J . Chem. SOC., Faraday Trans, 1, 1984, 80, 2417-2437 Effect of Organised Surfactant Systems on the Kinetics of Metal-Ligand Complex Formation and Dissociation BY PAUL D. I. FLETCHER AND BRIAN H. ROBINSON* Chemical Laboratory, University of Kent, Canterbury, Kent CT2 7NH Received 2nd September, 1983 The kinetics and mechanism of a range of metal-ligand complexation reactions have been studied in water, sodium dodecylsulphate micellar solutions and aerosol-OT-stabilised water- in-oil microemulsions. A generalised theory is developed for the interpretation of kinetic measurements in these dispersions and it is tested for metal-complex formation. In most cases the rate of complex formation is only affected by the concentration-enhancement effect of the surfactant/water interface on the reactants.Then the volume within the solution available for reaction can be deduced and reasonable values are obtained. For the reaction between Ni(phen)2+ and PADA, other factors influence the kinetics. As a result the nature of the micelle surface where reaction occurs can be investigated. For the ligand PAN there is evidence that it can partition between more than two pseudo-phases, with a consequent reduction in the rate of complex formation. The dissociation rates of the complexes at the interfaces are increased by up to a factor of ten as compared with bulk water. The presence of aqueous micelles can enhance or retard chemical reaction rates by large factors and equilibrium constants are altered in a corresponding manner. These characteristics can be exploited using a range of organised surfactant systems, which include micelles, oil-in-water and water-in-oil microemulsions and vesicular systems.Potential applications are in the diverse fields of photochemical energy storage,' novel enzyme processes2 and solvent extraction of metal ions. Previous studies of the kinetics of complex-formation reactions between Ni2+(aq) ions and hydrophobic ligands in sodium dodecylsulphate (SDS) micellar solutions3~ * have indicated that both reactants are bound in the surface layer of the micelles. The large rate enhancements observed for complex formation are shown to be caused by the reactants being localised at the micelle surface and their concentrations being effectively enhanced. There are no other significant effects on the reaction kinetics.In this paper the kinetic studies are extended to include water-in-oil microemulsion systems, and the effect of strongly bound ligands (to the metal ion) on the rate of ternary complex formation in micellar media is investigated. Accurate data for the effect of a change in the reaction environment on the kinetics of the (unimolecular) dissociation of the metal complex are also obtained. A generalised kinetic model is developed which is based on reaction in, and partitioning between, two pseudo-phases. Appropriate derived kinetic parameters are then compared for the different reaction media. The reactions investigated were all between metal-complexing agents (ligands), covering a range of hydrophobicities, and divalent metal ions.Kinetic studies included complex formation and dissociation involving Ni2+(aq), Co2+(aq) and Zn2+(aq) with the azo-dye ligands pyridine-2-azo-p-phenol (PAP), pyridine-2-azo-p-dimethylaniline (PADA) and 1 -(pyridyl-2-azo)-2-naphthol (PAN). The effects of SDS micelles on rates 79 241 7 FAR 1241 8 EFFECT OF SURFACTANTS ON COMPLEX FORMATION of ternary complex formation/dissociation involving Ni(dien)2+, where dien = di- ethylene triamine and Ni(phen)2+, where phen = 1 , 10-phenanthroline, with the ligand PADA were also investigated. The micellar system used was SDS in water. The water-in-oil microemulsion system was prepared by adding water to solutions of sodium bis(2-ethylhexyl)sulphosuccinate (AOT) in n-heptane. The microemulsion system for the composition and temperature range employed consisted of thermodynamically stable and optically clear dispersions of spherical water droplets in a continuous heptane solvent.At the oil/water interface there is an interfacial monolayer of AOT. The radii of the water droplets depend primarily on R( = [H,O]/[AOI) and are in the range 1-10 nm. For low values of R the system is essentially mon~disperse.~ Considering the micellar and microemulsion dispersions as reaction media they are similar in nature : both consist of a hydrophobic (hydrocarbon) region, a hydrophilic (aqueous) region and a charged interface region formed using a negatively charged surfactant. However, the volume fractions of the solvent domains are very different in the two systems. In addition, the properties of the dispersed water in the microemulsion system may be different from those of bulk water since the droplets contain, typically, only a few thousand water molecules.For example, there may be structural changes in the smaller droplets because of (a) the small number of water molecules present and (6) the very high ion concentration (effectively > 1 mol dm-3 Na+) in the droplets. In any case the water activity would be expected to differ from that in bulk water. The kinetic studies reported in this paper enable a direct comparison to be made of micellar and microemulsion systems insofar as they influence chemical reactivity. EXPERIMENTAL PADA was obtained from Sigma; found/calculated: C 68.8/69.0, H 6.27/6.19, N 24.7/24.8. PAP was synthesised according to the method of Betteridge and John;6 found/calculated : C 65.8/66.3, H 4.5/4.5, N 21.0/21.1.PAN was obtained from Aldrich; found/calculated: C 71.7/72.3, H 4.56/4.42, N 16.4/16.9. Phen was obtained as the analytical reagent from Fisons. Mono( 1, 10-phenanthroline)nickel(II)nitrate was prepared as described by Steinhaus and Margerum' and was used immediately after preparation; found/calculated : C 36.5/33.1, H 2.5/3.7, N 14.2/12.9, Ni 14.2/13.5. SDS was a B.D.H. specially pure reagent and was used without further purification. AOT was a Fluka purum reagent. The batch of AOT used contained a very small amount of a weak acid impurity but this did not affect the results. n-Heptane was distilled over sodium metal, stored over type 4A molecular sieve and filtered before use.Water was deionised and doubly distilled, the second time from alkaline permanganate solution. Solutions containing metal ions were prepared from AR grade nitrate salts. Solutions of Ni(dien)2+ were prepared as described by Cobb and Hague.8 Kinetic measurements were made using a small-volume stopped-flow instrument with spectrophotometric detection. This instrument has been described previou~ly.