 is approximately equal for citrate and DFOB species, average 1.58 vs. 1.73, respectively. This is explained by the effect of ionic strength primarily depending on the charge of the ions involved and free citrate and DFOB having the same electrostatic charge (−3). The ionic strength dependent parameter C shows no systematic change for neither citrate nor DFOB species. The good agreement between literature50,51,52,54,68,69,70 and our speciation models as well as the conditional logβ and pKa values validates the use of a single analytical method for the determination of the LEP. We note that the proposed formation of the trihydroxy Zn(II) citrate complex at pH above 10, needs to be investigated in greater detail using supplementary techniques. However, the formation of this species is not relevant for the pH range of interest in our study. As discussed below the main prevailing species in solution are those of 1:1:0 and 2:2:−2 stoichiometry for Zn:Cit:H.
Figure 4 shows intrinsic stability constants for the formation of [Zn(Cit)]− and [Zn(HCit)] determined (i) using the Davies equation and the conditional association constants determined at different ionic strengths and (ii) fitting the parameterised EDH equation to the full ionic strength dataset. We find statistically significant (p < 0.05) differences for the various logβ0, emphasizing that the method used for activity corrections is critical when studying the small changes in speciation happening during geochemical processes in the rhizosphere3,30,34. Intrinsic association constants seem over predicted below 0.1 mol dm−3 and underpredicted above 0.1 mol dm−3. The Excel file containing the calculations using Davies calculations is available on the Zenodo repository, https://doi.org/10.5281/zenodo.4548162.
Intrinsic stability constants (logβ0) for the formation of [Zn(Cit)]− and [Zn(HCit)] species calculated using the Davies equation and logβ values determined at different ionic strengths are shown as circles (open for [Zn(Cit)]– and closed for [Zn(HCit)]). The intrinsic stability constants for the same two species determined by fitting the parameterised Extended Debye-Hückel (EDH) equation to the full ionic strength dataset are shown as solid lines. The error for the intrinsic stability constants is reported in SI Table 2 and differences are statistically significant (p < 0.05).
Figure 5 shows the fraction of complexed zinc in a Zn(II)/Cit system modelled at infinite dilution using intrinsic stability constants determined (i) by fitting the EDH equation to the full citrate stability constant dataset or (ii-vi) using the Davies equation to calculate activity coefficients and adjust the citrate stability constants separately at 0.05, 0.15, 0.30, 0.50, and 1.00 mol dm−3. At pH 5.5, the 0.05 mol dm−3 Davies-based intrinsic speciation model overpredicts the fraction of complexed zinc by approximately 20% compared to the EDH-based intrinsic ion strength model. At the same pH value, the 0.15, 0.3, 0.5, and 1 mol dm−3 Davies-based intrinsic speciation models underpredict the fraction of complexed zinc by 18, 21, 20, and 38%, respectively, compared to the EDH-based intrinsic speciation model. These results demonstrate the inconsistencies in speciation calculations that arise when the same geochemical model is run using different sets of stability constants derived by applying the same method (e.g., Davies equation) to different sets of ionic strength data; even when the different sets of ionic strength data are within the activity model’s ionic strength range of applicability, i.e. for Davies equation < 0.5 mol dm−3 and from the same study3,30,34. This is a critical observation for the pH range close to the root. A significant improvement in the accuracy of geochemical speciation calculations is achieved by adopting an empirical method with adjustable parameter when studying the ionic strength dependence of stability constants, rather than using an indirect method, as is widely practised as shown before3,34.
(a) Fraction of complexed zinc in a system with [Zn] = 10–6 mol dm−3 and [citrate] = 10–5 mol dm−3 modelled at infinite dilution using intrinsic stability constants determined (i) by fitting the parameterised version of the Extended Debye-Hückel equation to the full set of conditional stability constant data (ii–vi) by using the Davies equation to calculate activity coefficients and adjusting the citrate stability constants separately at 0.05, 0.15, 0.30, 0.50, and 1.00 mol dm−3. The dashed lines show the error on the respective curves. The error was calculated by re-running the analysis, starting with high and low estimates for the experimental stability constants. For the EDH and 0.05 mol dm−3 Davies corrected models, the error is too small to display. (b) Formation of Zn-DMA complexes in the pH range 2 and 8 calculated using logβ values from Weiss and co-workers30 with no corrections made for ionic strength dependent changes in formation constants. Note the similar range where Zn is complexed and the sigmoidal curve shape. (c) pH profiles between root wall and bulk solution measured in flooded rice fields40,42. pH at the root/soil interface can be acidic (pH 4), leading to the release of Zn from the complex.
