Department of Applied Chemistry and Biotechnology, Niihana National College of Technology (Niihama, Ehime , JAPAN) 2

Transcription

1 Journal of Oleo Science Copyright 2011 by Japan Oil Chemists Society Premicelle Formation of Double-chain Surfactants and Bile Salts in the Neighborhood of the CMC Region: Application of a Differential Conductivity Technique to the Determination of Micellization Parameters Masahiro Manabe 1, Hideo Kawamura 1 and Keiichi Kameyama 2 1 Department of Applied Chemistry and Biotechnology, Niihana National College of Technology (Niihama, Ehime , JAPAN) 2 Department of Biomolecular Science, Faculty of Engineering, Gifu University (1-1 Yanagido, Gufu , JAPAN) Abstract: It has been demonstrated that differential conductivity, dκ/dc, is useful for experimentally extracting the contribution of micellar aggregates from the conductivity data of an ionic surfactant solution in which aggregates and monomers coexist. This extraction allows us to treat the micellization process using a simple two-state model (ns M) instead of the general mass action model of micellization (ns+qg M). As a result, the three parameters of micellization, i.e., aggregation number (n), micellization constant, and ionization degree (α) of micelles, for homologous double-chain surfactants and bile salt derivatives can be determined. It was found that when the side-chain was long enough, the double-chain surfactants examined formed highly ionized (α = ) and small (ca. n = 20) aggregates, regarded as premicelles. Key words: differential conductivity, double-chain surfactants, bile salts, aggregation number, micellization constant, ionization degree of micelles, premicelles 1 INTRODUCTION Measures of electric conductivity, such as specific conductivity κ and equivalent conductivity Λ, are useful for studying ionic surfactant solutions. The most familiar use of these conductivities is for determining the critical micelle concentration cmc 1 of surfactants based on the plot of κ vs. concentration C, and on that of Λ vs. C 1/2. For cmc determination, only the break point in respective plots is meaningful. In the κ vs. C plot, κ increases linearly to a break point at the cmc and then increases further with a decreased slope as a result of the formation of micelles bearing counter-ions. Evans 2 proposed the use of these slopes to determine the degree of micellar couter-ion dissociation α. In a few recent studies 3 5, this method was enormously simplified to estimate the approximate value of α which was taken simply as the ratio of the slopes above to below the cmc in the κ vs. C plot, ignoring the contribution of n. Sugihara et al. 5 discussed the significance of this ratio, comparing it with the ionization degree that can be determined from the Corrin-Harkins plot. In the Λ vs. C 1/2 plot, Λ decreases linearly at low concen- trations up to a break point at the cmc, and then decreases monotonically with increasing concentration. The linear relation represented by the equation Λ Λ o ac 1/2 is consistent with Kohlraush s square- root law and the Debye- Huckel theory of electrolyte solutions 6, which imply that an ionic surfactant behaves as a strong electrolyte and, therefore, ionizes completely and dissolves monomerically. In contrast, above the cmc, it is difficult to estimate the characteristics of micelles using only Λ because of the nonlinear concentration dependence past this point. This difficulty arises because the value of Λ defined as the quotient κ/c, is influenced by the value of the cmc itself. The question is, how can we extract information about the micelles themselves from conductivity data describing the micellar region where micelles coexist with monomers? Some attempts have been made to elicit micelle characteristics such as concentration, aggregation number, charge, and ionic interaction from the equivalent conductivity by assuming that Kohlraush s square-root law also applies to the micellar region. Kimizuka and Satake 7 assumed that a linear relation, Λ Λ o ai 1/2 where a is a constant and I the ionic strength holds in both the premicellar and micel- Correspondence to: Hideo Kawamura, Department of Applied Chemistry and Biotechnology, Niihama National College of Technology, Niihama, Ehime , JAPAN kawamura@chem.niihama-nct.ac.jp. Accepted June 2, 2011 (received for review April 1, 2011) Journal of Oleo Science ISSN print / ISSN online

