J . Phys. Chem. 1992, 96, 896-901
896
neutral polymers. The situation there too is quite complicated since the interaction forces are not amenable to any general form, their behavior depending on the amount of the dissolved polymer, solvent quality and the nature of polymer-surface interactions. However, one can establish a close correspondence between the results derived in this contribution and the force profile in the case of strongly adsorbed polymers at partial coverage.27 The interaction potential there remains repulsive at small separations but develop an attractive minimum at low werages (corresponding to small 'I in our case) that gradually disappears as the coverage is increased. Bridging is claimed as the only cause of this attraction. Work of Muthukumar and HoZ9which is methodologically quite close to our analysis also yields force curves that can be correlated with the behavior of our system. In their case the bridging of the polymeric chains is promoted by attractive van der Waals interactions between polymer beads and bounding surfaces. In fact our model system (electrostatic interactions between polymer beads are repulsive) would correspond closely to case 5 of their Conclusions section, which describes polymers above 0 temperature at different magnitudes of the van der Waals attraction between polymer beads and the bounding surfaces. Finally one should add a note on the experimental situation. At this point we were unable to find any systematic investigation (30)de Gennes, P.-G. Macromolecules 1982, 15, 492. (31) Olivares, W.; McQuarrie, D. A. J . Phys. Chem. 1980, 84, 863. Henderson, D.; Blum, L.; Lebowitz, J. L. J. Electroanal. Chem. 1979,102, 315. (32)Podgomik, R. Manuscript in preparation.
of forces between charged surfaces in the presence of polyelectrolytes that we could use for a direct comparison with our theoretical predictions. However, investigations of the short-range order of silica particles in the presence of cationic polymers" or the direct measurements of forces between mica surfaces in the presence of polypeptides" do suggest that strong attractions exist between charged particles in a solution of oppositely charged polyelectrolyte. Furthermore, a study of forces between mica surfaces in the presence of poly(2~inylpyridine)~~ that is fully charged in acidic solutions gives strong support to the bridging origin of attractive interactions. The polyelectrolyte bridges were inferred from the force curves following surface adhesion and were seen to disappear for shorter polymer chain lengths. The conclusions reached in our work are in sound qualitative agreement (see, e.g., Figure 8a) with the results of the above work. The problem of interactions between charged surfaces with intervening polyelectrolyte chains is of a far greater complexity than one would naively expect on the basis of our experience with the Poisson-Boltzmann equation. From the theoretical side it is indeed quite fascinating since it leads to a blending of different methods used profusely by the molecular force and the polymer community. (33) Cabane, B.; Wong, K.; Wang, T. K.; Lafuma, F.; Duplessix, R. Colloid Polvm. Sci. 1988. 266. 101. (34)Afshar-Rad, T.;Bailey, A. I.; Luckham, P. F.; Macnaughtan, W.; Chapman, D. Colloids Surf. 1988,31, 125. (35) Marra, J.; Hair, M. L. J . Phys. Chem. 1988,92,6044. (36)van Opheusden, J. H. J. J . Phys. A: Math. Gen. 1988,21,2739.
Physicochemical Studies on Microemulsions: Test of the Theories of Percolation Subinoy Paul, Satyaranjan Bisal, and Satya Priya Moulik* Department of Chemistry, Jadavpur University, Calcutta- 700032,India (Received: June 13, 1991)
On the basis of percolation results of 32 water/oil microemulsion systems, a detailed analysis of the validity of the effective medium theory (EMT), EMT with dipoledipole interaction (EMTDD), and Bemasconi-Weismann (BW) theory has been made. It has been found that most of the systems obey either the EMT or the EMTDD (chain) formalism whereas a slender few follow the EMTDD (cluster) and BW formalisms. The results suggest that the internal structure of microemulsions can be either isolated, randomly dispersed spheres or spheroidal aggregates formed by dipolar interaction.
Introduction A conducting microheterogeneous dispersion in a very weakly conducting or nonconducting medium may show a rapid rise in conductance above a threshold concentration. This phenomenon is called percolation.'" Water-in-oil (w/o) microemulsions stabilized by ionic surfactants or by an ionic surfactant and a cosurfactant are microheterogeneous dispersions of conducting water droplets. They often exhibit percolation in conductance after a threshold concentration of ~ a t e r . ~ - ' Quantitative l the(1) Bruggeman, D. A. G. Ann. Phys. (Leipz) 1935,24,636;1935,24,665. (2)Landauer, R. J . Appl. Phys. 1952,23,779. (3) Kirpatrick, S. Phys. Reu. Lett. 1971,27,1722;Reu. Mod. Phys. 1973, 45, 574. (4)Bernasconi, J. Phys. Rev. B 1973,7,2252;1974,9,4575. (5) Elliott, R. J.; Krumhansl, J. A.; Leath, P. L. Rev. Mod. Phys. 1974,
-
1 5 h6C .1-, . -.