~ For reactions occurring in times shorter than a few milliseconds, a conventional Joule-heating temperature- jump instrument (Messenlagen GmbH) was employed. For aqueous micellar solutions, no inert electrolyte was added since it was found that SDS (at concentrations > 0.05 mol dm-3) provided current-carrying capacity sufficient for a rapid discharge. In all cases, kinetic traces were indistinguishable from single exponentials. Values of observed first-order rate constants, kobs, were obtained by means of an analogue curve-matching procedure.Quoted values of kobs are the mean of between 5 and 10 values, and kobs is then known to better than & 5%. The pH of all aqueous and micellar solutions was controlled manually using small additions of HCl or NaOH solutions. The pH was measured by means of a Radiometer (model 26) pHP. D. I. FLETCHER AND B. H. ROBINSON 2419 meter incorporating a dual glass/calomel electrode (Radiometer type GK 2321C). In micellar solutions the pH values measured using a glass electrode were taken to be the values corresponding to the bulk-water region and not the aqueous region in the vicinity of the micelle surface.For SDS micellar solutions the ‘ pH’ in the surface region is known to be approximately two units lower than that of the bulk ~olution.~ In microemulsion solutions u.v.-vis. spectrophotometry, using a Cary 219 spectrophotometer, was employed to check that, at the pH of the kinetic experiment, the expected ligand and metal-ligand complex species were present. Where possible, pK, values were determined to ensure that no protonation (or deprotonation) of the reacting species had occurred. lo No attempt was made to control the ionic strength of the micellar solutions as addition of excess electrolyte might be expected to alter dramatically the properties of the aggregates, e.g. shape, surface potential, c.m.c. Since the ligands were uncharged the reactions are expected to be relatively insensitive to ionic strength (I) (< 10% change in rate for a change in I of 0.1 mol dm-3).KINETIC MODEL The model employed in the analysis of the kinetic data is essentially that developed by Berezin et uZ.ll An alternative but related approach has been developed by Romsted.12 In the Berezin model, the chemical reaction is assumed to occur in two pseudo-phases, one associated with the surfactant aggregates and the other with the bulk solvent. The reaction scheme for a reversible bimolecular association reaction is where the superscript S denotes a pseudo-phase associated with the surfactant and superscript B indicates the bulk solvent pseudo-phase. Since the reactions investigated in this work occur in the time range from 0.1 ms to 10 s, it is reasonable to assume that partitioning of the reacting species between the two pseudo-phases is rapid compared with the rate of chemical reaction.Hence partitioning can be described by the equilibrium parameters KA, KB and Kc. Photochemical studies13 have shown that partitioning of divalent metal ions between SDS micelles and water occurs on the ps-ns timescale, which implies that adsorption of metal ions onto the micelle surface is close to diffusion controlled. The exit rates of uncharged, aromatic, hydrophobic species from SDS micelles have also been measured by photophysical techniques.14 Values range from cu. lo4 to lo7 s-l and rate constants for ligands used in this study will have similar values. A kinetic process unique to water-in-oil microemulsion systems is solubilisate exchange.For water- soluble species, e.g. metal ions, this process occurs following droplet c~llision.~ The kinetics have been measured by two independent method^,^^ l5 and the process is fast on the timescale of these experiments. A further point to be considered in the kinetic analysis is the dynamics of the aqueous micellar system. In particular the ‘slow relaxation ’ associated with breakdown/reformation ofmicellesmight be acomplicating factor. However, the kinetics describing complex formation depend only on the total concentration of micellised surfactant, which does not change during the timescale of the experiment. Hence eqn (1) adequately represents the process. The appropriate concentration units applicable to reactions in colloidal dispersions has recently been discussed.ls For the case where reaction is slow on the timescale 79-22420 EFFECT OF SURFACTANTS ON COMPLEX FORMATION of transport processes it is simplest to use overall concentrations as proposed originally by Berezin.ll The equilibrium constant Kx for species X partitioning between the two pseudo- phases may be defined as K X = [xlS/[xlB (2) where C is the concentration of surfactant which contributes to the surfactant pseudo-phase volume.For aqueous micellar solutions this may be taken to be ([surfactant] -c.m.c.). For AOT microemulsions [AOT] may be used, which assumes that all the AOT is bound at the interface (this may not be the case as the phase boundaries for stability are