Fluorocarbon Surfactant

Langmuir 2002, 18, 8777-8785

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Thermodynamic Study of Mixed Hydrocarbon/ Fluorocarbon Surfactant System by Conductometric and Fluorimetric Techniques Toshi-Yuki Nakano,† Gohsuke Sugihara,*,† Toshio Nakashima,‡ and Soo-Chang Yu§ Department of Chemistry, Faculty of Science, Fukuoka University, Jonan-ku, Fukuoka 814-0180, Japan, Department of Chemistry, Faculty of Education and Welfare Science, Oita University, Dan-noharu, Oita 870-1192, Japan, and Department of Chemistry, Faculty of Science and Technology, Kunsan National University, Kunsan, Jeollabuk-do 573-701, Korea Received April 17, 2002. In Final Form: August 5, 2002 Micelle formation of a combination of hydrocarbon/fluorocarbon anionic surfactantsssodium n-tetradecyl sulfate (STDS) and sodium perfluorononate (SPFN) in waterswas studied, paying special attention to the interaction between the two surfactants and the aggregation number, N, as a function of composition in the mixture (XSTDS). The critical micellization concentration (cmc) at each composition was determined at discrete temperatures by plotting the derivative specific conductance (∂κ/∂C) against the root of molarity (xC) at 40 °C. This plot enabled us to determine the cmc even in solutions with addd salt (NaCl) and thus estimate the degree of counterion binding onto micelles (β) for both single systems from the CorrinHarkins relation. The micellar composition of STDS (YSTDS) and interaction parameter were estimated on the basis of Rubingh’s and our own theoretical equations, and the results obtained from the respective equations were compared. Although Rubingh’s and our own equations resulted in differing phase diagrams, both suggested that the interaction mode between two surfactants and the state of formed micelles are remarkably different depending on the net mole fraction in the surfactant mixture (XSTDS) or YSTDS. According to our equations taking into account the counterion effect on mixed micelle formation, that is, the degree of counterion binding, we found the existence of an azeotropic point and a region of mole fraction showing that almost completely demixing micelles are formed (0 < XSTDS < 0.2). Further, the aggregation number was measured by static fluorimetry using two pairs of probe P and quencher Q, and in addition, the microscopic environment inside micelles was investigated by the use of a pyrene probe. These fluorescence studies also revealed that the miscibility of the two surfactants and the properties of micelles are distinctive at XSTDS = 0.2; above this mole fraction the two surfactants can form well-mixed micelles.

Introduction The number of scientific reports relating to amphiphilic molecules has greatly expanded during the past three decades. In parallel with the expansion, there have appeared useful monographs which can be consulted to comprehend or further develop basic colloid-and-surface science and technology.1-3 Amphiphilic molecules, or amphiphiles, not only are highly interesting from a physicochemical viewpoint but also are fundamental to life and living bodies: it is no exaggeration to say that all living things are made up of colloids comprising a wide variety of amphiphiles.2 Most amphiphiles display very important phenomenassuch as surface activity, wetting, adsorption, and micelle or aggregate formationsand resultant functionsssolubilization or emulsification, dispersion, and so forth. Of these amphiphiles, the surface active substances are also called surfactants, showing strong action on surfaces and interfaces to change their properties profoundly. Surfaces and interfaces are, of course, present everywhere in our daily life and in many * To whom correspondence should be addressed. Fax: +81-92865-6030. E-mail: [email protected]. † Fukuoka University. ‡ Oita University. § Kunsan National University. (1) Rosen, M. J. Surfactants and Interfacial Phenomena; John Wiley: New York, 1989. (2) Moroi, Y. Micelles: theoretical and applied aspects; Plenum: New York, 1992. (3) Tsujii, K. In Surface Activity; Tanaka, T., Ed.; Academic Press: New York, 1998.

kinds of industries, so surfactants can be used in application fields of every sort.3 Surfactants are very often used in mixed systems to obtain some desired performance. In such cases, many kinds of blending effects occur, and these effects correspond to the so-called synergism. The synergistic effect can be obtained, as expected, when some interaction is present between surfactant components.1-3 Mixed systems of different combinations have been studied extensively to develop better functions or to make clear the nature of synergistic effects.4,5 Special attention to the hydrocarbon/ fluorocarbon surfactant mixtures has revealed the nonideal behavior in micelle formation experimentally as well as theoretically.6-11 The deviation from ideal mixing in micelle formation is sorted according to either positive (repulsive) interaction or negative (attractive) interaction. (4) Holland, P. M.; Rubingh, D. N. Mixed Surfactant Systems; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992. (5) Ogino, K.; Abe, M. Mixed Surfactant Systems; Surfactant Science Series 46; Marcel Dekker: New York, 1993. (6) Funasaki, N. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Surfactant Science Series 46; Marcel Dekker: New York, 1993; pp 145. (7) Kissa, E. Fluorinated Surfactants; Surfactant Science Series 50; Marcel Dekker: New York, 1994. (8) Nagarajan, R. In ref 4, Chapter 4. (9) Guo., W.; Fung, B. M.; Christian, S. D.; Guzman, E. K. In ref 4, Chapter 15. (10) Aoudia, M.; Huig, S. M.; Wade, W. H.; Schter, R. S. In ref 4, Chapter 16. (11) Clapperton, R. M.; Ingram, B. T.; Ottewill, R. H.; Rennie, A. R. In ref 4, Chapter 17.

