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Effects of Side Chain Length and Degree of Counterion Binding on Micellization of Sodium Salts of r-Myristic Acid Alkyl Esters in Water: A Thermodynamic Study Tomomichi Okano,† Takamitsu Tamura,† Toshi-Yuki Nakano,‡ Shu-Ichi Ueda,‡ Sannamu Lee,‡ and Gohsuke Sugihara*,‡ Better Living Research Lab./Material Science Research Center, Lion Company, 7-13-12, Hirai, Edogawa-ku, Tokyo 123-0035, Japan, and Department of Chemistry, Faculty of Science, Fukuoka University, Jonan-ku, Fukuoka 814-0180, Japan Received December 6, 1999 Temperature studies were performed on the micelle formation of a series of anionic surfactants, i.e. Na salts of R-sulfonatomyristic acid methyl, ethyl, and propyl esters (abbreviated as R-SMy‚Me, R-SMy‚Et and R-SMy‚Pr, respectively) in water, paying special attention to the effects of the number of carbon atoms in the alkyl chain attached near the hydrophilic group (-SO3) on micellar properties, such as critical micellization concentration (cmc) and the degree of counterion binding (β) or the degree of electrolytic dissociation of micelles (R). The correlation among cmc, β, and hydrophobicity was discussed in terms of thermodynamic parameters or the changes in the Gibbs free energy, enthalpy, and entropy upon micelle formation (∆G°m, ∆H°m, and ∆S°m, respectively). The cmc of the R-SMy‚series surfactants decreases with increased hydrophobicity, as is expected. The degrees of counterion binding (β) are ca. 0.7 for R-SMy‚Me, ca. 0.6 for R-SMy‚Et, and ca. 0.5 for R-SMy‚Pr in line with increasing hydrophobicity of the side chain, indicating that the larger alkyl group near the headgroup leads to less Coulombic repulsion between headgroups. The absolute value of negative ∆G°m increases in the order R-SMy‚Pr < R-SMy‚Et < R-SMy‚ Me, in parallel with the increasing order of β. A clear linear relation (the compensation rule) completely holds between ∆H°m and ∆S°m for each surfactant studied, as have been observed for different surfactants.
Introduction A novel series of anionic surfactants studied here are the sodium salts of R-sulfonatomyristic acid methyl, ethyl, and propyl esters (R-SMy‚Me, R-SMy‚Et, and R-SMy‚Pr, respectively). These relatively new surfactants have been known to show a good biodegradability1 and a quick availability from renewable vegetable material1-4 in addition to their high tolerance against calcium ions.1,5 From a scientific standpoint, thermodynamic analyses for a representative of this series, R-SMy‚Me, have been made on the basis of the data of critical micellization concentration (cmc) and degree of counterion binding to micelles (β) or degree of micellar electrolytic dissociation (R);6,7 the study on R-SMy‚Me was extended onto R-SMy‚Et by Nakamura et al.8 In previous papers, the differential conductance (derived from the specific conductance (κ) as a function of molarity (C)), dκ/dC, plotted against xC, was demonstrated to be applicable for not only pure surfactant systems but also * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +81-92-865-6030. † Lion Company. ‡ Fukuoka University. (1) Yoneyama, Y. J. Jpn. Oil Chem Soc. (Yukagaku) 1995, 44, 2. (2) Steber, J.; Wierrich, D. Tenside Surfactamte Deterg. 1989, 26, 406. (3) Masuda, M.; Odake, H.; Miura, K. J. Jpn. Oil Chem. Soc. (Yukagaku) 1994, 43, 617. (4) Satsuki, T.; Umehara, K. Yoneyama, Y. Am. Oil Chem. Soc. 1992, 69, 672. (5) Fujiwara, M.; Miyake, M.; Abe, Y. Colloid Polym. Sci. 1993, 271, 780. (6) Fujiwara, M.; Okano, T.; Nakashima, T. H.; Nakamura, A. A.; Sugihara G. Colloid Polym. Sci. 1997, 275, 474-479. (7) Sugihara, G.; Nakamura, A. A.; Nakashima, T. H.; Araki, Y. I.; Okano, T.; Fujiwara, M. Colloid Polym. Sci. 1997, 275, 790. (8) Nakamura, A. A.; Hisatomi, M.; Sugihara, G.; Fujiwara, M.; Okano, T. J. Surf. Sci. Technol. 1998, 14, 23.