2 M. Manabe, H. Kawamura and K. Kameyama lar regions, and that the slope at the cmc is identical to that in the monomer region. This assumption was made in order to estimate the micellar charge of anionic and cationic surfactants, and this method was used to estimate micellar aggregation number 8. Moroi and Matsuoka 9 analyzed the electric conductivities of sodium dodecyl sulfate SDS solution from the concentrations of counter-ion, surfactant ion, and micelle based on the mass action model of monodisperse micelle formation, using literature values for micellization parameters. Shanks and Franses 10 also analyzed the equivalent conductivity data of an SDS micellar solution. They estimated the cmc, counter-ion binding degree, and aggregation number using some conductivity models based on mass action micellization thermodynamics and the Debye1-Huckel-Onsager theory. In addition to these traditional conductivities κ and Λ, another conductivity, called the differential conductivity and defined as dκ/dc κ 2 κ 1 / C 2 C 1, has been found to be useful for elucidating the aggregation behaviors of ionic surfactants. So far, differential conductivity has been successfully applied to determine the following quantities in systems of ionic-nonionic amphiphilic mixtures 11 : 1 The critical composition of ionic-nonionic mixed micelles for counter-ion condensation 12 ; 2 the binding constant of ionic surfactant cyclodextrin complex formation 13 ; and 3 the partition coefficient and counter-ion releasing effect of nonionic amphiphiles normal alkanols 14, branched alkanols 15, and amphiphiles with various types of polar head groups 16 added to ionic micellar solutions, concerning the effects of hydrophobic interactions and the reduction of surface charge density on solubilization. In the present study, differential conductivity was used to analyze the micellar solutions of single ionic surfactants homologous double-chain surfactants and bile salt derivatives in order to determine the parameters, i.e., aggregation number n, equilibrium constant K, and ionization degree α, of highly ionized oligo-aggregates premicelles in the surfactants, using only the conductivity data in the cmc region. 2-ethyhexyl sulfosuccinate AOT Tokyo Kasei, Tokyo, Japan was purified following a previously described method 17. Bile salt derivatives, namely sodium deoxycholate NaDC, sodium taurodeoxycholate NaTDC, and sodium tauroursodeoxycholate NaTUDC were kindly provided after purification by Dr. Sugihara Fukuoka University, Japan. Water was passed through an ion-exchange resin for deionization and then distilled for use as a solvent. The specific conductivity of the water used was ca. 1 μs cm 1 at Procedure Stock solutions of the desired surfactants were prepared, and weighed aliquots of the mother solution were added successively into a conductivity cell cell constant: cm 1 containing an amount of water on concentrating, or weighed aliquots of water were added to the cell containing an amount of the mother solution on diluting. Conductivity measurements were carried with the Precision LCR meter Hewlett-Packard Model 4284A operating at 1kHz at 25. The temperature was increased to 35 when the solubility of the sample was too low at 25. The temperature of the water bath was controlled at each temperature within 1/100. To determine one resultant conductivity curve, at least four runs were measured. The surfactant solutions were all prepared on a weight basis. 3 RESULTS AND DISCUSSION The dependences on concentration of the conductivity 2 EXPEIMENTAL PROCEDURES 2.1 Materials α-sulfonated fatty acid ester sodium salts C m H 2m 1 CH SO 3 Na COOC n H 2n 1 α-sf m n : m 8,10, n 1,4,6,8 purity 95 by HPLC were kindly supplied by Lion Corporation, Tokyo, Japan. Dialkylsulfosuccinnate sodium salts C m H 2m 1 COOCCH SO 3 Na CH 2 COOC m H 2m 1 S m SS: m 7,8,9 were synthesized as follows. Maleic anhydride was esterified with the corresponding normal alcohol in the presence of chlorosulfonic acid and then sulfonated with sodium hydrogen sulfite. The crude product was purified by recrystallization several times from ethanol. Sodium di Fig. 1 Concentration dependence of specific conductivity for double-chain surfactants at 25. Surfactants: α-sf (10-1) ( ), α-sf (10-8) ( ) Straight line is drawn in pre-aggregate region. 516

3 Conductometric Study of Premicelle Formation Fig. 2 Concentration dependence of dκ/dc for α-sf (m-n) at 25. Surfactants: α-sf (10-1) ( ), α-sf (10-4) ( ), α-sf 10-6) ( ), α-sf (10-8) ( ), α-sf (8-8) ( ). Line indicates the best fitting curve, using the parameters shown in Table 2. Fig. 4 Concentration dependence of dκ/dc for S m SS. Surfactants: S 8 SS ( ) at 25, S 7 SS ( ), S 8 SS ( ), S 9 SS ( ) at 35. Line indicates the best fitting curve, using the parameters shown in Table 2. Fig. 3 Concentration dependence of dκ/dc for α-sf (m-n) at 35. Surfactants: α-sf (8-8) ( ), α-sf (10-6) ( ), α-sf (10-8) ( ) Line indicates the best fitting curve, using the parameters shown in Table 2. of the surfactants studied are shown in Figs The conductivity curves of some surfactants double-chain surfactants with long side-chain and bile salts differed from those of traditional single-chain surfactants. This distinction is illustrated in the plot of specific