(6)Stroud, D.Phys. Rev. B 1975,12,3368. (7)Lagues, M. J . Phys. Lett. 1979,40,L-331. (8) Bhattacharya, S.;Stokes, J. P.; Kim, M. W.; Huang, J. S. Phys. Reu. Lett. .1985,55, 1884. (9) Peyrelasse, J.; Moha-Ouchane, M.; Boned, C. Phys. Rev. A 198&38, 904;1988,38,4155. (10)Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. J . Chem. SOC., Faraday Tram. 1 1988.83, 985. (1 1) Geiger, S.; Eicke, H. F.; Spielmann, D. Z . Phys. E Condem. Matter 1987,68,175.
0022-3654/92/2096-896$03.00/0
oretical treatment on the percolation phenomenon in microemulsions has been attempted with the help of the effective medium theory (EMT).'**J2 In a recent work, Fang and Venable13 have used the EMT theory of Bijttcher12 for quantitative accounting of the structural parameters of several microemulsion systems. The equation has been also used by Bisal et al.I4 for quantitative description of a good number of w/o microemulsion systems with special reference to their structural properties. The results have been shown to be comparable with those obtained from other sophisticated methods, viz.,light scattering, small-angle neutron scattering, fluorescence quenching, etc. For microheterogeneousdispersions of metal and metal oxides in suitable media,l5 the EMT theory has been shown to be often inedaquate, and modifications of the equation have been put forward. The percolation threshold (one-third of the volume fraction of the dispersion) according to the EMT theory of B6ttcherlz is not always the practical limit. A number of aut h 0 r s ~ 9 ' have ~ ' ~ suggested that the percolation thresholds realized (12)Bbttcher, C. J. F. Recl. Trau. Chim. 1945,64,47. (13)Venable. R. L.; Fang, J. J . Colloid Interface Sci. 1987,116,269. (14)Bml, S. R.; Bhattacharya, P. K.; Moulik, S. P. J . Phys. Chem. 1990, 94,350. (15) Granqvist, C. G.; Hunderi, 0. Phys. Reu. B 1976,18, 1554. (16)Bernasconi, J.; Wiesmann, H. J. Phys. Rev. B 1976,13, 1131. (17) Clarhon, M. T.;Smedley, S. I. Phys. Rev. A 1988, 37,2070.
0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 897
Physicochemical Studies on Microemulsions Granqvist and HunderiI5 have shown in practice are often that the lower percolation threshold can be theoretically accounted for if dipole-dipole interaction among the dispersed entities is recognized. The theory has been termed as effective medium theory with dipole-dipole interaction (EMTDD). This kind of interaction may lead to the formation of chains or clusters in the dispersion. The EMT theory has considered only random distribution of spherical particles. Aggregation leading to chain or cluster formation has been ignored. In line with the modifications of Granqvist and Hunderi,Is Bernasconi and Wiesmann16 (BW) put forward a relation for percolation for cluster forming dispersions, which also recognizes a lower percolation threshold than that given in the EMT theory. The validity of the above theories has been established for microdispersions of solids in suitable media. The association of disperse particles due to interaction may form entities with shapes different than spheres. Prolate and oblate shaped aggregated dispersions may come into existence in solution. The theories, therefore, can treat samples containing nonspherical inclusions. The microwater droplets in microemulsions may undergo chain formation and clustering. It is considered that during percolation, association of microwater droplets occurs and either the surfactant ions travel by “hopping” mechani~m’~~J*J~ or the counterions are which effectively manifests in exchanged between rapid increase in conductance. It is, therefore, very pertinent that for a quantitative refined treatment, the improved equations for percolation as given by Granqvist and Hunderi and others should be used. To test the validity of a percolation equation an estimate of the volume fraction of the disperse phase is essential. For a microemulsion system this very often remains a guess owing to the ill-defined interphase between oil and water, particularly in the presence of a cosurfactant. In the absence of a cosurfactant, this interphase layer is considered to consist solely the surfactant. The volume fraction of the disperse phase is, therefore, defined as the sum total of the fraction of water and the surfactant. When a cosurfactant is required for the preparation, its distribution among the oil phase, interphase and water phase is an ambiguous matter that is difficult to assess. A direct estimation of volume fraction of the droplets is hardly possible, and it is not easy to put the percolation theories to test. The percolation study of microemulsions is, therefore, more challenging than ordinary binary dispersions. Very recently, Fang and VenableJ3as well as Bisal et al.14 have illustrated an analytical approach to deal with the above complexity of direct evaluation of volume fraction of the conducting microdroplets. This makes microemulsions amenable to analysis in the light of the EMT theory. In this report, an attempt has been made to test the various theories of percolation on the basis of the mode of analysis referred to above, on literature results of a number of w/o microemulsion systems exhibiting distinct percolation behavior. It will be seen that no generality can be made about the percolation behavior; the EMT, EMTDD, and BW theories are applicable, and the microemulsions show individual characteristics in this regard.
