J . Phys. Chem. 1990, 94, 381-395 terpreted on the basis of the effect of the solvent dielectric constant on interactions between head groups. The effect of head-group size was found to be opposite to the predictions of the Shah et a]. model. This is probably due to the fact that part o f t h e head group Of the 'ynthesized surfactant played the role Of a cosurfactant and passed from the Water side to the Oil side as the head-group Size Was increased. The effect Of the WSUrfaCknt Size overshadowed that of the head-group size, making our observations consistent with the Shah et al. model. Registry No. N l6,4,l,l,Br, 96018-76-7;N16,6,1,1,Br, 73458-93-2;
387
N16,8,1,1,Br, 107004-19-3;Nl6,O@,l,l,Br,17695-00-0;NlO,l@,l,l,Br, 32014-84-9; Nl8,l@,l,l,Br, 22546-65-2; Nl2,l@,l,l,Br, 7281-04-1; Nl6,
[email protected],l,Br,122699-34-7;N16S)@~l~l~CL 26038-94-8; NIO,l@*l~I~CL 965-32-2; NI8,14t1.I>CIt 122-194 N 1 2 * I ' b ~ l , I ~ c139-07-1; l~ Nl6,2@,l,l,Cl,122699-33-6;Nl4,l@,l,l,Cl, 139-08-2;Nl6,1@,1, I ,CI, 122-18-9; Nl2,4,1,1,Br(Bu), 29481-60-5;Nl2,4,1,1,Br(i-Bu), 11453279-5; PhMe2N, 121-69-7; (phCH2)Me2N,103-83-3;H20, 7732-18-5; hexadecyldimethylamine, 112-694; dodecyldimethylamine, 112- 18-5; benzene, 71 -43-2; toluene, 108-88-3;xylene, 1330-20-7;ethylbenzene, 100-41-4;1,3,5-trimethylbenzene,108-67-8;styrene, 100-42-5;chlorobenzene, 108-90-7;bromobenzene, 108-86-1; 1-bromonaphthalene,9011-9.
Ternary Water in Oil Microemulsions Made of Cationic Surfactants, Water, and Aromatic Solvents. 2. Droplet Sizes and Interactions and Exchange of Material between Droplets A. Jada, J. Lang,* R. Zana, Institut Charles Sadron (CRM- EAHP), CNRS- ULP Strasbourg, 6 Rue Boussingault. 67000 Strasbourg, France
R. Makhloufi, E. Hirsch, and S. J. Candau Laboratoire de Spectrometrie et d'lmagerie Ultrasonores, 4 Rue Blaise Pascal, 67000 Strasbourg, France (Received: March 2, 1989)
Ternary water in oil microemulsions made of cationic surfactants, water, and aromatic solvents have been investigated by means of time-resolved fluorescencequenching, quasi-elastic light scattering, and electrical conductivity in order to determine the surfactant aggregation number N per water droplet, the rate constant k, for the exchange of material between droplets through collisions with temporary merging, the droplet diffusion coefficient D, and the coefficient of interaction between droplets (Y and to study the Occurrence of electrical percolation as a function of the surfactant chain length, head-group size, and water content of system (expressed as the molar concentration ratio w = [water]/[surfactant]). Most measurements were performed with chlorobenzene as solvent. In one instance, chlorobenzenewas substituted by benzene in order to investigate the effect of the nature of the solvent. For a given surfactant, Nand k, increased with w and upon substituting chlorobenzene by benzene. Also, at a given w, Nand k, increased when the surfactant chain length was decreased. The increases of k, were always extremely large. The droplet hydrodynamic radii from quasi-elastic light scattering were found to agree with the droplet sizes calculated with the N values from fluorescence quenching. The droplet interaction coefficient a became more negative as the surfactant chain length decreased, indicating increasingly attractive interdroplet interactions. Finally, electrical percolation was found to occur in all systems were interdroplet interactions were sufficiently attractive. The percolation threshold w-values increased with surfactant chain length. Our results clearly showed that, under fixed experimental conditions, a decrease of surfactant chain length can result in a moderate increase of N, an increase of the magnitude of attractive interdroplet interactions, a very large increase of k,, and a decrease of the percolation-thresholdvalue. From a more quantitative viewpoint, it was noted that in all instances, including numerous other studies where conductivity data and k, values are available, the percolation threshold corresponds to k, values of about (1-2) X lo9 M-' s-I. This result led us to attribute the electrical conductivity of water in oil microemulsions above the percolation threshold to the motion of surfactant counterions within transient water channels arising in droplet clusters upon opening of surfactant layers separating adjacent water droplets.
Introduction The first part of this work,' reported the results of a systematic study of the solubility of water in binary systems made of cationic surfactants and aromatic solvents. The aim of this study was to investigate the effect of surfactant chain length, counterion and head-group size, and the oil nature on the water solubility in these binary systems. The results were discussed in terms of the two main effects that govern the stability of water in oil (w/o) microemulsions, namely, the curvature of the surfactant film separating the oil and water and the attractive interactions between water droplet^.^,^
In this second part of our work, we report results concerning the size of water droplets, interactions between droplets, and the rate of the exchange of material between droplets through collisions with temporary merging (sticky collisions: see Figure 1) and measurements of electrical conductivity, for some of the systems studied in part 1' and selected on the basis of their large water solubility. Two types of cationic surfactants have been studied: dodecylbutyldimethylammonium bromide: C12H25(C4H9)N+(CH3)2Br- referred to as N12,4,1,1 ,Br; alkyl(phenylalkyl)dimethylammonium chlorides: CmHWl[C6H~(CH2),]N+(CH3)2C1-
( I ) Jada, A,; Lang, J.; Zana, R. J . Phys. Chem.,the preceding paper in this issue. (2) Hou, M. J.; Shah, D. 0.Longmuir 1987, 3, 1086, and references cited
(3) Leung, R.; Shah, D. 0. J . Colloid Interface Sci. 1987, 120, 320 and 330. (4) Fletcher, P. D. I.; Robinson, B. H. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 863.
therein.
0 1990 American Chemical Society
388 The Journal of Physical Chemistry, Vol. 94, No. I , 1990
Figure 1. Exchange of material between droplets through collisions with temporary merging. The exchange is illustrated by the transfer of the black dot from one droplet to the other and is characterized by the overall second-order rate constant k,.
