Langmuir 2002, 18, 2471-2476
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Articles Refined Method of Assessment of Parameters of Micellization of Surfactants and Percolation of W/O Microemulsions S. K. Hait,† S. P. Moulik,*,† and R. Palepu‡ Centre for Surface Science, Department of Chemistry, Jadavpur University, Calcutta-700 032, India, and Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, B2G 2W5 Received July 13, 2001. In Final Form: December 6, 2001 The course of the differential heats of dilution of a surfactant measured in an isothermal titration microcalorimeter is normally of sigmoidal type. The course of percolation of conductance of a water in oil microemulsion induced by either temperature or the water content of the system is also of sigmoidal nature. Derivation of the critical micellar concentration and the enthalpy of micellization (∆Hm) in the former has been demonstrated to be conveniently obtained by employing the Sigmoidal-Boltzmann equation (SBE). The SBE has been shown also to be conveniently applicable for accurate determination of the threshold temperature (θp) and volume fraction (φp) of percolation in the latter.
Introduction Microcalorimetric determination of critical micellar concentration (cmc) following the differential enthalpy of dilution of a concentrated surfactant solution and evaluation of the threshold of percolation of conductance of water in oil (w/o) microemulsions are two important physicochemical aspects of self-organizing systems. The plots of the enthalpy of dilution versus [surfactant] and log(conductance) versus temperature or volume fraction of water are normally sigmoidal in nature whose differential forms yield maxima (or minima) that correspond to the cmc and the percolation threshold, respectively.1-15 The enthalpy change for micellization and the net conductance * To whom correspondence should be addressed. Fax: 91-33473-4266. E-mail:
[email protected]. † Jadavpur University. ‡ St. Francis Xavier University. (1) Analytical Solutions Calorimetry; Grime, J. K., Ed.; Wiley: New York, 1985; Chapter 6. (2) Bijma, J. K.; Engberts, J. B. F. N.; Haandrikman, G.; van Os, N. M.; Blandamer, M. J.; Butt, M. D.; Cullis, P. M. Langmuir 1994, 10, 2578. (3) Blandamer, M. J.; Cullis, P. M.; Engberts, J. B. F. N. Pure Appl. Chem. 1996, 68, 1577. (4) Paula, S.; Siis, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 93, 11742. (5) Majhi, P. R.; Moulik, S. P. Langmuir 1998, 14, 3986. (6) Majhi, P. R.; Moulik, S. P. J. Phys. Chem. B 1999, 103, 5977. (7) Johnson, I.; Olofsson, G.; Jonsson, B. J. Chem. Soc., Faraday Trans. 1 1987, 83, 3331. (8) Huang, J. S.; Kotlarchyk, M. Phys. Rev. Lett. 1986, 57, 2587. (9) Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1990, 94, 381. (10) Maitra, A.; Mathew, C.; Varshney, M. J. Phys. Chem. 1990, 94, 5290. (11) Mukhopadhyay, L.; Bhattacharya, P. K.; Moulik, S. P. Colloids Surf. 1990, 50, 295. (12) Bisal, S.; Bhattacharya, P. K.; Moulik, S. P. J. Phys. Chem. 1990, 94, 350. (13) Ray, S.; Bisal, S. R.; Moulik, S. P. J. Chem. Soc., Faraday Trans. 1993, 89, 3277. (14) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. J. Phys. Chem. 1995, 99, 8222 and references therein. (15) Moulik, S. P.; De, G. C.; Bhowmik, B. B.; Panda, A. K. J. Phys. Chem. B 1999, 103, 7122 and references therein.
