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Surface adsorption and aggregate formation of aqueous binary mixture of cationic surfactant and sugar surfactant
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Colloids and Surfaces A: Physicochem. Eng. Aspects 315 (2008) 183–188
Surface adsorption and aggregate formation of aqueous binary mixture of cationic surfactant and sugar surfactant H. Matsubara ∗ , H. Obata, T. Matsuda, T. Takiue, M. Aratono Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan Received 18 April 2007; received in revised form 23 July 2007; accepted 26 July 2007 Available online 8 August 2007
Abstract The surface tension of aqueous solutions of dodecyltrimethylammonium bromide (DTAB) and octyl--d-glucopyranoside (OG) mixture was measured as a function of the total molality of surfactants and the relative proportion of OG under atmospheric pressure at 298.15 K by drop volume technique. The results of surface tension measurements were analyzed by originally developed thermodynamic equations then phase diagrams of adsorption and micelle formation were constructed. From the analysis of surface tension data, it was suggested that the addition of relatively small amount of DTAB molecules helps the denser monolayer formation compared with the ideal mixing. Furthermore, it was also suggested that the phase diagram of micelle formation has a negative azeotropic point and that the interaction between different components is stronger in the mixed micelle than in the adsorbed film from the view point of the excess Gibbs energy. From these results, it is concluded that the hydrogen bond formation between OG molecules is the main contribution to determine the physical properties in the adsorbed film whereas the ion–dipole interaction between head groups of different components becomes main cause of attractive interaction in the micelle. © 2007 Published by Elsevier B.V. Keywords: Thermodynamics; Surface tension; Sugar surfactant; Adsorption; Micelle
1. Introduction Sugar surfactant is a series of surfactants consisting of a hydrophobic chain linked to a sugar ring residue and has widely used recently in pharmaceutical, cosmetic and food industries due to their harmlessness to human bodies [1,2]. One of the most important chemical characteristics of sugar surfactant is the bulky hydrophilic groups which form lateral hydrogen bond network and affect strongly the bulk phase behavior [3–10]. As a result of the lateral hydrogen bond network, most of sugar surfactants exhibit both lyotropic and thermotropic liquid crystals. We have recently showed that the molecular packing in the surfactant aggregates can be a crucial factor to determine the interaction between surfactant molecules by the surface tension measurements and thermodynamic analysis of surface tension data. For example, dodecyltrimethylammonium bromide (DTAB) and octyl methyl sulfoxide (OMS) molecules
∗
Corresponding author. E-mail address: [email protected] (H. Matsubara).
0927-7757/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.colsurfa.2007.07.034
mixed more effectively in the adsorbed film than in the micelle since the small hydrophilic group of OMS molecule allows filling the space among hydrocarbon chains of DTAB molecules which are loosely packed in the pure adsorbed film due to the bulkiness of the trimethylammonium heads [11]. Furthermore, a kind of synergetic effects is also caused when the difference of the hydrophobic chain length is matched with the hydration diameter of the hydrophilic group for mixed systems of alkyltrimethylammonium halides [12–14]. We interpreted this phenomenon by the staggered structure formation at the air/water interface proposed by Penfold et al. based on the neutron reflection experiments [15]. In this paper, we will apply the same experimental procedure to an aqueous binary mixture of a cationic surfactant, DTAB, and a sugar surfactant, octyl--d-glucopyranoside (OG) in order to examine the effect of the bulkiness of the head group and hydrogen bond formation between OG molecules on the molecular packing in the mixed adsorbed film and micelle. For this purpose, the surface tension of aqueous solutions of DTAB–OG mixtures was measured as a function of the total molality of surfactants and the bulk composition of OG under atmospheric pressure at 298.15 K by the drop volume technique. The results
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of the surface tension measurements were analyzed by originally developed thermodynamic equations then phase diagrams of adsorption and micelle formation were constructed. 2. Experimental 2.1. Material DTAB was purchased from Tokyo Kasei Kogyo Co. Ltd. and purified by recrystalization three times from the mixtures of ethanol and acetone (1:5 volume ratio) then dried in vacuum. OG was purchased from Anatrace INC. (>99%) and used as received. The purities of surfactants were confirmed by the absence of minimum on the surface tension versus molality curve around the critical micelle concentration (cmc). Water used for all experiments was distilled three times. The second and third stages of distillation were done from dilute alkaline permanganate solution. 2.2. Surface tension measurement Surface tension of aqueous solutions of DTAB–OG mixtures was measured at 298.15 K under atmospheric pressure by the drop volume method [16,17] as a function of the total molality and composition in the bulk solution defined by m ˆ = 2m1 + m2
(1)
and H ˆ 2H = Γ2 X Γˆ H
and ˆ 2 = m2 X m ˆ
ˆ 2 = 0, Fig. 1. Surface tension vs. molality curves for DTAB–OG system: (1) X (2) 0.1, (3) 0.2, (4) 0.3, (5) 0.4, (6) 0.5, (7) 0.6, (8) 0.7, (9) 0.8 and (10) 1.
