Langmuir 2006, 22, 2511-2515
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Effect of Preferential Adsorption on the Synergism of a Homologous Cationic Surfactant Mixture Hiroki Matsubara,* Takayuki Nakano, Takashi Matsuda, Takanori Takiue, and Makoto Aratono Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan ReceiVed August 1, 2005. In Final Form: January 13, 2006
To evaluate the effect of preferential surface adsorption of bromide ions on the synergism of homologous cationic surfactant mixtures reported previously, the surface tension of the aqueous solutions of the hexadecyltrimethylammonium chloride (HTAC)-dodecyltrimethylammonium bromide (DTAB) system was measured as a function of the total molality of surfactants and the relative proportion of DTAB at 298.15 ( 0.05 K under atmospheric pressure. The excess Gibbs energies calculated from them were -2.6 kJ mol-1 in the mixed adsorbed film and -2.0 kJ mol-1 in the mixed micelle, respectively. A useful analytical procedure to evaluate the composition of individual ions (hexadecyltrimethylammonium, dodecyltrimethylammonium, chloride, and bromide ions) in the adsorbed film and micelle was developed and applied.
Introduction The effect of geometries of surfactant molecules on adsorption and micelle formation is one of the key issues affecting the overall performance of surfactant mixtures. This has usually been discussed on the basis of the concept of the critical packing parameter proposed by Israerachivili;1 however, there are only a few experimental reports indicating the importance of molecular packing in the adsorbed films and the micelles because the geometrical contribution is not readily evaluated separately from other contributions such as electrostatic interactions.2,3 For the homologous surfactant mixtures, it is generally accepted for the degree of nonideality to be increased with increasing difference in the hydrocarbon chain length between surfactants. However, our previous study showed clearly that, for mixed systems of alkyltrimethylammonium halides, a kind of synergetic effect is caused when the difference in the hydrophobic chain length is matched with the hydration diameter of the hydrophilic group. We interpreted this phenomenon by the theory of staggered structure formation at the air/water interface as shown in Figure 1.4,5 Among the systems examined, hexadecyltrimethylammonium bromide (HTAB) and dodecyltrimethylammonium bromide (DTAB) showed a perfect match in length, and the van der Waals interaction between the hydrophobic chains was enhanced. This synergism is considerably weakened by replacing the bromide ions by chloride ions because the favorable chain-chain interactions were decreased by the increment of the electric repulsion between the hydrophilic groups. The reduction of the synergism in the mixed micelle also demonstrated the plausibility of this model. In this study, we will investigate how the synergism of the mixtures of cationic surfactants with different halides as their * Corresponding author. E-mail:
[email protected]. (1) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1985. (2) Villeneuve, M.; Sakamoto, H.; Minamizawa, H.; Ikeda, N.; Motomura, K.; Aratono, M. J. Colloid Interface Sci. 1997, 194, 301. (3) Bain, C. D.; Casson, B. D. J. Phys. Chem. B 1998, 103, 4678. (4) Kashimoto, K.; Matsubara, H.; Takahara, H.; Nakano, T.; Takiue, T.; Aratono, M. Colloid Polym. Sci. 2004, 329, 1435. (5) Matsubara, H.; Nakano, T.; Matsuda, T.; Takiue, T.; Aratono, M. Langmuir 2005, 21, 8131.
Figure 1. Schematic illustration of the staggered structure.
