J. Phys. Chem. B 2001, 105, 7145-7154
7145
Physicochemical Studies on Microemulsions. 7. Dynamics of Percolation and Energetics of Clustering in Water/AOT/Isooctane and Water/AOT/Decane w/o Microemulsions in Presence of Hydrotopes (Sodium Salicylate, r-Naphthol, β-Naphthol, Resorcinol, Catechol, Hydroquinone, Pyrogallol and Urea) and Bile Salt (Sodium Cholate) S. K. Hait and S. P. Moulik*,† Centre for Surface Science, Department of Chemistry, JadaVpur UniVersity, Calcutta-700 032, India
M. P. Rodgers, S. E. Burke, and R. Palepu*,‡ Department of Chemistry, St. Francis XaVier UniVersity, Antigonish, NoVa Scotia, Canada, B2G 2W5 ReceiVed: February 8, 2001
The temperature induced percolation of w/o microemulsions (water/AOT/isooctane and water/AOT/decane) has been studied at different [water]/[AOT] mole ratios (ω), and in the presence of hydrotopes (sodium salicylate, R-naphthol, β-naphthol, resorcinol, catechol, hydroquinone, pyrogallol, urea) and the bile salt sodium cholate. The results have been analyzed to quantify the threshold percolation temperature, performance of the Scaling equation, the activation energy for the percolation process, and the thermodynamics of the clustering of the dispersed nanodroplets. The influence of temperature and additives on the droplet dimension, the polydispersity, and the diffusion coefficient has been also investigated by the DLS studies. An attempt has been made to correlate the results with the differential activities of the hydrotopes. A possible mechanism of the varied activities of the hydrotopes is proposed.
Introduction The percolation of conductance in w/o microemulsion can be induced by a change in either the volume fraction of water (φ) or the temperature (θ).1-3 Investigations on the nature and the basic understanding of the percolation process have been the concern of a number of researchers.4-11 It is generally believed that during the percolation process dispersed water droplets cluster/associate and ions either “hop”12-17 from droplet to droplet or are transferred by way of “transient fusion and mass exchange”.18-25 As a consequence of the ion transfer, the conductance (σ) can be enhanced by 100- to 1000-fold, yielding a sigmoidal σ-φ or σ-θ profile. The point of maximum gradient of the profile corresponds to the transition of the percolation process and is designated as the threshold volume fraction (φt) or the threshold temperature (θt), characteristic features of the percolating system. The composition of the system and other environmental conditions such as the pressure and the presence of additives control the threshold values.26-31 In recent years, Scaling equations have been used to analyze percolating w/o microemulsion systems. The energy of activation of the physiochemical process has been worked out. The thermodynamics of clustering, which is the fundamental basis of the process, have been also evaluated. It is known that the introduction of additives into the system can significantly affect the process20,32-38 of percolation by altering the threshold values φt and θt, and the nature of the sigmoidal ln σ - φ and ln σ θ profiles. In this context, the effects of sodium salicylate, various aromatic solutes, as well as the bile salts sodium cholate and sodium deoxycholate, are particularly noteworthy.20-22,34,35 Sodium salicylate and aromatic solutes normally delay the
percolation (i.e., both φt and θt increase) while the bile salts cause a decrease in both φt and θt and promote the process. The influence of these additives has been explained on the basis of blocking effect and the easier channel formation; however, the quantification of these properties is yet to be done.17,32-34 The blocking effect of aromatic compounds, viz., naphthalene, benzene, anthracene, salicylic acid (and its sodium salt), involves a diminution of the adherence and subsequent fusion of dispersed water droplets, that is the basic requirement of conductance percolation. On the other hand, bile salts (sodium cholate and sodium deoxycholate) contain steroid ring and hydroxyl groups, which enable them to form channels between two adjacent droplets by adhering to their surfaces (the water/ oil interface). Hence, the extent to which the substituent of hydroxyl groups on the aromatic ring can influence the phenomenon of percolation is of great importance and has led us to study the effects of the hydrotopes R-naphthol, β-naphthol, catechol, resorcinol, pyrogallol, hydroquinone, sodium salicylate, and urea on the percolation of conductance of water/sodium bis(2-ethylhexyl) sulfosuccinate/isooctane (W/AOT/i-oc) and water/sodium bis(2-ethylhexyl) sulfosuccinate/decane (W/AOT/ dc) systems. The bile salt sodium cholate has been also used so that comparison can be made between its activity and that of the above hydrotopes. The determination of the percolation threshold, the performance of Scaling equation, the evaluation of the activation energy for percolation, the energetics of clustering,33,36,40-42 and the dimension, polydispersity, and diffusion coefficient of the said w/o microemulsion systems have been examined and discussed along with rational analysis of the results.43-54 Materials and Methods
* To whom correspondence should be addressed. † Fax: 91-33-473-4266. E-mail:
[email protected] ‡ E-mail:
[email protected] Materials. The AOT (sodium bis(2-ethylhexyl) sulfosuccinate, 99% pure), sodium cholate (NaC), and sodium salicylate
10.1021/jp0105084 CCC: $20.00 © 2001 American Chemical Society Published on Web 06/28/2001
