J. Chem. SOC., Faraday Trans. I , 1987, 83, 985-1006

The Kinetics of Solubilisate Exchange between Water Droplets of a Water-in-oil Microemulsion

Paul D. I. FletcherJ Andrew M. Howet and Brian H. Robinson9 Chemical Laboratory, University of Kent, Canterbury, Kent CT2 7NH

Exchange rates of aqueous solubilisates between water droplets in a water-in-oil microemulsion stabilised by sodium bis(2-ethyl-hexyl) sulpho- succinate (AOT) have been measured as a function of droplet size, tempera- ture and the chain length of the oil. The effects of additives (e.g. alcohols) on the exchange kinetics have also been investigated. Exchange rates were measured using very fast chemical reactions as indicators for exchange. Three types of reaction were investigated : proton transfer, metal-ligand complexation and electron transfer. Similar exchange rates were found for all three reactions. The indicator reactions involve the exchange of reactant ions of differing size and charge type; exchange rates were, however, independent of the ion transferred, but dependent on droplet size and temperature. For AOT as dispersant, exchange occurs with a second-order rate constant of lo6-los dm3 rno1-I s-l, two to four orders of magnitude slower than the droplet encounter rate as predicted from simple diffusion theory. The apparent activation enthalpy is high (and increases with droplet size) but is largely compensated by a positive activation entropy. Exchange, on balance, is a relatively facile process which typically takes place on a millisecond timescale (depending on the droplet concentration).

The exchange mechanism involves transient water droplet coalescence and separation. This is the dynamic process whereby the equilibrium properties of the microemulsion, e.g. droplet size and polydispersity, are maintained. There is a correlation between the exchange rate constants and the stability of the single-phase microemulsion. This relationship between the kinetic and equilibrium properties is discussed in terms of the ‘natural curvature’ of the surfactant interface and inter-droplet interactions.

Much of the interest in microemulsions is concerned with their unique properties as a reaction medium. Reaction rates and equilibria may be altered by several orders of magnitude as compared with the corresponding values in homogeneous solution. 1-3 In particular, the use of microemulsion water droplets as a novel environment for enzyme-catalysed reactions has attracted much interest4 and the potential for controlled and selective synthesis is now being ~ealised.~-’ For reaction in a water-in-oil micro- emulsion involving reactant species totally confined within the dispersed water droplets, a necessary step prior to their chemical reaction is transfer of reactants into the same droplet. When chemical reaction is fast (close to diffusion-controlled), the overall reaction rate is likely to be controlled by the rate of inter-droplet transfer of reacting species (so-called ‘ solubilisate exchange ’). In this paper data for exchange kinetics involving a range of reactant ions in water droplets stabilised by sodium bis(2-ethyl-hexyl) sulphosuccinate (AOT) in hydrocarbon solvents are reported. The inter-droplet transfer rate is studied as a function of droplet size and temperature. In addition, the hydrocarbon oil (dispersion medium) has been systematically varied, and the effects of surface-active additives have been studied.

t Present address: Department of Chemistry, University of Hull, Hull HU6 7RX. 1 Present address: AFRC Food Research Institute, Colney Lane, Norwich NR4 7UA. 4 Present address: School of Chemical Sciences, University of East Anglia, Norwich NR4 7TJ.

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986 Kinetics of Solubilisate Exchange The AOT-oil-water microemulsion system is particularly suitable for systematic

investigation since no cosurfactant is required. AOT itself forms a reverse hexagonal liquid-crystalline phase. With water and oil, an extensive L2 phase is present. The microemulsions are thermodynamically stable (they form spontaneously and droplet size is independent of variations in preparation method). Relatively large amounts of water (ca. 100 mol of water per mol of AOT) may be solubilised in n-heptane at room temperature. This figure does not change significantly with AOT concentration over the range 0.01-0.5 mol dm-3. Water is dispersed in the form of microdroplets; the sizes have been measured using a variety of techniques including ultracentrifugation,8 photon correlation spectroscopy (PCS),g~ lo small-angle neutron scattering (SANS),11-15 membrane diffusion,16 fluorescence dep~larisationl~ and time-resolved fluoresence quenching.ls The thickness of the AOT interfacial layer has been determined from SANS data to be 0.9 nm, which indicates only slight penetration of the AOT alkyl tail region by the alkane s01vent.l~ Shape fluctuations may occur, but the assumption of sphericity gives consistent results by different experimental techniques. Water droplet radii can be systematically varied from 0 to 20 nm, being proportional to the molar ratio water : AOT (R). Altering the amount of water and AOT but keeping R constant changes propor- tionally the droplet concentration but not droplet size. The droplet size may be calculated to a first approximation using the equation:1°

(1) where

r (hydrodynamic radius)/nm = 0.175R+ 1.5

R = [H,O]/[AOT]. Single-phase microemulsions are stable over a restricted temperature range which

depends on composition. At high R values the range is only a few degrees, whereas low R value systems are much more stable.12 The temperature corresponding to the maximum water uptake at constant [AOT] may be equated with the phase inversion temperature (p.i.t.),,O The value of the p i t . is dependent upon the oil used as continuous solvent, the presence of surface-active additives and the ionic strength of the aqueous component.

For the single-phase AOT microemulsion systems, decreasing the temperature below the lower temperature boundary produces a reduced water content microemulsion phase (i.e. lower R value) and a conjugate (almost pure) water phase. Increasing the temperature beyond the upper temperature stability limit does not produce separation of an 0-W microemulsion and a conjugate oil phase as observed for mixtures containing comparable volumes of oil and water.20 The W-0 microemulsion phases contain only small amounts of water, which leads to a more complex phase separation. For systems containing short-chain alkanes (e.g. heptane) phase separation produces a liquid- crystalline phase (probably lamellar in structure containing AOT and water) with a conjugate oil phase. For higher alkanes ‘critical’ phase separation into two W-0 microemulsion phases of different droplet concentrations is observed. This phase separation is driven by increasingly attractive inter-droplet interactions as the phase boundary is approached. l4 The phase separation sequence (i.e. water + AOT-oil below the p.i.t. and oil + AOT-water above the p.i. t.) reflects increasing hydrophobicity of AOT as the temperature is decreased.

In aqueous micellar solutions, surfactant molecules exchange rapidly between micelles and bulk aqueous solution and the micelles disintegrate/reform over a longer timescale.21 In contrast, very little is known about the dynamic processes which occur in water-in-oil microemulsions. Eicke et al. demonstrated exchange of hydrophilic solutes between droplets by a droplet collision mechanism on a timescale shorter than a few seconds22 and this was later confirmed.8 Atik and Thomas23 and Fletcher and Robinson24 measured the second-order rate constant for exchange in AOT microemulsions and obtained rate constants two to three orders of magnitude less than the diffusion-controlled limiting value. A mechanism for solute exchange was postulated whereby, in an initial step, two

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P. D. I. Fletcher, A . M . Howe and B. H. Robinson 987 droplets collide to form an encounter pair. In a small fraction of the encounters, droplets fuse to form a short-lived droplet dimer which then decoalesces. The two droplets then separate with concomitant randomisation of solute occupancy together with surfactant and water.24 Such a mechanism forms a basis for understanding the mechanism whereby microemulsions spontaneously form and break. (A microemulsion system that does not exchange cannot form spontaneously.) Equilibrium properties such as particle size and polydispersity are maintained in rapid dynamic equilibrium via this mechanism, which is therefore expected to be intimately related to the phase behaviour of the system. In view of the fundamental nature of exchange in determining microemulsion properties, this paper is concerned with a systematic investigation of the kinetics of the inter-droplet exchange process and its relation to phase behaviour.

