Capillary electrophoresis facilitates determination of metal complex stoichiometry by Job s method of continuous variation

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1 Supplementary material Capillary electrophoresis facilitates determination of metal complex stoichiometry by Job s method of continuous variation Nathan E. Boland A,B and Alan. Stone A A Department of Geography and Environmental Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 118, USA. B Corresponding author. Present address: Whitman College, Hall of Science, 345 Boyer Avenue, Walla Walla, WA 9936, USA. bolandne@whitman.edu Proof of Job s method of continuous variation Derivations provided here are based upon earlier treatments. [1 3] Suppose that the free metal ion and free ligand combine to form a single, simple complex with stoichiometry (M p Y q ) according to: pm qy M Y (1) he equilibrium constant corresponding to this reaction is defined as: K pq MY p q () p p M Y Rearranging yields: [M p Y q ] = K pq [M] p [Y] q (3) It is assumed that the metal ion and ligand are either free or part of this complex. Mass balance equations for total metal concentration (M ) and total ligand concentration (Y ) can be written as: M = M + p[m p Y q ] (4) Y = Y + q[m p Y q ] (5) Job s method of continuous variation (hereafter Job s method) is based upon a series of experiments where (i) the sum of M and Y is a constant, which we will call X, and (ii) the ratio of M to X, which we will call R, is increased: X = M + Y (6) M R X q M M Y q (7) Page 1 of 17

2 Eqns 4 and 5 can be rewritten using this ratio: [M] = X R p[m p Y q ] (8) [Y] = X (1 R) q[m p Y q ] (9) Next, absorbance or some other quantity proportional to [M p Y q ] is plotted as a function of R. he derivatives of Eqns 3, 8 and 9 with respect to R are relevant: d M Y p q p1 q dm p q1dy pk pq M Y qk pq M Y (10) dr dr dr dm pdm Y p q X (11) dr dr dy dr qdmpy q X (1) dr We would like to find R max, the value of R that yields the maximum value of [M p Y q ]. his maximum value should correspond to the point where d[m p Y q ]/dr is equal to zero. At this point in the Job s plot, Eqns 11 and 1 become: dm dr dy dr Rmax Rmax X X Inserting these results into Eqn 10 and again setting d[m p Y q ]/dr is equal to zero yields: (13) (14) p 1 q p q1 pk M Y X qk M Y X 0 (15) pq Rmax R pq max Rmax Rmax Algebra then yields: q p Y M 0 (16) Rmax Rmax Inserting Eqns 8 and 9 yields: px 1 R pq M Y qx R pq M Y 0 max p q max max p q max (17) Additional algebra yields: px px Rmax qx Rmax 0 (18) p prmax qrmax 0 (19) Page of 17

3 R max p p q (0) Eqn 0 can be rearranged to yield: p R q 1 R max max (1) In summary, Job s method requires completing a set of experiments where X = M + Y is kept constant while the quantity R = M /X is increased. Plots of absorbance or some other quantity proportional to [M p Y q ] as a function of R are then constructed. he maximum (or minimum) of these plots reveals R max, the value of R where the concentration of the metal ligand complex ([M p Y q ]) reaches its maximum value. Eqn 1 is then used to determine the stoichiometric ratio p/q of the complex. Electromigration in capillary electrophoresis (CE) he discussion provided below is based on prior publications. [4,5] Electroosmotic flow (EOF) is the net movement of the buffer solution (BGE) through the capillary under the influence of an applied electric field. When running in cation mode, the capillary wall comprises silanol groups that, owing to deprotonation, yield a net negative wall charge above ph 3. According to the Principle of Electroneutrality, the charge on the capillary wall must be counterbalanced by a layer of cationic counterions in overlying solution. Applying an electrical potential causes these cations to electromigrate towards the cathode. hrough friction, the electromigrating cations entrain the BGE solution, yielding a net electroosmotic flow (μ EOF ) of the BGE solution towards the cathode. When running in cation mode, sample is injected at the anode end of the capillary and the detector is placed near the cathode end of the capillary. Anion mode involves addition of a cationic surfactant such as tetradecyltrimethylammonium bromide (AB) to the BGE solution, which adsorbs to the capillary wall, giving it a net positive charge. hat charge, in turn, is counterbalanced by a layer of anions in the BGE solution. Applying an electrical potential causes these anions to electromigrate towards the anode, yielding an electroosmotic flow, μ EOF, in that direction. When running in anion mode, the sample is injected at the cathode end of the capillary and the detector is placed near the anode end of the capillary. he migration velocity of an anionic analyte (ν obs ) through a capillary is found by dividing the length of capillary from the point of injection to the point of detection (L d ) by the time required for the analyte to reach the detector (t m ). Dividing the entire length of the capillary (L ) by the applied potential (P) yields the electric field gradient (E). In order to compare runs performed using different capillary lengths and different applied potentials, it is first necessary to calculate an observed electrophoretic mobility (μ obs ): Page 3 of 17

