1301
Langmuir 1990, 6, 1301-1309
Interdroplet Exchange Rates of Water-in-Oil and Oil-in-Water Microemulsion Droplets Stabilized by &E5 Stephen Clark, Paul D. I. Fletcher,* and Xilin Ye School of Chemistry, University of Hull, Hull HU6 7RX, U.K. Received August 8, 1989.In Final Form: February 14, 1990 We have used a time-resolved fluorescence method to investigate the structure and dynamics of waterin-oil (W 0) and oil-in-water (O/W) microemulsions stabilized by the nonionic surfactant C12Ea. The measure aggregation numbers are consistent with the formation of spherical droplets with a low degree of polydispersity. The droplet sizes are in agreement with light-scattering values determined for systems close to the solubilization phase boundaries and at low droplet concentrations. The results of the present study also show the droplet sizes are reasonably constant throughout the temperature range over which the one-phase microemulsion is stable. Droplet sizes are independent of droplet concentration. The intradroplet fluorescence-quenchingrates indicate that the fluorescor and quencher probe molecules experience apparent microviscosities within the microemulsion droplets which are 10-100-fold larger than the viscosities of the corresponding bulk oils or water. Exchange of the probe molecules between the droplets occurs on the experimentaltime scale of a few microseconds for some systems. This exchange is thought to occur via a mechanism of droplet coalescence and reseparation. For both O/Wand W/O microemulsions, the rate of this process is slowest at the solubilization phase boundary where the microemulsion phase coexists with an excess phase of the dispersed component. The dynamics of the droplet coalescence process are discussed in terms of the interdroplet interactions and the energies required to bend the surfactant monolayer and to desorb surfactant from the oil-water interface.
i
Microemulsion droplets undergo continual coalescence followed by reseparation on a time scale of milliseconds to microseconds as illustrated schematically in Figure 1. This process forms the mechanism whereby the droplet size distribution is formed initially and is maintained in rapid dynamic equilibrium.' The kinetics of this process have been measured for a number of W/O microemulsion systems stabilized by ionic surfactants, and the rate is highly sensitive to the particular surfactant present and to the addition of cosurfactants.2-s Although studies of microemulsions over the past decades have led to an increased understanding of the equilibrium properties of oil/water mixtures containing surfactants?JO the role of the adsorbed surfactant monolayers in determining the rate of droplet coalescence remains unclear. With a view to relating the equilibrium and dynamic properties of oil/ water/surfactant systems, we report coalescence rates for both O/Wand W/Omicroemulsion droplets stabilized by the nonionic surfactant C12E6, for which some relevant equilibrium properties have been reported." It has been established that the type of macroemulsion formed (i.e., W/Oor O/W) when a two-phase mixture of a microemulsion plus a phase of excess dispersed component is emulsified is generally the same as the initial
microemulsion phase type.l0J2 For example, emulsification of a two-phase mixture of an O/W microemulsion with excess oil produces an O/Wmacroemulsion. The type of microemulsion formed a t equilibrium is a measure of the spontaneous curvature of the surfactant film, and it therefore appears that this spontaneous film curvature is an important parameter in determining macroemulsion type (and hence stability) of systems stabilized by the low molar mass surfactants considered here. This relationship has been expressed in various ways including Bancroft's rule,13the hydrophilic-lipophilic balance (HLB) system,14 and the phase inversion temperature (PIT) discussions of Shinoda.15 Although these considerations of spontaneous curvature give qualitative information on the type of emulsion which is expected to be stable, no estimation can be made of the stability of different systems which have the same spontaneouscurvature. Since emulsion stability is of prime importance in many industrial applications of surfactants,'s it is of interest to attempt to assess the equilibrium properties of surfactant monolayer films other than the spontaneous curvature which may be important in determining droplet coalescence rates.
Experimental Section (1) Fletcher,P. D. I., How, A. M.; Robinson,B. H.J.Chem. Soc., Faraday Trans. 1 1987,83,185.
