Thermodynamic Study on Surface Adsorption and Micelle Formation

The β value itself shows a little temperature dependency ranging around 0.57, ... in water where Tc is the compensation temperature and σ, the entro...
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Langmuir 2000, 16, 1515-1521

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Thermodynamic Study on Surface Adsorption and Micelle Formation of a Hybrid Anionic Surfactant in Water by Surface Tension (Drop Volume) Measurements Mihoko Hisatomi,† Masahiko Abe,‡ Norio Yoshino,§ Sannamu Lee,† Shigemi Nagadome,† and Gohsuke Sugihara*,† Department of Chemistry, Fukuoka University, Fukuoka 814-0180, Japan, Science University of Tokyo, Faculty of Science and Technology, Noda, Chiba 278-0022, Japan, and Science University of Tokyo, Faculty of Engineering, Kagurazaka, Tokyo 162-8601, Japan Received March 19, 1999. In Final Form: October 28, 1999 To study the formation of micelles in bulk water and adsorbed film at the air/water interface, we have thermodynamically studied a novel type of anionic surfactant, the so-called “hybrid type”. We used sodium 1-oxo-1[4-(tridecafluorohexyl)phenyl]-2-hexane sulfonate (here, abbreviated as FC6-HC4), which involves a perfluorocarbon chain attached to the phenyl group as the primary hydrophobic group and a short hydrocarbon side chain attached to a sulfonate group.The surface tension (γ) of solutions at different temperatures was measured by means of a drop volume technique. The critical micellization concentrations (cmc’s) were determined from the plot of γ vs logarithmic molality as a function of temperature ranging from 5 to 50 °C and the cmc-temperature curve was found to have a minimum of ca. 15 °C. The degree of counterion binding (β) was estimated at each temperature from the Corrin-Harkins plot. The β value itself shows a little temperature dependency ranging around 0.57, which is smaller than those of common surfactants (β ) 0.7-0.8), reflecting the low charge density on the micellar surface formed by top-heavy FC6-HC4 molecules. The collected data on the cmc and β as a function of temperature and a literature value of the aggregation number allowed us to calculate the Gibbs energy change (∆G°m) of micelle formation, and the Gibbs-Helmholtz plot of ∆G°m enabled us to estimate the enthalpy change ∆H°m and then the entropy change ∆S°m. Between ∆H°m and ∆S°m a compensation rule was found to hold as ∆S°m ) ∆H°m/Tc + σ as has been observed for more than 18 species of different kinds of surfactants in water where Tc is the compensation temperature and σ, the entropy change at ∆H°m ) 0. The effect of added salt on γ or the surface excess (the surface absorbed amount relative to H2O), Γ, was also discussed in detail. Compared with common surfactants, even a small addition of NaCl (below 5 mmol kg-1) strikingly enhanced the surface activity inducing a great depression not merely of surface tension but of cmc as well.

Introduction Fluorinated surfactants have been accurately called supersurfactants.1 In addition to their marked surface activity that can decrease the surface tension of water below the lower limit reached by hydrocarbon-type surfactants, the perfluorinated chain is not only extremely resistant to chemical attack and highly hydrophobic but also oleophobic, so that fluorinated surfactants can serve as oil and fat repellents.1 Mixed systems of hydrocarbon and fluorocarbon surfactants have been extensively investigated by many researchers, and their unique and synergistic properties that differ greatly from those of single surfactants have so far been reported, or theoretical interpretations about the properties have been made. Plenty of important information can be conveniently derived from some publications.1-3 Since compounds consisting of a fluorinated chain and a hydrocarbon group can function as surfactants even in hydrocarbon media,1 such hybrid-type surfactants in addition to the mixed * To whom correspondence may be addressed. Fax: +81-092865-6030. E-mail: [email protected]. † Department of Chemistry, Fukuoka University. ‡ Faculty of Science and Technology, Science University of Tokyo. § Faculty of Engineering, Science University of Tokyo. (1) Kissa, E. Fluorinated Surfactants; Surfactant Science Series; Marcel Dekker: New York, 1994; Vol. 50. (2) Holland, P. M., Rubingh, D. N., Eds. Mixed Surfactant Systems; ACS Symp. Ser. 501; American Chemical Society: Washington, DC, 1992. (3) Abe, M., Ogino, K., Eds. Mixed Surfactant Systems; Surfactant Science Ser. 46; Marcel Dekker: New York, 1993.

