3824
J. Phys. Chem. 1991, 95, 3824-3829
Extreme Nonkleal Micellar Solubllzatlon Behavior of Benzyl Alcohol in Binary Surfactant Mixtures of Benzyldimethyltetradecylammonlum Chloride and Trlmethyltetradecylammonlum Chloride Raymond Bury, Embarek Souhalia, and Claude Treiner* Laboratoire d'Electrochimie, UA CNRS 430, Universiti Pierre et Marie Curie, 4, Place Jussieu, Bat. F, Paris 75005, France (Received: May 29, 1990)
The thermodynamics of micellar solubilization of benzyl alcohol has been determined in mixtures of two cationic surfactants, trimethyltetradecylammonium chloride (I) and benzyldimethyltetradecylammoniumchloride (II), using a calorimetric method. Although the cmc of mixtures of I and I1 display a behavior close to ideality, the partition coefficient P between mixed micelles and water present several extrema as a function of micellar composition. After an initial increase in the component I rich region, P decreases in the component I1 rich region and increases again toward the single component I1 micellar solutions. The enthalpy and entropy of transfer of benzyl alcohol from mixed micelles to water present the same extrema. It is shown that the very unusual solubilization behavior observed can be simulated by using Wohl's expansion of the free energy of mixing function, assuming three-body-type interactions between the unlike surfactants. This approach does not take into account the possibility of specific interactionsbetween the solute and the mixed micelles. The implications of such an interpretation scheme are discussed.
+
display a large deviation from ideality to cationic nonionic systems with a nearly ideal mixing behavior. There have been important improvements in recent years in It appeared, therefore, that if an increased solubilization was the study of the micellar solubilization phenomenon. The deto be observed for a polar solute in a mixed surfactant solution, velopment of refined models for the treatment of thermodynamic an additional effect in terms of solute/surfactant interactions data,'" the accumulation of large numben of experimental results should be present. This effect should be induced by surfactant for a variety of model compounds in single surfactant solutions,6 mixing and thus had to be favored by the specific structure of the and the use of new experimental technique^'^ have made it mixed micelle. It seemed that the cationic pair composed of possible to detect general trends leading to semiquantitative trimethyltetradecyl ammonium chloride (TTACl) with benzylpredictions in terms of degree of micellar solubilization. Recent dimethyltetradecylammonium chloride (BzTACI) could be such studies1"-I3 have suggested that the process of micellar solubilia candidate. The solute chosen is benzyl alcohol (BzOH). The zation is different for polar and nonpolar compounds in single surfactant micellar solutions. The reason for the differences observed is still a matter of controversy; for example, the importance of the Laplace pressure conceptI4 in controlling the (1) Desnoyers, J. E.; Hetu, D.; Perron, G. J. Solution Chem. 1983,12,427. (2) Hetu, D.; Roux, A. H.; Desnoyers, J. E. J . Colloid Interfie Sci. 1988, solubilization of nonpolar gases in micellar is not clearly assessed, although evidence in favor of this hypothesis is a c c u m ~ l a t i n g . ~ ~ J ~122, ~(3) ~418. ~Treiner, C. J . Colloid Interface Sci. 1982, 90,444. Micellar solubilization in mixed surfactant solutions has raised (4) De Lisi, R.;Lizzio. A.; Milioto, S.; Turco Liveri, V. J. Solution Chem. comparatively much less interest from fundamental research 1986, 15, 623. ( 5 ) De Lisi, R.;Milioto, S.; Triolo, R. J . Solution Chem. 1988, 17, 673. groups than the micellar phenomenon in single surfactant solu(6) Treiner, C.; Manncbach, M.H. J . Colloid Inferface Sci. 1987, 188, t i o n ~ . This ~ ~ paucity * ~ ~ of ~ reliable ~ partitioning data is unfor243. tunate because the micellar structural changes which are induced (7) Hayase, K.; Hayano, S. Bull. Chem. Soc. Jpn. 1977, 50. 83. by surfactant mixing seem an interesting way to investigate (8) Stilbs, P. J . Colloid Interface Sci. 1982,87, 385. particularly the importance of the structure of micelles on their (9) Liana, P.; Viriot, M.L.; a n a , R. J . Phys. Chem. 1984, 88, 1098. (10) Matheson, I. B. C.; King, Jr. A. D. J . Colloid Interface Sci. 1978, solubilization properties. Moreover, many of the data are available 66, 464. only as representative curves, a situation which forbids the use ( 1 1 ) Rapaitrahl, W.; King, Jr., A. D. J. Colloid IntefweSci. 