10.1021/la020370w CCC: $22.00 © 2002 American Chemical Society Published on Web 10/05/2002

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The combinations of anionic surfactants such as sodium dodecyl sulfate (SDS) with sodium perfluorooctanoate (SPFO)12 and with sodium decyl sulfate (SDeS)13 showed a conspicuously positive deviation in micelle formation. This deviation was interpreted as mutual phobicity acting between hydrocarbon/fluorocarbon hydrophobic chains. In contrast, from the combinations of SPFO with nonionic surfactants such as alkyl N-methyl glucamines (MEGAn), the negative deviation from ideal mixing was found; exceeding the mutual phobicity between hydrophobic chains, the stronger interaction acting between headgroups led to a synergistic enhancement of micelle formation as well as surface activity.13,14 Since fluorocarbon surfactants have not only hydrophobicity but also lipophobicity, and accordingly show characteristic behavior in regard to colloidal and interfacial phenomena in media, the research continues with a great effort.15-17 Along with the critical micellization concentration (cmc), the main factor determining the properties of a surfactant solution is the aggregation number (the number of surfactant molecules in a micelle).1,2 The colligative and light-scattering properties of solution have been used to determine the micellar aggregation number, but these techniques involve the problem of dissociating counterions from the micelle. Photochemical determination completely avoids this problem.2 The photochemical processes of photosensitive probe molecules are very sensitive to the dielectric constant of the solvent. The precise solubilization site of a probe in a micelle depends on both the probe and the micelle studied: generally, hydrophobic probes enter the micellar core and hydrophilic probes localize at the micellar surface.2 These findings promoted the use of various spectroscopies for determining the aggregation number and for inspecting the microenvironment around surfactant molecules forming a mixed micelle. Static or steady state fluorimetry, in fact, has been successfully applied to the study of surfactants in solution.18,19 This method is superior to the light-scattering method, which requires a wider concentration range of samples to determine the aggregation number.2 In this paper, micelle formation of a mixed system of hydrocarbon/fluorocarbon anionic surfactant, sodium ntetradecyl sulfate (STDS) and sodium perfluorononate (SPFN) in water, was studied in terms of the critical micellization concentration (cmc), construction of a phase diagram indicating the singly dispersed phase curve (cmcXSTDS relation) and the micellar phase curve (cmc-YSTDS relation), and the relation of aggregation number as well as the microenvironment as a function of mole fraction of STDS in the mixture (XSTDS). Phase diagrams were constructed using two different equations (Rubingh’s and our own), and the difference between both sets of results was investigated in parallel with the result of the fluorescence study. Experimental Section (1) Materials. Sodium n-tetradecylsulfate (STDS; purity, higher than 99%; Lancaster,) was used as received. Sodium (12) Mukerjee, P.; Yang, A. Y. S. J Phys. Chem. 1976, 80, 1338. (13) Sugihara, G. In Surfactant in Solution; Mittal, K. L., Ed.; Plenum: New York, 1989; Vol. 7, pp 397. (14) Wada, Y.; Ikawa, Y.; Igimi, H.; Murata, Y.; Nagadome, S.; Sugihara, G. J. Jpn. Oil Chem. Soc. 1990, 39, 548. (15) Asakawa, T.; Hisamatsu, H.; Yoshida, S. Langmuir 1995, 11, 478. (16) Moroi, Y.; Take’uchi, M.; Yoshida, N.; Yamauchi, A. J. Colloid Interface Sci. 1998, 197, 221. (17) Stahler, K.; Slb, J.; Candau, F. Mater. Sci. Eng. C 1999, 10, 171. (18) Alargove, R. G.; Kochijashky, I. I.; Sierra, M. L.; Zana, R. Langmuir 1998, 14, 5412. (19) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039.

Nakano et al. perfluorononate (SPFN) was prepared by neutralizing heptadecafluorononanoic acid (C8F17COOH, MW ) 464.8, Aldrich Chemical Co.) with aqueous NaOH solution (Nakalai Tesque). Neutralization involved repeating filtration of the warmed solution, more than three times cooling and leaving to stand, and drying the recrystallized sample of SPFN under reduced pressure. The purity of both surfactants was confirmed using an automatic surface tensiometer of drop volume method (Yamashita Giken TDS94); the plot of surface tension versus logarithmic concentration gave no minimum around the critical micellization concentration (cmc). Fluorescent probes, pyrene (Pyr) and tris(2,2′-bipyridyl)dichlororuthenium(II) hexahydrate (TBDR), were obtained from Wako and Aldrich Chemical, respectively, and used as received. Quenchers, 1-laurylpyridinium chloride (LPC) and 9-methylanthracene (9-MA), were purchased from Wako and used as received. (2) Conductometry. The conductivity measurements were performed by means of the same apparatus as previously reported:20 a TOA electroconductivity meter (CM-40S) was used with a TOA electrode (CG-201 PL) being set in a Thomas thermostated bath (TRL-N11). A 100 µL Hamilton Microsyringe was used to inject the sample solution through the spout; 15 cm3 of solvent (pure water or aqueous solution of NaCl) was initially contained in the cell, and the solution was constantly well stirred by a magnetic stirrer. (3) Steady-State Fluorimetry. Fluorescence measurements were performed using a JASCO fluorescence spectrophotometer (FP-777, Tokyo, Japan). The temperature of the sample solutions in a quartz cell was kept at 40 °C, and it was directly measured by the use of an electronic thermometer (Yamashita Giken, YSC9211). The combination of probe with quencher and their concentrations were set according to the literature,18,21 as follows.