systems strongly compel our practical and theoretical interest in revealing their behaviors. Ito et al. have so far synthesized fluoro-hybrid-type surfactants with a fluorocarbon chain and a hydrocarbon chain in the molecule4 and reported their solution properties such as their critical micellization concentrations (cmc’s) and Krafft points.5-7 From these investigations it has been noted that the fluoro-hybrid type surfactants are remarkable for their ability to simultaneously emulsify both hydrocarbon oils and fluorocarbon oils. Furthermore, a concentrated aqueous solution of sodium 1-oxo-1[4(tridecafluorohexyl) phenyl]-2-hexane sulfonate (FC6HC4), one of the fluoro-hybrid-type surfactants, has been revealed to exhibit unusual viscoelastic behavior.8 (Its chemical structure is shown in Figure 1.) Tobita et al. reported the results of a temperature study on the viscoelasticity of an aqueous FC6-HC4 solution.9 The phenomenon found in their work was reversible with respect to temperature change, i.e., an aqueous solution (4) Yoshino, N.; Hamano, K.; Omiya, Y.; Kondo, Y.; Ito, A.; Abe, M. Langmuir 1995, 11, 466. (5) Ito, A.; Kamogawa, K.; Sakai, H.; Hamano, K.; Kondo, Y.; Yoshino, N.; Abe, M. J. Jpn. Oil Chem. Soc. 1996, 45, 479. (6) Ito, A.; Kamogawa, K.; Sakai, H.; Hamano, H.; Kondo, Y.; Yoshino, N.; Abe, M. Langmuir 1997, 13, 2935. (7) Ito, A.; Kamogawa, K.; Sakai, H.; Kondo, Y.; Yoshino, N.; Abe, M. Langmuir 1996, 12, 5768. (8) Abe, M.; Tobita, K.; Sakai, H.; Kondo, Y.; Yoshino, N.; Kasahara, Y.; Matsuzawa, H.; Iwahashi, M.; Momozawa, N.; Nishiyama, K. Langmuir 1997, 13, 2932. (9) Tobita, K.; Sakai, H.; Kondo, Y.; Yoshino, N.; Iwahashi, M.; Momozawa, N.; Abe, M. Langmuir 1997, 13, 5054.

10.1021/la990332l CCC: $19.00 © 2000 American Chemical Society Published on Web 12/28/1999

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of FC6-HC4 was found to show a certain thermoresponsive viscoelasticity. The solution properties of FC6-HC4 such as surface activity, surface excess (or surface adsorption amount, Γ/mol m-2), cmc, and degree of counterion binding (β) are very different from common surfactants. The effect of added salt was also required to examine surface tension as well as cmc. Since little thermodynamic study has so far been performed, we first measured the surface tension (γ) of solutions at different temperatures by means of an automated surface tensiometer using a drop volume technique, the temperature of which was strictly controlled by the circulation of thermostated water. Then we determined cmc as a function of temperature ranging from 5 to 50 °C, Γ and β. The collected data on cmc as a function of temperature, β, and literature value of the aggregation number allowed us to calculate the Gibbs energy change (∆G°m) of micelle formation, and the application of the Gibbs-Helmholtz expression (or the van’t Hoff plot of ∆G°m) enabled us to estimate the enthalpy change (∆H°m) and then the entropy change (∆S°m). For discussion of these thermodynamic parameters, FC6-HC4 is compared with various types of surfactants, on which thermodynamic studies have been previously performed. In this paper the effect of added salt on Γ will be discussed in detail. Materials and Methods 2.1. Materials. FC6-HC4 was synthesized and then purified in a similar manner as was reported previously.10 Sodium chloride (NaCl) as an added salt (from Nacalai Tesque Co. Kyoto) was of analytical grade and was roasted at 773 K to remove any surfaceactive impurities before the use. Thrice-distilled water was used as the solvent throughout the experiments. 2.2. Surface Tension Measurements. The surface tension (γ) measurements were performed on the basis of essentially the same drop volume method as reported previously, but an automated surface tensiometer (Yamashita Giken YDS94) was used in the present study. The measurement temperature was controlled by the use of a system (Yamashita Giken, YSC9211) for the surface tensiometer with an accuracy of (0.03 °C at any temperature ranging from 5 to 50 °C. The first drop was permitted to stand for 1.5 h in order to attain the temperature equilibrium, and then in order to estimate the approximate size of the drop the coarse shift of the micrometer was first determined. To attain the adsorption equilibrium, the drop squeezing process was composed of three steps using a computer system. First, a pendant drop whose size was given by ca. 80% of the micrometer shift for a drop was permitted to stand for 15 min (or 20 min if necessary, depending on the stability of measured values), and then an additional 5% was exposed taking 10 s as the second step. And finally the pendant drop (of ca. 85% of a falling drop) was squeezed out in a speed of 1 µm s-1. One measured point was determined from at least five measured values. Whether the measured values for a sample solution scatter or not depends in most cases on the chemical species (especially on the molecular structure) or its concentration.