1985,106, of such information as a basis for quantitative analysis. An 486. attempt has been recently made2' to classify some of the results (12) Smith, G. A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. J . Colloid Interface Sci. 1989, 130, 254. available in the literature and suggest a semiquantitative theo(13) Scheuing, D. R.;Wem, J. G. Langmuir 1990, 6, 665. retical guide line by making use of the regular solution approx(14) Mukerjee, P. Kolloid Z . Z . Polym. 1970, 236, 76. imation.1*-21 It was noted that in most cases the solubilization (15) Nishikido, N.; Abiru, K.; Yoshimura, N. Lungmuir 1987, 3, 729. of nonpolar solutes (e.g., hydrocarbons) was increased by sur(16) Tokiwa, F.; Tsujii. Bull. Chem. Soc. Jpn. 1973, 46, 1338. (17) Nishikido. N. J . Colloid Interface Sci. 1977, 60, 242. factant mixing. However, for polar solutes, a decreased micellar (18) Treiner, C.; Bocquet, J. F.; Pommier, C. J . Phys. Chem. 1986, 90, solubilization was observed when binary surfactant systems were 352. compared to the single surfactant solution results. The variation (19) Treiner, C.; Amar Khodja, A.; Fromon, M. Lungmuir 1987,3.729. of the partition coefficient between mixed micelles and water, (20) Treiner. C.; Nortz, M.; Vaution, C.; Puisieux, F. J . Colloid Interface Sci. 1988. 125, 261. which was used as a solubilization index, for barbituric acids as (21) Treiner, C.; Nortz, M.;Vaution, C.; Lungmuir 1990, 6, 1211. a function of micellar composition could be represented by the (22) Nagata, M.; Yotsuyanagi, T.; Ikeda, K. J. Pharm. Pharmacol. 1987, regular solution formulation using a single empirical parameter. 40, 85. For a particular solute in various mixed surfactant solutions, these (23) Muto, Y.; Asada, M.; Takasawa, A.; Esumi, K.; Meguro, K. J . parameters were found to be proportional to the interaction energy Colloid Interface Sci. 1988, 124, 632. (24) Nguyen, C. M.; Scamehorn, J. F.; Christian, S. D. Colloids Surf. between the unlike surfactant ions within the mixed micelles. The 1988,30, 335. larger the interaction the larger the decrease of micellar solu(25) Tanaka, K.; Takeda, T.; Nakamura, M.; Yamamura. S.; Miyajima, bilization upon surfactant mixing. The surfactant systems emK. Colloid Polym. Sei. 1989, 267, 520. ployed ranged from mixed anionic cationic binaries which (26) Cabrera, J. W.; Sepulveda, L. Lungmuir 1990, 6, 240. (27) Uchiyama, H.; Tokuoka, Y.; Abe, M.; Ogino, K.J. Colloid InterJace Introduction
+
To whom all correspondence should be addressed
0022-3654/91/2095-3824$02.50/0
Sci. 1989, 132, 88.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3825
Micellar Solubilization of Benzyl Alcohol very simplistic idea at the base of the present study is the following: in single BzTACl micelles, BzOH solubilization could be somewhat hampered by the favorable interactions between the surfactant aromatic moieties themselves; the added TTACl would separate these aromatic groups from each other, thus allowing easier interactions between the aromatic moieties of both the solute and the BzTACl ions. As this paper will show, the problem is somewhat more complicated that the schematic picture outlined. The calorimetric method which was used enables one to obtain, from a series of experiments, the partition coefficient as well as the enthalpy (and the entropy) of transfer of the solute between micelles and water. The solubilization results obtained were semiquantitatively confirmed by an independent method of investigation based on the measurement of the rate of change of the cmc with solute addition. Both experimental methods present the advantage of being free of analytical determinations of solute concentrations such as in the classical case of solubilization experiments. Especially in the present investigated systems, the surfactant and the solute bearing both an aromatic ring complicate the use of spectroscopic methods. Finally, the calorimetric method enables to control the activity of the solute in the micelles. Materials and Techniques BzTACl was a product from Fluka (puriss). TTACl was from TCI-EP and BzOH from Prolabo (Rectapur). All compounds were used without purification. The cmc of BzTACl and TTACl, as deduced from conductance measurements, were equal respectively to 0.001 96 and 0.0054 mol/L, in excellent agreement with literature values. The conductance data were analyzed from plots of equivalent conductance versus square root of surfactant concentration. The pseudoadiabatic calorimeter used is a homemade submarine type instrument. Calorimetric cells are completely immersed in a thermostated bath at 298.15 f 0.01 K. Thermistors (FenwallSagimeca 15K3 MCD2) are used for the determination of the temperature change upon chemical reaction. These exhibit remarkable constancy as a function of time, with a linear response in a temperature domain of at least 2 deg around the working temperature. The resistances (of the