pH and ionic strength dependent ligand exchange points (LEP) for between Zn(II)–citrate and Zn(II)–DFOB and stability windows for Zn(II)–ligand complexes
The ionic strength dependence models described above were subsequently applied to investigate the geochemical stability window of the Zn(II)/ligand systems of interest and to determine the point of ligand exchange, i.e., where the fraction of complexed Zn(II)–Cit over fraction of complexed Zn(II)–DFOB is at unity. Figure 6 shows the fraction of complexed zinc in Zn(II)/Cit and Zn(II)/DFOB systems as a function of (a) pH and (b) ionic strength in NaCl solutions. The raw data for these plots are supplied in the supporting information (SI Table 4 and 5). We also show the range of I and pH values characteristically found between the root and soil aggregate interfaces in rice soils.
Fraction of complexed zinc in Zn(II)/Cit and Zn(II)/DFOB systems in NaCl solutions ([Zn] = 10–6 mol dm−3 and [L] = 10–5 mol dm−3) as a function of (a) pH and (b) ionic strength. The shaded grey areas show the rhizosphere-relevant pH and ionic strength windows along with the root and aggregate interfaces (see Fig. 1). The raw data for these plots is supplied in the supporting information (SI Tables 3 and 4).
pH stability of Zn(II)–citrate and Zn(II)–DFOB complexes
For both the Zn(II)/citrate and Zn(II)/DFOB systems, the fraction of complexed zinc increases with pH as shown in Fig. 6.
For all the ionic strengths examined, Zn(II)–Cit complexes begin forming at approximately pH 3 (see SI Fig. 5 showing the species distribution for Zn(II)–Cit at different Zn:L molar ratios, ranging from 1:1 to 1:10 at 0.15 mol dm−3 NaCl solutions and different Zn and L concentrations). Once the citrate begins to bind to Zn, it takes between 6 to 7 pH units to reach total zinc complexation in the Zn(II)/Cit system. The fraction of zinc complexed by citrate increases fastest with pH in the lower ionic strength solution. At pH 6 in a 0.01 mol dm−3 NaCl solution, the fraction of zinc complexed by the citrate is 0.81 (SI Table 3). This is compared to just 0.07 at the same pH in a 1 mol dm−3 NaCl solution. The formation of Zn(II)–Cit complexes does not increase continuously with pH, there is a 2 to 3 pH unit plateau in the pH complexation curves for the Zn(II)/citrate system. Speciation diagrams for the Zn(II)/malate and Zn(II)/tartrate systems show similar trends to the Zn(II)/Cit pH complexation curves observed in this study; formation of Zn(II)–malate/tartrate complexes above 10% fraction of total zinc occurs at around pH 2 to 3 and there is then a plateau/only a small increase in the formation of Zn(II)–malate/tartrate complexes between pH 5 and 726.
In the Zn(II)/DFOB system, ionic strength has a negligible effect on the pH complexation curves. In all solutions, complexation of zinc begins at pH 5.5 and total zinc complexation is reached within 3 pH units; no free zinc remains in the Zn(II)/DFOB systems above pH 8. The pH complexation curves for the Zn(II)/DFOB system are sigmoidal and do not contain a plateau (Fig. 6). Speciation diagrams for the Zn(II)/deoxymugineic acid (DMA), a rice produced siderophore30, system show a very similar pattern to the Zn(II)/DFOB pH dependent complexation curves in this study, suggesting this is a typical behaviour of high affinity siderophores. Significant concentrations of Zn(II)–DMA complexes begin forming at around pH 5 and total complexation of zinc is completed within 1.5 pH units30.
The pH at which Zn(II)–DFOB complexes become more abundant than Zn(II)–Cit complexes, i.e., the fraction of complexed zinc in the Zn(II)/DFOB system becomes greater than the fraction of complexed zinc in the Zn(II)/Cit system, depends strongly on ionic strength. As ionic strength increases, the pH dependent LEP becomes more acidic. In the 0.01, 0.1, and 1 mol dm−3 solutions, the pH dependent LEP is at pH 7.4, 7.1, and 6.5, respectively. This suggests that the thermodynamic favourability of the reaction for the exchange of zinc between citrate and DFOB increases with ionic strength.
