A Convenient Stopped-Flow Experiment Demonstrating the Influence of Micelles on Reaction Kinetics

Vincent C. Reinsborough' Mount Allison University, Sackville, N.B., Canada

Brian H. Robinson University of Kent, Canterbury. U.K.

Fast reaction techniques are discussed now in most stan- dard texthooks in physical chemistry, hut demonstrations in these techniques suitable for the undergraduate laboratory are few. We describe in this article a kinetic system which we have found to be ideal for study by the stoppedflow technique. Good results can he ohtained easily with a relatively simple experimental arrangement using optical detection.

Recently, there has been an increased interest in the in- fluence of micelles and other tvoes of colloidal svstems on . . reaction kinetics particularly as aids to synthesis and reaction control. The reaction we describe aives dramatic rate en- - hancements in micellar solution and is amenable to a partic- ularly simple quantitative treatment. The results clearly demonstrate that the micelles promote this chemical reactivity hy increasing the local reactant concentrations. An appro- priate kinetic analysis for surface reactions in micellar solution is developed and shown to offer a reasonable explanation. The powerful link hetween kinetics and mechanism which is often only poorly demonstrated thus comes across strongly to the student. Furthermore, the system described in this article is capahle of further development and some suggested avenues to explore are offered at the end.

Nature of Micelles Molecules or ions which possess both water-insoluble (hy-

dro~hohic) and water-soluhle (hydrophilic) groups are sur- faceactive and are known variwdy as surfactants, soaps, detergents, and tensides. In aqueous solution above a certain concentration, known as the critical micelle concentration or cmr, these species can aggregate to form micelles. Such a micelle is composed typically of about 100 monomer surfac- tant units and is rouehlv soherical in shaoe. A schematic di- . . agram of the micelle'fnrmed hy the surfaitant sodium dode- cylsulfate (SDS) is shown in Figure 1A. Recent reviews on the structure and properties of micelles have been puhlished by Fisher and Oakenfull (1). Murkeriee (2), and Menger ( 3 ) . I t has been shown recently that aqueous micelles have a "dy- namic" structure such that monomers are exdhanging ex- tremely rnpidl? a,ith micrllrz in the mia.rosrc,md time ranyr and n>iwllvs ;arc d~wntecraring and r r l m n ~ n y ) In the rnil- lisecond to second time [ange 14). The extent of penetration of water into the micellar core ( 5 ) and the location of soluhi- lized molecules within the micelles (6) are still controversial topics.

Micelles can form also in non-aqueous solvents of low per- mittivity such as benzene and n-heptane. The resulting ag- gregate structures are known as reversed micelles (Fig. 1B). When small amounts of water are added to the system, this is soluhilized within the charged core, and water-in-oil mi- croemulsions are formed.

Dramatic "catalysis" effects are often observed in both aqueous and non-aqueous micellar solutions (7). This is of interest hecause it has been suggested that these micellar

' To whom correspondence should be addressed.

586 Journal of Chemical Education

Figure 1. a, Micells formed in aqueous solution from an anionic surfactant 8.g. ~Ddium decyisulfate. b, Reversed micelle famed from a doubly-chained anionic surfactant e g . Aerosol OT.

Figure 2. Complex formed between Ni,.,fi and PAOA.

systems can mimic reaction processes in enzymes and mem- branes. Berezin (8) and Romsted (9) have descrihed a general theory of reactivity based on simultaneous reaction in the aqueous and micellar "phases" assuming fast rommunicarim oireartants between the tu~,~"ohaae*." In this article we de- velop a more specific treatment which is applicable to reac- tions occurring exclusively in the charged micelle surface re- . gion.

In principle a range of fundamental processes might he selected for study and two such reactions have been reported previously inTHlS JOURNAL (10)(11). The reaction studied here is that between Ni(.q,2+ and the azo dye ligand pyri- dine-2-azo-p-dimethylaniline or PADA.(Fig. 2). Most divalent metal aquo-ions react too rapidly to he studied by stopped- flow methods, but Nic,,f2+ reacts more slowly. The progress of the reaction is convenientlv monitored soectroohotomet- rically using PADA as the ligand. Furthermore, tile mecha- nism of this reaction in aaueous solution is well understood (12)(13)(14).