those with added NaCl in the determination of cmc. This method was confirmed to be superior in accuracy to the conventional κ vs C plot. Thus the β-values were determined from the Corrin-Harkins plot at discrete temperatures. In addition, when the experimental results of the degree of micellar dissociation were taken as REX ) 1 β, and then the REX was tentatively plotted against the ratio of the slopes (SM/S1) above and below cmc, a linear relation was obtained for each (the ratio has often been regarded as R ) SM/S1). However, the relation exhibited neither the unity slope nor the zero intercept. Since there remains a problem to be solved for the estimation of degree of micellar dissociation from conductivity data,8 this problem should be further discussed. Standard Gibbs energies, enthalpies, and entropies of micelle formation are very important in understanding micellization of surfactants in solutions. With cmc and β as functions of temperature, the standard Gibbs energy change (∆G°m) was first evaluated using the phase separation model and then from the Gibbs-Helmholz plot (or the van’t Hoff plot). The standard enthalpy and entropy changes (∆H°m and ∆S°m) were evaluated and compared between R-SMy‚Me and R-SMy‚Et.8 In addition, the enthalpy-entropy compensation relation was found to hold true in micelle formation for both surfactants8 as well as for more than 15 different surfactants in aqueous solution.9 In this paper, following the previous studies for R-SMy‚Me6,7 and for R-SMy‚Et,8 we performed a thermodynamic study on micelle formation of R-SMy‚Pr systematically. By comparing the results for these three surfactants, we demonstrate not only the effect of the number of carbon atoms of the alkyl group attached closely to the sulfonic group on solution properties of the series (9) Sugihara, G.; Hisatomi, M. J. Colloid Interface Sci. 1999, 219, 31.
10.1021/la991585h CCC: $19.00 © 2000 American Chemical Society Published on Web 03/18/2000
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surfactants but also the contribution of counterion binding to the free energy change upon micelle formation. Experimental Section R-SMy‚Pr was synthesized in a manner similar to the ones used for R-SMy‚Me and R-SMy‚Et as reported previously.1-4 The purity of the sample (100%) was confirmed by using column chromatography of an Inertsil ODS (GL Science Co, φ 4.6 × 250 mm) and mixed solution of methanol/water/0.05 M Na citrate ) 85/13/2 including 0.1% tetramethylammonium chloride at flow rate of 0.5 mL‚min-1. Sodium chloride (obtained from Nacalai Tesque Co., Kyoto, Japan) was of analytical grade and used as an added salt after roasting at 800 °C to remove surface active impurity. The electroconductivity measurement was carried out using a TOA electric conductivity meter, model CM-40S, together with a spouted cylinder type cell combined with a TOA electrode (CG-201PL). A 250 µL Hamilton microsyringe was used for injecting the sample solution through the spout; 15 cm3 of solvent (pure water or aqueous solution of NaCl at each concentration) was initially contained in the cell. The solution was continuously stirred by an Acrobat stirrer (MS KiKi Co.) in the cell dipped in a water bath, the temperature of which was controlled within a range of (0.05 K by using a Thomas Kagaku thermostatic water bath (TRL-N11). Thrice-distilled water was used throughout the experiment.