counterions is affected when one species of the counterions is adsorbed preferentially over another at the air/water interface by the surface tension measurements of aqueous solutions of the hexadecyltrimethylammonium chloride (HTAC)-DTAB system. Experimental Section Surfactants purchased from Tokyo Kasei Kogyo Co., Ltd. were purified by recrystallization from ethanol/acetone mixtures of 1/5 volume ratio for DTAB and 1/9 volume ratio for HTAC. Their purities were confirmed by the absence of a minimum around the critical micelle concentration (cmc) on the surface tension versus molality curves. The drop volume technique was adopted for our surface tension measurements.6,7 The total molality of surfactants and relative proportion of DTAB are defined by the following equations m ˆ ) mHTA+ + mCl- + mDTA+ + mBr-
(1)
and Xˆ 2 )
mDTA+ + mBrm ˆ
(2)
where mHTA+, mCl-, mDTA+, and mBr- are the molalities of the HTA+, Cl-, DTA+, and Br- ions.8
Result and Discussion Strong Synergism in the Adsorbed Film and Micelle. Shown in Figure 2 are the data from surface tension measurements. The total differential of γ of binary surfactant mixtures (6) Lando, L. J.; Oakley, T. H. J. Colloid Interface Sci. 1967, 25, 526. (7) Motomura, K.; Iwanaga, S.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32. (8) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H. J. Colloid Interface Sci. 1998, 200, 161.
10.1021/la052096m CCC: $33.50 © 2006 American Chemical Society Published on Web 02/16/2006
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Figure 2. Surface tension vs molality curves of the HTAC-DTAB system. The values of Xˆ 2 are (1) 0, (2) 0.250, (3) 0.500, (4) 0.700, (5) 0.800, (6) 0.901, (7) 0.950, (8) 0.980, (9) 0.990, and (10) 1.
without common ions is expressed as
dγ ) -
( )
RTΓH RTΓH dm ˆ - (Xˆ H2 - Xˆ 2) dXˆ 2 m ˆ Xˆ 1Xˆ 2
(3)
at constant T and p.8 The total surface density of components and the composition of DTAB in the adsorbed film are defined respectively by H H H H Γˆ H ) ΓHTA + + ΓCl- + ΓDTA+ + ΓBr-
(4)
and
Xˆ H2 )
H H ΓDTA + + ΓBr-
(5)
Γˆ H
where the surface density ΓHi of component i is defined with reference to the two dividing planes that make the excess numbers of moles of water and air zero.9 From eq 3, the miscibility of surfactant molecules in the adsorbed film is elucidated by estimating the composition Xˆ H2 through the equation
( )( )
Xˆ 1Xˆ 2 ∂m ˆ Xˆ H2 ) Xˆ 2 m ˆ ∂Xˆ 2
(6)
Figure 3. Phase diagram of adsorption of the HTAC-DTAB system for γ values of (1) 60, (2) 55, and (3) 45 mN m-1; (s) m ˆ vs Xˆ 2; (---) m ˆ vs Xˆ H2 ; and (-‚-) ideal mixing.
T,p,γ
gives us the excess Gibbs energy of adsorption defined by and then by taking advantage of the phase diagram of adsorption (PDA), which expresses the quantitative relation among m ˆ , Xˆ 2, and Xˆ H2 . The PDA of the HTAC-DTAB system is shown in Figure 3 and has a negative azeotropic point at which the composition of the adsorbed film coincides with that of the bulk solution. The deviation of the m ˆ versus Xˆ H2 curves from the ideal mixing 8 line given by
m ˆ )m ˆ 01 + (m ˆ 02 - m ˆ 01)Xˆ H2 (9) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348.
(7)
H H gˆ H,E ) RT(Xˆ H1 ln ˆf 1( + Xˆ H2 ln ˆf 2( )
(8)
H Here ˆfi( is the mean activity coefficient of component i in the adsorbed film calculated from
H ˆf i( )
( )( ) m ˆ Xˆ i m ˆ 0i Xˆ Hi
1/2
(9)
The gˆ H,E values are given in Figure 4. Considering that the smallest value of gˆ H,E was -0.4 kJ mol-1 and no azeotropic point was observed at any surface tensions for the HTAB-DTAB system,
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Langmuir, Vol. 22, No. 6, 2006 2513
Figure 4. Excess Gibbs energy of adsorption vs composition curves of the HTAC-DTAB system at (1) 60, (2) 55, (3) 50, and (4) 45 mN m-1. The dotted curve shows the HTAB-DTAB system at 45 mN m-1.
