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1 Cetyl trimethylammonium bromide as an efficient catalyst for Regioselective Bromination of Alkoxy Naphthalenes with Trimethyl benzylammonium tribromide: Synthetic and Kinetic Approach K. Rajendar Reddy, K. C. Rajanna*, K. Uppalaiah, S. Ramgopal Department of Chemistry, Osmania University (O.U), Hyderabad-500 007, A.P., India Supplementary Information for the Determination of Binding Constants in Micellar Reactions To establish most plausible mechanism for micelle catalyzed reactions, it is necessary to have an insight into the (1) interaction of CTAB with Substrate (2) interaction of CTAB with TMBATB and finally (3) the interaction of CTAB with Substrate in presence of TMBATB. A detailed spectrophotometric study has been taken up under different conditions for this purpose. (A) Binary System: Model-I: Modified Benesi- Hildebrand Model for Micelle-Substrate interactions Kb M+S MS Menger-Portnoy’s first step of micellar reactions is taken into consideration. According to this model, formation of micelle-substrate complex (MS) is formed in the pre-equilibrium step due to the interaction of micelle (M) with substrate (S). Equilibrium constant K or (Kb) is the binding constant, which can be determined using modified approach of Benesi and Hildebrand. If the total concentration of substrate is CS, which is also considered as the algebraic sum of free, substrate species (S) and micelle bound substrate species (MS). CS = [S] + [MS] From micelle-substrate binding equilibrium, K = [MS]/[M][S] or [S] = [MS]/K[M] Substitution of [S] in the above equation gives [MS] [MS] + K[M][MS] CS = -------- + [MS] = ----------------------K[M] K[M] ⇒ K[M]CS [MS] = ---------------1 + K[M] ------------ (1) To observe one-to-one binding between a single substrate (S) and micelle (M) using UV/Vis absorbance, the BenesiHildebrand method can be employed. The basis behind this method is that the acquired absorbance should be a mixture of the micelle (M), substrate(S) and the micelle-substrate (MS) complex. A = AMS + AM+ AS Since the initial concentration of the substrate (S0) is much larger than the initial concentration of the micelle (M 0), it is assumed that the absorbance from M0 should be negligible. The UV-Visible spectrum of CTAB (M) shows that the absorbance of CTAB is almost negligible in this study. Therefore the observed absorbance (A) comes out as, A = AMS + AS 2 The absorbance can be collected before and following the formation of the MS complex. This change in absorbance (ΔA) is what is experimentally acquired, with A0 being the initial absorbance before the interaction of S with MS and A being the absorbance taken at any point of the reaction. ΔA = (A – A0) Using the Beer-Lambert law, the equation can be rewritten with the absorption coefficients and concentrations of each component. ΔA = (εMS[MS] + εS[S]) - εS[S]0 Due to the previous assumption that [S]0>> [M]0, one can expect that [S] = [S]0, Δε represents the change in value between εMS and εS. ΔA = Δε [MS]b (where b = path length) ⇒ [MS] = ΔA/ Δε b ; and When b = 1cm⇒ [MS] = ΔA/ Δε Substituting for [MS] in the binding isotherm equation (1), the equilibrium constant K can now be correlated to the change in absorbance due to the formation