Jada et al. t = 0, respectively, following excitation. A2, AS, and A4 are time-independent parameters that are obtained, together with I(O), by fitting eq 1 to the decay data, using a nonlinear weighed least-squares procedure. In the case where the probe and quencher distributions are frozen on the probe fluorescence time scale (no detectable interdroplet exchange of reactants), the expressions for A,, A,, and A, are1* A2 = k,:
with m = 10, 12, 14, 16, and 18 and p = 0-2, referred to as Nm,p$,I,l.CI. The organic solvent was chlorobenzene or benzene. The droplet sizes and exchange rate constants k, have been determined by the time-resolved fluorescence quenching method and the interactions between droplets by quasi-elastic light scattering (QELS). Both techniques have already been widely used for the study of w/o microemulsions. I t will be shown that the variations of droplet size with the surfactant structure can also be interpreted by the recent approach of Shah et aL2s3 More importantly, the results obtained in the present work reveal a strong correlation between the magnitude of interdroplet attractive interactions, rate of the exchange of material between droplets, and Occurrence of electrical percolation.
Materials and Methods I . Materials. The surfactants and solvents were the same as in the preceding paper in this issue. The water content of the microemulsions is expressed as the molar concentration ratio w
2. Methods. The time-resolved fluorescence quenching method used in this work is essentially the same as in many investigations carried out on direct micelle^,^ oil in water micro emulsion^,^ and water in oil micro emulsion^.^^^ The ruthenium tris(bipyridy1) ion (Rubpy, under the chloride salt form) was used as fluorescence probe for its long lifetime, and the methyl viologen ion (MV, under the chloride salt form) was used as quencher. Both probe and quencher, referred to as reactants in the following text, are cations that are solubilized in the water droplets. The probe was used at a [Rubpy]/[M] molar concentration ratio between 0.01 and 0.08 ([MI is the droplet concentration). The quencher concentration, [Q], was such that the molar concentration ratio R = [Q]/[M] was between 0.5 and 1.5, except in studies of the effect of the quencher concentration, in which case the ratio R was increased to 2.5. The fluorescence decay data of excited Rubpy solubilized in water droplets were collected by means of a single-photon counting apparatus? The excitation wavelength was 480 nm, and the emission was monitored above 530 nm with a high-pass cutoff filter. All solutions were thoroughly deoxygenated prior to each fluorescence measurement by carrying out at least four freezepump-thaw cycles. The fluorescence decay curves obey the equation1+l4
- A3[ 1 - exp(-A,t)])
A4 = kQ
(2)
where ko is the fluorescence decay rate constant of the probe in droplets without quencher and kQ the pseudo-first-order rate constant for intradroplet fluorescence quenching. In this case, the mean surfactant aggregation number (average number of surfactant per droplet), N , is given by (3) where Cis the total surfactant concentration. Equation 3 assumes that all the surfactant is used in making up droplets. In the case where interdroplet exchange of the quencher takes place on the fluorescence time scale by collisions between droplets, as shown in Figure 1, A,, A,, and A, are given byi3-15 A2 = ko
(k$q/A,)/[Q]
(4)
A3
= R(kq/A4),
(5)
A4
= kQ + k,[M]
(6)
From eq 4-6, N , k,, and k, are obtained as a function of the experimental quantities A,, A,, A,, and ko as follows:
= [H,O] / [surfactant]
I ( t ) = I(0) exp(-A,t
A3 = R = [Q]/[M];
(1)
where f(t) and f ( 0 )are the fluorescence intensities at time t and
(5) Malliaris, A.; Lang, J.; Zana, R. J . Chem. SOC.,Faraday Trans. I 1986, 82, 109, and references cited therein. (6) Malliaris, A.; Lang, J.; Sturm, J.; Zana, R. J. fhys. Chem. 1987, 91,
1475, and references cited therein. (7) Lang, J.; Jada, A.; Malliaris, A. J . fhys. Chem. 1988, 92, 1964. (8) Lang, J.; Mascolo, G.;Zana. R.; Luisi, P. L. Manuscript in preparation. (9) Pfeffer. G.; Lami, H.: Laustriat, G.;Coche, A. C. R. Hebd. Seances Acad. Sei. 1963, 257, 434. (IO) Infelta, P.; Gratzel, M.; Thomas, J. K. J . fhys. Chem. 1974, 78, 190. ( I 1 ) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (12) Atik, S. S.; Nam. M.; Singer, L. Chem. f h y s . Lett. 1979, 67, 75. (13) Atik, S. S.; Thomas, J . K. J . Am. Chem. SOC.1981, 103, 3543. (14) Dederen, J. C.; Van der Auweraer, M.; De Schryver, F. C. Chem. f h y s . Lett. 1979, 68, 451,
The fluorescence decay rate constant ko was obtained, for each system investigated, from an independent fluorescence decay experiment in the absence of quencher. Under our experimental conditions, the error in the determination of ko and A2 was &2.5%. Therefore, the exchange of reactants between droplets could be observed only when the condition A2 - ko > 0.05ko was fulfilled. Since ko was about 5 X IO6 s-l, the error in the value of k, was IO-20% for the largest k, values (above lo9 M-' s-I ) a nd more than 50% for k, values around lo8 M-' s-I. No k, values below lo8 M-' s-l could be reasonably measured. The error in the determination of N was f 15%. Almgren et a1.I6 have shown that eq 4-6 are not valid if exchange of excited probes by interdroplet collisions is taken into account. However, eq 7 and 8 are not modified, and only eq 9, which gives k,, is then different. It has been found,' in the study of reverse micelles based on the anionic surfactant sodium bis(2-ethylhexyl)sulfosuccinate (AOT) with [QJ/[M] = 1, that the k, values calculated with eq 9 were slightly lower, by less than 20%,compared to those obtained from the data analysis proposed by Almgren et a1.I6 Therefore, since this analysis is not straightforward, eq 9 has been used throughout this work. If it is assumed that all the water and the surfactant are in the form of water droplets and that'all droplets are spherical, monodispersed, and separated from the continuous oil phase by a monolayer of N surfactant ions, the radius of the water core R, ( 1 5) Grieser, F.; Tausch-Treml, R. J . Am. Chem. Soc. 1980, 102, 7258. (16) (a) Almgren, M.; Lbfroth, J.-E.; Van Stam, J. J . fhys. Chem. 1986, 90, 4431. (b) Almgren, M.; Van Stam, J.; Swarup, S.; Lofroth, J.-E. Langmuir 1986, 2, 432.