approached).17 [XI, and [XI, are the concentrations of X in the micellar and bulk pseudo-phases, respectively (expressed as mol dmP3 of total solution).K , is related to a normally defined dimensionless distribution coefficient Px( = ([x],/cv}/([x]B/( 1 - CV)}). When the volume fraction of surfactant pseudo- phase is small Kx = Px V (3) where V is the volume contributed per mole of micellised surfactant to the micellar pseudo-phase. Eqn (2) is only likely to be valid when the surfactant concentration, C, is large compared with the reactant concentrations. For eqn (l), the observed second-order rate constant for formation of complex, kfbs, is given by The observed first-order rate constant kEbs for the dissociation of the complex, C, is given by A limiting case of eqn (4) and (5) is of particular interest. When both reactants and the product partition strongly to the surfactant pseudo-phase, reaction can only occur in that pseudo-phase, and then for pseudo-first-order conditions (i.e.[Ale % [B],) the observed first-order rate constant for complexation is given by - where For C > c.m.c. and for KA and KB % C-l, this reduces to Equations of this form have been used previously in the interpretation of kinetics in micellar s01ution.~ Eqn (8) predicts kobs -+ 00 as C --* 0 for KA C and KB C B 1. In practice a maximum in kobs is observed for C slightly greater than C . ~ . C . ~ ' Eqn (2)-(8) are general and can be applied to any dispersion consisting of two (or more) pseudo-phases. Pseudo-phases present in aqueous micellar solution are the bulk (aqueous) solvent, the non-polar hydrocarbon micellar core and the micellar surface region.Pseudo-phases in the w/o microemulsion may be the central aqueous core, the charged surfactant interfacial region and the bulk oil solvent.P. D . I. FLETCHER AND B. H. ROBINSON 242 1 In practice, surfactant aggregate solutions do not generally consist of sharply defined discrete regions for the purposes of chemical reaction. For example, the distribution of reacting metal ions, attracted to a negatively charged micellar surface, may be more realistically considered to form a double-layer region surrounding the charged surface.l0 Hence, in this simplified model, I/ is defined as an 'effective' pseuso-phase volume in which reaction occurs. Obviously, a detailed interpretation of I/ would be derived from consideration of the overlap region of the radial distribution profiles of the reactants.RESULTS AND DISCUSSION REACTION OF Ni2+(aq) WITH PAP RATE PARAMETERS AND MECHANISM IN WATER At the pH used, the reaction is PA? At pH 5.0 and 25.0 "C, k, is found to be (l.OkO.1) x lo3 dm3 mol-1 s-l and k, is 0.36 k 0.02 s-l. From the temperature dependence of the rate constants, AH1 = 51 k 3 kJ mol-l and AHL = 74f 3 kJ mol-l. The mechanism for complex formation involves the rapid formation of an outer-sphere complex [with equilibrium constant Kos (in dm3 mol-l)] followed by rate-limiting loss of a water molecule from the inner solvation shell of Ni2+(aq), resulting in formation of a monodentate complex. The rate constant for water loss is identified with that for solvent exchange, kex, as measured by n.m.r.methods. This mechanism is known as the Eigen-Tamm-Wilkins mechanism. There is a ring-closure step involved in forming the final complex, which is sufficiently fast (for the similar ligand PADA) that the forward rate is still largely determined by k,,.18 KO, may be calculated using the Fuoss equation19 and values of ca. 0.1 dm3 mol-l are obtained for an uncharged ligand. Then kf = Kosk,,. (10) Measured values of k,, and AHL, (determined from 170 n.m.r. studies) are in the ranges (2.7-4.4) x lo4 s-l (at 25 "C) and 45-51 kJ mol-l, respectively.20 The experi- mental values of k, and A H ] are therefore consistent with this mechanism. The slight discrepancy between the measured and calculated values of kf may be due to a small contribution from the ring-closure step to the overall rate of complex formation.The rate constant k, for PADA complexation (1.1 x lo3 dm3 mol-1 s-l at 25 "C) is very similar to that measured for PAP. IN SDS MICELLAR SOLUTION The apparent pK, values (as determined spectrophotometrically) of PAPH+ and the protonated NiPAP complex were increased by ca. 1.5 units in the presence of SDS micelles because of an enhanced local hydrogen ion concentration in the micelle surface region.l0 The kinetics were .therefore monitored at pH 7, as measured using a glass electrode, so that the reaction was as shown in eqn (9).2422 EFFECT OF SURFACTANTS ON COMPLEX FORMATION -3 -2 -1 log,, ([SDSI -c.m.c.) Fig. 1. Plot of log,, [(A - A,)/A,] against log,, ([SDS], -c.m.c.) for the ligand PAP.The solubilities of PAP in water and SDS solutions were measured in order to determine KPAP. Using eqn (2), KpA = [PAP], / [PAP] B( [ s D s ] T - c . m . c . ) X ( S - So)/So([sDs]~ -C.m.C.) (1 1) where S and So are ligand solubilities for a given concentration of [SDS], (> c.m.c.) and for bulk water, respectively. An excess of solid' PAP in SDS solutions of various concentrations was shaken for ca. 3 days at pH ca. 7. The absorbances of the resulting filtered solutions, measured at 351 nm, are proportional to the solubilities. Fig. 1 shows a plot of log,, (A-Ao)/Ao against log,,([SDS],-c.m.c.) from which we obtain KpAp = 900 300 dm3 mol-l. PAP shows no detectable solubility in n-heptane, which, together with the pK, shift, suggests that the ligand is preferentially located in a region close to the micelle surface and is accessible for reaction with water-soluble reagents.KpAp is sufficiently large that the approximation KpAp C $= 1 may be made for C > 1W2 mol dmP3 (ie. PAP is totally associated with the micelle surfactant pseudo-phase). The Ni2+(aq) ion is known to be