Experiment a1

AOT (Sigma) (supplied as dioctyl sulphosuccinate, sodium salt) was used without further purification. AOT is a di-ester and some samples (from other suppliers) contain hydrolysis Batches used in this work were titrated using an acid-base indicator25 and were found to contain negligible acidic impurities. Interfacial tension measurements with Sigma AOT show it to be free of an impurity (presumably the alcohol hydrolysis product) which causes a minimum in interfacial tension vs. surfactant concentration plots for other AOT samples.? n-Heptane (Fison’s SLR grade) was distilled over sodium metal, stored over type 4A molecular sieve and filtered before use. Water was de-ionised and doubly distilled. Murexide (ammonium purpurate) was a B.D.H. laboratory reagent. Purity was checked spectrophotometrically (extinction coefficient at 522 nm = 1.4 x lo4 dm3 mol-1 cm-l).* Murexide solutions were used im- mediately after preparation since they fade slowly. Decomposition is accelerated in acidic solutions and provides a further check on acid impurity levels. 4-Nitrophenol-2- sulphonate (disodium salt) (NPSA) was obtained from the Alfred Bader Library of Rare Chemicals (Aldrich). Ammonium hexachloroiridate(1v) (99.9 % ) was obtained from Aldrich and potassium ferrocyanide from Fisons. Bis-bipyridyl bis-cyanoiron(I1) was generously supplied by Dr J. Holzwarth (Fritz Haber Institute, Berlin). All other reagents were of the highest grade available.

U.v.-visible absorption spectra were recorded using a Cary 219 instrument. The sample chamber was thermostatted to within 0.1 K of the desired temperature. Kinetic measurements were made using a small-volume stopped-flow instrument designed and built in this laboratory. The dead time was 1 to 2ms.19 Some kinetic measurements involving electron-transfer reagents were obtained using the continuous-flow method with integrating observation (CFIO). This equipment was used at the Fritz-Haber Institute, Berlin and was made available to us by Dr J. F. Holzwarth. The technique is valuable for kinetic studies in the sub-millisecond time range.2s

Microemulsion-phase stability maps were determined as follows : mixtures of AOT, oil and water in which the R value was changed systematically, were contained in tightly stoppered flasks, which were stored with occasional shaking in thermostatted baths for several days. Solutions which were, by visual inspection, transparent or faintly bluish (at high R values), but which showed no sign of sedimentation, were taken to be one-phase microemulsions.

Theory of Kinetic Measurements Solubilisate exchange rates were measured using fast chemical reactions where the product formation rate is limited by the inter-droplet exchange rate. To use the observed kinetics of the reaction to measure the exchange rate the following criteria must be

t Interfacial tensions were measured by Dr J. Mead, University of Hull.

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988 Kinetics of Solubilisate Exchange obeyed. First, reactant species must be confined within the water droplets to exclude the possibility of passage through the continuous oil solvent. This is ensured by the use of hydrophilic, charged reagents which show no solubility in the oil. Secondly, solubilisate exchange must be the rate-determining step of the reaction. This may be ensured by (i) the use of intrinsically fast reactions such that kchem is close to being diffusion-controlled and (ii) by decreasing the solubilisate exchange rate by lowering the concentration of water droplets. For reactants A and B confined within the water droplets the reaction scheme may be described by the limiting cases (a) and (6).

Scheme (a). Reaction in dimer

Scheme (b). No reaction in dimer

'Ikchem

0 The circles around the species symbols indicate that the species are located within the water droplets. The larger circles represent a short-lived droplet dimer of lifetime 1 /kdiss. ke, is the second-order rate constant for transfer of species A and B into the same droplet and kchem is the rate constant for chemical reaction [expressed as a second-order rate constant (dm3 of water mol-l s-l)]. When conditions (i) and (ii) above pertain, then d [ o ] / d t = k[@][@] where k = k,, in units of dm3 (of total solution) mol-1 s-l.

The essential difference between scheme (a) and scheme (b) is the following. If chemical reaction occurs as in scheme (a), then

0*7/kdiss ' 2/(kchem [Alwd) (2) where [AIwd is the aqueous concentration of one molecule of A inside a single droplet (i.e. [A]wd = ( N x the volume of water in one droplet)-'). This is equal to 0.03 mol dm-3 for one reactant molecule in an R = 10 droplet. In eqn (2) the factor 2 arises since the volume of water in the droplet dimer is twice that of a separated droplet. Also in eqn (2) , reaction involves one molecule of A reacting with one molecule of B inside a droplet. Hence, [AIwd is equal to [BIwd.

Alternatively, if 0*7/kdiss < /(kchem[Alwd) (3)

reaction occurs in a monomer droplet following decoalescence of the transient dimer [scheme (b)]. The chemical reactions we have used as indicators for the exchange process are sufficiently fast that scheme (b) is unlikely to operate, but there is a maximum statistical factor of two on the overall exchange kinetics depending on which scheme is applicable. Three types of fast reaction were investigated as shown below.

Electron Transfer

Ir(C1):- + Fe(CN)t- 3 Ir(C1):- + Fe(CN)g- (9

(ii)

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P. D. I. Fletcher, A . M. Howe and B. H . Robinson 989

(bp is the ligand bipyridyl.) Values of k, in aqueous solution have been measured by Holzwarth et al.27 For reaction (i) at

I(NaC1) = 0.1 mol drn-,, k, = 5 x lo7 dm3 mol-l s-l;

at

For reaction (ii) at I(NaC1) = 0.5 mol dm-3, k , is 1 x lo9 dm3 mol-l s-1.2s Both electron- transfer reactions are essentially irreversible. Reactants were assumed to be exclusively located inside the water droplets.

I(NaC1) = 1.0 mol drn-,, k, = 5 x lo8 dm3 mol-1 s-l.

Proton Transfer 0- OH

NO2 NO2 The pK, of HNPSA- (measured spectrophotometrically) is 6.80f0.05 at 25.0 "C in aqueous solution at I = 0. Using the joule-heating temperature-jump method the observed relaxation time [at pH 6.15, 25 "C, ionic strength 0.3 mol dm-, (NaNO,), indicator concentration mol drn-,] was faster than the heating time of the instru- ment (ca. 5 ps). Hence, k, must be greater than 1 O 1 O dm3 mo1-l s-l (i.e. close to the diffusion-controlled limit). (k, for 4-nitrophenolate is 3.8 x 1O1O dm3 mol-l s-l and k, is lo3 s - ~ . ~ ~ ) The solubilities of NPSA2- and HWPSA- are negligible in heptane but greater than mol dmd3 in water, so that the reactants are likely to be confined within the droplets.

Metal-Ligand Complexation

Complex formation between zinc(aq) and murexide (ammonium purpurate) was studied.

Zn2++ Mu-

\ I /

Zn+ Maas reported a value of (2.8f0.3) x lo7 dm3 mol-1 s-l for k, and (4.5k0.2) x lo4 s-l for k , in water at 20 OC.,O Again, both reagents show no solubility in heptane, but a high solubility in water, so they are confined within the droplets.

Calculations of k,, from Kinetic Data A microemulsion solution of reactant A was rapidly mixed in a fast-flow apparatus with a microemulsion solution containing reactant B. The reaction was monitored spect rop ho tometrically.