Results and Discussion 1. Critical Micellization Concentration (cmc) and Degree of Counterion Binding (β). As has been described previously,6-8 a more accurate determination of cmc is attained from the plot of differential conductivity (∂κ/∂C)T,P vs square root of concentration in mM (xC) as compared with what is possible using the conventional plot of specific conductivity (κ) vs concentration (C). In particular, the former plot is superior to the latter in determination of cmc for the systems with the addition of NaCl. In the plot of κ vs C, the intersection angle of the two curves of κ vs C above and below cmc is not so sharp that the determination of the intersection point encounters difficulty especially in solutions involving added salts. In a comparison of the methods of κ vs C and (∂κ/∂C)T,P vs xC h , 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 range is only (2%.7 Here it is noted that, in the plot h , (∂κ/∂C)T,P was assumed as being of (∂κ/∂C)T,P vs xC approximately equal to ∆κ/∆C, where ∆κ ) κi+1 - κi, ∆C h ) (Ci+1 + ) Ci+1 - Ci at the ith measured point and C Ci)/2, and that, in the actual treatment of concentration, molality m/mol‚kg-1 is regarded as being approximately equal to molarity C/mol‚dm-3 because the solutions investigated were very dilute. In this text, hereafter, (∂κ/ h will be expressed as dκ/dC and C, respectively. ∂C)T,P and C In the upper frame (A) of Figure 1, the specific conductance (κ) is plotted against the milimolality (mmol‚kg-1) of R-SMy‚Pr and the determination of cmc is indicated by the intersection of two straight lines in which the slopes below and above cmc are indicated by S1 and SM according to the literature.10,11 In the lower frame (B), the differential conductivity dκ/dC is plotted against the square root of milimolarity (mmol‚dm-3). On the basis of the definition in the literature,12,13 the cmc was regarded as the concentration giving a central point of the reverse sigmoid, similar to the previous works.6-8 In this figure, (10) Lianos, P.; Lang, J. J. Colloid Interface Sci. 1983, 96, 222. (11) Tamaki, K.; Kobayashi, K.; Nomura, T.; Iijima, M.; Shimoi, M. J. Jpn. Oil Chem. Soc. 1977, 46, 209. (12) Moroi, Y.; Matuura, R. Bull. Chem. Soc. Jpn. 1988, 61, 333. (13) Moroi, Y. In Micelles-Theoretical and Applied Aspects; Plenum: New York, 1992; Chapter 4.
Figure 1. Determination of cmc for R-SMy‚Pr in pure water. (A) Plot of specific conductivity vs concentration. S1 and SM indicate the slopes below and above cmc, respectively. (B) Plot of differential conductivity vs square root of concentration. The various Λ values are defined in the text.
Figure 2. The temperature dependence of cmc for R-SMy‚Me, R-SMy‚Et, and R-SMy‚Pr at different concentrations of added NaCl in mmol kg-1.
Λi’s (i ) 0, 1, C, ...) are the representative dκ/dC values (having the same dimension of molar conductance; S cm2 mol-1) corresponding to the values at infinite dilution (Λ0), at just below cmc (Λ1), at cmc (Λc), at just above cmc (ΛM′), and at a concentration sufficiently higher than cmc (ΛM). These different Λ values will be used for discussion later. Figure 2 shows the curves of cmc change with temperature for the present series of surfactants including those for displaying the effect of added salt (NaCl) concentration on the cmc for R-SMy‚Pr at the respective
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Table 1. Data for cmc and Degree of Counterion Binding β for r-SMy‚Me, r-SMy‚Et, and r-SMy‚Pr at Discrete Temperatures with Error Margins Indicated by Numerical Values with ( cmc/mmol‚kg-1 temp/°C R-SMy‚Me ((0.03) R-SMy‚Et ((0.02) R-SMy‚Pr ((0.02) 15 20 25 30 35 40 45 50
3.23 3.18 3.15 3.17 3.25 3.35 3.49 3.67
1.99 1.97 1.98 2.01 2.06 2.14 2.25 2.37
1.24 1.23 1.25 1.28 1.33 1.41 1.50 1.61
β temp/°C R-SMy‚Me ((0.01) R-SMy‚Et ((0.01) R-SMy‚Pr ((0.01) 15 20 25 30 35 40 45 50
0.72 0.72 0.72 0.72 0.71 0.71 0.71 0.70
0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58
0.50 0.51 0.49 0.49 0.48 0.48 0.47 0.47