(2) Fletcher, P. D. I.; Parrott, D. In Chemical and BiologicalReactions
in Compartmentalised Liquids; Knoche, W . , Schomacker, R., Eds.; Springer-Verlag: Berlin, 1989. (3) Lang, J.; Jada, A.; Malliaris, A. J. Phys. Chem. 1988, 92, 1946. (4) Jada, A.; Lang, J.; Zana, R.; Makhloufi, R.; Hirsch, E.; Candau, S. J. J. Phys. Chem. 19w),94,387. (5) Atik, S. S.; Thomas, J. K. J. Am. Chem. SOC.1981, 103, 3543. (6) Almgren, M.; Van Stam, J.; Swarup, S.; Lofroth, J.-E. Langmuir 1986,2,432. (7) Brochette, P.; Pileni, M. P. Nouo. J. Chim. 1985,9,551. (8)Verbeeck, A.; De Schryver, F. C. Lamnguir 1987,3,494. (9) Langevin, D. Acc. Chem. Res. 1988,21,255. (10) Aveyard, R.; Binks, B. P.; Lawless, T. A.; Mead, J. J. Chem. SOC., Faraday Trans. 1 1986,81,2155. (11) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I. Langmuir 1989,5, 1210.
0743-7463/90/2406-1301$02.50/0
The surfactant ClzEs (dodecylpenta(oxyethy1ene)ether) was
a pure (>99% by GLC) sample supplied by Nikkol. Measured
cloud points and phase boundaries were in good agreement with previous data.17JS Water was distilled and passed through a (12) Salager, J. L.; Maldonaldo, I. L.; Perez, M. M.; Silva, F. J . Dispersion Sci. Technol. 1982, 3, 279. (13) Bancroft, W. D. J.Phys. Chem. 1913,17, 501. (14) Griffin, W. C. J. Soc Cosmet. Chem. 1949, 1, 311. (15) Shinoda, K.; Friberg, S. Emulsions and Solubilization; Wiley: New York, 1986. (16)Encyclopaedia of Emulsion Technology; Becher, P., Ed.;Marcel Dekker: New York and Basel, 1983. (17) Shinoda, K.; Kunieda, H.;Arai, T.;Saijo, H. J. Phys. Chem. 1984,
88. 5126.
0 1990 American Chemical Society
1302 Langmuir, Vol. 6, No. 7, 1990
o +
Clark et al.
separated droplets
0
I1
00
dmpkt enmunter pair
11 transitionslate showing
u-
11 f-\
desorbed monomer surlactant
short-lved droplet
Figure 1. Postulated droplet coalescence mechanism. The
separated droplets diffuse together to form an encounter pair which coalesces via a transition state involving bending the surfactant film and surfactant monomer desorption. The unstable droplet dimer is short-lived and reseparates by the reverse route. Milli-Qreagent water system. n-Heptane (Fisons HPLC grade) was passed over alumina prior to use, and n-tetradecane (Fluka puriss grade) was used as supplied. Pyrene from Aldrich was extensively zone refined before use. Tris(2,2’-bypyridyl)ruthenium(I1) chloride (RB) (Strem chemicals) and methylviologen (MV) (Sigma) were used without further purification. Samples were contained in quartz cuvettes sealed with Young’s gas-tight taps. Since dissolved oxygen is an efficient quencher of the fluorescence of both pyrene and RB, samples were degassed with a minimum of six freeze-evacuate-thaw cycles. Fluorescence intensity decay curves were recorded by using an Edinburgh Instruments 199 photon counting instrument employing a thyratron gated spark gap lamp. In the case of pyrene, the lamp was operated in 0.8 bar of Hz, samples were excited at 325 nm, and the emission was selected by using a 380-nm interference filter (Ealing Corp., fwhm = 11 nm) with an additional long-pass filter (Schott type WG380) to further prevent scattered light. In the case of RB as fluorescor, the lamp was operated in 0.8 of bar Nz,samples were excited at 356 nm, and the emmision was selected by using 380- and 570-nm long-pass filters (Schott types WG380 and OG570). Excitation pulse profides were recorded by using a Ludox R scattering solution. The samples were thermostated within 0.2 K of the desired temperature by a water circulator and flow-through cell holder.
Analysis of TRF Data The fluorescence intensity decay of a surfactant aggregate solution containing solubilized fluorescent (F) and quencher (Q)probe molecules is given by the equati~n~~v~~
Z, = I, exp(-A$ - AJ1 - exp(-A,t)]) (1) where I t and IO are the intensities a t time t and 0, respectively. The three parameters
together with
lo, are obtained by computer fitting the experimental curve to a convolution of eq 1 together with the measured lamp (18) Mulley, B. A. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker; New York. (19) Infelta, P.; Gratzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190.