7146 J. Phys. Chem. B, Vol. 105, No. 29, 2001 (NaS) of AR grade were purchased from Sigma, U.S.A. Catechol (Cc), resorcinol (Rc), hydroquionone (Hq), pyrogallol (Py), R-naphthol (R-Np), β-naphthol (β-Np), and urea (U) of AR grade were purchased from Aldrich, U.S.A. Isooctane (ioc) and decane (dc) (AR grade) were purchased from E-Merck, Germany. They were all used as received. Triply distilled water, of specific conductance 2-4 µS cm-1 at 303 K, was used to prepare all solutions. Methods. Conductance Measurements. Conductance measurements (with (0.5% accuracy) were taken at a frequency of 1 kHz using a Jenway (England) conductometer in a temperature compensated dip-type cell of cell constant 0.92 cm-1 placed in a Neslab RTE-100 temperature-controlled bath of accuracy (0.1 °C. Microemulsions were prepared at different (ω) [water]/[AOT] compositions for both the W/AOT/i-oc and W/AOT/dc systems, and the conductance was measured as a function of temperature for each ω. For the W/AOT/dc system, conductance measurements were also made at a constant ω ) 25 with varied [AOT]. In presence of additives, temperature-dependent conductances of the first and the second systems were measured at ω ) 22.5 and ω ) 25, respectively. The thermodynamic parameters of clustering were also evaluated at ω ) 22.5 for the isooctane based system and at ω ) 25 for the decane counterpart in the presence and absence of additives at a constant [AOT]. Each of them was diluted several times with oil to vary droplet concentration, and percolation measurements were taken after each dilution. Dynamic Light-Scattering Measurements. Dynamic light scattering (DLS) measurements were performed using a DLS700 instrument from Otsuka Electronics Co. Ltd., Japan, fitted with a 5 mW He-Ne laser, operating at 632.8 nm, by placing the sample tube in the thermostated chamber of the goniometer. All measurements were taken at 90° angle. Each sample was filtered several times through a Millipore 0.22 µ membrane filter prior to taking measurement. The DLS intensity data were processed using the instrumental software to obtain the hydrodynamic diameter (dh), the polydispersity index (PDI), and the diffusion coefficient (D) of the samples. DLS measurements were taken at temperatures before and after the percolation threshold for the decane-based system at a fixed ω and constant [AOT]. The same procedure was followed for the additive Pg at 30 mM. DLS measurements were also performed on the W/AOT/dc system at a constant temperature 303 K and constant [AOT] with varying ω.
Hait et al.
Figure 1. Conductometric evaluation of θt by SBE fitting for water/ AOT/isooctane system at different ω. Differential plot is shown in the inset.
Figure 2. Conductometric evaluation of θt by SBE fitting for water/ AOT/decane system at different ω.
Results and Discussion Percolation Courses and Threshold Temperature, θt. The percolation courses of w/o microemulsions W/AOT/i-oc and W/AOT/dc at different [H2O]/[AOT] mole ratios, ω, are illustrated in Figures 1 and 2. It is observed that for both systems the phenomenon is enhanced with increasing ω, i.e., the sigmoidal curves shift toward lower temperature. For a constant composition, the nature of the microemulsion is considered to remain unchanged in the percolating range of temperature. Beyond the percolation range, there may be an overall change due to much enhanced droplet association leading to stable conduit formation. Similar curves for the two studied microemulsion systems in the presence of additives are exhibited in Figures 3 and 4. The influence of the additives on the percolation phenomenon can be appreciable. The determination of the threshold percolation temperature, θt, is usually done from the differential plot (d ln σ/dT) that shows a peak in the plot55 corresponding to θt. Very recently,
Figure 3. Conductometric evaluation of θt by SBE fitting for water/ AOT/isooctane system at fixed ω ) 22.5 for different additives at fixed concentration (27.9 mM).
Hait et al.56 have proposed to use the Sigmoidal-Boltzmann equation (SBE) for the determination of the threshold characteristics φt and θt in dealing with conductance percolation, as well as in the determination of critical micellar concentration (cmc) from microcalorimetric measurements of the enthalpy of
Physicochemical Studies on Microemulsions. Part 7
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7147 TABLE 2: Comparison of Percolation Threshold for Temperature Induced Percolation of Water/AOT/Decane Microemulsion Systems with Varying Concentration of [AOT] at Fixed ω ) 25
Figure 4. Conductometric evaluation of θt by SBE fitting for water/ AOT/decane system at fixed ω ) 25 for different additives at fixed concentration (10 mM).
TABLE 1: Comparison of Percolation Threshold for Temperature Induced Percolation of Water/AOT/Isooctane and Water/AOT/Decane Microemulsion Systems with Varying ω ω
θt K
ln σi
ln σf
ln P
n
corr. Ep kJ coeff. mol-1
15 20 22.5 30 40
A: Water/AOT/Isooctane; [AOT] ) 0.415 mol dm-3 316.3 -1.1926 6.1853 1.75 ( 0.18 1.53 ( 0.09 0.9965 315.3 -1.4155 6.9700 2.75 ( 0.07 1.49 ( 0.04 0.9978 312.0 -1.4097 6.6432 2.85 ( 0.10 1.49 ( 0.06 0.9965 308.8 -1.2260 6.5389 3.78 ( 0.10 1.33 ( 0.06 0.9945 303.7 -2.2010 7.6031 4.43 ( 0.06 1.29 ( 0.02 0.9975
235 235 350 336 344
20 25 30 35
B: Water/AOT/Decane; [AOT] ) 0.260 mol dm-3 307.8 2.3108 5.3963 4.27 ( 0.08 0.53 ( 0.07 0.9919 303.0 2.4927 5.5337 4.29 ( 0.05 0.71 ( 0.04 0.9944 300.0 2.2108 5.9909 4.71 ( 0.05 0.73 ( 0.04 0.9948 297.0 2.4560 6.4205 5.09 ( 0.06 0.76 ( 0.05 0.9942
159 220 225 298
dilution of surfactant systems. The average values of the initial and final conductance and the corresponding enthalpies of dilution can be also determined. The SBE57 is given below.