In water, the first step in the mechanism is the diffusion- controlled formation of an outer-sphere complex I in which the first hydration shell of the ion is intact. Since the overall rate of complex formation does not depend on the nature of the ligand when the ligands have the same charge, the rate-determining step is assumed to he the loss of a first water molecule adjacent to the Ni2+ ion to form the complex 11. The rate constant for this process (k.,) can also he deter- mined independently from NMR measurements. The kinetic scheme is therefore

Since I is present only a t very low concentrations this scheme can be simplified to

NiZ+ + L A NiLZt (11)

Under pseudo-first-order conditions ([Ni2+] >> [L]), -d[L]/dt = k,b,[L] and, we have

k,~,,(s-') = k l [ N i Z + ] ~ + kLl (1)

in which [ N i 2 + ] ~ (mol dm-" is the total (initial) concentration of Ni(,,I2+ in solution and kl (dm" mol-' sSL) = KOshex.

When micelles which have a negatively charged surface (as for SDSI are nresent. the reactants Ni2+ and L will no loneer he distributed homogeneously throughout the solution prior to reaction since both species will interact strongly with the micelles. Ni(J+ is attracted so strongly to the micelle surface region that for surfactant concentrations greater than twice the crnc over 90% of the Ni2+ ions are located within 1 nm of the micelle surface (15). Similarlv from solr~bilitv measure- ments in aqueous and micellar solutions, it can be shown that PADA is also partitioned strongly into the micelles probably in a more hydrophobic environment than the Ni2+ hut still close to the micelle-water interface (16). (Even molecules like benzene are thought to be solubilized close to the micelle surface.) The Ni2+-PADA complexation reaction in SDS so- lutions will, therefore, occur exclusively in the micelle surface region and should then be visualized as a surface phenomenon with surface concentration units being used. The surface concentration of the excess reactant, [Ni'"]s, in moles per m2 of micelle surface is calculated easily since all the NilC is bound for [SDS] > 2 crnc and the ionic part (head-group) of each micellar surfactant molecule is in contact with water, so that

where C(mol dm-" is the total surfactant concentration, A is the area per head group of the surfactant molecule, and NAV is Avoeadro's Number. (It should be noted that the crnc of SDS iidependent on the added Ni,.,," concentration; for examole. when INir..Pl = mo1 dm-3. the crnc of SDS is rediceh from k x ' - f~-~rnol dm-" in pure water to 4 x lo-" mol dm-"16). I t is assumed also that the monomer surfactant roncentrati'm in a mirnllnr sdltt~tm is p v e n hy I hewnc valur. While this is not strirtlv true, i t i*asatirfart,rs nppn,ximntim . .. in eqns. (2) and (3).)

Then by analogy with eqn. (2), we obtain for the surface reaction for C > 2 cmc:

cmc 2cmc C Figure 3. Micellar catalysis. ChanF of the rate enhancement with surfactant concentration (C).

where kl'(m2 mol-I S-I) is a second-order surface rate con- stant and h-l'(S-l) is the first-order rate constant for the micellar surface dissociation of NiL2+ com~lex.

The form of eqn. (3) suggests the behaviur shown below (Fie. 31 when the micelle concentration is varied a t fixed Nil+

L concentrations. I t should be noted that the rate of complex formation decreases as C increases and, that in the region crnc < C < 2 cmc, the analysis is more complex since some Nit,,12+ and PADA will be present in the aqueous phase 117) \ - . ,.

We predict from eqn. (3) that a linear plot of h,,b, against [Ni'+IT/(C - cmc) should he ohtained. A reasonable estimate for A is 60 X 10-2"m2 for SDS micelles (18) from which k i c a n he readily evaluated.

now availahle commercially for teaching purposes. The constructiun of such an instrument has been described previously in THIS JOIIR- NAI. (191. and a stopped~flow instrument with conductivity detection has been described also (20). A particular advantage of the Ni2+/ PADA reaction is the prunounred color change on complexation ( A M A x for PADA is 470 nm: AMAX for the complex is 540 nml so that it is not necessary to use a high resolution grating monochromator: a cheap intprference or color filter is perfectly adequate. A low power pnljeetor lamp is ideal as the light source and stabilized voltage supplies for these lamps are available cheaply. (We use WOTAN RV, 50W pre-focus hulhs). Hydrated nickel nitrate, PADA, and SDS are all rendilv availahle commerciallv and reasonahlv orieed. Hence the