4 obs L L d obs P tm () Next, we must subtract the electroosmotic flow contribution to mobility (μ eof ), which yields an effective electrophoretic mobility (μ eff ): μ eff = μ obs μ EOF (3) Electroosmotic flow acts equally on all solutes, and hence μ EOF can be calculated from values of t m obtained with a neutral chromophoric analyte. Effective electrophoretic mobilities are indicative of the charge and hydrodynamic radii of analytes, but are also influenced by the viscosity and ionic strength of the BGE. Modelling Ni DPA speciation Calculations including equilibrium constants for Ni hydroxo species and Ni-containing hydroxide and oxide precipitates [6] indicate that the sum of Ni hydroxo species is 0.1 % or less of Ni at ph 6.9 and neither Ni(OH) (s) nor NiO(s) is predicted to form. hese species are neglected in subsequent calculations. With equilibrium constants X and Ni /X as inputs, equilibrium concentrations of each Ni DPA complex were calculated (at ph 7 and 5-mM ionic strength). he mass balance equations for all Nicontaining species (Ni ) and DPA-containing species (DPA ) are relevant: Ni = [Ni + ] + [NiDPA] + [Ni DPA] + 3[Ni 3 DPA ] (4) DPA = [DPA] free + [NiDPA] + [Ni DPA] + [Ni 3 DPA ] (5) At ph 7, [DPA] free is present almost entirely as H (dtpa) 3. NiDPA has two relevant protonation levels, Ni(dtpa) 3 and NiH(dtpa). At ph 7, both Ni(dtpa) 3 and NiH(dtpa) are present in large percent amounts. However, during an electrophoretic separation, these species will interchange rapidly and will co-electromigrate and we need only consider the sum of the two species (simply NiDPA). As a result, we can write more specific forms of the mass balance equations above: Ni = Ni + + [NiDPA] + [Ni (dtpa) 1 ] + 3[Ni 3 (dtpa) 4 ] (6) DPA = [H (dtpa) 3 ] + [NiDPA] + [Ni (dtpa) 1 ] + [Ni 3 (dtpa) 4 ] (7) Using appropriate equilibrium expressions from able 1, we can write Eqns 6 and 7 in terms of equilibrium constants, [Ni + ] and [dtpa 5 ] 5 5 Ni Ni K 1Ni dtpa K1HK 1Ni H dtpa (8) KK 1 Ni dtpa 3KKK 1 3Ni dtpa Page 4 of 17

5 5 dtpa H 5 5 K 1 K1HK1 H H Ka1 Ka1Ka DPA Ni dtpa Ni H dtpa KK Ni dtpa KKK 1 3 Ni dtpa (9) Rearranging Eqn 9 gives a quadratic equation: 5 5 a dtpa b dtpa c0 (30) where, 3 a K K K Ni, 1 3 H b K 1 Ni K1HK1 Ni H K1K Ni H H K K K a1 a1 a and c = DPA Using the quadratic formula, we can solve for [dtpa 5 ]. dtpa 5 4 b b ac a (31) he flowchart in Fig. S1 describes how the equations above were implemented in a Microsoft Excel spreadsheet with iterative calculations enabled. he resulting equilibrium model allowed us to converge on the value of [Ni + ] and [dtpa 5 ] at each X and Ni /X, and calculate the equilibrium concentration of each Ni DPA complex. he results of this model are plotted as dashed lines in Fig. 5 (and Fig. S6, see Influence of differences in ionic strength on Job s plot maxima). A variation of the equilibrium model was used to calculate equilibrium concentrations of NiDPA and Ni DPA when formation of Ni 3 DPA is not considered. erms for Ni 3 DPA were omitted from the mass balance equations. he results of this model are plotted as solid lines in Fig. 5 (and Fig. S6, see Influence of differences in ionic strength on Job s plot maxima). Page 5 of 17

