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decane microemulsion with reference to the mechanism of conduction
Colloids and Surfaces,
50 (1990) 295-308
Elsevier Science Publishers
295
B.V., Amsterdam
Additive Effects on the Percolation of Water/AOT/Decane Microemulsion with Reference to the Mechanism of Conduction LANA MUKHOPADHYAY, Department
of Chemistry,
P.K. BHATTACHARYA Jadavpur
University,
and S.P. MOULIK
Calcutta 700032 (India)
ABSTRACT The results of temperature induced percolation behaviours of w/o microemulsion produced by the ternary system water/AOT/decane in the presence of alkanols, cholesterol and several of its esters, benzyl alcohol and a crown ether are presented. The percolation threshold has been increased by the additives, except for benzyl alcohol and the crown ether, where the conductancetemperature profile is less sharp and the threshold temperature is lowered. The activation energy for percolation has also been lowered by the additives. The findings support percolation transition by efficient transport of Na+ counter-ions through water channels formed in the clusters of microwater droplets upon collision. The clusters undergo structural rearrangements during percolation.
INTRODUCTION
The system water/AOT/decane can form a w/o microemulsion [ 1,2] at certain compositions specified by the ternary phase diagram. In the solution the water droplets, coated with the AOT anions containing the counter-ions (Na+ ions) in the pool, are dispersed in the low dielectric decane (oil) continuum, so that the specific conductance of the solution is small ( N 10-4-10-5 S cm-‘). But, the specific conductance of this w/o microemulsion is several folds higher than the oil (10-‘4-10-‘o S cm-‘) because the micro-droplets carry excess charges on them [ 31. The addition of water in the system may help to increase the conductance, and after a threshold volume fraction of water, the conductance can rise sharply in a narrow range and thereafter remains more or less unchanged. This phenomenon is called the percolation of microemulsion [ 410]. A similar percolation phenomenon can be achieved if the w/o microemulsion of a constant composition is subjected to variation in temperature; the conductance may be observed to increase significantly (even a thousand fold or more) within a narrow range after a threshold level of transition [ ll181. The underlying principle of the rise in conductance ought to be an efficient transfer of charge carriers (ions) through the oil continuum by way of a special
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transport mechanism [ 1,2,18-221. It is considered that during percolation, water microdroplets come in close contact, and either the surfactant ions from the surface of the droplets ‘hop’ along or the ‘sticky’ collisions among them form channels (conduits ) through which the counter-ions are transferred; the conductance is, thus, greatly enhanced after a threshold level. Very recently, Maitra et al. [ 131 have reported suppression of percolation by the blocking effect of cholesterol and enhancement of it by the channel forming effect of gramicidin on an AOT stabilized water-isooctane microemulsion system. Dutkiewicz and Robinson [20] have presented the effects of toluene and benzyl alcohol on the percolation of water/AOT/dodecane system. Their analysis favors channel formation whereas that of Huang et al. [ 191, on the same system, supports the hopping model [23,24] of transport of surfactant anions. With reference to the use of additives like benzyl alcohol, it may be said that the use of alkanols on the process of percolation have been reported earlier [ 141. Very recently, from time-resolved fluorescence measurements Jada et al. [ 21 have presented experimental evidence in support of channel formation for the percolation phenomenon. There, thus, exists two views about the mode of conduction for percolation. It is anticipated that the effects of additives may give an insight to the mechanism of percolative conduction. Only limited studies on the additive effects on percolation have appeared in the literature. We present the results of a detailed study of temperature induced conductance behavior of an AOT stabilized water/decane microemulsion system in the presence of additives viz., alkanols (C, to C,,), benzyl alcohol, cholesterol and several of its esters (acetate, benzoate and stearate) and cyclohexyl-l&crown-6 ether. The results of the effect of temperature on the viscosity of the ternary system in the presence of these additives are also presented. We have attempted to explain the results in the light of the organizational state of the emulsion system. It will be seen that the findings support the opening of the surfactant layers of the microdroplets to form water channels for the transfer of Na+ ions rather than hopping of the AOT anions from one droplet to another to account for the temperature induced percolation. EXPERIMENTAL
Materials
The AOT and the n-decane used were 99% pure products of Sigma, U.S.A. and pro analysi grade of E. Merck, F.R.G., respectively. The alkanols n-butanol, n-pentanol, n-hexanol, n-octanol and n-decanol were of AR grade, BDH, United Kingdom. The benzyl alcohol was of pro analysi grade obtained from E. Merck, F.R.G. Cyclohexyl-l&crown-6 ether was supplied by Aldrich, U.S.A. All these chemicals were used without further purification. The cholesterol
297
used was a purified sample [ 251. The esters cholesteryl acetate and benzoatewere obtained from SRL, India, cholesteryl stearate was a product of Sigma, U.S.A. The sterol derivatives were subjected to elemental analysis and were found to be 99-99.5% pure. Doubly distilled water (specific conductivity 2-4 &S cm-’ at 303 K) was used for all sample preparations. Phase studies The components AOT and n-decane were taken in different weight proportions and water was added under constant stirring conditions in a temperature controlled water bath at 303 t- 0.01 K. The samples were allowed sufficient time in the bath for equilibration and were observed for the phases formed. Liquid crystalline state of the preparations was detected under a polarizing microscope of SICO, India. Conductance measurements Four ternary mixtures of components water/AOT/decane in weight percent as 8/8/84 (S,), 10/15/75 (S,), 10/20/70 (S,) and 10/30/60 (S,) were prepared. The water/AOT mole ratios w of the four solutions were 24.7,16.5,12.3 and 8.2, respectively. Each sample was taken in the conductivity cell of cell constant 1.10 cm-’ and the conductance was measured with a Jenway, United Kingdom, conductivity meter at 1 kHz at different temperatures between lo60’ C in 5 ‘C intervals. At each temperature 1 h time was given to the solution, within this time the conductance remained unchanged after the lapse of 5-10 min in the beginning. For a detailed study, sample (S, ) was chosen and the conductances at different temperatures were measured in the presence of various additives at the concentration levels 0.1-l% (w/v) in n-decane. Viscosity measurements The viscosity of the medium n-decane and the microemulsion sample (S, ) with and without additives were measured at different temperatures in an Ostwald viscometer assuming Newtonian behaviour. The density of the solutions were measured at the corresponding temperatures in a calibrated pycnometer. Compressibility measurements The adiabatic compressibilities of n-decane and the sample (S, ) in the presence and absence of additive were obtained by measuring the ultrasound velocities in an ultrasonic interferometer of Mittal Enterprises, India. The compressibility p was found from the relation /3= - l/ (p u2 ), where p and u are the
298
density and the ultrasound velocity, respectively. The measurement procedure was described elsewhere [ 261.