Water/Oil Microemulsion Droplet Sizes and Interactions
The Journal of Physical Chemistry, Vol. 94, No.
I, 1990 389
and the spherical surface area, u, per surfactant ion at the water droplet surface are expressed as
Rw
=
{ CT
+ ux)
3N(wu, 4a
1
= 4aRW2/N
-t
1600 (11)
where R, is in A, u is in AZ,and u, represents the molecular volume of water (29.9 A3 at 25 " C ) and ux the apparent molecular volume of the counterion (Br- or CI- for the surfactants investigated here). In Tables I and 11, the values used were uBr- = 49.3 A3 and oc,- = 37.9 A3." The overall droplet radius RM can be taken as RM = R ,
+I
i
2ooo
1200
(12)
t
\
0.4 0.8
4
i
w=30
1.2
1.6
2'
where I represents the length of the fully extended surfactant ion. Figure 2. Variations of N with R at various w for water/chlorohave been used for the Values of 1 = 20.4, 22.9, and 25.5 benzene/Nl2,4,1,1,Br microemulsions: C = 0.27 M; T = 20 OC. surfactant ions Nm,l+,l,l with m = 12, 14, and 16, respectively. I I I I QELS measurements were carried out using an argon-ion laser I N ' .. operating at 488 nm. The scattered light was collected at a 2100 o =60 scattering angle fixed at 90". The time-averaged intensity and time-dependent correlation function of the scattered intensity were recorded on a Malvern correlator with 72 channels. The auto1500 correlation function of the photoelectric current of the photomultiplier g ( * ) ( t )was analyzed using the cumulant m e t h ~ d : ' ~ J ~ g'z)(t) = 1
+ B exp(-2D$t)
(13)
In eq 13, B is a constant that depends on the experimental setup, D is the translational diffusion coefficient of the droplets, t represents the time, and q is the wave vector, given by q=
900 -
W=
30
-t-
+-+,
4 ~ n sin (0/2) A0
where n is the refractive index of the solution, ho the wavelength of light in vacuo,and 0 the scattering angle. For interacting droplets, D can be written, in the low-concentration range, as
D = Do(1
+ a@)
Figure 3. Variations of N with R at various w for water/chlorobenzene/Nl6,1~,1,1,C1microemulsions: C = 0.27 M; T = 20 OC.
(14)
where Dois the intrinsic diffusion coefficient at infinite dilution and @ the droplet volume fraction in the microemulsion, given by VH~O + vs - C( 1 8 +~ US) @= 05) V 1000 where VHloand Vs are the volume of water and surfactant, respectively, in a volume Vof the microemulsion, Cis the surfactant concentration in moles per liter, and us is the apparent molar volume of the surfactant expressed in cm3/mole. In the following text, values of os equal to 369,406, and 443 cm3/mol have been used for the surfactants N m , l + , l , l , C l with m = 12, 14, and 16, respectively. In eq 14, a is the virial coefficient associated to the diffusion coefficient D. Recall that for hard-sphere-type interactions a = 1.5 and that negative values of a correspond to attractive interactions. The values of D can be used for the calculation of the hydrodynamic radius R H ,from the Stokes-Einstein equation RH = kT/6avD
(16)
where 7 is the solvent viscosity. Notice that RH is only an apparent hydrodynamic radius since it involves a contribution due to droplet interactions. Electrical conductivity measurements were performed using an automated autobalanced conductivity bridge (Wayne-Kerr type B905). operating at a frequency of 1 kHz. (17) Millero, F. J. Chem. Rev. 1971, 71, 147. (18) Dynamic Light Scattering Pecora, R., Berne, B. J., Ed.; Wiley: New
York, 1976. (19) Koppel. D. E. J . Chem. Phys. 1972, 57, 4814.
0
10
20
30
LO
50
60
Figure 4. Variations of N and k, with w for water/chlorobenzene/ Nm,l@,l,l,Clmicroemulsions with m = 10 ( O ) , 12 (+), 14 (B), 16 (0). and 18 ( X ) and for water/chlorobenzene/N12,4,l,l,Br ( 0 ) microemulsions: C = 0.27 M; T = 20 O C .
Results I . Time-Resolved Fluorescence Quenching. I . I . Variations of N and k,. We have first investigated the effect of the quencher concentration [Q] on the surfactant aggregation number N per droplet. Recall that a decrease of N upon increasing [Q]is an indicator of a system of polydisperse micellesZoif the quencher
171,0mj(S
390 The Journal of Physical Chemistry, Vol. 94, No. 1. 1990
::I @
Jada et al.
-
/I-
1200
0
0.05 0.1 015 0.2 0
0.05 0.1 0.15 0.2
Figure 6. Variations of N and k , with C for water/chlorobenzene/ Nl2,l@,l,l,Cl microemulsions with w = 20 ( 0 )and for water/chlorobenzene/Nl6,lI$I,l,l,CImicroemulsions with w = 20 ( X ) and w = 40 (0): T = 20 "C.
0 10
20
30
I0
10
20
30
IO
Figure 5. Variations of N and k , with w for water/chlorobenzene (+) or benzene (X)/Nl6,lI$I,l,l,Clmicroemulsions: C = 0.27 M; T = 20 OC.
