Kinetics and Mechanism of Fast Metal-Ligand Substitution Processes in Aqueous and Micellas Solutions Studied by means of a Dye Laser Photochemical Relaxation Technique BY BRIAN H. ROBINSON" AND NEAL C . WHITE Chemical Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NH Received 4th January, 1978 Rapid metal-ligand substitution reactions have been studied in aqueous and sodium lauryl sulphate (SLS) micellar solutions by means of a dye-laser induced photochemical relaxation method. Perturbation of the system involving Ni2+(aq) and the bidentate nitrogen ligand PADA produces two relaxation effects in both aqueous and micellar solutions. The faster relaxation process is concentration independent and is identified with a ring-closure reaction to reform the initial Ni(PADA)2+ complex.Rate constants and activation energies for this process are found to be similar in both media. The slower relaxation time is associated with the recombination reaction between Ni2+(aq) and PADA, for which kf298*2 in water is found to be 1.4~ lo3 dm3 mol-' s-', which is in good agreement with previous measurements. In the surfactant solutions, the rate of complexation is greatly enhanced close to the c.m.c. followed by a decrease as the concentration of SLS is further increased. This is due to the increased local concentration of Ni2+ at the micelle surface as the c.m.c. is approached. It is shown that it may not be valid to make the assumption kRC > k-2 in the kinetic scheme of the reaction. However, the effect on kf is small, such that kf is still dominated by the rate of loss of water from the metal ion.The faster reaction between Zn2+(aq) and PADA was also studied, but only one concentration dependent relaxation time was observed. This was consistent with the complex re-formation reaction and kZgsm2 was found to be 6.4 x lo6 dm3 mol-I s-l. The most frequently used relaxation technique for the study of fast reactions involving ground-state species in solution is temperature-jump relaxation spectro- scopy. The temperature-jump is usually generated by means of a capacitor discharge, a microwave pulse or a laser pu1se.l In non-aqueous solvents, an adiabatic expansion (in a pressure-jump apparatus) can produce a rapid temperature drop in 50-100 ,us.2 The temperature- and pressure-jump methods perturb the equilibrium position of a chemical reaction indirectly through a perturbation of the reaction medium, so that relatively high input energies are required. Furthermore, the resulting relaxation amplitude depends on the position of the equilibrium.However, the extent of a chemical reaction initiated by direct light absorption into a reacting species is dependent on the quantum yield for photodissociation and should therefore in favourable cases require less input energy. Also the equilibrium condition and related thermodynamic constraints (e.g. non-zero AHc for a temperature-jump perturbation) are eliminated. Since the light is absorbed by a specific reagent in the chemical system, the technique can be used to generate high concentrations of selected intermediates.This cannot be achieved by other perturbation techniques, which perturb the solvent, so the technique may be helpful for the analysis of complex reaction schemes, as is indicated in this paper. However, it is not easy to predict in advance whether a 26252626 FA S T M ETA L -L I G A ND S U B S T I T U T I 0 N given reaction can be studied by the photochemical method, since the relative probabilities of the various de-excitation pathways cannot easily be quantified. Early examples of a photochemical perturbation of a chemical equilibrium used a flash-lamp for e~citation,~ but recently several papers have referred to the use of a ruby or neodymium laser as the excitation source. An early exaaple using a Q- switched neodymium laser for excitation of vibrational modes was reported by Goodall and Greenh~w.