Results and Discussion 3.1. Adsorption and Added Salt Effect. The surface tension of FC6-HC4 in aqueous solution was measured by the drop volume technique at six temperatures in the range from 5 to 50 °C. First of all, the accuracy of the present drop volume method should be discussed. It might be considered that the use of this technique for investigation of surfactant solutions is dynamic and could give easily reproducible results that are wrong, because the drop interface is rapidly expanded as the drop detaches and (10) Yoshino, N.; Hamano, K.; Omiya, Y.; Kondo, Y.; Ito, A.; Abe, M. Langmuir 1995, 11, 466.

Figure 1. Molecular structures of FC6-HC4 (sodium 1-oxo1[4-(tridecafluorohexyl)phenyl]-2-hexane sulfonate), the RSMy series RSMy‚Me, ‚Et, and ‚Pr (R-sulfonatomyristic acid ethyl ester, methyl ester, and propyl ester, respectively), MEGA-10 (decanoyl-N-methylglucamide), NTM (n-nonyl-β-D-thiomaltoside), and the Eda series EdaC and EdaDC (hydrochloride salts of ethylenediamine monocholate and monodeoxycholate, respectively).

this could lead to higher values of apparent surface tension.11 However, according to Aratono who has employed this method for more than 2 decades for the investigation of surfactant solutions, the accuracy of this method has been confirmed to be sufficiently high from comparison with results determined by the most reliable method of “image analysis of pendant drop”.12 Figure 2 shows plots of the surface tension (γ) vs logarithmic surfactant concentration in pure water at 30 and 50 °C. For comparison, the curves reproduced from the previous work13 for n-nonyl-β-D-thiomaltoside (NTM) and decanoyl-N-methylglucamide (MEGA-10) in pure water are also given in the figure (their chemical structure is shown in Figure 1). In Figure 2, there are found concentrations giving a sharp break referred to as cmc’s. It is seen that FC6-HC4 has a very high surface activity in addition to its strong micelle forming ability and shows the lowest surface tension as well as the lowest cmc compared with the other surfactants (NTM and MEGA10). It is considered that the combination of alkyl (butyl) group, benzene ring with carbonyl group, and a fluorocarbon chain extensively and synergistically contribute (11) Aveyard, R. Private communication. (12) Matsubara, H.; Aratono, M. Submitted for publication in Langmuir. (13) Oda, H.; Nagadome, S.; Lee, S.; Ohseto, F.; Sasaki, Y.; Sugihara, G. J. Jpn. Oil Chem. Soc. 1997, 46, 559 (in Japanese); J. Surf. Sci. Technol. 1998, 14, 1 (in English).

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Figure 2. Surface tension vs concentration curves of FC6HC4 at different temperatures. For comparison, data of NTM and MEGA-10 are included. Table 1. Thermodynamic Parameters at Various Temperatures for FC6-HC4 T/°C

cmc/ mmol kg-1

∆G°m/ kJ mol-1 a

∆H°m/ kJ mol-1

∆S°m/ J K-1 mol-1

5.0 10.0 20.0 30.0 40.0 50.0

0.60 0.58 0.57 0.62 0.71 0.83

-41.5 -42.4 -44.0 -45.1 -46.1 -46.9

9.19 4.65 -3.96 -12.0 -19.5 -26.6

182 166 136 109 85 63

a ∆G° calculated on the basis of the mass action model at 25 °C: m -43.2 kJ mol-1 (aggregation number ) 22).