(a) Pyr/LPC ) 2.0 × 10-6 M/1.0 × 10-4 M (b) TBDR/9-MA ) 10 × 10-5 M/5.0 × 10-5 M where M corresponds to mol‚dm-3. As Pyr and 9-MA are hardly soluble in water, their solutions were prepared with ethanol of high purity (99.5%, purchased from Wako Pure Chemicals), while aqueous solutions of LPC and TBDR were prepared with thrice distilled water. After the respective probe and quencher solutions were added into surfactant solutions, the concentrations of which were varied in the range above the cmc, they were shaken for a day at 40 °C in a thermostated bath to attain solubilization equilibrium. The excitation wavelengths and scanning ranges were 335 and 355-500 nm for Pyr, and 450 nm and 500-720 nm for TBDR, respectively. The bandwidths of the excitation and fluorescence sides were set as 1.5 and 1.5 nm for Pyr, and 5.0 and 10.0 nm for TBDR, respectively, according to the literature.21,22 Each measurement was performed by two continuous runs to avoid any error in regard to temperature equilibrium and so forth. It was confirmed that no excimer formation of Pyr due to selfassembling took place by keeping the Pyr concentration low enough to prevent such formation.

Results and Discussion (1) Dependences of Cmc on Temperature and on Added Salt Concentration. The critical micellization concentrations (cmc’s) of single and mixed systems in water with and without the addition of sodium chloride were measured at different temperatures by the electroconductivity method, and the degrees of counterion binding (β) at 40 °C were determined from the plots of logarithmic (20) (a) Sugihara, G.; Nakamura, A. A.; Nakashima, T. H.; Araki, Y. I.; Okano, T.; Fujiwara, M. Colloid Polym. Sci. 1997, 275, 790. (b) Fujiwara, M.; Okano, T.; Nakashima, T. H.; Nakamura, A. A.; Sugihara, G. Colloid Polym. Sci. 1997, 275, 474. (c) Nakamura, A. A.; Hisatomi, M.; Sugihara, G.; Fujiwara, M.; Okano, T. J. Surf. Sci. Technol. 1998, 14, 23. (21) Moroi, Y.; Humphry-Baker, R.; Gratzel, M. J. Colloid Interface Sci. 1987, 119, 588. (22) Corrin, M. L.; Harkins, W. D. J. Am. Chem. Soc. 1947, 69, 679.

Mixed Hydrocarbon/Fluorocarbon Surfactant System

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Table 1. Effect of Added Salt (Sodium Chloride) on the Critical Micellization Concentration Determined by Electroconductivity Measurement at 40 °C STDS

SPFN

salt conc/mmol‚kg-1

cmc/mmol‚kg-1

ln mga

1.5 3.0 4.5 5.5 12.0 14.0 16.0 18.0 20.0

1.82 ( 0.05 1.35 ( 0.05 1.09 ( 0.04 1.04 ( 0.04 8.47 ( 0.26 8.35 ( 0.25 7.90 ( 0.30 7.67 ( 0.30 7.45 ( 0.30

-5.71 -5.44 -5.19 -5.03 -3.89 -3.80 -3.73 -3.66 -3.60

a ln m is the natural logarithmic molality of counterions, that g is, the concentration of added NaCl plus the cmc.

concentration of counterion (Na+), that is, the so-called Corrin-Harkins plots20,22 (the plot is not shown here). As has been described previously,20 the more accurate determination of cmc was found to be attained from the differential conductivity (∂κ/∂C)T,P versus square root of concentration (xC) compared with the conventional plot of specific conductivity (κ) versus concentration (C). In particular, the former plot is superior to the latter in determination of cmc for the systems with the addition of NaCl or for the mixed systems in some cases. In the plot of κ versus C, otherwise, the intersection angle of the two curves of κ versus C above and below the cmc is not so sharp that the determination of the intersection point can be made unambiguously. Comparing the two methods of κ versus C and (∂κ/∂C)T,P versus xC, in actual treatment with cmc determination, the former results in an error of (20% at most (when the concentration of added salt is very high), but the latter’s error ranges only (2%.20 Here, it is noted that, in the plot of (∂κ/∂C)T,P versus xC, (∂κ/∂C)T,P was assumed as being approximately equal to ∆κ/∆C, where ∆κ ) κi+1 - κi and ∆C ) Ci+1 - Ci at the ith measured point and C h ) (Ci+1 - Ci)/2. In addition, it is noted that although the conventional conductivity studies should employ the molarity (C), instead, the molality m (mol‚kg-1) is adopted, regarding the latter as being approximately equal to the former and better for thermodynamic treatment. The cmc’s in molality as a function of added NaCl concentration are listed for STDS and SPFN in Table 1. From the good linear relations in the CorrinHarkins plot, the degrees of counterion binding were determined as 0.85 for STDS and 0.47 for SPFN at 40 °C. It is noted here that the degree of micellar dissociation (R) has been assumed to be equal to the ratio of slopes below and above the cmc as R ) SM/S1, while the degree of counterion binding has been regarded as β ) 1 - R, supposing R + β ) 1. The present authors have reported that the micellar dissociation degree REX calculated from βCH, which was determined from the Corrin-Harkins plot (as REX ) 1 - βCH), does not agree with those from the SM/S1 ratio, and they had an argument in detail about the disagreement of R ()SM/S1) with REX ()1 - βCH).20 On the basis of the phase separation approximation of micelle formation with added salt, the standard Gibbs energy change upon micelle formation, ∆G°m at temperature T is related with β as follows.

ln Xcmc )

∆G°m - β ln(Xcmc + Xa) RT

(1)

where Xcmc and Xa are the concentrations in mole fraction of the surfactant at the cmc and of the added salt in aqueous media, and R is the gas constant. From this equation the cmc as a function of the counterion concen-

Figure 1. Temperature dependence for the cmc for STDS and SPFN pure systems.