Figure 5. Phase diagram of micelle formation of the HTACDTAB system: (s) C ˆ vs Xˆ 2, (---) C ˆ vs Xˆ M 2 , and (-‚-) ideal mixing.
the much smaller values definitely show that the preferential adsorption does significantly influence the synergism of the cationic surfactant mixture. The strong synergism also occurs in the mixed micelle although it was not observed in the HTAC-DTAC system and was quite weak in the HTAB-DTAB systems. This is demonstrated as a large negative deviation of the phase diagram of micelle formation (PDM) shown in Figure 5 and the negative excess Gibbs energy of micelle formation shown in Figure 6. Here, the composition of the micelle defined by
Xˆ M 2 )
M M NDTA + + NBr-
(10)
N ˆM
was evaluated numerically by applying
ˆ2 Xˆ M 2 )X
( )( ) 2Xˆ 1Xˆ 2 ∂C ˆ C ˆ ∂Xˆ 2
(11)
T,p
to the total molality at cmc C ˆ versus Xˆ 2, and the number of excess molecules of component i per micelle particle NM i is defined with reference to a spherical dividing plane that makes the number of excess water molecules zero.7 Evaluation of Compositions of Individual Ions in the Adsorbed Film and Micelle. We have previously shown that the excess Gibbs energy of adsorption of binary surfactant mixtures without common ions, gˆ H,E evaluated by eq 8, consists of two contributions; one is attributable to the intrinsic interaction between surfactant ions given by8
[ ( ) ( )]
ˆ H1 ln gˆ H,E in ) RT X
H γ1(
H,0 γ1(
+ Xˆ H2 ln
H γ2(
H,0 γ2(
H H,0 and γi( are respectively the mean activity coefficients Here γi( of surfactant i in the mixed and single adsorbed films at a given H,p surface tension and fi( is a factor arising from preferential adsorption. Because the electroneutrality in the adsorbed film requires only the condition
H H H H XHTA + + XDTA+ ) XBr- + XCl-
(12)
and the other is attributable to the preferential adsorption of ions given by H,p ˆ H1 ln f1( + Xˆ H2 ln f2H,p(] gˆ H,E pr ) RT[X
Figure 6. Excess Gibbs energy of micelle formation vs composition curve of the HTAC-DTAB system (solid curve) and that of the HTAB-DTAB system (dotted curve).
(13)
(14)
XHj could not be evaluated separately even if the surface tension was measured as a function of both m ˆ and Xˆ 2. In the following discussion, however, we will show that the evaluation becomes possible by introducing the concepts of nonpreferential and H,p preferential surface densities, ΓH,n j and Γj of ion j and using the gˆ H,E values of both the HTAC-DTAB and HTAB-DTAB systems.
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ΓH,n and ΓH,p are defined so as to satisfy the relations j j
H ΓBr - )
H,n H,n ΓHTA + + ΓCl- ) 0
(15)
H,n H,n ΓDTA + + ΓBr- ) 0
(16)
)
it is found that the preferential adsorption always contributes negatively to the excess Gibbs energy of adsorption as H,p H,p 2 1/2 ) [1 - (XiH,p e1 fi( + - Xi- ) ]
(19)
Substituting this equation to eq 13, we have
gˆ H,E pr H,p H,p 2 1/2 ) Xˆ H1 ln[1 - (XHTA + + - XCl-) ] RT H,p H,p 2 1/2 (20) Xˆ H2 ln[1 - (XDTA + - XBr-) ] By considering H H ΓHTA + - ΓCl-
(21)
Γˆ H1
and H H ΓDTA + - ΓBr-
(22)
Γˆ H2
equation 20 can be rewritten as
[ ( )]
gˆ H,E pr ∆Γ ) Xˆ H1 ln 1 - H H RT Γˆ Xˆ 1
2 1/2
[ ( )]
+ Xˆ H2 ln 1 -