conductivity κ against concentration C in Fig. 1. When the side-chain is short, as is the case of α-sf 10-1, κ deviates downwards after the break at the cmc, consistent with similar plots of Fig. 5 Concentration dependence of dκ/dc for bile-salt derivatives at 25. Surfactants: NaDC ( ), NaTDC ( ), NaTUDC ( ). Line indicates the best fitting curve, using the parameters shown in Table 2. single-chain surfactants. When the side-chain reaches a certain length, as α-sf 10-8, κ deviates upwards, in contrast to the plots of the short-chain surfactants. The differential conductivity is defined as dκ/dc κ 2 κ 1 / C 2 C 1, which describes the increments in κ at the corresponding concentration range dc. dκ/dc is plotted in Figs. 2-6 for all surfactants studied, against the squareroot of the mean concentration, C 1 C 2 /2, which is denoted by C, on the abscissa, without any discrimination in notation from the concentration C. The dκ/dc vs. C 1/2 plots of the two surfactants given in Fig. 1 are found in Fig. 517

4 M. Manabe, H. Kawamura and K. Kameyama Fig. 6 Concentration dependence of dκ/dc for AOT at 25. Straight line indicates differential conductivity of monomer ( ) and micellar ( ) species expressed in Eq. (1). Two linear relations give the best fitting curve ( ), using the parameters shown in Table It is apparent that for surfactants with short side-chains, including α-sf 10-1,4,6, the dκ/dc value decreases suddenly after a slight linear decrease. The concentration dependence is consistent with that of traditional surfactants, such as SDS 18. In contrast, the dκ/dc value for the long side-chain surfactants, including α-sf 10-8,8-8, increases to a maximum after a slight linear decrease at low concentrations. This maximum is followed by a linear decrease, and the graph can be described as a sigmoid curve, as discussed later. The upward deviation in κ Fig. 1 and the increase in dκ/dc Fig. 2 indicate an enhancement in conductivity, which is probably caused by the formation of multi-charged aggregates, e.g., the self-aggregates of surfactant ions. A maximum value was observed not only in certain homologs of α-sf m n with n 5, but also in those of S m SS with m 7, and the tendency toward this increase became more remarkable as the length of the sidechains increased Figs. 2-4, with no maximum being observed with the short side-chain homologs. It follows that there should be a critical side-chain length around six carbons which will yield a maximum. In addition to the double-chain surfactants, all three bile salts studied, having a bulky steroid structure, produced a maximum Fig. 5. This result implies that the necessary condition for yielding a maximum in the dκ/dc vs. C 1/2 plot is probably strong hydrophobicity of the hydrophobic group on a surfactant. To our knowledge, only one dκ/dc curve with a maximum has been previously reported that is consistent with the results presented in Fig. 5. This curve was reported by Mukerjee et al. 19 and was created using NaTDC. On the other hand, for an equivalent conductivity, maximum curves in Λ vs. C 1/2 plots, contrary to the typical decreasing plots, were reported for the following surfactants: tetradecylpentadecyl sulfate sodium salt 2, dioctyl- and ethylhexyl-surfosucinate sodium salts 20, hexadecyl- and octadexyl-pyridonium iodates 21, octadecyl-triamyl and -tributyl ammonium bromates 22, and dyes 23. In addition, in suitable water-ethanol mixtures, a maximum was observed for octadecylpyridonium chloride, but no maximum was obtained in water alone 24. In these studies, no quantitative explanation for the emergence of a maximum was proposed, although it was explained qualitatively as a charge effect. The relationship between micelle formation and the maximum curve was experimentally confirmed in AOT, which produced a maximum curve Fig. 6. The ESR spectra of the amphiphilic probe 5-doxyl-stearic acid added to the AOT solution indicated that the mobility of hydrocarbon chain in the probe is restricted around the transitional region of the dκ/dc curve, which exhibits micelle formation data not shown. Therefore, when the cmc of the surfactants is determined by interpolation at the break point on the maximum curve, there are two possibilities. One is that the concentration is at a minimum when the curve is at its maximum, which is consistent with the definition that the cmc is the concentration at which the aggregation of surfactant begins. The other possibility is that the concentration is at a maximum, and the micellization equilibrium is substantially saturated with micelles after the transitional region. These cmc values are denoted by CMC L and CMC H, respectively, and are summarized in Table 1. Accordingly, the transitional region is named the cmc region, to distinguish it from the cmc, which is a definite single concentration. In other words, any