strongly attracted by a coulombic interaction to the negatively charged SDS micellar surface, with a valuelg of KNi of ca. lo3 dm3 mol-l. The NiPAP2+ complex, being positively charged, is also expected to be strongly bound to the micelle surface. Therefore, for C > 1 x loP2 mol dm-3, both reactants and products are located exclusively in the micelle surface region andP. D. I. FLETCHER AND B.H. ROBINSON 2423 */ 40 20 0 0 0.01 0.02 [Ni2']~/([sDs]~ -C.m.C.) Fig. 2. Plot of kobs against mi2+]T/([SDS]T-c.m.c.) for the Ni2+(aq)/PAP reaction at 25.0 "C. Table 1. Kinetic parameters for the Ni2+/PAP reaction in water, aqueous micellar and water-in-oil microemulsion media (rate-constant data refer to 25 "C) k,B*/dm3 mol-l s-l medium or kZ*/s-l kz or k;**/s-l AHi/kJ mol-1 AHL/kJ mol-l water (1 .O f 0.1) x lo3* 0.36 f 0.02* 51f3 74f3 SDS micellar (2.0 f 0.25) x lo3** 0.96k 0.09** 48k3 91 f 5 water/AOT/heptane (3.6 & 0.2) x lo3** 1.2 f 1** 50+22 93 f 25 solution microemulsions eqn (8) is applicable. A plot of kobs against [Ni2+IT/C is shown in fig. 2. Small corrections to the c.m.c. were made to allow for the changing ionic strength.19 The linear plot gives a value of k,, where k, = k f / V (12) of (2.00k0.25) x lo3 s-l.The intercept of the plot is too small for an accurate value of kt to be determined. Hence it was measured directly by mixing a micellar2424 EFFECT OF SURFACTANTS ON COMPLEX FORMATION 01 I 1 0 5 10 lo3 [NiZ'l,,/[AOT], Fig. 3. Plot of kobs against [Ni2+],,/[AOT], for the Ni2+(aq)/PAP reaction at 25.0 "C. solution of the NiPAP2+ complex with a large excess of Co2+(aq).18 Enthalpies of activation for both complex formation and dissociation were found to be 48 f 3 and 91 _+ 5 kJ mol-l, respectively. All the derived kinetic parameters are shown in table 1. Coz+(aq) is known from density measurements to show a negligible volume change on binding to SDS micelles.21 The similarity of binding constants (Kg) for Ni2+(aq) and Zn2+(aq) suggest that this is also true for these ions, and so it is concluded that the metal-ion interaction with the micelle is purely electro~tatic.~~ The value of AHf for reaction, which is unchanged from that in bulk water, and the value obtained for k , (which is interpreted later) provide evidence that the mechanism of the reaction at the micelle surface is the same as in bulk water.IN AOT/WATER/n-HEPTANE REVERSED MICELLES (MICROEMULSIONS) PAP is only slightly soluble in water [So = (2.5k0.5) x mol dm-3 at 20 "C], insoluble in n-heptane but quite soluble in reversed micellar solutions. Therefore, PAP partitions strongly to the water/AOT interface region. The Ni2+(aq) ions are assumed to be totally contained within the water droplets.Preliminary calculations suggest that the metal ions are closely associated with the interface.22 Thus, eqn (8) is again applicable. The parameter C now refers to the concentration of AOT at the interface. This is difficult to estimate but it is thought that the percentage of AOT at the interface is large (> 90%) for small values of R (< 30) at temperatures removed from the upperP. D. 1. FLETCHER AND B. H. ROBINSON 2425 and lower temperature limits for microemulsion stability. l7 Spectrophotometric measurements confirmed that the reaction was as shown in eqn (9), at the effective ‘pH’ of the water droplets. A plot of kobs against [Ni2+]/[AOT], is shown in fig. 3, from which k, ( E @ / Y ) and k: were found to be (3.6f0.2) x lo3 and 1.2+ 1 s-l, respectively, at 25.0 “C.The enthalpies of activation for the forward and reverse reactions were found to be 50 _+ 2 and 93 f 25 kJ mol-l, respectively. The assumption that partitioning and exchange processes prior to chemical reaction are rapid was tested by mixing the reactants in different ways, but producing the same concentrations after mixing. Identical kinetic results were obtained in all cases, providing excellent support for this key assumption. (In a separate series of experiments, the exchange rate constant for divalent metal ions between microemulsion droplets has been measured directly;5 the process takes place on the ps-ms timescale for the droplet concentrations used in these experiments.) The kinetic data in table 1 permit a direct comparison of the two different types of surfactant assembly on the reaction.(The parameter k, = kS/V.) The parameter V essentially describes the contribution to the reaction volume of one mole of surfactant at the interface, so that CV represents the effective reaction volume per dm3 of total solution. Any difference between and k,B would reflect the changed environment in which the reaction occurs. Since there is no change in AHf for the reaction in the three media, it would appear that kf x k,B. If they are taken to be equal, Y is readily calculated. Values of Y of 0.5 and 0.28 dm3 mol-1 are obtained for micellised SDS and interfacial AOT, respectively. The area presented by each surfactant head-group at the interface is ca. 0.6 nm2 for both types of s~rfactant.~~’ 24 The ‘thickness’ of the volume element in which reaction occurs would then be ca.1.4 nm for SDS and 0.8 nm for AOT. Visualising the reaction pseudophase in both surfactant media as a spherical shell close to the charged interface, these values are entirely reasonable, which confirms the validity of the approach. Hence, the main conclusions are (i) k: z k,B, (ii) the simple pseudophase model and eqn (8) can successfully describe the kinetics in aqueous micellar and water-in-oil microemulsion systems and (iii) both surfactant media slightly enhance the rate constant for dissociation of the complex. Since this reaction is unimolecular, the comparison may be made directly with no assumptions. REACTION OF Ni2+(aq) WITH PADA This reaction has been studied previously in water25 and in SDS micellar sol~tions.