y)
yi - yr [1 + exp(x - x0)/dx]
+ yr
(1)
where y is a measured property of the system that depends on x; yi and yr are the left and right asymptotes of y; x0 is the center (where y takes on the average of yi and yr); dx is the constant that controls the rise or decay profile for yi to yr (for large dx the rise is gradual but steep for small dx). Also at (x0 + dx) and (x0 - dx), the function assumes a value that is 26% of the way from the closest asymptote. The function y in eq 1 is the cumulative probability distribution. In conductance percolation, the equivalent SBE equation has the form
log σ )
log σi - log σf [1 + exp(θ - θt)/dθ]
+ log σf
(2)
where σ and θ represent conductance and temperature, respectively, and the i, f, and t subscripts stand for initial, final, and percolation stages, respectively. In Table 1, the θt and initial (σi) and final (σf) conductances of the two studied w/o microemulsion systems with variable ω are presented. At a fixed [AOT], θt depends on ω; larger droplets
[AOT] M
θt K
ln P
n
corr. coeff.
Ep kJ mol-1
0.4082 0.3773 0.3509 0.3279 0.3077 0.2628 0.2414 0.2233 0.1942 0.1823
296.2 297.5 298.4 299.0 300.6 303.0 305.0 306.9 308.7 309.3
6.04 ( 0.07 5.99 ( 0.09 5.72 ( 0.10 4.97 ( 0.07 5.80 ( 0.07 4.29 ( 0.05 3.66 ( 0.07 3.92 ( 0.06 3.70 ( 0.07 3.70 ( 0.07
0.96 ( 0.11 0.95 ( 0.07 1.15 ( 0.13 1.47 ( 0.08 0.88 ( 0.07 0.71 ( 0.04 0.99 ( 0.04 0.89 ( 0.04 0.89 ( 0.04 0.82 ( 0.05
0.9923 0.9881 0.9865 0.9963 0.9928 0.9944 0.9971 0.9988 0.9979 0.9954
580 555 559 626 435 220 179 185 173 239
adhere and fuse at lower temperature for easier transfer of the conducting ions. The dependence of θt on [AOT] at a fixed ω ) 25 for the W/AOT/dc system is shown in Table 2. With increasing [AOT], θt decreases linearly; increasing [AOT] requires a higher [water] in order to maintain a fixed value of ω, and this leads to an increase in the droplet density for easier association and ion transport. The effects of additives on θt for the studied two w/o microemulsion systems are presented in Tables 3 and 4. It is seen that the additives NaS, R-Np, and β-Np have increased θt; the other additives Rc, Cc, Hq, Pg, U, and NaC have decreased θt. At equal concentration, additives NaS, R-Np, and β-Np increase θt more or less to the same extent for both W/AOT/ i-oc and W/AOT/dc systems. The decrease in θt in the presence of Rc, Cc, Pg, Hq, NaC, and U at equal additive concentration of 16.9 m mol dm-3 are 7, 0.3, 8, 9.4, 11, and 1°, respectively, for the first system; the decrease is 4, 0.4, 4.7, 7.2, and 12°, respectively, for the second system at 10 mmol dm-3 of the additive concentration. (Note that U is not a part of this comparison because no comparable concentration was available.) It is seen that the hydrotopes with one hydroxyl group as in NaS, R-Np and β-Np retard percolation (θt increases) by the blocking effect, whereas those having more than one hydroxyl group as in Rc, Cc, Pg, and Hq accelerate the process (θt decreases). In the latter group, 1,2 or ortho substitution (as in Cc) has a very mild effect; 1,3 or meta substitution is more effective for promoting percolation; and the substitution at 1,4 or para position is even more effective. Pg, having substitution at the 1,2,3 position, is less effective than Hq. With reference to the stabilization of droplets by the interfacially adsorbed bile salts (NaC and NaDc), it is likely that stabilization of a pair of droplets is easier with hydroxyl substituted in the para position. The efficiency order of hydrotopes in reducing θt is U < Cc < Rc < Pg < Hq. U is considered to lessen the interfacial rigidity by its property of reducing the amphiphile association, resulting in easier fusion of droplets at lower temperature, i.e., at lower θt. A possible mechanism of the activities of the rest of the hydrotopes is exemplified in Figure 5. The mechanism in favor of NaC is also presented therein for a comparison. The fusion of a pair of droplets in temperature-induced percolation at a constant ω depends on their mutual contact, which is caused by thermal energy manifested as θt. The presence of additive can assist such contact/linkage, enhancing easier fusion; it may also resist the process. The schemes 1-3 in Figure 5 depict the fusion process without and with additives (NaC and NaS). The hydrotopes Hq, Pg, and Rc with hydroxyl substitution in the 1,4-, 1,2,3-, and 1,3- positions, respectively, can enhance contact between droplets, hence lowering θt (scheme 4, Figure 5), resulting in fusion and mass transfer with a consequence of lowering of θt . Among these, the bridging by Hq is straightforward, whereas that of Pg and Rc are to some
7148 J. Phys. Chem. B, Vol. 105, No. 29, 2001
Hait et al.
TABLE 3: Comparison of Percolation Threshold, Scaling Law Parameters, and Energy of Activation for Temperature Induced Percolation of Water/AOT/Isooctane Microemulsion Systems with Varying Concentration of Additive at [AOT] ) 0.415 mol dm-3 and ω ) 22.5 additivea
[additive] mM
θt K
ln P
n
corr. coeff.
