Langmuir 1994,10, 4136-4141
4136
Effect of Dodecanol on Mixed Nonionic and Nonionic/ Anionic Surfactant Adsorption at the Air/Water Interface E. J. Staples, L. Thompson,* and I. Tucker Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, U.K.
J. Penfold ISIS Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. Received January 3,1994. I n Final Form: June 17,1994@ Neutron reflectionhas been used to investigate the adsorptionof mixed nonionic surfactant and nonionic/ anionic surfactant mixtures containing dodecanol, at the aidwater interface. The measurements clearly demonstrate the preferential adsorption of the more surface active shorter ethylene oxide nonionic surfactants, particularly of dodecanol. The usual trend for the more surface active componentsto decrease their presence in the surface layer as the total surfactant concentration increases is not observed for dodecanol. This results from the occurrence of unfavorable micellar geometries in mixtures containing dodecanol which control adsorption through their effect on monomer concentration. Regular solution theory cannot be used to describe the behavior of these systems.
Introduction In most applications, surfactants are used as mixtures, either to optimize performance' or simply to replace impure commercial surfactants. Surfactant systems are typically a mixture of alkyl chain lengths, isomeric forms, and in the case of alkyl ethoxylates, head group sizes, but the phase behavior of such mixtures can normally be identified with a n equivalent pure surfactant. The surface chemical properties of the mixtures are not necessarily identical to those of a n equivalent pure surfactant. It is known that close to the cmc both surface and micellar compositionscan vary markedly from the nominal solution composition, and while in the limit of high concentration the dispersed phase is constrained to adopt the bulk composition, the surface composition will always reflect the relative surface activity ofthe constituents. It is indeed well known that the surface tension of surfactant solutions can be significantly altered by the presence of quite small quantities of more surface active impurities.2 The neutron scattering technique was recently used to measure this effect for sodium dodecyl sulfate (SDS) solutions contaminated with d o d e ~ a n o l .At ~ concentrations close to the cmc an SDS solution containing 0.5mol % of dodecanol in bulk solution gives rise to a monolayer a t the aidwater interface which contains 54 mol % dodecanol. At higher concentrations partitioning into the interface is reduced drastically by a tendency for the dodecanol to be adsorbed into the micelles. Similar effects have been found by the present authors4 for mixtures of SDS with the nonionic surfactant triethylene glycol n-dodecanol ether (C12E3)a t a fwed SDS mole fraction of 0.35.Here the partitioning effect near the cmc is less dramatic, but preferential adsorption of the C12E3 was apparent up to 300cmc where the surface composition became close to the bulk composition. Adsorption from surfactant mixtures is frequently satisfactorily modeled using the regular solution theory
* Abstract published in Advance ACS Abstracts, October 1,1994.
(1)Thompson, L. J. Colloid Interface Sci. 1994,163, 61. (2) Moilliet, J. L.; Collie, B.; Black, W. Surface Activity, 2nd ed.; Van Nostrand New York, 1961;p 79. (3) Penfold, J.; Thomas, R. K.; Simister, E. A.;Lee, E.M.; Rennie, A. R. J.Phys. Condens. Matter 1990,2,SA411. (4)Staples, E.; Thompson, L.; Tucker, I.; Penfold, J.;Thomas, R. K.; Lu, J. R.Langmuir 1993,9(7),1651.