RESULTS
Phase behavior and conductance The ternary phase diagram of AOT/water/decane system at 30’ C (Fig. 1) shows distinctive features; the w/o or L2 region is non-viscous, there are also viscous, liquid crystalline gel-type regions. The compositions used for the demonstration of percolation are indicated by asterisks in the figure. Of the compositions studied (Fig. 2 ), the sample having the H,O/AOT mole ratio 25 with o/w ratio 11 (v/v) has shown striking percolation; the conductance increased sixteen fold. The percolative feature becomes less prominent with the decrease in the H,O/AOT ratio; the two compositions at H,O/AOT=8 and 12.5 have shown less distinct behavior. The sample S, has been used throughout to study the additive effects on the process. This sample and that with H,O/AOT mole ratio 16.5 have shown initial constant conductance, the other two samples have exhibited increment in conductance right from the beginning. The percolation transition for the first two samples occurs at 30’ C.
AOT
Fig. 1. Triangular
phase diagram of water/AOT/decane
microemulsion
system at 30°C.
299
b _8
Fig. 2. Temperature conductance profile of water/AOT/decane ratios.
systems at different water/AOT
Effects of additives on percolation The effects of alkanols (1% w/v in the oil) on the percolation are presented in Fig. 3. The longer the alkyl chain the more is the resistance to percolation, decanol has practically shown no percolation up to 60°C. The increment in the transition offered by butanol, pentanol, hexanol and octanol are 1.5,22,31 and 31 ‘C, respectively. The conductance of the solution prior to the transition threshold has been observed to increase with the alkyl chain length of the alkanols, the sequence follows the order decanol>octanol, hexanol> pentanol> butanol. Cholesterol as an additive had a significant effect on the percolation transition (Fig. 4). Prior to this phenomenon, the conductance has decreased irregularly with increased addition of cholesterol, there is also increased temperature for the transition with increased addition of the sterol.
300
5r
3
b (?i . 0
Fig. 3. Temperature (w/w)
conductance
profile of water/AOT/decane
system (S,)
in the presence of 1%
alcohols.
The addition of 1% (w/v) cholesterol has increased the threshold temperature from 30 to 52’ C. The effect is thus striking. The cholesterol derivatives (acetate, benzoate and stearate) have shown minor effects (Fig. 5) and their activities are more or less similar. At 0.1% (w/v) level the transition temperature has increased by 6.5’ C. Because of solubility problems, concentrations beyond 0.1% stearate could not be used. The crown ether also showed a distinct effect (Fig. 5). The effects of 0.1% and 0.3% ( w / v ) crown ether are very close to 0.1% cholesterol, 1% crown ether has lowered the transition by 4 ’ C. The crown ether has also increased the initial conductance of the microemulsion. The percolation transition temperature, the range of transition and the activation energy for percolation in the presence of different additives are presented in Table 1. The activation energies have been evaluated from the slopes of the linear portions of the plots of log crversus T -'in the temperature range specified (for each system) in the table. Except benzyl alcohol and crown ether at equal w/v% levels, all the additives have increased the threshold temperature and decreased the energy of activation, the effects of higher chain length alkanols are less on the latter, whereas a minimum of activation energy is ob-
301
Fig. 4. Temperature
conductance
profile of water/AOT/decane
system in presence of cholesterol.
served at 0.5% cholesterol. The activation energy has also decreased with increased concentration of crown ether. In Fig. 6, the effects of different additives on the viscosity of the microemulsion at different temperatures are presented. It is observed that there is a viscosity maximum at 40’ C without any additive, which shifts to 50 oC in the presence of 0.1% cholesterol, the maximum tends to be shifted to 60” C in the presence of 0.5% cholesterol, which is yet to be reached in the presence of 1% cholesterol. Almost identical viscosity behaviour has been observed when cholesterol acetate is the additive. Cholesterol benzoate and stearate have yielded the maximum at 40°C at 0.1% level. 1% cholesterol benzoate has shifted it to 5O”C, 0.1% crown ether has yielded the viscosity maximum at 50’ C, 0.3% and 1% crown ether have not shown the maximum, the viscosity increments have been mild (curves not presented), Percolation
and adiabatic compressibility
The adiabatic compressibilities of the microemulsion with 1% cholesterol and without any additive as a function of temperature are presented in Fig. 6.
302
Fig. 5. Temperature conductance profile of water/AOT/decane system (S,) in the presence of cholesteryl esters and crown ether. Curve 1, no additive; curve 2,0.1%, 0.5%, 1% cholesteryl benzoate, 0.1% cholesteryl stearate, 1% cholesteryl acetate; curve 3, 0.1% cholesteryl acetate; curve 4,0.1% crown ether; curve 5,0.3% crown ether; curve 6,0.7%, 1% crown ether.
An effect opposite to viscosity has been observed with a minimum in compressibility at 40 oC. 1% cholesterol has yielded decreasing compressibility with increasing temperature which is also the expected reverse of findings on viscosity. DISCUSSION
The alkanols imparted increased intrinsic conductance to the microemulsion which increased with the increased alkyl chain length. This is an uncommon phenomenon, for alkanols are nonconducting and nonpolar solvents. The conductance of aqueous solution of AOT decreases on addition of an alkanol. The charges on the micro-water droplets undergo fluctuations and it is considered that excess positive or negative charges possessed by the particles give rise to modest conductance to the dispersed system in the oil matrix [3], Addition of alkanols offers softness or flexibility to the interphase [24] with easier charge fluctuations and thereby enhanced conductance. The soft-
303 TABLE 1 Additive effects on the percolation characteristics of microemulsion (sample S,) Additive (wt/v% in oil)
Transition temperature ( ’ C )
Percolation range (“C)
E,
0
30.5 52 47.5 40 37.5 36.5 32 25 52.5 61.5 61.5
30-45 52-60 48-60 40-60 38-50 37-50 32-55 25-45 53-65 62-65 62-65
700 670 470 400 455 510 285 263 580 608 450
32
32-65
612
26.5 36 36
26-50 36-50 36-50
175 335 560
Cholesterol ( 1%) Cholesterol (0.75%) Cholesterol (0.5%) Cholesterol (0.25%) Cholesterol (0.1% ) Butanol ( 1% ) Benzyl alcohol (1% ) Pentanol ( 1% ) Hexanol ( 1% ) Octanol ( 1% ) Cholesteryl acetate (0.5%) 1%) Cholesteryl benzoate (0.5%, l%, 0.1%) Cholesteryl stearate (0.1% ) Crown ether (0.7%, 1%) Crown ether (0.3%) Crown ether (0.1%)
77
06
60
02
06
06
01
(kJ mol-‘)
2U
30
40 tot
50 -
60
01
20
30
40 t-c
50
60
-
Fig. 6. Temperature dependence of viscosity and compressibility of water/AOT/decane system (S,) in the presence of different additives. Curves l-10, no additive, 0.1% cholesterol, 0.5% cholesterol, 1% cholesterol, 1% cholesteryl acetate, 0.1% cholesteryl acetate, 0.1% cholesteryl stearate, 0.1% cholesteryl benzoate, 1% cholesteryl benzoate, 1% cholesterol.