Ep kJ mol-1
10.8 18.2 26.6 9.9 19.4 27.9 16.9 27.9 40.4 50 1.69 8.46 16.9 27.9 33.8 4.2 8.45 16.9 33.8 10.2 18.2 27.9 33.8 1.7 4.3 8.5 16.9 27.9 33.8 1.89 4.22 8.45 10 16.9 10 18 27.9
316 316.7 319.6 315.4 317.5 319.6 311.1 309.5 307.4 307.0 312.2 310.1 305.2 302.8 300.4 311.1 308.2 302.6 294.0 309.2 304.0 303.0 300.8 313.3 311.0 311.3 311.7 311.7 311.0 310.5 306.9 302.1 295.7 291.0 316.0 317.8 318.8
3.92 ( 0.09 3.51 ( 0.03 3.96 ( 0.1 3.79 ( 0.08 5.49 ( 0.03 3.63 ( 0.06 3.06 ( 0.05 2.16 ( 0.04 2.77 ( 0.02 2.43 ( 0.06 2.79 ( 0.02 2.37 ( 0.02 2.29 ( 0.10 2.76 ( 0.09 2.62 ( 0.06 2.79 ( 0.08 2.71 ( 0.11 2.43 ( 0.06 3.24 ( 0.07 3.48 ( 0.04 3.46 ( 0.07 3.52 ( 0.07 3.22 ( 0.04 2.68 ( 0.12 2.63 ( 0.03 2.92 ( 0.07 1.64 ( 0.23 2.57 ( 0.05 2.40 ( 0.02 3.45 ( 0.06 3.49 ( 0.05 3.76 ( 0.06 3.79 ( 0.06 3.09 ( 0.03 3.67 ( 0.05 3.38 ( 0.03 3.53 ( 0.04
1.28 ( 0.06 1.59 ( 0.02 1.38 ( 0.06 1.54 ( 0.06 0.61 ( 0.03 1.56 ( 0.03 1.55 ( 0.03 1.74 ( 0.02 1.66 ( 0.01 1.54 ( 0.04 1.62 ( 0.01 1.70 ( 0.01 1.34 ( 0.05 1.48 ( 0.05 1.60 ( 0.02 1.53 ( 0.05 1.57 ( 0.05 1.64 ( 0.03 1.65 ( 0.05 1.52 ( 0.02 1.51 ( 0.03 1.58 ( 0.04 1.66 ( 0.02 1.58 ( 0.07 1.77 ( 0.02 1.61 ( 0.04 2.04 ( 0.13 1.64 ( 0.02 1.72 ( 0.01 1.65 ( 0.03 1.68 ( 0.03 1.55 ( 0.04 1.48 ( 0.03 1.79 ( 0.01 1.49 ( 0.03 1.42 ( 0.02 1.32 ( 0.02
0.9970 0.9998 0.9968 0.9986 0.9977 0.9995 0.9992 0.9997 0.9998 0.9983 0.9999 0.9999 0.9946 0.9962 0.9991 0.9988 0.9977 0.9993 0.9988 0.9997 0.9985 0.9987 0.9997 0.9979 0.9999 0.9989 0.9959 0.9997 0.9999 0.9993 0.9996 0.9991 0.9989 0.9999 0.9995 0.9998 0.9996
325 401 327 324 259 327 386 267 323 469 265 344 264 327 284 314 324 254 305 343 337 330 352 271 231 275 365 308 337 343 423 347 236 333 341 305 330
R-naphthol β-naphthol urea
resorcinol
hydroquinone
pyrogallol
catechol
Na cholate
Na salicylate
a
θt at 0 additive ) 312 K.
extent staggered. The droplets must approach each other more closely; as a result of this staggered bridging, the energy requirements for ion transfer are higher for the Pg and Rc systems compared to that of Hq. The establishment of interdroplet contact by Pg is more efficient than Rc, which has its hydroxyl groups in the 1,3- positions. Such a contact by Cc (having ortho substitution) is very weakly efficient. The value of θt, therefore, follows the order Hq < Pg < Rc < Cc. It is also concluded from the results that the R-Np, β-Np, and NaS increase θt. This results because fusion and hence ion transfer are made more difficult in these particular cases. This is explained in scheme 5 of Figure 5. The θt-[hydrotope] profiles are found to be fairly linear; the slopes are indicative of the efficiency of the hydrotopes (Figure 6). Performance of Scaling Equation. The temperature-related conductance in the percolation range obeys the following Scaling equation
σ ) P(θ - θt)n
(3)
where σ is the specific conductance and corresponds to the temperature θ, and P and n are appropriate constants. The value of n has been shown to be 1.9 for static percolation, but the constant is not predictable.31,32 The logarithmic form of the equation was used for the evaluation of P and n.
ln σ ) ln P + n ln(θ - θt)
(4)
The high efficiency with which eq 4 fits the conducting data as a function of temperature for both microemulsion systems, with varying ω, is illustrated in Figure 7. The Scaling equation
displays similar efficiency in describing the systems containing the additives. The results are presented in Tables 3 and 4, which show that the n values are less than the predicted value of 1.9, except in the case of 16 mM Cc in W/AOT/i-oc where it is 2.04. Values of n lower than 1.9 have been also reported for W/AOT/hp w/o microemulsion system4 with and without additive. The ln P values have also varied in a wide range as reported earlier. In the presence of additives, the dc-containing system has shown relatively lower n values compared to the i-oc-containing system. Between i-oc and dc, n is lower for the latter. It means that the rate of increase of σ with temperature is lower when dc is the continuous medium. The longer hydrocarbon chain of the dc resists droplet association more than does the shorter chain of i-oc. This gets support from higher Ep at comparable [AOT] for the microemulsion system with dc than with i-oc presented in the next section and Tables 1 and 2. The deviation of n from the predicted value of 1.9 lies in the difference between the static and dynamic percolation. In the first, which is a mixture of conductors and insulators, conductance of the system remains virtually zero below θt. In the dynamic percolating system, as in w/o microemulsions, the microwater droplets are always in motion. The system conducts below θt because the droplets randomly rearrange and can approach each other, thus contributing to the system conductance. Near the threshold state, the droplets associate/cluster, forming interconnections through which ions get transferred or transported, leading to an increase in conductance. The motion of counterions both before and after the threshold state has been reported from self-diffusion measurements from NMR as well as conductivity studies. It has been shown4 that surfactant ion transfer by a “hopping” mechanism provides only a minor
Physicochemical Studies on Microemulsions. Part 7
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7149
TABLE 4: Comparison of Percolation Threshold, Scaling Law Parameters, and Energy of Activation for Temperature Induced Percolation of Water/AOT/Decane Microemulsion Systems with Varying Concentration of Additive at ω ) 25 additive R-naphthola β-naphthola ureaa
resorcinola
resorcinolb
hydroquinoneb
pyrogallolb
catecholb
Na cholateb Na salicylateb a
[additive] mM
θt K
ln P
n
corr. coeff.
