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2 Model-based analysis for kinetic complexation study of Pizda and Cu(II) Spectrochimica Acta Part A M. Vosough, M. Maeder, M. Jalali-Heravi, S.E. Norman

3 Chemical kinetic reactions : Model-based analysis kinetic model The main goals for model-based analysis of kinetic reactions : rate constants molar absorption spectra pure kinetic profiles of all reacting species Introduction

4 Many kinetic reactions in aqueous solutions are strongly pH-dependent and coupled to one or more protonation equilibria. The kinetic reactions have to be studied at feasible pH ranges. Introduction

5 Complications due to addition of buffers: I.The conjugate bases of the buffers can coordinate to the metal ions. II.Buffer anions can form outer-sphere complexes with highly charged polyprotonated ligand cations. III.Buffer components can absorb in the wavelength region where the complexation is observed. Introduction

6 Recent developments in model-based methods : incorporation of the effects of non-ideal experimental conditions into the fitting algorithm The quantitative analysis of kinetic measurements that are not buffered is possible. The complications due to addition of the buffers can be removed. Introduction

7 The concentration profiles in kinetic studies are defined by:  Model  rate constants  initial concentration of the reacting components Introduction

8 Y = CA + R A_hat= C + Y (C + = (C t C) −1 C t ) R = Y − Y calc = Y − CA ssq =ΣR 2 i,j = f (Y, model,parameters)

9 k new = k +Δk Δk = −J + R = −(J t J) −1 J t R

10 The complexation is between: copper(II) and 1-(2-hydroxyl cyclohexyl)-3- [aminopropyl]-4-[3-aminopropyl]piperazine (Pizda) in 50% ethanol–water Pizda is a five-dentate ligand. 1:1 complex forms in a very fast second order reaction and strongly dependent on the initial pH.

11 Scheme 2. Cu(II)–Pizda complex in all possible complexation sites

12 Cu 2+ + L (CuL’) 2+ kLkL (CuL’) 2+ CuL 2+ k (CuL’) 2+ k -1 (CuL’) 2+ Cu 2+ + LH + CuLH 3+ k LH k -1 LH Cu 2+ + LH 2 2+ CuLH + + H + k LH2 (CuL’) 2+ + H + CuLH 3+ K4K4 Mechanism:

13 L + H + LH + K1K1 LH + + H + LH 2 2+ K2K2 LH H + LH 3 3+ K3K3 Protonation equilibria:

14 Forward reaction (F): the kinetics of complex formation Proton releases and therefore the pH decreases and finally would reach to its equilibrium value.

15 Backward reaction (B): the kinetics of complex dissociation The complex decomposes and therefore pH increases and finally would reach to its equilibrium value.

16 Globalization of second-order data Elimination of linear dependencies of concentration profiles Combination of all information gathered in the individual measurements More robust determination of the fitted parameters

17 Scheme 1. Representation of global analysis Y tot = C tot A + R tot

18 Fig. 1. Concentration distribution diagram obtained for all chemical species in complexation of Cu(II) by Pizda in equilibrium state as a function of pH

19 Table 1 Protonation and complexation constants obtained from potentiometric study of complex formation equilibria between Pizda and Cu 2+ in 50% ethanol–water solution and 25±0.5 ◦ C and ionic strength of 0.1M (NaClO 4 )

20 Fig. 2. pH trends calculated by Newton–Raphson method in: forward pre-kinetic, backward pre-kinetic and equilibrium states.

21 Fig. 3. Two kinetic series in 21 wavelengths with stopped-flow measurements: (a) in forward case with initial concentration of acid 2.97×10 −2 M (b) in backward case with initial concentration of acid 4.70×10 −2 M

22 Fig. 4. Some results obtained using global analysis. The results depicted for two kinetics traces in Fig. 3 in some selected wavelengths (520,565 and 655 nm) contains the calculated absorbance measurements and residual plots : (a) forward and (b) backward reactions.

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24 The main advantage: The possibility of working in unbuffered solutions. The tedious measurements and analysis of buffer dependences is replaced by few reactions. All pH ranges can be covered. The main disadvantage : The time consuming of the fitting process relative to the other methods which use the buffer solutions.

25 This procedure delivers : Nonlinear parameters which are rate constants and define the matrix C. The fitted equilibria constants involved in kinetics. The matrix of molar absorptivity spectra A for all absorbing species.

26 Table 2 Rate constants and the protonation constants for complexation reaction between Pizda andCu 2+ in50%ethanol–water solution and 25±0.5 ◦ C and ionic strength of 0.1M (NaClO 4 )

27 Fig. 5. The calculated concentration profiles for the measurement series in Fig. 3: (a) forward and (b) backward reactions.

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29 Fig. 6. pH profiles calculated with global analysis in the selected kinetic measurements (Fig. 3).

30 Fig. 7. Calculated absorption spectra in kinetic measurements for four absorbing species of Cu, CuL, CuL’ and CuLH in a global way.

31 M. Maeder, Y.M. Neuhold, G. Puxty, P. King, Phys. Chem. Chem. Phys. 5(2003) Reference:

32 Thanks