~ Precise values for the dissociation rate constant were obtained in water and SDS micellar solutions by reaction of the complex with Co2+(aq) (as used for the ligand PAP).Results are shown in table 2. The forward rate constants kf and ks are very similar for PADA and PAP, suggesting the same mechanism is operative for both ligands. The structural formula for PADA is shown in (I) below, while that for PAN is given in reaction (15) (uide infra). IN AoT/WATER/n-HEPTANE MICROEMULSIONS Unlike PAP, PADA is soluble in n-heptane. Therefore, in the microemulsion system the PADA ligand will distribute into the heptane phase. Values of the solubility of PADA at 25.0f0.5 “C in the various media of interest are shown in table 3.2426 EFFECT OF SURFACTANTS ON COMPLEX FORMATION Table 2.Kinetic parameters for the Ni2+/PADA reaction in water, aqueous micellar and water-in-oil microemulsion media (rate-constant data refer to 25 "C) k:/dm3 mol-l s-l medium or kz*/s-' kz or kF*/s-l AHr/kJ mol-l AHl/kJ mol-1 water (1.2..+0.1) x lo3* 0.06+0.004* 55+4 87f3 SDS micellar (3.0k0.3) x lo3** 0.28+0.04** 5014 69+5 water/AOT/heptane (8 2) x lo3** 0.6 & 0.2** solution microemulsions - - Table 3. Solubility of PADA in various media at 25 "C medium solubility/ mol dm-3 water (1.5f0.2) x lo-* heptane (1.9 & 0.2) x 0.1 mol dm-3 AOT in heptane (3.0k0.2) x 0.1 mol dm-3 AOT/l.O mol dm-3 H,O in heptane (3.3 kO.2) x lod3 20 " rn 1 n 0 Ado 10 0 0 5 10 15 lo3 [N"] /[AOT], Fig. 4. Plot of kobs against [Ni2+)/[AOT], for the Ni2+(aq)/PADA reaction, at 25.0 "C.[AOT]/moldm-3, R: 0, 0.1, 10; V, 0.075, 10; 0, 0.05, 5; 0, 0.05, 10; A, 0.05, 13.9; ., 0.05, 2.78; m, 0.038, 10; A, 0.025, 10.P. D. I. FLETCHER AND B. H. ROBINSON 2427 0 0 10 20 30 40 [ AOT] T-1/dm3 mol-' Fig. 5. Plot of (KPP)-l against [AOTj,' for the Ni2+(aq)/PADA reaction at 25.0 "C. A plot of kobs against [Ni2+]/[AOT], is shown in fig. 4. In contrast to the situation with PAP, a number of straight lines is observed, each corresponding to a particular microemulsion composition. The gradients increase with increasing AOT concentration at fixed R, but vary only slightly with R at fixed [AOT]. Since PADA partitions rapidly into the n-heptane phase, we can define KpADA as Then an apparent value of k, ( = kipp) may be derived using eqn (7) and (12) kkpp = ks/ 1 + (KPADA[AOTIT)-~- (14) Hence a plot of (kgPP)-l against [AOT],l should be linear with intercept kgl and slope (kSKPADA)-l.This plot is shown in fig. 5, and at 25 "C ks = (8 f 2) x lo3 s-l and KpADA = 4.8 If: 1.3 dm3 mol-l. An approximate value of KPADA may be derived from the solubility data (table 3) using eqn (1 1). A value for KpADA of 6 f 2 dm3 mol -l is obtained at R = 0, increasing slightly as R is increased. This good agreement with the value from the kinetic data shows that the pseudo-phase kinetic treatment adequately describes the system when one of the reactants is rapidly partitioning into a second phase. Table 2 gives a summary of the kinetic data for the Ni2+/PADA reaction in the three media of interest.If we again take kf = k,B then V is 0.40 dm3 mol-l in SDS micelles and 0.15 dm3 mol-1 in AOT microemulsions. These values are remarkably similar to those derived for the Ni2+/PAP reaction. Also, as for the Ni2+/PAP reaction, k,(kt) values are increased in the surfactant-containing media relative to bulk water solutions. REACTION OF Co2+(aq) WITH PADA IN AQUEOUS SOLUTION The average value for the water-exchange rate constant for Co(H20)t+ is 2.4 x lo6 s-l, with a corresponding AHI, of 46 kJ mo1-1.20 Values of kf = 7.6 x lo4 dm3 mol-1 s-l and k, = 36 s-l have been measured using the temperature-jump method.25 Values of AH: = 43 kJ mol-l and AHL = 63 kJ mol-12428 EFFECT OF SURFACTANTS ON COMPLEX FORMATION (4 4 3 - v) 1 O Z 0 2 4 6 8 lo3 ([Coz+l,, + [PADAl,,)/([SDSl -c.m.c.) Fig.6. Plot ofk,,, (z-l) against ([Cozf],, + [PADA],,)/([SDS] -c.m.c.) for the Co2+(aq)/PADA reaction at (a) 19.6, (b) 24.6, (c) 34.6 and ( d ) 44.6 "C. have also been These results are again consistent with the Eigen-Tamm mechanism (k, = K,,k,,), but with some contribution to the overall rate from the ring-closure step. IN SDS MICELLAR SOLUTION Since the Co2+/PADA reaction is similar to the Ni2+/PADA reaction, the kinetics can be described by eqn (8), provided that partitioning is fast. The temperature-jump method was used to study the kinetics as rates are too fast for the stopped-flow method. The surfactant solutions had a sufficiently low resistance at [SDS], 2 0.05 mol dm-3 for the method to be applied successfully. To test for the absence of electric-field effects, the Ni2+/PADA reaction was also studied by the temperature-jump method in order to compare it with the stopped-flow method.Identical results were obtained. A plot of kobs against ([Co2+Ies + [PADA],,/[SDS]-c.m.c.) is shown in fig. 6 . The subscript ' eq' refers to equilibrium concentrations at the final temperature. (To obtain an acceptable relaxation amplitude, it was not possible to work under pseudo-first-order conditions). The derived kinetic parameters (at 25 "C) are k, = (1.8 k0.2) x lo5 s-l, k: = 310f50 s-l, AH!' = 30+4 kJ mol-l and AH&' = 47+6 kJ mol-l. Taking k,B = k:, the value of the V parameter (= k,B/k,) of 0.42 dm3 mol-1 is in agreement with results for the Ni2+(aq)/PAP and Ni2+(aq)/PADA reactions. Eqn (8) is found to be applicable, showing that partitioning is rapid on the (ca.100 s-l) time- scale of the reaction. However, the activation enthalpy does appear to be low when compared with the value in bulk water. The dissociation rate constant is again increased in the micellar medium. REACTION OF Ni(dien)2+ WITH PADA IN AQUEOUS SOLUTION The ligand dien (diethylenetriamine) is tridentate and complexes strongly