~ More recent examples 5 - 9 involve studies of the structural inter- conversions of Ni" complexes in water and acetonitrile, processes which occur in the microsecond time range.have discussed the factors which influence the amplitude of the photochemical perturbation, and have compared photochemical and temperature-jump methods for studies on the same system. HasinofFIO employed a ruby laser for photochemical excitation in a study of the reaction between carbon monoxide and haemoglobin as a function of pressure, and a variation of the method, using indirect photochemical excitation, hax been reported by Hubbard et aZ.,I1 for proton transfer reactions. Meyer et al.24 have recently demonstrated the applicability of the flash perturbation relaxation technique to electron-transfer reactions which have essentially gone to completion.Several other instruments and applications have been discussed in a recent publication.' In this paper, we report results obtained (by means of a 3 p s pulse from a Rhodamine-6G dye laser) on the photochemical dissociation and subsequent recom- bination of metal complexes. The systems studied demonstrate the applicability of the method and give some indication of the origin of the relaxation perturbation. The ligand used was pyridine-2-azo-p-dimethylaniline (PADA) (fig. l), and the kinetics of complexation have been studied in bulk water with both Ni2+(aq) and Zn2+(aq). In addition, the influence of micelles formed by sodium lauryl sulphate (SLS) on the rate of reaction between Ni2+(aq) and PADA has been investigated.The kinetics of the association reaction between Ni2+(aq) and PADA have been studied previously by both stopped-flow and joule-heating temperature-jump methods. Results obtained by the laser method can therefore be compared with those obtained by other well-established techniques. The reaction between Zn2+(aq) and PADA is much faster, and has been studied only by the temperature-jump method. l4 The complexation reaction between a metal ion and a bidentate ligand involves several discrete steps : as shown in Scheme 1, step 1 involves the rapid (diffusion- controlled) formation of an outer-sphere complex ; step 2 represents monodentate complex formation, for which the forward rate constant can be identified with that for water exchange (kX) as measured by n.m.r.methods. Since PADA is a bidentate ligand, ring closure (RC) is required to form the final product, and this is usually assumed to be rapid compared with dissociation of the monodentate complex (i.e. kRc % k-2). This mechanism is generally referred to as the Eigen-Wilkins mechanism. Sutin and Creutz SCHEME 1 N KO, N ke, f i (H20)5Ni2+(H,0) + ) f (H20)5Ni2+(Hz0) ) + (H20),Ni2+N N+ H20 N N k - 2 (2) monodentate complex (3) N N k - 3 11 kRc (H20)4Ni2+ ) + H 2 0 bidentate complexB . H . ROBINSON AND N . C . WHITE 2627 Provided that [Ni2+] $ [PADA], and KO, < [Ni2+]-l, we have (for metal complex formation induced by mixing the separate reagents in a stopped-flow experiment) the complete kinetic expression : When kRc & k--3, the ratio of monodentate to bidentate complex at equilibrium is insignificant, and it is therefore difficult to determine kRc by conventional relaxation methods. However, as will be shown later, this is possible using the laser technique. FIG.1 .-Pyridine-2-azo-p-dimethylaniline (PAD A). The reaction between Ni2+ and PADA in the presence of SLS micelles has been studied previously by the stopped-flow method.16 Results reported in this paper using the laser technique extend the range of measurments to the region around the critical micelle concentration (c.rn.c.) of the detergent, where the reaction is too fast for the st opped-flow method. EXPERIMENTAL MATERIALS AND METHODS Purification of SLS and PADA and buffering of the solutions were carried out as described previously.16 Ni(N03)2 6H20 and ZII(NO~)~ 6H20 were both B.D.H.AnalaR grade, and were used without further purification. The stopped-flow apparatus used in the pH- jump studies has been described previously. l7 An Electrophotonics SUA-9 dye laser coupled to a spectrophotometric detection arrangement was used for perturbation of the chemical systems under investigation. A block diagram of the apparatus is shown in fig. 2. Untuned emission