temperatures. The curve of R-SMy‚Me reaches its minimum at ca. 24 °C as have been observed for various ionic surfactants.13-17 Those for the other two surfactants are likely to have a minimum at a lower temperature than that studied. (In regard to the ∆H-∆S relation, the temperature giving a minimum will be discussed later.) As the number of carbon atoms of the alkyl ester group is increased, cmc is lowered; R-SMy‚Et is lower by ca. 1 mmolality than R-SMy‚Me and R-SMy‚Pr is lower by ca. 0.8 mmolality than R-SMy‚Et as is expected from the enhancement of total hydrophobicity. As for the added salt effect, it should be noted that cmc decreases markedly within the low concentration range of the added NaCl. All the cmc data obtained for the present series of surfactants at the respective temperatures are listed in Table 1. The logarithmic cmc values at different counterion concentrations are plotted against logarithmic concentrations of counterion (Na+) at discrete temperatures, as shown in Figure 3. This plot is known as the CorrinHarkins relation, usually giving us a linear relation the slope of which corresponds to the degree of counterion binding (β). The determined β values are tabulated in Table 1 in which the values for R-SMy‚Me and R-SMy‚Et are also included for comparison. The β values are found to range around 0.5 for R-SMy‚Pr, 0.6 for R-SMy‚Et,8 and 0.7 for R-SMy‚Me6 and to be a little dependent on temperature. Each value of β has an experimental error margin of (0.01, corresponding to 2% at most. The decreasing order of the β value, comparing among three surfactants the hydrophobicity near the headgroups or the geometrical largeness of headgroup moiety, indicates that the larger hydrophobic shoulder of top-heavytype molecules keeps the distance between charged headgroups longer, and as a result, the necessity of partial neutralization by counterions becomes less. This growth of shoulder with an increase in the number of carbon atoms must affect the energetics of micelle formation in a different manner than the growth of hydrocarbon tail (14) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986. (15) Shinoda, K.; Katsura, K. J. Phys. Chem. 1964, 68, 1568. (16) Mukerjee, P.; Korematsu, K.; Okawauchi, M.; Sugihara, G. J. Phys. Chem. 1985, 89, 5308. (17) Shinoda, K. In Colloidal Surfactants; Shinoda, K., Nakagawa, T., Tamamushi, B.-I., Isemura, T., Eds.; Academic Press: New York, 1963; Chapter 1.
Figure 3. Corrin-Harkins plots for R-SMy‚Pr at various temperatures, where mg denotes total concentration of counterion (mg ) mcmc + mNaCl). The slope or β-value is indicated for each straight line.
length, as will be demonstrated later. It may be of interest to introduce here that a top heavy and hybrid-type anionic surfactant, sodium 1-oxo-1[4-(tridecafluorohexyl)phenyl]2-hexanesulfonate (FC6-HC4) also has a β value as small as 0.57 compared with those of other general surfactants which range from 0.7 to 0.8 and that the added salt effect on lowering cmc was prominently marked.18 Table 1 indicates that the β value for each species has a trend to decrease with temperature; this, accordingly, implies that the degree of ionization of micelles or counterion dissociation (R) increases with raised temperature. In other words as the temperature becomes further away from the Krafft point at which β ) 1 and R ) 0 are attained, the R-value increases. If one looks at the cmctemperature curves (shown in Figure 2), even though a shallow minimum is observed, the respective curves on an across-the-board basis show an increasing trend of cmc. If cmc is regarded as the solubility of micelles, R increases with temperature in parallel with the increased solubility of micelles. To begin with, R and β involve complicated factors such as temperature, electrical potential around the micelle, micellar radius, dielectric constant of the medium, etc. (pp 61-66 in ref 13). The gross features of the counterion binding or distribution between the kinetic micelle and the bulk solution can be understood in simplified electrostatic models,13 and the stabilization of micelles by counterion binding is attained on a balance between kinetic motion of ions and electric potential on micellar surface; this balance eventually results in the decrease in β or the increase in R with increased temperature. In other words, the binding of counterions (their adsorption onto micellar surface) is an exothermic process while the electrolytic dissociation of micelles (desorption of counterions) is an endothermic one. 2. Thermodynamic Analysis. In the meantime, the collected data of cmc and β as a function of temperature as shown in Table 1 enabled us to analyze thermodynamic energetics of micelle formation in water. First, the standard Gibbs energy change upon micelle formation should be examined. With application of the following equation, the standard Gibbs energy change, ∆G°m, can be calculated by the use of the basic data in Table 1: (18) Hisatomi, M.; Abe, M.; Yoshino, N.; Lee, S.; Nagadome, S., Sugihara, G. Langmuir 2000, 16, 1515.
