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Langmuir 1990,6, 843-846
Study on the Adsorption and the Micelle Formation of a (Decylsulfiny1)ethanoland (0ctylsulfinyl)ethanol Mixture Makoto Aratono,' Tomoko Kanda, and Kinsi Motomura Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashiku, Fukuoka 812, Japan Received March 6, 1989. In Final Form: October 27, 1989 The surface tension y of the aqueous solution of a (decylsulfiny1)ethanol(DeSE) and (octylsulfiny1)ethan01 (OSE) mixture was measured as a function of its total molality m and composition X , at 298.15 K under atmospheric pressure. The surface density rHand composition X,H of the surfactant mixture in the adsorbed film were evaluated by applying the thermodynamic equations to the surface tension values measured. At the critical micelle concentration (cmc), furthermore, the composition in the micelle, XZM,and the composition difference X,M - XZHvCmC were evaluated respectively by use of the cmc vs X and ycmcvs X, curves, where XPH*cmc and ycmcrepresent the values of X2Hand y at the cmc. The refations between X, and XZHand between X, and X,M are expressed by diagrams similar to the threedimensional phase diagram, and the miscibility of surfactants in the adsorbed film and mixed micelle is discussed.
Introduction Adsorbed films and micelles of surfactant mixtures generally have different compositions from their aqueous solutions. Our studies on the mixed adsorbed films have clarified the relation between compositions of the adsorbed film and aqueous solution for some combinations of two surfactants by applying the thermodynamic equations to the surface tension values measured as a function of the composition and total molality of the surfactant mixture in the aqueous Further, the thermodynamics of micelle formation' developed on the basis of that of adsorption a t interfaces6 has been extended so as to investigate the miscibility of surfactants in micelles.' It is important to obtain information about the relation of the composition of the surfactant mixture in the aqueous solution to the compositions in the adsorbed film and micelle by use of the thermodynamics of adsorption and micelle formation. Our previous apers were concerned with cationic surfactant mixturesJ8 Now the study of a nonionic surfactant mixture is highly necessary, because this system is a simple one that does not need to take account of the electrostatic interaction between ions and the distribution of counterions around the adsorbed film and mixed micelle and because it can be employed as a criterion for the ideal mixing of surfactants in the adsorbed film and micelle. In this paper, we choose the mixture of (octylsulfiny1)ethanol (OSE) and (decylsulfiny1)ethanol(DeSE). Some reports have been published on the properties of adsorbed films and micelles
of these surfactants"2 and mixtures of surfactants havchemical structure to (alkylsulfinyl)Experimental Section (Alkylsulfiny1)ethanolwas synthesized from alkyl mercaptan and 2-chloroethanol according to the method described previously? It was purified by recrystallization from a petroleum ether-chloroform mixture and then a diethyl ether-ethano1 mixture. The purity was checked by gas-liquid chromatography ( L
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Figure 4. Total surface density vs total molality curves at constant composition:X, = (1)0, (2) 0.350, (3) 0.506, (4) 0.700, (5) 0.800, (6) 0.900, (7) 0.950, (8) 0.980, (9) 1.
Figure 2. Surface tension vs composition curves at constant total molality: m = (1)1 mmol kg-', (2) 2, (3) 3, (4) 4, (5) 5, (6) 6, (7) 8, (8) 10, (9) ycmcvs X , .
In Figure 1 are shown the plots of experimental values of the surface tension y against m at constant X, and 298.15 K under atmospheric pressure. The y value decreases steeply with increasing m in the concentration region below the break point on the curve, while it remains constant or increases slightly with m in the concentration region above the break point. The total molality of the break point is referred to as the critical micelle concentration (cmc) at this composition. The y value at a given concentration was picked up from Figure 1and plotted against X, at a concentration below the cmc in Figure 2. It is seen that the surface tension depends strongly on the composition at constant total molality. The surface tension at the cmc ycmcvs X, curve is also included in Figure 2; the ycmcvalue increases slightly with increasing X,. It should be noted that its shape is appreciably different from that of the y vs X, curve. Therefore, the y vs X, and ycmcvs X, curves are expected to give different kinds of information. The variation of m with X, at a given surface tension is shown in Figure 3 together with the cmc vs X, curve. We can see that the m and cmc values increase with an increase in X,,and the shape of the m vs X, curve becomes similar to that of the cmc vs X, curve as the y value lowers. It is important to note that there is a big difference in the magnitude of the X, dependence between the cmc and ycmc. Now let us derive the thermodynamic equations applicable to the adsorption of nonionic surfactant mixture
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Figure 5. Total surface density vs com osition curves at constant total molality: m = (1) 1 mmol kg-P, (2) 2, (3) 3, (4) 4, (5) 6, (6) 10, (7) rHVcmc vs X,.