Ep kJ mol-1
8.8 17.6 26.5 8.8 17.6 26.5 18.06 23.78 34.05 43.87 54.00 8.81 13.21 18.02 25.02 5 10 15 20 30 10 15 20 30 5 10 15 20 30 5 10 20 30 55 5 10 5 10
306.2 311 314.8 306.6 310.4 314.7 299.4 297.7 296.2 293.6 289.8 297.5 294.8 291.8 288.3 293.0 292.3 289.6 287.9 284.6 289.3 286.9 285.0 280.1 292.6 291.5 290.2 288.7 284.8 294.5 295.6 296.3 294.5 294 289.7 283.9 298.3 300.0
3.74 ( 0.04 4.00 ( 0.03 3.81 ( 0.08 4.30 ( 0.08 3.90 ( 0.03 4.01 ( 0.08 6.36 ( 0.01 4.20 ( 0.04 4.54 ( 0.08 4.00 ( 0.06 3.24 ( 0.04 4.30 ( 0.08 4.40 ( 0.08 4.27 ( 0.07 3.94 ( 0.05 5.39 ( 0.07 5.03 ( 0.05 5.94 ( 0.04 6.08 ( 0.02 6.15 ( 0.06 5.16 ( 0.04 5.34 ( 0.04 6.03 ( 0.07 6.24 ( 0.03 5.22 ( 0.04 5.74 ( 0.03 6.01 ( 0.07 6.37 ( 0.04 5.45 ( 0.04 4.81 ( 0.02 6.08 ( 0.06 6.33 ( 0.07 5.75 ( 0.05 6.45 ( 0.08 5.67 ( 0.04 5.99 ( 0.04 6.20 ( 0.03 6.17 ( 0.03
0.96 ( 0.02 0.85 ( 0.02 0.98 ( 0.04 0.78 ( 0.06 0.92 ( 0.01 0.91 ( 0.05 0.70 ( 0.02 0.90 ( 0.03 0.79 ( 0.06 0.92 ( 0.04 1.23 ( 0.02 0.79 ( 0.07 0.78 ( 0.06 0.84 ( 0.05 0.95 ( 0.02 1.57 ( 0.03 1.54 ( 0.04 1.29 ( 0.07 1.18 ( 0.03 1.22 ( 0.02 1.51 ( 0.02 1.45 ( 0.05 1.15 ( 0.03 1.00 ( 0.03 1.66 ( 0.03 1.47 ( 0.04 1.27 ( 0.07 1.04 ( 0.02 1.54 ( 0.04 1.67 ( 0.04 1.07 ( 0.08 0.96 ( 0.11 1.33 ( 0.06 0.66 ( 0.01 1.23 ( 0.07 1.09 ( 0.07 0.90 ( 0.06 0.94 ( 0.04
0.9995 0.9995 0.9967 0.9950 0.9995 0.9984 0.9999 0.9983 0.9972 0.9958 0.9991 0.9963 0.9945 0.9969 0.9990 0.9946 0.9957 0.9975 0.9963 0.9949 0.9942 0.9911 0.9939 0.9648 0.9947 0.9995 0.9983 0.9945 0.9931 0.9972 0.9913 0.9982 0.9987 0.9817 0.9954 0.9949 0.9978 0.9963
106 123 139 175 118 168 220 217 183 177 181 196 174 183 105 630 568 637 583 480 629 567 519 520 721 648 614 559 578 901 751 476 595 507 628 627 491 499
[AOT] ) 0.263 mol dm-3; θt at 0 additive ) 303 K. b [AOT] ) 0.408 mol dm-3; θt at 0 additive ) 296.2 K.
contribution to the conductance in the latter stages of percolation. The nature of oil and the additives can influence the droplet clustering and ion transference during dynamic percolation, and thus affect the value of both P and n. As in the case of θt, there is no observable trend in the value of n in relation to the nature of the additives under investigation. Activation Energy of Percolation. The activation energy of conductance percolation (Ep) has been determined using an Arrhenius-type equation.