(RST). The theory, however, contains a central assumption, that of ideal entropy of mixing in which a single interaction parameter is assumed to apply a t all micelle compositions, that may render it invalid for some surfactant systems. In this case it becomes a n empirical tool which is nevertheless extremely useful in its ability to describe the variation of cmc with composition. It seems less likely that the theory could be successful in predicting micellar, monomer, and surface compositions, especially where the ideal entropy of mixing assumption may no longer be valid. Clearly it is important to define the useful predictive range of RST. In our earlier work,4the SDS/C12E3system was selected because the areas per molecule of the constituents are similar and the underlying assumption of ideal mixing entropy is most likely to be satisfied, and the adsorption behavior of this system was indeed consistent with the predictions of RST. The study has since been extended5 to a system (SDS/C12EG)in which the components have significantly different areas, and again, RST provided a n adequate framework for the adsorption behavior. In the present work, the neutron reflectivity technique has been used to investigate adsorption from mixtures containing various monodisperse alkyl ethoxylate nonionic surfactants together with an anionic surfactant (SDS) and dodecanol. Dodecanol is not a micelle-forming surfactant itself but is particularly interesting because it adsorbs strongly at interfaces when solubilized into the micelles of other materials. It is a real contaminant in commercial nonionics, and it also provides a good model with which to look a t adsorption from surfactant systems containing solubilized material. As a vehicle for testing regular solution theory, dodecanol has the advantage of the minimum molecular area possible for a surfactant with a dodecyl chain. Moreover, it has limited solubility in micelles, which implies that the structure of the micelle will be disrupted at some composition. It therefore provides a more stringent test of the predictive ability of RST than our previous systems. Experimental Details Protonated nonionic surfactants C&, ClzEs, and ClzEs were obtained fromNikko1. SDS and n-dodecanol were obtained from
BDH.Deuterated nonionic surfactants for the neutron reflection ( 5 ) Penfold, J., Staples, E. J., Thompson, L., Tucker I., Thomas R. K. and Lu J., Submitted for publication.
0743-746319412410-4136$04.50/00 1994 American Chemical Society
Langmuir, Vol. 10,No. 11,1994 4137
Effect of Dodecanol on Surfactant Adsorption measurements,c183,c186,C12E8,and C12E12, were synthesized at Unilever, Port Sunlight, by a procedure involving addition of the appropriate ethoxylate oligomer to 1-bromododecanewith a fully (98%) deuterated alkyl chain. Protonated ClzElz was synthesized by the same procedure, using nondeuterated 1-bromododecane. Deuterated 1-bromododecane,deuterated SDS,and deuterated dodecanol were obtained from MSD Isotopes Ltd. and used without further purification. The deuterated SDSused here is known to contain an n-dodecanol impurity in sufficient quantity for the surface tensiodog concentration curve to be perturbed from that expectedfor the pure material. In previous E ~ , ~ it has work with this material in a mixture with C ~ Z however, been established that, at concentrations above about 1.5 cmc, the dodecanol is not significantly adsorbed at the airlwater interface. The hydrogenated SDS is of much better surface chemicalquality, and a dodecanol impurity is not likely to cause problems in the present mixtures. Deuterium oxide (DzO) was suppliedby Sigma. High-puritywater(ElgaUltrapure)was used throughout,and the methods of cleaningthe glassware and Teflon troughsfor the neutron reflection measurementsinvolved soaking in 1%Decon solution followed by extensive rinsing. The neutron reflection measurementswere carried out on the reflectometerCRISP at the ISIS pulsed neutron source, where the measurements have been made using the fixed geometry (angle of incidence of 1.5")white beam time of flight method (using wavelengths from 0.5 to 6.5 A) in the Q range 0.05-0.65 A-l. The experimental procedures are now well established and are described in detail elsewhere.' The absolute reflectivities are obtained by reference t o a pure DzO surface, and the incoherentbackground in the reflectivityprofiles can be estimated by extrapolation t o high values of Q. In the study here, there is an additional contribution to the background from the smallangle scatteringfrom the bulk solutionbecause the concentration is always more than the cmc. A position sensitive detector is used to resolve the specular intensityfrom the diffuse background and is described in detail el~ewhere.~ The background in this case arises from the incoherent and small-anglescattering from the transmitted beam within the bulk micellar solution. The neutron reflectivity measurements have been made with the aqueous subphase comprising a mixture of HzO and DzO (92% HzO) to give a neutron refractive index matched to air. The adsorbed amount for each component in the surfactant mixtures has been evaluated using procedures described in detail elsewheresf9when each component is in turn selectivity deuterated. The small but finite contributionfrom the protonated components to the determined value is corrected by following the procedure described in ref 10.