∆Γ Γˆ HXˆ H2
2 1/2
(23) where H H H H ∆Γ ≡ ΓHTA + - ΓCl- ) - (ΓDTA+ - ΓBr-)
(24)
Thus one can calculate the surface density of individual ions by the following relations if ∆Γ is known: H ΓHTA + )
∆Γ + Xˆ H1 Γˆ H 2
(25)
H ΓCl - ) -
∆Γ - Xˆ H1 Γˆ H 2
(26)
H ΓDTA + ) -
and
∆Γ/Γˆ H - Xˆ H1 X 2
(30)
∆Γ/Γˆ H - Xˆ H2 )2
(31)
∆Γ/Γˆ H + Xˆ H2 X 2
(32)
H XCl - ) -
H XDTA +
(18)
ΓiH+ + ΓiH-
H,p H,p XDTA + - XBr- )
(29)
(17)
ΓiH,p +
H,p H,p XHTA + - XCl- )
∆Γ/Γˆ H + Xˆ H1 2
H XHTA + )
Employing the ratio of the preferential surface density of an ion to the surface density of the surfactant defined by
XiH,p +
∆Γ - Xˆ H2 Γˆ H 2
(27)
(28)
Furthermore, the composition of ions in the adsorbed film is calculated by
and
+ ΓH,p ΓHj ) ΓH,n j j
∆Γ + Xˆ H2 Γˆ H 2
and H XBr - )
The evaluation procedure was as follows. First, we regarded gˆ H,Eas gˆ H,E ˆ H,E versus pr and found a proper ∆Γ value to fit the g H H Xˆ 2 curve at several Xˆ 2 values for a given γ by using eq 23 and Figure 4. We then determined the tentative surface densities of ions from eqs 25-28. Because gˆ H,E in represents the contribution of the intrinsic interaction between surfactant ions, we estimated it from the gˆ H,E values of the HTAB-DTAB system at the tentative H H H composition calculated from ΓDTA +/(ΓHTA+ + ΓDTA+) by using the dotted curve in Figure 4, and then we found the more plausible magnitude of gˆ H,E ˆ H,E ˆ H,E. pr by subtracting the estimated g in from g We iteratively calculated surface densities of ions until they converged. The results of the calculation are shown in Table 1 H H for γ ) 45 mN m-1. It is clearly shown that XHTA + > XDTA+ and H H XBr- > XCl- over the wide surface composition range. To see the preferential adsorption visually, the proportion of H H H bromide ion to the total number of anions, XBr -/(XCl- + XBr-), and that of dodecyltrimethylammonium ion to the total number H H H of surfactant ions, XDTA +/(XHTA+ + XDTA+), were plotted as a function of the bulk composition in Figure 7. From this Figure, it is found that the mixed adsorbed film is substantially formed by more surface-active hexadecyltrimethylammonium ions and bromide ions over a considerably wide range of bulk composition. H H H Open circles and squares represent XDTA +/(XHTA+ + XDTA+) in the HTAC-DTAC and HTAB-DTAB systems, respectively. By considering that the proportions of dodecyltrimethylammonium ions are similar to each other in three systems, the large negative excess Gibbs energy of the HTAC-DTAB system can occur from the preferential adsorption of bromide ions against chloride ions. However, from the fact that the minimum gˆ H,E value of the dodecylammonium chloride-decylammonium bromide system, for which a staggered structure is not expected in the adsorbed film, is only -0.8 kJ mol-1,8,10 it may be concluded that the staggered structure formation triggers the entire energetic stabilization of the adsorbed film. Similar relations can be also derived for the mixed micelle as
gˆ M,E pr 2 1/2 ) Xˆ M ˆ MXˆ M + 1 ln[1 - (∆N/N 1) ] RT 2 1/2 ˆ MXˆ M (33) Xˆ M 2 ln[1 - (∆N/N 2) ] (10) Yamanaka, M.; Amano, T.; Ikeda, N.; Aratono, M.; Motomura, K. Colloid Polym. Sci. 1992, 270, 682.