to these high abilities, although the extent of contribution has not been separately evaluated yet for the respective parts. Table 1 lists the cmc data as a function of temperature determined by the above method. It was found that the curve of the cmc (not shown here) indicates the temperature dependence having a minimum of about 15 °C; this temperature is lower than that for the common ionic hydrocarbon surfactants14 or anionic perfluorocarbon surfactants.15 This suggests that for FC6-HC4 the entropy term in the Gibbs energy change on micelle formation may be comparatively smaller than the enthalpy term, this being different from other surfactants. Next, we examined the effects of added salt (NaCl) on surface tension and on cmc for FC6-HC4 at 30 °C (Figure 3). The concentrations of the added salt are 0.5, 1, 3, and 5 mmol kg-1, respectively. For comparison, the curves, reproduced from our previous work16 for the hydrochloride salts of ethylenediamine monodeoxycholate (EdaDC), a cationic derivative of deoxycholic acid (a kind of bile acid, its chemical structure is shown in Figure 1), is also given (14) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986. (15) Mukerjee, P.; Korematsu, K.; Okawauchi, M.; Sugihara, G. J. Phys. Chem. 1985, 89, 5308. (16) Araki, Y.-I.; Yanagida, T.; Hisatomi, M.; Kiyota, T.; Lee S.; Sugihara, G. J. Jpn. Oil Chem. Soc. 1999 48, 307.

Figure 3. Plot of γ (at a fixed surfactant concentrated below cmc) vs logarithmic molality of counterion.

in the figure. It was found that the effect of added NaCl is very conspicuous on the solution property of FC6-HC4, because the surfactant shows a large lowering of surface tension as well as of cmc within a narrow concentration change of added NaCl ranging from 0.5 to 5 mmol kg-1 compared with that ranging up to 100 mmol kg-1 for EdaDC. Here it is noted that EdaDC has two R-hydroxyl groups attached at positions 3 and 12 of the steroid skeleton and a cationic side chain as the hydrophilic group, while its hydrophobicty mainly comes from the β-side surface of the skeleton. Thus the amphiphilicity resulting from the chemical structure is quite different between the two surfactants, causing a great contrast. To examine the surface adsorption behavior, let us consider thermodynamically the adsorption isotherm. For a 1/1 electrolyte type surfactant, NaS ) Na+ + S- in pure water with no added NaCl, the adsorption amount, Γ(0), is given from the Gibbs adsorption isothermal equation

Γ(0) ) -

dγ 1 2RT d ln mNaS

(1)

where RT is the product of the gas constant in degrees Kelvin and mNaS is the molality of surfactant NaS. Γ is the surface excess.17 And when NaS is in aqueous solution with added NaCl at very high (swamping) concentration, the adsorption amount, Γ(H), is given as the following equation17

Γ(H) ) -

dγ 1 RT d ln mNaS

(2)

But we are now considering the system in aqueous solution with addition of NaCl at a low concentration range so that eq 2 may not be applied to the present system. (17) Aveyard, R.; Haydon, D. A. An Introduction to the Principle of Surface Chemistry; Cambridge Chemistry Texts, Cambridge University Press: London, 1973.

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Hisatomi et al. Table 2. Effect of Added Salt on Surface Excess at a Fixed Concentration of Each Surfactant at 30 °C surfactant

Γtot × 10-6 (mol m-2)

Γ(0) × 10-6 (mol m-2)

∆Γ/∆mNaCl

EdaCa EdaDCb FC6-HC4c

0.15 0.78 1.39

1.31 2.13 3.58

1.16 × 10-2 1.35 × 10-2 43.8 × 10-2

-1 a The fixed concentration for estimate on Γ tot is 2 mmol kg . The fixed concentration for estimate on Γtot is 1 mmol kg-1. c The fixed concentration for estimate on Γtot is 0.15 mmol kg-1.

b

Table 3. cmc, Surface Excess Γ, and Mean Molecular Occupation Surface Area of FC6-HC4 for Added NaCl Concentration at 30 °C

Figure 4. Effect of added NaCl on sarface tension for aqueous solutions of FC6-HC4 and EdaDC at 30 °C. The logarithmic value of mtot is based on molality (mol kg-1).