304
ness of the interphase increases with the chain length offering higher conductance to the system. The addition of cholesterol and its esters has, on the other hand, a decreasing effect on the intrinsic conductance of the microemulsion. The sterols produce more compact interphases [ 131 and reduce the effective excess charges on the droplets by restricting the charge fluctuations thereby lowering the conductance. The crown ether can complex Na+ ions and can transport it through the medium, this explains the increased conductance of the microemulsion in its presence. The course of percolation is also less steep because the ion transport by the crown ether follows a special mechanism. The activation energy for the transport is lower (173.3 kJ mol-’ at the 1% level). The temperature induced percolation in w/o microemulsion systems is a striking but established phenomenon. It is expected that the effects of the additives may throw light on the mechanism of the process. The additives employed in the present study all have hindered percolation, except the crown ether and benzyl alcohol which have shown a less sharp phenomenon. The probable mechanisms for percolation transition are the hopping mode and the transient channel forming mode. Both alkanols and cholesterol and its ester derivatives have shifted the transition to higher temperature; the charge transport in the microemulsion has been resisted. For AOT/water/isooctane microemulsion, the transition temperature for conductance has been shown [ 141 to be dependent on the type of alkanol. Short chain alkanols decrease the percolation temperature, whereas longer chain alkanols increase it, the minimum being provided by propanol. Our microemulsion sample has been observed to be unstable in the presence of alkanols lower than butanol, and we could not study their effects. In line with the previous findings, we have observed increased percolation temperature up to decanol (alkanols higher than hexanols were not used in the previous study). Compared to the emulsion stabilizer AOT molecules, the alkanols used are longer in length, whereas the size of cholesterol is smaller. For the hopping phenomenon to operate, the microdroplets with a surfactant coat ought to approach within a reasonable distance; for the formation of a channel, the droplets must stick together upon collision. The polar -OH group of the alkanol adheres to the surface of the micro-water pool and becomes a part of the assembly, the effective size of the inner micro-water droplet decreases with increase of their number. The hopping length between two particles, on the other hand, increases in the presence of higher alkanols; the formation of a channel for ion transport is also not favored. The small sized benzyl alcohol anchors its hydroxyl groups on the polar droplet surface, the portruding aromatic ring offers increased local hydrophobicity, the droplets therefore undergo attractive interaction [ 201 facilitating ion transfer. Lower alkanols may act in a similar way, as has been observed for the water/AOT/ isooctane microemulsion system [ 141. The crown ether complexes Na+ ions and acts as a carrier for the transport of it through the oil, the transition temperature is thus lowered in the presence of a reasonable amount of it. Choles-
305
terol is a small but rigid molecule. In the interphase, like the alkanols, its hydroxyl group remains attached to the surface of the micro-water droplet and the interphase becomes stiffer. Although closer approach of droplets is feasible, effective conductance remains low. The rigidity of the interphase restricts transfer of ions between particles. The esters of cholesterol are less effective; they are equally effective percolation suppressors among themselves. The compounds are more apolar and cannot conveniently approach the water/AOT interface; remaining in the oil medium they act as a barrier [ 201 to percolation. It should be noted that 1% cholesterol in oil contributes 1.6.10zo molecules and taking the whole amount to be present in the interphase the ratio of cholesterol/AOT molecules in the interphase is 0.163. The ratio of the molecules of cholesteryl acetate, benzoate, stearate, benzyl alcohol, crown ether, butanol, pentanol, hexanol, octanol and decanol with AOT in the interphase (assuming 50% of the alkanols being present, because of partition with the oil) are 0.146, 0.127, 0.01, 0.58, 0.168, 0.422, 0.36, 0.306, 0.27 and 0.20, respectively. Except butanol, hexanol and benzyl alcohol, all the other values are too small to indicate specific effects of the additives on the percolation threshold. Lesser number of molecules of longer chain alkanols are effective since the central water pool between two droplets in contact are more separated by the increased interphase offered by the longer alkanols. Using a time-resolved fluorescence method Jada et al. [2,27] have estimated the rate constant for the exchange of materials between two droplets on collision and have shown that for percolation to take place the rate constant must have a threshold value which supports movement of counter-ions through the water channel formed by the sticky collision among the droplets. Irrespective of surfactant chain length, head group or nature of the oil, the percolation thresholds correspond to l-2.10’ mol-’ s-l as the interdroplet exchange rate constant, this has lent support to the channel mechanism which is also our view. Assuming the diameter of a microdroplet to be 100 A, 2, the number of the droplets colliding in 1 ml s-l, can be calculated from the kinetic theory by the formula, Z= [ 2 n a2 un’ ] ‘I2 where a is the diameter of a particle, u is the velocity [u= 0.921 (3RT/M)““] and n is the number of particles in 1 ml, it4being the weight of the Avogardro number of particles. The bimolecular rate constant k = Zq, where q = e -Ea’RT (q is the ratio between the number of activated particles and the total number of particles and E, is the activation energy). Therefore, k=ZecEaIRT. The Z at 303 K has been calculated to be 9.3*10z5 ml-’ s-l. The activation energy for bimolecular reactions usually fall in the range 80-160 kJ mol- ‘. Taking the value of E,= 100 kJ mol-’ [ 201 and the above value of Z= 9.3*1025,the rate constant k=0.7.10g mol-’ dme3 at 303 K. This is the rate constant for a fruitful collision leading to exchange of materials between the droplets for percolation in the absence of additive. This result closely agrees with l-2.10’ mol-’ dm3 s-l reported by Jada et al. [ 2,271. The activation energy for conduction in the region of percolation has been reported [ 131 to be roughly 550-600 kJ mol-‘.
