Langmuir 1998, 14, 3749-3753
3749
Volume and Compressibility Study of Dissolved State of Mixed MicellessMega-8-Mega-9 and Decyltrimethylammonium Bromide-Dodecyltrimethylammonium Bromide Systems Fumio Kawaizumi,* Tatsuyuki Kuzuhara, and Hiroyasu Nomura School of Engineering, Nagoya University, Chikusa-ku, Nagoya-shi 464-8603, Japan Received January 23, 1998 A series of solutions of constant composition of the mixed micelles but different in total concentration of surfactants were prepared with the help of the Clint theory for mixed micelles consisting of octanonylN-methylglucamide (Mega-8) and nonanoyl-N-methylglucamide (Mega-9), and the partial molar volumes V2 were measured. The result demonstrated that the conventional procedure for investigation of the composition dependence of physical properties like V2 of mixed micelles is acceptable for the systems containing homologous surfactants. Then, the composition dependence of the partial molar volume V2 and the partial molar adiabatic compressibility Ks° were measured for the cationic mixed micelles decyltrimethylammonium bromide (C10TAB) and dodecyltrimethylammonium bromide (C12TAB) at 25 °C. In both mixed micelle systems Ks° of the micelle showed deviation from the linear relation with composition, while V2 varied linearly with the composition of the micelles. The dimension of the mixed micelles of Mega-8 and Mega-9 was also estimated from the diffusion coefficients, which showed much larger values than that of V2.
Introduction Physicochemical properties of mixed micelles formed by the association of different amphiphile molecules have attracted much attention of many investigators. For thermodynamic treatment of these multicomponent systems, various approaches have been proposed to date. In the first approach,1 mixed micelles are considered as if they were binary liquid mixtures and the regular solution theory is applied to express the relation between composition and partial concentration of singly dispersed surfactants. The second approach is by Motomura et al.,2 who express the thermodynamic relations after transforming the molar concentration of surfactant and the mole fraction in mixed micelles into appropriate parameters. Recently, Maeda3 proposed another route to analyze the thermodynamic stability of the mixed micelles composed of the ionic-nonionic surfactants. Our viewpoint is as follows: Most experimental work of mixed micelles related to the variation of physical properties with the composition of mixed micelles has been carried out under the condition of constant composition of the sample solutions prepared and not under the condition of constant micelle composition. The composition of mixed micelles varies successively with the total concentration of the surfactants in solution. It has been conventionally and intuitively assumed that at sufficiently high surfactant concentrations the composition of mixed micelles is equal to the composition of the sample solution as a whole. The validity of this assumption has not been confirmed in an explicit way. The purposes of this work are dual. In the first step of this work, the Clint theory4 was used to prepare a series (1) Shinoda, K.; Nomura, T. J. Phys. Chem. 1980, 84, 365. (2) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 1948. (3) Maeda, H. J. Colloid Interface Sci. 1995, 172, 98. (4) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 3320.
of solutions for which the concentration of mixed micelles of constant composition is an experimental setting parameter, and we examined the conventional assumption through determination of the partial molar volume V2 of the mixed micelles of constant composition. For this step, two homologous nonionic surfactants octanonyl-N-methylglucamide and nonanoyl-N-methylglucamide, abbreviated hereafter respectively as Mega-8 and Mega-9, were used as samples. The mixed micelle system of these samples has recently been studied by Harada and Sahara,5 but the approach to the evaluation of partial molar volumes V2 of the mixed micelle is different from that in the present work. To our knowledge, no measurement has been reported on the evaluation of some thermodynamic properties of mixed micelles as a function of micelle composition under the condition of constant composition of micelles. As will be clarified below, the validity of the conventional assumption was confirmed by the determination of the partial molar volume of the micelle species dissolved in solutions. Hence, in the second step of this work, we relied fully upon the conventional method for preparation of sample solutions in elucidation of the dissolved state of mixed micelles formed by the homologue amphiphilic molecules. The samples we used are the cationic surfactants decyltrimethylammonium bromide (C10TAB) and dodecyltrimethylammonium bromide (C12TAB). The critical micelle concentration of the former is approximately three times higher than that of latter, the situation being similar to the case of Mega-8 and Mega9. The properties investigated are the partial molar volume V2 and the partial molar adiabatic compressibility Ks°. As is well-known, combination of V2 and Ks° data permits us to shed more light on the interaction working between solute and solvent.6 (5) Harada, S.; Sahara, H. Langmuir 1994, 10, 4073. (6) For example, Kawaizumi, F.; Nomura, H.; Nakao, F. J. Solution Chem. 1987, 16, 133.