6 SAR Read: X, Ni /X (Ratio), olerance (), Iteration Interval (I) Ni,actual = X * Estimate [Ni + ] Calculate [DPA 5- ] Calculate Ni (Eqn 34) Δ = Ni Ni,actual [Ni + ] = 10 (log [Ni+ ] + I) YE S Is Δ < -? NO Is Δ >? YE S [Ni + ] = 10 (log [Ni+ ] I) NO Use [Ni + ] and [DPA 5 ] to calculate concentration of each Ni-DPA species Output concentrations of [Ni-DPA] species END Fig. S1. Flowchart for calculating Ni diethylenetriaminep entaacetate (DPA) speciation. Page 6 of 17

7 able S1. Consideration of stoichiometries for possible Ni diethylenetriaminepentaacetate (DPA) complexes DPA free, Ni free, NiDPA, Ni DPA, p, q and R max have already been described in the literature. Positive values for Coordinative unsaturation indicate excess DPA Lewis base groups and negative values indicate excess Ni coordinative positions. Bold entries indicate known (1:1 and :1) and proposed (3:) stoichiometries. Stoichiometry (p:q) Empirical formula (Ni p DPA q ) R max (p/(p + q)) Number of components (p + q) Overall charge Coordinative unsaturation (8q 6p) 0:1 DPA free :6 NiDPA :5 NiDPA :4 NiDPA :7 Ni DPA :3 NiDPA :5 Ni DPA : NiDPA :5 Ni 3 DPA :3 Ni DPA :4 Ni 3 DPA :5 Ni 4 DPA :1 NiDPA :4 Ni 5 DPA :3 Ni 4 DPA : Ni 3 DPA :3 Ni 5 DPA :1 Ni DPA : Ni 5 DPA :1 Ni 3 DPA : Ni 7 DPA :1 Ni 4 DPA :1 Ni 5 DPA :1 Ni 6 DPA :1 Ni 7 DPA :1 Ni 8 DPA :0 Ni free Job s plots developed using different detection wavelengths If each CE peak corresponds to a unique chromophore, then moving to a different detection wavelength should alter the magnitude of the detector response at each value of Ni /X, reflecting different molar absorptivities at the different wavelengths. General trends in the Job s plot, and the position of the Job s plot maximum, should not change. Recall that effective electrophoretic mobilities of free DPA and NiDPA are similar. With Peak A, at low values of Ni /X, both species contribute significantly to the CE response. In Fig. S, the portion of Page 7 of 17

8 the Job s plots using 194, 14 and 54-nm detection when Ni /X is less than 0.3 are a reflection of this. At higher values of Ni /X, the contribution from NiDPA is predominant. As a result, all three detection wavelengths yield the same trend, and indeed yield the same maximum. he CE response for Peak B comes almost entirely from Ni 3 DPA, whereas the CE response for Peak C comes from Ni DPA. As a result, all three detection wavelengths yield the same Job s plot trends and the same maxima. Fig. S. Job s plots for electropherogram peaks at three different wavelengths (194, 14 and 54 nm) for solutions with X = 1000 μm. Capillary electrophoresis (CE) response corresponds to normalised absorbance output of the CE instrument. Page 8 of 17

9 Job s plots and assignment of Ni DPA complex stoichiometry For each possible stoichiometry for a Ni DPA complex, denoted as Ni p DPA q, an expected Job s plot maximum, R max, can be calculated. As noted in Proof of Job s method of continuous variation, R max corresponds to p/(p + q). NiDPA and Ni DPA have already been described in the literature. hey yield R max values of 0.50 and 0.67, which coincide with our experimentally observed R max values for Peaks A and C. wenty-seven possible stoichiometries are compiled in able S1. DPA possesses eight Lewis base groups and Ni has a coordination number of six. Hence, it was not necessary to consider stoichiometries requiring one Ni cation to coordinate more than six DPA molecules, or one DPA molecule to coordinate more than eight Ni cations. he number of components refers to the sum (p + q). Although it is true that the concentrations of all species decrease as X is decreased, the decrease becomes more pronounced as the number of components is increased. (Recall from Eqn 3 that [M p Y q ] is proportional to [M] p [Y] q.) able S1 is restricted to complexes where the number of components is nine or less, i.e. those most likely to be significant at the values of X investigated. UV spectroscopy of Ni DPA solutions Complex formation constants available in the literature for NiDPA and Ni DPA enabled us to calculate speciation for a wide range of Ni and Y conditions. All solutions contained 5.0 mm 3- morpholinopropane sulfonic acid (MOPS, ph 6.9) and enough NaCl to fix the ionic strength at 5 mm. When Ni is equal to 50 μm and DPA equal to 375 μm, NiDPA represents nearly 100 % of all Ni DPA species. We prepared this solution and recorded the whole-sample spectrum shown in Fig. S3a using a conventional UV spectrometer. When Ni is equal to 1000 μm and DPA equal to 375 μm, Ni DPA represents nearly 94 % of all Ni DPA species. We prepared this solution and recorded the whole-sample spectrum shown in Fig. S3c. Using the CE results and Job s plots, we were able to estimate a complex formation constant for the species Ni 3 DPA, as described in the main text. Using this new complex formation constant, a new set of calculations can be performed. Calculations indicate that the concentration of Ni 3 DPA is highest when Ni is equal to 750 μm and DPA equal to 500 μm. (Under these conditions, 146 μm NiDPA, 100 μm Ni DPA and 109 μm Ni 3 DPA are calculated.) We prepared this solution and recorded the whole-sample spectrum shown in Fig. S3b. Page 9 of 17