σ ) Ae-Ep/RT
(5)
where A is a constant and R and T have their usual significance. The Ep value has been obtained from the slope (-Ep/R) of the ln σ vs T-1 plot (Figure 8, Tables 3 and 4). A number of attempts have been made to determine Ep for various microemulsion systems.4,21,34 In general, the stronger the percolating system, the larger is the value of Ep. It has been also reported that systems may not follow specific trends with respect to ω, and some even pass through a maximum. In this study we have observed that Ep increases with ω for the W/AOT/i-oc system. It has been also found that at a constant ω ) 25, Ep increases with [AOT] (Table 2) for the W/AOT/dc system. These facts suggest that fission of the fused droplets (scheme shown in Figure 5) is the rate-determining step for the percolation. With increasing ω, droplet size increases and fusion is favored, leading to a decrease in θt. Fission of bulky droplets into a pair of droplets associated with transfer/transport of counterion (Na+ ion) has a high activation energy. At a constant ω, increasing [AOT] produces increased droplet density that enhances the probability of refusion of the separated droplets that occur via
fission. Consequently, establishment of an activated state for mass transfer by effective fission ends up with higher energy. An increase in the activation energy with ω for interdroplet mass transfer has been recently reported by Mays58 from time-resolved luminescence quenching (TRLQ) measurements. In this study there is no correlation between Ep and the additives employed. At a fixed ω, the Ep values do not show an orderly trend (Table 3 and Table 4); the W/AOT/i-oc system has produced lower Ep values compared to the W/AOT/dc system. This means that the dynamic process of conductance percolation is different from normal conductance and the activation energy is expected to be higher. For the W/AOT/i-oc system, the Ep values in the presence of hydrotopes are slightly lower, and the values do not differ to a great extent. For the W/AOT/dc system, the Ep values in the presence of R-Np, β-Np, Rc, and U are lower than without additives; for the rest of the additives Cc, Hq, Pg, NaC, and NaS, the Ep values are significantly higher. Hence, the activation energy for percolation is oil specific. In this respect, the former system is more uniform. How the percolation assisting additives (Pg, Hq, and NaC) and the resisting additive NaS both yield high Ep values in the W/AOT/dc system is intriguing. In addition to clustering, fusion, mass transfer, and fission, there may be other steric and interacting factors for the process of percolation. Higher Ep values in the presence of NaC and NaS compared to their absence have been reported for the W/AOT/hp w/o microemulsion system.4 Energetics of Droplet Clustering. The clustering of droplets is the essential feature for conductance percolation. The process depends on the type of microemulsion, the droplet density and size (i.e., ω), presence of additives, etc. It is reported that the
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Figure 5. Proposed scheme for “fusion-mass transfer-fission” in the presence of different additives.
clustered droplets on the whole retain their identity, and the assembly exists in a different phase (a pseudophase-like micelles).21,41,43 At the threshold temperature, the standard Gibbs free energy change for the clustering phenomenon (∆G°cl) is given by the relation
∆G°cl ) RT ln Xd
(6)
where Xd is the mole fraction of droplets. The Xd value can be obtained from the following relation:
Xd )
nd AtMVt ) nd + noil (MA V + 4000πr2NVd) t t d
(7)
where nd and noil are number of moles of droplet and oil, respectively; At is the total surface area covered by the AOT headgroup; and Vt is the total volume of the system. The terms V, d, and M are the volume, density, and molar mass of oil, respectively; rd is the average radius of the droplet, and N is the Avogadro number. The Gibbs-Helmholtz equation can be used to obtain the standard enthalpy change for clustering.
d
( ) ∆G°cl T 1 d T
()
) ∆H°cl
(8)
The standard entropy change for clustering then follows from
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J. Phys. Chem. B, Vol. 105, No. 29, 2001 7151
Figure 6. Variation of θt with additive concentration for isooctane and decane.
Figure 7. Variation of n with ω for water/AOT/isooctane and water/ AOT/ decane system.
the Gibbs equation,
∆S°cl )
∆H°cl - ∆G°cl T
(9)
To derive ∆H°cl, a microemulsion prepared at a fixed ω (22.5 and 25 for W/AOT/i-oc and W/AOT/dc systems, respectively) was diluted with several portions of oil and the θt values for all the diluted samples were determined from conductance measurements. The ∆G°cl values were obtained from the sample compositions, and the analysis of the plots of ∆G°cl/θt as a function of 1/θt yielded the values of ∆H°cl. As shown in Figure 9, the plots display a linear behavior within the studied range of concentration. The thermodynamic parameters for the clustering process are presented in Tables 5 and 6. The process is endothermic with positive entropy change. Prior to droplet association, the surrounding oil barrier must be removed. This endothermic event is followed by the exothermic clustering; energetically, the first exceeds the second, making the overall effect endothermic. At comparable [AOT], the process is more endothermic for the W/AOT/dc than for W/AOT/i-oc. This is because the removal of dc (having longer chain length) requires more heat than for the shorter hydrocarbon i-oc. In the case of i-oc, the energy
Figure 8. Conductrometric evaluation of Ep for water/AOT/isooctane and water/AOT/decane system at fixed ω for different additive concentration.
change is either smaller or slightly greater in the presence of hydrotopes. The energy change is quite endothermic in the presence of NaC. On the other hand, for the dc-based microemulsion, the energy change for the clustering process is quite endothermic in the presence of hydrotopes, except for Cc. It is reasonable that the additives can affect the enthalpies of both the oil removal and droplet association phenomena. On the whole, the enthalpy difference in the presence and absence of additives is within (5 units for both systems. The extents of additive influence on the clustering process are thus comparable. Explanation for the influence of the different additives on the enthalpy of the clustering process is kept pending until more systematic data are at hand. The endothermicity of the clustering process with and without additives has been reported in the literature.4,35,41 Despite a number of reports of significant ∆H°cl in the literature, Mays58 has recently treated it to be insignificant in the calculation of ∆S°cl. Thus, the reported activation entropy of droplet association is underestimated. The ∆H°cl herein reported and reported by others are based on an equilibrium concept similar to the formation of micelles from amphiphile aggregation. It is different from the enthalpy or entropy of binding of one droplet to another as proposed by Mays.58 The comparison of the enthalpy of droplet binding obtained by the time-resolved fluorescence (TRF) method with the enthalpy of clustering obtained by the conductometric method does not have a convincing justification. The ∆S°cl presented in Tables 5 and 6 show comparable magnitudes with and without additives for both of the microemulsion systems investigated. As in the case of ∆H°cl, the ∆S°cl for the W/AOT/dc system at constant [AOT] is greater than that of the W/AOT/i-oc system. The disruption of the oil prior to droplet association is greater for dc than for i-oc. This compares to the disruption of hydrophobic hydration of a nonpolar segment of an amphiphile prior to micellization. The influence of the additives on the value of ∆S°cl parallels that observed for ∆H°cl as discussed above. The near equivalence in the magnitude of ∆G°cl results in the compensation between ∆H°cl and ∆S°cl, which is illustrated in Figure 10A and B. The compensation temperatures obtained for the i-oc and dc systems are 285 and 306 K, respectively. A comparable enthalpy-entropy compensation has been obtained for W/AOT/hp microemulsion system in the absence and presence of the additives NaC and NaS.4,41
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Figure 9. Evaluation of energetics of clustering for water/AOT/decane system at fixed ω for different AOT and additive concentrations.