has no effect on micelle size, as is the case of MV ions at the low concentration used in this work. The results in Figures 2 and 3 for water/chlorobenzene/N I2,4,1,1 ,Br and water/chlorobenzene/N 16,1$, 1 , I ,Cl microemulsions show that N remains constant or decreases only slightly as R increases, up to 2.5 in some cases. Moreover, the value of N at R = 1 is only a few percent below that extrapolated to R = 0. Other systems also showed a small change of N upon increasing R up to 1.5. This is why all time-resolved fluorescence data reported below were obtained with 0.5 < R < 1.5. The small changes of N with R indicate that the polydispersity was small. Figure 4 shows the variations of N and k , (rate constant of exchange between droplets) with the ratio w for water/chlorobenzene/Nm,I$,l,l,CI or N12,4,1,1,Br microemulsions. Table I lists the corresponding values of R, and u. The low solubility of water in the NIO,I$,I,I,Cl/chlorobenzenesolutions prevented determinations of N a n d k , for w > 5. As expected, the droplet size (Nand R,) increases with w . Our results also show that N increases when the surfactant chain length decreases, at a given w . They provide the first clear experimental evidence that the effects of surfactant chain length and oil (alkane) chain length on droplet size are opposite, in agreement with theoretical predictions.*I2' Figure 4B and Table I show that the k, values increase with w for the m = 12 and 14 surfactant-containing microemulsions. The main result, however, is the very large increase of k , upon decreasing m. Thus, for the m = 16 and 18 surfactants, k, is very small with values around or below IO8 M-'s-I, at the limit of detection of our setup in the experimental conditions used. For the m = 12 and 14 surfactants, k, is much larger, with values as high as 6 X IO9 M-' s-I. Recall that the process characterized by the rate constant k, corresponds to the opening of the surfactant layers separating the water cores of two collided droplets. It thus represents a measure of the surfactant layer facility to open. In the following text, the word rigidity is used to refer to this property of the surfactant layer. Figure 4 and the values listed in Table 1 show that there is no direct correlation between the values of N (or R,) and k,, when one substitutes one surfactant for another. Indeed, for a given value of N , the values of k, dramatically depend on the surfactant. For instance, the value N = 1000 corresponds to k , = 5 X IO9 M-'s-I for the N12,1@,1,1,CIsystem and to k , < 1O8 M-I s-' for the N 18,1$,l, 1,Cl system. Thus, two droplets of nearly equal sizes can have very rigid or rapidly opening surfactant layers, depending on the surfactant chain length. The effect of the surfactant head-group size on N a n d k , has been investigated with the four surfactants: N16,p@,l,l,C1with p = 0-2 and N12,4,1,1,Br. Table I1 gives the values of N, R,, u, and k, for the two systems water/chlorobenzene/N16,1$,1,l,C1 and water/chlorobenzene/N16,0@,1,1,C1+ N16,2@,1,l,CI with (20) Almgren, M.; Lofroth, J.-E. J . Chem. Phys. 1982, 76, 2734. (21) Mukherjee, S.; Miller, C. A.; Fort, T., Jr. J . Colloid Interface Sci. 1983, 91. 223.
0
01 0 2
03 O I 0
01
02
03
04
Figure 7. Variations of N and k, with C for water/chlorobenzene/ N l 4 , l ~ , l , l , Cmicroemulsions l with w = 10 ( X ) and w = 40 ( 0 ) : T = 20 O C
a mole fraction of N 16,0$, 1,l ,Cl surfactant equal to 0.2. Recall that this composition corresponds to the maximum of water solubility as the composition of this surfactant mixture is varied (see the preceding paper in this issue). Table 11 shows that the values of N,R,, and u are very close for the two systems whereas a factor of 2 exists between the values of k,. This shows again that droplets of equal size may have different film rigidity. Notice that the microemulsion based on the surfactant mixture p = O / p = 2 behaves similar to those made of pure surfactant: N a n d R, increase with w, and an increase of k , parallels that of N. The comparison of the values of N and k, for the systems with NI2,I$,I,l,CI and N12,4,1,1,Br (see Table I) reveals large differences between the two systems. The butyldimethylammonium bromide head-group gives smaller droplets and lower k, values than the benzyldimethylammonium chloride head group. Figure 5 shows the effect of the nature of the oil (chlorobenzene or benzene) on N and k, for water/oil/N 16,1$, 1,l ,Cl microemulsions. For both systems, N increases with w . At a given w, N is larger for the microemulsions made with benzene than with chlorobenzene but the relative difference decreases upon increasing w . The most striking effect of substituting chlorobenzene by benzene is, however, in the very large increase of k,, from below lo8 M-' s-l to well above lo9 M-' s-I. The comparison of Figures 4 and 5 indicates that chlorobenzene/benzene substitution is equivalent to reducing the surfactant chain length by about three carbon atoms. The above results clearly show that the exchange of material upon droplet collision and the rigidity of the surfactant layer strongly depend on the nature of the oil through its penetration in the surfactant layer and the resulting effect on the properties of this layer. These results confirm those previously reported for the effect on the alkane chain length in waterlnalkane/AOT microemulsions: a large increase of k, was found in going from n-hexane to n-dodecane.' The effect of the surfactant concentration C,at constant w, on the values of N and k, in chlorobenzene microemulsions is shown in Figures 6-8. Figure 6A (Nl6,l$,l,l,Cl systems at w = 20 and 40 for C between 0.01 and 0.18 M, that is, for dispersed-phase
Water/Oil Microemulsion Droplet Sizes and Interactions
The Journal of Physical Chemistry, Vol. 94, No. 1 . 1990 391
I-
01
W
0.2
0.3 0.4
0 1 0.2
x-l
0.3 0 L
Figure 8. Variations of N and k, with C for water/chlorobenzene/ N12,4,1,1,Br microemulsions with w = I O (+), w = 20 (X), and w = 30 ( 0 ) : T = 20 OC.
750
I
- T '(ns) ~
I
600 -
2
I
2 2
-N1"
0000
x
550-
,
10
30
-
I
I
x
+ + + + I
I
50
70
I
90 ,110 R, ( A )
Figure 9. Variation of the lifetime T~ of Rubpy with the water-pool radius R, for water/chlorobenzene/Nm,l&l,l,Clmicroemulsions with m = 10 (O), 12 ( O ) , 14 (m), 16 (X), and 18 (+), for water/benzene/ Nl6,l@,l,l,Cl microemulsion (0) and for water/chlorobenzene/ N12,4,1,1,Br microemulsions (A): C = 0.27 M; T = 20 "C.
II h
..