with aquo-metal ions. Bound aliphatic nitrogen ligands often exert a labilising effect onP. D. I. FLETCHER AND B. H. ROBINSON 2429 0 2 4 [Ni (dien)"] /([SDSl -c.m.c. at (a) 19.6, (b) 24.6, (c) 34.6 and ( d ) 44.6 "C. Fig. 7. Plot of kobs against [Ni(dien)]++/([SDS] - c.m.c.) for the Ni(dien)2+/PADA reaction the remaining water molecules in the inner solvation shell of the metal ion.This effect is of importance in the mode of action of metallo-enzymes.s Since many enzymes are membrane bound, it is of interest to determine the effect of micelles on complexation reactions of this type. The water-exchange rate for Ni(H,0),dien2+ has been found to be 1.2 x lo6 s-l at 25 "C, with a corresponding AH:, of 23 kJ mo1-1.20 For the reaction of Ni(dien)2+ with PADA, the kinetic parameters in waters are k,B = 4.7 x lo4 dm3 molI1 s-l, k,B(corr) = 9.4 x lo4 mol-1 s-l, k t = 36 s-l, AH! = 43 kJ mot1 and AH?, = 65 kJ mol-l. k,(corr) is the value of kf after a statistical correction has been applied for the number of exchanging water molecules in the complex. This arises since only three out of six possible coordinating positions are occupied by water molecules. The value obtained for k,B then implies either a low value for KO, or an additional complication in the mechanism, such as rate-limiting ring closure.However, the value of k,B for re- action with NH, (where no ring-closure step is present) is k,B = 7.8 x lo4 dm3 mol-1 s-l, which is similar to that for PADA. Therefore it appears that an additional effect is involved; this may be steric hindrance or an orientational effect. IN SDS MICELLAR SOLUTION Kinetic measurements were obtained using the Joule-heating temperature-jump met hod. Plots of kobs against [Ni(dien)2+]T/([SDS]-c.m.c.) at various temperatures are shown in fig. 7. Linear plots are obtained, consistent with both reactant species being strongly bound to the micelles. Derived kinetic parameters are k, = 2.2 0.1 x lo4 s-l, kt = 220 & 30 s-l, AHs = 42 5 kJ mol-1 and AGs = 56 _+ 8 kJ mol-l.2430 EFFECT OF SURFACTANTS ON COMPLEX FORMATION The derived value of Y (taking kB = kfB) is 2.1 dm3 mot1, which is significantly higher than values obtained for the aquo-metal-ion reactions ( V x 0.5 dm3 mol-l).Since there is no reason for V to change, the assumption that kp = k,B must be invalid and so it is likely that the kinetics of this reaction are specifically modified in the micelle surface region. A likely explanation is that Ni(dien)2+ and PADA are mutually orientated in the micellar surface in a manner which is unfavourable for complexation; in particular the dien ligand may tend to penetrate into the hydrocarbon interior of the micelle.This steric effect, which would be absent for the symmetrical aquo-metal ion, would be reflected by a decrease in A S l . This interpretation is supported by the unchanged value of AH! for the reaction. As is generally observed, ki is significantly increased compared with the water value. REACTION OF Ni(phen)2+ WITH PADA IN AQUEOUS SOLUTION As for Ni(dien)2+, the strongly bound 1,lO-phenanthroline (phen) might be expected to modify the kinetics of the complexation reaction. For Ni(phen)2+ the sigma-electron donation of the nitrogen atoms is largely compensated by back-bonding to the aromatic system of the ligand so the labilising effect of the bound ligand on the water molecules is As a result, complex-formation rate constants for NH, with Ni(phen)2+ and Ni2+(aq) are similar (1.5 x lo3 and 2.8 x lo3 dm3 mol-l s-l, respectively).26 Rates of ternary complex formation and dissociation were measured for Ni(phen)2+ with PADA using the stopped-flow method.The derived kinetic parameters are k,B = 8.710.8 x lo4 dm3 mol-l s-l, k t = 3.7f0.3 s-l, AH? = 46+ 5 kJ mol-l and AHL = 78 f 8 kJ mol-l. Rate constants measured at 25 "C are in good agreement with those obtained by Cayley and M a r g e r ~ m ~ ~ (kf = 9.6 x lo4 dm3 mol-1 s-l and kb = 3.6 s-'). The much larger value for k, over that for the Ni(~hen)~+/NH, reaction is attributed to a hydrophobic stacking intera~tion~~ between the incoming PADA ligand and the bound phen ligand. This hypothesis is supported by the fact that the rate enhancement is drastically reduced in water + methanol mixtures.IN SDS MICELLAR SOLUTION If it is assumed that both reactants are strongly bound to the micelles in an essentially hydrophobic environment, then it is possible that the favourable stacking interaction would be absent and kf would be reduced. In addition, the orientational factor postulated for the Ni(dien)2+/PADA reaction might be expected to further reduce the micellar rate. The kinetics were determined using both the stopped-flow and temperature-jump methods. A plot of kobs against (mi(phen)2+],, + [PADA],)/([SDS] -c.m.c.) at 26.3 "C is shown in fig. 8. Again a linear plot is obtained, consistent with eqn (8). The derived kinetic parameters at 25 "C are k, = 2.3( kO.2) x lo4 s-l, @ = 3 4 kO.7) s-l and A m s = 54( _+ 7) kJ mol-l. The parameter V (when k,B = kf) is calculated to be 3.8 dm3 mol-l. As expected, this value is unreasonably large and is a factor of 10 larger than is found for reaction of Ni2+(aq).A more likely explanation is that V has a normal value and kf x 0.1 k,B. The micellar rate reduction is fairly small when it is expected that both stacking and orientation effects are acting to decrease the rate in the micellar solution. It is expected that there will be a significant effect due to the orientational effect, as observed for the Ni(dien)2+/PADA reaction. Therefore, the data suggest that the stacking interaction may persist to some extent in the micellar solution.P. D. I. FLETCHER AND B. H. ROBINSON 243 1 100 .