For electron-transfer reactions the kinetic analysis is straightforward. These reactions are irreversible, so low concentrations of reactants can be used and only singly occupied droplets need be considered. Thus, the reaction scheme is:

A1 + Bl -+ products

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990 Kinetics of Solubilisate Exchange where A1 and B1 represent droplets containing single molecules of A and B. The experimentally determined second-order rate constant may then be equated directly with k,,. A knowledge of droplet concentrations is not required to obtain values of k,, provided that :

(4) For proton transfer and metal-ligand complexation, analysis is more complex since

these reactions are not irreversible. In general, for a process A + B -P C occurring within the water droplet, the situation may be represented by the following scheme:

overall concentrations of A and B + [water droplets].

x, Y, 2-0, 00

Since the reactions proceed to equilibrium, higher reactant concentrations are required to achieve a detectable level of product formation such that each water droplet contains a low integral number of reactant molecules. (A droplet containing n molecules of species A is represented by An.) The reaction scheme represented by eqn (5) includes all product-formation reaction steps such as A1 + BI -+ Cl + 0 (where 0 represents an ‘empty’ droplet), A2+B1 -+ C1 +Al , A2+B1 -+ A, C1+ 0 etc. and also the mechan- istic steps that do not form product such as A2+ 0 + A1 + A l . For proton transfer and metal-ligand complexation reactions, concentrations were limited such that the simplified eqn (6) was applicable:

This equation was used to generate all the elementary transfer steps. It was assumed that reactant species are distributed randomly (Poisson distribution) throughout the droplets at equilibrium. This appears justified from fluorescor/quencher studies in the same AOT microemulsion system.ls Furthermore, this assumption is equivalent to the statement that all elementary transfer steps proceed with the same second-order rate constant (k,,) modified only by calculable statistical factors. Initial reactant concen- trations (Al, B1, B2 etc.) were calculated from the known overall reactant concentrations and experimentally determined droplet concentrations using the Poisson distribution equation : P(n) = P / n ! exp ( - R ) ~ (7) P(n) is the probability that a droplet contains n species whose average occupancy is A. The mechanism [eqn (6)] contains 74 elementary steps. This, together with initial concentrations, was used as input for a large numerical integration computer p r o g ~ a m . ~ ~ f 31 The program was run to simulate the kinetic course of the reaction. It was checked that running the program with zero concentration of A (i.e. with an initial non-Poisson distribution of B alone) yielded the correct Poisson distribution of species B amongst the droplets in the limit of long simulation times. Only two parameters in the procedure were unknown; the rate constant k,, and an equilibrium constant K (since these reactions are not irreversible). The experimental data are close to a single- exponential decay and this decay is correctly simulated by the program. Values of k,, and K were varied until coincidence between experiment and simulation was obtained. Details of the analysis procedure are given in ref. (19).

The use of different reactions as indicators for droplet exchange enabled us to investigate ion charge and size effects on the exchange process.

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P. D . I . Fletcher, A . M . Howe and B. H . Robinson 99 1

Table 1. Values of k,,/106 dm mol-l s-l in AOT-stabilised water-in-n-hep tane-microemulsions"

10 20

10 15 20 30

10 15 20 30

10 15 20 30

1 Ob 15 20b 30b*

- 5 -

10 4.2k0.5 3.1 f0 .5 1.7 k 0.3 -

15 7.4f 1 4.3 k 0.7 2.9 f 0.5 -

20 1 0 f 2 7.3 f 1 6.6& 1 -

25 -

1 6 f 3 11 + 2 -

1.8k0.2 1.0 fO.1

3.1 f0 .3

2.0 & 0.2 1.4 +O. 1

4.9 & 0.3

3.5 k 0.3 2.7f0.1

-

-

-

-

7.5 f 1.5 6.6f 1.1

1 4 f 4

1 4 f 2 14f 1

-

" Data are shown for various R, temperatures and reactions. The reactions are; (a) H+/NPSA2-; (b) Zn2+/murexide and (c) Ir(Cl):-/Fe(CN)t-. The values of the droplet hydrodynamic radii are 3.25, 4.13, 5.00 and 6.75 nm for R = 10, 15, 20 and 30, respectively. Values of lie,/ lo6 dm3 mol-l s-' of 14,lO and 10 for R = 11, 22 and 33, respectively, have been measured using the quenching of an excited stateof pyrene tetrasulphonate by copper ions or Fremy's salt at 25 0C.23 A value of k,, of ( lo+ 1) x lo6 dm mol-l s-' was measured for the electron- transfer reaction between Ir(C1):- and Fe(bipyridyl),(CN),.

Results and Discussion Exchange in Microemulsions containing n-Heptane as a Continuous Phase Values of k,, for different indicator reactions, microemulsion compositions and tem- peratures are shown in table 1. A priori, there is no reason to expect k,, to be related for the different reactions. However, for a particular R value and temperature, k,, values determined with different chemical reactions are remarkably similar. This has clear implications for the exchange mechanism. It should be noted that values of k,, from the proton-transfer and metal-ligand complexation reactions were determined at low AOT concentrations (varied in the range 1-10 mmol dmV3) and rely on experimentally measured droplet concentrations. Results obtained with the electron-transfer reactions cover higher AOT concentrations and a knowledge of droplet concentrations was not required. Included in table 1 are time-resolved triplet excited-state quenching data which also provide k,, data for comparison purposes.23 Again, the same values of k,, are obtained. Rather higher values of k,, (> los dm3 mol-l s-l) have, however, been reported for propyl viologen sulphonate exchange in quenching experiments with magnesium tetraphenyl porphyrin triplet.32 In this case, quenching might be possible by

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992 Kinetics of Solubilisate Exchange

Table 2. Comparison of k,, values for AOT-heptane-water microemulsions using different concentrations of reactants and

3 3.5 4.5 3 3.5 4.5 3.5 3

2.5 2 3 3.5 2.5 2 3.5 2.5 3.5 2

200 200 1 00 100 100 100 100 100 100 50 50 50 50

5.4 10.8 21.6

2.7 5.4

10.8 16.2 8.1

12.6 6.3

18.9 25.2

8.4 4.2

16.8 4.2 8.4 8.4

25 5

57 52 25 14 10 10 5 5 5 5 5

k,, conditions

2.84 2.84 2.84 2.84 2.84 2.84 2.84 2.84

3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 2.17

7 8 3 3 5 2 2.8

58 3 4.6 5.6 3.6 5.8

4.1 A = Zn2+ 4.3 B = murexide 4.3 R = 15 3.7 T = 15°C 3.5 4.5 4.2 3.6

4.0 A = Hf 4.5 B = NPSA2- 4.3 R = 15 4.4 T = 15°C 4.1 4.5 4.0 4.2 4.2 5.0

20 A = Fe(CN):- 16 B = IrC1:- 12 R = 10 14 T = 24°C 16 17 14 14 14 21 16 13 14

a AOT concentrations are in mmol dm-3, the concentrations of A and B are in pmol dm-3 and k,, values are in lo6 dm3 mol-' s-l. Proton-transfer and ligand-exchange results were obtained using the stopped-flow method ; electron-transfer results by the CFIO technique.

a different mechanism. Owing to the large size of the porphyrin, quenching may take place during an encounter between droplets without exchange. Then, higher values of k,, might be expected.

The results in table 2 show k,, is independent of the reactant or AOT concentrations. The independence of k,, on the reactant concentrations and the different (but always rapid) kchem values indicates that chemical reaction is never the rate-determining step. This also supports scheme (a) as the predominant mechanism for the overall chemical reaction.