tration (Cg) can be expressed as20

ln cmc ) const (T,P) - β ln Cg A linear relationship between ln cmc and ln Cg or ln(Xcmc + Xa) has been observed in a number of experiments, indicating that the present approximation is correct.2 However, the above relation might hold only within a restricted concentration range of the added salt, because higher concentration of added salt would lead to a change of micelles in terms of aggregation number, micellar shape, and so forth. It has been known that for ionic surfactants having simpler chemical structure of counterions such as Na+, K+, Cl-, or Br- the temperature dependence in β is so little that the use of a β value may be allowed in approximate calculation of enthalpy or entropy charges on micellization at different temperatures other than at the actual temperature studied; the change with temperature ranges only within 2-3%.20a,23 Therefore, the β value in this study was determined only at one temperature (40 °C). The low value of β for SPFN (0.47) may be ascribed to the larger cross section of fluorocarbon chains, the aggregation of which can form a surface with lower density of negative charge that requires less counterions (of positive charge) for stabilization of colloidal micelles compared with hydrocarbon surfactant micelles.24 The cmc data at discrete temperatures are given for both single systems in Table 2 in addition to various thermodynamic parameters. In Figure 1 the temperature dependence of the cmc is shown for each single system. SPFN clearly shows a minimum at ∼40 °C; it is wellknown that the cmc-temperature curve of fluorocarbon surfactants has a minimum around this temperature.7,24 In contrast, the cmc of STDS slightly increases with temperature, the minimum of which is known to appear below 30 °C.25 (2) Thermodynamic Analysis of the Respective Surfactant Systems. As will be shown in the fluorescence study, the micellar aggregation numbers of the present two single surfactant systems are large enough to allow us to apply the phase separation approximation2,25 to thermodynamic analysis of micelle formation. The standard Gibbs energy change ∆G°m on micelle formation at (23) Okano, T.; Tamura, T.; Nakano, T. Y.; Ueda, S. I.; Lee, S.; Sugihara, G. Langmuir 2000, 16, 3777. (24) Mukerjee, P.; Korematsu, K.; Okawauchi, M.; Sugihara, G. J. Phys. Chem. 1985, 89, 5308.

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Table 2. Thermodynamic Parameters at Various Temperatures for STDS and SPFN Single Systems STDS

SPFN

T/°C

cmc/mmol‚kg-1

30 35 40 45 50 35 40 45 50

2.08 2.16 2.23 2.30 2.42 11.0 10.2 10.4 11.0

β (binding degree)

(0.85)

(0.47)

∆G°m/kJ‚mol-1

∆H°m/kJ‚mol-1

∆S°m/102 J‚K-1‚mol-1

-47.5 -48.1 -48.8 -49.4 -49.9 -32.1 -32.9 -33.4 -33.7

-8.0.2 -9.7 -11.1 -12.5 -13.8 24.8 7.7 -8.9 --25.0

1.30 1.25 1.20 1.16 1.12 1.85 1.30 0.72 0.27

temperature T was calculated using the following equation.2

∆G°m ) (1 + β)RT ln Xcmc

(2)

The enthalpy change on micelle formation, ∆H°m, and the corresponding entropy change, ∆S°m, were calculated on the basis of the Gibbs-Helmholtz relations:

{

}

∂(∆G°m/RT)

) ∆H°m

(3)

∆S°m ) (∆H°m - ∆G°m)/T

(4)

∂(1/T)

P

Here it is noted again that a value of β determined at 40 °C was used for calculation of ∆G°m even at temperatures other than 40 °C for each single system, because temperature dependence was assumed to be negligible. Table 2 lists the thermodynamic parameters at various temperatures for STDS and SPFN single systems. The temperature dependence of these parameters was not so marked for STDS, as suggested from the cmc-temperature curve (Figure 1). In contrast, ∆H°m as well as ∆S°m of SPFN changed conspicuously with temperature. The results are shown in terms of ∆H°m and T∆S°m in Figure 2. The ∆H°m of SPFN changes its sign from positive to negative at the temperature where a minimum appears in the cmc-temperature curve, and in parallel with this, the entropy term well compensates the disadvantage in ∆H°m to make ∆G°m negative by a larger negative value at the lower temperature. As the temperature is raised, the enthalpy term plays a more important role than the entropy term. This trend in the enthalpy term reflects a marked temperature dependence in heat capacity of fluorocarbon surfactant solution, as is shown by a calorimetric study on micelle formation.26 The different behavior with regard to the thermodynamic parameters of SPFN in comparison with STDS, might be ascribed to the thicker water structure of hydrophobic hydration and to the easier melting of the structured water around hydrophobic chains with raised temperature. This means that, compared with a hydrocarbon chain, a fluorocarbon chain has a larger cross section and higher number of structured water molecules; therefore, the extent of breaking of the structured water corresponding to the entropy increase upon micelle formation (transfer of singly dispersed state in bulk to micelle) is larger at lower temperatures but lessens as the temperature is increased. This trend is more conspicuous in fluorocarbon surfactants than hydrocarbon surfactants,24 as is seen from the fact that the positive value of ∆S°m becomes smaller as temperature becomes

higher (see Table 2). This decrease in positive entropy value is compensated well by the great decrease of ∆H°m toward negative value. The ∆H°m changing from the smaller positive to the more negative value with temperature reflects a stability due to a kind of condensation of singly dispersed surfactant molecules. Examining the enthalpy-entropy compensation phenomena, a perfectly linear relation of ∆H°m with ∆S°m was obtained for each single system (not shown here) and the so-called compensation temperature27 was determined as 313 K for STDS and 315 K for SPFN. The self-compensation temperatures are included within the reported value 307 ( 8 K for micelle formation of various surfactants in water.28 One of the present authors has concluded that the self-compensation temperature is only an average of temperature studied;28a the obtained values are just the case for the average of experimental temperature. In the previous paper,28b it was shown that only when ∆G values have a linearity with ∆H values of similar reactions in water, such as micelle formation for different species at a fixed temperature Tf , is a common (constant) cross-

(25) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous surfactant Systems; National Standard Reference Data Series 36; National Bureau of Standards (U.S.): Washington, DC, 1971. (26) Pestman, J. M.; Kavelam, J.; Blandemer, M. J.; Doren, H. A.; Kellogg, R. M.; Engberts, J. B. F. N. Langmuir 1999, 15, 2009-2014.