(2)
where m1 and m2 are molalities of DTAB and OG, respectively. In these definitions, the dissociation of DTAB molecules into DTA+ and Br− ions are taken into account. Advantages of these definitions were explained thermodynamically elsewhere [18,19]. The experimental error of surface tension measurements was <0.1 mN m−1 .
(5)
with respect to two dividing planes which make the excess number of moles of air and water zero simultaneously.
3. Result and discussion The results of surface tension measurement are shown as γ versus m ˆ curves at constant bulk composition in Fig. 1. γ values decrease rapidly with increasing m ˆ and each curve has a distinct break point at the concentrations corresponding to the cmc then takes almost constant value at high molalities. The total differential of surface tension is given by [19] RT Γˆ H dγ = −sdT + vdp − dm ˆ m ˆ H RT Γˆ H ˆ2 −X ˆ2 ˆ2 − X dX (3) ˆ 1X ˆ2 X where the total surface density of surfactants and the composition of OG in the adsorbed film are defined as Γˆ H = 2Γ1H + Γ2H
(4)
Fig. 2. Total surface density vs. molality curves for DTAB–OG system: (1) ˆ 2 = 0, (2) 0.1, (3) 0.2, (4) 0.4, (5) 0.5, (6) 0.6, (7) 0.7, (8) 0.8 and (9) 1. X
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Fig. 3. Eestimation of occupied area of OG molecule at air–water interface from CPK model (left: top view, right: side view). 0.44 nm2 roughly corresponds to the minimum occupied area of OG molecule at the air–water interface and 0.65 nm2 is the area occupied by freely rotating, vertically orientated OG molecule.
From these equations, the total surface density of surfactants can be evaluated by applying m ˆ ∂γ H ˆ Γ =− (6) RT ∂m ˆ T,p,Xˆ 2 to γ versus m ˆ curves (Fig. 2). The surface density increases monotonically with increasing m ˆ and approaches to a saturation value around cmc. It should be noted here that the mean area per molecule in the adsorbed film calculated from 1 ˆ = A (7) NA Γˆ H 0.40 nm2
is for pure OG system, which is almost identical with the cross sectional area of OG molecule calculated from CPK model (Fig. 3). Considering that the occupied area per surfactant molecule of a typical nonionic surfactant such as pentaethylene glycol monooctylether (C8E5) is twice as large as its cross sectional area around the cmc [20], the hydroxyl groups of glucoside units of OG are considerably dehydrated in the adsorbed film to form hydrogen bonds between OG molecules. As a result of dehydration of OG molecules followed by hydrogen bond formation between them, OG molecules can compactly pack in the adsorbed film in spite of their bulky head groups. This adsorption behavior of OG molecules is probably correlated to the fact that the lamellar liquid crystal phase of some sugar surfactants appeared in relatively dilute region compared with other nonionic surfactants. ˆ 2 curves obtained by plotting the m The m ˆ versus X ˆ values at a given γ are shown in Fig. 4 together with the m ˆ versus ˆ H estimated from composition of adsorbed film X 2 ˆ ˆ ∂m ˆ ˆ 2H = X ˆ 2 − X 1 X2 X (8) ˆ m ˆ ∂X2 T,p,γ ˆ2 The endpoints of a horizontal line connecting the m ˆ versus X H ˆ curve with m ˆ versus X2 curve correspond to the compositions of the bulk solution and to that of the adsorbed film in equilibrium with each other at the given γ, hence, this figure is called the ˆH phase diagram of adsorption. It is noted that the m ˆ versus X 2 curves show a slightly negative deviation from the straight line showing the ideal mixing in the adsorbed film ˆ 2H m ˆ =m ˆ 01 + (m ˆ 02 − m ˆ 01 )X
(9)
ˆ 02 are the molalities of the pure surfactant systems where m ˆ 01 and m at the given surface tension. To look more closely into the intermolecular interaction between DTAB and OG molecules, we
Fig. 4. Phase diagram of adsorption of DTAB–OG system at (1) 41 mN m−1 , (2) 45 mN m−1 and (3) 50 mN m−1 . Solid, dotted, and straight lines respectively ˆ 2 curve, m ˆ H curve, and ideal mixing line. show m ˆ vs. X ˆ vs. X 2
introduce the activity coefficients of component i then estimate the excess Gibbs energy in the adsorbed film defined by H ˆ 1H lnfˆ 1± ˆ 2H lnfˆ 2H ) gˆ H,E = RT (X +X
(10)
ˆH The fˆ iH values are calculated by substituting the evaluated X 2 from the Eq. (8) in to the equation ˆi m ˆX fˆ iH = 0 H ˆi m ˆiX
(11)
ˆ H curves at 41, 45, 50 mN m−1 are shown in The gˆ H,E versus X 2 H,E Fig. 5. The gˆ values are negative and their absolute value increases with decreasing surface tension. The former indicates that the mutual interaction between DTAB and OG molecules in the adsorbed film is stronger than that between the same molecules and the latter relates to the packing of the molecules in the adsorbed film through the excess surface area per molecule defined by [21,22] H,E ˆ E = − ∂ (ˆg /NA ) A (12) ∂γ ˆH T,p,X 2
By applying this equation to Fig. 5, it is found that the excess surface area is negative and the adsorbed molecules tend to occupy smaller area compared with the ideal mixing. In actual, the total number of hydrocarbon chains in the mixed adsorbed film ˆH = further increases up to Γ1H + Γ2H = 4.36 μmol m−2 at X 2 0.9 from that in the single component adsorbed film of OG molecules (Γˆ H = Γ1H = 4.1 μmol m−2 ). The plausible conformation between DTA+ ions and OG molecules in the adsorbed film which allows the increase in the surface density is not fully understood; however, considering that the minimum of the
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Fig. 5. Excess Gibbs energy of adsorption vs. composition of adsorbed film plot at (1) 41 mN m−1 (black circle), (2) 45 mN m−1 (grey) and (3) 50 mN m−1 (white).