The total concentration of both electrolytes, mtot, is the same as the respective sums of anionic and cationic species as mtot ) mNaS + mNaCl ) mNa+ ) mS- + mCl-. The adsorption amount of the total system (NaS + NaCl), Γtot, at a fixed concentration of NaS is given by the following equation for the aqueous solution with NaCl added at a low concentration

Γtot ) -

(

)

1 ∂γ 2RT ∂ ln mtot

(3)

mNaS

when mNaS is constant. This expression implies that if the surface tension data are read in the range below cmc at different fixed surfactant concentrations (mNaS) as a function of added NaCl concentration (shown in Figure 3) and the values are plotted against the total concentrations of NaS and NaCl (as given in Figure 4), the surface excess of both electrolytes Γtot can be estimated. (As for derivation of eq 3, see Appendix.) In other words, if surface tension, γ, at a particular surfactant concentration is plotted against the total of surfactant and added NaCl concentrations, the total adsorption amount, Γtot, can be determined from the slope. Since the Γtot is determined at a fixed concentration of surfactant, this enables us to know directly the effect of added salt on Γ or γ, meaning that Γtot or dγ /d ln mtot corresponds to a measure of the effect of added NaCl in surface adsorption. Figure 4 shows plots of γ (at a fixed surfactant concentration below cmc) vs logarithmic molality of total counterion for aqueous solution of FC6-HC4 together with the hydrochloride salts of ethylenediamine monocholate (EdaC) and EdaDC.16 To look at the effect of added NaCl on surface excess estimated at a fixed concentration of each surfactant, in Table 2, the data of Γtot together with Γ(0) are given for different surfactants. The effect of added NaCl on Γtot of FC6-HC4 seems apparently very large when compared with other surfactants. Comparing FC6-HC4 with EdaC, the former is 9.3 times more highly effected than the latter. Only comparison of Γtot and Γ(0) does not lead to an understanding of the actual effect of added salt; therefore, the difference between them must be divided by the added salt concentration range, that is, ∆Γ ()Γ(0) - Γtot)/∆mNaCl, e.g., ∆Γ/∆mNaCl ) (1.31 - 0.15) mol‚m-2/100 mol‚m-3 ) 1.16 × 10-2 for EdaC. In this regard, FC6-HC4 is 38 times more strongly affected by the added salt than EdaC. It is

cmc (mmol kg-1)

added NaCl concn (mmol kg-1)

Γ × 10-6 (mol m-2)

A (Å2)

0.62 0.44 0.37 0.24 0.17

0.0 0.5 1.0 3.0 5.0

3.1 2.1 1.7 1.3 1.0

54 78 95 127 163

noted that the ratio of ∆Γ/∆m lacks physical significance, because it has a dimension of length (e.g., m). For reference, however, calculated values are included in Table 2. On the other hand eq 1 is applicable for the estimation of ΓNaS at a given concentration of added salt, as well. Therefore, it is confirmed that the slopes of the curve below cmc shown in Figure 3 can give the surface excess of the surfactant itself. The estimated Γ values and the mean molecular surface area, A (see eq 4), are included in Table 3 and shown in Figure 5. The above discussion tells us that surfactants such as bile salts (having a few hydroxyl groups as their hydrophilic groups) are resistant to added salts in regard to surface activity or micelle formation, indicating that the status of hydration of hydroxyl groups differs greatly from that of ionic functional groups. However, it should be noted here that the effect of added salt is observed at very low concentrations, so that the ΓNaS value may be affected by the dilution of the surfactant concentration itself, accompanying the lowered cmc in the case of FC6-HC4. Therefore, we need to examine the relation of the surface excess ΓNaS or the mean molecular surface area A with bulk concentration. The ΓNaS and A (A was calculated from the relation A ) 1 /ΓNaSL, where L is the Avogadro constant) were plotted against the cmc of FC6-HC4, as shown in Figure 5. Figure 5B also indicates that A becomes 1/3 when the cmc (the bulk concentration itself) is tripled and the curve resembles a hyperbola. The A is given from eq 1 as follows

A)

RT d ln m dm 1 1 ))K ΓNaSL L dγ dγ m

(4)

and within a range where dm/dγ is almost constant

A ≈ K′

1 m

(5)

where, K and K′ are constants under given conditions. The relation shown in Figure 5B may be interpreted by eq 5, in other words, the large change in A must come mainly from the decrease in bulk concentration. But, regrettably it is not understood why the cmc of FC6-HC4 is subject to a strong effect from added salt. 3.2. Micelle Formation and Added Salt Effect. Turning to the added salt effect on cmc examined at 30 °C, the cmc values as a function of added NaCl concentra-

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Figure 6. Corrin-Harkins plot for determination of degree of counterion binding (mg ) mcmc + mNaCl). The natural logarithmic values were converted from the cmc as well as mg in molality (mol kg-1).