change during percolation can be estimated from the difference between the initial and final states of the aforesaid sigmoidal plots. The illustrations in Figure 1 depict the above situations for ideal conditions. As demonstrated in the figure, the cmc and the enthalpy of micellization, ∆Hm, as well as the threshold of percolation temperature, θp, and the volume fraction of percolation, φp, can be estimated without ambiguity. In practice, this is hardly achieved and evaluation of the parameters cmc, ∆Hm, θp, and φp needs careful processing of the graphical presentations associated with experimental errors for which minimization can be attempted by increasing the experimental data points. The procedure for such evaluation has been put forward in the literature as cited above. In the evaluation of ∆Hm, the final height of the enthalpy of dilution of the micellar solution and the initial height (pertaining to micellar dilution, demicellization, and counterion dissociation (for ionic surfactant)) are considered whose difference becomes the estimate of ∆Hm. In most situations, the judgment on the point of beginning of the micellar dilution may not be straightforward. The ionic dissociation of the micelles may also influence the differential enthalpy of dilution in the postmicellar state causing continuous change in the dilution course. Bach et al.16 have proposed a procedure for handling such nonideal situations considering the experimental results of several cationic surfactants. In this procedure, information on the aggregation number, counterion binding, ion-ion interaction, enthalpy of micellization, and so forth of the self-organizing systems is required which is only very limitedly known in varied environmental conditions. Kresheck17 has used an equation for sigmoidal variation in the differential enthalpy of dilution of micellar solution but without going into details of its general performance. (16) Bach, J.; Blandamer, M. J.; Burgess, J.; Cullis, P. M.; Soldi, L. G.; Bijma, K.; Engberts, J. B. F. N.; Kooreman, P. A.; Kacperska, A.; Rao, K. C.; Subha, M. C. S. J. Chem. Soc., Faraday Trans. 1995, 91, 1229. (17) Kresheck, G. C. J. Phys. Chem. B 1998, 102, 6596.
10.1021/la0110794 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/09/2002
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a transition at x0 with the change in independent variable x. The term in the third bracket in eq 2 is the modulating factor. A cooperative process (be it micellization or percolation) showing sigmoidal dependence of its property on an independent variable (concentration or temperature) can be accurately analyzed for the transition point as well as the magnitudes of the asymptotes in terms of SBE by way of statistical fitting procedures. Although the evaluation of the transition point can be done from a differential plot, the exact values of the asymptotes are to be obtained from visual judgment. In the SBE method, the arbitrariness of the latter is removed. Hence, it is a better method for evaluation. The non-SBE curve fitting procedure cannot yield the required information. In the case of differential heat of dilution (∆Hd) of micellar solution, the SBE eq 2 takes the form
[ (
∆Hd ) ∆Hd(f) 1 +
)
∆Hd(i) - ∆Hd(f) ∆Hd(f)
×
]
{1 + exp(Cs - Ccmc)/∆Cs}-1 (3) Figure 1. The microcalorimetric determination of the cmc and ∆Hm (A) and conductometric determination of the threshold of percolation (B) in ideal conditions.
In this presentation, we shall discuss the origin of this equation and demonstrate its performance on a large number of micellar and w/o microemulsion systems for the evaluation of cmc and ∆Hm in the former and θp and φp in the latter. This procedure has been preliminarily adopted by us only on temperature-induced percolation of a w/o microemulsion system.18 Its usefulness in the micelle-forming and volume-induced percolating microemulsion systems has been left out. A generalization of the procedure and a pragmatic treatment for characterizing both micellar and microemulsion systems are herein presented. The Equations The Sigmoidal-Boltzmannn equation (SBE) has the following form:
y)
yi - yr [1 + exp(x - x0)/∆x]
[ ( )
log σ )
[ (
log σf 1 +
)
]
log σi - log σf {1 + exp(θ - θp)/∆θ}-1 (4) log σf
where σ and θ represent conductance and temperature, respectively; ∆θ is the constant interval of θ; and the i, f, and p stand for initial, final, and percolation stages, respectively. For volume-induced percolation, the form of eq 4 is
[ (
log σ ) log σf 1 +
)
log σi - log σf × log σf
]
{1 + exp(φ - φp)/∆φ}-1 (5) + yr
(1)
or
y ) yr 1 +
where Cs is the concentration of the surfactant in the system, Ccmc is its concentration at cmc, ∆CS is the constant interval of CS, and i and f are initial and final stages, respectively. In conductance percolation, the equivalent equation can be written as
]
yi - y r {1 + exp(x - x0)/∆x}-1 yr
(2)
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), and ∆x is the constant interval of the independent variable that controls the rise or decay profile from yi to yr (for large ∆x rise is gradual while for small ∆x rise is sharp). The function y in eq 1 is the cumulative probability distribution.19 The equation thus essentially deals with the changeover of a variable from an initial unaffected state of yi to also an unaffected final state of yr through (18) Hait, S. K.; Moulik, S. P.; Rodgers, M. P.; Burke, S. E.; Palepu, R. J. Phys. Chem. B 2001, 105 (29), 7145. (19) Fundamentals of Statistical and Thermal Physics; Reif, F., Ed.; McGraw-Hill: Singapore, 1985.