ˆ vs. Fig. 6. Phase diagram of micelle formation for DTAB–OG system: (1) C ˆ vs. X ˆ 2 curve (solid line), (2) C ˆ M curve (dotted line), and (3) ideal mixing line X 2 (straight line).
excess Gibbs energy is observed on the OG rich side in the phase diagram of adsorption, the attractive interaction between DTA+ ions and hydroxyl group of OG molecules in the adsorbed film becomes more effective when DTA+ ion is surrounded by some OG molecules, namely, it is considered that DTA+ ion fills the gap space among OG molecules. Similarly the composition of OG in the micelle
is much more negative in the micelle than the excess Gibbs energy in the adsorbed film at the cmc, gˆ H,E,C , obtained by extrapolating gˆ H,E versus γ curves to the surface tension at the cmc as shown in Fig. 7. Here the composition in the adsorbed film at the cmc and activity coefficients in the mixed micelle were
ˆ 2M = X
N2M 2N1M + N2M
(13)
can be evaluated by applying the following equation ˆ ˆ 1X ˆ2 X ∂C M ˆ ˆ X2 = X2 − ˆ2 ˆ ∂X C
(14)
T,p
ˆ versus X ˆ 2 curve. The results of calculation are plotto the C ted as the form of the phase diagram of micelle formation in Fig. 6 analogously to the phase diagram of adsorption in Fig. 4. The straight lines in the figure correspond to the ideal mixing criterion for the mixed micelles given by ˆ =C ˆ 10 + (C ˆ 20 − C ˆ 10 )X ˆ 2M C
(15)
The phase diagram of micelle formation has a distinct negative azeotropic point indicating that the mixing of molecules is energetically favorable in the whole composition. The stronger mutual interaction between DTA+ ions and OG molecules compared with that in the adsorbed film can be manifested from that the excess Gibbs energy of micelle formation calculated from gˆ
M,E
=
M ˆ 1M lnfˆ 1± RT (X
ˆ 2M lnfˆ 2M ) +X
(16)
Fig. 7. Excess Gibbs energy of micelle formation vs. composition of micelle plot (grey circle). Open circle shows the excess Gibbs energy of adsorption extrapolated to cmc by using the plots in Fig. 4.
H. Matsubara et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 315 (2008) 183–188
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Table 1 Comparison of excess Gibbs energy of adsorption, micelle formation and excess surface area Entry 1 2 3 4 5 6 7 8
DTAB–OG HTAB–DTAB13 Tetradecyltrimethylammonium bromide (TTAB)–DTAB13 Tetradecyltrimethylammonium chloride (TTAC)–decyltrimethylammonium chloride (DTAC)13 Hexadecyltrimethylammonium chloride (HTAC)–DTAC13 HTAC–DTAB14 Sodium dodecylsulfate (SDS)–C8E423 Decylammonium chloride (DAC)–C8E424
evaluated respectively by applying the following equations: C ˆ 1X ˆ2 ∂γ X H,C M ˆ ˆ X 2 = X2 − (17) ˆ 2 T,p ∂X RT Γˆ H,C and ˆX ˆi C fˆ iM = 0 M ˆ X ˆ C i
(18)
i
The energetic superiority of the micelle over the adsorbed film suggests that the hydrogen bond formation between OG molecules is less effective in the pure OG micelle due to its spherical geometry than in the pure OG adsorbed film. Therefore, it is said that the penetration of DTA+ ions into the wedge-like space between OG molecules can stabilize the mixed micelles by the ion–dipole interaction instead of the hydrogen bond between OG molecules. On the contrary, the OG molecules stabilize DTAB micelles by shielding the electric repulsion between DTA+ ions and also by the ion–dipole interaction on the DTAB-rich side of the phase diagram. For the mixed systems of alkyltrimethylammonium halides, the synergism occurs by the shorter surfactant molecules filling space among hydrocarbon chains of the longer surfactant molecules. Since the resultant staggered arrangement is suitable for the planar aggregates, the mixing of surfactant molecules is more favorable in the adsorbed film than in the micelle and the excess surface area takes a negative value as shown in Table 1 (entry 2–6). For the typical ionic–nonionic surfactant mixtures, on the other hand, the main cause of the synergism is an attraction with a directionality between the hydrophilic groups which has a relatively large optimal interaction distance compared to the van der Waals interaction between hydrophobic groups [23,24]. This configuration can be taken more easily in a loosely packed adsorbed film or in a wedge-like space in a spherical micelle; however, it becomes more difficult to keep the optimal interaction distance in a tightly packed adsorbed film. Therefore, the mixed micelle formation becomes more advantageous compared to the mixed adsorbed film around the cmc and the excess surface area takes a positive value (entry 7 and 8). Taking account of all experimental data obtained in the present system, it is found that the interplay between DTAB and OG molecules is suitable to form effectively packed aggregates both in the planer (adsorbed film) and spherical (micelle) geometry; however, the way of molecular packing in each aggregate seems to be somewhat different. OG molecules can