E
N P
1 % 3
volume fraction 0 between about 0.01 and 0.2) and Figure 8 ( N 12,4,1,1,Br microemulsions) show that N is independent of, or varies only a little with, increasing C. Such results support the usually made assumption that the droplet size in water in oil microemulsions remains unchanged when @ is increased at constant w. However, these results are by no means general. Thus for Nl2,14,1,l,Cl (Figure 6A) and Nl4,14,1,l,Cl (Figure 7A) microemulsions, a notable increase of N (and thus of droplet size) with C is observed. In general, the largest variation of N is observed with the surfactant having the shortest chain, Le., that for which the k, values are the largest and, as will be seen below, where the attractive interactions between droplets are the largest. A similar result was found for the AOT/n-alkanelwater microemulsions.' At this stage, it is noteworthy that a variation of N by a factor of 2, as observed in Figure 6A or 7A for instance, corresponds to a variation of R, by a factor of only 1.26. Thus, the time-resolved fluorescence quenching method is more sensitive to variations of droplet size than methods that directly determine droplet radii. As the latter are usually also sensitive to interdroplet interactions and droplet shape, moderate changes of droplet radius can fall within the experimental uncertainty. As a final remark, Figures 6B, 7B, and 8B show that k, follows the trends of the variations of N with C. 1.2. Probe Lifetime 7,,.Figure 9 shows that the Rubpy lifetime, T ~ measured , in the absence of quencher, is sensitive to the size of the water pool where the probe. is solubilized. Thus, r0 decreases from a high value indicative of a not so polar environment22at low R , to a smaller value, close to that in pure water, at large R,. Recall that in AOT/n-alkanelwater microemulsions the Rubpy lifetime was found to be independent of R,. This difference between the two types of microemulsions is clearly due to the interaction between the positively charged Rubpy and the charged surfactant layer. In the AOT (anionic)-based microemulsions it (22) Kalyanasundaram, K.; Thomas, .I.K. J . Am. Chem. SOC.1977, 99, 2039.
392
The Journal of Physical Chemistry, Vol. 94, No. I , I990
Jada et al.
TABLE 11: Surfactant Aggregation Number ( N ) , Radius of the Water Pool ( R , ) , Surface Area (a)per Surfactant Molecule at the Surface of the Water Pool, and Second-Order Rate Constant ( k , ) for Collision with Transient Merging and Exchange of Reactant between Droplets for Water/Chlorobenzene/N16,l~,l,l,CI ( C = 0.1 M) and Water/Chlorobenzene/N16,O~,l,l,CI+ N16,2+,1,1,CI with a Molar Fraction of the p = 0 Surfactant Equal to 0.2 (Total Surfactant Concentration, C = 0.1 M) for Various Values of w at 20 O C mixt of surfact NI6,p4,l,l,CI with p = 0 and 2 N 16,1$~,1.1,CI U' 'L R,, A u, A2 10-9k,. M-1 s-1 N R,, 8, a, A2 10-9ke, M-1 s-I 10 IS
20 30 40 50
320
36.5
52.3
0.2
I155
69.8
53.0
0.4
1 I I 2 It
1
A\
iI
\\
0.8 I
\x
20 40
16
1
\ \
0.15 0.33 0.34 0.7 I .4 3.9
TABLE 111: Virial Coefficient (a)for the Translational Diffusion Coefficient ( D ) Calculated from Equation 14 at L o w 4 for Various Water/Chlorobenzene/Nm, 1$,I, 1,CI Microemulsions" m w N
i
6 8\
55.0 50.9 53.4 50.2 53.1 55.0
18.4 28.7 35.7 55.9 69.7 83.7
77 203 3 00 783 1150 1600
14
10
12
40 20
0 0 -3.9 -4.8 -1 2.4
T = 20 "C.
i 0
10
20
30
40
50
60
Figure I O . Variations of the intramicellar quenching rate constant k, of Rubpy by methyl viologen with w for water/chlorobenzene/ Nm,l~,I,l.CI microemulsions with m = 10 ( O ) , 12 (+), 14 (D), 16 (O), and 18 (X), for water/benzene/N16,l~.1,1,Cl microemulsions (A)and for water/chlorobenzene/N12,4,l , l , B r microemulsions (0): C = 0.27 M ;T = 20 OC.
is likely that Rubpy remains bound to the surfactant head groups, irrespective of the value of R,, thus sensing the same microenvironment and therefore retaining the same lifetime, as w increases. In the cationic surfactant based microemulsions, Rubpy is repelled by the surfactant layer and, as w is increased, the probe moves farther and farther away from this layer. Its microenvironment at low w is highly concentrated in chloride ions (several moles/liter) that can ion-pair Rubpy. It becomes progressively more dilute in chloride ions, as w increases, resulting in the observed change of T ~ . The difference between the T~ vs R, curves for the Nm, 16,I , 1 ,C1 and N 1 2,4, I , I ,Br systems reflects the difference of interaction between Rubpy and the counterions CI- and Brin the two types of systems. I .3. Rate Constants kQ for Intradroplet Quenching. This quantity is directly obtained from the fitting of eq 1 to the decay curves and the use of eq 2 or 8. It is known that kQ decreases as the size of the water pool increases (the mean distance between probe and quencher then increases) and as the microviscosity increases.23 These two effects can explain the results in Figure 10 that represent the variations of kQ with w in various microemulsions. It is seen that a change of any parameter that produces an increase of water-pool size (increase of w , decrease of m, substitution of chlorobenzene by benzene) gives rise to a decrease of kQ. Moreover for some systems, a maximum or a leveling off of kQ is observed when w decreases. This is due to the two antagonistic effects mentioned above: the increase of kQ due to decreasing water-pool size and decrease of kQ due to increasing water-pool microviscosity as w decreases. Indeed, it is known that
0
0.04
0.0 8
0.16
for low w-values, the water droplet microviscosity is highz4because the water in the system is mainly under the form of hydration water of surfactant head groups and counterions. 2. QUELS Measurements. Figure 11 shows the variation of the droplet diffusion coefficient D with the dispersed-phase volume fraction 9 for water/chlorobenzene/Nm, Id,],1 $1 microemulsions. It is seen that at low @, the D versus CP plots have an increasingly negative slope when m decreases, indicating increasingly attractive interactions between droplets. The values of the interaction coefficient, a , calculated with eq 14 are given in Table 111. The values of (Y go from 0 (slightly attractive interactions) for m = 16 to -3.9 or -4.8 (moderately attractive interactions) for m = 14 and to -12.4 (strongly attractive interactions) for m = 12. Thus, interdroplet interactions become more attractive upon decreasing surfactant chain length. Recall that these interactions become more attractive also upon increasing oil chain length. Such variations agree with recent theoretical treatments of microemulsion stability. They also confirm the conclusions inferred in the preceding paper in this issue on the basis of solubility data; namely, that in water/chlorobenzene/Nm,l~$,l, I ,Cl systems the attractive interactions between droplets increase as m decreases. The analysis of the autocorrelation function of the scattered intensity by the cumulant method always yielded small values of the variance. This result indicates that the droplet-size polydispersity is small and supports the conclusion reached in the above fluorescence studies, on the basis of the very small dependence of N on the quencher concentration. Moreover, we have checked that, for all systems investigated by light scattering, the intensity of scattered light was independent of the scattering angle. This
(23) Lianos, P.: Lang, J.; Strazielle, C.; Zana, R.J . Phys. Chem. 1982, 86, 1019.