where φ and φp are the volume fraction of water in the solution and at the state of percolation threshold, and ∆φ is the constant interval of φ. Equations 3-5 are advantageous in the sense that the sigmoidal data points when fitted to them yield the initial and final values of physical properties (herein ∆Hm and log σ) and the transition points (herein cmc, θp and φp). The difference between values of the final and initial physical property gives the extent of its change during the process under study which is otherwise usually estimated visually from the levels of the initial and final trends in the related courses, a method that requires judgment and experience, and obviously is seldom free from associated uncertainties. We shall subsequently see with examples the results obtained using the SBE and the differential plot as well as the visual estimation for the evaluation of cmc and ∆Hm on one hand and θp and φp on the other. Representative examples of systems showing good as well as average types of sigmoidal variation will be illustrated, and results obtained by the conventional procedure and the Sigmoidal-Boltzmann equations on a good number of systems will be presented
Parameters of Micellization of Surfactants
Figure 2. Microcalorimetric determination of ∆Hm and cmc by the SBE fitting for AOT at 328 K. The differential plot is shown in the inset.
Figure 3. Microcalorimetric determination of ∆Hm and cmc by the SBE fitting for SDS at 318 K. The differential plot is shown in the inset.
and discussed. In an earlier publication, the SBE has been only limitedly used18 on temperature percolation of a w/o microemulsion system. Micellization of Surfactants The experimental results of differential heats of dilution of surfactants Na-bis(2 ethylhexyl)-sulfosuccinate (AOT), sodium dodecyl sulfate (SDS), cetyl pyridinium chloride (CPC), and Triton X 100 at 303 K are exemplified in Figures 2-5. The differential plots are shown in the inset of each figure. The cmc and ∆Hm are directly obtained with their errors from the Sigmoidal-Boltzmann fit. The trend of the heat change in the cmc region determines the overall shape and hence the ∆Hm. The data acquisition in close intervals preferably in the cmc region is, therefore, required for pinpointing the cmc and the associated enthalpy change for micellization. The results obtained on several surfactants in an aqueous medium are presented in Table 1. The reported cmc values obtained by the differential method applied on the data points fairly agree with those obtained by the SBE. The SBE values are on the whole to some extent higher. Of course, a serious difference of results obtained by the differential and the integral methods of evaluation is not observed. The discrepancy between the reported differential method and
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Figure 4. Microcalorimetric determination of ∆Hm and cmc by the SBE fitting for CPC at 323 K. The differential plot is shown in the inset.
Figure 5. Microcalorimetric determination of ∆Hm and cmc by the SBE fitting for TX-100 at 298 K. The differential plot is shown in the inset.
the SBE is more for SDS. The differential heats of dilution of SDS at 298 K and CPC at 293 K with the [surfactant] are both very low so that the evaluation of cmc and ∆Hm in these two cases by the visual method is not without ambiguity. Very low values of ∆Hm have been estimated by the method of interpolation for SDS and CPC at 298 and 293 K, respectively.20 The enthalpy values by the SBE method (Table 1) are found to be to some extent higher than that obtained by the visual method. The SBE results obtained from the differences between the levels of the two asymptotes in the sigmoidal fitting are less ambiguous since they are not contaminated with uncertainties in the visual judgment, which is critical particularly when the experimental points do not run parallel to the concentration axis. Mathematical evaluation of the asymptotes by the SBE is, therefore, recommended. It is also worthy to examine the correlations between the visually obtained and the SBE-derived cmc as well as the ∆Hm. This is illustrated in Figure 6. The correlation between the cmc’s obtained by the SBE and the differential method (Figure 6A) is fairly good. Such a correlation for the ∆Hm (Figure (20) A value of ∆Hm ) 0.35 kJ mol-1 has been obtained by the method of interpolation of the results given in ref 4. At 293 K, ∆Hm ) 0.53 kJ mol-1 has been obtained by us.