Percolation Theory In the percolation domain, the conductivity follows the scaling law Q
a
(4 - 4 2
(1)
where u is the conductanceof the mixture, 4 is the volume fraction of the microdisperse phase, dCis the volume fraction at the percolation threshold, and t is a constant which is unity at higher concentration. (18) Kim, M. W.; Huang, J. S. Phys. Rev. A 1986, 34, 714. (19) Maitra, A.; Mathew, C.; Varshney, M. J . Phys. Chem. 1990, 94,
5290. (20) Jada, A.; Lang, J.; Zana, R.; Makhloufi, P.; Hirsch, E.; Candau, S. J. J . Phys. Chem. 1990, 94, 387. (21) Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1989, 93, 10. (22) Mukhopdhyay, L.; Bhattacharya,P. K.; Moulik, S. P. Colloids Surf. 1990, 50, 295.
In the effective medium theory (EMT), the equation of Bijttcher12is equivalent to the scaling law under certain boundary conditions. For a binary mixture having a,,, and ad as the conductances of the continuous medium and the dispersed phase, respectively, Bijttcher proposed that the conductance of the mixture is related to the volume fraction of the dispersed phase by
For a continuous medium of very low or practically zero conductance (u,,, = 0), eq 2 transforms into the scaling form for t = 1: (3)
The equation suggests a percolation threshold at 4 = and, if valid, it can evaluate the disperse-phase conductance Ud from the measured values of u at several volume fractions of the disperse phase. Since accurate determination of conductance is feasible, the test of validity of eq 3 entirely rests on the accurate determination of 4, which is not always an easy task, particularly for solvated disperse phase and microemulsions having a not welldefmed interphase containing the surfactant and the cosurfactant. Interaction among the microparticles leading to formation of aggregates of different categories (chains, clusters, etc.) may also offset the validity. Introducing the effects of dipole-dipole interaction and the resulting formation of chains and clusters, Granqvist and HunderiI5 modified the EMT theory to EMTDD (effective medium theory for dipole-dipole interaction introducing depolarization factors). The resulting equation has the form
y34a + ( 1 - ‘#‘)(am - udd)/(um + 2ud) = 0
(4)
where (0
- Ud)/
+ t / 3 ( 0 - ‘Jd)
(5)
The factor a is proportional to the polarizability (for a sphere the depolarization factor is l/J. For randomly oriented ellipsoid the general form is
where Lidenotes the triplet of depolarization factorI5dictated by the axial ratios. The combined form of eqs 4 and 6 can d d b e the conductance behavior of nonspherical dispersions. Since aggregation of spheres can form infinite chains (with overall prolate geometry) and closed-packed clusters (with overall oblate geometry), they can be considered as separate nonspherical entities to which the EMTDD theory can be applied. The above equations predict that the dipole-dipole interaction should always shift the percolation threshold toward lower concentration of the conducting material. For u,,, = 0 (i.e., for pure percolation case), the +FmD becomes15 0.271 for chains and 0.156 for clusters. The equivalent depolarization factors L1,&, and & for isolated spheres are each equal to which for singlestranded chain are 0.133,0.435, and 0.435, respectively, and for close-packed lattice the values are 0.0865, 0.0865, and 0.827, respectively. Recognizing u,,, = 0 and transforming eq 6 in terms of the L values and its subsequent insertion into eq 4 yield the following relations: For isolated spheres =
72‘Jd(’$
- y3>
(3)
Le., the equation of BBttcher. For chains U = -0.1519~d [0.15664 + 1.721642 - o.72943]ud (7) For clusters
+
u
= -0.0984~d+ [0.5394
+ 0.567942]~d
(8)
It is imperative that precise values of u and 4 be determined for the verification of the theories and to derive Ud.
898 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992
In an exercise of modifying the EMT theory, Bernasconi and Wiesmann16have proposed a cluster extension of the EMT theory and derived the equation u = 1.05ud(4 - 0.157) for 4 3 0.157 (9) The percolation threshold of EMTDD for clusters (40EMTDD = 0.156) is in exact agreement with that in the BW eq 9. They have shown that the theory may be valid up to 4 6 3/4. For greater 4, the equation transforms into the form of EMT. In the following discussion, results on percolation of a number of microemulsion systems will be tested in the light of eqs 3 and 7-9. It is aimed to ascertain the internal structural organization of w/o microemulsion system influenced by dipole-dipole interaction among the microwater droplets by virtue of charge fluctuation in the interphase.