S0743-7463(98)00093-6 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/09/1998
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Experimental Section Materials. Mega-8 and Mega-9 were purchased from Dojin Kagaku Co. Ltd. These samples were recrystallized from the mixture of methanol and acetone, as reported by Harada et al.5 The samples C10TAB and C12TAB were of reagent grade of Tokyo Kasei Co. Ltd. These were used after being dried more than 48 h in vacuo. Measurements. Throughout the measurements temperature was controlled at 25 ( 0.005 °C. The digital densitometer Anton Paar DMA 60 was used for the measurement of solution densities of surfactants. The apparent molar volumes of the solute were calculated from the solution densities as usually using the relation
ΦV )
1000(d1 - d) M2 + mdd1 d
∂(mΦV) ∆(mΦV) ) ∂m ∆m
R
c/mol kg-1
density/g cm-3
0.2600 0.2800 0.3000 0.3200 0.3599 0.3999
0.053 96 0.058 86 0.064 75 0.071 94 0.092 52 0.129 5
0.999 945 1.000 174 1.000 457 1.000 787 1.001 732 1.003 356
Table 2. Critical Micelle Concentrations of Mega-8 and Mega-9 cM1 or cM2/mol kg-1
(1)
where M2 is the molar mas of the solute, m is the molality of the solute, d is the density of the solution, and the subscript 1 refers to the solvent system. The partial molar volumes were then determined using the ΦV values. For the solute in micellar form, the partial molar volume V2 was determined by numerical differentiation of the relation
V2 )
Table 1. Values of r and c for Preparation of Solutions Containing Mixed Micelles of Mega-8 and Mega-9 with x ) 0.5
(2)
The partial molar adiabatic compressibilities Ks and the infinite dilution values Ks° were determined by combining the density data with the ultrasonic propagation velocities of sample solutions measured using the laboratory-constructed sing-around apparatus. Similarly as for partial molar volume, the values of Ks are calculated from the apparent molar adiabatic compressibility Ksφ given as
surfactant
density
ultrasonic velocity
lit. (density)5
Mega-8 Mega-9
0.0741 0.0223
0.0684 0.0192
0.0742 0.0240
they are given in terms of the respective critical micelle concentrations cM1 and cM2 as
cm 1 ) xcM1
(7)
cm 2 ) (1 - x)cM2
(8)
and
Then the total solute concentration c is expressed as
c)
xcM1 - [(1 - x)cM2 + xcM1]x R-x
(9)
where the parameter κs (bar-1) refers to the adiabatic compressibility and is calculated from the density and the ultrasonic propagation velocity u (m s-1) through the relation
Thus, with the help of eq 9, we can prepare a series of solutions with constant values of x but different in c and R. Diffusion Coefficient of Mixed Micelles of Mega-8 and Mega-9. Tracer diffusion coefficients have also been measured at 25 °C in the Laboratory of Prof. Tominaga, Okayama University of Science, using the Taylor dispersion technique. Sample solutions were prepared according to the Clint theory in order that the micelle composition be specified unequivocally.