(27) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (28) (a) Sugihara, G.; Hisatomi, M. J. Colloid Interface Sci. 1999, 219, 31. (b) Sugihara, G.; Nakano, T.-Y.; Sulthana, S. B.; Rakshit, A. K. J. Oleo Sci. 2001, 50, 29.

Figure 2. Changes in enthalpy and entropy upon micelle formation for STDS and SPFN pure systems as a function of temperature.


Langmuir, Vol. 18, No. 23, 2002 8781

Table 3. Values of Critical Micellization Concentration, Micellar Composition (Y), Interaction Parameter (ω), and Activity Coefficient (f) for Mixed Micelles of STDS/SPFN Binary Combinations at 40 °C (A) Rubingh’s theory cmc/ XSTDS mmol‚kg-1 YSTDS ωR f1a f2 0 0.05 0.08 0.15 0.18 0.33 0.57 0.75 0.86 1 a

10.17 10.22 9.51 7.09 5.75 3.73 2.94 2.77 2.51 2.23

0.05 0.16 0.44 0.50 0.64 0.79 0.93 0.97

1.8 1.0 0.3 -0.3 -1.0 -0.9 0.0 0.1

1.0 1.0 1.1 0.9 0.7 0.6 1.0 1.1

(B) our theory YSTDS ω0 f1 f2

5.0 0.05 2.0 ≈1 1.1 ≈1 0.9 ≈1 0.9 0.86 1.0 0.95 1.0 0.97 1.0 0.98

3.2 1.0

0.1 0.3 0.3 0.1

1.1 1.3 1.3 1.1

1.0 1.0 1.0 1.0

Subscripts 1 and 2 correspond to SPFN and STDS, respectively.

compensation temperature, Tc, determinable, as indicated by the following equation.

∆G ) (1 - Tf/Tc)∆H + Tf(∆H1/Tc - ∆S1)

(5)

where the subscript 1 denotes (an arbitrarily selected) species 1 among many different ones. In this situation, the observed compensation temperature can be attributed to the ratio of enthalpy change difference to entropy change difference (∆∆H/∆∆S), which is required to be a constant.28b Returning attention to our data given in Table 2, the results of (∆∆H°m/∆∆S°m), which were calculated from the respective differences between STDS and SPFN at the discrete temperatures, are widely dispersed, for example, 535 K at 35 °C and 131 K at 50 °C. The apparent crosscompensation temperature thus obtained for the present two surfactants did not range around 300 K or around the average temperature studied. As has been previously noted for micelle formation of various surfactants, although they have a self-compensation temperature definitely determined from the ∆H°m-∆S°m plot, they did not satisfy an expectation that the cross-compensation temperature would give a ∆H°m-∆S°m relation whose slope might be near to 300 K. This conflict seems to come from various factors that may lead to compensatory errors in ∆H and ∆S when both are derived from the temperature dependence of ∆G.28b Our data shown in Table 2 are likely to involve such errors. On the other hand, it may be said that the so-called compensation temperature itself has no significant meaning other than the ratio of ∆H difference to ∆S difference (∆∆H/∆∆S), which is a constant or commonly similar to the overall systems studied.28b (3) Estimation of Micellar Composition and Interaction Parameters in Mixed Surfactant Systems. The cmc values of the mixed systems at discrete mole fractions are tabulated in Table 3. To analyze the cmc as a function of the net mole fraction (Xi) in the mixed systems of surfactants 1 and 2 in terms of the composition of micelles formed at the cmc (Yi) and the interaction parameter between 1 and 2, the following Rubingh’s equation29 has so far been widely known and conveniently used:

Y12 ln(CmX1/C°1Y1) (1 - Y1)2 ln{Cm(1 - X1)/C°2(1 - Y1)}

)1

(6)

(29) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, pp 337.

Figure 3. Phase diagram of STDS/SPFN mixed surfactant systems at 40 °C and 1 atm based on Rubingh’s theory. Closed circles indicate the measured cmc valued as a function of mole fraction of STDS in the surfactant mixture (XSTDS). Open circles (simulated using Rubingh’s equations) correspond to the respective micellar composition curve (cmc-YSTDS curve). Dotted and solid straight lines are projections of singly dispersed phase curves of ideal mixing calculated from Raoult’s law and the micellar phase curve of ideal mixing, respectively.

where C°i (i ) 1, 2) and Cm denote the cmc values of the single system of i and the mixed system, respectively. Rubingh has introduced an interaction parameter, ωR, in the mixed micelle (his notation is β) on the basis of the regular solution approximation:

ωR ) ln(CmX1/C°1Y1)/(1 - Y1)2

(7)

The substitution of Y1 values calculated from eq 6 into eq 7 produces an ωR value at each X1. Here, the interaction parameter is related to the activity coefficients f1 and f2 and the micellar composition Y1 as follows.

f1 ) exp{ωR(1 - Y1)2} f2 ) exp(ωRY12)

}

(8)

Applying these equations to the cmc data given in Table 3, ωR, YSTDS for STDS, and fi values were calculated. The results are also listed in the same table, while the obtained phase diagram is shown in Figure 3. In Figure 3 the cmc-XSTDS curve corresponding to the singly dispersed phase curve was calculated using Clint’s equation30 (derived from the Raoult’s law) for ideally mixed micelle formation and indicated by a dotted line. The relation of cmc with micellar composition should be, needless to say, a straight line (as indicated by a solid line in Figure 3), when the two surfactants can form micelles of ideal mixing. Figure 3 demonstrates, however, considerably complicated behavior in regard to the cmc-XSTDS relation: the measured cmc values (indicated by closed circles) deviate positively from ideal mixing in the range 0 < XSTDS < 0.2, while they deviate negatively in the region between 0.2 and 0.75, followed by riding on the curve of ideal mixing in the range above XSTDS ) 0.75. Substituting these cmc values to the above eqs 6-8, the micellar composition YSTDS, ωR, and f1 and f2 (1 and 2 correspond to SPFN and STDS, respectively) were cal(30) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1327.