0.1 2
Figure 11. Variations of the translational diffusion coefficient D with for water/chlorobenzene/Nm,l4,l,I,Cl microemulsions for m = 12 (w = I O (+)), m = 14 (w = 10 (V)and 40 (D)), and m = 16 (w = 20 ( 0 ) and 40 (A)): T = 20 'C.
(24) Zinsli. P. J . Phys. Chem. 1979, 83,3223.
Water/Oil Microemulsion Droplet Sizes and Interactions I
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I
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The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 393
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I
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I
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-
2802LO-
-
200 -
-
160
0.01
-
120 -
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0.05
0.09
0.13
Figure 14. Variations of the hydrodynamic radius R H and of the droplet radius RM with 3 for water/chlorobenzene/N16,ld,l,l,Cl microemuland 40 @,A): T = 20.5 0.5 O C . sions with w = 20 (*,0)
*
0.vt
0.1
0.06
0.02
Figure 12. Variations of the hydrodynamic radius R H and of the droplet radius R M with 3 for water/chlorobenzene/N12,l~,l,1,C1 microemulsions: w = 20; T = 20.5 i 0.5 OC.
110
w = LO
90
t
70
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I
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I
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Figure 13. Variations of the hydrodynamic radius RH and of the droplet radius R, with 3 for water/chlorobenzene/N14,l~,l,l,CI microemulsions with w = IO (v,V)and 40 (.,0): T = 20.5 f 0.5 OC.
result indicates that the particles are small with respect to the wavelength of light. The above results, small polydispersity and small size, suggest that the droplets are close to spherical. This conclusion justifies the assumption of spherical water pools made above and the use of eq 10 for the calculation of their radius. Notice however that the quasi-elastic light scattering studies were performed on systems with w > 10. One cannot exclude nonspherical shapes at w < 10, when the water present in the system is mostly under the form of hydration water. At this stage, we can already stress the correlation that appears to exist between interdroplet attractive interactions characterized by the coefficient CY and the values of the rate constant k, for the exchange of material between droplets for the water/chlorobenzene/Nm,l$,l, 1,Cl microemulsions: as the surfactant chain length decreases, a becomes more negative (increase of attractive interactions, see Table 111) and k, increases rapidly (Table I and Figure 4). The same qualitative correlation has already been reported for water/alkane/AOT micro emulsion^.^^ However, in these systems, k, and ICYI increased with the oil chain Figures 12-1 4 show the variations of the hydrodynamic radius RH calculated from eq 16 and of the droplet radius RM calculated from eq 12, as a function of the dispersed-phase volume fraction 9, for various water/chlorobenzene/Nm, 1d,l,1,Cl microemulsions. It can be seen that the RH values extrapolated to 9 = 0 are very close to the RM values at 0 for systems with m = 12 (Figure 12) and m = 14 (Figure 13), indicating a good agreement between
-
(25) Jada, A.; Lang, J.; Candau, S.J.; Zana, R. Colloids S w j . 1989, 38, 251. (26) Hou, M. J.; Kim,M.; Shah, D. 0.J . Colloid Interface Sci. 1988, 123,
398.
Figure 15. Variation of the electrical conductivity K with 3 for water/ chlorobenzene/Nm,ld,l,l,C1 microemulsions with m = 12 (0) and 14 (+): u = 20; T = 20 "C.
the results of time-resolved fluorescence quenching and QELS measurements. For the m = 16 system (Figure 14), RM is found to be about 8 A larger than RH. This difference is probably the result of the calculation of RM with eq 12, which involves the length of the fully extended surfactant chain. Most likely, this chain becomes rapidly increasingly coiled as m increases. This coiling would explain both the difference between RH and RM and the decrease of attractive interdroplet interactions. Recall that such attractions are thought to arise from the interpenetration of the droplet interfacial film upon collision^.^ This interpenetration is certainly easier when the chains are extended, with much space between them, than in a coiled or folded conformation where they would form a compact and rigid film. In Figure 13 (m = 14), the difference between the values of RH and RM increases with It reflects the increase of the contribution of intermicellar interactions to the value of RH.The same is true for the m = 12 system (Figure 12) up to 9 N 0.03. At higher 9,however, the increase of RH with 9 is much too large to be only due to attractive interdroplet interactions. Critical effects are probably largely responsible for this increase. Indeed, the interdroplet attractions are very strong ( a = -12.4), and under the experimental conditions used (w = 20, T = 20 "C), the system is close to phase separation (w, = 25 at T = 20 OC, see the preceding paper in this issue). In these conditions, the measured RH represents the correlation length of the fluctuations of droplet concentration in the system. The critical behavior of the m = 12 system was not studied further as it was beyond the scope of the present study.
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The Journal of Physical Chemistry, Vol. 94, No. 1 , 1990
Jada et al. continue to the point where attractive interactions between droplets become predominant and give rise to percolation. In the case of N 12,1+,1, I ,CI systems, the percolation takes place at such a low w that the decrease of K is not observed. The fact that the maximum of K is not observed in the K vs 0 plots (Figure 15) supports the above interpretation. Indeed, these last experiments were performed at constant and large w where the ion pairs are all of the solvent-separated type and the droplet radius has nearly a constant value. A last remark must be made about the large difference between the K-values of the systems at very low @ (Figure 15) and w (Figure 16). Indeed, K is about 100 times smaller for the first systems than for the second ones. This difference comes from the fact that, for the first systems at @ close to 0, w = 20 and all surfactant ions and counterions make up droplets that are much larger than the small aggregates of surfactant present at w close to 0 in the second systems. The conductivity of these small aggregates is much larger than that of the large droplets.