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Table 1. Results on Micellization of Surfactants Treated by the SBE and the Differential Method ∆Hm/kJ mol-1 cmc/mM diff
AOT
2.746 2.594 2.680 2.800 2.934 2.933 3.102 3.043 8.375 8.028
2.927 ( 0.010 10.42 11.48 ( 0.09 2.709 ( 0.013 7.36 8.21 ( 0.08 2.603 ( 0.016 3.12 3.69 ( 0.04 2.474 ( 0.053 1.49 1.76 ( 0.11 3.373 ( 0.057 -2.58 -2.56 ( 0.11 3.339 ( 0.032 -4.06 -4.97 ( 0.12 3.289 ( 0.022 -6.49 -7.54 ( 0.12 3.179 ( 0.018 -12.04 -12.76 ( 0.17 8.221 ( 0.056 5.16 5.701 ( 0.09 7.441 ( 0.190 2.43 2.69 ( 0.11
8.013 7.904 8.410 8.487 1.028
8.657 ( 0.134 -3.50 -3.45 ( 0.12 8.625 ( 0.095 -6.88 -7.34 ( 0.22 8.722 ( 0.071 -9.56 -10.02 ( 0.20 8.883 ( 0.067 -12.33 -12.75 ( 0.23 0.987 ( 0.011 3.65 4.48 ( 0.11
SDS
CPC
Triton X 100
CTABa DTABa TTABa a
288 293 298 303 308 313 318 328 288 293 298 303 308 313 318 288 293 298 303 308 313 318 323 288 293 298 303 308 313 303 303 303
SBE
visual ∆Hd(f) - ∆Hd(i) method (SBE)
surfactant temp/K
1.017 1.166 ( 0.017 1.099 1.252 ( 0.015 1.189 1.182 ( 0.011 1.152 1.207 ( 0.008 1.198 1.236 ( 0.007 1.261 1.320 ( 0.007 0.436 0.436 ( 0.002 0.333 0.367 ( 0.004 0.314 0.342 ( 0.004 0.302 0.329 ( 0.007 0.295 0.358 ( 0.008 0.277 0.261 ( 0.007 1.027 1.028 ( 0.004 16.132 16.670 ( 0.198 3.957 4.026 ( 0.020
-4.46 -7.80 -10.40 -14.38 -17.94 -20.62 12.90 10.65 8.93 6.04 3.64 2.40 -14.73 -4.90 -8.76
Figure 7. Conductometric evaluation of θp by SBE fitting for the water/AOT/isooctane system at ω ) 20. The differential plot is shown in the inset.
-5.23 ( 0.14 -8.46 ( 0.21 -11.16 ( 0.24 -12.35 ( 0.24 -19.34 ( 0.27 -22.79 ( 0.24 13.54 ( 0.16 11.09 ( 0.19 9.39 ( 0.17 6.41 ( 0.18 3.87 ( 0.13 2.84 ( 0.08 -14.39 ( 0.17 -4.97 ( 0.16 -8.90 ( 0.13
Taken from ref 5.
Figure 8. Conductometric evaluation of θp by SBE fitting for the water/AOT/decane system at ω ) 25. The differential plot is shown in the inset.
Figure 6. (A) Correlation between cmc(SBE) and cmc(Diff) obtained from microcalorimetry. (B) Correlation between ∆Hm(SBE) and ∆Hm(Visual) obtained from microcalorimetry.
6B) is better. Procedurally, the SBE method is straightforward, unambiguous, more accurate, and convenient. The errors in the evaluated cmc and ∆Hm can be also directly obtained from the SBE fit of the collected data (Table 1). Percolation of W/O Microemulsions It is known that log σ versus temperature or volume fraction of water plots for a percolating w/o microemulsion produces a sigmoidal course; the threshold point for the
Figure 9. Conductometric evaluation of φp by SBE fitting for the water/AOT/heptane system at 322 K. The differential plot is shown in the inset.
process is ascertained from the differential plot of the data points showing a maximum. Here also, the SBE can be conveniently used to get θp and φp. The effective conductance change during the process can be obtained from the difference between the σf and σi of eq 4. Representative plots of log σ versus temperature and log σ versus φ are presented in Figures 7-10 with Sigmoidal-Boltzmann
Parameters of Micellization of Surfactants
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Figure 10. Conductometric evaluation of φp by SBE fitting for the water/AOT/heptane system at 322 K with 0.1 M aqueous NaC. The differential plot is shown in the inset.
fitting curves. Figures 7 and 8 represent temperature percolation, while Figures 9 and 10 represent volume percolation. The threshold values of θp and φp obtained
from the differential plots are shown in the respective insets. The fittings are found to be excellent. The σi, σf, and θp or φp values obtained for a good number of systems are presented in Tables 2-4 with their associated errors. The ∆log σ values are measures of the conductance enhancement following percolation. A first-hand knowledge about the efficacy of the percolation process can be obtained from this parameter. It is observed that ∆log σ for a percolating system normally increases with ω if other parameters remain invariable. This does not hold in the presence of additives. The type of the additive has a say on the percolating behavior as well as on the rise in σ, that is, on ∆log σ. A detailed analysis and explanation for the effects of additives on the process of percolation can be found in recent publications from our laboratory.15,18 Depending on the nature of the additives, the mechanism of the percolation process, that is, of “fusion-mass transfer-fission”, is either assisted or resisted which is reflected in the magnitude of the percolation threshold. Like micellization of surfactants, the SBE can also conveniently and unambiguously characterize the percolating w/o microemulsion systems.