Figure 5. Corelationships between Γ and cmc and between A and cmc in the systems with addition of NaCl. cmc may be regarded as the bulk concentration of monomeric surfactant.

tion are listed in Table 3. As is well-known, the data are indispensable for thermodynamic analysis of micelle formation. The degree of counterion binding to micelle (β) is derived from the following relations.13,15,16,19

∆G°m ) RT ln Xcmc(Xcmc + Xa)β ∆G°m - β ln (Xcmc + Xa) ln Xcmc ) RT

(6)

small β value is ascribed to the lower charge density of micellar surface; this comes from the bulky structure of hydrophobic groups attached to a hydrophilic group (-SO3) or the “top-heavy type” of molecule widening the distance between anionic headgroups. It may be of interest to introduce here that in another paper we have reported the β values for a series of surfactants: sodium salts of R-sulfonatomyristic alkyl (methyl, ethyl, and propyl) esters (RSMy‚Me, ‚Et, and ‚Pr, respectively), which are somewhat similar to FC6-HC4 in terms of “top-heavy type” molecular structure. The β data are 0.7, 0.6, and 0.5 for the methyl, ethyl, and propyl esters, respectively, indicating that as the hydrocarbon side chain attached to R-carbon is lengthened, the β value decreases.19 Next, let us try a thermodynamic analysis and discussion. Here the β value was assumed to be the same at any temperature because it was found that the temperature dependence of β is in general negligible, at least in the case of Na+.18-20 First, the standard Gibbs energy change upon micelle formation should be examined. Applying the following equation derived from eq 6 when no salt is added (Xa ) 0), the standard Gibbs energy change can be calculated using the basic data in Table 3 and β ) 0.57.

∆G°m ) (1 + β)RT ln Xcmc (7)

where ∆G°m is the standard Gibbs energy change upon micelle formation, Xcmc and Xa are concentrations in mole fraction of the surfactant at cmc and of the added salt in aqueous media, respectively. From eq 7 the cmc as a function of added salt concentration is more concisely expressed as, ln cmc ) const.(T,P) - β ln mg. This equation indicates that the β corresponds to the slope of the curve in the plot of logarithmic cmc against logarithmic counterion concentration, i.e., mg ) mcmc + mNaCl; this is called the Corrin-Harkins plot. The plot showed a good linearity with a regression of more than 0.99 at 30 °C and is shown in Figure 6. The β value thus determined from the slope was found to be about 0.57 for FC6-HC4. The β value 0.57 is small as compared with those of other general surfactants ranging 0.7-0.8. This (18) Okano, T.; Tamura, T.; Abe, Y.; Ueda, S.-I.; Lee, S.; Sugihara, G. Submitted for publication in Langmuir. (19) Nakamura, A. A.; Hisatomi, M.; Sugihara, G.; Fujiwara, M.; Okano, T. J. Suf. Sci. Technol. 1998, 14, 23.

(8)

Here it is well-known that, strictly speaking, this equation is derived from the charged phase separation model (PSM)21 and eq 8 must be given with a different expression if based on the mass action model (MAM),22,23 but both models lead to the same expression when the aggregation number of micelles is greater than several tens.22,23 And when it is smaller than several tens, the following equation derived from the MAM is more adaptable.22,23

∆G°m ) (1 + β)RT ln Xcmc +

(RTn) ln[2n (1 + β)] 2

(9)

Here, it may be necessary to examine the standard Gibbs energy change by eq 9 (MAM), because only a small aggregation number (22 at 25 °C) was found for FC6(20) Sugihara, G.; Hisatomi, M. J. Jpn. Oil Chem. Soc. 1998, 47, 661. (21) Shinoda, K. In Colloidal Surfactants; Shinoda, K., Nakagawa, T., Tamamushi, B.-I., Isemura, T., Eds.; Academic Press: New York, 1963; Chapter 1. (22) Moroi, Y. In MicellessTheoretical and Applied Aspects; Plenum: New York, 1992; Chapter 4. (23) Mukerjee, P. Adv. Colloid Interface Sci. 1996, 21, 331.

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Figure 7. Gibbs-Helmholtz plot or the van’t Hoff plot for FC6-HC4.