(20) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289.
pulse profile. Since the lamp pulse duration, of the order of 1 or 2 ns, was short compared with the fluorescence lifetimes considered here (several hundred nanoseconds), this correction for the finite pulse duration had only a minor effect on the derived parameters. If it is assumed that (i) the probes F and Q are confined entirely within the surfactant aggregates,(ii) they are distributed according to the Poisson distribution (i.e., randomly) among the aggregates, and (iii) no redistribution of the fluorescor and quencher probe molecules between aggregates occurs on the experimental time scale, then A, = k,; A, = [Q]/[aggregates]; A, = k , (2) where ko is the fluorescence decay rate constant in the absence of quencher and is determined separately. The rate constant, 12, is the first-order quenching rate constant for an aggregate containing a single quencher molecule. The number of surfactant molecules per aggregate (Nagg) may be obtained by using eq 2 since NaBg= ([surfactant] - cpc)/ [aggregates]. The concentration of surfactant monomer not adsorbed a t the surfaces of the microemulsion droplets is equal to the minimum concentration of surfactant required before microemulsion droplets may be formed. By analogy with the critical micelle concentration, we have designated this quantity the critical microemulsion concentration (cpc).ll For systems where migration of the probes either out of the aggregates or between aggregates occurs on the experimental time scale (ca. 5 / k 0 ) , the experimental curves are still described by eq 1, but eq 2 is not valid. This situation is clearly indicated by the observation that A2 is larger than ko. For this case, a particular mechanism of transfer must be assumed in order to derive the appropriate rate constants and the aggregation number from the parameters A2-A4.21 For the experiments with W/O microemulsions, F and Q were RB and MV, respectively. Both species are positively charged and are insoluble in alkanes in the absence of the microemulsion droplets. Hence, these species are confined within the aggregates. It is assumed here that the interdroplet exchange of these species occurs via a mechanism involving the temporary coalescence of droplets followed by reseparation with a consequent “scrambling” of the components between the droplets (so called “fusion-fission”).1*21 An alternative mechanism whereby a fragment of the aggregate breaks away and acts as a “carrier” between aggregates is thought to be less likely since it is associated with nonspherical, polydisperse aggregate^,^^.^^ whereas the microemulsion droplets in this study are close to spherical.” It is also assumed here that quenching of a fluorescor by a quencher in an adjacent but noncoalesced droplet (i.e., through the surfactant bilayer separating touching droplets) does not occur at a significant rate. The quenching of RB fluorescenceby MV in homogeneous solution occurs by an electron-transfer mechanism;” hence interdroplet quenching without droplet coalescence would involve electron transfer across a surfactant bilayer of approximately 6-nm thickness and is considered unlikely. The rate constant of quenching (9.6 X 108 dm3 mol-’ s-1 in aqueous acetate buffer solution a t pH 5) is close to that expected for a diffusion-controlled process involving species of the same charge.24 For the O/W droplets, pyrene was used as both quencher and fluorescor. Ground-state pyrene quenches the excited (21) Almgren, M.: Lofroth, J.-E.; Van Stam, J. J.Phys. Chem. 1986, 90,4431. (22) Malliaris, A.; Lang, J.; Zana, R. J. Phys. Chem. 1986, 90,655. (23) Luo, H.; Boens, N.; Van der Auweraer, M.; De Schryver, F. C.; Malliaris, A. J. Phys. Chem. 1989, 93, 3244. (24) Johansen, 0.;Mau, A. W. H.; Sasse, W. H. F. Chem. Phys. Lett. 1983, 94, 113.
Langmuir, Vol. 6, No. 7, 1990 1303
Interdroplet Exchange Rates of Microemulsion Droplets species through the formation of an excimer which occurs with a rate constant of 1.23 X 1Olo dm3 mol-’ in heptane at 25 0C.2s Again, this quenching rate is close to the value expected for a diffusion-controlled process. However, the quenching of pyrene monomer fluorescence by excimer formation is not irreversible since the excimer can dissociate at a rate k b comparable with the excimer decay rate ke. The main effect of this process is to reduce the effective quenching rate from the excimer formation rate by an approximate factor z (= ke/(ke kdiss) estimated to be between 0.5 and 0.8.25 In order to avoid undue complexity, the excimer dissociation was not included in the kinetic analysis of the fluorescence intensity decay curves used here. This approximation introduces errors in t h e values of k , and exchange r a t e of factors approximately equal to t. These approximation errors are of the same order as the total uncertainties in the derived parameters (10-50 % ) and do not significantly affect the conclusions reached in this