gˆ H,E (kJ mol−1 )
gˆ M,E (kJ mol−1 )
ˆE A
−0.3 −0.4 +0.2 +0.1 −0.2 −2.6 −1.3 −0.2
−0.5 −0.1 +0.2 +0.2 +0.4 −2.0 −1.7 −0.8
<0 <0 <0 <0 <0 <0 >0 >0
form hydrogen bond in the planer geometry and this hydrogen bond formation is probably the main contribution to determine the physical properties of the adsorbed film. However, the ion–dipole interaction between head groups of different components becomes more effective in the curved geometry and main cause of attractive interaction in the micelle as same as other ionic–nonionic surfactant systems. The existence of different interaction mechanisms in the adsorbed film and micelle makes it possible to show the intermediate behavior between the cationic–cationic surfactant mixtures and the typical ionic–nonionic surfactant mixtures. 4. Conclusion We have measured the surface tension of aqueous solutions of cationic surfactant (DTAB) and sugar surfactant (OG) mixture and analyzed them by originally developed thermodynamic equations. Our results suggest that OG molecules form hydrogen bond on their own and form densely packed monolayer at the air–water interface compared to the other nonionic surfactants and the addition of the cationic surfactant enhances the molecular packing by filling the space among OG molecules. By ˆ E values of the present system with comparing gˆ H,E , gˆ M,E and A those published in the previous papers, it was also suggested that the synergism of the surfactant mixture can be classified into three categories. Normally, the ionic and nonionic surfactant molecules interact each other mainly through the ion–dipole interaction between hydrophilic groups. gˆ M,E is smaller than ˆ E takes a positive value. If a combination of surfacgˆ H,E and A tants is geometrically suitable to form planer aggregates, gˆ H,E ˆ E takes a negative value. In becomes smaller than gˆ M,E and A this case, in order to form vacant spaces available to surfactant molecules, at least, one surfactant has to have a bulky head group. In other words, any particular interaction is not necessary between hydrophilic groups as clearly shown in the synergism of cationic–cationic surfactant systems. In this study, it has been firstly shown that both the adsorbed film and the micelle can take effective molecular packing by mixing ionic surfactant with nonionic surfactant with bulky hydrophilic group. References [1] B. Hoffmann, G. Platz, Curr. Opin. Colloid Interface Sci. 6 (2001) 171. [2] M. Hato, Curr. Opin. Colloid Interface Sci. 6 (2001) 268. [3] C. Dupuy, X. Auvray, C. Petipas, Langmuir 13 (1997) 3965.
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[4] G. Garofalakis, B.S. Murray, D.B. Sarney, J. Colloid Interface Sci. 229 (2000) 391. [5] B.J. Boyd, C.J. Drummond, I. Krodkiewska, A. Weerawardena, D.N. Furlong, F. Grieser, Langmuir 17 (2001) 6100. [6] P.D. Burgo, E. Janquera, E. Aicart, Langmuir 20 (2004) 1587. [7] J.M. Vanderkooi, J.L. Dashnau, B. Zelent, Biochem. Biophys. Acta 214 (2005) 1749. [8] H. Kahl, S. Enders, K. Quitzsch, Colloid Interface Sci. A 183–185 (2001) 661. [9] C. Stubenrauch, Curr. Opin. Colloid Interface Sci. 6 (2001) 160. [10] P. Sakya, J.M. Seddon, V. Vill, Liquid Cryst. 23 (1997) 409. [11] M. Villeneuve, H. Sakamoto, H. Minamizawa, N. Ikeda, K. Motomura, M. Aratono, J. Colloid Interface Sci. 194 (1997) 301. [12] K. Kashimoto, H. Matsubara, H. Takahara, T. Nakano, T. Takiue, M. Aratono, Colloid Polym. Sci. 329 (2004) 1435. [13] H. Matsubara, T. Nakano, T. Matsuda, T. Takiue, M. Aratono, Langmuir 21 (2005) 8131. [14] H. Matsubara, T. Nakano, T. Matsuda, T. Takiue, M. Aratono, Langmuir 22 (2006) 2511.