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∆G°m ) (1 + β)RT ln Xcmc
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(1)
Here, RT is the product of the gas constant and the Kelvin temperature and Xcmc is the cmc in terms of the mole fraction in the solution. Here, it is well-known that, strictly speaking, this equation is derived from the charged phase separation model17 and eq 1 must be given by a different expression if it is to be based on the mass action model.13,19 But both models lead to the same expression when the aggregation number of micelles is greater than several tens.13 The previous light scattering study has shown that the aggregation number of R-SMy‚Me is several tens5 so that eq 1 also satisfies the mass action model within a good approximation. This may also be the case for R-SMy‚Et and R-SMy‚Pr. In Figure 4, ∆G°m divided by RT is given as a function of reciprocal temperature for three surfactants (Figure 4 indicates the curves of (1 + β) ln Xcmc vs 1/T). From this figure it is known that all the curves are downward convex (in contrast to nonionic surfactants which show a cmc-temperature curve that is upward convex), ∆G°m of R-SMy‚Pr is the highest (the negative ∆G°m value is the lowest), and the three surfactants exhibit a slightly increasing trend with raised temperature. Figure 4 corresponds to the Gibbs-Helmholtz plot from which the enthalpy change on micelle formation, ∆H°m, can be evaluated. Here, the product of the slope with the gas constant is equal to the enthalpy change as follows:
[
]
∂(∆G°m/RT) ∂(1/T)
p
)
∆H°m R
(2)
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. All the thermodynamic parameters are tabulated in Table 2, including those of R-SMy‚Me and R-SMy‚Et. Comparing enthalpy changes determined by calorimetry and those determined from the temperature dependence of the cmc, Kresheck and Hargraves concluded that the two approaches should not be assumed to yield identical values.20 Naghibi et al.21 have also shown that the usual assumption is not valid in many cases. The assumption is, as is taken in studies of temperature variation of equilibrium constants (K) for equilibria of the form A + B a AB, that a plot of ln K vs 1/T is to give a straight line with slope equal to ∆HvH/R (∆HvH ) van’t Hoff or apparent enthalpy). Very recently, Pestman et al.22 have demonstrated that enthalpies of micellization can be accurately obtained using titration microcalorimetry for various carbohydrate-derived surfactants in water. As they have pointed out, the present data of enthalpy change on micellization may involve a certain difference from the calorimetrically measured enthalpy, if the calorimetry could be carried out. However, in the present study, not only the cmc data but also those of β for ionic surfactants were precisely determined as a function of temperature so that the plots of ∆G°m/RT vs 1/T (we call the plots not van’t Hoff but Gibbs-Helmholtz plots23) give (19) Mukerjee, P. Adv. Colloid. Interface. Sci. 1996, 21, 331. (20) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (21) Naghibi, H.; Tamura, A.; Sturtevant, J. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 5597. (22) Pestman, J. M.; Kavelam, J.; Blandemer, M. J.; van Doren, H. A.; Kellogg, R. M.; Engberts, J. B. F. N. Langmuir 1999, 15, 2009. (23) Okano, T.; Tamura, T.; Abe, Y.; Tsuchida, T.; Lee, S.; Sugihara, G. Langmuir 2000, 16, 1508.
Figure 4. Gibbs-Helmholtz plots for R-SMy‚Me, R-SMy‚Et, and R-SMy‚Pr. Table 2. Thermodynamic Parameters of r-SMy‚ Series Surfactants at Various Temperatures ∆G°m/kJ mol-1 T/°C
R-SMy‚Me
R-SMy‚Et
R-SMy‚Pr
15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
-39.5 -40.2 -40.7 -41.2 -41.7 -42.0 -42.4 -42.7
-40.1 -40.9 -41.6 -42.2 -42.8 -43.3 -43.7 -44.0
-38.7 -39.1 -39.5 -40.1 -40.3 -40.8 -40.9 -41.3
∆H°m/kJ mol-1 T/°C
R-SMy‚Me
R-SMy‚Et
R-SMy‚Pr
15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
8.28 3.24 -1.63 -6.35 -10.9 -15.3 -19.6 -23.7
-2.73 -6.27 -9.69 -13.0 -16.2 -19.3 -22.3 -25.2
-10.5 -12.8 -15.1 -17.3 -19.4 -21.5 -23.4 -25.4
∆S°m/J K-1 mol-1 T/°C
R-SMy‚Me
R-SMy‚Et
R-SMy‚Pr
15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
190 160 133 106 80.7 56.6 33.6 11.8
128 116 104 93.0 82.6 72.5 63.0 54.1
98.1 89.9 81.9 75.3 67.9 61.7 54.9 49.2
a line with curvature and accordingly a marked temperature dependence of the enthalpy change. Our ∆H°m data are considered to approximate true enthalpy. In the case of the ∆G°m/RT vs 1/T plot, the temperature dependence of ∆H°m may come from the changes in aggregation number (size) and shape18 as well as heat capacity change with temperature,20 being different from the equilibria of the A + B a AB type.21 Here it may be noted that, in the study of pure sugar surfactants in hydrocarbon + water systems, Aveyard et al. have shown a very linear relation in the van’t Hoff plot of the distribution coefficients for the distribution of decyl β-glucoside between toluene and water.24 (24) Aveyard, R.; Binks, B. P.; Chen, J.; Esquena, J.; Fletcher, P. D. I. Langmuir 1998, 14, 4699.