Data in fig. 1 and table 1 were used to calculate apparent enthalpies and entropies of activation for the exchange process. It is known from SANS measurements that droplet size for a particular R is virtually independent of temperature and AOT

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P. D. I . Fletcher, A . M. Howe and B. H. Robinson 993

Fig. 1, Ir(C1):

1 I I

3.3 3.4 3.5 3.6 1 0 3 K I T

Arrhenius plots for the AOT-water-heptane microemulsion system, determined using the -/Fe(CN)i- reaction. 0, R = 10; A, R = 20; +, R = 30. Am = E,-RT; where

d In k,,/d( 2-l) = - EJR.

Table 3. Apparent activation parameters for the droplet exchange process in AOT-heptane microemulsions"

10 70f10 93f13 - 6 7 f 7 116+20 15 83+15 140f20 - - -

20 95+20 180f20 86f11 87+9 180_+40 30 - - - 108f 11 250f60

a A H / k J mol-l and A S / J K-l mol-l. The different reactions are (a) proton transfer, (b) ligand exchange and (c) electron transfer.

concentration for microemulsion compositions not too close to phase b0~ndar ies . l~ Plots of Ink,, us. 1 / T provide activation enthalpies from the slopes; some typical plots are shown in fig. 1 and activation parameters in table 3. Large positive activation enthalpies and entropies for exchange are indicated which increase with increasing R (and hence droplet size).

All three types of reaction have low activation enthalpies (of the order of 10-30 kJ mol-l) in a bulk water medium but show the same (greatly altered) activation parameters in the microemulsion. This provides additional evidence that the rate- determining step has changed from the chemical reaction step to that involving communication of the reactants [scheme (a)].

Two extreme mechanisms for inter-pool solubilisate exchange may be postulated. Mechanism A involves initial diffusion together of two droplets to form an encounter pair. While the droplets are in contact, the solubilisate species may diffuse through the

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994 Kinetics of Solubilisate Exchange surfactant bilayer at the point of contact of the droplets. The droplets then separate without having coalesced. Droplet encounters can be ' sticky' (i.e. experience short-range attractive interactions) and the contact time of an encounter increases as the upper temperature limit for microemulsion stability is a~pr0ached . l~ This should be reflected in k,, values (see later discussion). Mechanism B involves fusion of two droplets to form a transient, unstable droplet dimer of some indeterminate shape insofar as the interface may have fluctuating curvature on a fast (sub-microsecond) timescale. However, if the dimer species is sufficiently long-lived, the aqueous contents of the coalesced droplet will distribute randomly by diffusion. Simultaneous redistribution of AOT and water, previously identified with the separate droplets, will also occur. This process is not predicted by mechanism A. The dimer, which we can anticipate to have a lifetime in the microsecond time range, then breaks down into two separate droplets with random- isation of solubilisates between droplets. Mechanism B is thought to operate in AOT- stabilised droplets for the following reasons. First, k,, is independent of the exchanging species. This is true for H+, Zn2+, the electron-transfer reagents (negatively charged), Cu2+ and Fremy's Rates of permeation of ions through the surfactant bilayer (mechanism A) would be expected to be highly species dependent, whereas randomisation within the transient dimer (mechanism B) should be species independent as observed. Secondly, we have observed that mixing microemulsions of large droplet size (large R ) with microemulsions of small droplet size (low R ) produces, within a few seconds, a microemulsion containing droplets of intermediate size. Intuitively, it seems unlikely that such a major reorganization of the droplet population can occur without droplet transient coalescence and re-separation. An intermediate mechanism may be proposed involving generation of water 'channels' during the lifetime of the encounter pair. This may be achieved by cooperative movements of a surfactant 'block' and such processes have been postulated to occur in membrane^.^^ Such channels would have to be large to obviate charge effects at the surfactant-water interface on the migrating ionic solubilisate. If large channels are postulated, the mechanism is essentially that given by B.

If every encounter between droplets resulted in solubilisate exchange, k,, should be comparable with the collision frequency of droplets. The diffusion-controlled rate constant, kDc, for encounters between droplets of overall radius Y and diffusion coefficient D (in units of m2 s-l) is given by the Smoluchowski equation:

(8)

= 8000RT/3q (9)

k,,/dm3 mol-l s-l = 8N(2r) 103D

where R is the gas constant, T is the absolute temperature and q is the solvent viscosity (in units of kg m-l s-l). For n-heptane at 25 "C, q = 3.86 x lop4 kg m-l s-l and hence kDc is ca. 1.7 x 1O1O dm3 mol-l s-l. For a droplet concentration of mol dmp3, the time between encounters is ca. 60 ns (= {kDc[droplets]}-l). Comparison of kDc with k,, (table 1) shows that 1 in 1000 to 10000 encounters results in solubilisate exchange. There is, therefore, a free-energy barrier to the exchange process. The apparent enthalpy of activation is substantial, but this is largely offset by a high, positive entropy of activation (table 3) .

However, the implication of these results is that only the fastest chemical reactions in AOT-stabilised microemulsion systems are likely to be controlled by transport of reactants between droplets. Furthermore, generalising from these results and those we have obtained for other surfactant-stabilised systems, we believe AOT-stabilised droplets are among the most kinetically stable droplet dispersions so far investigated. Thus k,, values we have determined tend to reflect lower limits in microemulsion systems. Increasing k,, and/or prolonging the lifetime (k;&s) of the dimer (or higher-order aggregates) results in a progressive transition from a well defined droplet dispersion to a bi-continuous structure.

The rate constant k,, may be considered to be made up of at least two steps, the first

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P. D . I . Fletcher, A . M . Howe and B. H . Robinson 995

of which represents association of two droplets to give an encounter pair (a fast pre-equilibrium with equilibrium constant Ken). The fusion step (characterised by a first-order rate constant kfUs) is a subsequent slow step during which solubilisate exchange occurs. Thus we have:

. I

fast encounter slow fused pair dimer

k,, (dm3 mol-1 s-l) = Ken kfus and Ken = k,n/k-en. The process described in eqn (10) is apparently reversible, but in practice the collapse

of the dimer to reform the encounter pair is expected to involve randomisation both of the water core contents and of the surfactant shell. Hence the product (k,,[droplets])-l essentially defines the lifetime of an individual discrete droplet in the system.

Encounter-pair formation is expected to be diffusion-controlled and hence ken is equal to k,, [eqn (9)] and depends only on viscosity. The equilibrium constant Ken (and hence k,,) is affected by the presence of inter-droplet interactions through the rate of encounter-pair dissociation k-en. For ' hard-sphere ' droplet behaviour

kPen = 6D/(2r)2 (1 1)

and Ken = (4/3~)N(2r)~. (12) Ken [eqn (1 2)] is temperature-independent, consistent with a ' hard-sphere ' interaction. A typical value of Ken (R = 20 system, r = 5 nm) is 2500 dm3 mol-l. For interactions between AOT-stabilised droplets in n-decane a SANS structure-factor analysis suggests that an additional short-range attractive interaction is present which increases sharply in the vicinity of the upper-temperature phase transition.'*. l5 This attractive interaction would have the effect of increasing Ken (and hence kex). Decreasing the temperature more than ca. 15 "C below the upper transition or decreasing the chain-length of the alkane solvent (which raises the upper transition temperature; see fig. 2) causes the attractive interaction to become negligible.