[15] E.M. Lee, R.K. Thomas, J. Penfold, R.C. Ward, J. Phys. Chem. 93 (1989) 381. [16] J.L. Lando, H.T. Oakley, J. Colloid Interface Sci. 25 (1967) 526. [17] K. Motomura, S. Iwanaga, Y. Hayami, S. Uryu, R. Matuura, J. Colloid Interface Sci. 80 (1981) 32. [18] H. Matsubara, A. Ohta, M. Kameda, N. Ikeda, M. Aratono, Langmuir 16 (2000) 7589. [19] M. Aratono, M. Villeneuve, T. Takiue, N. Ikeda, H. Iyota, J. Colloid Interface Sci. 200 (1998) 161. [20] K. Wongwailikhit, A. Ohta, K. Seno, A. Nomura, T. Shinozuka, T. Takiue, M. Aratono, J. Phys. Chem. B 105 (2001) 1462. [21] H. Iyota, N. Todoroki, N. Ikeda, K. Motomura, A. Ohta, M. Aratono, J. Colloid Interface Sci. 216 (1999) 41. [22] M. Aratono, A. Ohta, H. Minamizawa, N. Ikeda, H. Iyota, T. Takiue, J. Colloid Interface Sci. 217 (1999) 128. [23] H. Matsubara, S. Muroi, M. Kameda, N. Ikeda, A. Ohta, M. Aratono, Langmuir 17 (2003) 7752. [24] H. Matsubara, A. Ohta, M. Kameda, M. Villeneuve, N. Ikeda, M. Aratono, Langmuir 16 (2000) 7589.
Colloids and Surfaces A: Physicochem. Eng. Aspects 315 (2008) 183–188
Surface adsorption and aggregate formation of aqueous binary mixture of cationic surfactant and sugar surfactant H. Matsubara ∗ , H. Obata, T. Matsuda, T. Takiue, M. Aratono Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan Received 18 April 2007; received in revised form 23 July 2007; accepted 26 July 2007 Available online 8 August 2007
Abstract The surface tension of aqueous solutions of dodecyltrimethylammonium bromide (DTAB) and octyl--d-glucopyranoside (OG) mixture was measured as a function of the total molality of surfactants and the relative proportion of OG under atmospheric pressure at 298.15 K by drop volume technique. The results of surface tension measurements were analyzed by originally developed thermodynamic equations then phase diagrams of adsorption and micelle formation were constructed. From the analysis of surface tension data, it was suggested that the addition of relatively small amount of DTAB molecules helps the denser monolayer formation compared with the ideal mixing. Furthermore, it was also suggested that the phase diagram of micelle formation has a negative azeotropic point and that the interaction between different components is stronger in the mixed micelle than in the adsorbed film from the view point of the excess Gibbs energy. From these results, it is concluded that the hydrogen bond formation between OG molecules is the main contribution to determine the physical properties in the adsorbed film whereas the ion–dipole interaction between head groups of different components becomes main cause of attractive interaction in the micelle. © 2007 Published by Elsevier B.V. Keywords: Thermodynamics; Surface tension; Sugar surfactant; Adsorption; Micelle
1. Introduction Sugar surfactant is a series of surfactants consisting of a hydrophobic chain linked to a sugar ring residue and has widely used recently in pharmaceutical, cosmetic and food industries due to their harmlessness to human bodies [1,2]. One of the most important chemical characteristics of sugar surfactant is the bulky hydrophilic groups which form lateral hydrogen bond network and affect strongly the bulk phase behavior [3–10]. As a result of the lateral hydrogen bond network, most of sugar surfactants exhibit both lyotropic and thermotropic liquid crystals. We have recently showed that the molecular packing in the surfactant aggregates can be a crucial factor to determine the interaction between surfactant molecules by the surface tension measurements and thermodynamic analysis of surface tension data. For example, dodecyltrimethylammonium bromide (DTAB) and octyl methyl sulfoxide (OMS) molecules
∗
Corresponding author. E-mail address: [email protected] (H. Matsubara).