Table 2. Results on Temperature-Induced Percolation Treated by the SBE and the Differential Method θp ωa
a
[AOT]/M
15 20 22.5 30 40
0.5 0.5 0.5 0.5 0.5
20 25 30 35 20 25 30 35
0.2691 0.2628 0.2566 0.2508 0.4082 0.4082 0.4082 0.4082
log σi
SBE
diff
-1.207 ( 0.043 -1.416 ( 0.067 -1.409 ( 0.073 -1.222 ( 0.183 -1.872 ( 0.386
(A) Water/AOT/Isooctane System 6.194 ( 0.096 7.401 ( 0.061 6.968 ( 0.085 8.384 ( 0.095 6.637 ( 0.157 8.046 ( 0.103 6.538 ( 0.088 7.760 ( 0.259 7.607 ( 0.193 9.479 ( 0.546
log σf
316.30 ( 0.16 315.29 ( 0.17 311.99 ( 0.19 308.83 ( 0.12 303.74 ( 0.29
316.65 314.42 311.49 308.57 303.08
2.386 ( 0.223 2.487 ( 0.127 2.229 ( 0.327 2.596 ( 0.141 2.237 ( 0.027 2.352 ( 0.030 2.149 ( 0.028 2.295 ( 0.029
(B) Water/AOT/Decane System 5.288 ( 0.168 2.902 ( 0.315 5.484 ( 0.119 2.997 ( 0.180 5.939 ( 0.156 3.71 ( 0.462 5.993 ( 0.118 3.397 ( 0.199 7.598 ( 0.138 5.361 ( 0.038 7.671 ( 0.164 5.319 ( 0.042 8.234 ( 0.084 6.085 ( 0.040 7.832 ( 0.163 5.537 ( 0.041
307.67 ( 0.32 303.54 ( 0.17 300.13 ( 0.27 296.97 ( 0.13 299.30 ( 0.13 297.44 ( 0.11 295.35 ( 0.05 293.05 ( 0.08
307.80 303.00 300.00 297.00 298.70 296.34 294.98 292.86
∆log σ
ω ) [AOT]/[water]. Table 3. Results on Temperature-Induced Percolation in the Presence of Additives Treated by the SBE and the Differential Method θp additive
[additive]/(mM)
log σi
log σf
SBE
diff
(A) Water/AOT/Isooctane System at ω ) -0.081 ( 0.056 7.514 ( 0.068 7.596 ( 0.079 0.014 ( 0.066 7.470 ( 0.059 7.456 ( 0.093 -1.584 ( 0.093 6.462 ( 0.099 8.046 ( 0.132 -1.393 ( 0.0.68 6.875 ( 0.085 8.268 ( 0.096 -3.396 ( 0.082 6.506 ( 0.143 9.902 ( 0.116 -1.041 ( 0.197 7.563 ( 0.115 8.605 ( 0.279 -1.679 ( 0.126 6.295 ( 0.093 7.975 ( 0.178 -4.487 ( 0.074 7.604 ( 0.204 12.091 ( 0.107 -0.192 ( 0.076 6.930 ( 0.056 7.122 ( 0.091
319.64 ( 0.07 319.70 ( 0.07 310.23 ( 0.15 311.99 ( 0.12 295.99 ( 0.56 303.32 ( 0.19 302.94 ( 0.12 290.05 ( 0.05 318.49 ( 0.09
319.55 319.64 309.52 311.60 296.40 302.78 302.28 289.89 318.61
(B) Water/AOT/Decane System at ω ) 25b 1.656 ( 0.23 5.909 ( 0.124 4.252 ( 0.325 1.981 ( 0.143 5.840 ( 0.151 3.858 ( 0.202 2.089 ( 0.089 7.196 ( 0.147 5.107 ( 0.126 2.209 ( 0.125 7.638 ( 0.056 5.429 ( 0.177 2.258 ( 0.036 7.522 ( 0.091 5.264 ( 0.051 1.950 ( 0.053 7.689 ( 0.155 5.739 ( 0.075 1.844 ( 0.024 7.529 ( 0.068 5.685 ( 0.034 2.269 ( 0.09 7.392 ( 0.103 5.123 ( 0.127 2.384 ( 0.032 7.850 ( 0.124 5.466 ( 0.045
307.14 ( 0.34 306.63 ( 0.28 298.56 ( 0.09 295.66 ( 0.06 290.09 ( 0.05 291.63 ( 0.07 293.00 ( 0.04 284.00 ( 0.04 299.90 ( 0.08
306.20 306.60 299.40 295.60 289.31 291.47 292.26 283.93 300.02
∆log σ 22.5a