concentration in the cmc region can be regarded as a reasonable estimate of the cmc, as discussed below. For SDS, all values for the cmc determined by various methods can be found in the transitional region of the dκ/dc vs. C 1/2 plot 18. Another characteristic of the maximum curve is that the curve found in a concentration region just above the maximum can be regarded as linear, as representatively illustrated using AOT Fig. 6. The linear decrease could be the result of the dependence of a definite ionic aggregate species on concentration monodisperse micelles with a certain aggregation number and charge, following the Kohlrausch square-root law of electrolyte solution 6, as well as the linear relationship found below the cmc region. Here, it should be noticed that the differentiation of κ with C allows for extraction of the conductometric contribution of a certain ionic species formed at that particular concentration. This is even possible with micellar species found above the maximum. The linear relations for monomer species and micellar aggregate species both above and below the cmc region are respectively expressed as 518

5 Conductometric Study of Premicelle Formation Table1 Cmc's for Double-chain Surfactants and Bile Salt Derivatives at 25 and 35. T/ Surfactant CMC L mmol kg -1 C m /CMC L % CMC H mmol kg -1 C m /CMC H % 25 α-sf(8-8) ) 25 α-sf(10-1) 25 α-sf(10-4) 25 α-sf(10-6) 25 α-sf(10-8) ) 25 S7SS S8SS ) 25 AOT ), ) 25 NaDC ) 25 NaTDC ), ) 25 NaTUDC α-sf(8-8) α-sf(10-6) α-sf(10-8) S 7 SS S 8 SS S 9 SS AV= AV= 14.0 The unit of cmc in literature data is mm. κ f Λ 0 f ε f C 1/2 and κ m Λ 0 m ε m C 1/2 1 where κ i and Λ 0 i represent the differential conductivity at any C and at infinite dilution, and ε i is the slope in each concentration region. Note that the differential conductivity defined as dκ/dc and the equivalent conductivity κ/c are formally equal to each other at infinite dilution, so the notation Λ 0 0 i is used as the intercept term. The values of Λ i and ε i are listed in Table 2. Moreover, it can be shown that both the monomerically ionized surfactant ion S and its counter-ion G contribute conductometorically to κ f and that micelle ion M and its dissociated counter-ion G contribute to κ m, as expressed later in another form. Another characteristic feature is that the maximum curve may be regarded as sigmoid. This signifies that the two reaction species being analyzed, monomer and micelle in the present case, are in equilibrium. Based on a twostate model, dκ/dc at any concentration can be associated with the contributions of each species in Eq. 1. As this is being considered, the micellization parameters associated with the equilibrium will be estimated. The short side-chain surfactants with no maximum in their conductivity curve will be analyzed in another paper together with other homologous single-chain surfactants. 3.1 Determination of K and n In the present discussion, the surfactant of a 1:1 electrolyte is used. In previous conductometric studies, the traditional equivalent conductivity was used for the determination of micellization constants 7, 8 on the basis of the mass 519

6 M. Manabe, H. Kawamura and K. Kameyama Table 2 Characteristic Parameters of Pre-micelle Formation for Double-chain Surfactants and Bile Salt Derivatives at 25 and 35. T/ Surfactant CN o Λ f ε f o Λ m ε m n ln (K) (1/n) lnk α n* n/n* 25 α-sf(8-8) α-sf(10-1) α-sf(10-4) α-sf(10-6) α-sf(10-8) S7SS S8SS AOT , 35 28) ) 25 NaDC ), 19 31) ) 25 NaTDC ) ) 25 NaTUDC α-sf(8-8) α-sf(10-6) α-sf(10-8) S 7 SS S 8 SS S 9 SS CN is total carbon number in alkyl-chains. The units for Λ o i and ε i are taken from Figs n and K are from regressive analysis. n is assigned as a integral number. α is from Eq. (20). n* is from Eq. (21). action model of micelle formation 9,10. The process can be represented generally as ns qg M S n G q, α 1, to form micelles consisting of n surfactant ions and q counterions. Micellization leads to the equilibrium constant C M / C f n C G q. However, it is difficult to calculate the equilibrium constant from the equivalent conductivity data because additional unknown parameters n and q are present 10. Compared to the equivalent conductivity, the present differential conductivity provides a new approach for estimating micellization parameters. In this approach, the following simple two-state model, i.e., the Hartley model 25, represented by Eq. 2, is applied to the sigmoid curve: n free monomer species M micellar aggregate species 2 An extreme case is demonstrated in the self-aggregation M S n, α 1 of the surfactant ions S themselves, where the aggregation process is expressed in simple form as ns M. Even if an aggregate M S n G q, α 1 associates with a number of counter-ions q, the two-state model represented by Eq. 2 is valid. In this case, κ m in Eq. 1 reflects the conductometric contribution of each species M S n G q, and G at α. Accordingly, irrespective of the value of the ionization degree of the micelles α n q /n, the micellization constant K is simply expressed as K C M / C f n C m /n / C f n 1/n C m / C f n 3 where the subscripts of concentration C indicate the following species: free monomer f, and aggregates in micellar unit M and monomer unit m. Namely, total concentration C is correlated with respective concentrations using these notations: C C f C m C f nc M 4 These concentrations will be correlated with the experimentally determined differential conductivity dκ/dc, by means of Eq. 1. In general, the specific conductivity is re- 520