0927-7757/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.colsurfa.2007.07.034
mixed more effectively in the adsorbed film than in the micelle since the small hydrophilic group of OMS molecule allows filling the space among hydrocarbon chains of DTAB molecules which are loosely packed in the pure adsorbed film due to the bulkiness of the trimethylammonium heads [11]. Furthermore, a kind of synergetic effects is also caused when the difference of the hydrophobic chain length is matched with the hydration diameter of the hydrophilic group for mixed systems of alkyltrimethylammonium halides [12–14]. We interpreted this phenomenon by the staggered structure formation at the air/water interface proposed by Penfold et al. based on the neutron reflection experiments [15]. In this paper, we will apply the same experimental procedure to an aqueous binary mixture of a cationic surfactant, DTAB, and a sugar surfactant, octyl--d-glucopyranoside (OG) in order to examine the effect of the bulkiness of the head group and hydrogen bond formation between OG molecules on the molecular packing in the mixed adsorbed film and micelle. For this purpose, the surface tension of aqueous solutions of DTAB–OG mixtures was measured as a function of the total molality of surfactants and the bulk composition of OG under atmospheric pressure at 298.15 K by the drop volume technique. The results
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of the surface tension measurements were analyzed by originally developed thermodynamic equations then phase diagrams of adsorption and micelle formation were constructed. 2. Experimental 2.1. Material DTAB was purchased from Tokyo Kasei Kogyo Co. Ltd. and purified by recrystalization three times from the mixtures of ethanol and acetone (1:5 volume ratio) then dried in vacuum. OG was purchased from Anatrace INC. (>99%) and used as received. The purities of surfactants were confirmed by the absence of minimum on the surface tension versus molality curve around the critical micelle concentration (cmc). Water used for all experiments was distilled three times. The second and third stages of distillation were done from dilute alkaline permanganate solution. 2.2. Surface tension measurement Surface tension of aqueous solutions of DTAB–OG mixtures was measured at 298.15 K under atmospheric pressure by the drop volume method [16,17] as a function of the total molality and composition in the bulk solution defined by m ˆ = 2m1 + m2
(1)
and H ˆ 2H = Γ2 X Γˆ H
and ˆ 2 = m2 X m ˆ
ˆ 2 = 0, Fig. 1. Surface tension vs. molality curves for DTAB–OG system: (1) X (2) 0.1, (3) 0.2, (4) 0.3, (5) 0.4, (6) 0.5, (7) 0.6, (8) 0.7, (9) 0.8 and (10) 1.
(2)
where m1 and m2 are molalities of DTAB and OG, respectively. In these definitions, the dissociation of DTAB molecules into DTA+ and Br− ions are taken into account. Advantages of these definitions were explained thermodynamically elsewhere [18,19]. The experimental error of surface tension measurements was <0.1 mN m−1 .
(5)
with respect to two dividing planes which make the excess number of moles of air and water zero simultaneously.
3. Result and discussion The results of surface tension measurement are shown as γ versus m ˆ curves at constant bulk composition in Fig. 1. γ values decrease rapidly with increasing m ˆ and each curve has a distinct break point at the concentrations corresponding to the cmc then takes almost constant value at high molalities. The total differential of surface tension is given by [19] RT Γˆ H dγ = −sdT + vdp − dm ˆ m ˆ H RT Γˆ H ˆ2 −X ˆ2 ˆ2 − X dX (3) ˆ 1X ˆ2 X where the total surface density of surfactants and the composition of OG in the adsorbed film are defined as Γˆ H = 2Γ1H + Γ2H
(4)
Fig. 2. Total surface density vs. molality curves for DTAB–OG system: (1) ˆ 2 = 0, (2) 0.1, (3) 0.2, (4) 0.4, (5) 0.5, (6) 0.6, (7) 0.7, (8) 0.8 and (9) 1. X
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Fig. 3. Eestimation of occupied area of OG molecule at air–water interface from CPK model (left: top view, right: side view). 0.44 nm2 roughly corresponds to the minimum occupied area of OG molecule at the air–water interface and 0.65 nm2 is the area occupied by freely rotating, vertically orientated OG molecule.
From these equations, the total surface density of surfactants can be evaluated by applying m ˆ ∂γ H ˆ Γ =− (6) RT ∂m ˆ T,p,Xˆ 2 to γ versus m ˆ curves (Fig. 2). The surface density increases monotonically with increasing m ˆ and approaches to a saturation value around cmc. It should be noted here that the mean area per molecule in the adsorbed film calculated from 1 ˆ = A (7) NA Γˆ H 0.40 nm2