order of 15 000 ohms) are measured to 0.1 ohm, on a Digital multimeter (Keithley type 195A), which corresponds to baseline oscillations of fO.OOO 02 K. The raw experimental results are treated by an Amstrad microcomputer. The calibrations using the Joule effect are performed before and after each injection using a platinum resistance with a dc power supply. Liquid solutes are added (usually by 0.1-mL aliquots) to the calorimetric cells by a 2-mL Gilmont syringe with a precision of fO.001 mL. The alcohol concentration is of the order of 0.02 mol/L. With this type of instrument, heats can be measured up to a few joules with a precision of 0.5%; thus, taking all sources of possible errors into account, the overall accuracy on the solution enthalpies are of the order of 1.5%. Methods The calorimetric technique makes it possible, as noted before, to determine the partition coefficient of the solute as well as the standard enthalpy of transfer AH,between micelles and water from a single series of experiments. The following calculation is based on the pseudophase model. The measured enthalpy of solution of the alcohol is expressed by the relation = Y m m i c + (1 - Y ) M ~
(1)
where the subscripts mic and w refer respectively to the enthalpy in the micellar phase and in pure water. The degree of alcohol association to the micelle y may be expressed by
P(C - C,) = P ( C - C,)
+ 55.5
(2)
where P is the solute partition coefficient between micelles and water on the mole fraction basis, C and C, being respectively the total surfactant and the total monomer concentrations; for mixed micelles, the latter quantity may be different from the cmc as will
be discussed below. From eq 1 and 2, the following expression is obtained:
By choosing the appropriate P value, a plot of the experimental left-hand side of eq 3 versus the quantity between brackets (noted R'on Figure 1) provides a straight line passing through the origin, if the model is strictly correct. The slope of the line is equal to the enthalpy of transfer. A regression analysis is performed for different P values with a constant step and the calculation is ended for the value of the minimum standard deviations uM for the plot representing eq 3. The thermodynamic quantities employed refer implicitly to infinitely dilute solutions. However, in the present case of BzOH, this experimental condition is not entirely fulfilled. It has been recently shown2*that the enthalpy change of BzOH with concentration in the case of hexadeyltrimethylammonium bromide is relatively large, suggesting solute/solute interactions within cationic micelles even at dilute alcohol solutions. The present data omit, therefore, the reference to standard thermodynamic conditions. However, all data were obtained for the same BzOH concentration of 0.02 mol/L. A second method was tentatively used to obtain P values. It is based on the following thermodynamic equation:
where cmc and cmc' are respectively the critical micelle concentration in presence and in absence of solute of molality mN, M Iis the molecular weight of water and k, is the solute Setchenow constant. De Lisi et al. have shown29that, in dilute solutions, F may be taken as equal to 1/(1 + a) where a is the degree of dissociation of the micelles in absence of solute. This quantity can be obtained from classical potentiometric measurements using, for the present investigated system, a chloride ion selective electrode with a calomel reference electrode. The electrometer was a Keithley Model 614. The cmc values were obtained from conductance measurements. All experiments where performed at 298.15 f 0.01 K.
Results I . Calorimetric Analysis. The standard enthalpy of solution of BzOH in pure water was found equal to AHw = 0.46 kJ/mol in agreement with literature values. Table I presents the experimental enthalpy data. It should be recalled that the composition of mixed micelles changes with total surfactant concentration. This may complicate the analysis of data which should be performed at constant micellar composition. Theory show^^*^' that the larger the deviation from ideality displayed by the free energy of mixing of the micelles and the difference between the single surfactant CMCs the larger the difference, at a given surfactant concentration, between the stochiometric and the actual micellar compositions. In the present case, as shown below, the deviation from ideality is relatively small. This deviation may be represented within the regular solution approximation from an analysis of the variation of cmc with micelle composition. The following equation may be used3' i3 = In ( ( E x l / C , x ) / ( l - x ) * )
(5)
(28) Pons, R.; Bury, R.; Erra, P.; Treiner, C. Colloid Polym. Sci. 1991,
269. 62.