306
We have observed an average value of 700 kJ mol-l without additives and lower values in the presence of additives (Table 1). The conductivity curves indicate that once the process starts, it proceeds very efficiently. The threshold temperature for percolation is like the ‘one-and-none’ law observed in nerve conduction [ 281, where transport of Na+ and K+ ions through specific channels plays a key role; a minimum or threshold stimulation is required for the generation of an impulse. In the present context the thermal energy makes the skin of the microemulsion droplet dilate or soften and assists transport of charge carriers among the clustered droplets. The lowering of activation energy supports easier charge transport through the oil matrix. After the threshold temperature, due to increased thermal energy, the polar alkanol molecules get distributed (dispersed) more into the oil and they make the microenvironment in the oil matrix polar and charge transport becomes convenient, the activation energy is thus lowered. Longer alkanols are less polar and the reduction in the activation energy is less. It is to be noted that the effects of hexanol and octanol are not in order; compared to the lower concentrations, the decreasing effects of 0.75 and 1% cholesterol are also not orderly. The activation energy for conduction of H+ ions in an aqueous medium is distinctly lower (10 kJ mol-‘) than ether ions ( - 15 kJ mol-‘) [29]. The proton jump way of conduction of H+ ions therefore crosses a lower energy barrier. Before and after the percolation range, the activation energies for conduction of the microemulsion system without additive are 5 and 50 kJ mol-’ respectively; these roughly fall in the range of activation energies for ions, the system thus shows a normal mode of conduction. A value of 700 kJ mol-l in the percolation state advocates a significant energy barrier, a hopping mode of conduction is not consistent with it, the transient channel formation by sticky collision is more likely to be the mode. Direct and unambiguous evidence is, however, wanted for a conclusive decision in this regard. Viscosity
The viscosity-temperature profiles of the microemulsion in the presence of different additives are presented in Fig. 6. A viscosity maximum is observed in the absence of additive; at lower concentrations of the additives, the maximum shifts towards higher temperature, which disappears at higher additive concentrations. Borkovec et al. [l] have also reported similar viscosity phenomenon of AOT stabilized w/o microemulsion without additives. The clustering of the microdroplets with increase of temperature may end up with an increased viscosity [ 11.The first stage of the viscosity-temperature profile resembles percolation. It should be noted that simultaneous increase in viscosity and conductance is contrary to normal findings (conductance is inversely proportional to viscosity); this is possible in microemulsions, because clustering assists efficient ion transport and percolation. The decreased viscosity in the
307
second stage can be reasoned through the change of the overall shape of the clusters from nonspheres towards spheres at higher temperature. Monte Carlo simulations has shown [ 181 that the globules form network-like structures if the attractive interaction is negligible, and compact separated cluster-like arrangements if the attractive interaction is strong. A transition between two types of structures may decrease the effective viscosity without affecting the ion-transport mechanism for which formation of clusters and transfer of ions are the key factors. The additives help to keep the overall structure of the clusters more towards spheres, so that the viscosity is comparatively small and with increasing concentration it decreases further and temperature has only a mild effect on it. The non-linear course of log q versus T -'plot has advocated progressive change in the activation energy for viscous flow. The formation of clusters and changes of cluster shape with temperature contribute primarily to the magnitude of viscosity, the overall process is complex. The adiabatic compressibility coroborates the viscosity data. In the absence of additive, the compressibility passes through a minimum at 40’ C, whereas in 1% cholesterol the compressibility decreases progressively with temperature, the system becomes less and less compressible; an internal structure or organized state is in progress through which transfer of ions is favoured by a special mechanism resulting in effective percolation of conductance. ACKNOWLEDGEMENT
This work has been financially supported by the department of Science and Technology, Government of India.
REFERENCES M. Borkovec, H.F. Eicke, H. Hammerich and B. Das Gupta, J. Phys Chem., 92 (1988) 206. A. Jada, J. Lang and R. Zana, J. Phys. Chem., 93 (1989) 10. H.F. Eicke, M. Borkovec and B. Das Gupta, J. Phys. Chem., 93 (1989) 314. M. Lagues, J. Phys. Lett., 40 (1979) 331. G.S. Grest, I. Webman, S.A. Safran and A.L.R. Bug, Phys. Rev. A, 33 (1986) 2842. S. Bhattacharya, J.P. Stokes and M.W. Kim, Phys. Rev. Lett., 55 (1985) 1884. H.F. Eicke, R. Hilfiker and H. Thomas, Chem. Phys. Lett., 55 (1985) 1884. A.L.R. Bug and Y. Gefen, Phys. Rev. A, 35 (1987) 1301. J. Peyrelasse, M. Moha-Ouchane and C. Boned, Phys. Rev. A, 38 (1988) 4155. S.R. Bisal, P.K. Bhattacharya and S.P. Moulik, J. Phys. Chem., 94 (1990) 350. 11 H.F. Eicke, S. Geiger, R. Hilfiker, F.A. Sauer and H. Thomas, in R. Pynn andT. Riste (Eds), Time Dependent Effects in Disordered Materials, Plenum, New York, 1987, p. 219. 12 S. Geiger, H.F. Eicke and D. Spielmann, Z. Phys. B, Condensed Matter, 68 (1987) 175. 13 C. Mathew, P.K. Patanjali, A. Nabi and A.N. Maitra, Colloids Surfaces, 30 (1988) 253. 14 H.F. Eicke, R. Kubik, R. Hasse and I. Zschokki, in K.L. Mittal and B. Lindman (Eds), Surfactants in Solution, Plenum, New York, 1984, p. 1533. 2 3 4 5 6 7 8 9 10
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
A.M. Cazabat, D. Chatenay, P. Guering, D. Langevin, J. Meunier and 0. Sorba, in K.L. Mittal and B. Lindman (Eds), Surfactants in Solution, Plenum, New York, 1984, p. 1737. A.M. Cazabat, D. Langevin, J. Meunier and A. Poncelon, J. Phys. Lett., 43 (1982) 89. M.W. Kim and J.S. Huang, Phys. Rev. A, 34 (1986) 719. S.A. Safran, G.S. Grest and A.L.R. Bug in H.L. Rosano and M. Clausse (Eds), Microemulsion Systems, Marcel Dekker, New York, 1987, p. 235. J.S. Huang, S.A. Safran, M.W. Kim, G.S. Grest, M. Kottarchyk and N. Quirke, Phys. Rev. Lett., 53 (1984) 593. E. Dutkiewicz and B.H. Robinson, J. Electroanal. Chem., 251 (1988) 11. S.S. Atik and J.K. Thomas, J. Am. Chem. Sot., 85 (1981) 3921. P.D.I. Fletcher, A.M. Howe and B.H. Robinson, J. Chem. Sot. Faraday Trans. 1,83 (1988) 985. R. Hilfiker, H.F. Eicke, S. Geiger and G. Furler, J. Colloid Interface Sci., 105 (1985) 378. S. Bhattacharya, J.P. Stokes, M.W. Kim and J.S. Huang, Phys. Rev. Lett., 55 (1985) 84. S.R. Bisal, P.K. Bhattacharya and S.P. Moulik, J. Surf. Sci. Technol., 4 (1988) 121. P.K. Dasgupta and S.P. Moulik, J. Phys. Chem., 91 (1987) 5826. A. Jada, J. Lang and R. Zana, J. Phys. Chem., 94 (1990) 381. M.V. Volkenstein, MIR Moscow, 1983, p. 381. S. Glasstone, An Introduction to Electrochemistry, Van Nostrand, New York, 1965, pp. 6162.