is for pure OG system, which is almost identical with the cross sectional area of OG molecule calculated from CPK model (Fig. 3). Considering that the occupied area per surfactant molecule of a typical nonionic surfactant such as pentaethylene glycol monooctylether (C8E5) is twice as large as its cross sectional area around the cmc [20], the hydroxyl groups of glucoside units of OG are considerably dehydrated in the adsorbed film to form hydrogen bonds between OG molecules. As a result of dehydration of OG molecules followed by hydrogen bond formation between them, OG molecules can compactly pack in the adsorbed film in spite of their bulky head groups. This adsorption behavior of OG molecules is probably correlated to the fact that the lamellar liquid crystal phase of some sugar surfactants appeared in relatively dilute region compared with other nonionic surfactants. ˆ 2 curves obtained by plotting the m The m ˆ versus X ˆ values at a given γ are shown in Fig. 4 together with the m ˆ versus ˆ H estimated from composition of adsorbed film X 2 ˆ ˆ ∂m ˆ ˆ 2H = X ˆ 2 − X 1 X2 X (8) ˆ m ˆ ∂X2 T,p,γ ˆ2 The endpoints of a horizontal line connecting the m ˆ versus X H ˆ curve with m ˆ versus X2 curve correspond to the compositions of the bulk solution and to that of the adsorbed film in equilibrium with each other at the given γ, hence, this figure is called the ˆH phase diagram of adsorption. It is noted that the m ˆ versus X 2 curves show a slightly negative deviation from the straight line showing the ideal mixing in the adsorbed film ˆ 2H m ˆ =m ˆ 01 + (m ˆ 02 − m ˆ 01 )X
(9)
ˆ 02 are the molalities of the pure surfactant systems where m ˆ 01 and m at the given surface tension. To look more closely into the intermolecular interaction between DTAB and OG molecules, we
Fig. 4. Phase diagram of adsorption of DTAB–OG system at (1) 41 mN m−1 , (2) 45 mN m−1 and (3) 50 mN m−1 . Solid, dotted, and straight lines respectively ˆ 2 curve, m ˆ H curve, and ideal mixing line. show m ˆ vs. X ˆ vs. X 2
introduce the activity coefficients of component i then estimate the excess Gibbs energy in the adsorbed film defined by H ˆ 1H lnfˆ 1± ˆ 2H lnfˆ 2H ) gˆ H,E = RT (X +X
(10)
ˆH The fˆ iH values are calculated by substituting the evaluated X 2 from the Eq. (8) in to the equation ˆi m ˆX fˆ iH = 0 H ˆi m ˆiX
(11)
ˆ H curves at 41, 45, 50 mN m−1 are shown in The gˆ H,E versus X 2 H,E Fig. 5. The gˆ values are negative and their absolute value increases with decreasing surface tension. The former indicates that the mutual interaction between DTAB and OG molecules in the adsorbed film is stronger than that between the same molecules and the latter relates to the packing of the molecules in the adsorbed film through the excess surface area per molecule defined by [21,22] H,E ˆ E = − ∂ (ˆg /NA ) A (12) ∂γ ˆH T,p,X 2
By applying this equation to Fig. 5, it is found that the excess surface area is negative and the adsorbed molecules tend to occupy smaller area compared with the ideal mixing. In actual, the total number of hydrocarbon chains in the mixed adsorbed film ˆH = further increases up to Γ1H + Γ2H = 4.36 μmol m−2 at X 2 0.9 from that in the single component adsorbed film of OG molecules (Γˆ H = Γ1H = 4.1 μmol m−2 ). The plausible conformation between DTA+ ions and OG molecules in the adsorbed film which allows the increase in the surface density is not fully understood; however, considering that the minimum of the
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Fig. 5. Excess Gibbs energy of adsorption vs. composition of adsorbed film plot at (1) 41 mN m−1 (black circle), (2) 45 mN m−1 (grey) and (3) 50 mN m−1 (white).
ˆ vs. Fig. 6. Phase diagram of micelle formation for DTAB–OG system: (1) C ˆ vs. X ˆ 2 curve (solid line), (2) C ˆ M curve (dotted line), and (3) ideal mixing line X 2 (straight line).
excess Gibbs energy is observed on the OG rich side in the phase diagram of adsorption, the attractive interaction between DTA+ ions and hydroxyl group of OG molecules in the adsorbed film becomes more effective when DTA+ ion is surrounded by some OG molecules, namely, it is considered that DTA+ ion fills the gap space among OG molecules. Similarly the composition of OG in the micelle
is much more negative in the micelle than the excess Gibbs energy in the adsorbed film at the cmc, gˆ H,E,C , obtained by extrapolating gˆ H,E versus γ curves to the surface tension at the cmc as shown in Fig. 7. Here the composition in the adsorbed film at the cmc and activity coefficients in the mixed micelle were
ˆ 2M = X
N2M 2N1M + N2M
(13)
can be evaluated by applying the following equation ˆ ˆ 1X ˆ2 X ∂C M ˆ ˆ X2 = X2 − ˆ2 ˆ ∂X C
(14)
T,p
ˆ versus X ˆ 2 curve. The results of calculation are plotto the C ted as the form of the phase diagram of micelle formation in Fig. 6 analogously to the phase diagram of adsorption in Fig. 4. The straight lines in the figure correspond to the ideal mixing criterion for the mixed micelles given by ˆ =C ˆ 10 + (C ˆ 20 − C ˆ 10 )X ˆ 2M C
(15)
The phase diagram of micelle formation has a distinct negative azeotropic point indicating that the mixing of molecules is energetically favorable in the whole composition. The stronger mutual interaction between DTA+ ions and OG molecules compared with that in the adsorbed film can be manifested from that the excess Gibbs energy of micelle formation calculated from gˆ
M,E
=
M ˆ 1M lnfˆ 1± RT (X
ˆ 2M lnfˆ 2M ) +X
(16)
Fig. 7. Excess Gibbs energy of micelle formation vs. composition of micelle plot (grey circle). Open circle shows the excess Gibbs energy of adsorption extrapolated to cmc by using the plots in Fig. 4.