7 Conductometric Study of Premicelle Formation garded as being a function of the concentration of each component ionic species. Accordingly, the total differential of the specific conductivity in the present system consisting of free monomer and micellar aggregate species can be represented as dκ dκ/dc f dc f dκ/dc m dc m κ f dc f κ m dc m 5 Dividing dκ with dc, we can derive the differential conductivity corresponding to that which was experimentally determined. dκ/dc κ dc f f /dc κ m dc m /dc κ f κ m κ f dc m /dc 6 where Eq. 4 is taken into account. Eq. 6 implies that the differential conductivity is correlated with dc m /dc, in addition to the conductometric contribution of each component κ f and κ m in Eq. 1. The quantity dc m /dc represents the micellization fraction of the surfactant on each addition of the surfactant to its solution, its value lying between 0 and 1. In the next step, the term of dc m /dc will be correlated with the parameters K and n. By differentiating C m in Eq. 3 with C, we can derive dc m /dc as a function of K and n. dc m /dc n 2 K C f n 1 / 1 n 2 K C f n 1 7 Further, when a pair of values of K and n is given, the value of C f at any C can be calculated through the logarithmic relation of Eq. 3. log C m log nk nlog C f log C C f 8 Through Eqs. 6 8, the regression analysis of dκ/dc in Eq. 6 allows us to determine both K and n as fitting parameters. The representative example from our analysis is illustrated using AOT in Fig. 6. Note that the resultant best fitting curve for each surfactant is drawn with a solid line in Figs. 2 to 6, and the values for K and n are listed in Table 2. It should be noted that the plots of dκ/dc at high concentrations tends to deviate from the linear relation represented in Eq. 1, as seen in Figs This may be the result of an increase in the size of the aggregates as they associate more counter-ions through complex processes. 3.2 Estimation of In general, for a certain ionic species, the specific conductivity κ i is a function of its ionic mobility U i, concentration C i, and charge Z i, as in κ i U C i i /1000 Z i F 9 where F is the Faraday constant. The differential conductivity of the ionic species, κ dκ i i /dc i can be derived by differentiating κ i with C i, κ i U i Z i F / where the term of du i /dc i is ignored under conditions of low concentration. For a micelle M S n G q, the contribution of the aggregate itself to the specific conductivity κ M is described by Eqs. 4 and 9 : κ M U M C M /1000 n q F U M C m /1000n n q F U C M m /1000 αf 11 The differential conductivity is then derived by differentiating Eq. 11 with C M,: κ M dκ M /dc M dκ M /dc m dc m /dc M U M 1/1000 αfn U 1/1000 n q F M 12 For the free monomer surfactant ion, specific conductivity κ S and differential conductivity κ S are also expressed. κ S U C s s /1000 F; κ S U 1/1000 F S 13 From Eqs. 12 and 13, the ratio of differential conductivities can be obtained: κ M / κ S U M /U S αn n q U M /U S 14 The ionic mobility of an ion is a function of charge and hydrodynamic radius R i, in accordance with Stokes law. Provided that the volume ratio of an aggregate to its constituent monomer is equal to the aggregation number, the ratio is U M /U S n q /R M / 1/R S n q /n 1/3 Accordingly, κ M /κ S is rewritten as 15 κ M /κ S n q 2 / n 1/3 α 2 n 5/3 16 Eq. 5 can now be represented in another form by taking the contributions of the surfactant ion S, micelle ion M, and counter-ion G into account. dκ κ S dc S κ G dc G κ M dc M κ S dc S κ G dc S α dc m κ dc M m /n κ S κ G dc S κ M /n ακ G dc m 17 Comparing this equation with Eq. 5, the following expressions for the differential conductivity both below and above the cmc region are derived. κ f κ S κ G ; κ m κ M / n ακ G 18 The relations in Eq. 18 are variations of the expressions in Eq. 1. By inserting the κ M of Eq. 16 into Eq. 18, the following equation can be obtained. κ m α 2 n 5/3 κ S /n ακ G α 2 n 2/3 κ S ακ G α 2 n 2/3 κ f κ G ακ G 19 As a result, the quadratic equation for α can be derived: 521