(29) De Lisi, R.; Turco Liven, V.; Castagnolo, M.; Inglese, A. J . Solution Chem. 1986, 15, 23.
(30) Holland, P. M.; Rubingh, D. N. J . Phys. Chem. 1983, 87, 1984. (31) Rubingh, D. N . In Solution Chemistry ojsurfclcranrs; Mittal K.L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 337.
3826 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 TABLE I: Enthalpy of Solution of Benzyl Alcobol in Mixed Micelles of ‘TTACI (Pure. x = 0) BzTACl at 298.15 K4 x “-AHw c-cm x AH,-AHw c-c,
+
0.0
0.15
-4.73 -4.08 -3.28 -1.75 -0.72 -3.52 -3.04 -2.40 -2.15 -1.80
0.25
0.35
0.45
-0.85 -3.29 -3.02 -2.81 -2.3 1 -1 3 6 -1.20 -0.55 -2.84 -2.46 -2.12 -1 -86 -1.32 -0.84 -0.64 -2.71 -2.32 -2.16 -1.08 -0.71 -0.46
0.0957 0.0757 0.0557 0.0279
0.55
0.01 11
0.0964 0.0764 0.0564 0.0487 0.0397 0.0164 0.0969 0.0769 0.0669 0.0492 0.0369 0.0219 0.0094 0.0973 0.0773 0.0573 0.0473 0.0293 0.0173 0.0129 0.0975 0.0775 0.0675 0.0288 0.0175 0.0125
0.75
0.85
1.0
-2.54 -2.30 -2.18 -2.01 -1.35 -1.29 -0.85 -2.25 -2.10 -1 -92 -1.72 -1.41 -1.09 -2.30 -2.04 -1.65 -1.28 -0.85 -1.69 -1.61 -1.48 -1.35 -1.05 -0.74 -0.50
0.1176 0.0976 0.0776 0.0696 0.0376 0.0336 0.01 76 0.0879 0.0779 0.0679 0.0579 0.0479 0.0371 0.098 0.078 0.058 0.0427 0.0273 0.098 1 0.0904 0.078 1 0.0631 0.0427 0.028 1 0.0182
Bury et al. TABLE II: Tbermodynamka of Micclhr Solubilhtloa for Benzyl A l c o ~in M i x d Mi& of lTACl (Pure, x = 0) BzTACT
+
T U P AH, b #An 0.0 360 -12.8 0.166 0.0054 1.8 -10.5 0.15 290 -0.015 0.0015 3.5 -7.28 0.25 540 -0.06 0.00 14 8.3 -5.44 -0,059 0.0028 10.6 0.35 640 -6.40 -0.10 0.0024 8.7 0.45 440 -6.79 0.55 270 -0.32 0.001 1 7.0 -8.30 0 0.7Sb 240 0.0095 5.3 -6.22 0.0039 8.3 0 ONb 340 -3.35 0.0027 12.5 0 I.@ 580 AH and TPS are expressed in kJ/mol. bAnalysis of q 4 including AH,,,- AHw= 0 for R1= 0, as an experimental point (see text). X
TABLE III: Critic81 Micelle Coaceatntion of the Mixed ‘TTACI (Pure, x = 0) BzTACl System, rad Actual Micellar Composition at tbe Cmc and Regular sdutiom Parameter (from 4 s 5 sad 6)
+
9 0.0
X
0.0
0.221 0.42 0.441 0.571 0.61 1 0.67 1 0.73 1 0.871
0.062 0.18 0.204 0.35 0.W
0.50 0.604 0.804
1.o
1 .O
B
cmc 0.0054 0.00435 0.0035 0.0033 0.00272 0.00264 0.00232 0.0022 0.0021 0.00196
-0.84 -0.7 1 -0.86 -0.88 -0.83 -1.16 -1.13 -0.96 av -0.92 t 0.16
a
Reference 21.