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Table 1 Comparison of excess Gibbs energy of adsorption, micelle formation and excess surface area Entry 1 2 3 4 5 6 7 8
DTAB–OG HTAB–DTAB13 Tetradecyltrimethylammonium bromide (TTAB)–DTAB13 Tetradecyltrimethylammonium chloride (TTAC)–decyltrimethylammonium chloride (DTAC)13 Hexadecyltrimethylammonium chloride (HTAC)–DTAC13 HTAC–DTAB14 Sodium dodecylsulfate (SDS)–C8E423 Decylammonium chloride (DAC)–C8E424
evaluated respectively by applying the following equations: C ˆ 1X ˆ2 ∂γ X H,C M ˆ ˆ X 2 = X2 − (17) ˆ 2 T,p ∂X RT Γˆ H,C and ˆX ˆi C fˆ iM = 0 M ˆ X ˆ C i
(18)
i
The energetic superiority of the micelle over the adsorbed film suggests that the hydrogen bond formation between OG molecules is less effective in the pure OG micelle due to its spherical geometry than in the pure OG adsorbed film. Therefore, it is said that the penetration of DTA+ ions into the wedge-like space between OG molecules can stabilize the mixed micelles by the ion–dipole interaction instead of the hydrogen bond between OG molecules. On the contrary, the OG molecules stabilize DTAB micelles by shielding the electric repulsion between DTA+ ions and also by the ion–dipole interaction on the DTAB-rich side of the phase diagram. For the mixed systems of alkyltrimethylammonium halides, the synergism occurs by the shorter surfactant molecules filling space among hydrocarbon chains of the longer surfactant molecules. Since the resultant staggered arrangement is suitable for the planar aggregates, the mixing of surfactant molecules is more favorable in the adsorbed film than in the micelle and the excess surface area takes a negative value as shown in Table 1 (entry 2–6). For the typical ionic–nonionic surfactant mixtures, on the other hand, the main cause of the synergism is an attraction with a directionality between the hydrophilic groups which has a relatively large optimal interaction distance compared to the van der Waals interaction between hydrophobic groups [23,24]. This configuration can be taken more easily in a loosely packed adsorbed film or in a wedge-like space in a spherical micelle; however, it becomes more difficult to keep the optimal interaction distance in a tightly packed adsorbed film. Therefore, the mixed micelle formation becomes more advantageous compared to the mixed adsorbed film around the cmc and the excess surface area takes a positive value (entry 7 and 8). Taking account of all experimental data obtained in the present system, it is found that the interplay between DTAB and OG molecules is suitable to form effectively packed aggregates both in the planer (adsorbed film) and spherical (micelle) geometry; however, the way of molecular packing in each aggregate seems to be somewhat different. OG molecules can
gˆ H,E (kJ mol−1 )
gˆ M,E (kJ mol−1 )
ˆE A
−0.3 −0.4 +0.2 +0.1 −0.2 −2.6 −1.3 −0.2
−0.5 −0.1 +0.2 +0.2 +0.4 −2.0 −1.7 −0.8
<0 <0 <0 <0 <0 <0 >0 >0
form hydrogen bond in the planer geometry and this hydrogen bond formation is probably the main contribution to determine the physical properties of the adsorbed film. However, the ion–dipole interaction between head groups of different components becomes more effective in the curved geometry and main cause of attractive interaction in the micelle as same as other ionic–nonionic surfactant systems. The existence of different interaction mechanisms in the adsorbed film and micelle makes it possible to show the intermediate behavior between the cationic–cationic surfactant mixtures and the typical ionic–nonionic surfactant mixtures. 4. Conclusion We have measured the surface tension of aqueous solutions of cationic surfactant (DTAB) and sugar surfactant (OG) mixture and analyzed them by originally developed thermodynamic equations. Our results suggest that OG molecules form hydrogen bond on their own and form densely packed monolayer at the air–water interface compared to the other nonionic surfactants and the addition of the cationic surfactant enhances the molecular packing by filling the space among OG molecules. By ˆ E values of the present system with comparing gˆ H,E , gˆ M,E and A those published in the previous papers, it was also suggested that the synergism of the surfactant mixture can be classified into three categories. Normally, the ionic and nonionic surfactant molecules interact each other mainly through the ion–dipole interaction between hydrophilic groups. gˆ M,E is smaller than ˆ E takes a positive value. If a combination of surfacgˆ H,E and A tants is geometrically suitable to form planer aggregates, gˆ H,E ˆ E takes a negative value. In becomes smaller than gˆ M,E and A this case, in order to form vacant spaces available to surfactant molecules, at least, one surfactant has to have a bulky head group. In other words, any particular interaction is not necessary between hydrophilic groups as clearly shown in the synergism of cationic–cationic surfactant systems. In this study, it has been firstly shown that both the adsorbed film and the micelle can take effective molecular packing by mixing ionic surfactant with nonionic surfactant with bulky hydrophilic group. References [1] B. Hoffmann, G. Platz, Curr. Opin. Colloid Interface Sci. 6 (2001) 171. [2] M. Hato, Curr. Opin. Colloid Interface Sci. 6 (2001) 268. [3] C. Dupuy, X. Auvray, C. Petipas, Langmuir 13 (1997) 3965.
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