Regular Solution Theory
f , = exp px2
NW,,
B=
+ w,,- 2W1,) RT
where W11 and W22 are the pairwise molecular interaction energies within pure micelles and W12 is the equivalent quantity in the mixed micelle: N is Avogadro's number. In RST, 8 , is related to the enthalpy of mixing by
AHm= pRTxl(1 - xl) and it is thus tied to the central assumption that the excess entropy of mixing is zero. Its relevance is a theoretically meaningful quantity rather than a n arbitrary fitting parameter resting on this assumption. Through this approach, it is possible to evaluate p by using the cmc's of the pure components and of a mixture and also to predict the micelle composition and monomer concentration for any given total composition and concentration. The micelle composition ( x ) at the cmc and the interaction parameter p for monomers in a mixed micelle are then obtained by iterative solution of the following:
p=-
1 C*a In (1 - d2 c1x
and
The supra cmc micelle composition was derived by iterative solution of X =
-(c- D)+ ((c- D),+ 4
a ~ ~ ) ' ~
20
where D = f2C2 - f1CI and C is the total surfactant concentration, from which the monomer concentrations C Mand ~ C Mcan ~ be derived, where
For a mixed surfactant system, the variation of mixed cmc, C* with composition (mole fraction, a)is given by11J2
1 - a
c*
flC1
;l-a f2C2
where C1 and C2 are the cmc's of the pure components and fi are activity coefficients. Within the regular solution theory the activity coefficients can be expressed in terms of a micelle composition, x , and a single interaction parameter,
~~~
~
~
(6)Penfold, J.;Ward, R. C.; Williams, W. G. J.Phys. E , Sci. Instrum. 1987,20,1411. (7)Lee, E.M.; Thomas, R. K.; Penfold, J.;Ward, R. C. J.Phys. Chem. 1989,93, 381. (8)Penfold, J.;Staples, E.; Tucker, I.; Thomas, R. K.; Lu, J. R. Faraday Trans,submitted for publication. (9)Penfold, J.;Thomas, R. K.J. Phys. Condens.Mutter 1990,2,1369. (10)Lee, E.M.;Thomas, R. K.; Penfold, J.; Simister, E. A. J.Phys. Chem. 1992,96, 1373. (11)Rubingh, D.N. In Solution Chemisty ofSurfactunts; Mittal, K. L., Ed.; Plenum Press: New York, 1979;Vol. 1, p 337. (12)Holland, P. M.Colloids Surf. 1986,19,171.
Holland12extended this approach to the determination of the surface composition above the cmc. The change in monomer activity associated with surface pressure was explicitly included, and a n interaction parameter pSwas used to describe excess free energy of mixing at the air1 water interface. An expression was derived that provides a direct comparison between the activity coefficient and mole fraction in the micellar and adsorbed "phases". The surface interaction parameter ps and surface composition are derived from iterative solution of ~t =
RT fFi -In + qmax Ai fsPsi
where A is the area per molecule of surfactant i, ximaX is the surface pressure of surfactant i above the cmc, x i s the surface pressure of mixed surfactant, andfi, = exp@&).
Results and Discussion Adsorption from a Complex Surfactant Mixture. Before we embark on a detailed investigation of concen-
Staples et al.