For all ionic strengths tested, the predicted pH of the LEPs (pH 6.5 to 7.4) falls within the pH gradients expected in rhizospheres, which in the case of rice ranges between pH 4.0 and 8.040,42. This suggests that pH gradients make it possible for Zn(II)–Cit and Zn(II)–DFOB complexes to dominate in different parts of the rice rhizosphere and, therefore, for the ligands to function synergistically. At the root interface, if pH is below 5.5 as previously suggested, neither Zn(II)–Cit nor Zn(II)–DFOB complexes are stable, excluding the possibility of an uptake of the Zn–ligand complex. It suggests that the role of the organic ligands in the uptake of metals and Zn is in increasing the leaching from soil aggregates and not in the actual uptake. Pairing of organic ligands with low and high affinity for Fe has been demonstrated by abiotic studies showing that a combination of siderophores and oxalate enhances Fe dissolution19.
Ionic strength stability for Zn(II)–Cit and Zn(II)–DFOB complexes
As ionic strength increases, the stability of the Zn(II)–Cit complexes decreases. Between 0 and 1 mol dm−3 ion strength, the fraction of Zn(II) complexed by citrate decreases by 0.05, 0.84, and 0.89 at pH 4, 6, and 8, respectively; in all instances this represents a relative reduction in ligand binding efficiency of approximately 92%. The Zn(II)–Cit ionic strength complexation curves initially descend sharply, two-thirds of the reduction in binding efficiency occurs before 0.2 mol dm−3, the critical range relevant to rhizosphere gradients. For Zn(II)–DFOB complexes, ionic strength only influences the stability at pH 6. At pH 4, no Zn(II)–DFOB complexes are stable and at pH 8 Zn(II) is fully complexed by the siderophore at all ionic strength investigated. At pH 6, between 0 to 1 mol dm−3, the decrease in fraction of complexed Zn(II) is 0.09 in the Zn(II)/DFOB system. This represents a relative reduction in ligand binding efficiency of 45%. Hence, the ionic strength controls more the stability of Zn(II)–Cit complexes than the stability of Zn(II)–DFOB complexes; it is larger (relative reduction in ligand binding efficiency 92% vs. 45%) and it is relevant over a wider pH range.
The ionic strength for the LEP at pH 6 is approximately 0.7 mol dm−3 (Fig. 6). At pH 4, the citrate remains dominant over the DFOB up to 1 mol dm−3 and at pH 8, the siderophore is already dominant over the citrate at 0 mol dm−3. This suggests that ionic strength controlled LEP occurs at a lower ionic strength as pH increases and consequently the thermodynamic favourability of the reaction for the exchange of zinc between citrate and DFOB increases with pH. Between pH 6 and 8, the predicted LEP is at an ionic strength smaller than 0.7 mol dm−3. Between pH 7 and 7.5, the predicted LEP ranges from ion strengths of between 0.01 and 0.1 mol dm−3, which overlaps with the estimated ionic strength gradient expected in the rhizosphere, in the case of rice ranging between 0.01 to 0.30 mol dm−3. Hence, our calculations suggest that when the pH of the rhizosphere is circumneutral, ionic strength gradients make it possible for Zn(II)–Cit and Zn(II)–DFOB complexes to dominate in different parts of the rhizosphere and, therefore, for the ligands to function synergistically.
Geochemical speciation calculations of the Zn/Cit/DFOB system in rice soil
Figure 7 and Table 2 show calculated LEPs for the exchange of zinc between citrate and DFOB in solutions with the chemical composition similar to that of rice soil porewater44,45,71. This modelling experiment aimed to assess the effect of competitive complexation by metals, dissolved organic carbon (DOC), and bicarbonate ions on the positions of the LEP and gaining insights into the importance of cooperative ligand interactions and of siderophores during zinc transport in rice soils at relevant metal and ligand concentrations as postulated previously30,72. The concentration of DOC used was 40 mg dm−3. The predicted LEP from the analysis in NaCl using standard zinc and ligand (for citrate and DFOB) concentrations are included for comparison. The LEPs are reported as ranges because different sets of citrate (1 to 50 µmol dm−3) and DFOB (0.1 to 1 µmol dm−3) concentrations were analysed in solutions with 2 mmol and 8 mol dm−3 HCO3−, denoted as solution A and B.