Enthalpies are in kJ/mol; concentrations in mol/L. where the indexes m and 1 refer to the cmc of the surfactant mixture and of the single surfactant cmc respectively. iis the stochiometric mole fraction, and x is the micellar mole fraction. x can be calculated at the cmc using an iterative procedure from the expres~ion’~
Using previously published data2’ and the present cmc determinations at zero alcohol concentration (see Table III), an average interaction parameter @ = -0.92 f 0.16 has been calculated. It is at the cmc that the composition change with surfactant concentration is at a maximum. The actual micellar composition x at a total surfactant concentration C can be calculated by the expression [-(C X =
- A) + ((C- A)’ + 4iCA)’/*] 2A
(7)
i
x.0
and 0
R -1
0.5
Figure 1. Illustration of eq 3 for benzyl alcohol in pure TTACI ( x = O),
x = 0.45 and pure
As far as the calorimetric experiments are concerned, the smallest surfactant concentration investigated, for which the difference between stochiometric and actual micellar composition is the largest, is around 0.01 M. Using the @ value cited above, the difference between both quantities is only about 5% and can be neglected. Expression 7 will be more useful when the cmc data are analyzed. Table I1 presents the final results.
BzTACl ( x = 1.0) micellar solutions.
In the surfactant mole fraction range from 0 to 0.55, the model conditions are fulfilled; Le., the experimental plots for eq 3 extrapolate close to zero (intercepts noted b as Table 11) at zero micellar concentration. This is illustrated in Figure 1. However, at higher surfactant compositions, a slight divergence occurred. In these cases ( x = 0.75,0.85, and 1.O) the experimental curves were forced through zero, so that AH,,,= - AH, = 0 at zero
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3827
Micellar Solubilization of Benzyl Alcohol
t
TABLE I V Characteristic P~rametenrof the Comluctance Dah through tbe Use of Eq 3: BzOH in lTACI (Pure, x = 0) BzTACl
1I \\
Mixhws
h
-2.6
+
P
X
0 0.062 0.18 0.35 0.50 1.o
0 0.221 0.42 0.57 0.67 1.o
KM
4.1 k 3.3 4.1 k 2.7 3.4 4.0
0.1
* 0.2
*
0.3 0.2 0.2 0.2
a
w
0.76 0.71 0.66 0.72 0.74 0.61
4 4 4 4
5 4
'Number of cmc determinations in the presence of benzyl alcohol for a given mixed surfactant composition. Maximum alcohol concentrations in all cases: mN < 0.05 M.
1 0
\,\ ,
, mN
,
\
X:l.O,
0.05
t X,0.50
-
Figure 2. Variation of the cmc of various single and mixed surfactant solutions with benzyl alcohol concentration. micellar concentration. The adopted P value corresponded to that which minimized the standard deviation of the linear relation 3. On Table I1 the values of the entropy term TAS are calculated as usual, using AG, = -RT In P and ASo, = (AHo, - AGot)/T. 2. Critical Micelle Concentration Analysis. As noted above, eq 4 can be used to determine partition coefficients. This method has been used before in the case of single surfactant solution^.^^^ However, its application to the present chemical system raises a number of problems of general interest which deserve some comments. Furthermore, the variation of cmc with solute addition in mixed surfactant solutions is of interest of its own as such measurements have never been published before. First, a specific analytical problem was found with the conductance of BzTACl and their mixtures with TTACI in the presence of BzOH. The cmc values depended somewhat upon the type of representation of the conductivity data. If the classical plot of equivalent conductance A versus square root of surfactant concentration is used, then the variation of log (cmc) as a function of alcohol concentration is linear as predicted by eq 4 (Figure 2). However, if the cmc values are obtained by plotting the specific conductivity as a function of surfactant concentration, then these cmc values apparently slightly increase with BzOH concentration in the low alcohol concentration domain, reaching a maximum value and then decreasing at higher alcohol concentration (above mN = 0.02 M). The latter behavior had been noted before by Todinson et al.32for dimethylbenzylhexadecylammoniumchloride in the presence of aromatic alcohols using the conductivity versus concentration plot. The present data were obtained, as pointed out before, by using the more sensitive equivalent conductance versus square root of concentration plot. It should be recalled that by using the specific conductivity procedure, A is assumed constant below the cmc. In the present situation, this assumption may introduce an artifact in the observed trend. The discussion section will confirm this point of view. Furthermore, the A versus c ' / ~plot enables one to check if, in the dilute concentration range studied (and at least for the single electrolyte solutions), the Debye-Onsager limiting law is observed. The cmc data of Table 111 were obtained for zero BzOH concentrations and were used to calculate the actual micellar composition at the cmc and the /3 parameter of the regular solution approximation by using eq 5 and 6. Table IV presents the experimental K M values, a reduced parameter from which the P values can be calculated by using eq 4. Ku is defined by log [cmco/cmc] = KumN
(8)
(32) Tomlimn, E.; Guveli. D.E.; Davis,S.S.;Kayes, J. B.Reference 31, p 355.