Data Acquisition (Collection) and Data Treatment The experimental results treated in this exercise are taken from literature. Twenty-three microemulsion systems studied by Bisal et al.,I4 five systems studied by Fang and Venable,13two systems studied by Clarkson and Smedley,]’ one system by Moha-Oue~ h a n e and , ~ ~one system by LagouretteZ4have been considered for analysis. In the papers of Fang and Venable, Moha-Ouchane and Lagourette conductance and 4 values of the studied w/o microemulsion are not available. These are obtained by photographic enlargement of their u vs 4 graphs, tracing them on millimeter coordinate papers and directly reading the values from the traced figures. On a comparative basis with the report of Bisal et al., it has been found that the above procedure of data collection is associated with an average error of not more than 3%. Clarkson and Smedley” reported both u and 4 for their systems. The water/AOT/undecane microemulsion of M ~ h a - O u c h a n ehad ~~ no cosurfactant; the volume fractions were, therefore, obtained by summing up the volume of water and the surfactant AOT considering the latter to be entirely present in the interphase and the mixing is ideal. The twenty-three systems of Bisal et a1.14 and the five systems of Fang and VenableI3contained cosurfactants butanol and hexylamine whose distributions in different phases were not known. In line with the mass balance scheme of the latter authors, it has been shown that the volume fraction of the disperse microdroplets of water is given by the relation where Pd and pt are the densities of the disperse phase and the total solution respectively. W,, W k , and Ww are the weight fractions of surfactant, cosurfactant in the interphase and water, respectively; M, and M,are the molar masses of cosurfactant and surfactant, respectively, and r is their mole ratio in the interphase ( r = m,/m,). In eq 10, all the terms except r are measurable quantities. A reasonable guess of r can evaluate only 4. To test the eqs 3 and 7-9 trial method has been adopted. With several guess values of r in eq 10, the corresponding 4 values have been found at various levels of water addition. At each r, the u and (4 values for eq 3 and the u and (4 - 0.157) values for eq 9 have been processed by the linear least-squares method to find out the corresponding intercepts. The r values with their corresponding intercepts have been further analyzed by the least-squares method to find out the r for which the intercept is zero. This has been considered as the true r of a microemulsion system. To test eqs 7 and 8, u vs the bracketed functions of 4 at different r values have been least squared to estimate the coefficient of the intercept by eliminating b d known from the slopes. These coefficients have been then linearly least squared with the r values to derive the true r values corresponding to the coefficients -0.15 19 and -0.0984 of the intercepts of eqs 7 and 8 for EMTDD (chain) and EMTDD (cluster), respectively. Where 4 values are directly known, test u and (4 - 0.157), of least-squaresfittings between u and (4 and u and functions of 4 have straightforwardly evidenced the ~~~~
~~~
(23) Moha-Ouchane, M.; Peyrelasse, J.; Boned, C. Phys. Rev. A 1987, 35, 3027. (24) Lagourette, B.; Peyrelasse, J.; Boned,C.; Clause, M. Narure 1979, 60, 281.
Paul et al. I
lle.111
P 04+020
O3I
02 010 Ol5I
oi
4
0;o
dm o d d 4 0 @n*o
-
0’50 0’60
i
Figure 1. u vs &H plots of microemulsions: I, AOT/butanol/heptane/water system;‘)II, SDS/hexylamine/heptane/water system;13111, potassium oleate/butanol/toluene/water system;24IV, AOT/undccane/water system.23
performance of the equations. Once a reasonable fitting has been observed by this procedure, the a d values have been derived from the slopes as well as the intercepts. It is implicit in the above procedure that a valid equation should correspond to a positive value of r. A negative r should mean it is not valid. The results described in the next section will make this point clear.