study. The solubility of pyrene in water is 0.5 X 1o-B mol dm-3, whereas the solubility in alkanes is of the order of 0.05 mol dm-3.26 Hence, the pyrene is assumed to be confined within the oil droplets. Interdroplet exchange of pyrene was assumed to occur only via the droplet fusion-fission mechanism. For the general case where exchange of fluorescor and quencher probe molecules occurs, an approximate expression of the same form as eq 1was derived by Almgren et a1.21 According to this, the fitted parameters APA4 are related to the average number of quenchers per aggregate n (from which Naggis derived since n = [quencher]N,,/ [surfactant]), k,, and the average number of quenchers in aggregates containing excited fluorescent probes in the steady-state phase of the decay, ( x ) *
4t
+
j
n = A3/(1- B)*
(3)
( x ) , = B,
(4)
It, = Ad(1- B ) (5) B is equal to (A2 - ko)/(Az+ A 4 4 - ko). Having calculated n, ( x ) , , and k,, we may obtain the first-order rate constant for droplet coalescence, kt, by interpolation of numerical results for the variation of k t / k , with ( x ) , / n calculated for exchange by the fusion-fission mechanism.21 The second-order rate constant for coalescence, k,, is obtained by measuring kt for microemulsion samples of various droplet concentrations, since kt = kJdroplets]. Good computer fits to the data were obtained by using eq 1 with the reduced x2 generally being lower than 1.2. A representative fitted fluorescence intensity decay curve together with a residuals plot is shown in Figure 2. The residuals show no systematic deviations from zero, and only a few data points out of the 512 fitted show residuals larger than 2 standard deviations. Samples containing two or three different quencher concentrations were run for each microemulsion composition, and it was found that the derived parameters were self-consistent. Computer fitting of the experimental intensity decay curves to eq 1 yields unreliable parameter values when A4 < A z . ~Since A4 is mainly determined by the rate at which F and Q diffuse together in the same aggregate (which is slower for larger aggregates), this condition effectively limits the size of aggregate that can be studied by using this TRF method. For this reason, the present study is restricted to a rather small range of microemulsion droplet sizes. (25) Fletcher, P. D. I. J . Chem. SOC.,Faraday Trans I 1987,83,1493.
0 &ah
I
I
I
.!!
Figure 2. Representative fluorescence intensity decay curve showing computer fit to eq 1 together with a plot of the residuals. The sample was a W/Omicroemulsion containing 0.3 MClzEs, 3.75 M water, 0.03 mM RB, and 0.5 mM MV. The calculated “best fit” curve has the parameters A2 = (2.44 f 0.07)X 106 s-1, AB = (1.15 f 0.02) X 106 a 5-1 and A4 = (4.74 f 0.2) X 10s 5-1 with x2 = 1.094.
It was found that incorporation of the fluorescors and quenchers within the microemulsions shifted the phase boundary temperatures by no more than 1-2 K, implying that the system was not perturbed to any large extent by the presence of the probe molecules.
Results and Discussion Water-in-Oil (W/O) Microemulsions. Microemulsions stabilized by nonionic surfactants of the alkyl poly(oxyethylene) ether type have been studied extenSystematic measurements of the phase boundaries, droplet sizes, and interfacial tensions for microemulsion phases stabilized by C&S have been reported recently.’’ The single-phase W/O microemulsion stability region for ClzE5/heptane/water mixtures is bounded at low temperatures by t h e haze curve and a t high temperatures by the solubilization curve as shown in Figure 3. An excess water phase separates at the solubilization curve whereas a surfactant-rich phase separates at the haze curve. The microemulsions contain dispersed water droplets stabilized by a monolayer of surfactant. A t temperatures close to the solubilization phase boundary, the droplets are close to spherical and interact only weakly. As one moves toward the haze curve (by reducing the temperature), the droplets become increasingly mutually attractive. At the solubilization boundary (and at droplet concentrations extrapolated to zero), the droplet radius is proportional to the molar ratio of dispersed component (water in this case) to aggregated surfactant (R’water= [water]/([surfactant]- cpc)). This behavior is in agreement with a simple geometrical model where the droplets are assumed to be spherical and monodisperse. In this case, the droplet radius r (which includes the surfactant shell thickness 6) is given by where v d c is the molecular volume of the dispersed component and A, is the area occupied per surfactant molecule at the droplet surface. (26) Kahlweit, M. et al. J. Colloid Interface Sci. 1987, 118, 436. (27) Ravey, J. C.; Buzier, M.; Picot, C. J. Colloid Interface Sci. 1984, 97, 9. (28) Aveyard, R.;Lawleea, T. A. J. Chem. SOC.,Faraday Trans 1 1986, 82, 2951. (29) Kizling, J.; Stenius, P. J. Colloid Interface Sci. 1987, 118, 482.
Clark et al.