For the measurements in n-heptane, where the upper temperature transition is greater than 60 "C for the R range studied, the kinetic results apply to temperatures more than 35 "C below the transition. Hence, the attractive interactions are likely to be negligible. Also, there is no correlation between k,, and r3 [eqn (1 2)] so variations in k,, are thought to be dominated by the factors determining the magnitude of kfus. This is not necessarily true for higher alkane solvents for which the upper transition temperature is reduced (fig. 2). Clustering of AOT-stabilised droplets in dodecane has been observed using PCS at temperatures around 25 0C,34 indicating attractive interactions are present at lower temperatures for this alkane. However, all the kinetic results for the different oils and additives are generally confined to temperatures more than 20 "C below the upper transition. Hence the conclusion that variations in k,, are dominated by the kfus term is likely to be valid for all the results presented here.

For k,, = lo7 dm3 mol-l s-l, kfus for an R = 20 system is 4 X lo3 s-l [eqn (lo)]. The tendency of droplets to fuse is given by kfus/k-fus. There is evidence from SANS form factor analysis for the existence of these higher fused aggregates,12 but kfus/k-fus is clearly less than 1, and is probably typically 0.1, suggesting a dimer lifetime of ca. 25 ps.

The fusion of two droplets in contact to give a transient droplet dimer involves some decrease in oil/water interfacial area. Area contraction may be associated either with desorption of surfactant from the interface (into the continuous oil solvent) or a compression of the surfactant film and a corresponding decrease in the interfacial area occupied per AOT molecule. In addition, the dimer may be considered a non-spherical, irregular, disordered entity with rapid fluctuations in local interfacial curvature and surfactant density. In any case, fusion of two droplets must occur through a series of

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996 Kinetics of Soluhilisate Exchange

R 5(

C 1 I

15 30 45 TI" C

Fig. 2. One-phase microemulsion stability region maps for 0.1 mol dm3 AOT in various straight-chain alkane solvents. The numbers indicate the number of carbon atoms in the solvents. The ringed and un-ringed numbers indicate the low- and high-temperature phase boundaries, respectively. The bar on the upper temperature transition line for n-pentane marks the boiling point

of the solvent.

structural states containing local interfacial regions of unfavourable surfactant film curvature. It is likely that most if not all of the factors mentioned above contribute to the enthalpy and entropy of activation for the droplet fusion step.

Apparent activation enthalpies and entropies both increase with increasing droplet size (increasing R). As a result, k,, becomes independent of droplet size at a particular temperature.

Since, in the absence of water, AOT in alkane solvents readily forms reversed micelles, the concentration of monomeric AOT in alkanes is ~ub-mil l imolar .~~ Hence desorbed surfactant in the microemulsion system is likely to be in the form of reversed micelles in the continuous oil medium. There is some evidence for the existence of such reversed micelles in AOT water-in-oil microemulsions from small-angle X-ray ~ c a t t e r i n g ~ ~ and kinetic data.25~37 In summary, a droplet dispersion may be considered to consist of the following entities maintained in dynamic equilibrium: 2 droplets +encounter pair f transient fused dimer (+monomeric surfactant or reversed micelles ejected from droplets as a consequence of fusion).

Oil Solvent Variation Exchange is a fundamental dynamic process and it is reasonable to expect a correlation between exchange and the thermodynamic stability. The simplest way to explore this correlation is to change the oil component, which shifts the microemulsion stability map on the temperature axis. Fig. 2 shows the single-phase microemulsion regions for different

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p. D. I . Fletcher, A . M. Howe and B. H. Robinson 997 n-alkane solvents. Higher chain-length alkanes shift the region of microemulsion stability to lower temperatures. The microemulsion phase boundaries are described by plots of maximum R (or water solubilisation) us. temperature. The temperature at which the highest R is achieved may be equated with the phase inversion temperature (pit .) . The positions of the phase boundaries are essentially independent of AOT concentration (at fixed R ) since the AOT does not significantly partition from the water-oil interface to the oil. (This is not true for many microemulsion systems, e.g. with non-ionic surfactants or when cosurfactants are present. In these systems, surfactant and cosurfactant partition between the interface and the oil and the droplet composition alters on dilution. A pseudo-binary representation of these systems would not be useful.)

The value of the p.i.t. is sensitive to the oil, the salt concentration in the water and the presence of surface-active additives (cosurfactants). The effect of these variables may be rationalised in terms of the surfactant film curvature. For mixtures containing comparable volumes of oil and water, and a fixed quantity of AOT, increasing the temperature through the p.i.t. causes transfer of AOT from the oil phase to the water

39 This transfer is associated with a change in surfactant film curvature from that of a W-0 aggregate structure (i.e. surfactant polar headgroups on the interior of the aggregate and the apolar tails on the exterior surface, defined here as negative curvature) to that of an 0-W aggregate structure (positive curvature). At temperatures close to the p.i.t. the AOT film curvature is in the region of zero. The third, surfactant-rich phase which is often observed near the p.i.t. has a 'bicontinuous' structure with zero net surfactant film curvature.*O

A distinction must be made between natural curvature and actual curvature of the surfactant film. Natural (or spontaneous) film curvature (which is a function of temperature, alkane chain-length, salt concentration etc.) is the observed surfactant film curvature when the droplet phase is in equilibrium with a conjugate phase of the dispersed component. At the p.i.t. the natural radius increases to infinity. The actual surfactant film curvatures observed in single-phase microemulsions are, however, very much determined by the constraints of the microemulsion composition. For the AOT microemulsions studied in this paper, the droplet size (= 1 /actual curvature) is deter- mined by R as described in eqn (1) and shows only a very slight dependence on temperature and alkane s o l ~ e n t . ~ ~ ! ~ * Thus the tendency of the AOT to locate at the oil-water interface dominates over resulting unfavourable curvature effects. However, at the lower-temperature boundary, the actual curvature is equal to the natural curvature. Since the actual curvature in the AOT one-phase microemulsions is virtually independent of temperature, whereas the natural curvature becomes less negative with increase in temperature, the discrepancy between the natural and actual curvatures increases as the upper boundary is approached.

Table 4 shows k,, data obtained in different alkane solvents. k,, increases with increasing carbon number of the solvent at a fixed temperature ( 5 "C) as shown in fig. 3. It is an interesting point that a 50/50 molar ratio of hexane-decane gives the same kc?x as octane.

All data in alkane solvents may be represented on a common graph by using a temperature scale relative to the relevant microemulsion stability maps. The temperature dependence of all the data (including alkane solvent variation, additives and heavy-water substitution) is shown in fig. 4 as a plot of Ink,, us. ( T - TPIT)/(TPIT)z. TPIT is the p.i.t., taken as equal to the lower temperature boundary at R = 50. TpIT values were corrected for addition of reactants (typically by + 3 "C). Fig. 4 is a differential form of the normal Arrhenius plot with a slope equal to -E , /R . The data are coincident for all systems of equal R. Therefore, these are corresponding states (related by TPIT or p.i.t.) in the different AOT-stabilised microemulsions. Hence, changes in k,, correspond closely to the shifts in the microemulsion stability maps. The analysis in fig. 4 implies a common mechanism for exchange in all the solvents. Values of Ea are 61 +4 kJ mol-l (R = lo),

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998 Kinetics of Solubilisate Exchange

Table 4. Values of k,,/106 dm3 mol-l s-l for water-oil micro- emulsions formed by 0.1 mol dm-3 AOT in various oil solventsa