TABLE 5: Energetic Parameters for Droplet Clustering in the Water/AOT/Isooctane w/o Microemulsion Systems in the Presence and Absence of Additives at ω ) 22.5a additive R-naphthol β-naphthol urea resorcinol hydroquinone pyrogallol catechol Na cholate Na salicylate a
[additive] mM (θt /K)
-∆G°cl kJ mol-1
∆H°cl kJ mol-1
∆S°cl JK-1 mol-1
0 (312.0) 28 (312.9) 28 (319.4) 27.9 (309.3) 50 (306.0) 27.9 (300.3) 27.9 (296.3) 27.9 (302.5) 27.9 (311.3) 10 (295.7) 27.8 (318.5)
21.1 21.2 21.6 21.0 20.8 20.4 20.1 20.5 21.1 20.0 21.6
16.4 ( 0.93 18.7 ( 0.94 11.2 ( 0.71 15.1 ( 0.95 18.7 ( 0.93 53.5 ( 1.15 13.3 ( 0.71 10.6 ( 0.69 13.1 ( 0.82 21.5 ( 1.10 9.1 ( 0.59
120 ( 14 128 ( 3 103 ( 3 117 ( 5 129 ( 5 246 ( 6 113 ( 6 101 ( 6 110 ( 6 141 ( 7 96 ( 2
[AOT] ) 0.415 mol dm-3.
TABLE 6: Energetic Parameters for Droplet Clustering in the Water/AOT/Decane w/o Microemulsion Systems in the Presence and Absence of Additives at ω ) 25 additive
[additive] mM (θt/K)
0 (303.0) 0 (296.2) R-naphthol 18 (310.8) β-naphthol 16.3 (309.4) urea 18.06 (299.4) resorcinol 18.06 (291.8) 20 (287.9) hydroquinone 20 (285.0) pyrogallol 20 (288.7) catechol 20 (296.3) Na cholate 10 (283.9) Na salicylate 10 (300.0)
[AOT] -∆G°cl M kJ mol-1 0.2628 0.4082 0.2628 0.2382 0.2628 0.2628 0.4082 0.4082 0.4082 0.4082 0.4082 0.4082
22.5 20.5 23.1 23.4 22.2 21.7 19.9 19.7 20.0 20.5 19.6 20.7
∆H°cl kJ mol-1
∆S°cl JK-1 mol-1
10.3 ( 0.73 21.8 ( 2.19 7.9 ( 0.92 11.8 ( 2.1 13.2 ( 1.52 14.3 ( 0.91 27.0 ( 0.94 17.4 ( 2.28 23.3 ( 2.65 53.9 ( 1.78 23.1 ( 1.63 22.0 ( 3.71
108 ( 2 143 ( 7 100 ( 3 114 ( 7 118 ( 5 123 ( 3 163 ( 3 130 ( 8 150 ( 9 251 ( 6 150 ( 6 143 ( 10
Dimension, Polydispersity, and Diffusion Coefficient of the Nanoparticles. The dimension (dh), polydispersity index (PDI), and the diffusion coefficient (D) of the dispersed microemulsion droplets in W/AOT/dc system at ω ) 25 have been determined
by the DLS method by varying ω and temperature and in the presence of an additive. Such measurements on the W/AOT/ioc system were inconsistent: meaningful results could not be derived, so they are not presented. The values of the measured parameters are presented in Table 7. We have observed that the results are virtually independent of the type of hydrotope employed. The results tabulated for Pg, therefore, represent the general behavior of the studied hydrotopes. It is found that dh increases with ω, resulting in a consequent decrease in D (Table 7A) because they are interrelated by the Stokes-Einstein equation
D)
kT 3πηdh
(10)
where the terms k, η, and T represent the Boltzmann constant, viscosity coefficient of the continuous medium (dc), and the absolute temperature, respectively. The microemulsion solution was fairly dilute with respect to the droplet concentration, and hence the use of eq 10 is valid. An increase in dh with ω for W/AOT/hp system has been reported in a separate study.4 The results presented in Table 7B show that a variation in temperature of 9° does not have great effect on the measured parameters. Also, the additive Pg has shown little influence on these parameters. Comparable results obtained for other hydrotopes are not shown, to save space. The polydispersity index of the nanodispersions is an important parameter that was obtained from DLS measurements. The ratio SE/dh, where SE is the standard error in dh, is called the polydispersity index (PDI).59 A PDI value of 0.1 means monodispersity; higher values mean polydispersity. The PDI values herein presented (Table 7A and 7B) are predominantly in the 0.2-0.4 range, indicating fairly polydispersed systems. Water/oil microemulsions having fair polydispersity have been reported earlier.4 The temperatures
Physicochemical Studies on Microemulsions. Part 7
J. Phys. Chem. B, Vol. 105, No. 29, 2001 7153 of their unaltered individual identity before and after the percolation threshold. Reasonably higher temperature can produce significant increase in dh by way of droplet coalescence.4 Mays58 has also reported nonvariant droplet structure for percolating AOT derived microemulsion systems. Conclusions 1. The conductance percolation of the studied w/o microemulsion systems is favored with increasing ω, where, from the threshold percolation temperature, θt can be obtained using the Sigmoidal-Boltzmann equation. 2. The hydrotopes NaS, R-Np, β-Np, Rc, Cc, Hq, Pg, and U and the bile salt NaC can influence the percolation process. Hq, Pg, U, Rc, and NaC assist the process, whereas NaS, R-Np, and β-Np retard it, which results by way of (1) bridging and efficient fusion and (2) blocking and resisting fusion of droplets toward counterion exchange, respectively. 3. The Ep for the percolation process has been found to be oil specific. It does not show a possible correlation with the studied hydrotopes. 4. The clustering of the microemulsion droplets is an endothermic process with associated positive entropy change parallel to the micellization of the surfactants. The ∆H°cl and ∆S°cl nicely compensate each other. 5. The dispersed droplets retain their physical characteristics, dh, PDI, and D. The hydrotopes and NaC also do not affect these parameters in the pre and post percolation states. The nanodroplets are fairly polydisperse.