1304 Langmuir, Vol. 6, No. 7, 1990 single phase O f f l microemulsion
20
15
25
30
single phase W/O microemulsion
30
40
IempoC
50 lempOC
Figure 3. Single-phase stability regions for (a) the O/W and (b) the W/O microemulsions. The weight ratio of C12E6 to continuous solvent is 1:lO in both cases. The dashed lines show the solubilization phase boundaries. the solid curves show that cloud point curve (a) and the haze point curve (b).
6
e
E
.j t D
4
2
In addition to confirming the droplet size at the solubilization phase boundary, two further features of the droplet system are seen in Figure 4. Firstly, as expected from eq 3, the droplet size is independent of droplet volume fraction when Rlwatsris kept constant. Secondly, there is little effect of temperature on the droplet size as the onephase region is crossed. Both the solution viscosity and the apparent hydrodynamic radius increase sharply as one moves toward the haze curve in these systems.ll The TRF results (which are independent of assumptions concerning interparticle interactions) demonstrate these effects are not due to changing droplet size and hence must be due to changing interactions between the droplets. Hence, the droplet size in a one-phase “made-up” microemulsion is, to a reasonable approximation, controlled by the geometrical constraints imposed by the fixed sample composition as described by eq 6 and is therefore independent of temperature. This is in contrast to the behavior of a two-phase system of microemulsion coexisting with an excess phase of the dispersed component where the droplets are free to swell or shrink by solubilizing more or less of the dispersed component. As discussed earlier, the droplet size in this case is generally close to the “natural” size dictated by the spontaneous film curvature and varies strongly with temperature as indicated by the shape of the solubilization phase boundaries (Figure 3). Hence, the effect of temperature on the single-phase microemulsion droplets can be described as one in which moving from the solubilization curve to the haze curve causes an increased difference between the actual and spontaneous film curvatures. This increased difference appears to be associated with an increase in the attractive interactions between the droplets as one moves further from the solubilization curve. This is true for both O/W and W/O microemulsions stabilized by C12Es.” The variation of the apparent aggregation number with the concentration of quencher can be interpreted in terms of the polydispersity in Nagg.According to the analysis presented by Warr and Grieser30
0 0
20
40
tempemurm
Figure 4. Variation of CIzEa-stabilized water-in-heptane microemulsion droplet radius with temperature. The points refer to ClzEs concentrations and R’,,* values as follows: (e)0.184 mol dm-3, Rwater = 8;( 0 )0.184mol cm-3, Rlantsr = 16.4;(0)0.340 mol dm-3, R’,* = 8; (e)0.340 mol dm-3, = 16.4;(0)0.558 mol dm-3, Pwatsr = 8: ( 0 )0.558 mol dm-3, R’water = 16.4.
The droplet radii were calculated from the measured aggregation numbers of the microemulsiondroplets (Nsg) by using (7) r = ((3/4?r)~,(v,, + RlwaterVde))1/3 Veurfand Vdc are the molecular volumes of the surfactant and dispersed components, respectively. Radii calculated in this way for different surfactant concentrations, R’watervalues and temperatures are shown in Figure 4. The values are in reasonable agreement with the droplet hydrodynamic radii determined previously by light scattering, which were 3.7 f 1.5 and 5.8 f 1.5 nm for R’,,*, equal to 8 and 16.4, respectively.1l Since the hydrodynamic radii include the thickness of entrapped solvent, they might be expected to be slightly larger than the values derived from TRF data. However, no significant difference can be seen owing t o the large uncertainty in the lightscattering values caused by the low scattering intensity in these systems.”
= N,,, - a2/(2([quencher]/([surfactant]CPC))) (8) where a is the root mean square deviation in N- and N , is the weighted average. Within the uncertainty in NBgl (estimated to be of the order of 10-20% 1, no systematic variation of N,&apparent) with quencher concentration was found, indicating the value of u/Nw is less than approximately 30%. It should be remembered, however, t h a t a variation of Nag,(apparent) with quencher concentration can also arise as a result of a nonrandom distribution of probe molecules among the aggregates. The rate of quenching of RB fluorescence by MV in aqueous solution is close to the diffusion-controlled limit. Hence, the first-order rate constant for quenching within a micelle containing a single quencher molecule (k,) is a measure of the time taken for the fluorescor and quencher to diffuse together within the same micelle. A rigorous interpretation of 12, requires detailed knowledge of the locations of the probe molecules within the droplets (Le., whether they are located within the droplet core or interfacial region) and considerations of bounded or twodimensiond diffusion. Since we do not have such detailed knowledge, we have interpreted the data in terms of a greatly simplified model in which it is assumed that the
“(apparent)
(30)Warr, G. G.; Grieser, F.J. Chem. SOC.,Faraday Trans 1 1986,82, 1813.