HC4; it seems too small to apply to PSM. But the ∆G°m, calculated by substituting n ) 22 into eq 9 (MAM), was found to give only a small difference of 800 J between MAM and PSM. So, for simplicity the former PSM is hereafter employed. Calculated ∆G°m values are tabulated in Table 1. The well-known van’t Hoff plot (based on the GibbsHelmholtz equation) was applied for evaluating the enthalpy change on micelle formation, ∆H°m, from the Gibbs energy change; the obtained curve is shown for FC6HC4 in Figure 7. The curvature itself suggests that the enthalpy change upon micellization changes with temperature in parallel with the temperature change in heat capacity (∆CP); this phenomenon has been observed by calorimetry.24-26 Here, the product of the slope with the gas constant corresponds to the enthalpy change as follows:15

[

]

∂(∆G°m/RT) ∂(1/T)

P

)

∆H°m R

(10)

It is seen from the curve that FC6-HC4 forms the most stable micelles at around 15 °C; this temperature is lower than common ionic surfactants. Further, using the estimated ∆H°m value, the entropy change, ∆S°m, can be calculated from the relation ∆S°m ) (∆H°m - ∆G°m)/T. In Table 1 it is shown that the enthalpy term changes from positive (endothermic) to negative (exothermic) at the temperature corresponding to the minimum of the cmc-temperature curve. On the other hand, although temperature is raised, the entropy term on micelle formation decreases monotonically with temperature. This arises because the “structured water layer” around the hydrophobic moiety of a monomer surfactant ion becomes “thinner” as temperature increases or alternatively the degree of structure in the water layer decreases. Therefore, the extent of randomness increase (producing a free energy gain) upon micelle formation becomes less and less with increasing temperature, meaning that the contribution of entropy term to the free energy change is lowered. Concerning the relationship between entropy and enthalpy it has been observed in general that both the (24) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (25) Naghibi, H.; Tomura, A.; Sturtevant, J. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 5597. (26) Pestman, J. M.; Kavelam, J.; Blandamer, M. J.; van Doren, H. A. Langmuir 1999, 15, 2009.

Figure 8. Enthalpy-entropy compensation phenomena observed for various surfactants. Cited from ref 15 for R-SMy‚Pr (b), ref 14 for EdaDC (2), and EdaC (0) and ref 11 for MEGA-10 (4). The numerical figures by the measured points indicate the temperature in °C.

thermodynamic quantities compensate each other; when the enthalpy term is less contributable to free energy, its counterpart the entropy term more effectively contributes to leading the free energy to become a larger negative value and vice versa.27 This is known as the so-called compensation phenomenon and also, in the plot of enthalpy vs entropy, is seen as good linearity with a slope having the dimension of the Kelvin temperature, called the compensation temperature24,27 (in Figure 8). This temperature was found to be 307 ( 8 K for almost all the surfactants in water.28,29 Kresheck and Hargraves obtained about 300 K of the compensation temperature for micellization of various surfactants.24 It has been considered that the compensation temperature has no significant meaning but a geometric mean of temperatures studied, and discussion about it has been made in more detail elsewhere.28,29 The entropy values corresponding to the intercept at ∆H°m ) 0 are characteristic of the respective surfactant species, because the Gibbs free energy change on micelle formation is contributed only from the entropy term. Therefore, the temperature at the intercept corresponds to that of the minimum of the temperature-cmc curve, so that it may be called a characteristic temperature. As for the characteristic temperature, R-SMy‚Pr has the lowest and is followed by FC6-HC4, while those having several hydroxyl groups in their hydrophobic group such as EdaC and MEGA-10 have characteristic temperatures higher than room temperature. Examining the location of values at the room-temperature range (20-30 °C), (27) Lumry, R.; Rajender, S. Biopolymeres 1970, 9, 1125. (28) Sugihara, G.; Hisatomi, M. J. Colloid Interface Sci. 1999, 219, 31. (29) Sugihara, G.; Hisatomi, M.; Nakano, T.-Y.; Sulthana, S. B.; Rakshit, A. K. Submitted for publication in Colloids Surf., A. (30) Aveyard, R.; Brinks, B. P.; Chen, J.; Esquena, J.; Fletcher, D. I. Langmuir 1998, 14, 4699.