of the MS complex. ⇒ ⇒ ΔA --------Δε ΔA --------CS K[M]CS = [MS] = -----------1 + K[M] = [MS] = ΔεK[M] ------------1 + K[M] Further modifications results in an equation where a double reciprocal plot can be made with (CS /ΔA) as a function of 1/[M], and Δε can be derived from the intercept while K can be calculated from the slope. CS ----ΔA = 1 ------------ + ΔεK[M] 1 ----Δε (II)Ternary Complex formation in micellar media The model for Ternary Complex formation in micellar mediais represented in the following equilibria: K1 M+S MS K2 MS + TMBATB [MS- TMBATB] In the above scheme M, S and TMBATB represent micelle, substrate, brominating reagent while [MS] and [MSTMBATB] refer to binary and ternary complexes formed due to the interaction of micelle, substrate, and TMBATB respectively. [MS-TMBATB] = K2 [MS][TMBATB] [MS] = K1 [M][S] ⇒ [S] = [MS]/ K1 [M] But the total substrate concentration ([S]t) is the sum of free substrate (S) and micelle bound substrate (MS) concentrations respectively. [S]t = [S] + [MS] ⇒ [S] = [S]t - [MS] 3 [MS] Substituting for [S] we have [S]t = [MS] + ------------K1 [M] [MS] K1 [M] +[MS] [MS]( 1 + K1 [M]) ⇒[S]t = --------------------------------- = ---------------------------K1 [M] K1 [M] ⇒ K1 [M][S]t [MS] = -----------------(1+ K1 [M]) [S]t Similarly [S]t = [S] + K1 [M][S] = [S] (1+ K1 [M]) ⇒ [S] = -----------------(1+ K1[M]) K1K2[M][S]t [TMBATB] and [MS -TMBATB] =----------------------------------(1+ K1 [M]) Now if we apply the condition, [TMBATB]t = [TMBATB] + [MS -TMBATB] [MS -TMBATB] (1+ K1 [M]) Substituting for [TMBATB] = --------------------------------------- in the above equation, K1K2[M][S]t [MS -TMBATB] (1+ K1 [M]) ⇒[TMBATB]t = -------------------------------------- + [MS -TMBATB] K1K2[M][S]t [MS -TMBATB] (1+ K1 [M]) + K1K2[M][S]t [MS -TMBATB] [TMBATB]t = -------------------------------------------------------------------------------K1K2[M][S]t [MS -TMBATB] {(1+ K1 [M]) + K1K2[M][S]t} [TMBATB]t = ---------------------------------------------------------------K1K2[M][S]t ⇒ K1K2[M][S]t[TMBATB]t = [MS -TMBATB]( 1+ K1 [M] + K1K2[M][S]t) K1K2[M][S]t[TMBATB]t ⇒[MS -TMBATB] = -------------------------------------( 1+ K1 [M] + K1K2[M][S]t) The basis behind this method is that the acquired absorbance should be a mixture of the micelle (M), substrate(S) and the micelle-substrate (MS)binary complex, brominating reagent (TMBATB) and ternary complex [MS -TMBATB]. A = AMS + AM+ AS+ A (TMBATB) + A (MS –TMBATB) The absorbance can be collected before and after the formation of the (MS –TMBATB) complex. The absorbance for (MS –TMBATB) complex could therefore be equal to the change in absorbance (ΔA) which is obtained from the following relationship. 4 A (MS –TMBATB) = ΔA = (A) ~ (AMS + AM+ AS+ A (TMBATB)) Using the Beer-Lambert law, the equation can be rewritten with the absorption coefficients and concentrations of each component. ΔA = Δε [(MS –TMBATB)]b (where b = path length) ⇒ [(MS –TMBATB)] = ΔA/ Δε b ; and When b = 1cm⇒ [MS] = ΔA/ Δε Substituting for [(MS –TMBATB)] in the binding isotherm equation (1), the equilibrium constant K2 can now be correlated to the change in absorbance due to the formation of the [(MS –TMBATB)] complex. K1K2[M][S]t[TMBATB]t ΔA ⇒ [MS -TMBATB] = -------------------------------------- = ------( 1+ K1 [M] + K1K2[M][S]t) Δε ⇒ Δε (K1K2[M][S]t[TMBATB]t) ΔA = ---------------------------------------------( 1+ K1 [M] + K1K2[M][S]t) Taking reciprocals to the above equation affords a reciprocal plot with (1 /ΔA) as a function of 1/[M], and Δε can be derived from the intercept while K can be calculated from the slope. 