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culated (Table 3). The cmc-Y2 curve, that is, the micellar composition curve, is presented in Figure 3. At a glance the curve seems to express well the micellar composition; however, including the maximum cmc value found at XSTDS ) 0.05, a complete simulation curve of cmc versus XSTDS was hard to obtain, so in the figure a smoothed curve was drawn along the measured points. The change in the sign of ωR with XSTDS also makes us feel it is difficult to comprehend its behavior by relating the aggregation states of the present mixed system. It is noted that Rubingh’s equations are generally applicable to any type of combinations of binary mixed systems, such as ionic-ionic, ionic-nonionic, and nonionic-nonionic surfactants; however, his equations do not account for the mutual counterion effect in the binary ionic surfactant mixture. We have applied the following equations for micelle formation of ideal mixing to binary ionic surfactant systems.31-33

Y1 ) X1(Cm/C°1)1+β1 X1 )

1 - (Cm/C°2)

(9)

1+β2

(Cm/C°1)1+β1 - (Cm/C°2)1+β2

(10)

where β1 and β2 denote the degrees of counterion binding for surfactants 1 and 2, respectively. These equations allow us to calculate Cm from eq 10 as a function of X1, if C°1, C°2, β1, and β2 are known. Then, micellar composition Y1 can be also calculated from eq 9. Further, for any mixed system of either ideal or nonideal mixing, we have derived equations including an interaction parameter, ω0, from the idea introduced in eqs 9 and 10 so as to be more generally applicable to given systems, as follows.13,30-321

ln

ln

Y1 + κ1 ln C°1 + (1 - Y1)2ω0 ) κ1 ln Cm X1

(11)

X1u Y1u + [U(1 - Y1)2 - Y12]ω0 - ln ) 1 - Y1 1 - X1 C°2 Uκ1 ln (12) C°1

where U ) κ2/κ1 ) (1 + β2)/(1 + β1). Applying eqs 11 and 12 in addition to eq 8, the values of YSTDS, ω0, and the activity coefficients f1 and f2 were determined, as listed in Table 3. First of all, it should be noted that the uniquely high value of ω0 at XSTDS ) 0.05 is regarded as an azeotrope (XSTDS ) YSTDS ) 0.05): this point was confirmed by repeated measurements which always produced a good agreement. Interestingly, the values of YSTDS at the range 0.05 < XSTDS < 0.2 were found to be approximately unity. These measured and calculated results are plotted in Figure 4. In this figure the curves of the singly dispersed phase and of the micellar phase, which were calculated for ideally mixed micelle formation, are given by a dotted line and a broken line, respectively. A comparison of the respective phase curves of ideal mixing obtained from Rubingh’s equations (Figure 3) with those from ours (Figure 4) makes us recognize a great difference. Further, Figure 4 indicates a clear distinction above and (31) Sugihara, G.; Nakamura, D.; Okawauchi, M.; Sakai, M.; Kuriyama, K.; Ikawa, Y. Fukuoka Univ. Sci. Rep. 1987, 17, 31. (32) Sugihara, G.; Nagao-Omoto, F.; Tanaka, T.; Lee, S.; Sakaki, Y. J. Colloid Interface Sci. 1995, 171, 246. (33) Sugihara, G.; Era, Y.; Funatsu, M.; Kunitake, T.; Lee, S.; Sakaki, Y. J. Colloid Interface Sci. 1997, 187, 435.

Figure 4. Phase diagram of STDS/SPFN mixed surfactant systems at 40 °C and 1 atm based on our theory. Closed circles indicate the measured cmc values as a function of mole fraction of STDS in the surfactant mixture (XSTDS). Open circles (simulated using our theoretical equations) correspond to the respective micellar composition curve (cmc-YSTDS curve). Dotted and broken lines are projections of singly dispersed phase and micellar phase curves of ideal mixing using our theory, respectively. The solid curves along the open circles on the righthand side of graph represent the cmc-micellar composition relation calculated using eqs 12 and 13.

below XSTDS ) 0.2. In the r egion below XSTDS ) 0.2, on the left-hand side of the azeotropic point (XSTDS ) 0.05), fluorocarbon rich or fluorocarbon only micelles are formed, while, on the right-hand side up to XSTDS ) 0.2, STDS dominant micelles (with few SPFN molecules) are formed. It is interesting that, in the region above XSTDS ) 0.2 up to 1.0, the mixing of STDS and SPFN seems to be approximately ideal, and the activity coefficient values obtained also suggest nearly ideal mixing. Figure 4 as well as Table 3 shows us that the mixing behavior, or mixed micelle formation, depends greatly on the mixing ratio itself, meaning that the interaction mode between STDS and SPFN reflects directly the relativity in composition, that is, either minority or majority. As for the values of activity coefficients obtained from Rubingh’s equations, f2 (for STDS) at XSTDS ) 0.05 is the largest, corresponding to the large positive value (ωR ) 1.8), and the region showing negative deviation from ideal mixing leads to f2 values of decimal fraction (see Table 3), as expected. On the other hand, f1 and f2 values over the XSTDS range from 0.05 to 0.18 could not be exactly estimated from our own theory, because the computer gave nonsensically huge values, suggesting that sparingly mixed (almost immiscible) micelles are formed (YSTDS ≈ 1). Here, it is desired to know the dependence of the aggregation number of micelles on composition. (4) Analysis by Steady-State Fluorescence Spectroscopy. (a) Determination of Aggregation Number. We employed static fluorescence spectroscopy for determination of the average aggregation number of micelles N h in this study. The first step in determining N h by this method is to select a fluorescence probe P and a quencher Q, both of which are incorporated exclusively into the micellar domain. For the two anionic surfactants of the present study, two kinds of P and Q pairs were used: (a) pyrene (Pyr) with 1-laurylpyridinium chloride (LPC) and (b) tris(2,2-bipyridyl)dichlororuthenium(II) hexahydrate (TBDR) with 9-methylanthracene (9-MA). In these com-