Results The percolation of several representative microemulsion systems is graphically depicted in Figure 1. A steep rise in conductance in a narrow zone of increasing volume fraction of water evidences a special mechanism of conductance of the microdispersions of water in an oil-continuous medium. The results of the tests of EMT, EMTDD, and BW theories on thirty-two such percolative systems are presented below. The first set of results of Clarkson and Smedley” treated in light of eqs 7 and 8 for EMTDD (chain) and EMTDD (cluster), respectively, are presented in Figure 2. The values of the coefficients of the intercepts obtained from the least-squares analysis are -0.043 and -0.084 for chain and cluster, respectively. Those for the second set (graphical presentation not shown) are -0.052 and -0.085, respectively. The first two values of both the sets are far off from the expected coefficient of chain-forming systems (-0.1519), whereas the other two values of the sets are closer to the coefficient of cluster-formingsystems (-0.0984). The attempt to analyze the data in terms of the EMT eq 3 has yielded a negative r for zero intercept. A positive value of r for zero intercept has been realized in terms of the BW eq 9. Since BW theory is a cluster extension of EMT, the results of Clarkfon and Smedley advocate clustering of particles in the microheterogeneous phase of their system. The CTd values realized from eqs 8 and 9 are 8.18 and 8.10 S m-l respectively for set 1, and those for set 2 are 5.62 and 3.62 S m-l, respectively. A similar treatment of the results of Moha-OuchaneZ3on the water/AOT/undecane system has yielded the coefficients -0.091 4 and -0.125 for the chain and cluster assumptions, respectively. The system appears to be more towards cluster. The results do not obey the EMT eq 3 but fairly fit into the BW eq 9 with positive r for zero intercept. The bd values derived from eqs 8 and 9 are 0.21 and 0.19 S m-l, respectively. The fitting to the BW equation is better than eq 8. The results of the twenty-three microemulsion systems of Bml et al.I4 formed in the presence of cosurfactants have all exhibited invalidity of the EMTDD (cluster) eq 8 as well as the BW eq 9. The r values required to achieve the coefficient -0.0984 of the intercept of eq 8 and the zero intercept of eq 9, respectively, have been found to be all negative. While all the systems have supported the EMT eq 3, eleven of them have also shown agreement with
The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 899
Physicochemical Studies on Microemulsions
TABLE I: Nature of Validity of Percolation Theories on Various w/o Microemulsion Systems'vb no. svstem (wt ratio) temn K CTAB/butanol/heptane (20:6020) CTAB/butanol/heptane (26.67:53.33:20) CTAB/butanol/heptane (26.67:53.33:20) CTAB/butanol/decane (26.67:53.33:20) SDS/butanol/heptane (20:60:20) SDS/butanol/heptane (26.67:53.33:20) SDS/butanol/heptane (26.67:53.33:20) SDS/butanol/decane (26.67:53.33:20) SDS/butanol/xylene (26.67:53.33:20) SDS/butanol/30% (w/v) cholesterol in xylene (26.67:53.33:20) AOT/butanol/heptane (20:60:20) AOT/butanol/heptane (26.67:53.33:20) AOT/butanol/heptane (26.67:53.33:20) AOT/butanol/decane (26.67:53.33:20) CTAB/hexylamine/heptane (26.67:53.33:20) CTAB/hexylamine/heptane (26.67:53.33:20) CTAB/hexylamine/decane (26.67:53.33:20) SDS/hexylamine/heptane (26.67:53.33:20) SDS/hexylamine/heptane (26.67:53.33:20) SDS/hexylamine/decane (26.67:53.33:20) AOT/hexylamine/heptane (26.67:53.33:20) AOT/hexylamine/heptane (26.67:53.33:20) AOT/hexylamine/decane (26.67:53.33:20) potassium oleate/butanol/toluene (1 3.33:26.67:60) SDS/hexylamine' (33.33:66.67) SDS/hexylamine/heptane (20:60:20) SDS/hexylamine/heptane (1 5:63.75:21.25) SDS/hexylamine/heptane (2050:30) SDS/hexylamine/heptane (20:40:40)
1. 2. 3. 4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
293 293 303 293 293 293 303 293 293 293 293 293 303 293 293 303 293 293 303 293 293 303 293 295 298 298 298 298 298
r 4.88 (4.89) 2.48 (1.78) 2.55 (1.93) 2.64 (1.77) 2.20 (0.97) 0.45 (-ve) 0.60 (-ve) 0.23 (-ve) 0.13 (-ve) 0.19 (-ve) 3.78 (2.98) 0.65 (-ve) 1.14 (0.59) 0.73 (-ve) 1.03 (0.10) 1.18 (0.32) 1.00 (0.13) 0.50 (-ve) 0.60 (-ve) 0.49 (-ve) 0.63 (-ve) 1.14 (0.11) 0.57 (-ve) 1.5 (-ve) 2.0 (0.72) 1.40 (0.74) 3.5 (2.10) 1.7 (0.61) 1.8 (0.47)
conclusion EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT EMT EMT EMT EMT EMT and EMTDD (chain) EMT EMT and EMTDD (chain) EMT EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT EMT EMT EMT EMT and EMTDD (chain) EMT EMT EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain) EMT and EMTDD (chain)
'Systems 1-23 are taken from ref 14. System 24 is taken from ref 24. Systems 25-29 are taken from ref 13. bNonparenthesized and parenthesized values in columns 4 and 5 are according to EMT and EMTDD (chain), respectively. 'Ternary mixtures of SDS/water/hexylamine (as oil).