Figure 10. Compensation plot in the presence and absence of additives for (A) water/AOT/isooctane system and (B) water/AOT/decane system.
TABLE 7: Hydrodynamic Diameter (dh), Polydispersity Index (PDI), and Diffusion Coefficient (D) of Water/AOT/ Decane w/o Microemulsion Systems at Different Conditions A: [AOT] ) 0.38 mol
Total Volume ) 13.157 mL; T ) 303 K
dm-3;
ω
dh/nm
PDI
diffusion coeff. cm2 s-1 × 106
20 25 30 35
2.5 2.6 17.1 26.1
0.212 0.220 0.296 0.642
1.87 1.79 0.280 0.183
B: [AOT] ) 0.38 mol dm-3; ω ) 25 additive no additivea
pyrogallol (30 mmol dm-3)
T/K 289.6 291.8 294.2 298.2 283.8 286.7 289.6 293.2
a
dh/nm 2.5 3.3 3.6 1.5 3.4 2.6 4.1 2.2 Ave 2.9 ( 0.8
PDI
diffusion coeff. cm2 s-1 × 106
0.383 0.367 0.356 0.325 0.408
1.39 1.37 1.29 3.42 0.823
0.383 0.424 0.326
1.36 1.03 2.09
θt ) 296.2. b θt ) 284.8.
of measurements in this study were slightly below and above θt. The measured droplet dimensions are found to be virtually independent of temperature, which supports the maintenance
Acknowledgment. S.K.H. thanks the University Grants Commission, Government of India for a Junior Research Fellowship to perform this work. R.P. acknowledges the Natural Sciences and Engineering Council of Canada for support in the form of an operating grant. We thank Mr. A. Gayen and Mr. L. Digout for their help in the experimental work. The help from Dr. J. Beck, Department of Chemistry, St. Francis Xavier University, Antigonish, Canada, in the preparation of the manuscript is acknowledged with appreciation. References and Notes (1) (1)Microemulsions; Robb, I. D., Ed.; Plenum Press: New York, 1982. (2) Bothorel, P. Microemulsions, Cour. CNRS 1982, 48, 39. (3) Paul, B. K.; Moulik, S. P. J. Dispersion Sci. Technol. 1997, 18, 301. (4) Moulik, S. P.; De, G. C.; Bhowmik, B. B.; Panda, A. K. J. Phys. Chem. B 1999, 103, 7122. (5) Moulik, S. P.; Pal, B. K. AdV. Colloid Interface Sci. 1998, 78, 99. (6) Kunieda, H.; Asaoka, H.; Shinoda, K. J. Phys. Chem. 1988, 92, 185. (7) (7)Microemulsions: Theory and Practice; Prince, L. M., Ed.; Academic Press: New York, 1977. (8) Eicke, H. F.; Brokovic, M.; Dasgupta, B. J. Phys. Chem. 1989, 93, 314. (9) Jada, A.; Lang, J.; Zana, R.; Makhlouffu, R.; Hirsch, E.; Candau, S. O. J. Phys. Chem. 1994, 94, 387. (10) Moha-Ouchane, M.; Peyrelasse, J.; Boned, C. Phys. ReV. A 1987, 35, 3027. (11) Safran, S. A.; Webman, I.; Grest, G. S. Phys. ReV. A 1985, 32, 506. (12) Bug, A. L. R.; Safran, S. A.; Grest, G. S.; Webman, I. Phys. ReV. Lett. 1985, 55, 1896. (13) Safran, S. A.; Grest, G. S.; Bug, A. L. R. In Microemulsion Systems; Rosano, H. L., Clausse, M., Eds.; Marcel Dekker: New York, 1987; p 235. (14) Lagues, M.; Santerey, C. J. Phys. Chem. 1980, 84, 3503. (15) Hilfilker, R.; Eicke, H. F.; Geiger, S.; Furlur, G. J. Colloid Interface Sci. 1985, 105, 378. (16) Grest, G. S.; Webman, I.; Safran, S. A.; Bug, A. L. R. Phys. ReV. A 1986, 33, 2842. (17) Peyrelasse, J.; Moha-Ouchane, M.; Boned, C. Phys. ReV. A 1988, 38, 904.
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