R-naphthol β-naphthol urea catechol hydroquinone pyrogallol resorcinol sodium cholate sodium salicylate
27.9 27.9 27.9 27.9 27.9 27.9 27.9 16.9 27.9
R-naphthol β-naphthol urea catechol hydroquinone pyrogallol resorcinol sodium cholate sodium salicylate
10 10 18 10 10 10 10 10 10
a [Additive] ) 27.9 mM except for sodium cholate which is 16.9 mM; [AOT] ) 0.5 M. b [Additive] ) 10 mM except for urea which is 18 mM; [AOT] ) 0.2628 M for R-naphthol, β-naphthol, and urea and 0.4082 M for catechol, hydroquinone, pyrogallol, resorcinol, sodium cholate, and sodium salicylate.
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Table 4. Results on Volume-Induced Percolation Treated by the SBE and the Differential Methoda φp system 1.5 g AOT + 8 mL n-heptane
1.5 g AOT + 8 mL n-heptane + 0.1 M aqueous NaC
1.5 g AOT + 8 mL n-decane
a
temp/K
log σi
log σf
∆log σ
SBE
diff
303 308 313 318 322 303 308 313 318 322 304 308 313 318
2.007 ( 0.126 2.360 ( 0.058 2.574 ( 0.114 2.496 ( 0.065 2.288 ( 0.056 2.102 ( 0.035 2.415 ( 0.043 2.380 ( 0.012 2.246 ( 0.098 2.199 ( 0.025 2.343 ( 0.055 1.495 ( 0.057 1.591 ( 0.044 1.633 ( 0.023
6.411 ( 0.099 7.067 ( 0.124 7.254 ( 0.009 7.497 ( 0.172 7.941 ( 0.059 7.489 ( 0.025 7.562 ( 0.035 7.386 ( 0.058 7.937 ( 0.064 7.535 ( 0.066 7.967 ( 0.034 8.163 ( 0.025 8.081 ( 0.011 7.751 ( 0.007
4.404 ( 0.160 4.707 ( 0.137 4.680 ( 0.114 5.000 ( 0.184 5.653 ( 0.081 5.386 ( 0.043 5.147 ( 0.055 5.006 ( 0.059 5.691 ( 0.117 5.336 ( 0.071 5.625 ( 0.065 6.668 ( 0.062 6.490 ( 0.045 6.118 ( 0.024
0.343 ( 0.001 0.325 ( 0.003 0.311 ( 0.008 0.282 ( 0.002 0.266 ( 0.001 0.251 ( 0.005 0.241 ( 0.003 0.230 ( 0.004 0.226 ( 0.001 2.134 ( 0.001 0.244 ( 0.001 0.215 ( 0.002 0.203 ( 0.002 0.195 ( 0.001
0.3423 0.3288 0.3088 0.2775 0.2607 0.2504 0.2326 0.2239 0.2134 0.2064 0.2463 0.2105 0.2004 0.1926
Deduced from the report in ref 15.
Conclusions The SBE is a better proposition for the determination of the cmc and the enthalpy of micellization, ∆Hm, of surfactants based on the results obtained with isothermal titration microcalorimetric measurements. The SBE is also convenient for the determination of the threshold percolation temperature and volume fraction of water, θp and φp, respectively, and the conductance rise for percolating w/o microemulsion systems. The results are directly
realized with their associated errors, which are otherwise difficult to estimate. The accuracy of the results and unambiguous realization of physicochemical information on self-organizing systems make the SBE versatile. Acknowledgment. S.K.H. thanks the University Grants Commission, Government of India, for a Junior Research Fellowship to perform this work. LA0110794