R

solvent T/OC 10 20 30

Cn5

Cn6

Cn7

Cis08

Cn8

Cn9

CnlO

Cnl l

Cn12

cyclohexane cycloheptane cyclo-octane decalin

oct- 1-ene

5 10 15 20

5 10 15 20

5 10 15 20 25

5 10 15 20

5 10 15

5 10

5 10

5

5

15 15 15 15

5 10 15 25

1 .Of 0.1 1.8f0.3 2.8 f0.3 4.3 f 0.4

1.3kO.l 2.1 f0.2 3.3 f0.4 5.1 f 0.6

1.8 k 0.2 3.1 f0.3 4.9 k 0.3

14+2

2.3 f 0.3 4.1 kO.5 6.6 f 0.9

-

-

2.7 f0.2 4.6k0.5 7.1 f0.7

4.4 k 0.7 -

5.8 f0.8 -

7.9 f 0.7

11 f 4

0.80 f 0.05 1.1 fO.1 2.1 f0.3 2.1 & 0.3

1.4f0.1 2.5 f 0.2 3.3 f 0.4 -

-

0.80 & 0.08 1.6f0.2 3.2 f0.3

0.66 k 0.04 1.4f0.1 2.2 f0.2 3.7 f 0.4

1,OfO.l 2.0 k 0.2 3.5 f0.3 7.5k1.5 14 f2

1.2 fO.1 2.3 f 0.2 4.2 +_ 0.4 -

1.7 f 0.1 3.0 f 0.2 5.3 & 0.4

2.7 f 0.3 3.8 f 0.3

4.1 f0.7 -

6.3 f0.5

7.0 f 0.5

- - - -

- - -

2.1 & 0.2

- - - -

- -

1.5f0.2 2.6f0.3

-

1.4 & 0.1 2.7 f 0.1 6.6f 1.1 14& 1

0.75 f 0.08 1.9 & 0.2 3.5 f0.3 8.1 & 1.2

1.3kO.l 2.6 & 0.2 4.7 f 0.1

2.2 f 0.3 3.4 f 0.2

3.1 fO.l 4.3 k0.3

4.8 f 0.7

-

-

- - -

- - - -

a Cnx indicates a straight-chain alkane of x carbon atoms and Cis08 is iso-octane.

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P. D. I . Fletcher, A . M . Howe and B. H . Robinson 999

I 20

5 6 7 8 9 1 0 1 1 12 alkane solvent chain length

Fig. 3. Plot of k,, (log scale) at 5 "C against chain length of solvent. Upper line, R = 10; lower line, R = 20. The triangular symbols refer to solvent mixtures of hexane and decane.

77+7 kJ mol-l ( R = 20) and 94+ 12 kJ mol-l ( R = 30). The figure also shows the temperature (on this reduced scale) at which k,, becomes independent of R.

The exchange rate is slowest ( 105-10s dm3 mol-1 s-l) at the low-temperature boundary and rises to lo8 to lo9 dm3 mol-1 s-l as the upper boundary is approached (estimated by extrapolation of the linear Arrhenius plot to high temperatures). The droplets are most stable (i.e. show the slowest exchange rate) at temperatures close to the lower-temperature phase boundary where the actual surfactant film curvature is equal to the natural film curvature. Droplet fusion proceeds through a series of states in which the surfactant film of the coalescing (exchanging) droplets has to adopt high positive curvatures. A likely structure for the transition state is shown below. At * there is a very high local positive

curvature (i.e. an expanded head region and compressed tail region). From the discussion of phase behaviour, increasing the temperature above the lower-temperature boundary favours increased positive (or less negative) natural curvature. Hence, regions of local positive curvature become energetically less unfavourable facilitating exchange. Increas- ing temperature therefore reduces the free-energy barrier to droplet fusion [kfus step of

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1000 Kinetics of Solubilisate Exchange

Fig. 4. Plot of the k,, (log scale) us. ( T - TPIT)/(TPIT):! for AOT-stabilised W-0 microemulsions in a range of oils and with a variety of additives. 0, R = 10; +, R = 20; 0, R = 30.

eqn (lo)]. Hence the temperature dependence of k,, does not correspond to the normal situation of a greater fraction of species achieving sufficient thermal energy to overcome a fixed energy barrier to reaction. The situation for droplet exchange is better described as one in which the energy barrier reduces with increasing temperature. For this reason the activation parameters derived from the Arrhenius plots are referred to as apparent values. Changes in the free-energy profile for exchange are illustrated in fig. 5, which also shows interaction energy changes which occur in the close vicinity of the upper- temperature transition.

An interesting corollary to this discussion is that the rate of exchange between hydrophobic species in dispersed oil droplets in an 0-W microemulsion stabilised by an ionic surfactant should decrease with increasing temperature. 0-W microemulsion droplets possess interfacial surfactant films with positive curvature. If the exchange process proceeds by a fusion mechanism then 0-W droplet fusion would require the formation of regions of local negative curvature. Since increasing temperature favours positive curvature the energy barrier to fusion in this case is expected to increase with increasing temperature. Increasing the temperature also increases the degree of counter- ion dissociation for charged droplets which would also lead to increased repulsive electrostatic inter-droplet interactions. Both these effects would result in a decreased rate of exchange with increasing temperature.

Fig. 6 shows the microemulsion stability regions using various hydrocarbons based on eight carbon atom (a) and also various cyclic alkanes (b). Cyclisation, chain-branching

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P . D. I . Fletcher, A . M . Howe and B. H . Robinson 1001

distance

Fig. 5. Schematic free-energy profiles of the droplet fusion process at ( i ) a temperature close to the lower temperature phase boundary, (ii) an intermediate temperature and (iii) a temperature close to the upper temperature boundary. The separation distances correspond to (a) separated droplets, (b) a droplet encounter, (c) the energy maximum in the fusion process (the transition

state) and (d ) the fused droplet dimer species.

101

R 51

101

5

65 15 30 TIo C

B

20 LO 60

Fig. 6. Microemulsion stability maps for 0.1 mol dmP3 AOT in various solvents. A, Various eight- carbon solvents; (a) n-octane; (b) iso-octane; (c) oct-1-ene. B, Various cyclic alkanes: C6,

cyclohexane ; C7, cycloheptane; C8, cyclo-octane; D, decalin.

and non-saturation of the hydrocarbon solvent all cause a shift of the stability region to higher temperatures. This implies that these solvents are all more effective than the straight-chain oil in favouring increased negative curvature of the surfactant interface by packing in the alkyl-tail region. Table 4 shows some values of k,, for these microemulsion systems. A comparison of these data with those for the corresponding straight-chain alkanes shows k,, is decreased for these oils as expected.

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1002 Kinetics of Solubilisate Exchange

0 1 2 15 30 45 [cholesterol]/ 1 O-* mol dm-3 T/" C

Fig. 7. Effect of cholesterol on the exchange rate and microemulsion stability map. (a) k,, us. cholesterol concentration for 0.1 mol dm-3 AOT in n-heptane at 10.0 "C and R = 10. (b) Phase stability map for 0.1 mol dm-3 AOT in n-heptane. The numbers indicate the concentrations

(mol dmd3) of cholesterol.

R

I 1 0 0.1 0.2 0.3 0 15 30 45 [ benzyl alcohol]/mol dm-3 T / O C

Fig. 8. Effect of benzyl alcohol on the exchange rate and microemulsion stability map. (a) k,, us. benzyl alcohol concentration for 0.1 mol dm-3 AOT, 24f 1 "C: +, R = 10; A, R = 20; 0, R = 30. (b) Microemulsion phase stability map for 0.1 mol dm-3 AOT in n-heptane with (0.1) and

without (0) 0.1 mol dmW3 benzyl alcohol.