-( 'rn % \ 5a 0 0 1 2 3 10 [Ni hen)^'],, + [PADAleq/([SDSl,-c.m.c.) Fig.8. Plot of kobs against [Ni(phen)]zG + [PADA],,/([SDS] -c.m.c.) for the Ni(phen)2+/PADA reaction at 26.3 "C. REACTION OF Ni2+(aq) AND Znz+(aq) WITH PAN IN AQUEOUS SOLUTION The ligand PAN (see fig. 1) is markedly different from the other ligands used in this work. An intramolecular hydrogen bond can form between the napthol OH group and an azo nitrogen atom as in eqn (15) (vide infra). This has been confirmed by infrared and n.m.r. spectroscopy.6 The existence of this intramolecular hydrogen bond may explain the much lower solubility of PAN in water as compared with PADA or PAP. Also, in contrast to PADA and PAP, PAN can bind to the metal ion through two nitrogen atoms and the oxygen of the napthol group to form a tridentate complex. This has been confirmed for the Ni2+(aq) complex by infrared spectroscopy.6 As a consequence, the stability constants of metal-ion complexes with PAN are very much larger than those for bidentate complexes like PADA and PAP.28 For this reason, PAN finds application in analytical chemistry as an extractant to effect analytical separations of various metal ions.29 Even though PAN is only slightly soluble in water, the complexation kinetics with Zn2+(aq) and Ni2+(aq) have been determined at 25 "C.Values of k, for Zn2+(aq) and Ni2+(aq) were found to be (5.4 f 0.2) x lo4 dm3 mol-1 s-' and 95 If: 3 dm3 mol-l s-l,2432 EFFECT OF SURFACTANTS ON COMPLEX FORMATION Fig. 9. Plot 2 0 0 0.25 0.5 0.75 [Ni"] /([ SDS] -c.m.c.) of kobs against wi(aq)l2+/([SDS] - c.m.c.) for the Ni(aq)2+/PAN at 25.0 "C.reaction respe~tively.~~ If KO, = kf/kex, then derived values of KO, are of the order of dm3 mol-l. Since such values are far too small for KO, it was concluded that the final ring-closure step is rate determining. This is not unexpected since the formation of the tridentate complex requires rupture of the internal hydrogen bond and rotation of the naphthol ring as follows +H* A similar conclusion regarding the mechanism of the Ni2+/PAN reaction was reached following a comprehensive kinetic study by Reeves et IN SDS MICELLAR SOLUTION A pH of 7.5 was chosen for the kinetic experiments. At this pH (equivalent to a pH at the micellar surface of 1-2 pH units lower) the concentrations of charged PAN and hydroxy-metal-ion species were negligible. Since PAN is virtually water-insoluble but quite soluble in SDS micellar solutions,P.D. I. FLETCHER AND B. H. ROBINSON 2433 it is clear that PAN associates strongly with micelles. The micellar kinetics should therefore be described by eqn (8) since, although ring-closure is rate limiting for the Ni2+/PAN reaction in water, the complex-formation kinetics still obey a simple bimolecular rate law. A plot of kobs (at 25 "C) against [Ni2+]/([SDS]-c.m.c.) is shown in fig. 9. Results at high SDS concentrations were obtained using a Unicam SP8000 spectrophotometer. Otherwise the stopped-flow method was used. The plot is linear at low molar ratios of Ni2+: micellised SDS but tends towards a limiting value for a molar ratio of ca. 0.3. The limiting slope at low molar ratios is identified with k, and the plateau region corresponds to saturation of the micelle surface with Ni2+(aq) ions.It might appear that the surface would be saturated at a molar ratio of 0.5 (since Ni2+ is divalent) but the presence of Na+ counter-ions may well account for the value observed. The value of k, is found to be 9.5 f 1 s-l, which is considerably smaller than was obtained with other ligands. Consequently the derived parameter V is found to be 10 f 1 dm3 mol-l, which is anomalously large. None of the factors suggested so far to explain kp < k,W apply in this situation and a further partitioning process of PAN into the micellar core is postulated to account for the slow micellar rate. When the PAN is in the micellar core it is considered that it would be inaccessible for reaction with Ni2+(aq) ions.A parameter KkAN is defined where KbAN = [PANmS]/[PANmC] and the superscripts ms and mc refer to the micellar surface and core, respectively. If this partitioning process is rapid on the timescale of the reaction, then eqn (8) must be modified as follows: @[ Ni 2+] kobs = V([SDS] - c.m.c.) [ 1 + (K;AN)-l] ' (The reverse rate constant may be neglected as the overall stability constant is large.) When PAN is predominantly located in the micellar core (i.e. K;PAN 6 l), eqn (17) becomes K;PAN ka[Ni2+] V([SDS] - c.m.c.) ' kobs = If a value of 0.5 dm3 mol-l is taken for V and it is assumed that the water loss rate is unchanged at the micelle surface as compared with bulk water, and also that there is no change in mechanism, then KbAN is calculated to be 0.05.The following experiment was performed to test the postulate that PAN partitions to the micellar core. Addition of organic, apolar material, e.g. dodecane, to the SDS solutions should ' swell' the micelles and increase partitioning of PAN to the micellar core pseudo-phase. This would result in a decrease of kobs. An attempt was made to achieve this with dodecane as additive, but it was not sufficiently soluble in the micellar solutions. However, toluene was soluble. Table 3 and fig. 10 show the results obtained. A linear reduction in kobs with increasing amounts of toluene is noted. The same experiment performed with PADA instead of PAN showed no decrease in kobs, confirming that PADA is located exclusively at the micelle/water interface when associated with SDS micelles. In contrast, PAN is only available for reaction for 5% of the time when it is bound to SDS micelles.IN AOT/WATER/HEPTANE MICROEMULSIONS were investigated using the stopped-flow method. The kinetics of reaction of both Ni2+(aq) and Zn2+(aq) with PAN in microemulsions PAN was found to have a solubility in heptane of (3.3 f 0.3) x lov3 mol dm-3. It is2434 