0.50-
I -
A , ral.50 0. r=l.ll , ri2.20
OAO-
E
m
b' 0.300.20O
0
0.1
0.2
0.3
0.4
0.5
0.6
U 0.7
F-
F (function of 4) plots of the first set of results of Clarkson and Smedley." F for EMT, BW, EMTDD (cluster), EMTDD (chain) are (4 - I / ) ) , (4 - 0.157), (0.5394 + 0.5679b2), (0.15669 + 1.7216$~~ - 0.7291$)), respectively. @, EMT; 0 BW; A, EMTDD (cluster); 0, Figure 2.
IJ vs
0.10 -
EMTDD (chain).
the EMTDD (chain) eq 7. The quantitative evaluations have been made on the basis of linear least-squares analysis. To save space, only one graphical representation (Figure 3) is shown on CTAB/butanol/decane system at three different r values, one of them being the correct r. In Table I, the type and compositions of the systems and the realized r values are compared in light of both EMT and EMTDD (chain). Similar to the eleven microemulsion systems of Bisal et al.14 all the five microemulsion systems of Fang and VenableI3 con-
01 0
lJI 0.15
I
0.30
I
045
-
C 60
(0.1566@*
[email protected]@3J)
Figure 3. u vs (0.15664 + 1.7216$2 - 0.7299)) plots according to eq 7 of CTAB/butanol/decane system14 at r values 1.50, 1.77, and 2.20.
taining both surfactant and cosurfactant have supported both EMT and EMTDD (chain). The equations for EMTDD (cluster) and BW are invalid on them. Only one set of results from ref 13 is graphically presented in Figure 4 to demonstrate the correlation
900 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992
Paul et al. 5 t
01 0
,
1
OB
16
32
24
LO
r ( EMTDD)
Figure 5. r(EMT) vs r(EMTDD) plot of microemulsions. 0 , data collected from ref 14; 0,data collected from ref 13. Correlation = 0.966.
01 0
I
0.05
I
0.10
J
0.15
I
0.20
I
0.25
I
1
0.30 0.35
-
1
0 4
(0~1566~+1.7216~’-0.729@~
Figure 4. u vs (0.15664 + 1.72164* - 0.7296)) plot according to eq 7 of SDS/hexylamine/heptane system at r value 2.1.
with eq 7. The r for the correct coefficient of the intercepts (-0.15 19) has been obtained to be 2.1. A support to the EMT theory has been also given by the results of Lagourette et alez4 on water/toluene/potassium oleate/butanol system. The a p propriate r and od values obtained have been 1.5 and 2.64 S m-I, respectively, at 22 O C .
Discussion For random dispersions of spheres in a continuum, the EMT is a restricted form of EMTDD. In terms of the percolation threshold, the BW theory is equivalent to the EMTDD (cluster). When applied to the percolation of microemulsion systems taken from various sources, none of the theories has emerged as unique. All thirty-two systems processed more or less fit to one theory or the other. Two systems have responded to both EMTDD (cluster) and the BW, and one has preferably obeyed the BW theory. The agreement of the same system with both EMTDD (chain) and the BW theory has justification for the latter as a cluster extension of EMT. Both have almost identical percolation thresholds, 0.156 and 0.157, respectively, but in respect to q they are not equivalent. For example, the data of Clarkson and Smedley” have yielded (rd = 9.2 S m-’ from EMTDD (cluster) and g d = 7.45 S m-l from the BW theory. It is to be noted that about 50% of the microemulsion systems have obeyed both EMT and EMTDD (chain) whose threshold volume fraction (#I~)are 0.333 and 0.271, respectively. These are not close and, therefore, simultaneous validity of two equations on the same sets of data is intriguing. The inapplicability of the phenomenon on the other 50% of the systems advocates some intrinsic physicochemical difference between these two sets of systems. It has been found that the q values obtained from EMT are all lower than the corresponding ud from EMTDD. It has been further observed that the rEMT bears a linear relation with rEMTDD chain. The least-squares correlation is rEMT = 1.1 + 0 . 8 4 r ~ ~ ~ ~ ~ ( C h a i n ) (1 1) Further the 6d(EMT) also bears a linear relation to b d (EMTDD-chain). The least-squares form is ud(EMT) = 0.22 + 0.75ud(EMTDD-chain) (12) The correlations are depicted in Figures 5 and 6, which also include the results of Fang and Venable.” The least-squares relations are, therefore, general rather than specific. It is noteworthy that the microemulsion systems that satisfy both EMT and EMTDD (chain) have rEMT 3 1, while those with rEMT < 1 do not satisfy EMTDD (chain). Such behavior is difficult to
01 0
I
,
I
10
20 U d (EMTOO)
-
I
40
30
Figure 6. ud(EMT)vs ud(EMTDD)plot of microemulsions. Symbols as in Figure 5. Correlation = 0.988.