was obtained at 580nm (f 5 nm) or 470 nm (f 5 nm) using the dyes Rhodamine-GG or Esculin respectively in " Ultra " methanol (Hopkin and Williams). The laser beam diameter was 5 mm and the pulse-width at half-height was found to be ~3 ys. The energy output was measured by an ITL power meter (Model LOMB 102/K101), and laser energies in the region of 100 mJ were generally employed, The sample cell was a fluorescence-type rectangular cell (Hellma 6040F) located in a thermostatted holder such that the detection path length is 10 mm and the laser path length is 4 mm.Temperature control was to k0.05 K and the temperature in the cell was measured directly by a Comark electronic thermometer (1604 Cr/Al). The monitoring light source was a 50 W pre-focus tungsten lamp (Wotan A1/17). The output was adjusted to focus at the input end of a 3 mm diameter quartz light-guide (Schott- Jena). A shutter and heat filter are located inside the lamp housing. There is also provision for inserting an optical filter in front of the light-guide to prevent exposure of the sampIe to the full spectral output of the lamp The other end of the light guide is attached to the sample cell-holder, and a second light-guide transmits the emergent beam to a Bausch and Lomb high intensity u.v./visible grating monochromator.The photomultiplier (IP21) housing and control circuitry (for amplification and time constant control) were fitted directly to the exit side of the monochromator. The exit slit-width of the monochromator was set to 1.3 mm, which gives a spectral bandwidth of %5 nm. The narrow bandwidth was required to eliminate scattered laser light when it was necessary to work at wavelengths2628 F A S T MET A L-LI G A ND SUB ST IT U T I 0 N close to that of the laser output. The fastest relaxation which can be studied is limited by the laser pulse-width and is ~5 p.The transients were recorded on a Tektronix 549 storage oscilloscope for photography and trace-matching or on a Datalab 905 transient recorder linked to a Telequipment D65 monitoring oscilloscope. Stored digitised data from the transient recorder were transferred to paper tape for subsequent computer analysis. Errors in relaxation times and amplitudes are standard deviations of approximately six transients. ORIGIN OF THE PHOTOCHEMICAL PERTURBATION The dye laser pulse induces photochemical dissociation of the metal complex, a process which is well known in inorganic photochernistry.l8 The reaction scheme may be described generally as follows [where S is a solvent (water) molecule and L-L is a bidentate ligand] : 2s + SS-SSML L monoden tate k - 2 k i ' SsMSL L n L L+SGM, B - 1 outer-sphere complex The excited-state complex S4& ') can in general be deactivated by radiationless decay L (thermal deactivation), by fluorescence or by " chemical reaction ", i.e. photosubstitution processes (A) or (B), where (A) respresents concerted loss of both ligand groups from the metal ion.When kRC >> k-z, the outer-sphere complex can only be produced by (A). When kRC - k--2 the outer-sphere complex can also be produced via (B) and dissociation of the monodentate complex. After perturbation the ground state species SsML L or S5MSL L must be obtained rapidly to ensure that the subsequent recombination reactions are ground state processes. Any S5MSL L formed will rapidly produce SsM and L L by diffusion apart of the reagents, since k-l/k,, - lo5 for reactions involving Ni2f.Therefore as a result of the photochemical perturbation, we can predict that two relaxation times might be observed in m A nB . H . ROBINSON A N D N. C. WHITE 2629 a favourable case when the various complexes have different spectra. A faster relaxation would be associated with ring-closure and a slower one (identical to that measured by stopped-flow and temperature-jump techniques) would be identified with recombination of free metal ion with ligand. Therefore, as a result of the photochemical perturbation, we would hope to be able to measwe ~ R C , ( k ~ c k ~ ~ x kl/k-l)/(k-z+kRC) and k-2k-3@-2+k~c). The relaxation amplitudes of the two processes are determined by: (i) the optical properties of the absorber in the system, (ii) the quantum efficiencies 41 + 42 of the photo- substitution processes (A) and (B), (iii) the ratio of the rate constants k ~ ~ / k - ~ .monochromator FIG. 2.