κs ) 100/u2d
Results and Discussion
M2 1000 Ksφ ) κ (κ d - κs,1d) + mdd1 s 1 d s
(3)
(4)
As for the partial molar volume V2, the partial molar adiabatic compressibility Ks was evaluated by numerical differentiation of the following relation:
Ks )
∂(mKsφ) ∆(mKsφ) ) ∂m ∆m
(5)
Attention should be paid to what the “solvent” and the “solute” mean, since, in the first part of this work, the species in the micelle form are taken as solute and the aqueous solutions containing the freely dispersed surfactant molecules are taken as solvent, while, in the latter part of this work, the word solvent refers to pure water. Preparation of Solutions for Examination of the Clint Theory. The Clint theory was originally proposed for mixed micelles of nonionic surfactants. The essential points in the theory are that the micelle phase behaves ideally and that the activity coefficients of free monomers are equal to unity. Then, above the cmc the mole fraction of component 1 in the mixed micelles x in the surfactant solution of concentration c is given as
x)
Rc - cm 1 m c - cm 2 - c1
(6)
where R is the mole fraction of surfactant 1 in the mixed solute m as a whole. The parameters cm 1 and c2 are the concentration of unassociated monomeric surfactants 1 and 2, respectively, and
Examination of the Clint Theory. Sample solutions were prepared in molality scale, although the notation c is used in the above. The concentration ranges of the solutions to be studied are limited on account of the solubility and the precision of density measurements. An example of the measurements is given in Table 1. The cmc values of the surfactants Mega-8 and Mega9 cM1 and cM2 were determined as the break point in the linear relationship between solution density and concentration. As shown in Table 2, values of cM1 and cM2 obtained from solution density are in excellent agreement with the reported values.5 The partial molar volumes of the solute in mixed micellar form were determined on the assumption that the concentration of mixed micelle cM is given as m cM ) c - (cm 1 + c2 )
(10)
and the density value extrapolated to cM ) 0 is taken as the solvent density d1 in eq 1. The cM dependence of the apparent molar volume ΦV of the micelle is shown in Figure 1 for the system in Table 1. The scattering in the low concentrations can be attributed to the errors in evaluating the solution density at cM ) 0. The apparent molar volume of the mixed micelle with x ) 0.5 is reasonably considered to show no concentration dependence. The value of ΦV extrapolated to cM ) 0 corresponds to the partial molar volume of the hypothetically isolated micelle, and it is designated as VM.
Dissolved State of Mixed Micelles
Langmuir, Vol. 14, No. 14, 1998 3751
Figure 1. Variation of the apparent molar volume ΦV of the mixed micelle Mega-8-Mega-9 at the composition x ) 0.5 with micelle concentration.
Figure 3. Comparison of the partial molar volumes of mixed micelles of the Mega-8-Mega-9 system determined in two different ways: (O) measured at constant composition of sample solution (conventional procedure); (b) measured at constant composition of micelle.
Figure 2. Concentration dependence of ΦV and V of the mixed micelle Mega-8-Mega-9 in solutions having the composition R ) 0.5 Table 3. Partial Molar Volumes of Mega-8 and Mega-9 in Micellar Form Determined in Different Ways
Mega-8 Mega-9
x ) const/cm3 mol-1
R ) const (conventional)/ cm3 mol-1
lit./cm3 mol-1
274.5 288.6
273.6 288.9
269.55 287.15
On the other hand, the conventional procedure for the evaluation of ΦV of the micelle solutes under the condition of constant R was also adopted. In this case, d1 is the density of pure water. Variation of ΦV and V2 with total concentration of surfactant is illustrated in Figure 2 for the case of R ) 0.5. As is well-known,5,7-11 the ΦV and V2 of the surfactant solute vary largely after passing the cmc. The value of V2 at sufficiently high concentration and depending negligibly on the concentration is considered as the VM with R ) x ) 0.5. The VM values of Mega-8 and Mega-9 determined are summarized in Table 3, and the dependence of VM on micelle composition is shown in Figure 3. As for the VM values of pure Mega-9, our two values agree well with the reported value 287.1 cm3 mol-1, while, for Mega-8, our values differ to some extent from the reported value. The (7) Yamanaka, M.; Kaneshina, S. J. Solution Chem. 1990, 19, 729; 1991, 20, 1159. (8) Achouri, M. El.; Hajji, M. S.; Salem, M.; Essassi, E. M. J. Chem. Soc., Faraday Trans. 1995, 91, 4105. (9) Bloor, D. M.; Gormally, J.; Wyn-Jones, E. J. Chem. Soc., Faraday Trans. 1 1984, 80, 1915. (10) Zielinski, R.; Ikeda, S.; Nomura, H. J. Colloid Interface Sci. 1984, 119, 398. (11) Harada, S.; Nakagawa, T. J. Solution Chem. 1979, 8, 1159.