Discussion
10-'l 0
I
I
I
I
I
10
20
30
40
50
I
w
60 70
Figure 16. Variations of the electrical conductivity K with w for water/chlorobenzene/Nm,l~,I,l,CI microemulsions with m = 12 (0), 14 (+), and 16 ( 0 ) and water/chlorobenzene/N12,4,1,1,Brmicroemulsions ( X ) : initial surfactant concentration in the binary chlorobenzene/surfactant system, C = 0.27 M; T = 20 " C .
3. Electrical Conductivity of Microemulsions. Figures 15 and 16 show the variations of electrical conductivity K as a function of either CP or w for various microemulsions. A large increase of K , by a factor of 102-103is seen to take place for all systems but the one based on the N 16, I+,], 1 ,CI surfactant, above a value of w or CP, which strongly depends on the surfactant nature. These increases correspond to the onset of percolative electrical conduction and are referred to as percolation in the literature. The percolation thresholds (values of w or @ above which percolation takes place) are seen to increase rapidly with m. Notice that the percolation thresholds are nearly identical for the N14,1+,1,l,Cl and N12,4,131,Br systems (CP = 0.24-0.25, even though the corresponding U-values are about 35 and 42, respectively). It is also remarkable that the k, values for these two systems are very close (see Figure 4 and Table I). Further comparison between the k , vs w or 9 plots and the K vs w or @ plots reveal that the percolation thresholds correspond to k, values of (1-2) X lo9 M-' s-l. For instance, in the Nl2,1+,1,1,Cl system, the onset of percolation corresponds to w = 5 , Le., CP = 0.1 1 (Figure 16) where k, N 1.5 X 1 O9 M-' s-I (extrapolation of Figure 4 data). For the N 14,1+,I , 1 ,CI and N 12,4,1,I ,Br systems, the percolation threshold is at @ = 0.24-0.25 (Figure 16), where again k, = (1-2) X IO9 M-' s-' (Figure 4 and Table I). Recall that an identical condition has been evidenced for the occurrence of percolation in microemulsions based on the anionic surfactant AOT.27 This is further discussed below. Note that simultaneous increases of electrical conductivity and k, values, qualitatively similar to the ones found in the present work, have been reported for the toluene/water/ Triton X - 100 w/o microemulsions.'6b Figure 16 shows the existence of a maximum of K at low w for the m = 14 and 16 systems, which can be explained as follows. In the absence of water, the system contains small aggregates of surfactant ion-counterion contact ion pairs that act as charge carriers. Upon addition of water these ion pairs become progressively more ionized, whereas the number of aggregates decreases rapidly as their size increases with w . The first effect is predominant at very low @ but is rapidly overwhelmed by the second one. As a result, K goes through a maximum upon increasing w and then decreases at larger w . This decrease will (27) Jada. A.: Lang, J.; Zana, R . J . Phys. Chem. 1989, 93, IO.
1. Droplet Structural Parameters. As already mentioned, the observed increase of R, with w (see Table I) is as expected. Similar variations have been reported for other w/o microemulsion^.^-^^-^^ Tables I and I1 show that, for a given surfactant, u increases only slightly with w. However, for a given w , u shows a notable dependence on the surfactant structure. In particular, for the Nm,l+,l,l,Cl series, the increase of u with m may be due to an increase of the space occupied by the surfactant alkyl chain in the interfacial film with the length of this chain because the extent of chain folding increases with m. The folding of the surfactant main chain has already been invoked in the previous section to account for the difference between the RM and RH values for the Nl6,l+,l,l,Cl system. The most important result, however, is the increase of N and R, when m decreases, for a given w , in the water/chlorobenzene/Nm,l+,l,l,Cl microemulsions (see Figure 4 and Table I). This result can be understood on the basis of a recent theoretical approach for the stability of w/o microemulsions.2' This approach predicts that the spontaneous radius of curvature of the surfactant film at the oil/water interface increases when m decreases. Thus, surfactants with low m tend to form larger water droplets than surfactants with large m thereby explaining the increase of droplet size as m decreases. QELS measurements have been performed at 20 OC on water/benzene/N16,1+,1,1,CImicro emulsion^.^^ Using the reported RH values, extrapolated to @ = 0, we calculated N = 750 for w = 33. Our fluorescence data indicate N = 1350 at @ = 0.28 (C = 0.27 M) and w = 33 (see Figure 5). The difference between the two values most likely arises from the difference in Q values in the two sets of measurements. Recall that an increase of N with CP has been observed in several other systems (see Figure 6 and 7 ) . We have pointed out in the previous section that the increase of N with @ is particularly important in systems with large interdroplet attractive interactions. This is indeed the case system as indicated by its of the water/benzene/N16,1+,1,1,C1 large k , values (see Figure 5) and Icul-val~e.~~ To conclude this section, we again emphasize that whereas an increase of the surfactant chain length decreases the size of the water droplets, an increase of the solvent (alkane) chain length results in an opposite variation in w/o microemulsions whose stability is determined by interdroplet interactions. 2. Interdroplet Attractive Interactions, Exchange of Material between Droplets, and Electrical Percolation. Our results show that there is a direct correlation between the rate of interdroplet (28) Eicke, H. F.; Rehak, J. Helu. Chim. Acta 1976, 59, 2883. (29) Zulauf, M.; Eicke, H. F. J . Phys. Chem. 1979, 83, 480. (30) Day, R. A.; Robinson, B. H.; Clarke, J . H. R.; Doherty, J. V. J . Chem. SOC.,Faraday Trans. I 1979, 7S3 132. (31) Cabos, C.; Delord, P. J . Appl. Crystallogr. 1979, 12, 502. (32) Cabos, C.; Marignan, J. J . Phys. Lett. 1985, 46, L-267. (33) Chatenay, D.; Urbach, W.; Cazabat, A. M.; Langevin, D. Phys. Rev. Lett. 1985. 54. 2253.