-Block diagram of the laser apparatus with spectrophotometric detection. From a semi-quantitative consideration of our results, it is clear that the quantum efficiency of process (B) is greater than for process (A). Following Sutin et aZ.,’ we can calculate the overall quantum efficiency, +l+q52, to be of the order of 1 % for the incident photon intensity (as used) of 7x 10l6 photons cm-2 and &580 nm of (H20)4Ni2+N) of 2x lo4 dm3 mol-’ cmn-’. A precise treatment is difficult because of the uncertainties regarding the extinction coefficient of the monodentate complex.N RESULTS AND DISCUSSION Under most conditions two relaxation times are observed, as predicted in the preceding section. All individual transients were found (within experimental error) to be exponential decay curves when the systems were studied under pseudo-first-order conditions (i.e. [Niz+] $ [PADA]). Following perturbation, the absorbance of the solution always returned to its initial value; this indicates that there is no overall photodecomposition of the complex as a result of perturbation. When PADA alone was irradiated with laser light of 580 nm, no relaxation was observed. However, when laser light of 470nm was employed (the free ligand absorbs strongly at this wavelength), a relaxation was observed, decaying in a time ( N 100 ,us) which was independent of ligand concentration and temperature.2630 FAST METAL-LIGAND SUBSTITUTION THE SYSTEM Ni2++PADA I N WATER The Ni2+ + PADA system, perturbed at 580 nm, gave rise to two relaxation times, well separated on the time axis, which are independent of the detection wavelength over the spectral absorption range.The faster relaxation time (-40 ps) is indepen- dent of Ni2+ and PADA concentrations, but is dependent on temperature. The slower relaxation time (10-1000ms) is dependent (when [Nil, 9 [PADA].) on the concentration of Ni2+ (but not PADA) and temperature [subscript T = total (initial) concentration]. C wavelength Inm FIG. 3.-Spectra of (a) PADA, (b) NiPADA2+ and (c) PADAH+. The visible absorption spectra of PADA and Ni(PADA)2+ are shown in fig.3. The dependence of the amplitudes of the two separate transients on detection wave- length (fig. 4) shows that the species which are involved in the two relaxation processes are different, isosbestic points being located at 490 nm (slow z) and 535 nm (fast z). Zero amplitude is observed for the slow relaxation time at a wavelength which corresponds to the isosbestic point between PADA and Ni(PADA)2+ (fig. 3). The magnitude of the relaxation amplitude, however, does not depend on the position of equilibrium, but is directly proportional to the concentration of Ni(PADA)2f complex and the incident laser energy (fig. 5).B . H. ROBINSON AND N. C . WHITE 263 1 420 440 460 480 500 520 5 4 0 560 wavelength/nm FIG. 4.-Amplitude wavelength dependence for the fast ( x - X ) and slow (0-0) relaxation processes. pH = 6.5, T = 298.2 K.[Ni2+]~ = 1 X mol dm-3; [PADAIT = 2 X mol dmd3. In bulk water, at 298.2 K, the fast relaxation time (T~) has a value of 35 +4 ps corresponding to a first order rate constant of 2.9k0.3 x lo4 s-l. This fast process will be identified with ring-closure [step (3) of Scheme 11, following photo- chemical generation of the monodentate complex. The activation energy (E,)f is 8 - 6- 4 - 2 - /-/-- / X Y X o e I I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 absorbance (A) FIG. 5.-Relaxation amplitude as a function of NiPADA2+ absorbance. pH = 6.5, T = 298.2 K, 1 = 550 nm. ( x - X ) fast relaxation process, (0-0) slow relaxation process.2632 FAST METAL-LIGAND SUBSTITUTION 40 Ifr 4 kJ mol-l, so that the process is clearly different from that measured in solutions containing only PADA, for which E, 21 0 for laser excitation at 470 nm.The slow relaxation time (7,) shows a linear dependence on Ni2+ concentration as shown in fig. 6 and the data fit the simple rate expression : where and 110 100” 90 80 70 - - - - * ?, 60- 0” A? 50- 4 0 30 20 - - - (7, ’) = k(obs)s = kf[Ni2+] + kb ” 1 2 3 4 5 6 7 8 9 [Ni2+]/10-2 mol dm-3 FIG. 6.