4138 Langmuir, Vol. 10,No. 11, 1994 Table 1. Adsorption from (a) W10 Mole Ratio C1aEdSDS Mixture and from (b) DodecanoYClzE$ClaEdClsE$ClaEl$ SDS Mixture in Which the Average Ethoxylate Content of the Nonionic Portion Was E k mole fraction r (mol m-2 x 106) surface solution SDS CizEs total
(a) 0.22 3.42 3.64
SDS CizOH C12E3 CizEs CizEs CizEiz total by addition total by experiment average ethoxylate
0.12 1.48 1.74 1.14 0.70 0.70 5.18 4.94
0.06 0.94
0.1 0.9
0.02 0.29 0.34 0.22 0.13 0.13
0.1 0.11 0.27 0.27 0.18 0.18
3.6
5.0
(b)
a Overall surfactant concentrationwas 3 x mol dm-3, and mol dm-3. the temperaturewas 25 "C. NaCl concentrationwas
tration effects in the adsorption of some relatively simple mixtures, we have briefly investigated adsorption from a complex six-fold mixture of dodecanol,C12E3, ClzEs, C12E8, C12E12, and sodium dodecyl sulfate (SDS).The distribution of the ethoxylates and dodecanol in this mixture was designed to mimic that in a typical commercial ethoxylate of average structure C12-14ES(e.g. Synperonic A5). This was done first to demonstrate the overriding importance of dodecanol in the behavior of commercial materials and, second, to establish the ability of the neutron reflection technique to measure the individual adsorption levels of the various components in a highly complex mixture. Table 1gives details of the adsorption a t the aidwater interface of this mixture and of an "equivalent" mixture containing only SDS and pure C12E5. In both cases the SDS, present in bulk solution as 10%of the total surfactant, is almost eliminated from the interface, being present in amounts too small to measure directly. The figures for SDS in Table 1were obtained by subtracting the adsorption of all species other than SDS from the total adsorption determined from the surface scattering with all species deuterated. Total adsorption from the complex mixture is about 40% higher, largely due to the preferential adsorption of dodecanol. Overall, this effect reduces the average ethoxylate chain length at the interface to 3.6 compared to the bulk average of 5.0. These experiments were carried out a t a concentration of 3 x mol dm-3, which is greatly in excess of the cmc (5 x mol dm-3 in both cases). At this surfactant concentration it may, from previous have been expected that the partitioning of dodecanol into the interface would be less pronounced in that the possibility of absorption into the micellar aggregates exists. The failure of this to occur is a feature we examine more systematically in the following discussion. Effect ofDodecanol onAdsorption from SDS/C and C12EdC12ES Mixtures. In further measurements we have investigated adsorption from mixtures comprising anionic/nonionic and nonionicdnonionic surfactants together with dodecanol. Table 2 compares the behavior of a 65/35% mole ratio mixture of C12E3 and SDS with that of an "equivalent" mixture in which the C12E3 was replaced by a 3/2 mole ratio mixture of ClzEddodecanol. The average ethoxylate chain length in this mixture is 3.0, and it gives cloud points in a range of mixtures with SDS which are within 2 "C of those obtained with C12E3 itself. As with the data summarized in Table 1,total adsorption is much greater in the system containing dodecanol
Table 2. Comparison of SDSIClpEs Adsorption with SDS/Cl&/Dodecanol Adsorptiona mole fraction surfactant adsorption (mol m-2 x 109 surface bulk (a) SDS/C12E3 SDS 1.38 0.29 0.35 3.31 0.71 0.65 Cl2E3 total 4.74 (b) SDSIClzE@odecanol 1.46 0.27 0.35 SDS Cl2E6 1.54 0.25 0.39 dodecanol 2.77 0.48 0.26 total 5.77 a The concentration of surfactant was 3 x mol dm-3, and the temperaturewas 25 "C. NaCl concentrationwas 10-lmol dm-3.
Table 3. Comparison of Cl&&&s Adsorption with C&$C&flodacanol Adsorptiona mole fraction surfactant adsorption (mol m-2 x 109 surface bulk Ci2Es Cl2E3 total CizEs Cl2ES dodecanol total
(a) C I Z E ~ C I Z E ~ 1.46 3.03 4.53 (b) ClzEdClzEflodecanol 1.35 1.21 2.60 5.26
0.32 0.67
0.5 0.5
0.29 0.25 0.49
0.5 0.3 0.2
a The concentration of surfactant was 3 x mol dm-3, and the temperaturewas 25 "C;NaCl concentrationwas 10-l mol dm-3.