Water/Oil Microemulsion Droplet Sizes and Interactions exchange of material (k,), interdroplet attractive interactions ( a ) , and occurrence or nonoccurrence of electrical percolation phenomenon. In the water/chlorobenzene/Nm,l$,l,l,CImicroemulsions, k , decreases, a becomes less negative, and electrical percolation appears at a higher 9, as m increases. The percolation disappears for m = 16 (Nl6,l$,l,l,Cl system) under the experimental conditions used. Actually the surfactant NI6,l$,I,l,CI gives us a very clear illustration of the correlation between interaction, rate constant k,, and percolation. Indeed, we have seen above that the substitution of chlorobenzene by benzene results in a dramatic increase of k, value and also of the strength of the attractive interactions as measured by a. Even more striking is the occurrence of an electrical percolation in the water/ benzene/N 16,1$, I , I ,CI system33contrary to the water/chlorobenzene/N l6,l$,l ,l,Cl system. For all systems investigated in the present work, including the one just discussed the comparison of the k, vs w (or +) plots and of the K vs w (or 9) plots clearly shows that the percolation threshold always corresponds to k , values of about (1-2) X IO9 M-' s-I. This condition has been found to hold also for water/ n-alkane/AOT microemulsions, where the alkane chain length was variedz7 and percolation induced by either a change of w (or 9) or temperature. It is hoped that the above experimental results and the clear correlation evidenced between some very basic properties of the systems will stimulate further theoretical studies, taking fully into account the dynamic character of w/o microemulsions. 3. Percolation Threshold and Mechanisms of Electrical Conductivity above the Threshold. The fact that percolative conduction is observed only for those systems where the rate constant k, for the exchange of material between droplets is larger than (1-2) X IO9 M-' s-I has some implication concerning the mechanism of electrical percolation. On a purely geometric basis, the threshold volume fraction for percolative conduction is 9, = 0.16.34,35 This value corresponds to the formation in the system of the first infinite cluster of conducting particles. The number of such clusters then increases rapidly at 9 > aP.In the present study, percolation-threshold volume fractions higher (0.24-0.25, Figure 16) or lower (0.1 1, Figure 16) than 0.16 were observed. The results clearly show that systems with strong interdroplet interactions ( a = -12) are characterized by a percolation threshold lower than that expected for geometric percolation whereas for systems with moderately attractive interactions (a N -4) the percolation threshold is larger than for geometric percolation. We are presently trying to determine for a model system the variation of the percolation threshold with a. Various mechanisms have been proposed to explain the large electrical conductivity above the percolation threshold in w/o micro emulsion^.^^^^ In the most often proposed mechanism, this (34)Lagiies, M.; Ober,R.; Taupin, C. J . Phys. Lett. 1978, 39, L-487. , M.;Sauterey, C. J . Phys. Chem. 1980, 84, 3503. Safran, S. A.; Webman, I.; Crest, G. S . Phys. Reu. A 1985, 32, 506. Hilfiker, R.; Eicke, H. F.; Geiger, S.;Furler, G.J . Colloid Interface Sci. 1985, 105, 378. (37)Bhattacharya, S.;Stockes, J. P.; Kim, M. W.; Huang, J. S . Phys. Reo. Leu. 1985. 55. 84. (38)Matthew, C.;Patanjali, P. K.; Nabi, A.; Maitra, A. Colloids Surf. 1988, 30, 353. I
The Journal of Physical Chemistry, Vol. 94, No. I , 1990 395 conductivity is attributed to the motion of surfactant ions on the surface of water droplets and surfactant ion hopping from droplet to droplet in the droplet clusters then present in the system or upon droplet collision^.^^^^^ Such a mechanism, however, does not explain why percolation is observed only when k, > (1-2) X IO9 M-' s-l. This fact is better understood if one assumes that above the experimental threshold the percolative conduction is due to the motion of counterions within transient water tubes formed in droplet clusters upon opening of surfactant layers separating water cores. Note that the opening of surfactant layers between two collided droplets should not be visualized as resulting in droplet coalescence. Rather, it yields a droplet dimer with connected aqueous cores39(see Figure 1). It must also be pointed out that the interpenetration of the surfactant layers upon droplet collisions is the first requirement for layer "opening", in order that the exchange of material takes place. This interpenetration of surfactant layers is directly related to interdroplet attractive interactions as determined for instance by quasi-elastic light scattering40 In the above model, an increase of k, results in the formation of increasing amounts of droplet dimers, trimers, ..., polymers, Le., in longer and longer tubes in which counterions can diffuse more and more freely. Conduction by surfactant ions would be predominant below the percolation threshold (as is suggested by the fact that below the threshold the K vs w or 9 curves depend only a little on the surfactant for a series of homologous surfactants in experiments at constant w and increasing 9) whereas conduction by counterions would become predominant above the threshold.
Conclusions The above study of cationic surfactant/water/aromatic solvent w/o microemulsions has permitted us to show that droplet sizes, interdroplet attractive interactions, and rate constants of the interdroplet exchange of material increase upon decreasing surfactant chain length. These variations are opposite to those resulting from increasing oil (alkane) chain length and confirm theoretical predictions. Electrical percolation has been evidenced in several of the investigated systems. The value of the percolation threshold has been shown to increase with surfactant chain length, that is, decreasing strength of intermicellar attractive interactions. Our results also show that the percolation thresholds correspond to values of the interdroplet exchange rate constant of about (1-2) X IO9 M-I SKI , irrespective of the surfactant chain length or head group or nature of the solvent, confirming our previous observations for AOT-based w/o microemulsions. This result led us to postulate that above the percolation threshold the electrical conductivity arises from the migration of surfactant counterions within transient water tubes upon opening of surfactant layers separating contiguous water droplets. Registry No. NI 2,4,l,l,Br, 29481-60-5;NlO,l@,l,l,Cl, 965-32-2; N 12,1@,l,l,Cl, 139-07-1; N14,1@,1, I ,CI,139-08-2; N 16,l @,I, 1,CI,12218-9; N18,1@,l11,C1, 122-19-0; N16,0@,1,1,CI, 26038-94-8; Nl6,2@,l,l,Cl,122699-33-6;PhCI, 108-90-7;C6H6, 71-43-2;R U (bpy)& 14323-06-9; methyl viologen chloride, 191 0-42-5. (39) Dutkiewicz, E.; Robinson, B. H. J . Electroanal. Chem. 1988, 251, 1 1 . (40)Lemaire. B.: Bothorel. P.: Roux. D. J . Phvs. Chem. 1983. 87. 1023. Brunetti, S.; Roux, D.; Bellocq, A. M.;'Fourche,*G.; Bothorel, P. J : Phys. Chem. 1983, 87, 1028.