Langmuir, Vol. 18, No. 23, 2002 8783

Figure 5. Example of determination of aggregation number as well as cmc at 40 °C (XSTDS ) 0.86).

binations, the quenching process is considered to take place only in the micellar region. The concentrations of P and Q and the intensity of the excitation light should be kept low so as not to conflict with the theory.2,18,21 According to the literature,18,21 the concentrations were given as (a) 2.0 × 10-6 M/1.0 × 10-4 M for pyr/LPC and (b) 1.0 × 10-5 M/5.0 × 10-5 M for TBDR/9-MA, respectively. The ratio of fluorescence intensity, I/I0, in the presence of Q to that in the absence of Q is related to N h , the concentration of Q ([Q]), and the total concentration of a given surfactant Ct as follows.

[ln(I0/I)]-1 ) (1/[Q]N h )(Ct - cmc)

(13)

Plots of the left-hand side of eq 13 against the surfactant concentration at constant Q concentration should be linear, and the slope and the intercept of the abscissa are ([Q]N h )-1 and the cmc, respectively.34 As is clear from eq 13, it is also possible to obtain the aggregation number at constant concentration by changing the Q concentration. In the present study, however, we employed the former method. Each example of the results obtained from the two pairs of P and Q is shown in Figure 5. According to the literature, the excitation wavelength was set at 335 and 450 nm for Pyr and TBDR, respectively.21,35 Although the cmc estimated from the intercept of the plot must be in accordance with that determined from the conductivity method, scattering of measured values (deviating from linearity) of [ln(I0/I)]-1 did not always allow us to obtain reliable cmc values. Judging from the scattering extent of the measured data, the estimated aggregation number may have (15% of error at most, especially in the cases of mixed system. In Table 4 the determined aggregation number at each mole fraction of the surfactant mixture is listed, and in Figure 6 those are plotted against XSTDS. The N h values of the respective single systems were determined as 87 ( 2 for STDS and 23 ( 2 for SPFN. These values were evaluated by averaging the well-agreed results obtained from both methods using two pairs of P and Q, and they may be reasonable, judging from the literature.21 Since the micellar aggregation number generally depends on the length of the hydrocarbon chain, it (34) Turro, N. J.; Yekta, A. J. Am. Chem. Soc. 1978, 100, 5951. (35) Asakawa, T.; Miyagishi, S. Langmuir 1999, 15, 3464.

Figure 6. Mole fraction dependence of aggregation number determined for STDS/SPFN mixed surfactant systems by the two pairs of fluorescent probe and quencher at 40 °C. The data points of open circles and closed circles were obtained from Pry/LCP and TBDR/9-MA pairs, respectively. Table 4. Values of Micellar Aggregation Numbers (Nagg) and the Ratio I3/I1 Determined for STDS/SPFN Mixed Surfactant Systems by the Two Pairs of Fluorescent Probe and Quencher at 40 °C XSTDS

Nagg(pyr/LPC)

Nagg(TBDR/9-MA)

I3/I1

0 0.05 0.08 0.15 0.18 0.33 0.57 0.75 0.86 1

21 24 64 87 109 112 110 95 91 89

25 112 114 111 117 118 117 109 96 85

0.68 0.70 0.72 0.78 0.81 0.83 0.86 0.87 0.87 0.87

is understandable that SPFN having the shorter chain length shows the smaller number. It is noted that the two combinations of P and Q resulted in markedly different values from each other in the fluorocarbon rich region, that is, at 0 < XSTDS < 0.15 (see Figure 6). This disagreement reflects the immiscibility of