Micellization of R-Myristic Acid Alkyl Esters
Figure 5. Enthalpy and entropy terms as a function of temperature.
In Figure 5, ∆H°m and the entropy term T∆S°m are plotted against the Kelvin temperature, respectively. Since the larger negative values of ∆G°m and ∆H°m and the larger positive value of T∆S°m are generally favorable to micelle formation, the ordinates are taken as -∆H°m and T∆S°m. It should again be noted that although cmc values are lowered in the order of R-SMy‚Me, R-SMy‚Et, and R-SMy‚ Pr, the ∆G°m values are raised in the same order (their absolute values become smaller). This order is increasing order of total hydrophobicity, but the free energetical gain on micellization goes into reverse. This reversion is caused by the decreased β values, indicating that the Coulombic interaction term works very effectively for free energetical stabilization in micelle formation. In the examination of T - ∆H°m relations (see Figure 5A), R-SMy‚Pr has the largest negative ∆H°m which plays the most important role in micelle formation (to make ∆G°m negative) in comparison with the other surfactants, at least in the temperature range studied. Further, R-SMy‚ Pr exhibits the smallest temperature dependence in ∆H°m; this must come from the lowest β value as well as the most hydrophobic headgroup, although the details are unknown yet. In contrast, with respect to the contribution of the entropy term (-T∆S°m) to resulting in the largest negative ∆G°m, R-SMy‚Pr is inferior to the other two, as is seen from Figure 5B, over the temperature range studied. All the R-SMy‚alkyl surfactants have a decreasing trend in the absolute value of -T∆S°m with increasing temperature, indicating that the raised temperature leads to reduction in entropy or randomness in the total system. Comparing the enthalpy and entropy terms (see Figure 5A,B), we become aware of something related to the mutual correspondency, that is, the enthalpy-entropy compensation phenomenon which has been found for a variety of processes of small solutes25-27 including surfactants9,20,28-31 in aqueous solution. (25) Lumry, R.; Rajender, S. Biopolymers 1970, 9, 1125. (26) Jolicoeur, C.; Philip, R. P. Can. J. Chem. 1974, 52, 1834. (27) Krishnan, V. C.; Friedman, L. H. J. Solution Chem. 1974, 2, 37.
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Figure 6. Plots of the estimated entropy changes against the estimated enthalpy changes for R-SMy‚Me, R-SMy‚Et, and R-SMy‚Pr. The enthalpy-entropy compensation relation (empirically expressed as ∆H°m ) (1/303)∆S°m + σ) holds for all R-SMy series surfactants. The numbers near the measured points indicate the temperature in °C (of some points for R-SMy‚ Me and R-SMy‚Pr and of all points for FC6-HC4).