1 ( 1+ K1 [M] + K1K2[M][S]t) ----- = ----------------------------------ΔA Δε (K1K2[M][S]t[TMBATB]t) 1 1 1 1 ----- = ---------------------------------- + ------------------------- + ------------------ΔA Δε (K1K2[M][S]t[TMBATB]t) Δε (K2[S]t[TMBATB]t) Δε[TMBATB]t Now from the reciprocal plot with (1 /ΔA) as a function of 1/[M], and Δε can be derived from the intercept, while K2 can be calculated from the slope with proper substitution of K1 evaluated earlier for binary system. Derivation of Rate equation: Rate of the above reaction (V) can be written as, V = kb[S][ TBATB] + km[MS -TMBATB], Where [MS TMBATB] = K2 [MS][TMBATB] and [MS] = K1 [M][S] ⇒ [S] = [MS]/ K1 [M] But the total substrate concentration ([S]t) is the sum of free substrate (S) and micelle bound substrate (MS) concentrations respectively. [S]t = [S] + [MS] ⇒ [S] = [S]t - [MS] and Substituting for [S] we have [MS] [S]t = [MS] + ----------K1 [M] [MS] K1 [M] +[MS] [MS]( 1 + K1 [M]) ⇒[S]t = -------------------------- = ----------------------K1 [M] K1 [M] K1 [M][S]t ⇒ [MS] = -----------------(1+ K1 [M]) 5 Again from [S]t = [S] + K1 [M][S] = [S] (1+ K1 [M]) [S]t ⇒ [S] = -----------------(1+ K1[M]) and K1K2[M][S]t [TMBATB] [MS -TMBATB] = -----------------------------(1+ K 1 [M]) Now, if we apply the condition that [TMBATB] t = [TMBATB] + [MS -TMBATB] and Substituting for [TMBATB] as, [MS -TMBATB] (1+ K1 [M]) [TMBATB] = -----------------------------------K1K2[M][S]t in the above equation we get, [MS -TMBATB] (1+ K1 [M]) ⇒[TMBATB]t = -------------------------------------- + [MS -TMBATB] K1K2[M][S]t [MS -TMBATB] (1+ K1 [M]) + K1K2[M][S]t [MS -TMBATB] [TMBATB]t = -------------------------------------------------------------------------------K1K2[M][S]t [MS -TMBATB] {(1+ K1 [M]) + K1K2[M][S]t} [TMBATB]t = ---------------------------------------------------------------K1K2[M][S]t ⇒ K1K2[M][S]t[TMBATB]t = [MS -TMBATB]( 1+ K1 [M] + K1K2[M][S]t) K1K2[M][S]t[TMBATB]t ⇒[MS -TMBATB] = -------------------------------------( 1+ K1 [M] + K1K2[M][S]t) (K1K2[M][S]t [TMBATB] Similarly, [TMBATB]t = [TMBATB] + ----------------------------------(1+ K1 [M]) [TMBATB] (1+ K1 [M]) + K1K2[M][S]t [TMBATB] ⇒ [TMBATB]t = ----------------------------------------------------------------(1+ K1 [M]) [TMBATB] (1+ K1 [M] + K1K2[M][S]t) ⇒ [TMBATB]t = ------------------------------------------------(1+ K1 [M]) ⇒ [TMBATB] = [TMBATB]t(1+ K1 [M]) ---------------------------------(1+ K1 [M] + K1K2[M][S]t ) Substituting for [S], [ TBATB] and [MS -TMBATB] in rate equation, V = kb[S][ TBATB] + km[MS -TMBATB] kb[[S]t[TMBATB]t(1+ K1 [M]) V = ---------------------------------------------------(1+ K1[M])(1+ K1 [M] + K1K2[M][S]t ) kmK1K2[M][S]t[TMBATB]t + -------------------------------------(1+ K1 [M] + K1K2[M][S]t ) 6 kb[[S]t[TMBATB]t(1+ K1 [M]) + kmK1K2[M][S]t[TMBATB]t(1+ K1 [M]) V = -------------------------------------------------------------------------------------------------(1+ K1[M])(1+ K1 [M] + K1K2[M][S]t ) (1+ K1 [M]){kb[[S]t[TMBATB]t+ kmK1K2[M][S]t[TMBATB]t} V = ---------------------------------------------------------------------------------------(1+ K1[M])(1+ K1 [M] + K1K2[M][S]t ) This equation further simplifies to, V= {kb[[S]t[TMBATB]t+ kmK1K2[M][S]t[TMBATB]t} ---------------------------------------------------------------------(1+ K1 [M] + K1K2[M][S]t ) V= kb[[S]t[TMBATB]t+ kmK1K2[M][S]t[TMBATB]t ---------------------------------------------------------------1+ K1 [M](1+ K2[S]t) --- (3) According to this rate law reaction kinetics should indicate first order kinetics with respect to [TMBATB] and fractional order in both [substrate] as well as [Surfactant-M]. But kinetics of the study indicated first order in both the reactants [TMBATB] and [substrate]. This change could be explained due to the small contribution of the product of (K1K2[M][S]t). If (1+ K1 [M]) >> K1K2[M][S]t in the denominator of the above rate equation, the contribution of (K 1K2[M][S]t) could be neglected. The rate equation now takes the form, kb[[S]t[TMBATB]t+ kmK1K2[M][S]t[TMBATB]t -----------------------------------------------------------------1+ K1 [M] Rearranging the rate law, V= V= [[S]t[TMBATB]t(kb + kmK1K2[M]) ------------------------------------------------1+ K1 [M] Table S.1 & Fig. S.1: Pseudo first order Kinetics Plots for Order in [2-Methoxy naphthalene] in d/dt[1-bromo,2methoxy naphthalene]; in the reaction between 2-Methoxy naphthalene(2-MNP) & TMBATB [TMBATB] =1*10-3 mol dm-3; [2- MNP] =1*10-2 mol dm-3; [CTAB] = 2.5*10-4 mol dm-3 ln (C∞ -Ct) 303K Time 10 6.44254 20 6.37332 30 6.313548 40 6.257668 50 6.20859 60 6.156979 70 6.104793 80 6.052089 Fig. S.1: Pseudo first order Kinetic Plot of 2MNP 7 Table. S.2 & Fig.S.2: Second order Kinetics Plots for Order in [2-Methoxy naphthalene] in d/dt[1-bromo,2-methoxy naphthalene]; in the reaction between 2-Methoxy naphthalene & TMBATB [TMBATB] =0.1 mol dm-3; [2- MNP] =0.1 mol dm-3; [CTAB] = 2.5*10-4 mol dm-3 (1/(C∞ -Ct)) 303K Time 5 0.001664 10 0.001795 20 0.001942 30 0.002101 40 0.00237 50 0.002538 60 0.002793 70 0.003096 80 0.001664 90 0.001795 Fig.S.2: Second order Kinetic Plot of 2MNP Ultraviolet spectroscopic Spectras: Fig.S.3. Interaction of CTAB with 2-MNP in presence of TMBATB -Vis Spectrum (Over Layed Channel) Fig.S.4. Interaction of CTAB with 2-MNP in presence of TMBATB -Vis Spectrum (Over Layed Channel) 8 Fig.S.5. Interaction of CTAB with 2MNP (1 × 10-2 mol.dm-3) - UV-Vis Spectrum (Over Layed Channel) at 30 0C Fig.S.6. Interaction of CTAB with 2MNP (1 × 10-2 mol.dm-3) -UV-Vis Spectrum (Over Layed Channel) at 50 0C Fig.S.7. Interaction of CTAB with 2ENP (1 × 10-2 mol.dm-3) UV-Vis Spectrum - (Over Layed Channel) at 30 0C 9 Fig.S.8. Interaction of CTAB with 2ENP (1 × 10-2 mol.dm-3) UV-Vis Spectrum - (Over Layed Channel) at 50 0C Fig.S.9. Interaction of CTAB with 2PNP (1 × 10-2 mol.dm-3) UV-Vis Spectrum-(Over Layed Channel) at 30 0C Fig.S.10. Interaction of CTAB with 2PNP (1 × 10-2 mol.dm-3) UV-Vis Spectrum -(Over Layed Channel) at 50 0C 10 Fig.S.11. Interaction of CTAB (mol.dm-3) with TMBATB (1 × 10-2 mol.dm-3) UV-Vis Spectrum - (Over Layed Channel) at 30 0C Fig.S.12. Interaction of CTAB (mol.dm-3) with TMBATB (1 × 10-2 mol.dm-3) UV-Vis Spectrum - (Over Layed Channel) at 50 0C