ADSORPTION ( ~ o ~ " P ' E 6 )
-1
3t
't7
0
1 .OE-05
1. O E 4 1.OEQ3 CONCENTRATIONh o t 4
Figure 1. Effect of concentration on the adsorption of a C12Ed Cl2Eddodecanol mixture (mole ratio 50/30/20)at the aidwater interface: (O), total adsorption; (O),dodecanol; (+), C12E6; (*),
CizEs. because of the larger quantities of this material present in the adsorbed layer. Indeed, this factor reduces the average ethoxylate chain length (E6 Eo) on the surface to 1.77 compared t o 3.0 in bulk solution. Although the bulk properties ofthe ClzEddodecanolmixtures are similar to those of C12E3, the surface properties are not. Table 3 provides a similar comparison of the adsorption of a mixture of C12E8 and C12E3 (50/50 mole ratio) with that of an "equivalent" in which the C12E3 is again replaced by a 312 mixture ofC12Eddodecanol. The ClzEdC12E3mixture shows the similar preferential adsorption of the more
+
Langmuir, Vol. 10,No. 11, 1994 4139
Effect of Dodecanol on Surfactant Adsorption ADSORPTION (mo~"P'E6) 61
the present authors4 in which the surface composition was found to approach the bulk composition a t a total surfactant concentration of about 300 times the cmc. For the systems examined here, however, we find that total adsorption increases with concentration. This is indicated in Figures 1 and 2, where adsorption data from total concentrations of 3 x 3x and 6 x mol dm-3 are displayed. The increase is due to the continued increase in dodecanol adsorption. The behavior of the other components is different in the two systems studied. For C12E$CI2Eddodecanol, the quantities of and C12E5 in the adsorbed layer do not change appreciably with concentration (C12E8 increasing slightly), but for dodecanoVCl2Es/SDS,the SDS level increases, in part by displacing C12E5. This behavior is unusual but can be explained in trend if not in detail. The crux is that the composition of the monolayer is determined by the monomer concentrations of the various components, where the monomer concentrations themselves are mediated in turn by the micelle composition. At totalconcentrations only slightly in excess of the cmc, the most surface active component is preferentially adsorbed both at the interface and into the micelles. As the total solution concentration increases, the micelle composition must evolve toward the bulk composition because a n increasing proportion of the surfactant is in micelle form. This would normally be associated with a reduction in the monomer concentration of the more surface active component with a consequent decrease in its surface concentration. This typical observation is consistent with the predictions of regular solution theory (RST) as indicated in Figures 3 and 4. Figure 3 represents a n RST analysis based on surface tension measurements on the system SDS/C12E3/0.1 M NaC1. In Figure 3 the evolution of the micelle composition with total surfactant concentration for the mixture 35 mol % SDS/65 mol % C12E3is indicated (curve a), as is the locus of micelle composition at the cmc for all other combinations (curve b). Curve c shows the variation of the cmc with surfactant composition. Thus a solution with a bulk composition of 35 mol % SDS has
I
ii
5 -
4-
3-
'I
0
,
, ,, ' /
, ,~
( , ,
,
,
1.OE-04 1 .OE03 CONCENTRATION (mob)
1 .OE-05
,I
Figure 2. Effect of concentration on the adsorption of a SDS/ ClzEddodecanol mixture (mole ratio 35/39/26)at the aidwater interface: (01,total adsorption; (O),dodecanol; (+I, ClzEs; (*I, SDS.
surface active component at the interface, and again the presence of a large amount of dodecanol in the adsorbed layer reduces the average ethoxylate chain length at the interface to 3.24 compared to 5.46 for the C12E$C12E3 mixture. The data in Tables 1-3 refer to a total surfactant concentration of 3 x mol dm-3, which exceeds the cmc by a factor of about 50. Effect of Concentration on Adsorption from Mixtures Containing Dodecanol. One might expect, from experience with dodecanol a s a trace impurity, that the surface concentration of the more surface active component would decrease with increasing concentration. This was the situation in the work ofpenfold et al. on SDS/dodecanol mixtures3 and in earlier work on SDS/C12E3 mixtures by
C
0 3
0
'10-2 M i c e l l e Composition
L 3 C P)
U
C
0 3
C
0 3
U
0 Q-
L J
II)
0 3 0
+
L 2
4
6
8
I
M o l e F r o c t i o n SDS
Figure 3. Regular solution theory analysis for SDS/C12E3/0.1mol dm-3NaCl showing (a) the concentration dependenceof micelle composition, (b)the micelle composition at the cmc, and ( c ) the composition dependence of the cmc.