50 (1990) 295-308
Elsevier Science Publishers
295
B.V., Amsterdam
Additive Effects on the Percolation of Water/AOT/Decane Microemulsion with Reference to the Mechanism of Conduction LANA MUKHOPADHYAY, Department
of Chemistry,
P.K. BHATTACHARYA Jadavpur
University,
and S.P. MOULIK
Calcutta 700032 (India)
ABSTRACT The results of temperature induced percolation behaviours of w/o microemulsion produced by the ternary system water/AOT/decane in the presence of alkanols, cholesterol and several of its esters, benzyl alcohol and a crown ether are presented. The percolation threshold has been increased by the additives, except for benzyl alcohol and the crown ether, where the conductancetemperature profile is less sharp and the threshold temperature is lowered. The activation energy for percolation has also been lowered by the additives. The findings support percolation transition by efficient transport of Na+ counter-ions through water channels formed in the clusters of microwater droplets upon collision. The clusters undergo structural rearrangements during percolation.
INTRODUCTION
The system water/AOT/decane can form a w/o microemulsion [ 1,2] at certain compositions specified by the ternary phase diagram. In the solution the water droplets, coated with the AOT anions containing the counter-ions (Na+ ions) in the pool, are dispersed in the low dielectric decane (oil) continuum, so that the specific conductance of the solution is small ( N 10-4-10-5 S cm-‘). But, the specific conductance of this w/o microemulsion is several folds higher than the oil (10-‘4-10-‘o S cm-‘) because the micro-droplets carry excess charges on them [ 31. The addition of water in the system may help to increase the conductance, and after a threshold volume fraction of water, the conductance can rise sharply in a narrow range and thereafter remains more or less unchanged. This phenomenon is called the percolation of microemulsion [ 410]. A similar percolation phenomenon can be achieved if the w/o microemulsion of a constant composition is subjected to variation in temperature; the conductance may be observed to increase significantly (even a thousand fold or more) within a narrow range after a threshold level of transition [ ll181. The underlying principle of the rise in conductance ought to be an efficient transfer of charge carriers (ions) through the oil continuum by way of a special
0166-6622/90/$03.50
0 1990 -
Elsevier Science Publishers
B.V.
296
transport mechanism [ 1,2,18-221. It is considered that during percolation, water microdroplets come in close contact, and either the surfactant ions from the surface of the droplets ‘hop’ along or the ‘sticky’ collisions among them form channels (conduits ) through which the counter-ions are transferred; the conductance is, thus, greatly enhanced after a threshold level. Very recently, Maitra et al. [ 131 have reported suppression of percolation by the blocking effect of cholesterol and enhancement of it by the channel forming effect of gramicidin on an AOT stabilized water-isooctane microemulsion system. Dutkiewicz and Robinson [20] have presented the effects of toluene and benzyl alcohol on the percolation of water/AOT/dodecane system. Their analysis favors channel formation whereas that of Huang et al. [ 191, on the same system, supports the hopping model [23,24] of transport of surfactant anions. With reference to the use of additives like benzyl alcohol, it may be said that the use of alkanols on the process of percolation have been reported earlier [ 141. Very recently, from time-resolved fluorescence measurements Jada et al. [ 21 have presented experimental evidence in support of channel formation for the percolation phenomenon. There, thus, exists two views about the mode of conduction for percolation. It is anticipated that the effects of additives may give an insight to the mechanism of percolative conduction. Only limited studies on the additive effects on percolation have appeared in the literature. We present the results of a detailed study of temperature induced conductance behavior of an AOT stabilized water/decane microemulsion system in the presence of additives viz., alkanols (C, to C,,), benzyl alcohol, cholesterol and several of its esters (acetate, benzoate and stearate) and cyclohexyl-l&crown-6 ether. The results of the effect of temperature on the viscosity of the ternary system in the presence of these additives are also presented. We have attempted to explain the results in the light of the organizational state of the emulsion system. It will be seen that the findings support the opening of the surfactant layers of the microdroplets to form water channels for the transfer of Na+ ions rather than hopping of the AOT anions from one droplet to another to account for the temperature induced percolation. EXPERIMENTAL
Materials
The AOT and the n-decane used were 99% pure products of Sigma, U.S.A. and pro analysi grade of E. Merck, F.R.G., respectively. The alkanols n-butanol, n-pentanol, n-hexanol, n-octanol and n-decanol were of AR grade, BDH, United Kingdom. The benzyl alcohol was of pro analysi grade obtained from E. Merck, F.R.G. Cyclohexyl-l&crown-6 ether was supplied by Aldrich, U.S.A. All these chemicals were used without further purification. The cholesterol
297
used was a purified sample [ 251. The esters cholesteryl acetate and benzoatewere obtained from SRL, India, cholesteryl stearate was a product of Sigma, U.S.A. The sterol derivatives were subjected to elemental analysis and were found to be 99-99.5% pure. Doubly distilled water (specific conductivity 2-4 &S cm-’ at 303 K) was used for all sample preparations. Phase studies The components AOT and n-decane were taken in different weight proportions and water was added under constant stirring conditions in a temperature controlled water bath at 303 t- 0.01 K. The samples were allowed sufficient time in the bath for equilibration and were observed for the phases formed. Liquid crystalline state of the preparations was detected under a polarizing microscope of SICO, India. Conductance measurements Four ternary mixtures of components water/AOT/decane in weight percent as 8/8/84 (S,), 10/15/75 (S,), 10/20/70 (S,) and 10/30/60 (S,) were prepared. The water/AOT mole ratios w of the four solutions were 24.7,16.5,12.3 and 8.2, respectively. Each sample was taken in the conductivity cell of cell constant 1.10 cm-’ and the conductance was measured with a Jenway, United Kingdom, conductivity meter at 1 kHz at different temperatures between lo60’ C in 5 ‘C intervals. At each temperature 1 h time was given to the solution, within this time the conductance remained unchanged after the lapse of 5-10 min in the beginning. For a detailed study, sample (S, ) was chosen and the conductances at different temperatures were measured in the presence of various additives at the concentration levels 0.1-l% (w/v) in n-decane. Viscosity measurements The viscosity of the medium n-decane and the microemulsion sample (S, ) with and without additives were measured at different temperatures in an Ostwald viscometer assuming Newtonian behaviour. The density of the solutions were measured at the corresponding temperatures in a calibrated pycnometer. Compressibility measurements The adiabatic compressibilities of n-decane and the sample (S, ) in the presence and absence of additive were obtained by measuring the ultrasound velocities in an ultrasonic interferometer of Mittal Enterprises, India. The compressibility p was found from the relation /3= - l/ (p u2 ), where p and u are the
298
density and the ultrasound velocity, respectively. The measurement procedure was described elsewhere [ 261.