Calculated LEPs for the exchange of zinc between low affinity (citrate) and high affinity (DFOB) ligands in the presence of DOC (40 mg/l), Ca (64 mg dm−3), K (4.8 mg dm−3), Mg (22 mg dm−3), P 0.8 (mg dm−3), Si (8.7 mg dm−3), Co (2.2 μg dm−3), Ni (15.3 μg dm−3), Cu (11.1 μg dm−3), Se (2.5 μg dm−3), Cd (0.2 μg dm−3), Pb (1 μg dm−3), Fe (2.1 μg dm−3), Mn (3.2 μg dm−3), Na (0.1 mol dm−3) and Cl (0.1 mol dm−3). Concentration of Zn (10 nmol dm−3) and of other elements and DOC were based on published composition of pore water solutions of rice-growing soils40,45,71. Two model solutions were differentiated by the concentration of bicarbonate ions, i.e., solution A with 2 mmol dm−3 HCO3− and solution B with 8 mmol dm−3 HCO3−. The predicted LEPs from the experiments in NaCl solutions with [Zn] = 10–6 mol dm−3 and [L] = 10–5 mol dm−3 (see Fig. 6 and Table 2) are included for comparison. The LEPs calculated for solution A and B are reported as ranges because different sets of citrates (1 and 50 µmol dm−3) and DFOB (0.1 and 1 µmol dm−3) concentrations were analysed.
We find that at all ionic strengths tested, the pH of the LEPs calculated in NaCl fall within the range calculated for the pH dependent LEPs in solutions with the chemical composition similar to that of rice soils. In line with the conclusions drawn above, it is not possible to calculate the ionic strength dependent LEPs in solution A or B at pH 4 or 8. This is because for the concentration and ion strength ranges tested, citrate is dominant at pH 4 and siderophore is dominant at pH 8. The ionic strength dependent LEP predicted in NaCl solutions at pH 6 falls within the range calculated for the ionic strength dependent LEPs in the model soil solutions. The pH dependent LEPs calculated in solution A and B at individual ionic strengths vary by between 0.9 and 2 pH units depending on the concentrations of citrate and DFOB used in the speciation calculations. The ionic strength depended LEPs vary by between 0.42 and 0.44 mol dm−3, depending on the concentrations of citrate and DFOB used in the speciation calculations. This evidence suggests that the LEPs in soil solutions are highly sensitive to ligand concentration ratios. Previous investigations have indeed highlighted the ligand concentration ratio as an important factor controlling the ligand-exchange process73. The size of the range calculated for the pH dependent LEPs decreases as ionic strength increases. This suggests that the ligand concentration ratio becomes less important in controlling the position of pH of the LEPs at higher ionic strength. The pH and ionic strength dependent LEPs in solution A and B are consistent i.e., the ranges broadly overlay one another. The two model solutions are differentiated by the concentration of bicarbonate ions, i.e., 2 and 8 mmol dm−3. The agreement would imply that the LEPs are not sensitive to bicarbonate concentration. This is in line with bicarbonate ions forming significant complexes with zinc only at higher pH29. Indeed, numerical modelling of Zn(II) speciation with Cl–, OH–, CO32–, SO42–, and PO43– using reliable stability (formation) constants showed that in acidic and weakly alkaline freshwater systems, in the absence of organic ligands, Zn(II) speciation is dominated by Zn2+29. The speciation of Zn(II) is dominated by ZnCO3 only at pH > 8.4. In seawater systems, the speciation at pH 8.2 is dominated by Zn2+ with ZnCl+, ZnCl2, Zn(CO3), and Zn(SO4) as minor species. Our results suggest furthermore that competition from DOC for zinc is not strong enough to shift the position of the LEPs. The role of DOC regarding possible complexation with zinc is expected to be minor given the structural properties of fulvic acids and the known low conditional stability constants for Zn(II)–DOC complexes, i.e., logK between ~ 3.8 and 4.274.
SI Figs. 6 and 7 show the chemical speciation of Zn with DOC and environmental significant inorganic ligands (OH−, Cl−, CO32−, SO42−, PO43−) in aqueous solutions with concentrations and elemental ratios found in rice soil pore waters. Within the pH range of importance to the rice rhizosphere, we find formation of Zn(HPO4), ZnDOC, ZnCl+, Zn(SO4) and Zn(CO3) only at very small abundances (below 20%).
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