10 Fig. S3. Representative whole-sample spectra for solutions where (a) NiDPA (DPA, diethylenetriaminepentaacetate) predominates; (b) concentrations of NiDPA, Ni DPA and Ni 3 DPA are all significant and (C) Ni DPA predominates. All solutions contained 5.0 mm MOPS (ph 6.9) and enough NaCl to attain an ionic strength of 5 mm. Equilibrium calculations were performed using the equilibrium constants listed in able 1. Page 10 of 17

11 Quantification of Ni DPA complex concentrations Identification and quantification of the three Ni DPA complexes solely on the basis of whole-sample UV spectroscopy would be challenging given the similarity of the spectra in Fig. S. Separation by CE is beneficial. A CE separation method for separating the three Ni DPA complexes is described in Capillary electrophoresis of the main text. Calibration curves (Fig. S4) were generated for free DPA (as described in Capillary electrophoresis peak assignments in the main text), and for the three Ni DPA complexes (as described in Quantification of Ni DPA complexes in the main text). Fig. S4. Calibration curves for (a) DPA free, (b) NiDPA, (c), Ni DPA and (d) Ni 3 DPA (DPA, diethylenetriaminepentaacetate). Page 11 of 17

12 Influence of differences in ionic strength on Job s Plot maxima Variations in ionic strength and ph influence chemical equilibria and cause deviations in Job s plot maxima. [7] Species with high charge may be influenced significantly by shifts in ionic strength. In Fig. S5, equilibrium concentrations of Ni DPA complexes in solutions with X = 5000 μm were calculated at 10 and 5-mM ionic strength. he concentration of Ni 3 (dtpa) 4 formed at 10-mM ionic strength is 4 significantly lower than at 5-mM ionic strength. In addition, the Job s plot maxima of the Ni 3 (dtpa) complex has deviated slightly to lower values of Ni /X. Fig. S5. Calculated concentrations of Ni diethylenetriaminepentaacetate (DPA) complexes at two different ionic strengths, 10 and 5 mm, represented by thin solid lines and dashed lines. X = 5000 μm. Activity coefficients calculated using the Davies equation were used to convert reported c K (able 1 in main text) to the c K at the desired ionic strength. All data used to determine stoichiometries and log Ks in the main text are shown in able S. able S3 shows data that was excluded due to insufficient ph buffer and indifferent electrolyte to fix the ph and ionic strength. For X = 500 μm the ph was 6.94 ± 0.16 and the ionic strength was 0 ± 5 mm. For X = 5000 μm, the ph was 6.9 ± 0.3 and the ionic strength was 17 ± 7 mm. Deviations from predicted speciation (at ph 7 and 5-mM ionic strength) are apparent when the data from able S3 are used to generate Job s plots (Fig. S6). Page 1 of 17

13 Fig. S6. Concentrations of Ni diethylenetriaminepentaacetate (DPA) complexes as a function of Ni /X at two different values of X. Symbols correspond to experimentally determined concentrations. Solid lines correspond to results from equilibrium calculations that consider only NiDPA and Ni DPA. Dashed lines correspond to results from equilibrium calculations that include the proposed Ni 3 DPA species. Equilibrium calculations are described in the main text. Page 13 of 17