Langmuir, Vol. 6, No. 7, 1990 1305
......
6.0
2.5
. ...
li
.- .. ...
‘8
5 ‘ 0
P 2.0
I
5.0
,/ / ’
0
1.5
4.0
3.0
I
I
3.2
3.4
1 .o 3.6
0
1TT/1@3 K-1
Bo
40 t
Figure 5. log (kqNwRtwater)versus 1/T for R’wabr = 8 (0)and Rantsr= 16.0 (0) water-in-heptanemicroemulsions. The dashed line is calculated assuming the microviscosity is equal to that of
bulk water.
molecules show normal three-dimensional diffusion behavior within the volume of the droplet cores. In this approximation, the relationship between k,, the microemulsion droplet volume u, and the apparent “microviscosity” qm within the droplets (i.e., that experienced by the probe molecules) is25
k, = 8RT/ (37,vNA)
m
(9)
The microemulsion droplet volume which is accessible to the probe molecules (u) is taken here as being equal to NaggR’waterVdc,where v d c is the molecular volume of the dispersed component (water in this case). It is assumed here that the accessible volume of the microemulsion droplets does not include a significant fraction of the surfactant shell volume. (Including the volume of the hydrophilic headgroups of the surfactant would yield an estimated of qm lower than the value calculated here by a factor of approximately 2). The collected values of kqNeggR‘wabr,predicted by eq 9 to be proportional to l/qm, for the different surfactant concentrations and droplet sizes are shown in Figure 5 as an Arrhenius type plot. The dashed line shows the behavior expected if qm is equated with the viscosity of bulk water. Although the temperature variation of the calculated and experimental values is similar, the experimental points are approximately 10fold lower than the calculated values. Hence, the apparent microviscosityexperienced by the probe molecules within the water droplets is approximately 10 times that of bulk water (i.e., approximately 10 cP). It should be noted that this analysis in terms of apparent microviscosity provides only one possible explanation for the primary observation, which is that the intradroplet quenching rate is 1 order of magnitude slower than would be expected on the basis of normal three-dimensionaldiffusion within a homogenous solvent. Other explanations, such as unfavorable partitioning of the probe molecules between the droplet core and surface regions, cannot be excluded. The first-order fluorescence intensity decay rate constant ko is independent of surfactant concentration and Rlwater value but increases with temperature as shown in Figure 6. The dashed curve in Figure 6 shows the values measured
”
w
c
Figure 6. Unquenched fluorescencedecay rate constant ko for RB in W/O microemulsion droplets stabilized by C ~ Z EThe ~. dashed line shows the behavior in water. The points refer to [ C I ~ Eand ~ ] R‘wabr values as follows: (0) 0.184 mol dm-3, R’wabr = 8; (0)0.184 mol dm-3, R’,, = 16.4; (0)0.340mol dm-3, Pant, = 8; (0)0.340 mol dmS, RrWter= 16.4; (e)0.558mol dm-3, Rtwnte, = 8; ( 0 )0.558 mol dm-3, R’watar = 16.4.
in bulk water (data from ref 31). The rates are independent of microemulsion droplet size for RB in droplets stabilized by the negatively charged surfactant AOT whereas they increase with increasing droplet size for cationic surfactant stabilized droplets.4 The independence of ko on droplet size is thought to suggest that RB is associated with the surfactant monolayer in the water d r ~ p l e t s .The ~ photophysical behavior of RB has a complex dependence on solvent properties; however, the lower values of ko for RB in microemulsions are consistent with the idea that the local environment experienced by the probe in the microemulsions is somewhat less polar than bulk water.32 Having assumed the interdroplet exchange of probe species occurs by the fusion-fission mechanism, we can derive values of the first-order rate constant for coalescence, k t , from the data. The first-order rate constant kt is proportional to the droplet concentration within the estimated uncertainties (Figure 71, and the slopes yield the values of the second-order rate constant for coalescence, k,, for the different temperatures. Arrhenius plots of k, for droplets with R’water values of 8 and 16.4 are shown in Figure 8. The rate constants increase with decreasing temperature giving apparently negative enthalpies of activation. Droplet coalescence is slowest a t the high temperature phase limit of the single-phase W/O microemulsion stability range, which corresponds to the solubilization phase boundary. The dashed line in Figure 7 shows the temperature variation of the diffusion-controlled rate constant k d c predicted for noninteracting spheres having no energy barrier to coalescence. This is calculated according to the Smoluchowski equation33 where q is the viscosity of the continuous solvent. The diffusion-controlled rate is approached at low temperatures as the haze curve phase boundary is approached. The (31) Van Houten, J.; Watte, R. J. J. Am. Chem. SOC.1976,98,4853. (32) Caspar, J. V.;Meyer, T. J. J. Am. Chem. SOC.1983,105, 5683. (33) Smoluchowski, M. V. 2.Phys. Chem. 1917,92, 129.