8 M. Manabe, H. Kawamura and K. Kameyama α 2 n 2/3 κ f κ G ακ G κ m 0 20 This equation corresponds to the one derived by Evance 2. By using the value of n determined above Table 2, α can be evaluated from the conductivity data. The calculation for α is carried out under the condition of limiting dilution, using the values Λ o f and Λ o m in Table 2 and κ G for which the literature values 6 for equivalent conductivity of the Na ion at infinite dilution, denoted by λ o G, are used: λ o G 50.1 at 25 and λ o G at 35 having the units of cm 2 S eqiv 1. These values are numerically identical to the values presented in this paper, but with different units. The calculated α value is given in Table 2. If self-association of the surfactant ion occurs α 1, the hypothetical aggregation number denoted by n can be estimated from Eq. 20 at infinite dilution: n κ m κ G / κ f κ G 3/2 Λ m o λ G o / Λ f o λ G o 3/2 21 The obtained values of n are also listed in Table 2. Here, the mechanism of the emergence of a maximum in the dκ/dc vs. C 1/2 plot is discussed using Eqs. 15 and 16. The concentration dependence of dκ/dc is explained by competition between two factors, i.e., the conductivity increase from the increase in charge as a result of aggregation Z i n q and the conductivity decrease from the increase in size R M /R S. The conductivity enhancements that yield maximums in the dκ/dc curves in the present cases can be explained by the former factor being predominant over the latter. In contrast, when the latter size effect and /or the charge effect a decrease in Z i as a result of an increase in q caused by increased counter-ion condensation are governing, the conductivity is predicted to weaken on aggregation, as in the case with the traditional single-chain surfactants 18. The conductivity competing mechanism is sometime called the McBain effect 23. There should be a critical value for the aggregation number and the degree of counter-ion binding for the emergence of a maximum at the condition of κ m /κ f Correlation between Parameters The values for the micellization parameters K, n, n, and α estimated by the differential conductivity technique are listed in Table 2, together with data for characteristic conductivity Λ f o, Λ m o, ε f, and ε m. Some values of n, α, and cmc are compared in Tables 1 and 2 to literature values determined by the following methods: conductivity 70 26, surface tention 27, NMR 28, pna electrode 29, heat capacity 30, solubilization 31, ion-selective electrode 32, and gel-filtration chromatography 33. This comparison indicates reasonable agreement among values. It should be noticed that in all the intended surfactants in this paper, the aggregation number ca. 6 n 21 is much smaller than that of traditional single-chain surfactants such as SDS ca. n These small aggregates can be regarded as premicelles or oligo-micelles. In addition, the ionization degree of micelles ca α 0.95 is much higher than that of traditional surfactants ca. α , which causes the conductivity enhancement to produce a maximum curve. These two characteristic aspects seem to be mutually interrelated. The correlation between n and α are shown in Fig. 7, where a reduced quantity, n/n, is plotted instead of n. It is apparent that n/n tends to decrease asymptotically toward n/n 1 with an increase in α, despite molecular structural differences. This correlation can be expressed as the following relation derived from Eqs. 20 and 21. n/n Λ o m α λ o G / α 2 Λ o m λ o G 3/2 22 In fact, surfactants with long side-chain α-sf 10-6,8 and S 9 SS are located in the region where both α and n/n are near unity, indicating that they exist mostly as highly ionized micelles. On the other hand, it was found that n/n increases with a decrease in α from ca. 0.8 to 0.6, which suggests that counter-ion condensation reduces the electrostatic repulsive force among surfactant ions, yielding larger aggregates. It follows that the critical values of n and α, denoted by n c and α c, should exist at the point where the maximum in the dκ/dc vs. C 1/2 curve disappears at the condition of κ m / κ f 1, as previously mentioned. The relation between n c and α c can be derived by substituting κ f for κ m in Eq. 20. Fig. 7 Correlation between n/n* and α for surfactants at 25 and 35. Surfactants: α-sf (m-n) ( ), S m SS( ), bile-salt ( ). indicates the plot for self-aggregate (α = 1). 522