RESULTS
Phase behavior and conductance The ternary phase diagram of AOT/water/decane system at 30’ C (Fig. 1) shows distinctive features; the w/o or L2 region is non-viscous, there are also viscous, liquid crystalline gel-type regions. The compositions used for the demonstration of percolation are indicated by asterisks in the figure. Of the compositions studied (Fig. 2 ), the sample having the H,O/AOT mole ratio 25 with o/w ratio 11 (v/v) has shown striking percolation; the conductance increased sixteen fold. The percolative feature becomes less prominent with the decrease in the H,O/AOT ratio; the two compositions at H,O/AOT=8 and 12.5 have shown less distinct behavior. The sample S, has been used throughout to study the additive effects on the process. This sample and that with H,O/AOT mole ratio 16.5 have shown initial constant conductance, the other two samples have exhibited increment in conductance right from the beginning. The percolation transition for the first two samples occurs at 30’ C.
AOT
Fig. 1. Triangular
phase diagram of water/AOT/decane
microemulsion
system at 30°C.
299
b _8
Fig. 2. Temperature conductance profile of water/AOT/decane ratios.
systems at different water/AOT
Effects of additives on percolation The effects of alkanols (1% w/v in the oil) on the percolation are presented in Fig. 3. The longer the alkyl chain the more is the resistance to percolation, decanol has practically shown no percolation up to 60°C. The increment in the transition offered by butanol, pentanol, hexanol and octanol are 1.5,22,31 and 31 ‘C, respectively. The conductance of the solution prior to the transition threshold has been observed to increase with the alkyl chain length of the alkanols, the sequence follows the order decanol>octanol, hexanol> pentanol> butanol. Cholesterol as an additive had a significant effect on the percolation transition (Fig. 4). Prior to this phenomenon, the conductance has decreased irregularly with increased addition of cholesterol, there is also increased temperature for the transition with increased addition of the sterol.
300
5r
3
b (?i . 0
Fig. 3. Temperature (w/w)
conductance
profile of water/AOT/decane
system (S,)
in the presence of 1%
alcohols.
The addition of 1% (w/v) cholesterol has increased the threshold temperature from 30 to 52’ C. The effect is thus striking. The cholesterol derivatives (acetate, benzoate and stearate) have shown minor effects (Fig. 5) and their activities are more or less similar. At 0.1% (w/v) level the transition temperature has increased by 6.5’ C. Because of solubility problems, concentrations beyond 0.1% stearate could not be used. The crown ether also showed a distinct effect (Fig. 5). The effects of 0.1% and 0.3% ( w / v ) crown ether are very close to 0.1% cholesterol, 1% crown ether has lowered the transition by 4 ’ C. The crown ether has also increased the initial conductance of the microemulsion. The percolation transition temperature, the range of transition and the activation energy for percolation in the presence of different additives are presented in Table 1. The activation energies have been evaluated from the slopes of the linear portions of the plots of log crversus T -'in the temperature range specified (for each system) in the table. Except benzyl alcohol and crown ether at equal w/v% levels, all the additives have increased the threshold temperature and decreased the energy of activation, the effects of higher chain length alkanols are less on the latter, whereas a minimum of activation energy is ob-
301
Fig. 4. Temperature
conductance
profile of water/AOT/decane
system in presence of cholesterol.
served at 0.5% cholesterol. The activation energy has also decreased with increased concentration of crown ether. In Fig. 6, the effects of different additives on the viscosity of the microemulsion at different temperatures are presented. It is observed that there is a viscosity maximum at 40’ C without any additive, which shifts to 50 oC in the presence of 0.1% cholesterol, the maximum tends to be shifted to 60” C in the presence of 0.5% cholesterol, which is yet to be reached in the presence of 1% cholesterol. Almost identical viscosity behaviour has been observed when cholesterol acetate is the additive. Cholesterol benzoate and stearate have yielded the maximum at 40°C at 0.1% level. 1% cholesterol benzoate has shifted it to 5O”C, 0.1% crown ether has yielded the viscosity maximum at 50’ C, 0.3% and 1% crown ether have not shown the maximum, the viscosity increments have been mild (curves not presented), Percolation
and adiabatic compressibility
The adiabatic compressibilities of the microemulsion with 1% cholesterol and without any additive as a function of temperature are presented in Fig. 6.
302
Fig. 5. Temperature conductance profile of water/AOT/decane system (S,) in the presence of cholesteryl esters and crown ether. Curve 1, no additive; curve 2,0.1%, 0.5%, 1% cholesteryl benzoate, 0.1% cholesteryl stearate, 1% cholesteryl acetate; curve 3, 0.1% cholesteryl acetate; curve 4,0.1% crown ether; curve 5,0.3% crown ether; curve 6,0.7%, 1% crown ether.
An effect opposite to viscosity has been observed with a minimum in compressibility at 40 oC. 1% cholesterol has yielded decreasing compressibility with increasing temperature which is also the expected reverse of findings on viscosity. DISCUSSION
The alkanols imparted increased intrinsic conductance to the microemulsion which increased with the increased alkyl chain length. This is an uncommon phenomenon, for alkanols are nonconducting and nonpolar solvents. The conductance of aqueous solution of AOT decreases on addition of an alkanol. The charges on the micro-water droplets undergo fluctuations and it is considered that excess positive or negative charges possessed by the particles give rise to modest conductance to the dispersed system in the oil matrix [3], Addition of alkanols offers softness or flexibility to the interphase [24] with easier charge fluctuations and thereby enhanced conductance. The soft-
303 TABLE 1 Additive effects on the percolation characteristics of microemulsion (sample S,) Additive (wt/v% in oil)
Transition temperature ( ’ C )
Percolation range (“C)
E,
0
30.5 52 47.5 40 37.5 36.5 32 25 52.5 61.5 61.5
30-45 52-60 48-60 40-60 38-50 37-50 32-55 25-45 53-65 62-65 62-65
700 670 470 400 455 510 285 263 580 608 450
32
32-65
612
26.5 36 36
26-50 36-50 36-50
175 335 560
Cholesterol ( 1%) Cholesterol (0.75%) Cholesterol (0.5%) Cholesterol (0.25%) Cholesterol (0.1% ) Butanol ( 1% ) Benzyl alcohol (1% ) Pentanol ( 1% ) Hexanol ( 1% ) Octanol ( 1% ) Cholesteryl acetate (0.5%) 1%) Cholesteryl benzoate (0.5%, l%, 0.1%) Cholesteryl stearate (0.1% ) Crown ether (0.7%, 1%) Crown ether (0.3%) Crown ether (0.1%)
77
06
60
02
06
06
01
(kJ mol-‘)
2U
30
40 tot
50 -
60
01
20
30
40 t-c
50
60
-
Fig. 6. Temperature dependence of viscosity and compressibility of water/AOT/decane system (S,) in the presence of different additives. Curves l-10, no additive, 0.1% cholesterol, 0.5% cholesterol, 1% cholesterol, 1% cholesteryl acetate, 0.1% cholesteryl acetate, 0.1% cholesteryl stearate, 0.1% cholesteryl benzoate, 1% cholesteryl benzoate, 1% cholesterol.