Clark et al.
1306 Langmuir, Vol. 6, No. 7, 1990
1.0
f 0.5
0.0
0
3
2
1
dmplel mmntri1110~103mol dm-3
Figure 7. First-orderrate constant for exchange (k,)versus W/O droplet concentration for R‘,,,, = 8 droplets at 52.2 O C (O), 34.5 O C (e),and 21.0 O C (0). 1.5 r
,h-
9d
5
i
10
05
0 3.0
3.2
34
3.6
lfl110-3K-1
Figure 8. Arrhenius plot of log k, versus 1/T for R‘wahr = 8 (e) and R’wa-r = 16.4 (0) W/O microemulsion droplets.
unusual temperature dependence of the coalescence rate implies that the magnitude of the energy barrier to exchange alters as the temperature is changed within the microemulsion stability range, as has been suggested previously.’ Droplet coalescence rates have been reported for W/O microemulsions stabilized by the anionic surfactant AOT1939798 for microemulsions stabilized by the cationic surfactant dodecyltrimethylammoniuinchloride (DTAC) with butanol as cosurfactant2 and for droplets stabilized by a series of alkyl and alkylphenylammoniumsalts.4 For W/O microemulsions stabilized by ionic surfactants, the solubilization boundary corresponds to the low-temperature limit, and, in all the cases referred to above, the coalescence rate is slowest as the lower temperature phase boundary is approached. Coalescence rates have also been measured for W/O droplets stabilized by the nonionic surfactant Triton X-100.6,21 The rate constants are of a similar magnitude
to those reported here (between 0.2 X 109 and 2 X 1Og dm3 mol-’ s-l, dependent on sample composition). Oil-in-Water(O/W) Microemulsions. There are two major differences between the O/W and W/O microemulsion droplets stabilized by C12E5 which are relevant to the discussion here. Firstly, the cpc in water (assumed to be similar in magnitude t o the critical micelle concentration) is very low34as compared with the value in oil. Secondly, the temperature dependenceof the system is reversed; i.e., the solubilization phase boundary forms the lower temperature phase boundary and the cloud point curve (the equivalent of the haze curve) forms the upper temperature limit of the stable microemulsion temperature range (Figure 3). As described previously, the temperature dependencesof the equilibriumdroplet sizes formed in twophase systems, the droplet interactions, and interfacial tensions are similar in magnitude but inverted with respect t o temperature as compared with the WO microemulsions. The droplet hydrodynamic radius is proportional to the molar ratio of dispersed oil to surfactant in the microemulsion droplets R’dkme (=[alkane]/([Cl~E5] - cpc)). For the systems considered here, the hydrodynamic radii are 5.2 f 0.2 and 7.1 f 0.2 nm (heptane as oil, R’dkane = 1and 2, respectively) and 5.2 f 0.3 and 7.5 f 0.3 nm (tetradecane as oil, R ’ d h e = 0.5 and 1.0, respectively).ll The radii at the solubilization limit calculated by using the TRF data are 4.1 and 5.8 nm for the low and high R’dkane values, respectively, for both heptane and tetradecane as oil (Figure 9). These values are significantly lower than the light-scattering data. It is estimated from viscosity data that approximately 40 water molecules are associated with each surfactant molecule.ll When the volume of this entrapped water is taken into account in calculating the droplet radius by using Naeg(eq 71, the TRF radii are increased to 5.4 and 7.3 nm, in agreement with the measured hydrodynamic radii. As shown in Figure 9, no large changes in droplet radius occur when the temperature or surfactant concentration is changed at constant R. The internal “microviscosity”experienced by the pyrene probe molecules within the microemulsion droplets can be estimated by using the intradroplet quenching rate constants (k,) and the procedure described for the W/O microemulsions. The Arrhenius type plots, together with the rates calculated assuming bulk alkane viscosities, are shown in Figure 10. The apparent microviscosities are 1-2 orders of magnitude larger than the bulk oil component values, with higher viscosities observed in the smaller microemulsion droplets. Similar microviscosity behavior has been estimated for O/W microemulsion droplets stabilized by the anionic surfactant sodium bis(2-ethylhexy1)sulfosuccinate (AOT).z5 As for the W / O microemulsions, the mobility restriction of the pyrene molecules may be a consequence of factors other than the oil microviscosity, and the derived apparent microviscosities may encompass effects such as association of the pyrene with the surfactant film. The unquenched fluorescence intensity decay rate constant ko was found to be independent of the droplet size and concentration. The value is 2.48 X lo6 s-l at 5 O C to 3.00 X 106 s-1 at 30 OC. The rate constant in bulk heptane at 25 “C is 2.35 X lo6 s-1.25 The first-order rate constant for droplet coalescenceK t shows an approximately linear dependence on the droplet concentration as shown in Figure 11. For the O / W droplets, the coalescence rate (expressed as the second(34) Mukerjee, P.;Mysels, K.J . Critical micelle Concentrations of Aqueous Surfactant Systems; NSRDS-NBS 36, 1970.