Since the compensation phenomenon was for the first time found as early as in 1938 by Barkley and Butler,32 little literature about micellization is available other than cited here.9,20,28-31 The details of the enthalpy-entropy compensation phenomena observed for aqueous surfactant systems have been very recently described elsewhere by Chen et al.31 as well as by us.9 However, it is worthwhile discussing in more detail the respective contributions of ∆H°m and ∆S°m to the micelle formation (or to ∆G°m) of the present systems, so we plotted ∆S°m against ∆H°m (see Figure 6). Interestingly, the three surfactants have almost the same slope (ca. 1/303 (K-1)), indicating that (i) the reciprocal of the slope, which is called the compensation temperature (Tc), is ca. 303 K, (ii) the intercept is not much different but its value clearly depends on species, and (iii) ∆H°m values of R-SMy‚Pr and R-SMy‚Et between 15 and 50 °C are restricted to the negative region while that of R-SMy‚Me in the same temperature range changes most widely (going into the positive region). We have examined the ∆H°m - ∆S°m relations of more than 15 species of surfactants including nonionic, anionic, and cationic ones reported in the past and found that each surfactant shows a fine linear relation having almost the same slope of 1/307 (K-1) within a small margin of error but a different intercept (σ) depending on the species. The empirical expression is as follows:
∆S°m )
1 ∆H°m + σ Tc
(3)
Here, σ corresponds to the entropy change at a specific (28) Goto, A.; Takemoto, M.; Endo, F. Bull. Chem. Soc. Jpn. 1985, 58, 247. (29) Aoki, K.; Noda, T.; Fuji, K.; Murata, M.; Hiramatsu, H. J. Oil Chem. Soc. Jpn. (Yukagaku) 1984, 33, 20. (30) Singh, N. H.; Saleem, M. S.; Singh, P. R.; Birdi, S. K. J. Phys. Chem. 1980, 84, 2191. (31) Chen, L.-J.; Lin, S.-Y.; Huang, C.-C. J. Phys. Chem. B 1998, 102, 4350. (32) Barkley, I. M.; Butler, J. A. V. Trans. Faraday Soc. 1938, 34, 1445.
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Figure 8. Correlation between REX and ΛM′/Λ° (Λ1).
ΛM and Λ° are the molar conductances of micelles and of monomeric surfactants at infinite dilution, respectively (see Figure 1), and gave a relation as7 Figure 7. Correlation between the Gibbs energy change upon micelle formation and number of carbon atoms of side alkyl chain attached to a carbon of myristic acid at different temperatures.
temperature giving ∆H°m ) 0 at which the driving force of micelle formation comes only from the entropy term. When the phase separation model is applied to micelle formation, σ is R ln cmc for nonionic surfactants and (1 + β)R ln cmc for ionic surfactants.9 Previously we reported that Tc ranges 307 ( 8 K for different surfactants. For comparison, Figure 6 includes the ∆H°m - ∆S°m relation for FC6-HC4, which has a steric structure similar to R-SMy‚Pr but includes a fluorocarbon chain. The compensation temperatures are 303 K for all the R-SMy series surfactants and 299 K for FC6-HC4.9,18 The latter exhibits that the temperature of minimum cmc is ca. 16 °C and a higher intercept σ compared to the former. Chen et al.31 employed the plot of ∆H°m against ∆S°m and expressed the relation as
∆H°m ) ∆H/m + T∆S°m They evaluated the intercept ∆H/m as a function of carbon atom numbers, showing that the stronger the hydrophobicity, the larger the negative value of ∆H/m. Figure 6 also indicates that FC6-HC4 has a larger negative value compared to the R-SMy series; however, interestingly, the latter ones almost have the same ∆H/m values irrespective of difference in hydrophobicity. To view the effect of the number of carbon atoms of alkyl side chain esterified R-carbon of myristic acid on the Gibbs energy change upon micelle formation, the correlationship of ∆G°m with the number of carbon atoms is demonstrated at several temperatures (see Figure 7). Interestingly, in contrast to the ordinal decrease in ∆G°m with increasing numbers of carbon atoms in the hydrophobic hydrocarbon tail,13 the results show an increasing trend; from the slope, for instance at 30 °C, ∆G°m per methylene group is estimated as ca. +1 kJ. In conclusion, introducing alcohols esterified at R-carbon of fatty acids accompanies not only a decrease in cmc as well as β but also a reduction in free energy gain. 3. Examination of Electroconductivity Data in Connection with r and β. Returning to the problem with the relation between electroconductivity data and the degree of micellar electrolytic dissociation (R) or the degree of counterion binding to micelles (β), we have discussed the relation of R with the ratio of ΛM/Λ°, where