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hydrocarbon surfactants into fluorocarbon dominant micelles. The pyr/LCP pair led to an apparently lower N h (open circles), while TBDR/9-MA exhibited a higher N h for a few systems (closed circles) at the same mole fractions in the surfactant mixture. This suggests that the respective two types of micelles, or STDS rich micelles and SPFN rich micelles, selectively solubilized the probes; that is, STDS rich micelles, having a higher degree of counterion binding (β ) 0.85), did solubilize TBDR, while SPFN rich micelles, having a higher hydrophobic core, did solubilize Pyr. Recently, a demixing state such as that in the present case has been similarly observed for the mixed system of sodium dodecyl sulfate (SDS) with sodium perfluorooctanoate (SPFO) by fluorescence spectroscopy.35 It should also be considered that a surfactant of the two in the binary mixed ionic surfactant systems can act as a counterion on the other surfactant. Looking at Figure 6 again in more detail, in the region from XSTDS ) 0 to 0.15 in which an azeotropic point is found at XSTDS ≈ 0.05, we observed a great difference in the results between the two P and Q pairs, as described above. However, at the range above XSTDS ) 0.15, both pairs resulted in nearly equal values of N h . As for the data from TBDR/9-MA between XSTDS ) 0.05 and 0.20, the aggregation number may be regarded as constant. This corresponds to the fact that in this region (0.05 < XSTDS < 0.20) the micelles formed are composed of nearly 100% STDS and have almost the same aggregation number. Further the aggregation number depends neither on XSTDS nor on YSTDS in the range XSTDS ) 0.2-0.6. Here, the formed micelles consist of nearly 100% STDS, and the size and aggregation number are made larger by SPFN playing the role of added salt, because SPFN molecules are in the state of monomeric dispersion. Similarly, in the range above XSTDS > 0.6, STDS dominant micelles are formed; however, as the composition becomes nearer to XSTDS ) 1, the aggregation number becomes closer to that of pure STDS. In this situation, since XSTDS f 1 corresponds to XSPFN f 0, the concentration of SPFN acting as an added salt becomes lower so that the added salt effect itself is weakened to reduce the micellar size down to that of pure STDS. (b) Estimation of Micellar Microenvironment Using a Pyrene Fluorescent Probe. It is well-established that the fluorescence intensity of pyrene monomers reflects the polarity of media. And thus the environment of the media where the pyrene probe exists can be easily monitored by employing it. The intensities of the vibronic bands depend on the solvent, so the intensity ratio of peak III to peak I decreases with increasing dielectric constant of the solvent.2,18,19,36,37 In other words, the higher hydrophobic environment gives the higher I3/I1 ratio, as was reported for n-hexane (1.65) > n-butanol (0.98) > methanol (0.75) > acetonitrile (0.54).2,19 Figure 7 demonstrates the I3/I1 ratio of pyr monomer fluorescence as a function of mole fraction of STDS. An abrupt increase also occurred in the region of lower STDS (higher SPFN) mixing ratio (below XSTDS ) 0.15) in a manner similar to that of the phase diagram in Figure 4 as well as the N h versus XSTDS diagram in Figure 6. The low value given by fluorocarbon rich micelles may come from the low mutual miscibility with hydrocarbon or the low solubilization ability of fluorocarbon cores against pyr molecule, suggesting that the I3/I1 ratio depends not only on the polarity of the hydrophobic core of the micelles but also on the situation of the pyr solubilized. (36) Nakajima, A. Bull. Chem. Soc. Jpn. 1971, 44, 3272. (37) Ham, J. S. J. Chem. Phys. 1953, 21, 756.

Nakano et al.

Figure 7. Plot of the ratio of intensities (I3/I1) of the vibrational bands in the pyrene fluorescence spectrum in an aqueous solution of STDS/SPFN mixed surfactant systems as a function of mole fraction in the surfactant mixture at 40 °C. (The dotted line indicates the value in pure water, I3/I1 ) 0.55.)

Even from this Figure 7 the miscibility of the two surfactants and the property of micelles may be divided into two at XSTDS ≈ 0.2. In the region from X ≈ 0.05 (azeotrpic point) to ∼0.2, there are micelles of YSTDS ≈ 1, but their concentration is very low so that I3/I1 values are lower than that of pure STDS micelles. Although the I3/I1 ratio itself reflects directly the polarity of the microenvironment, it is considered to depend on micellar concentration or total surfactant concentration, which may accompany a change in micellar aggregation state. In this region, however, as the concentration of STDS rich micelles increases with raised XSTDS, the I3/I1 value will also increase. In the region of 0.2 < XSTDS < 0.6, the I3/I1 shows a slight increase, suggesting an effect of increased concentration of STDS dominant micelles which have almost constant aggregation number. At the range above XSTDS ) 0.6, the constant I3/I1 value indicates that there exist STDS dominant micelles giving no change in the surroundings of Pyr. In the above section the micellar state of the present mixed system was estimated on the basis of the regular solution theory (RST) approach modified by considering the counterion effect. The estimated result is likely to be considerably supported by the present fluorescence study. Here, we should pay attention to Hines’ indication that the RST relies on a single adjustable parameter (ωR or wO) to calculate various mixed surfactant micellization properties; on the other hand, recent molecular thermodynamic (MT) approaches are superior to the RST-based ones: the MT approaches provide a deep molecular perspective on the relation between molecular structure, including solution conditions, and the macroscopic behavior of the surfactant mixture, and in particular, the MT approaches enable the prediction of mixed micelle shape and size (these two important properties cannot be predicted in the context of RST).38,39 Conclusion In conclusion, when the results of fluorescence studies are correlated with the correspondence in the thermodynamic behavior shown in Figures 3 and 4 (and Table (38) Aveyyard, R.; Blankenschtein. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 338. (39) Hines, J. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 350.


3), the analysis according to our theory seems to lead to a better accordance than those not taking into account the counterion effect on mixed micelle formation. The Corrin-Harkins plot results in the degree of counterion binding as 0.85 for STDS and 0.47 for SPFN micelles at 40 °C. The temperature dependence of ∆S°m as well as ∆G°m which was estimated from the Gibbs-Helmholtz relations was found for SPFN to be more conspicuous as compared with that of STDS; this difference was ascribed to the difference in hydrophobic hydration around the hydrophobic chain. The existence of an azeotropic point and a region of mole fraction shows that almost completely

Langmuir, Vol. 18, No. 23, 2002 8785

demixing micelles are formed (0 < XSTDS < 0.2). Further, the aggregation number was measured by static fluorimetry using two pairs of probe P and quencher Q, and in addition, the microscopic environment inside micelles was investigated by the use of a pyrene probe. These fluorescence studies also revealed that the miscibility of the two surfactants and the properties of micelles are distinctive at XSTDS = 0.2; above this mole fraction the two surfactants can form well-mixed micelles. LA020370W

Fluorocarbon Surfactant

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