304
ness of the interphase increases with the chain length offering higher conductance to the system. The addition of cholesterol and its esters has, on the other hand, a decreasing effect on the intrinsic conductance of the microemulsion. The sterols produce more compact interphases [ 131 and reduce the effective excess charges on the droplets by restricting the charge fluctuations thereby lowering the conductance. The crown ether can complex Na+ ions and can transport it through the medium, this explains the increased conductance of the microemulsion in its presence. The course of percolation is also less steep because the ion transport by the crown ether follows a special mechanism. The activation energy for the transport is lower (173.3 kJ mol-’ at the 1% level). The temperature induced percolation in w/o microemulsion systems is a striking but established phenomenon. It is expected that the effects of the additives may throw light on the mechanism of the process. The additives employed in the present study all have hindered percolation, except the crown ether and benzyl alcohol which have shown a less sharp phenomenon. The probable mechanisms for percolation transition are the hopping mode and the transient channel forming mode. Both alkanols and cholesterol and its ester derivatives have shifted the transition to higher temperature; the charge transport in the microemulsion has been resisted. For AOT/water/isooctane microemulsion, the transition temperature for conductance has been shown [ 141 to be dependent on the type of alkanol. Short chain alkanols decrease the percolation temperature, whereas longer chain alkanols increase it, the minimum being provided by propanol. Our microemulsion sample has been observed to be unstable in the presence of alkanols lower than butanol, and we could not study their effects. In line with the previous findings, we have observed increased percolation temperature up to decanol (alkanols higher than hexanols were not used in the previous study). Compared to the emulsion stabilizer AOT molecules, the alkanols used are longer in length, whereas the size of cholesterol is smaller. For the hopping phenomenon to operate, the microdroplets with a surfactant coat ought to approach within a reasonable distance; for the formation of a channel, the droplets must stick together upon collision. The polar -OH group of the alkanol adheres to the surface of the micro-water pool and becomes a part of the assembly, the effective size of the inner micro-water droplet decreases with increase of their number. The hopping length between two particles, on the other hand, increases in the presence of higher alkanols; the formation of a channel for ion transport is also not favored. The small sized benzyl alcohol anchors its hydroxyl groups on the polar droplet surface, the portruding aromatic ring offers increased local hydrophobicity, the droplets therefore undergo attractive interaction [ 201 facilitating ion transfer. Lower alkanols may act in a similar way, as has been observed for the water/AOT/ isooctane microemulsion system [ 141. The crown ether complexes Na+ ions and acts as a carrier for the transport of it through the oil, the transition temperature is thus lowered in the presence of a reasonable amount of it. Choles-
305
terol is a small but rigid molecule. In the interphase, like the alkanols, its hydroxyl group remains attached to the surface of the micro-water droplet and the interphase becomes stiffer. Although closer approach of droplets is feasible, effective conductance remains low. The rigidity of the interphase restricts transfer of ions between particles. The esters of cholesterol are less effective; they are equally effective percolation suppressors among themselves. The compounds are more apolar and cannot conveniently approach the water/AOT interface; remaining in the oil medium they act as a barrier [ 201 to percolation. It should be noted that 1% cholesterol in oil contributes 1.6.10zo molecules and taking the whole amount to be present in the interphase the ratio of cholesterol/AOT molecules in the interphase is 0.163. The ratio of the molecules of cholesteryl acetate, benzoate, stearate, benzyl alcohol, crown ether, butanol, pentanol, hexanol, octanol and decanol with AOT in the interphase (assuming 50% of the alkanols being present, because of partition with the oil) are 0.146, 0.127, 0.01, 0.58, 0.168, 0.422, 0.36, 0.306, 0.27 and 0.20, respectively. Except butanol, hexanol and benzyl alcohol, all the other values are too small to indicate specific effects of the additives on the percolation threshold. Lesser number of molecules of longer chain alkanols are effective since the central water pool between two droplets in contact are more separated by the increased interphase offered by the longer alkanols. Using a time-resolved fluorescence method Jada et al. [2,27] have estimated the rate constant for the exchange of materials between two droplets on collision and have shown that for percolation to take place the rate constant must have a threshold value which supports movement of counter-ions through the water channel formed by the sticky collision among the droplets. Irrespective of surfactant chain length, head group or nature of the oil, the percolation thresholds correspond to l-2.10’ mol-’ s-l as the interdroplet exchange rate constant, this has lent support to the channel mechanism which is also our view. Assuming the diameter of a microdroplet to be 100 A, 2, the number of the droplets colliding in 1 ml s-l, can be calculated from the kinetic theory by the formula, Z= [ 2 n a2 un’ ] ‘I2 where a is the diameter of a particle, u is the velocity [u= 0.921 (3RT/M)““] and n is the number of particles in 1 ml, it4being the weight of the Avogardro number of particles. The bimolecular rate constant k = Zq, where q = e -Ea’RT (q is the ratio between the number of activated particles and the total number of particles and E, is the activation energy). Therefore, k=ZecEaIRT. The Z at 303 K has been calculated to be 9.3*10z5 ml-’ s-l. The activation energy for bimolecular reactions usually fall in the range 80-160 kJ mol- ‘. Taking the value of E,= 100 kJ mol-’ [ 201 and the above value of Z= 9.3*1025,the rate constant k=0.7.10g mol-’ dme3 at 303 K. This is the rate constant for a fruitful collision leading to exchange of materials between the droplets for percolation in the absence of additive. This result closely agrees with l-2.10’ mol-’ dm3 s-l reported by Jada et al. [ 2,271. The activation energy for conduction in the region of percolation has been reported [ 131 to be roughly 550-600 kJ mol-‘.