ΛM ) RkΛ° ) Rk′ Further, assuming that R + β ) 1 or REX ) 1 - β, where β is experimentally determined as in Table 1, REX was plotted against ΛM/Λ° and found that
REX ) 0.40(ΛM/Λ°) + 0.08 for R-SMy‚Me. It was pointed out that REX corresponds roughly to 40% of ΛM/Λ° and that the simple ratio of slopes below and above S1 and SM (see Figure 1) is not always equal to REX.7,8 The ratio SM/S1 has been assumed as R by Lianos and Lang (L & L)10 and Tamaki et al.11 Noting that Tamaki et al. determined S1 and SM at ranges close to cmc, S1 is not the same as our Λ° but nearly equal to Λ1 (see Figure 1), and also SM may be a little larger than our ΛM, suggesting that their SM/S1 is not the same as our ΛM/Λ°. Recently, however, it was found for R-SMy‚Pr that ΛM does not always approach a constant but lasts to change with concentration in the range studied, so ΛM was not definitely determinable. In this paper, REX ()1 - β) is tentatively plotted against ΛM′/Λ° and ΛM/Λ1 or simply SM/S1 to examine the correlationship between them. The results are shown in Figure 8, in which the previous data7,8 are also included for comparison. As is seen from Figure 8, a linear relation seems to hold. In the plot of REX against SM/S1 ()RLL defined by L & L), a similar relation was also obtained for each, as expected. Here, REX is correlated with ΛM/Λ1 for each as follows:
REX ) 0.13(ΛM′/Λ1) + 0.22 R-SMy‚Me (R ) 0.612) REX ) 0.23(ΛM′/Λ1) + 0.26 R-SMy‚Et (R ) 0.777) REX ) 0.39(ΛM′/Λ1) + 0.24 R-SMy‚Pr (R ) 0.854) Here the regression value R is given inside parentheses. These relationships exhibit neither the slope of unity nor the zero intercept, meaning that the electrolytic dissociation degree of micelles estimated from the CorrinHarkins plot (REX) is not in accordance with the value estimated by a simple ratio of slopes below and above cmc (RLL). This tells us that there still remains a problem to be solved with the estimate of degree of micellar dissociation from conductivity data, although the ratios of ΛM′/Λ1 or SM/S1 are at least likely to be directly related to R as has been reported elsewhere.33 The slope of the linear relation in Corrin-Harkins plot is considered to cor-
Micellization of R-Myristic Acid Alkyl Esters
respond to the real degree of counterion binding (β) as long as based on the thermodynamics of micelle formation,13 so the degree of electrolytic dissociation R seems to be naturally equal to 1 - β. But the present R-values estimated from conductivity data were not in accordance with 1 - β. Consequently, in order to determine the R-value it may be essential to use a direct electrochemical method such as ion-selective electrode method, and it is necessary to examine the correlation between 1 - β from the CorrinHarkins plot and the R detemined by the potentiometry. Conclusions (1) cmc: The cmc of R-SMy‚ series surfactants decreases with the increase in hydrophobicity, as is expected. The temperature-cmc curve has a minimum at a temperature giving the enthalpy change on micellization, ∆H°m ) 0. (2) Degree of counterion binding β: β values of R-SMy‚ Pr, R-SMy‚Et, and R-SMy‚Me are ca. 0.5, ca. 0.6, and ca. 0.7, respectively, and decrease slightly with temperature (0.51 to 0.47 for R-SMy‚Pr, 0.61 to 0.58 for R-SMy‚Et, and 0.72 to 0.70 for R-SMy‚Me) at the range from 15 to 50 °C. The lower β value results from the more hydrophobic and (33) Sugihara, G.; Hisatomi, M. J. Jpn. Oil Chem. Soc. 1998, 47, 661.
Langmuir, Vol. 16, No. 8, 2000 3783
larger shoulder near the headgroup leading to the less Coulombic repulsion between headgroups. (3) Gibbs energy change upon micellization ∆G°m: The absolute value of negative ∆G°m increases in the order R-SMy‚Pr < R-SMy‚Et < R-SMy‚Me in parallel with increasing order of the degree of counterion binding. (4) Enthalpy-entropy compensation relation: A clear linear relation (empirically expressed as ∆S°m ) (1/303) ∆H°m + σ) holds completely between ∆H°m and ∆S°m for the three surfactants as well as for different surfactants. (5) Degree of electrolytic dissociation R: The experimental degree (REX), calculated from the relation REX ) 1 - β, did not agree with those estimated using conductivity data. Acknowledgment. This work was in part supported by the Ministry of Education, Science, Sports, and Culture of Japan (Grant-in-Aid for Scientific Research (C) 09680661 and Grant-in-Aid for Scientific Research on Priority Area 09261240), as well as by grants from the Central Research Institute of Fukuoka University. LA991585H