from its aqueous solution in place of those of ionic surfactant mixtures developed in the previous st~dies.'*~"~* By adopting the two dividing planes making the excess numbers of moles of water and air the surface tension is expressed as a function of temperature T, pressure p , and the chemical potentials p 1 and p, of the surfactants: dy = -sHdT + v'dp - rlHdpI- r2'd~lZ (3) Here sH, uH, and riHare the surface excess entropy, volume, and number of moles of component i per unit area with reference to the two dividing surfaces, respectively. Here we restrict ourselves to the formulation at con-
Langmuir, Vol. 6, No. 4, 1990 845
Adsorption and Micelle Formation of Surfactant Mixture
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Figure 6. Composition difference X , - XZHvs composition curve at y = 40 mN m-'. 1
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stant T and p . Then eq 3 is rewritten as eq 4 by employing m and X , and assuming an ideal behavior of the aqueous solution:
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Figure 7. Total molality vs compositions in the solution and the adsorbed film curves at constant surface tension: J = (1) 50 mN m-', (2) 40, (3) 30; (-) m vs X,,(- - -) m vs X, .
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where we have introduced the total surface density and composition of surfactants in the adsorbed film defined respectively
rH= r: + rtH x , =~r2*/rH
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x2 , x ;
1
(5)
(6) Equation 4 is the starting one, which enables us to evaluate the compositions of the nonionic surfactant mixture in the mixed adsorbed film and micelle. At ConcentrationsBelow the cmc. When the aqueous solution of the OSE and DeSE mixture is free from micelles, the total surface density is evaluated by applying the equation
to the curves in Figure 1. The rHvalues are plotted against m at fixed X , in Figure 4 and against X , at fixed m in Figure 5. It is seen that the total surface density increases with increasing the total concentration and reaches the maximum at the cmc. The rHvalue at the cmc, rHPcmc, is also plotted against X , in Figure 5. It is noted that the vs X , curve is fairly different in shape from the rH vs X , curve. I t has been demonstrated in previous paper~l-~.'.~ that the X,H value is calculated thermodynamically from the experimental results without relying on any specific model of the interface and plays an important role in the examination of the miscibility of the surfactants in the adsorbed film. For the mixture under consideration, the relation
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x2 x: Figure 8. Surface tension vs compositions in the solution and the adsorbed film curves at constant total molalit m = (1) 1 mmol kg-', (2) 2, (3)6; (-) y vs X,,(- - -1 y vs X F , ( 0 )y values at the cmc. I
rHscmc
X , - x,H = (X,X2/m)(am/aX,)T,p,u (8) is derived from eq 4. Since the right-hand side of eq 8 is evaluated from the m vs X , curve shown in Fi ure 3, we can obtain the numerical values of X , - X 2 8 The value at 40 mN m-l is illustrated in the form of the X , - X,H vs X , plot in Figure 6. It is seen that the curve has the maximum; its value goes up to about 0.6, although the difference in carbon number between two surfactants is two. The combination of Figure 6 with Figure 3 leads to the m vs X , and m vs X,H plots drawn in Figure 7, where the plots at other surface tension values are also included. It is noted that the diagram in Figure 7 can be looked on as an analogue of the three-dimensional phase diagram designating the equilibrium compositions of coexisting two phases. It is easily understood that the two surfactants are completely miscible with each other in the adsorbed film, which abounds in
the more surface-active surfactant (DeSE), compared with the aqueous solution at a given surface tension. Equation 4 gives another route which leads to the X 2 H value by applying
X,H = X2 - (XIX,/RTrH)(ay/ax,)~,p,~ (9) to the curves depicted in Figure 2 and using the rHvalues given in Figures 4 and 5. The X 2 Hvalues evaluated are shown in the form of the y vs X , and y vs X2Hplots at constant total molality in Figure 8, where the diagram terminated by the cmc is also included. The composition of OSE in the adsorbed film is smaller than that in the aqueous solution at a given molality. It is seen that the higher the total molality, the more swollen the diagram. Such behavior is observed in Figure 7, where the diagram is swollen as the surface tension is lowered. At the Critical Micelle Concentration. We have proved that the micelle formation can be treated like an appearance of a new macroscopic phase in the aqueous solution by use of the thermodynamic quantities of a micelle defined as the excess ones with reference to the dividing spherical interface, which makes the excess number of moles of water Therefore, the total concentration of the surfactant mixture is approximately replaced by the cmc at concentrations near the cmc, and accord-
846 Langmuir, Vol. 6, No. 4, 1990
Aratono et al.