306
We have observed an average value of 700 kJ mol-l without additives and lower values in the presence of additives (Table 1). The conductivity curves indicate that once the process starts, it proceeds very efficiently. The threshold temperature for percolation is like the ‘one-and-none’ law observed in nerve conduction [ 281, where transport of Na+ and K+ ions through specific channels plays a key role; a minimum or threshold stimulation is required for the generation of an impulse. In the present context the thermal energy makes the skin of the microemulsion droplet dilate or soften and assists transport of charge carriers among the clustered droplets. The lowering of activation energy supports easier charge transport through the oil matrix. After the threshold temperature, due to increased thermal energy, the polar alkanol molecules get distributed (dispersed) more into the oil and they make the microenvironment in the oil matrix polar and charge transport becomes convenient, the activation energy is thus lowered. Longer alkanols are less polar and the reduction in the activation energy is less. It is to be noted that the effects of hexanol and octanol are not in order; compared to the lower concentrations, the decreasing effects of 0.75 and 1% cholesterol are also not orderly. The activation energy for conduction of H+ ions in an aqueous medium is distinctly lower (10 kJ mol-‘) than ether ions ( - 15 kJ mol-‘) [29]. The proton jump way of conduction of H+ ions therefore crosses a lower energy barrier. Before and after the percolation range, the activation energies for conduction of the microemulsion system without additive are 5 and 50 kJ mol-’ respectively; these roughly fall in the range of activation energies for ions, the system thus shows a normal mode of conduction. A value of 700 kJ mol-l in the percolation state advocates a significant energy barrier, a hopping mode of conduction is not consistent with it, the transient channel formation by sticky collision is more likely to be the mode. Direct and unambiguous evidence is, however, wanted for a conclusive decision in this regard. Viscosity
The viscosity-temperature profiles of the microemulsion in the presence of different additives are presented in Fig. 6. A viscosity maximum is observed in the absence of additive; at lower concentrations of the additives, the maximum shifts towards higher temperature, which disappears at higher additive concentrations. Borkovec et al. [l] have also reported similar viscosity phenomenon of AOT stabilized w/o microemulsion without additives. The clustering of the microdroplets with increase of temperature may end up with an increased viscosity [ 11.The first stage of the viscosity-temperature profile resembles percolation. It should be noted that simultaneous increase in viscosity and conductance is contrary to normal findings (conductance is inversely proportional to viscosity); this is possible in microemulsions, because clustering assists efficient ion transport and percolation. The decreased viscosity in the
307
second stage can be reasoned through the change of the overall shape of the clusters from nonspheres towards spheres at higher temperature. Monte Carlo simulations has shown [ 181 that the globules form network-like structures if the attractive interaction is negligible, and compact separated cluster-like arrangements if the attractive interaction is strong. A transition between two types of structures may decrease the effective viscosity without affecting the ion-transport mechanism for which formation of clusters and transfer of ions are the key factors. The additives help to keep the overall structure of the clusters more towards spheres, so that the viscosity is comparatively small and with increasing concentration it decreases further and temperature has only a mild effect on it. The non-linear course of log q versus T -'plot has advocated progressive change in the activation energy for viscous flow. The formation of clusters and changes of cluster shape with temperature contribute primarily to the magnitude of viscosity, the overall process is complex. The adiabatic compressibility coroborates the viscosity data. In the absence of additive, the compressibility passes through a minimum at 40’ C, whereas in 1% cholesterol the compressibility decreases progressively with temperature, the system becomes less and less compressible; an internal structure or organized state is in progress through which transfer of ions is favoured by a special mechanism resulting in effective percolation of conductance. ACKNOWLEDGEMENT
This work has been financially supported by the department of Science and Technology, Government of India.
REFERENCES M. Borkovec, H.F. Eicke, H. Hammerich and B. Das Gupta, J. Phys Chem., 92 (1988) 206. A. Jada, J. Lang and R. Zana, J. Phys. Chem., 93 (1989) 10. H.F. Eicke, M. Borkovec and B. Das Gupta, J. Phys. Chem., 93 (1989) 314. M. Lagues, J. Phys. Lett., 40 (1979) 331. G.S. Grest, I. Webman, S.A. Safran and A.L.R. Bug, Phys. Rev. A, 33 (1986) 2842. S. Bhattacharya, J.P. Stokes and M.W. Kim, Phys. Rev. Lett., 55 (1985) 1884. H.F. Eicke, R. Hilfiker and H. Thomas, Chem. Phys. Lett., 55 (1985) 1884. A.L.R. Bug and Y. Gefen, Phys. Rev. A, 35 (1987) 1301. J. Peyrelasse, M. Moha-Ouchane and C. Boned, Phys. Rev. A, 38 (1988) 4155. S.R. Bisal, P.K. Bhattacharya and S.P. Moulik, J. Phys. Chem., 94 (1990) 350. 11 H.F. Eicke, S. Geiger, R. Hilfiker, F.A. Sauer and H. Thomas, in R. Pynn andT. Riste (Eds), Time Dependent Effects in Disordered Materials, Plenum, New York, 1987, p. 219. 12 S. Geiger, H.F. Eicke and D. Spielmann, Z. Phys. B, Condensed Matter, 68 (1987) 175. 13 C. Mathew, P.K. Patanjali, A. Nabi and A.N. Maitra, Colloids Surfaces, 30 (1988) 253. 14 H.F. Eicke, R. Kubik, R. Hasse and I. Zschokki, in K.L. Mittal and B. Lindman (Eds), Surfactants in Solution, Plenum, New York, 1984, p. 1533. 2 3 4 5 6 7 8 9 10
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
A.M. Cazabat, D. Chatenay, P. Guering, D. Langevin, J. Meunier and 0. Sorba, in K.L. Mittal and B. Lindman (Eds), Surfactants in Solution, Plenum, New York, 1984, p. 1737. A.M. Cazabat, D. Langevin, J. Meunier and A. Poncelon, J. Phys. Lett., 43 (1982) 89. M.W. Kim and J.S. Huang, Phys. Rev. A, 34 (1986) 719. S.A. Safran, G.S. Grest and A.L.R. Bug in H.L. Rosano and M. Clausse (Eds), Microemulsion Systems, Marcel Dekker, New York, 1987, p. 235. J.S. Huang, S.A. Safran, M.W. Kim, G.S. Grest, M. Kottarchyk and N. Quirke, Phys. Rev. Lett., 53 (1984) 593. E. Dutkiewicz and B.H. Robinson, J. Electroanal. Chem., 251 (1988) 11. S.S. Atik and J.K. Thomas, J. Am. Chem. Sot., 85 (1981) 3921. P.D.I. Fletcher, A.M. Howe and B.H. Robinson, J. Chem. Sot. Faraday Trans. 1,83 (1988) 985. R. Hilfiker, H.F. Eicke, S. Geiger and G. Furler, J. Colloid Interface Sci., 105 (1985) 378. S. Bhattacharya, J.P. Stokes, M.W. Kim and J.S. Huang, Phys. Rev. Lett., 55 (1985) 84. S.R. Bisal, P.K. Bhattacharya and S.P. Moulik, J. Surf. Sci. Technol., 4 (1988) 121. P.K. Dasgupta and S.P. Moulik, J. Phys. Chem., 91 (1987) 5826. A. Jada, J. Lang and R. Zana, J. Phys. Chem., 94 (1990) 381. M.V. Volkenstein, MIR Moscow, 1983, p. 381. S. Glasstone, An Introduction to Electrochemistry, Van Nostrand, New York, 1965, pp. 6162.