Figure 4. Concentration dependence of ultrasonic velocities (above) and compressibilities (below) of aqueous solutions of the Mega-8-Mega-9 system at R ) 0.5.
important facts illustrated in Figure 3 are first that the essential assumption of the ideal mixing of the micelle holds for the volume of the mixed system Mega-8 and Mega-9 and second that the two different ways adopted for evaluation of the VM of the mixed micelle lead to the same VM values within the precision of measurement. In short, the validity of the Clint theory and the conventional procedure for evaluation of the partial molar properties of a micellar solute are confirmed. Ks of the Mixed Micelle of Mega-8 and Mega-9. As mentioned above, we can safely rely upon the conventional procedure for the evaluation of Ks. Hence, the ultrasonic velocity measurements have been carried out for the solutions at different concentrations with R ) 0, 0.3, 0.5, 0.6, 0.7, and 1.0. The concentration dependence of ultrasonic velocity and that of adiabatic compressibility are illustrated in Figure 4 for the case R ) 0.5. In both plots in Figure 4 the slopes are different depending on the concentration ranges, and the intercept of the two straight lines indicates the cmc values, which are also included in Table 2. The cmc values obtained from the ultrasonic
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Figure 5. Partial molar adiabatic compressibilities of the mixed micelle of the Mega-8-Mega-9 system.
Figure 7. Partial molar volumes and partial molar adiabatic compressibilities of the C10TAB-C12TAB system. Table 4. Comparison of Ks and K j 2° of Surfactants monomeric state
Figure 6. Critical micelle concentration of the C10TABC12TAB system.
velocity are smaller than those from density measurement. It is generally accepted that the values of the cmc differ to a certain extent according to what physical properties are considered for the determination of the cmc. Using the data of the adiabatic compressibility of the solution κs and setting κs,1 to that of pure water and m equal to the total concentration of surfactant, the quantity Ksφ of eq 3 is calculated. Variation of Ksφ and Ks with total concentration of surfactant is similar to that for ΦV and V2. The Ks values at high concentrations were taken as Ks° of the mixed micelle at the composition R, and they are expressed hereafer as KM. The relationship between R and KM values for the Mega-8-Mega-9 system is shown in Figure 5. In comparison with the results shown in Figure 3, appreciable deviation of the parameter KM from the linear variation with composition is observed in Figure 5. VM and KM of the Mixed System C10TAB-C12TAB. Measurements were carried out at R equal to 0, 0.2, 0.5, 0.7, and 1.0. The cmc at each composition was determined as the breaking point in the density-concentration relation in a series of sample solutions with constant R. Figure 6 shows the variation of cmc with R. The dotted curve in Figure 6 refers to the one based on the Clint theory. Obviously, the theory holds for this mixed micelle composed of the homologous ionic surfactants C10TAB and C12TAB. Hence, as permitted for the mixed system Mega8-Mega-9, at reasonably high concentrations the composition of mixed micelles is taken as that of the surfactants added to the solvent. Variation of the Ks° values of the monomeric form with the composition of the mixed system was satisfactorily linear (255.4 cm3 mol-1 for C10TAB and 285.4 cm3 mol-1 for C12TAB). The composition dependence of the partial molar volume and the partial molar adiabatic compressibility of the micelle VM and KM is shown in Figure 7. Here
surfactant
104Ks°/ cm3 mol-1 bar-1
Mega-8 Mega-9 C10TAB
-24 -34 -19
C12TAB
c
C12H25O(CH2CH2O)6
-23b
104κj2°/ bar-1 -0.090 -0.121 0.076 -0.058a c -0.149a -0.053
micellar state 104KM/ cm3 mol-1 bar-1 68.5 80.3 100.0 120.1 185.2b
104κj2°/ bar-1 0.250 0.278 0.381 0.377,a 0.403b 0.407 0.404,a 0.412b 0.414
a Reference 10. b Reference 9. Micelle compressibility was evaluated in a different way. c Unsuccessful to obtain in this work.