EFFECT OF SURFACTANTS ON COMPLEX FORMATION 6o t I I I 1 0 0.05 0.1 0.15 % v/v toluene Fig. 10. Variation of the Ni2+/PAN reaction rate in SDS solutions with added toluene at 25.0 "C ([SDS] = 0.02 mol dm-3). D, Data for PADA (see text). expected, therefore, to partition strongly to the bulk heptane pseudo-phase. We can define where the subscripts S and H indicate pseudo-phases associated with the surfactant and bulk heptane, respectively.Assuming the metal ions are located exclusively in the surfactant/water interface region over the R range studied and reaction occurs at this location, then the kinetics are described by a modified form of eqn (8): KPAN = [PANIs/[PANIH [AOTl, (19) In the case of very weak partitioning of PAN to the interface region (i.e. KpAN[AOT]T 4 l), eqn (20) reduces to and hence kobs varies linearly with metal-ion concentration and is independent of AOT concentration. Plots of kobs against [M2+] for Zn2+(aq) and Ni2+(aq) are shown in fig. 11 and 12, respectively. The gradients are (5.9 & 0.3) x lo3 and 30 f 1.5 dm3 mol-1 s-l. If kf is taken to be equal to k r and a reasonable value of V is assumed (we have take V to be 0.22 dm3mol-l, which is the mean of VpAp = 0.28 dm3mol and = 0.15 dm3 mol-l), then KPAN may be calculated for both systems.Values of 2.4 x dm3 mol-l are found for the Zn2+ and Ni2+ reactions. This general agreement is reasonable and indicates that PAN partitions very strongly away from the surfactant/water interface where reaction takes place. Solubility measurements were performed to check independently the partitioning hypothesis. The solubility of PAN in heptane in the presence of AOT and water is and 6.9 xP. D. I. FLETCHER AND B. H. ROBINSON 2435 6 - 4 'Y, Y" .I P 2 0 0 5 10 [Zn2+(aq)] / l o 4 mol dm-j Fig. 11. Plot of kobs against [Zn(aq)] for the Zn2+/PAN reaction at 25 "C. 0 5 10 [ Ni(aq)] '+/ 1 O4 mol dm" Fig. 12. Plot of kobs against [Ni(aq)12+ for the Ni2+/PAN reaction at 25 "C.2436 EFFECT OF SURFACTANTS ON COMPLEX FORMATION 0 0.1 0.2 0.3 [AOT]/mol dm'3 Fig.13. PAN solubility in various microemulsions. shown in fig. 13. A slight increase in solubility is observed. KPAN is calculated from these solubility data and is of the order of 2 dm3 mol-l. There is a large discrepancy between the two determinations of KPAN which may be rationalised by the following argument. Although PAN may partition to the interfacial region, it may not be accessible for reaction with metal ions. PAN may partition to the surfactant/heptane interface region (which would be included in the solubility estimation of KPAN) but it would have to move further (to the surfactant/water interface region) before it could react with M2+ ions.The value of KPAN measured kinetically is thus the product of two partition coefficients, and it would appear that when PAN is associated with AOT in the microemulsion system it is only available for reaction with M2+ for ca. 1-3% of the time. Hence both micellar and microemulsion surfactant assemblies significantly reduce the rate of complexation by an essentially similar mechanism. This type of process may be of importance in metal-ion extraction processes in which surfactants are employed. CONCLUSIONS The kinetics of a series of metal-ion/ligand exchange reactions have been studied in both aqueous micellar and water-in-oil microemulsion media. The kinetics of complex formation involving aquo-metal ions and simple ligands are well described in both types of media using equations derived from a simple pseudo-phase model.The large observed rate enhancements are due to localised concentration enhancements of the reactants in the volume element of solution in which the reaction occurs. If the assumption is made that rate effects are due entirely to localised concentration enhancements, then the volume of the reaction pseudo-phase in the solution can be deduced. Reasonable values are obtained in all cases where this is possible. In the limiting case of very favourable partitioning to the pseudo-phase where the reaction occurs (as in the hTi2+/PAP reaction), the activation enthalpy is unaltered from its value in bulk water and k,B = kp. Distribution of reactants between more than two pseudo-phases (as in reactions of PAN) requires that the kinetic equations be modified and, in general, smaller rate enhancements or even rate retardations are observed. Secondary rate effects are observed for reactions involving the formation of ternaryP.D. I. FLETCHER AND B. H. ROBINNSON 2437 complexes. Rates are reduced because of unfavourable mutual orientation of reactants at the surfactant/water interface. The Ni(phen)2+/PADA reaction has an unusually high rate constant in water due to a favourable stacking interaction. This interaction is still present in the micelle reaction suggesting that the reactants experience an ‘aqueous’ environment at the micelle surface. The dissociation rate constants may be compared directly in different media since they are unimolecular processes.Rate enhancements of up to a factor of 10 are observed for the interface reaction as compared with bulk water. The results may be explained in terms of stabilisation of the transition state by electric-field effects at the interface. We thank the S.E.R.C. and Shell (Thornton Research Centre) for support of this work by a CASE award (to P.D.I.F.). We also thank Dr George Brunton (T.R.C.) for useful discussions. M. Grltzel, Ber. Bunsenges. Phys. Chem., 1980,84,981. K. Martinek, A. N. Semanov and 1. Berezin, Biochim. Biophys. Acta, 1981,658.76. A. D. James and B. H. Robinson, J. Chem. Soc., Faraday Trans. I , 1978,74, 10. V. C. Reinsborough and B. H. Robinson, J. Chem. Soc., Faraday Trans. I , 1979,75, 2395. P. D. I. 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