Effect of Cosurfactants and H,O/D,O Substitution

Toluene, benzyl alcohol and cholesterol are known to have dramatic effects on the stability and permeability of lipid bilayers. Many single-tail surfactants, such as sodium dodecyl sulphate, do not form single-phase water-in-oil microemulsions in the absence of a medium-chain-length alcohol, e.g. pentanol. The effect of alcohol cosurfactants (of medium to long chain-length) is to produce increased negative curvature of the surfactant film so as to favour the formation of reversed micelles or water-in-oil microemulsions. The alcohols screen inter-headgroup electrostatic repulsions and pack the alkyl tail regions of the surfactant films, both factors favouring increased negative curvature. (The ' wedge-shaped' molecular geometry of AOT makes it a favourable surfactant for water-in-oil microemulsion stabilisation without a cosurfactant.) There- fore, these additives play a fundamental role in determining phase behaviour.

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P. D. I . Fletcher, A . M . Howe and B. H . Robinson 1003

1

1 0 l - 2 0.5 1 0 o? 15 30 L5 0- 0 0.5 1

fraction D 2 0 TI" C fraction D20

Fig. 9. Effect of H,O/D,O substitution on the exchange rate and microemulsion stability map. (a) k,, us. fraction of D,O for 0.1 mol dmP3 AOT in n-heptane at 10 "C: +, R = 10; 0, R = 20. (b) Microemulsion phase stability map in n-heptane with H 2 0 (H) and D20 (D). (c ) k,, us. fraction

of D,O for 0.1 mol dm-3 AOT in n-decane at 10 "C: 0, R = 10; A, R = 20; +, R = 30.

Fig. 7 and 8 show representative effects of cholesterol and benzyl alcohol on the exchange rate and microemulsion stability. Cholesterol and also toluene decrease the exchange rate and shift the stability region to higher temperatures. This behaviour is consistent with these additives favouring increased negative curvature of the interface. Benzyl alcohol has the opposite effect. The exchange rate is increased and the micro- emulsion region is shifted to lower temperatures. Benzyl alcohol must be located at the interface in such a way as to swell the headgroup region of the surfactant shell more than the tail region, thus favouring decreased negative curvature. The hydroxy group of the alcohol presumably serves to locate it close to the AOT head; the aromatic group then expands the headgroup region more than the tail region.

Fig. 9 shows the effect of substituting D20 for H 2 0 . A shift in stability to higher temperatures with D20 is accompanied by a decrease in exchange rate. It appears, therefore, that D,O favours the increased negative natural curvature of the interface.

As for alkane variation, additives which increase the p.i.t. also decrease the exchange rate. Both effects are associated with an increased tendency of the surfactant film to favour negative curvatures. The temperature dependence of all the data (for alkane solvent variation, additives and heavy water substitution) is shown in fig. 4 and it can be seen that the k,, data for all the variables which affect the microemulsion system fall on coincident lines for equal R. Independent measurements have confirmed that droplet sizes do not change significantly for the concentrations of additives It appears, therefore, that the corresponding states of the microemulsions (related by the p i t . ) may be reached either by changing the alkane solvent or by addition of additives.

Droplet Exchange, Microemulsion Structural Properties and Phase Behaviour Experiments, using quasi-elastic incoherent neutron scattering, have shown that addition of toluene or benzyl alcohol has no significant effect upon the rate of short-range local diffusion of AOT within the microemulsion interfacial layer.42 The fast local diffusion of the AOT is also found to be independent of droplet size.43 It appears, therefore, that k,, is not correlated with surfactant mobility but rather with the energy required to produce localised regions of high positive curvature in the interface.

Clarke and co-workers used dynamic light scattering to study concentrated AOT

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1004 Kinetics of Solubilisate Exchange microemulsions. They observed a biexponential decay of the intermediate scattering function for droplet volume fractions greater than 0.25 and assigned the slower relaxation to polydispersity fluctuation^.^^ They conclude that the timescale of the polydispersity fluctuations is at least three orders of magnitude slower than the particle collision frequency. These polydispersity fluctuations are predicted from the exchange results reported in this paper to occur on this timescale.

Attempts using the stopped-flow method to measure pool exchange kinetics with other microemulsion systems [e.g. hexadecyltrimethylammonium bromide (CTAB)-water 50/50 heptane+hloroform] have shown that these systems all exchange faster than the system studied here (and too fast for stopped-flow study). Preliminary data for the AOT-glycerol-heptane system indicate that exchange is very rapid and comparable to that of the AOT-water-heptane system. These results for glycerol as the dispersed component are particularly interesting since the kinetics indicate that the viscosity of the dispersed component does not determine the exchange rate. (The viscosity of glycerol is some 1500 times that of water.) Measurements of AOT local diffusion in glycerol dispersions using quasi-elastic incoherent neutron scattering show that AOT diffusion is slowed by a factor of two as compared with the corresponding water d i ~ p e r s i o n . ~ ~

Using a fast laser photolysis method, Thomas and co-workers measured k,, values of ca. lo8 dm3 mol-1 s-l for microemulsions stabilised by potassium oleate and hexanol. Substitution of hexanol by pentanol increases k,,,459 46 which is consistent with the exchange rate being dominated by the energy needed to form regions of local positive curvature in the surfactant film since the shorter chain-length alcohol is expected to be more effective in favouring positive film curvature.

Lindman and c ~ - w o r k e r s ~ ~ - ~ ~ measured, using an n.m.r. technique, the self-diffusion coefficients (over macroscopic distances) of all components in a variety of water-in-oil microemulsion systems. Microemulsions with a ‘ discrete ’ droplet structure are expected to show slow diffusion of surfactant and dispersed water relative to the continuous oil component since these are contained within the slow-moving, large aggregates for the major time (10-100 ms) of the measurement. Only for AOT-water-p-xylene and oleate plus decanol cosurfactant systems are relatively slow diffusion of water and surfactant observed, which implies that these droplets retain their discrete nature on the millisecond timescale. Oleate plus short-chain alcohols, the non-ionic surfactant CI2E4, sodium dodecyl sulphate plus pentanol and octyl benzene sulphonate plus pentanol surfactant systems all show fast diffusion of all components on this timescale. These studies indicate that many microemulsions are ‘ bicontinuous’ as probed by this technique; i.e. exchange is fast on the timescale of the n.m.r. technique used. This conclusion is consistent with our observation that the AOT-stabilised microemulsions are amongst the most kinetically stable (i.e. show the lowest k,, values).

The :discreteness’ of the droplets is, of course, related to the timescale of the exchange process as compared with the timescale probed by the particular technique employed. The concentration of droplets depends on the AOT concentration and R. For 0.1 mol dm-3 AOT and R = 10, the droplet concentration is 1.0 mmol dm-3.18 Hence, for this solution, the time of independent existence of a droplet ranges from 1-10 ms close to the lower phase boundary to 1-lops at the upper boundary. On timescales slower than the exchange rate, the water in the microemulsion can be considered, from the point of view of a reaction medium, as effectively continuous, since a long timescale would allow the sampling of many water droplets via exchange. On these slow timescales, the analysis of kinetic data for water-soluble reactants in microemulsions can be based on concentrations per volume of dispersed water (i.e. the dispersed water component may be treated as a separate continuous phase, a ‘pseudo-phase’).

On a nanosecond timescale, as probed by fluorescence lifetime measurements, exchange does not have time to occur. On this timescale, the droplets may be considered to be discrete entities. A time-resolved fluorescence quenching study of the acridinium

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P. D. I . Fletcher, A . M . Howe and B. H . Robinson 1005 ion has shown that exchange does not occur in the AOT system over 100 ns.18 In this situation, local reactant concentrations within the droplet must be considered and so only certain concentrations are permitted, according to the statistical occupancy of the droplets.