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xpmc Figure 11. Surface tension at the cmc vs compositions in the solution, adsorbed film, and micelle curves: (1) ycmcvs X,,(2) ycmc vs X , M , (3) ycmc vs x,H.cmc. x2
x2
Figure 9. Composition difference vs composition curves at the (2) X, - X,M, (3) XZM- X2H.emC. cmc: (1) X, - X2H,cmc,
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the composition of OSE at the cmc, respectively. Then the composition difference between the adsorbed film and micelle at the cme is related to the variation of ymc with the composition of the aqueous solution depicted by the curve 9 in Figure 2 as
X2M- xZH,emc = (XlX,/RTI'"Cmc)(dy~c/dX2)T,p (14) Figure 9 shows the relationship between the composias a function of X,. It is clearly tions XZMand XZHpcmc seen that both the micelle and adsorbed film are enriched in DeSE. The clear difference between the value of X,M and that of X2H*cmc may arise from the difference in geometry between a micelle having a spherical interface and an adsorbed film having a flat interface. Since the value is small, however, we can presume that of XZM- XZH*cmc the micelle shows a resemblance to the adsorbed f i i from the viewpoint of the composition. Here it is useful to note that, in the case of the system of which the ycmc value decreases with increasing the composition of the 0 0.2 0.4 0.6 0.8 1 component having a higher cmc value in contrast to the x2 , x: x y m c present system, the composition in the adsorbed film is Figure 10. Critical micelle concentration vs compositions in larger than that in the micelle. The system of dodecylthe solution, adsorbed film, and micelle curves at the cmc: (1) trimethylammonium chloride and decylammoniua chlocmc vs X,,(2) cmc vs X,M, (3) cmc vs X2HgCmC. ride, investigated previously, is one example.6 Figure 9 is redrawn in the form of the plots of the cmc against ingly the following equation is derived at constant temX,, X2M,and X,H*cmcin Figure 10; the cmc vs composiperature and pressure: tion diagrams look like swollen cigars and have the advantage of offering the equilibrium compositions in the aque(RT/cmc)dcmc = (X, - X2M)(RT/X,X2)dXz(10) ous solution, the adsorbed film, and the micelle at a given Here XZMis the composition of surfactant 2 in the micelle cmc. defined by Figure 9 is redrawn also in the form of the plots of the ycmc against X,, X M, and XZHvcmc in Figure 11. The X,M = NzM/(NIM + NzM) (11) ycmcvs X, and XIt diagram is particularly important NiMis the number of surfactant molecules i in the micelle. because it provides useful information regarding the change From eq 10 we have the relation of surface tension with total molality in a range of concentration above the cmc. Since the ymc vs XZMcurve - x , =~( X ~ X ~ / C ~ C ) ( ~ C ~ C (12) / ~ X , ) is ~ ,situated ~ in the upper area of the ymc vs X, curve in Figure 11, it is expected that, as the total concentration which enables us to evaluate the difference of the composition in the aqueous solution from that in the micelle. increases, the composition in the micelle approaches the overall composition and hence the surface tension increases Furthermore, the substitution of eq 10 into eq 4 yields gradually. It is noted that the shallow minimum observed dy'"" -rH1cmc(RT/XIX,)(X~Cmc - XZM)dX2 (13) on some curves in Figure 1 supports this view. and XZHScmc are the interfacial density and Registry No. DeSE, 7305-32-0; OSE, 7305-30-8. where ~
xZ
rHScmc