-Plot of k(&s)s against [Ni2+] for the system Ni2++PADA-!-Hz0. (-0-O), T = 308.2 K ; (- x-x), T = 298.2 K ; (-n-n), T = 288.2 K ; pH = 6.5. [PADAIT = 2 x r n ~ l d m - ~ . Excellent agreement for k,2 8.2 (= 1.4 x lo3 dm3 mol-1 s-l) and kE9 8 * 2 is obtained on comparison with other fast reaction techniques (table 1). The value of (&JS is 57 & 5 kJ mol-l, again in excellent agreement with previous determinations.13 This agreement, with the additional evidence from the isosbestic point for the slow process, allows us to conclude that, following photochemical excitation, the complex must dissociate to give separated Ni2+(aq) and ligand.B .13. ROBINSON AND N. C . WHITE 2633 THE SYSTEM Zn2++PADA I N WATER When Zn2+ is substituted for Ni2+, only one relaxation proportional to the Zn2+ concentration is observed. The complexation rate constant, kf, is found to be 6.4 x lo6 dm3 mol-1 s-l at 298.2 K (fig. 7) which is again in excellent agreement with the value obtained by the joule-heating temperature jump method, l4 confirming that the rate of reaction is not significantly ionic strength dependent.'i- [Zn2+]/10-3 rnol dm-3 FIG. 7.-Plot of kobs against [Zn2+] for the system Zn2++PADA+Hz0. (T = 298.2 K), pH = 6.5. [PADAIT = 2 X mol dm-3. INFLUENCE OF MICELLAR SLS ON THE REACTION BETWEEN Ni2+ AND PADA From previous stopped-flow studies,16 it has been found that the presence of micellar sodium lauryl sulphate (SLS) has a pronounced effect on the association rate constant for the reaction between Ni2+ and PADA. It was shown that the reaction occurs at the negatively-charged surface of the anionic micelle, since PADA is a relatively hydrophobic ligand and hence is located in the surface region of the micelle. Ni2+ is also readily adsorbed onto the surface.16 Using the laser perturba- tion method, two relaxations are again observed which have qualitatively the same features as those for the bulk reaction.The fast relaxation time is independent of Ni2+ and PADA concentrations and the isosbestic point is at 535 nm. The fast relaxation time (7;) is loo+ 10 ps at 298.2 K corresponding to a first order rate process with k; - 104s-', which may be again identified with kRc for the complexation reaction on the micelle surface. This is slightly slower than the value (3 x lo4 s-l) measured in the absence of SLS. The slow relaxation time, corresponding to (kLbs)C1 is independent of the monitoring wavelength, and the wavelength corresponding to zero amplitude is at 485 nm. 7; depends linearly on the nickel ion concentration, and shows a dramatic dependence on the SLS concentration, especially in the region of the critical micelle concentration (c.m.c.).I N WATER2634 FAST METAL-LIGAND SUBSTITUTION A plot of log (kLb& against log [SLS] is shown in fig. 8, and a plot of (k&& against ([Ni2+]/[SLS], - c.m.c.) for concentrations of SLS above twice the c.m.c. is shown in fig. 9. ([SLS], is the weighed-in concentration of SLS). The results obtained previously for (k;& by the stopped-flow method l6 under the same final conditions are also plotted in fig. 8 for comparison. Excellent agreement is again obtained by the two methods. [SLS]/mol dm-3 FIG. 8.-Plot of log,, (k&& against log,, [SLS]. (-0-0), T = 308.2 K ; (- x - x), T = 298.2 K ; (-A-A), T = 288.2 K ; (-@-a), results obtained by stopped-flow method at 298.2 K ; pH = 7.7. [Ni’f]~ = 1 X mol drnd3.mol dm-3; [PADAIT = 2 X { [NiZf]/([SLS], - ~.m.c.)}/lO-~ FIG. 9.-Plot of (k&bs)s against { [Ni2+]/([SLSl0 -~.m.c.)