I ;
I
0
0.5
0
X
1.0
F v 3. Variation of the partition coefficient of benzyl alcohol between micelles and water as a function of micellar composition (pure TTACI, x = 0).
-TIS,
-4
--lo
0
0.6
X
1
Figure 4. Variation of benzyl alcohol thermodynamic functions of transfer between micelles and water (pure TTACI, x = 0).
An additional difficulty with the use of eq 4 lies in its application to mixed micelles. Free energy terms should be added to the original derivation in order to take into account the surfactant mixing. These terms are difficult to evaluate with precision. Nevertheless, K M of eq 8 should be proportional to P as deduced from the form of eq 4. The counterion degree of dissociation a for the single surfactant micelles which enters eq 4 through the parameter F was obtained from classical potentiometric measurements from the deviation of the classical Nernst plot of E versus log C,where C is the total surfactant concentration (Table IV). Discussion The main features of the present thermodynamic data are presented on Figures 3 and 4. Contrary to all published micellar solubilization data, the P values of BzOH present several extrema in the mixed TTACl/BzTACl surfactant system. The values of P first decreases upon addition of either surfactant. The decrease is much larger on the BzTACl end than at the TTACl one. The
3828 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 maximum P value obtained (for a BzTACl mole fraction of 0.35) is close to the P value obtained in the pure BzTACl micellar solution. It is interesting to point out that the KM values obtained from the cmc determinations present essentially the same profile as the P values obtained by calorimetry. Using the actual micellar compositions x as calculated by eq 7 to the representation of the cmc results, one finds the extrema at the same compositions as those obtained from the calorimetric results. This observation supports the validity of the cmc data as obtained by the analytical procedure used (A versus C’I2)and suggests a warning against the determination of the cmc using the specific conductivity versus concentration plot. It must be pointed out that the unexpected result is not so much the maximum P value observed in the TTAC1-rich region but rather the minimum that follows in the BzTAC1-rich end. In effect, a maximum solubilization could be the consequence of the suggested stacking phenomenon induced by the separation of the BzTACl benzene rings. The minimum cannot be interpreted by the same chemical model. Note finally, that the variation of the enthalpy (and of the entropy) of transfer of BzOH with micellar composition present two extrema. This behavior is at variance with previous results obtained for thermodynamics of transfer of 1-pentanol in decyltrimethylammonium bromide sodium decyl sulfate and in sodium decyl sulfate dodecylpolyoxyethylene surfactant mixtures.” For both systems a single extremum (a maximum) in the AH,versus x plot was observed. The previously adopted model used to interpret these and other literature micellar solubilization results in mixed surfactant systems relied upon the regular solution approximation for which a single empirical parameter, representing solely the interaction energy between the unlike surfactant molecules of the mixed micelle, could reproduce the variation of the partition coefficients with micellar composition. In the notation which will be used in the present article, the regular solution approximation could be represented in the case of a dilute solution with respect to the solute by34935
+
In P, = x In PI
+
+ (1 - x) In P3 + Bl-3x(1 - x)
(9)
where PI and P3 are the solute P values in the single micellar solutions 1 and 3 and P, the same parameter in the mixed micelles. B1-3 is an empirical parameter which represents the interaction energy between the unlike surfactant ions. Within the framework of the regular solution approximation BI-3 should be equal to the j3 coefficient determined above for the intramicellar interactions. This is not so, even for the relatively ideal situation for which such an equation was derived, Le., a nonpolar gas in a classical mixed fluid system.35 This equation was found nevertheless useful for comparison purposes. Equation 9 makes no provision for solute/mixed micelle interactions (the interaction between solute and single micelles being implicitly introduced in the PI and P3 values) but it was shown experimentally for a few chemical systems and confirmed by a literature survey2I that, for most available cases, the sign and amplitude of the coefficient were controlling the solubilization pattern of polar solutes in micellar surfactant binaries. It is clear that a one-parameter equation such as eq 9 cannot describe the present partition data. However, it is instructive, before invoking specific interactions between solute and mixed micelle, to investigate to what extent surfactant/surfactant interactions alone may be responsible for a profile such as that of Figure 3. Equation 9 may be looked upon as a particular case of Wohl’sM representation of the excess free energy of mixing in multicomponent mixtures where only pairwise interactions between two solvents in a ternary system are allowed. If three-body interactions (33) Bury, R.;Treiner, C. J. Solution Chem. 1989, 18, 499. (34) OConnell, J. P.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1964, 4, 341. ( 3 5 ) OConnell. J. P. AIChE J . 1971, 17, 658. (36) Wohl, K. Trans Am. Imr. Chem. Eng. 1946, 42, 215.