Langmuir, Vol. 6, No. 7, 1990 1307
Interdroplet Exchange Rates of Microemulsion Droplets
(a)
1
-- -- ------- - - --
3.4
20
10
0
3.5
temperaturePC 1-
3.6 l”3-3
I
K1
I
-
1
2t
-0
2
0
10
20
30
3.3
3.4
temperaturePC
Figure 9. Droplet radius versus temperature for O/W micro-
emulsion droplets. (a) The oil is heptane, and the points refer to [ClZEa] and R’dbne values as follows: (e) 0.026 mol dm-3, R’dkane = 2; (0) 0.049 mol dm-3, R ’ d h e = 2; ( 0 )0.198 mol dm-3, R’dkme = 2; ( 0 )0.049 mol dm-3, R ’ d h e = 1. (b) The oil is tetradecane, and the points refer to 0.049 mol dm-3, R’dkane = 0.5 (0) and 0.049 mol dm-3, R’dkme = 1.0 ( 0 ) .
order rate constant k,) is large enough to be determined only at temperatures close to the cloud point curve (the upper temperature phase boundary). For the lower temperatures, A2 does not differ sufficiently from ko to allow the reliable estimation of kt, and it is possible only to specify a lower limit for k,. In spite of this constraint, it can be seen in Table I that the values of k, for heptane and tetradecane as oil increase with i n c r e a s i n g temperature. As for the W/O microemulsion droplets, the coalescence rate is slowest at the solubilization phase boundary, although this corresponds to a reversal in the temperature dependence. For the case of heptane as oil, k, at temperatures close to the cloud point curve is larger than the diffusion-controlled limit calculated for “hardsphere” particles, implying attractive interdroplet interactions are present. This interpretation of the TRF measurements is supported by the self-diffusion studies of Olsson et al.35 They conclude that rapid fusion-fission of oil-in-water miE ~ as the croemulsion droplets stabilized by C I ~ occurs upper temperature stability limit is approached. Factors Affecting the Droplet Coalescence Rate. The coalescence process can be broken down into the formation of a droplet encounter pair which then coalesces to form a transient droplet dimer.’ The coalescence of the encounter pair is postulated to proceed via an “hourglass”(35) Olsson, U.; Nagai, K.;Wennerstrom, H.J.Phys. Chem. 1988,92, 6675.
3.5
3.6
1ffH0-3 K-1
Figure 10. log (kgNeggR_ldbe)versus 1/T for (a) heptane-inand (b) tetwater droplets, R ’ d b a - ( 0 )and R’ame = 2 (0) radecane-in-waterdroplets, R’dkme = 0.5 ( 0 )and R’qlkane = 1.0
(0). The dashed lines are calculated assuming the microviscosities are equal to those of the bulk oils.
0
0.5
1.0
dmpletmrrentmtbNl(r3mol dm3
Figure 11. First-order rate constantfor exchange (kt)versus heptane-in-waterdroplet concentration for R ’ d b e = 2 at 19.1 O C . shaped transition state as shown in Figure 1. According to this mechanism, the second-order rate constant, k, should become larger for all factors which increase the “stickiness” of droplet collisions, thus enhancing the formation of the encounter pair, and for all factors which reduce the energy cost of forming the transition state.
1308 Langmuir, Vol. 6, No. 7, 1990
Clark et al.
Table I. Summary of Droplet Coalescence Rates for O/W Microemulsions Stablized by CllEs k,, 1P dm3 kde, 109 dm3 R'dkana
temp,
O C
1.0 1.0 1.0 2.0 2.0
5.8 13.2 18.6 13.0 19.0
0.5 0.5 1.0 1 .o
21.0 30.0 21.1 30.3
mol-'
8-1
mol-' s-l
Heptane