TABLE Ik Parameters of Microemulsions According to EMT and EMTDD (chain)system (no.as in Table I) IJd, S m-I R,, nm Re, nm Re/Rw 1 2 3 4 5 11 13 15 16 17 22 25 26 27 28 29
1.14 (1.02) 1.61 (1.69) 1.46 (1.53) 1.41 (1.52) 1.69 (1.95) 0.65 (0.66) 0.76 (0.76) 2.67 (3.23) 2.86 (3.31) 2.46 (2.92) 0.83 (0.99) 1.72 (2.10) 1.81 (2.24) 1.42 (1.76) 2.28 (2.74) 2.56 (3.41)
4.05 4.52 4.48 4.45 5.25 4.55 5.32 5.30 5.13 5.35 5.05 4.99 5.63 4.57 5.27 5.17
(4.13) (5.01) (4.91) (5.03) (6.86) (4.93) (5.93) (6.74) (6.37) (6.69) (6.24) (6.78) (6.74) (5.59) (7.04) (7.43)
4.81 (4.89) 5.34 (5.87) 5.30 (5.87) 5.26 (5.89) 6.06 (7.76) 5.29 (5.68) 6.11 (6.77) 6.10 (7.75) 6.04 (7.35) 6.27 (7.69) 5.86 (7.08) 5.82 (7.72) 6.73 (7.68) 5.38 (6.45) 6.13 (7.99) 6.03 (8.40)
1.19 (1.18) 1.18 (1.17) 1.18 (1.17) 1.18 (1.17) 1.15 (1.13) 1.16 (1.15) 1.15 (1.14) 1.15 (1.15) 1.18 (1.15) 1.17 (1.15) 1.16 (1.13) 1.16 (1.14) 1.19 (1.14) 1.18 (1.15) 1.16 (1.14) 1.16 (1.13)
“VbSameas in Table I. ‘All calculations done at W, = 0.20.
rationalize. A mechanistic possibility is, however, indicated. Increasing r corresponds to decreasing particle size. For an equal amount of water in the microemulsions, there will be a greater number of droplets if r increases. Increased population of particles gives rise to an increased tendency of self-interaction, leading to aggregation. If the aggregates are in the form of chains, the system correlates with EMTDD (chain). In the above data treatment the isolated microemulsion droplets have been taken to be spheres. In lime with Granqvist and Hunderi it is considered that these spherical inclusions undergo association with increased concentration forming chains and clusters having overall prolate and oblate geometry. Fang and Venable” as well as Bisal et a1.I4 have presented analyses to derive the radius of
J. Phys. Chem. 1992,96,901-904
where the new terms a, and a, represent the cross-sectionalareas of the head groups of the surfactant and cosurfactant molecules respectively and N is the Avogadro number;
TABLE IIk Derived Droplet Number (Ne), Aggregation Number of Surfactant (A,), Aggreg8tion Number of Cosurfactant ( A = ) , and TOWSurface A m of the Dropkts/ml of Dispersion (At) According to EMT and EMTDD ( ~ h a i i ) ~
Re = ( 3 ~ / 4 u ) ' / ~
system (no. as in Table I) 1 2 3 4 5 11 13 15 16 17 22 25 26 27 28 29
901
1 O-8A,,
10-23Ne, m-3 A. A, 139 (145) 679 (708) 15.70 (18.20) 11.62 (8.07) 257 (367) 636 (653) 249 (340) 635 (656) 11.85 (8.52) 12.40 (8.13) 241 (369) 636 (655) 439 (1086) 965 (1054) 6.50 (2.60) 182 (239) 686 (713) 9.98 (7.66) 393 (555) 448 (327) 6.28 (4.41) 463 (1078) 476 (108) 6.35 (2.70) 414 (871) 487 (279) 7.00 (3.08) 477 (1045) 475 (136) 6.25 (2.86) 333 (694) 380 (76) 7.30 (3.46) 7.73 (2.60) 1090 (358) 784 (716) 568 (1067) 795 (789) 4.88 (2.60) 214 (449) 749 (942) 9.61 (4.58) 6.11 (2.22) 450 (1241) 765 (757) 420 (1488) 756 (692) 6.49 (1.83)
(14)
where v = 4/3uR,3+ A,Ms/psN+ A,M,/p,N, with p s and p, as the densities of the surfactant and cosurfactant, respectively, and
m2/m3 3.23 (3.9) 2.98 (2.55) 2.99 (2.58) 3.09 (2.57) 2.25 (1.54) 2.60 (2.33) 2.23 (1.95) 2.24 (1.54) 2.31 (1.57) 2.25 (1.61) 2.34 (1.69) 2.42 (1 30) 1.94 (1.89) 2.52 (1.80) 2.13 (1.38) 2.18 (1.27)
Ne = 34/4uRW3
(15)
A, = 4uRW2Ne
(16)
In Tables I1 and 111, the results on systems which show dual validity of EMT and EMTDD (chain) are compared. The differences in the two sets of results are obvious; the ratios RJRw from EMTDD is in the same order proposed by Lagourettez4and supported by Bisal et al.14
Conclwions The present analysis supports that the EMT, EMTDD, and BW theory can correlate the water-induced percolation in w/o microemulsions and indicate the nature of association of the dcrodroplets. The same systems may fit in both EMTDD (cluster) and BW theory, since the latter is a cluster extension of EMT. The systems containing cosurfactants have a tendency to fit in the EMT. They may also fit in the EMTDD (chain), if rEMT 3 1.