4140 Langmuir, Vol. 10,No. 11, 1994
Staples et al.
m
5 c
I B - ~
iJ
0
L r’
c
Iu U
c
0 iJ
E 0
8
0 E ~
0-5 Toto1
10-4 10-3 10-2 Surfactant Concentrotlor-
10-1
(MI
Figure 4. Effect oftotal surfactant concentrationon SDS and C12E3 monomer concentration for a 35/65 mole ratio mixture in 10-l mol dm-3 NaC1.
a cmc of 4 x mole dm-3, corresponding to a micelle compositionof 7 mol % SDSat the cmc. As total surfactant concentration increases, the micelle composition follows curve a as it approaches 35 mol % SDS. The resulting variation in SDS monomer concentration with total surfactant concentration for the mixture is indicated in Figure 4. It can be seen that large variations in monomer concentration are associated with the evolution of the micelle from the lowest energy state (at the cmc) to the relatively high energy state that must exist in the limit of high concentration. The decrease in the monomer concentration of the “most surface active” component with increasing concentration is found to be a feature of all compositions for this system. It is a direct result of this monomer concentration decrease that the adsorption of the most surface active component (C12E3)may be expected to decrease with increasing total surfactant concentration for all compositions. Where dodecanol is present, the increase with concentration in the adsorption of dodecanol must be matched by an increase in dodecanol monomer concentration together with a n increase in the dodecanol content of the micelle. Such a n increase is possible in systems which exhibit a minimum cmc below that ofthe pure components. This situation is simulated by the RST calculation in Figure 5 where the application of a /3 parameter of -3.0 to the cmc data for SDS and C12E8 in 10-1 mol dm-3 NaCl produces a cmc curve (curve c) with a slight minimum between 0.1 and 0.2 mole fraction of SDS. This minimum indicates the composition of the micelle with the lowest energy, and obviously, as the micelle composition is identical to that of the bulk, the micelle composition is invariant with total concentration. The micelle composition a t the cmc for other mole fractions will be biased toward the “minimum energy” composition with respect to the total composition and will approach the nominal bulk composition only in the limit of high total concentration (curves a). As a consequence in such systems, it is always possible to select a composition in which the monomer concentration of either component, even that with the lowest cmc, “themost surface active”,will increase with total surfactant concentration. The general rule is that adsorption of the most surface active material increases with total surfactant concentration when it is present in insufficient proportion to bring about the minimum value of the cmc. It is not straightforward to prove that this condition is met in the SDSI ClzEddodecanol and Cl2E$C1zEEJdodecanol systems because accurate identification of the cmc for the threecomponent systems is difficult. (The yAog c curves do not
Figure 5. Regular solution theory analysis for a simulated system exhibiting a minimum cmc. Curves a show the concentrationdependenceof micellar composition at bulk SDS mole fractions of 0.1, 0.2, 0.3, etc. Curve b shows the micelle composition at the cmc, and curve c shows the composition dependence of the cmc with a minimum value at 0.15 mole fraction SDS.