again, VM varies linearly in a quantitative manner, while KM shows a negative deviation from the linear relationship with composition of the mixed micelle. h 2° Values. In Table Discussion on the Ks°, KM, and K 4 are listed the values of these parameters. The partial specific compressibility κj2° is given as κj2° ) Ks°/V2. The parameter κj2° refers to the compressibility of solutes at their dissolved state and has been widely used for elucidation of solute-solvent interaction.12 In the monomeric state, the values of κj2° are negative for the surfactants Mega-8 and Mega-9, showing the hydration (formation of incompressible solvent layer12) around Mega-8 and Mega-9. The existence of a hydration layer can be attributed to the OH groups of these solute molecules. On the other hand, the compressibility of micelles of Mega-8 and Mega-9 is smaller than that of the representative nonionic surfactant polyoxyethylene glycol. The partial molar volume V2 and the partial molar adiabatic compressibility of a solute consist of the contributions of the group forming the solute. From the values in Table 4, the following results are obtained for the CH2 group in the micelles; from Mega-8 and Mega-9, VM(CH2) ) 14.1 cm3 mol-1, KM(CH2) ) 9.3 × 10-4 bar-1 cm3 mol-1, (12) See the following and the papers cited therein. Nomura, H.; Kawaizumi, F.; Iida, T. Bull. Chem. Soc. Jpn. 1987, 60, 25.
Dissolved State of Mixed Micelles
Langmuir, Vol. 14, No. 14, 1998 3753
Table 5. VM, KM, and K j 2° of Hydrophobic and Hydrophilic Moieties in Micelles
surfactant
VM/cm3 mol-1
104KM/ cm3 mol-1 bar-1
104κj2°/ bar-1
Mega-8 hydrophobic hydrophilic C10TAB hydrophobic hydrophilic C10TA+ hydrophilic
98.7 175.8 166 96.2 66.0
65.1 5.9 101 -1.0 8.5
0. 660 0.034 0.608 -0.01 0.128
Table 6. Tracer Diffusion Coefficients of Mixed Micelle of Mega-8 and Mega-9 and the Related Parameters composition of solution
1011D/ m2 s-1
Stokes radii/nm
1026(micelle volume)/m3
aggregation no.