The exchange process is fundamental to an understanding of many phenomena in microemulsions, including chemical reaction kinetics, electrical conductivity and self- diffusion processes. The microemulsion structure may appear to consist of discrete droplets or to be bicontinuous depending on whether the timescale probed is slow or fast relative to the exchange process. The concept of a ‘ bicontinuous’ microemulsion structure is understandable in terms of a system of rapidly exchanging droplets.

It is a pleasure to thank Dr J. Holzwarth and his co-workers (Fritz-Haber Institute, Berlin) for kindly making available to us the CFIO instrument. We also wish to thank the S.E.R.C. for a studentship and DAAD for a travel/support grant (A.M. H.).

References 1 J. H. Fendler, Membrane Mimetic Chemistry (Wiley, New York, 1982). 2 C. J. O’Connor, T. D. Lomax and R. E. Ramage, Adv. Colloid Interface Sci., 1984, 20, 21. 3 P. D. I. Fletcher and B. H. Robinson, J . Chem. Soc., Faraday Trans. I , 1984,61, 1594. 4 P. L. Luisi, Angew. Chem., 1985, 24, 439. 5 R. Hilhorst, C. Laane and C. Veeger, FEBS Lett., 1983, 159, 31. 6 P. Luthi and P. L. Luisi, J . Am. Chem. Soc., 1984, 106, 7285. 7 P. D. I. Fletcher, R. B. Freedman, B. H. Robinson and R. Schomacher, Biochim. Biophys. Acta, 1986,

8 B. H. Robinson, D. C. Steytler and R. D. Tack, J. Chem. Soc., Faraday Trans. 1, 1979, 75, 481. 9 M. Zulauf and H. F. Eicke, J . Phys. Chem., 1979, 83, 480.

in press.

10 J. D. Nicholson and J. H. R. Clarke, Proc. Int. Symp., Surfactants in Solution, ed. K. Mittal and

11 C. Cabos and P. Delord, J . Appl. Crystallogr., 1979, 12, 502. 12 B. H. Robinson, C. Toprakcioglu, J. C. Dore and P. Chieux, J. Chem. Soc., Faraday, Trans. I, 1984,

13 C. Toprakcioglu, J. C. Dore, B. H. Robinson, A. M. Howe and P. Chieux, J . Chem. SOC., Faraday

14 M. Kotlarchyk, S. H. Chen, J. S. Huang and M. W. Kim, Phys. Rev. A , 1984,29, 2054. 15 J. S. Huang, S. A. Safran, M. W. Kim, G. S. Grest, M. Kotlarchyk and N. Quirke, Phys. Rev. Lett.,

16 S. I. Chou and D. 0. Shah, J . Colloid Interface Sci., 1980, 78, 249. 17 E. Keh and B. Valeur, J . Colloid Interface Sci., 1981, 79, 465. 18 N. J. Bridge and P. D. I. Fletcher, J . Chem. Soc., Faraday Trans. I, 1983, 79, 2161. 19 P. D. 1. Fletcher, Ph.D. Thesis (University of Kent, 1982). 20 H. Kunieda and K. Shinoda, J . Colloid Interface Sci., 1980, 75, 601. 21 E. A. G. Aniansson, S. N. Wall, M. Almgren, H. Hoffmann, I. Kielmann, W. Ulbricht, R. Zana,

22 H. F. Eicke, J. C. W. Shepherd and A. Steinmann, J . Colloid Interface Sci., 1976, 56, 168. 23 S. S. Atik and J. K. Thomas, J . Am. Chem. SOC., 1981, 103, 3543. 24 P. D. I. Fletcher and B. H. Robinson, Ber. Bunsenges. Phys. Chem., 1981, 85, 863. 25 P. D. I. Fletcher, N. M. Perrins, B. H. Robinson and C. Toprakcioglu, in Reverse Micelles,

ed. P. L. Luisi and B. E. Straub (Plenum Press, New York, 1984), p. 69. 26 J. F. Holzwarth, in Techniques and Applications of Fast Reactions in Solution, NATO ASI Symp. Ser.,

ed. W. J. Gettins and E. Wyn-Jones (Elsevier, Amsterdam, 1979), p. 509. 27 H. Bruhn, S. Nigam and J. F. Holzwarth, Faraday Discuss. Chem. Soc., 1982, 74, 129. 28 H. Bruhn and J. F. Holzwarth, Ber. Bunsenges. Phys. Chem., 1978, 82, 1006. 29 M. Eigen, W. Kruse, G. Maas and L. DeMaeyer, Prog. React. Kinet., 1964, 2 , 286. 30 G. Maas, Z. Phys. Chem. N. F., 1968, 60, 138. 31 D. DeTar, Computer Programs for Chemistry (Benjamin, New York, 1969), vol. 2. 32 M. P. Pileni, J. M. Furois and B. Hickel, in Surfactants in Solution, ed. K. Mittal and B. Lindman

33 P. Fromherz, personal communication. 34 A. M. Howe, J. A. McDonald and B. H. Robinson, J . Chem. Soc., Faraday Trans. I , 1987, 83, 1007.

B. Lindman (Plenum Press, New York, 1984), vol. 3, p. 1663.

80, 13.

Trans. I , 1984,80,413.

1984, 53, 592.

J. Lang and C. Tondre, J. Phys. Chem., 1976,80,905.

(Plenum Press, New York, 1984), p. 1471.

34 F A R 1

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1006 Kinetics of Solubilisate Exchange 35 B. Djermouni and H. J. Ache, J. Phys. Chem., 1979,83, 2476. 36 J. C . Dore, A. North, J. McDonald, A. M. Howe, R. K. Heenan and B. H. Robinson, Colloid Surf.,

1986, 19, 21. 37 P. D. I. Fletcher, A. M. Howe, N. M. Perrins, B. H. Robinson, C. Toprakcioglu and J. C. Dore, in

Surfactants in Solution, ed. K. Mittal and B. Lindman (Plenum Press, New York, 1984), vol. 3, 1745. 38 R. Aveyard, B. P. Binks, S. Clark and J. Mead, J . Chem. SOC., Faraday Trans. 1, 1986, 82, 125. 39 R. Aveyard, B. P. Binks and J . Mead, J. Chem. SOC., Faraday Trans. 1, 1986,82, 1755. 40 E. W. Kaler, H. T. Davis and L. E. Scriven, J . Chem. Phys., 1983, 79, 5685. 41 A. M. Howe, C . Toprakcioglu, J. C. Dore and B. H. Robinson, J . Chem. SOC., Faraday Trans. I , 1986,

42 P. D. I. Fletcher, B. H. Robinson and J. Tabony, J . Chem. Soc., Faraday Trans. I , 1986, 82, 231 1. 43 J. Tabony, A. Llor and M. Drifford, Colloid Polym. Sci., 1983, 261, 938. 44 J. H. R. Clarke, J. D. Nicholson and K . N. Regan, J. Chem. SOC., Faraday Trans. I , 1985, 81, 1173. 45 S. S. Atik and J . K. Thomas, J . Am. Chem. SOC., 1981, 103, 7403. 46 S. S. Atik and J. K . Thomas, J . Phys. Chem., 1981, 85, 3921. 47 B. Lindman, P. Stilbs and M. E. Moseley, J . Colloid Interface Sci., 1981, 83, 569. 48 P. G. Nilsson and B. Lindman, J. Phys. Chem., 1982,86, 271. 49 T. Warnheim, E. Sjoblom, U. Henriksson and P. Stilbs, J . Phys. Chem., 1984, 88, 5420.

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