-Same as Table 11. the water core of a droplet (R,), their effective radius (Re),the number of droplets per milliliter of the dispersion (Ne),the total surface area of the droplets per milliliter of the dispersion (A,), the aggregation number of the surfactant per droplet (As),and the aggregation of the cosurfactant per droplet (A,) in terms of adequate relations:
Acknowledgment. We thank Jadavpur University, Calcutta, and CSIR, Government of India, New Dehli, for laboratory and financial assistance.
Rate Enhancements of 1,2-Eiimination in Micelles of Hydroxy-Functionaiized Quaternary Ammonium Bromides Kazimiera A. Wilk Institute of Organic and Polymer Technology, Technical University of Wroclaw, 50370 Wroclaw, Poland (Received: September 6, 1990; In Final Form: September 5, 1991)
The dehydrobromination reaction of para-substituted 2-phenylethyl bromides, pY-C6H4CH2CH2Br(Y = NOz and H), has been studied in micelles of hydroxy-functionalized quaternary ammonium bromides having the structures la-c and 2 in the
+
RNMe2CHzCH(R1)OHBr-
+
C14H29CH(OH)CHzNMe3 Br1a-c 2 presence of sodium hydroxide, where for 1 R = C16H33 and R1 = H (la), CH3 (lb), and C2HS(IC). The rate enhancements of the studied dehydrobrominations when compared to those due to a monomeric choline model compound in water can be attributed primarily to increased reactant concentration at the micellar surface. The greater basicity of the alkoxide zwitterionic components of partially deprotonated micelles of la-c and 2 and the site at which the alkoxide group is bonded to the surfactant head group also seem to affect the rate. The relative reactivities of the studied micelles depend upon the kind and position of the micelle deprotonated functional group on the surfactant.
Introduction Reactions in most functional micellar reagents1 involve nucleophilic attack by an anionic moiety, e.&, oximate, hydroxamate, thiolate, and alkoxide, and the reaction rates are pH dependent.z ~
~
_
_
_
(1) (a) Bunton, C. A. In Solution Chemistry ofSurficrms; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 2, p 519. (b) Bunton, C. A. Caral. Rev.-Sci.Eng. 1979.20, 1. (c) Fornasier, R.;Tonellato, U. J . Chem. Soc., Faraday Trum. I 1980.76, 1301. (d) Moss, R. A.; Lee,Y.-S.; Alwis, K. W. In Solurion Behwior ofSurjuctants; Mittal, K. L., Fendler, E. F., E&.; Plenum Press: New York, 1982; Vol. 2, p 993.
0022-3654/92/2096-901$03.00/0
_
Therefore, the sources of large rate enhancements in functional micelles, over those for reaction in water, can be attributed to at least three factors: (i) a high concentration of nucleophile in the Stem layer at the micellewater interface, (ii) an increased extent of deprotonation of the functional group at the interface, and (iii) a favorable environmental effect of the micelle on the r e a ~ t i o n . ~ (2) (a) Bunton, C. A.; Ionescu, L. G. J . Am. Chem. Soc. 1973,95,2912. (b) Bunton, C. A.; Diaz, S. Ibid. 1976, 98, 5663. (3) Bunton, C. A.; Savelli, G. Adv. Phys. Org. Chem. 1986, 22, 213.
0 1992 American Chemical Society