Bury et al.
300
1 0.5
0
X
Figure 5. Simulation of eq 10: (1) A I + = 3; = 1; C, = I; (2) A,-, = 3; A&, = 1; c, = 0; (3) 4 - 3 = 3; , 4 3 4 = 0; c, = 0.
are taken into considersti~n~~J* one may write, using the definition of the partition coefficient in the pseudophase model: In P, = x In PI + (1 - x) In P3 - Al+x(l - x)(2x - l)Ql A3-12~2(l - x)Q3 C2x(l - x ) (10) QI = q2/qI and Q3 = 42/43 are the ratios of the volumes of solute to that of component 1 and 3, respectively. C2 represents the interaction between the solute 2 and the mixed micelle. A3-I = q3(2a13 + 3al13) (1 1) AI-3 = 41(2a13 + 30133) The (113 coefficients represent the interactions between molecules 1 and molecule 3 and the coefficients a113 and a133 the interactions between three interacting molecules. The reader should consult the original paper^^^,^' for mathematical details. Taking into account three-body interactions, AI-3 is different from A3-1. Examination of eq 10 shows that the C2x(1 - x) term cannot be responsible for the profile of Figure 3. However, the third term presents a profile analogous to that of Figure 3. Figure 5 presents the variation of P as a function of composition x as calculated by using eq 10 with various values of the parameters AI-3, A3-1, and C,. The values of these various coeffcients which were chosen serve merely for illustration purposes as there is no conceivable way to evaluate them numerically. Their order of magnitude, however, are the same than those used in classical macroscopic fluids.3g The Q values were taken as equal to 1 for the sake of simplicity. It is clear that, with these parameters, eq 10 may simulate the results of Figure 3 save for the swallow minimum in the TTAC1-rich region. Introduction of a specific solute/mixed micelle interaction term may have considerable effects on the shape of the curves of Figure 5 . The coefficient C, may be positive or negative. If the interaction between the solute and the mixed micelle is favored by the surfactant mixing, C2should be positive; in the opposite case, it should of course be negative. A strongly negative (but still numerically reasonable) C, coefficient may completely overshadow the P maximum observed. In the present case, as stated already in the Introduction section, it was thought that BzOH solubilization might be favored in the mixed micelles over the single surfactant solutions. From the present discussion, it seems that this effect should be small. It is sufficient for Cz to be of the order of 1, for the minimum of Figure 5 to disappear in favor of a larger maximum. It is also clear that the analogy found between the simulated and the experimental curves does not constitute a direct evidence
+
+
+
~
~~
(37) Williams, N . A,; Amidon, G. L. J. fharm. Sci. 1984, 73, 9. (38) Williams, N . A.; Amidon, G. L. J . fharm. Sci. 1984, 73, 15. (39) Engberts, J. B. F. N. In Warer; Franks, F., Ed.; Plenum Press: New York, 1979; Vol. 6.
Micellar Solubilization of Benzyl Alcohol in favor of the hypothesis that the change of P is entirely due to surfactants intramicellar interactions. A solubility profile such as that of Figure 3 has apparently never been observed before, but its Occurrence was predicted based on an analysis of the same basic equation in the case of the solubility of a polar solute in water ethanol mixtures.38 One may simply note that if pursued to its normal conclusion, the comparison between Figures 3 and 5 implies that one of the two components of the 'solvent" mixture interacts more strongly with itself than the other. In the real system, it may correspond to the property of BzTACl component to self-interact by its aromatic moieties. One may look upon Figure 5 as the simulation of an energetical (therefore structural) dissymmetry between the two components of the mixed micelle, which is represented in the present formalism by a relatively large difference between the A terms of eq 10. There is, unfortunately, even less theoretical ground to interpret the variation of the other thermodynamic functions than the free energy one. However, an analogous approach, with all its evident dangers, may be useful. Figure 4 presents the variation of AHt and -TASt with micellar composition. The striking feature of these thermodynamic functions is the magnitude of the observed changes. They are reminiscent of the type of curves obtained for various physicochemical processes which occur in hydroorganic mixtures, where dramatic structural changes may occur upon solvent mixing. Numerous examples of the same thermodynamic changes can be found in the literature39such as in the case hydrolysis or solvolysis of organic compounds in water organic solvents in cases for which the addition of the organic component enhances the water structure. The accepted interpretation of such variations of the nonelectrolyte solute thermodynamic function of transfer as mirror images is in terms of compensation between enthalpy and entropy induced by the large modification of the structure of the medium. The variations of AHt and -TAS, on Figure 4 also display a mirror image and are of a magnitude which suggest large structural changes within the mixed micelles. It must be reminded, however, that in the classical cases, the compensation between enthalpy and entropy results in a smooth variation of the free energy function, whereas the compensation