Study of Hybrid Anionic Surfactants

MEGA-10 and EdaC are entropy-dominant (the enthalpy change is positive), while the “top-heavy type” surfactants are enthalpy-dominant, and EdaDC is between both types. Above all, FC6-HC4 exhibits the largest extension covering the same temperature range from 10 to 50 °C and the highest entropy value, even in this regard FC6-HC4 is a unique surfactant. In regard to thermodynamics of the adsorption and micelle formation of such surfactants as studied here, it is important to pay special attention to a very recent study (by Aveyard et al.30) on the effects of changes in temperature and electrolyte (NaCl) concentration on the surfaceand-colloid chemistry of systems containing pure sugar surfactants. Reading their fruitful work will enable one to derive more comprehensive information from the present work. In conclusion, the surface excess Γ and the cmc of FC6HC4 were determined as functions of temperature and added salt (NaCl) concentration. A conspicuous effect of added salt on the surface activity of aqueous solution was observed when compared to common surfactants. With respect to the adsorption at air/water interface, a theoretical analysis was made in the treatment with the Gibbs adsorption isotherms obtained at different conditions and it demonstrated that FC6-HC4 is subject to a markedly high influence from added salt as compared with any other surfactant. The low degree of counterion binding (determined from the Corin-Harkins plot) was attributed to the “top-heavy” structure of FC6-HC4 molecules. The thermodynamic parameters, ∆G°m, ∆H°m, and ∆S°m were determined as a function of temperature, and the compensation rule was confirmed to hold between ∆H°m and ∆S°m. Even in the ∆H°m - ∆S°m compensation phenomenon, FC6-HC4 showed unique behavior. Acknowledgment. The present work was in part supported by grants from the Ministry of Education, Culture and Science of Japan (Grant in Aid for Scientific Research, C-07680729, and that on Priority Areas, 09261240), and the Central Institute of Fukuoka University. Appendix Equation 3 is derived by quoting ref 17 as the following. First, if the chemical potential of species i is denoted as µi, the slight change in surface tension, taking account of the surface phase is represented as

-dγ ) ΓNa+ dµNa+ + ΓS- dµS- + ΓCl- dµCl- + ΓH+ dµH+ + ΓOH- dµOH- + ΓH2O dµH2O (1′) The terms for H+ and OH- may be neglected, and from the combination of eq 1′ with the Gibbs-Duhem expression, the following equation may be derived

nNa+ nSnCldµNa+ dµS- dµ (2′) dµH2O ) nH2O nH2O nH2O Clwhere, nj denotes the molar quantity (mole number) of species j.

Langmuir, Vol. 16, No. 4, 2000 1521

(

-dγ ) ΓNa+ -

)

(

)

nNa+ nSΓH2O dµNa+ + ΓS- Γ × nH2O nH2O H2O

(

dµS- + ΓCl- -

)

nClΓ dµCl- (3′) nH2O H2O

For convenience or simplicity, here, two anions, S- and Cl-, are treated as X- ) S- + Cl-. Considering that both bulk and surface phases should be electrically neutral, eqs 4′ and 5′ are given. Here, it is noted that the concentration of Na+ is always the same as the total concentration of NaS and NaCl. Then eq 3′ is rewritten as eq 6′, using eqs 4′ and 5′.

(

nNa+ ) nS- + nCl- ) nX- ≡ ntot

(4′)

ΓNa+ ) ΓS- + ΓCl- ) ΓX- ≡ Γtot

(5′)

-dγ ) ΓNa+ -

)

nNa+ Γ dµNa+ + nH2O H2O

(

ΓX- -

)

nXΓ dµX- (6′) nH2O H2O

When eq 6′ is expressed with the activity, a, the following relation is obtainable by using eqs 4′ and 5′.

-

(

)

nNa+ dγ ) ΓNa+ Γ d ln aNa+aX- ) RT nH2O H2O

(

Γtot -

)

ntot Γ d ln aNa+aX- (7′) nH2O H2O

Here, the mean activity of NaS + NaCl is given by

a2( ) aNa+ aX-

(8′)

where, aX- was regarded as a mean activity of S- and Clions (a2X- ) aS-aCl-). Therefore, eq 7′ is rewritten in terms of the total surface excess Γtot of NaS + NaCl relative to H2O (on the basis of the Gibbs’ dividing surface17), as follows.

-

dγ ) 2Γtot d ln a( RT

(9′)

In addition, since the system is a dilute solution, the mean activity may be assumed to be equal to the molality of the solutes, as

a( ≈ mX- ) mNa+ ) mNaS + mNaCl ) mtot and then in eq 9′ ln mtot is used instead of ln a(. Thus, we have the following relations.

-

dγ ) 2 Γtot d ln mtot RT

Γtot ) -

(

)

dγ 1 2RT d ln mtot

(10′)

This equation may be applied to either the case where mNaS is kept constant but mNaCl is changed or the case where mNaS is changed at a constant mNaCl. The former is to examine the added salt effect on γ and the latter is to see the effect of NaS concentration on γ at a given NaCl concentration. LA990332L