0 0.3041 0.6971 1
9.21 9.03 8.59 8.13
2.65 2.72 2.85 3
274.5 279 284.2 288.6
171 182 205 236
and κj2°(CH2) ) 0.660 × 10-4 bar-1, and from C10TAB and C12TAB, VM(CH2) ) 16.6 cm3 mol-1, KM(CH2) ) 10.1 × 10-4 bar-1 cm3 mol-1, and κj2°(CH2) ) 0.602 × 10-4 bar-1. The two sets of values are in reasonable agreement. The surfactant is composed of hydrophobic and hydrophilic moieties. The neglection of the difference of CH2 and CH3 in the hydrophobic tail of the sample surfactants may be acceptable in view of the number of the carbon atoms in the hydrophobic tail. This approximation leads to the VM and KM values of the hydrophobic and hydrophilic moieties of the surfactants as given in Table 5. The values of κj2° clearly illustrate the large difference in the hydrophilic and hydrophobic parts of the micelle. One may consider that the slight negative KM and therefore κj2° value of the micelle of C10TAB reflects the electrostrictive effect due to the positive charge on the nitrogen atom. However, the value for C10TAB contains the contribution from the counterion Br-. For this, the following values have been known; V2(Br-)13 ) 30.2 cm3 mol-1 and Ks°(Br-)14 ) -9.5 × 10-4 bar-1 cm3 mol-1. If these contributions can simply be subtracted from the contribution of the hydrophilic moiety, then the values given in the last row in Table 5 are obtained. With this correction, it becomes apparent that the pressure responses of the micelle of Mega-8 and C10TAB are nearly similar in magnitude and that no incompressible region exists around both micelles. Diffusion Coefficients. Results of diffusion coefficient measurements are shown in Table 6. Measurements have been carried out at concentrations two to three times the cmc. The diffusion coefficients D depend on the surfactant concentration. However, the coefficient D varies at most 3-4% even if the concentrations increase from the cmc to three times of the cmc of the mixed micelle.15 The parameter D can be converted to the Stokes radius a using (13) Zana, R.; Yeager, E. J. Phys. Chem. 1967, 71, 521. (14) Mathieson, J. G.; Conway, B. E. J. Solution Chem. 1974, 3, 455. (15) Tominaga, T.; Nishinaka, M. J. Chem. Soc., Faraday Trans. 1 1993, 89, 3459.
the relation
a ) kbT/(6πηD)
(11)
where kb is the Boltzmann constant and η is the viscosity of the solvent ) 0.895 Pa s. The plot of the parameter a against micelle composition indicates an apparent negative deviation from the additivity with composition. The aggregation number may be obtainable through division of the micelle volume calculated from the Stokes radii with the partial molar volume VM, the result being included in Table 6. The aggregation numbers in Table 6 are too high to accept them as reasonable. In the case of C10TAB and C12TAB,15 the above-mentioned procedure gives aggregation numbers which are more than two times larger than the one obtained by the other method. The inter- and intramicellar and micelle-solvent interactions reduce the diffusion coefficients, which in turn gives rise to larger Stokes radii than predicted volumetrically. In view of the excellently linear relation between VM and the composition of the micelle illustrated in Figure 3, the diffusion coefficients demonstrate that the significant micelle-micelle and micelle-solvent interactions work for the case of the mixed micelle of the nonionic surfactants Mega-8 and Mega-9. Interpretation of the Mixed State. As clearly shown in this work, the mixed micelles formed by the two homologous molecules different only in the length of the alkyl chain by one or two CH2 units behave ideally with regard to volume but not so for compressibility. We may interpret the values given in Tables 4 and 5 in two alternative ways: One is to assume that the surface of the mixed micelle is irregular. If the micelle is formed predominantly by the surfactant with shorter tail, then the head group of the surfactant with the longer tail is extended outward. Conversely, if the surfactant with the longer tail is rich in the micelle, the head group of the surfactant with the shorter tail is largely buried. The head groups, however, contribute to the increase of the solvation layer with the result of negative deviation of the compressibility behavior from additivity. The other is that the longer and shorter hydrocarbon tails entangle in the mixed micelle. In this case, the surface is smooth in every composition of the mixed micelle. Addition of a longer hydrocarbon tail to the micelles mainly composed of shorter tails gives rise to the slight increase in the core of the micelle and the further change of compressibility. Acknowledgment. This work stems from discussions with Prof. Shigeharu Harada, University of Shizuoka Prefecture, who has given us valuable suggestions in carrying out this study. The cooperation of Prof. Toshihiro Tominaga, Okayama University of Science, for the measurement of the diffusion coefficient is also deeply acknowledged. LA980093M