tails. Values of k l and kl' can he obtained in an afternoon's work, or i t

may he desired to extend the study in the form of a longer term project. To familiarize the students with the operation of the stopped-flow instrument, we recommend, if time permits, that the kinetics of the Ni"t/PADA reaction he examined first in the ahsence of SDS. Suitable concentrations would he to mix Nil,,12+ solutions over the range 2 X IOP to 5 X 10F3mol dm-Jwith PADA solutions a t 1 X 10-"01 dm-:'. (Note that the final concentrationsare half the pre-mixed ones.) The pH of the sdutians hefhre mixing should be adjusted to pH - 7 to avoid protonation of the ligand (pK. of PADAHt - 4.5) and hvdrolvsis of Nii..iz+ laK. - 9.5) which un-

about 0.1 s-' (24). Reactions in the micellar solutions can be studied by variation of

the NiZ+ concentratian as above o r by variation of the SDS concen- tration keeping in either instance the PADA concentration constant. The pH should he adjusted to - 8.2 since the pK.'s of PADAHt and Nii.,{'+ areshifted to higher values on hinding 10 the micelle (241. The SDS concentration after miring should he kept within the 1 0 F - 10-' mol dm-," range. A value of /<I' uf 1.1 X 10" m' mul-' s-' has heen obtained previously a t 298.2 K (24).

It would be of obvious interest to calculate k., values for the reac- tion occurring an the micelle surface (k,.') and fur the reaction oc- curring in aqueoussalution with no mieelle present. Fmm k,, = k t /K, , (see eqn. ( I ) ) , it is easily shown that k., - k,,' within a factor of 2 (K, = +a Nnv $and K,,,' = 4 a Nav a 2 E where E accounts for coulomhic interaction and has a value -0.1) (lfil. Important to the argument is that the rate-determining step in both situations is the loss of a water molecule. It has been shown that the rateof complex formation in hoth situations is independentof the nature of the ligandso thisassump- tion is a reasonable one.

Conclusion

Two maior conclusions are, therefore, possible from this experiment: the rate constant for water loss from the metal ion a t the micelle surface is similar to that in aqueous solution in the absence of micelles and, secondly, the "catalytic" effect of the micelles upon the rate enhancement stems largely from the preferential adsorption of hoth of the reactants to the surface region of the micelle.

Volume 58 Number 7 July 1981 587

These results raise manv interesting issues. For example, are the micelles acting as true catalysts? Note that the extent of product fixmation, i.e. the equilibrium constant, and the forbard rate constants have heen changed greatly in the presence of micelles. Calculation of the activation energies for each situation reveals that there has heen no lowering of AH', the usual situation for catalysis. Therefore, the micelles must, he affecting the rate of reaction hy an entropic effect.

Many other avenues exist for further study in this particular system. Variation of temperature, of ligand, of surfactant (in chain length or head group), and of added ions are just a few of'the possibilities open to the enterprising student.

These areas are unexplnred and, wit.h an afternoon or two spent in mastering the basic technique, the student can he doing original work.

Literature Cited

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Y w k . 1977. \',>I. 2. TI. MI9 I lol ('wrorc,, l; rnnd Smlth,.J ti. .I. ?HEM. Enll?..52,6X9 11976!. i l 1 1 Cnrsnri,. 1L.l rHEM ELWC.6ll.57S 11!17:11.

119iX!. 1181 S W m l>, ,J ~ ' d l m d I n # ~ ~ r / o c ~ c ,Sc8 , 17, 47:! 119741. , I :BI MII.PIII.H . . I . I .HLM.EI~~I~. .s~. ~ m i ~ s m , . 12111 P11t.1. R. (.. Atkmxm. i;.. and HIIF. K . I . .I. l'HPM. KnI1T..II,R*i 119701. i 2 l l Srh~lly, Z A and liyrm&E. M . . l I'HI'Y. EI~I 'C. .4X,E!I I I I 'Jill. i??! ?ahlin. E. F.. "Fast Kear l lmr #n Ri lut~~~n; Hlaukurll*. OxPlrd. 1104. im t iurtln. K.. " ~ ~ f h d ~ in ~ ~ ~ ~ m ~ ~ l ~ ~ g y . vill XVI. ~ a s t R o a a m a . " cade emir PIWS, New

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588 Journal of Chemical Education