conc*I0 5 (mole/l)
81
I
I
I Micelles 6
-
Free Dodecanol
4 1
’
‘;v /
Monomer
2‘
0
20
40
1
60
80
100
mole% C12E5
Figure 6. Cmc of dodecanoVClzE5 mixtures. 0 denotes the solubility of dodecanol. exhibit the normal sharp discontinuity.) It is, however, clear from a consideration of the cmc data for ClzEd dodecanol mixtures that the three-component systems including either SDS or ClzEs may be expected to exhibit such a minimum cmc. Figure 6 shows the cmc data for ClzEddodecanol, and the presence of a minimum is clearly indicated. The “C12E3 equivalent” component of our mixtures is a 60I40 mole ratio ClzEddodecanolcomposition which has a cmc significantly greater than the minimum value. The cmc increases above the minimum value at higher dodecanol levels because micelles containing large quantities of dodecanol are difficultto form, in turn because dodecanol itself does not form micelles. Thus, addition of a third component, SDS or C12E8, to the 60140 C12Ed dodecanol mixture must initially reduce the cmc by reducing the amount of dodecanol in the micelle before it again increases toward a limiting value of the SDS or C1zE8 cmc. An analysis of the C12EE data using the standard format of regular solution theory12 is not possible in that the solubility of dodecanol(2.3 x mol dm-3) is too low for a micellar phase to form, and a value for the cmc is
Langmuir, Vol. 10,No. 11,1994 4141
Effect of Dodecanol on Surfactant Adsorption
Table 4. Surface Chemical Data Used in the Regular Solution Treatment surfactant” cmc (mol dm-3) aredmolecule (nm2)
Beta I
I
I
/
C12E3
3
Cl2E.5 CizEs SDS C12EJSDS (65/35) dodecanol/ClzEs (40/60)
6.4 10-5
@
10-5
10-4
1.5 x 10-3 4.2 x 5.6 x
0.38 0.5 0.55 0.37
All measurements were carried out in the presence of 10-1 mol
dm-3 NaCl.
-0.5
‘
0
1 10
20
30
40
Mol% Dodecanol Figure 7. Variation of the interaction parameter composition for ClaEddodecanol mixtures.
with
normally required for the calculations. Two approaches to this problem have been adopted. The first is to assume that dodecanol would micellize if not prevented from doing so by packing and solubility constraints, to estimate its “virtual” cmc, and to use this in RST calculations. A molecular modeling approach,13in which the free energies of transfer of the various elements of the molecule from bulk solution to a micellar environment are calculated, results in an estimated cmc of 2.5 x mol dm-3. This is about the same as the figure obtained by extrapolating a plot of cmc for Clz ethoxylates against ethoxylate chain length to zero EO. Using this figure, together with the cmc for pure and the experimental data for each composition in turn, j3 has been calculated as a function of dodecanol mole fraction. The results, in Figure 7, show that j3 increases with dodecanol content, implying that RST, which requires a single value for #?, is not applicable to this system. A similar conclusion is reached by a second approach in which we have reformulated the regular solution expression such that, given the cmc’s of one pure surfactant and two additional mixed compositions, the ~~
(13)Nagarajan, R.;Ruckenstein, E. Langmuir 1991,7,2934.
cmc’s of all other compositions are predicted. Applying this approach to the data in Table 4, however, results in interaction parameters which vary significantly with the compositiodcmc combinations used and can even predict an infinite dodecanol cmc. The failure of the regular solution approach to produce a single interaction parameter is not surprising in this instance. The form of the concentration dependence of the cmc’s of surfactant mixtures predicted using regular solution theory, which involves symmetric functions, is such that if a minimum exists a t an intermediate composition, then it must occur toward the axis with the lowest cmc. Model calculation and extrapolation from the cmc’s of Clz ethoxylate surfactants would suggest a low cmc for dodecanol if the constraint of solubility were absent. Our observation of a cmc minimum a t compositions with low dodecanol concentrations is a clear indication that a regular solution approach is not valid in this system. The failure of RST reflects the difficulty of forming a micelle containing large amounts of dodecanol. It is likely that geometric, and hence entropic, factors exert a dominant influence on the variation with composition of the micelle energy of formation. The variation of the interaction parameter then reflects the generation of drastically different micelle geometries as the monomer concentration of dodecanol is increased. This could occur if dodecanol were incorporated into the micelle core rather than the palisade layer or, alternatively, through the formation of disk micelles with significantnonideal mixing of the constituent surfactants.
Acknowledgment. The authors gratefully acknowledge the contribution of Mr. M. P. Nicholls in synthesizing the deuterated nonionic surfactants, and Dr. I. Stott for carrying out the molecular modeling calculation of the “cmc” of dodecanol.