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Langmuir, Vol. 22, No. 6, 2006 2515
Table 1. Compositions of Ions Calculated for Mixed Adsorbed Film at γ ) 45 mN m-1 H Xˆ H2 XHTA +
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.498 0.498 0.498 0.496 0.478 0.396 0.298 0.199 0.1
H XCl -
H XDTA +
H XBr -
H H XHTA + + XBr-
gˆ Hin
gˆ HPr
0.402 0.302 0.202 0.104 0.022 0.004 0.002 0.001 0
0.002 0.002 0.002 0.004 0.022 0.104 0.202 0.301 0.4
0.098 0.198 0.298 0.396 0.478 0.496 0.498 0.499 0.5
0.600 0.699 0.799 0.896 0.958 0.889 0.795 0.697 0.599
0.00 -0.01 -0.01 -0.03 -0.25 -0.43 -0.33 -0.25 -0.12
-0.74 -1.31 -1.90 -2.34 -2.27 -1.86 -1.44 -0.91 -0.51
Table 2. Compositions of Ions Calculated for the Mixed Micelle M Xˆ M XHTA + 2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.500 0.499 0.498 0.494 0.468 0.388 0.292 0.193 0.095
M XCl -
M XDTA +
M XBr -
M M XHTA + + XBr-
gˆ M in
gˆ M Pr
0.400 0.301 0.202 0.106 0.032 0.012 0.008 0.007 0.005
0.000 0.001 0.002 0.006 0.032 0.112 0.208 0.307 0.405
0.100 0.199 0.298 0.394 0.468 0.488 0.492 0.493 0.495
0.600 0.699 0.797 0.888 0.936 0.876 0.785 0.687 0.590
0.00 0.00 0.00 0.00 -0.02 -0.05 -0.02 0.00 -0.01
-0.66 -1.19 -1.60 -1.82 -1.77 -1.44 -1.01 -0.56 -0.21
where M M M M ∆N ≡ NHTA + - NCl- ) -(NDTA+ - NBr-)
(34)
The aggregation number of mixed micelle N ˆ M and the difference ∆N cannot be evaluated solely from the surface tension measurements; however, it is possible to calculate the ratio ∆N/ N ˆ M from eq 33 and thus the composition of each ion in the mixed micelle through the following equations: M XHTA +
∆N/N ˆ M + Xˆ M 1 ) 2
(35)
Xˆ M ˆM 1 - ∆N/N 2
(36)
M XCl - )
M XDTA + )
∆N/N ˆ M - Xˆ M 2 2
(37)
and M XBr - )
∆N/N ˆ M + Xˆ M 2 2
(38)
The results are given in Table 2. It is clear that HTA+ and Brare preferentially incorporated into the mixed micelle.
Figure 7. Relative proportion of the bromide ion to the total number of anions (9) and that of the dodecyltrimethylammonium ion to the total number of surfactant ions in the adsorbed film (b). Open circles and squares represent the proportions of dodecyltrimethylammonium ion calculated from the PDAs of the HTAC-DTAC and HTABDTAB systems.
In this article, we have shown the extremely strong synergetic adsorption and micelle formation in a cationic surfactant mixture without common ions have and presented thermodynamic relations that make it possible to evaluate the compositions of individual ions in the adsorbed film and micelle. Furthermore, we have concluded on the basis of the calculated compositions that the occurrence of synergism is closely related to the preferential adsorption of bromide ions over chloride ions. When the two different species of counterions coexist in the adsorbed film, the entropy of mixing is likely to be important in addition to the energetic advantage arising from the shielding of the electric repulsion between surfactant heads due to the preferential adsorption of bromide ions and staggered structure formation accompanied by it. To clarify the origin of synergism in more detail, a titration calorimetric study is now being performed because titration calorimetry gives us information on the excess enthalpy of micelle formation. Acknowledgment. This work was supported in part by the Kao Foundation for Arts and Sciences and by a Grant-in-Aid for Scientific Research (B) (no. 16350075) from the Japan Society for the Promotion of Science. LA052096M