>/lO-~ for sodium lauryl sulphate (pH = 7.7).B. H. ROBINSON AND N. C. WHITE 2635 The rate increases sharply from the bulk value when the concentration of SLS exceeds the c.m.c. (-7.5 x mol d n r 3 at 298.2 K). Close to but above the c.m.c., (k&& is approximately constant but at higher concentrations of micelle it falls gradually to values close to that measured in bulk water. Above the c.m.c., the reaction occurs on the micelle surface, and a simple argu- ment suggests that the association rate constant should be inversely proportional to the concentration of micellar binding sites at the surface, and first-order in the excess reagent.This behaviour is confirmed by fig. 9. Detailed considerations of the mechanism of the reaction are given in a previous paper.16 TABLE 1 .--SUMMARY OF THE KINETIC DATA kr/103 dm3 mol-1 s - ' kb/S-l kill04 s-1 (E&/kJ mol-1 (E&/kJ mol-1 Ni2+ 1.3 a 0.1 a 55+4 a S.F. Ni2+/SLS 1.1" 52.3+4 S.F. Zn2+ 6.6 x lo3 2.2 x lo4 35.8 T. J. 1.4 0.1 2.9 57+5 40k4 L. 1.1" 1.0 55+4 40+4 L. 6 . 4 ~ 103 c 2.1 x 104 c L. a Ref. (16), b ref. (16), C this work, dref. (14), * calculated from eqn (15) of ref. (16). S.F. = stopped-flow. T.J. = temperature-jump. L = laser photochemical perturbation. Activation energies are (E& - 40 +4 kJ mol-l and (E& - 55 +4 kJ mol-I. These measurements are made at a constant SLS concentration of lo-' mol dm-3 assuming a temperature independent c.m.c.(Fig. 8 shows the actual effect of temperature on the kinetics in the c.m.c. region). The value of (I?;), is very similar to that measured in bulk solution (table 1) suggesting that the energetics of the reaction on the micelle surface are not significantly changed compared with the bulk aqueous phase. In particular the enthalpies of activation for water-exchange and ring closure appear to be little affected by the change in environment. The results further confirm that the dependence of zs on the concentration of micelles is due to an entropic effect involving the concentrative effect of the micelle surface on the reagents. DISSOCIATION KINETICS INVOLVING THE NiPADA2+ COMPLEX A T 298.2 K Using the stopped-flow technique in a pH-jump mode, it is possible to determine k-3 independently, using the procedure originally developed by Basolo et al.' Measurements were made over a range of final pH values in the region 3.5-5.5.The value of k-3 obtained (0.3 s-l) was found to be independent of pH. Values of kb (= k-2k-3/k-2+kRC) can either be measured as the intercept on the plot of (ko& against [Ni2+] (fig. 6) or by reacting the NiPADA2+ complex with Hg2+. In both cases a value of k, of 0.1 s-I was obtained. By means of the value of kRc obtained from the laser perturbation, it is possible using eqn (2) and (3) to calculate all the postulated rate and equilibrium constants for complexation. We find, if outer-sphere complex formation is assumed to be diffusion-controlled : K,,,k,, = 1.5 x lo3 dm3 rnd-1 s-1 kRC = 2.9 x 104 s-' k-3 = 0.3 S-' k-, = 1.4 x lo4 s-' K2 = 2.1 K3 = 0.97 x 10'.agreement with that obtained by spectrophotometry l 3 of 1.2 x lo4 dm3 mol-'. The kinetic value of K( = Kl x K2 x K3 = 1.02 x lo4 dm3 mol-I) is in excellent2636 FAST METAL-LIGAND SUBSTITUTION It seems from our analysis that the assumption k-2 < kRc should not be made. Ring closure can in some instances be rate limiting, as was observed by Hoffinann 21 in studies of nickel malonate complex formation. However, the effect on kf of the term kRC/(k-2+kRC) is small, such that kf is still dominated by the rate of water loss from the metal ion. k,, obtained from our kinetic measurements will be of the same order as that obtained from n.m.1. measurements (3 x lo4 s - ~ ) . ~ * However, it should be noted that published data 22 on the stability constant (K') for formation of the monopyridine nickel(I1) complex (which would be expected to be a good model for monodentate complex formation with PADA)23 suggests that k e x / L 2 - 800 since the value of K' measured experimentally was 80 dm3 mol-l.We thank the S.R.C. for the provision of apparatus associated with this work, and for a postdoctoral research assistantship (N. C. W.). We especially thank Prof. E. F. Caldin for guidance and helpful discussions. I E. F. Caldin, Chem. in Britain, 1975, 11, 4. H.-J. Buschmann, W. Knoche, R. A. Day and B. H. Robinson, J.C.S. Faraday I, 1977,73,675. e.g. R. L. Strong and J. E. Willard, J. Amer. Chem. 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