14 able S. Experimental data All solutions contained 10 mm 3-morpholinopropane sulfonic acid (6.94 ± 0.07). n.d., not detected. DPA, diethylenetriaminepentaacetate, X = Ni + DPA Solution composition Capillary electorphoresis response (in absorbance units 10 3 ) X (μm) Ni (μm) DPA (μm) [NaCl] (mm) Peak A Peak B Peak C n.d. n.d n.d n.d n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d n.d n.d n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d. Page 14 of 17

15 able S3. Experimental data not used in determination of stoichiometries and log Ks owing to greater variability in ionic strength and ph All solutions contained 10 mm 3-morpholinopropane sulfonic acid (6.94 ± 0.07). n.d., not detected. DPA, diethylenetriaminepentaacetate, X = Ni + DPA X (μm) Ni (μm) Solution composition DPA (μm) [NaCl] (mm) Ionic strength (mm) Capillary electorphoresis response (in absorbance units 10 3 ) Peak A Peak B Peak C n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d n.d. n.d. Page 15 of 17

16 Proof that concentrations of NiDPA and Ni DPA are equal when Ni /X is equal to 0.6 In Quantification of Ni DPA complexes of the main text it is asserted that when Ni /X = 0.6, the concentrations of NiDPA and Ni DA are equal. his is true because of the correlation between the ratios of Ni /X in the stoichiometry of each species at Ni /X = 0.6. Let us first examine the speciation of NiDPA and Ni DPA while ignoring the formation of Ni 3 DPA. At Ni /X = 0.6, the mass balance of total nickel (Ni ) and total DPA (DPA ) are defined by Ni 0.6X Ni NiDPA NiDPA (33) DPA 0.4X DPA NiDPA Ni DPA (34) free At Ni /X = 0.6, several Ni DPA complexes form so it is reasonable to assume that [Ni + ] and [DPA] free, the sum of concentrations of all DPA species not bound to Ni, are both small. Solving Eqns 33 and 34 simultaneously gives: 0.6 NiDPA 0.6 Ni DPA 0.4 NiDPA 0.8 Ni DPA (35) which simplifies to NiDPA Ni DPA (36) hus, at Ni /X = 0.6, the concentrations of NiDPA and Ni DPA are the same. he result remains the same if we include Ni 3 DPA. Here the mass balance equations for Ni and DPA are: Ni 0.6X Ni NiDPA NiDPA 3 Ni3DPA (37) DPA 0.4X DPA NiDPA Ni DPA Ni DPA (38) free 3 Again, it is reasonable to assume that both [Ni + ] and [DPA] free are small. Solving Eqns 37 and 38 simultaneously gives: NiDPA 0.6 Ni DPA 1. Ni DPA 0.4 NiDPA 0.8 Ni DPA 1. Ni DPA 3 which, again, simplifies to: [NiDPA] = [Ni DPA] (40) hus, at Ni /X = 0.6, the concentrations of NiDPA and Ni DPA are also the same even when formation of Ni 3 DPA is included. (39) Page 16 of 17

17 References [1] P. Job, Formation and stability of inorganic complexes in solution. Annales de Chimie 198, 9, 113. [] F. Woldbye, On the method of continuous variations. Acta Chem. Scand. 1955, 9, 99. doi: /acta.chem.scand [3] M.. Beck, I. Nagypál, Chemistry of Complex Equilibria. (Eds D. R. Williams, D. A. Durham) 1990 (Halsted Press: New York). [4] D. R. Baker, Capillary Electrophoresis, 1st edn 1995 (Wiley: New York). [5] A. Jouyban, E. Kenndler, heoretical and empirical approaches to express the mobility of small ions in capillary electrophoresis. Electrophoresis 006, 7, 99. doi:10.100/elps [6] A. E. Martell, R. M. Smith, R. Motekaitis, NIS Critically Selected Stability Constants of Metal Complexes Database v (National Institute of Science and echnology: Gaithersburg, MD). [7] M. M. Jones, K. K. Innes, Restrictions on the use of Job s method. J. Phys. Chem. 1958, 6, doi:10.101/j150566a031. Page 17 of 17

Implementing a Generic Methods Development Strategy for Enantiomer Analysis

2 Chapman and Fu-Tai Chen Implementing a Generic Methods Development Strategy for Enantiomer Analysis Jeff Chapman and Fu-Tai A. Chen, Beckman Coulter Inc., Fullerton, California, USA. Introduction Whether