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Speciation models, conditional and intrinsic stability constants and EDH model parametersThe 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.Figure 3Experimental 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.Full size imageThe 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  More

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