9 Conductometric Study of Premicelle Formation α 2 c n 2/3 c κ f κ G α c κ G κ f 0 23 With these considerations, it is possible to judge which is more favorable, the charge effect or the hydrophobic effect, to aggregate formation. For example, with AOT, if n n c 18 Table 2 is inserted into Eq. 23, α c 0.54 is calculated, which is smaller than the value of 0.61 listed in Table 2. This result implies that hydrophobic interactions overcome the electrostatic repulsion to form the aggregate, which is consistent with the emergence of a maximum in the conductivity curve Fig. 6. In fact, Zana 4 reported that α increases from 0.2 to 0.7 with an increase in side-chain length in homologous ternary alkylammonium bromides. In the case of surfactant ions bearing a large and/or bulky hydrophobic moiety, the strong hydrophobicity enables the formation of highly ionized aggregates. When the hydrophobicity is great enough, it is probably possible to form smaller aggregates, such as dimmers or trimmers, without any counter-ion binding. It should be noted that the differential conductivity technique presented here is efficient for determining the aggregation number of such small aggregates. The validity of the determined K is discussed with respect to the free energy change. The free energy change of micellization for surfactants can be expressed 34 as ΔG o 1/n RT ln K 24 The contribution of each CH 2 group to ΔG o, denoted by ΔG o CH 2, is a measure of the hydrophobicity of a hydrocarbon chain such as a surfactant tail. It has been established that the value of ΔG CH o 2 is about 1.3RT for the process of oil-water transfer and about RT, for the micellization of a straight alkyl-chain 35, and that this magnitude decreases when the chain is branched 15. In order to evaluate ΔG o CH 2, 1/n ln K is plotted in Fig. 8 against the carbon number in the alkyl-chain CN indicated in Table 2 for each surfactant. Generally, for all surfactants except AOT, a linear regression line with a slope of 0.732, drawn in Fig. 8, is obtained. In the present case, the increment of CN can be regarded as representing carbons in the side-chain, and not the main alkyl-chain. It is known that the branching of an alkyl-chain weakens its hydrophobicity 15. Therefore, in the case of the double-chain surfactants studied, it is acceptable that ΔG CH o RT from the slope, which is smaller in magnitude than RT. In the graph of AOT shown in Fig. 8, the plot at CN 16 deviates downward from the strait line. If the CN value is considered to be located on the straight line at the value of 1/n lnk, an effective CN value can be taken to be 14.7, which is less than 16. This smaller value of CN can be explained by branching 2-ethylhexyl group in AOT that is more extensive than a simple double-chain, resulting in a greater weakening of hydrophobicity. These results support the validity of the present differential conductivity technique. Fig. 8 Correlation between (1/n) ln (K) and CN (carbon number) at 25 and 35. Surfactants: α-sf(m-n)( ), S m SS ( ), AOT ( ) CN values of surfactants are shown in Table 2. Straight line is regression curve for surfactants except AOT. Finally, we will discuss the C m at the cmc. In the present analysis, C f and C m can be calculated at any C, using the obtained parameters, K and n, without needing the cmc value. The concentration dependence of the calculated C f and C m values is exemplified with α-sf 8-8 in Fig. 9. In this figure, the graphically determined values of the cmc, i.e., CMC L and CMC H, are indicated for comparison. It is apparent that C m begins to increase close to CMC L, and C f almost saturates close to CMC H. The fraction of C m at each cmc CMC L and CMC H was calculated for each surfactant, Fig. 9 Concentration dependence of C f and C m for α-sf (8-8) at 25. Curves indicate C f ( ) and C m ( ). Vertical lines indicate CMC L ( ), and CMC H ( ). 523

10 M. Manabe, H. Kawamura and K. Kameyama the average being 0.69 at CMC L and 14.0 at CMC H see Table 1. Broadly speaking, the fraction increases significantly from 1 at CMC L to 10 at CMC H in the cmc region. According to Philips definition of the mass action model, the cmc is the concentration at the inflection point of the curve representing the solution property of concentration dependence 36. The cmc value must be located in the middle of the cmc region. It is reasonable to assume that any cmc value determined using any of the various methods based on the respective definitions of the cmc will be located between CMC L and CMC H. 4 CONCLUSION The differential conductivity method was applied to determine the three parameters of micellization aggregataion number, micellization constant and ionization degree of micelles for homologous double-chain surfactants and bile salt derivatives in the critical micelle concentration cmc region. It was demonstrated from this method that micellization may be treated using a simple two-state model which considers the equilibrium between free monomers and micellar aggregates. It was found that double-chain surfactants with long side-chains and bile salt derivatives formed highly ionized small aggregates, regarded as premicelles, in the cmc region. References 1 Mukerjee, P,; Mysels, K. J. Critical Micelle Concentration of Aqueous Surfactant Systems. Natl. Stand. Ref. Data Ser. U.S.Natl.Bur.Stand Evans, H. C. Alkyl sulfates. Part I. Critical micelle cncentrations of the sodium salts. J. Chem. Soc Hoffmann, H.; Tagesson, B. Z. The influence of substituted ammonium-ions on the thermdynamics and kinetics of micelles of perfluorated octanesulfonate. Z. Phys. Chem. N. F. 110, Zana, R. Ionization of cationic micelles: effect of the detergent structure. J. Colloid Interface Sci. 78, Sugihara, G.; Hisatomi, M. Roles of counterion binding in the micelle formation on ionic surfactants in water. J. Jpn. Oil Chem. Soc. 47, Robinson, R. A.; Stokes, R. H. Electrolyte Solution. 