in not complete in the micellar systems investigated. The endothermic maximum, with respect to the single TTACl micellar solutions, may be identified as the consequence of a destructuring effect, brought about by the presence of BzTACl, resulting in a more disorderly structure of the mixed micelles. At the end of the micellar composition, the enthalpy minimum cannot be easily reconciled with a decrease of the solubilization power of the micellar media, and the opposite behavior of the free energy function would be more adequate. Thus, here too, the changes of the thermodynamic functions seem to be more easily interpreted as the consequence of micellar structure changes (whatever the exact nature of these changes) than by specific interactions between mixed micelle and BzOH. It may be recalled, however, that the interaction between the single micelles and BzOH is builtup in eq 10 through the respective experimental P values. The highly dissymmnetrical values of the empirical interaction term of eq 10 which have been used for the construction of Figure 5 can therefore be looked upon as indicative of profound structural modifications upon surfactant mixing. The conflicting ideas in this discussion are the following. As noted above, the fl interaction coefficient is only slightly negative, which suggests a very small deviation from ideality for the excess free energy of the system at the cmc. Moreover, the fl values are remarkably constant in the whole micellar composition range showing the validity of the regular solution approximation in its
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The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3829 simplest form (Table 111). On the other hand, the solubilization profile for BzOH may be grossly reproduced by assuming a strong asymmetrical interaction coefficient to describe the interactions between the unlike surfactants of the mixed micelle. If the general model to be retained is that of intramicellar interactions governing the solubilization behavior of a polar solute, then the following picture emerges. The binary system BzTACl TTACl appears close to ideality at the cmc most certainly as the result of opposite compensation forces. However, upon increasing the total surfactant concentration or/and by the addition of a particular solute, the micellar structure is rapidly modified. A segregation of each type of surfactant within the mixed micelle may destabilize the aggregates or decrease the mixed micelle aggregation number. The solubilization maximum in the TTAC1-rich composition region could be interpreted either by the mechanism suggested in the Introduction section of this paper, a stacking effect on diluted aromatic moieties at the mixed micellar surface, or, more likely, as the consequence of the disymmetrical interaction energies within the mixed micelles. Both phenomena might in fact interfere and the added aromatic solute could enhance the structural modifications which are induced by the suggested increase of total surfactant concentration. The present data do not allow further speculation on that point. If this intepretation scheme is correct, the effect of the solute on the mixed micelle could not be described by a specific interaction term without taking into account simultaneously its effect on the mixed micellar structure, even in dilute solutions. This would considerably complicate any thermodynamic analysis of the micellar solubilization phenomenon in mixed micellar media such as those of the type discussed in this work.
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Conclusions Calorimetric and conductance experiments have shown that the micellar solubilization of BzOH in binary TTACl+ BzTACl micellar solutions present a very specific behavior characterized by the Occurrence of several extrema of the main solute thermodynamic functions of transfer between micelles and water. Such a behavior, never observed before, can be simulate semiquantitatively in the case of the free energy function by using Wohl's series expansion formulation involving a three-body-type interactions between the surfactants, assuming a negligible interaction energy between the solute and the mixed micelle. However, this overall conclusion rests to some extent on the choice of the empirical parameters which were adopted to describe the interaction between the unlike surfactants. Whether these parameters have any real physical meaning in the case of microstructures such as mixed micelles remains unclear for the moment. It is also shown that the TTACl + BzTACl mixtures display a quasi-ideal behavior at the cmc. In order to reconcile this quasi-ideal micellization behavior with the extreme nonideal solubilization behavior depicted, it is suggested that the structure of the mixed micelles may change with surfactant concentration even in the dilute concentration range. This phenomenon may be enhanced in the TTACl BzTACl binary system by the slightly favorable interaction occurring between the aromatic moieties by BzTACl which may induce a segregation between the unlike surfactants of the mixed micelle which could be responsible of the peculiar solubilization behavior of the aromatic alcohol in the mixed micelles.
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Registry No. I, 139-08-2; 11, 4574-04-3; benzyl alcohol, 100-51-6.