2 nd ed. Butterworths. London Kimizuka, H.; Satake, I. Estimation of micellar charge from conductivity data of aqueous detergent solutions. Bull. Chem. Soc. Jpn. 35, Mata, J.; Varade, D.; Bahadur, P. Aggregation behavior of quaternary salt based cationic surfactants. Thermochimica Acta 428, Moroi, Y.; Matsuoka, K. Electric conductivity analysis of micellar solution of sodium dodecyl Sulfate. Bull. Chem. Soc. Jpn. 67, Shanks, P. C.; Franses, E. I. Estimation of micellization parameters of aqueous sodium dodecyl sulfate from conductivity data. J. Phys. Chem. 96, Manabe, M. Mixed Surfactant Systems. 2 nd ed. Abe, M.; Scamehorn, J. F. ed.. Marcel Dekker Inc. New York. p Manabe, M.; Funamoto, M.; Kohgami, F.; Kawamura, K.; Katsuura,H. Critical composition of ionic-nonionic mixed micelles for counterion condensation. Colloid Polymer Sci. 281, Manabe, M.; Kawamura, H.; Katsuura, H.; Shiomi, M. Proceedings of the Ninth International Symposium on Cyclodextrins Torres Labandeira, J. J.; Vila-Jato, J. L. ed.. Kluwer. Dordrecht. p Manabe, M.; Kawamura, H.; Yamashita, A.; Tokunaga, S. Effect of alkanols on intermicellar concentration and on ionization of micelles. J. Colloid Interface Sci. 115, Manabe, M.; Tokunaga, A.; Kawamura, H.; Katsuura, H.; Shiomi, M.; Hiramatsu, K. The counterion releasing effect and the partition coefficient of branched alkanols in ionic micellar solution. Colloid Polymer Sci. 208, Manabe, M.; Kaneko, M.; Miura, T.; Akiyama, C.; Kawamura, H.; Katsuura, H.; Shiomi, M. Counter ion release of ionic surfactant micelles: size effect of a polar head group. Bull. Chem. Soc. Jpn. 75, Manabe, M.; Ito, T.; Kawamura, H.; Kinugasa, T.; Sasaki, Y. Conductometric and volumetric studies on the ionization, hydration, aggregation, and coagulation of AOT in dodecane. Bull. Chem. Soc. Jpn. 68, In Ref.11, p. 95, in Fig Mukerjee, P.; Moroi, Y.; Murata, M.; Yang, A.Y.S. Bile salts as atypical surfactants and solubilizers. Hepatology 4, 61S-65S Miller, M. L.; Dixon, J. K. Conductance of dialkyl sodium sulfosuccinate surface-active agents. J. Colloid Sci. 13, Brown, G. L.; Grieger, P. F.; Evers, E. C.; Kraus, C. A. On the maximum in the equivalent conductivity of two paraffin-chain salts in water. J. Am. Chem. Soc. 69, McDowell, M. J.; Kraus, C. A. Properties of electrolytic solutions. XLIX. Conductance of some salts in water at 25. J. Am. Chem. Soc. 73, Robinson. C.; Garret, H. E. The degree of aggregation of dyes in dilute solution. Part I: Conductivity mea- 524

11 Conductometric Study of Premicelle Formation surements. Trans Faraday Soc. 35, Evers, E. C.; Kraus, C. A. Properties of electrolytic solutions. XXXIV. Conductance of some long chain electrolytes in methanol-water mixtures at 25. J. Am. Chem. Soc. 70, Murray, R. C.; Hartley, G. S. Equilibrium between micelles and simple ions, with particular reference to the solubility of long-chain salts. Trans Faraday Soc. 31, Okano, T.; Tanabe, J.; Fukada, M.; Tanaka, M. α-sulfonated fatty acid esters: I. Structual effects of sodium α-sulfonated fatty acid higher alcohol esters on surface-active properites and emulsification ability. J. Am. Oil Chem. Soc. 69, Williams, E. F.; Woodberry, N. T.; Dixon, J. K. Purification and surface tension properties of alkyl sodium sulfosuccinates. J. Colloid Sci. 12, Kilpatrick, P. K.; Miller, W. G. Aggregation of doubletail sulfonate surfactants probed by sodium-23 NMR. J. Phys. Chem. 88, Sugihara, G.; Tanaka, M. A ph and pna study of aqueous solutions of sodium deoxycholate. Bull. Chem. Soc. Jpn. 49, Rajagopalan, N.; Vadenere, M.; Lindenbaum, S. Thermodynamics of aqueous bile salt solutions: heat capacity, enthalpy and entropy of dilution. J. Solution Chem. 10, Nagadome, S.; Okazaki, Y.; Lee, S.; Sasaki, Y.; Sugihara, G. Selective solubilization of sterols by bile salt micelles in water. Langmuir 17, Murata, Y.; Okawauchi, M.; Kawamura, H.; Sugihara, G.; Tanaka, M. Surfactant in Solution. Vol. 5 Mittal, K. L.; Bothorel, P. ed.. Plenum. New York. p Funasaki, N.; Ueshiba, R.; Hada, S.; Neya, S. Stepwise self-association of sodium taurocholate and taurodeoxycholate as revealed by chromatography. J. Phys. Chem. 98, Moroi, Y. Micelles Theoretical and Applied Aspects. Plenum. New York. p Tanford, C. The Hydrophobic Effect. Wiley. New York. p Phillips, J. N. The energetics of micelle formation. Trans Faraday Soc. 51,