Langmuir 1993,9, 1651-1656
1651
Surface Composition of Mixed Surfactant Monolayers at Concentrations Well in Excess of the Critical Micelle Concentration. A Neutron Scattering Study E. Staples,* L. Thompson, and I. Tucker Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, United Kingdom
J. Penfold Isis Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, United Kingdom
R. K. Thomas and J. R. Lu Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, United Kingdom Received September 21,1992. In Final Form: April 13, 1993
Specular neutron reflection has been used to determine the adsorptionof sodium dodecyl sulfate (SDS) and n-dodecyl triethylene glycol (CIZE~) at the air-solution interface at a fiied bulk composition ratio (65 mol 9% ClzEs) over a wide range of concentrations in excess of the critical micelle concentration. The results are compared with those obtained from the application of regular solution theory to surface tension data for the same system. The proportion of SDS in the adsorbed layer is in good agreement with the theoretical predictions.
Introduction Most technological applications of surfactants involve mixtures, either because surfactants are deliberatelymixed in order to optimize their performance or because commercial surfactants contain mixtures of different alkyl chain lengths and isomericforms. Until relatively recently the quantitative aspecta of the scienceof Surfactantmixing have lagged seriously behind the art. Since the introduction of regular solution theory (RST),initially attributed to Corkill’ and subsequently developed by others,% it has been possible to predict solution and surface properties of mixtures, including critical micellar concentrations (cmc), monomer and micelle composition, adsorbed layer composition, and surface tension, using readily obtainable surface chemical data for the pure components and for a single mixture. This very useful semiempiricalapproach provides an insight into surfactant adsorptionat concentrationsrelevant to most applications, i.e. well above the cmc. The objective of the present work is to establish the value of the neutron reflection technique as a means of investigating the applicability of RST to surfactant adsorption at concentrations of relevance to the detergency process. The regular solution theory contains two major assumptions which suggest that it may not be universally applicable. The first of these is that the existence of a “regular solution” requires ideal entropy of mixing which in turn requires that molecules of different types have similar packing cross sections to each other in the micelle or at the interface. The second concerns Holland’s extension of the theory3 to the prediction of surface (1) Clint,J.H.InTheStructure,Dy~micsandEquilibriumRoperties
ofColIoi&lSystemcr;Bloor,D.M.,WynJones,E.,Eds.;KluwerAcademic Publishers: Amsterdam, 1990, p 76. (2) Rubingh, D. N.In Solution Chemistry of Surfactants; Mittal, K. L., Ed.;Plenum P r w : New York, 1979, Vol. 1, p 337. (3) Holland, P. M. Colloids Surf. 1986,19, 171. (4) Scamehom, J. F. ACS Symp. Ser. No. 311, 1986, 1.
compositions,in which it is assumed that the area/molecule of each component is invariant with composition. Despite these potential limitations, regular solution theory has had a great deal of success in predicting both the cmc and surface tension of surfactant mixtures. More rigoroustests of the theory have however confirmed that it has its limitations. For example, Davidson? using surfactant sensitive electrodes, found deviations from theory in the aggregation behavior of sodium dodecyl sulfate (SDS)/ n-dodecyl hexaethylene glycol (C12E6) mixtures which implied that the assumption of a regular solution was not justified. Moreover Rosen et al.6 have shown, using data derived from surface tension measurements at the oil/ water interface, that contraction of effective molecular area can occur in mixed adsorbed layers. The present work is related to recent investigations718 of the surface chemical origins of oily soil detachment in the detergency process and it reflects a need to interpret interfacial tension and contact angle effects in mixed surfactant systems in terms of the adsorbed layer composition. In this paper we examine the surface concentrations of one composition (65 mol 7% C12E3) of the nonideal mixed surfactant system of C12E3/SDS in 0.1 M NaCl and contrast the findings with the regular solution theories of Rubingh2and of H ~ l l a n d The . ~ measurements have been made over a wide concentration range from the cmc to 300 times the cmc. In addition to its validity as a detergency model, the system was selected for three reasons. Firstly, it may be predicted, because of the intrinsically higher surface activity of the nonionic, that changes in concentration over this range will lead to a wide range of surface compositions. Secondly, the bulk (5) Davideon, C. J. Thesis, University of Aberdeen, August 1983.
(6) h e n , M. J.; Murphy, D. Langmuir 1991, 7, 2630. (7) Thompson, L. In Surfactants in Lipid Chemistry; Tyman, J. H. P., Ed.;Royal SocietyofChemistry SpecialPublication 1lS;Royal Society of Chemistry: Herb, 1992; p.56. (8) Thompson, L. J. Colloid Interface Sci., in preas.
0143-1463/93/2409-l651$04~oo/o0 1993 American Chemical Society
Staples et al.
1652 Langmuir, Vol. 9, No. 7, 1993 solution at this composition consists of dispersed lamellar phase in equilibrium with a solution of monomeric surfactant, and it is well-knowns that deposition of dispersed phases renders molecular adsorption measurement by the usual depletion techniques invalid. It is therefore most important to establish that accurate measurements of molecular adsorption can be achieved in systems of this type from neutron reflectivity measurements. Thirdly, the system is such that large deviations from regular solution theory are not expected. We are attempting an accurate assessment of adsorption over a wide range of conditions using a surfactant system which exhibits a significant level of nonideality but where the bulk and surface phases would be expected to be of similar composition (asindicated by the invariance of the surface tension above the cmc) and for which the constituents have similar areadmolecule. In these circumstances the assumptions of the RST are most likely to be fully satisfied. In subsequent work a range of surfactant systems whose behavior cannot be described by RST will be examined and their structures contrasted. Regular Solution Theory For a mixed surfactant system in which the only contribution to the free energy of mixing is entropy, the surface, bulk, and micelle composition are equal and the variation of mixed cmc C* with composition(molefraction) a is given by21 -=-+1 a l-a c * c, c, where C1 and C2 are the cmc's of the pure components. Nonideal mixing is usually only identified when the observed mixed cmc's vary markedly from those predicted by eq 1, although in principle the areas per molecule obtained from surface tension of the pure and mixed surfactants may also indicate a nonideal surface composition. The regular solution approach due to Rubingh2has had a remarkable success in predicting the nonideal cmc behavior in many systems
+-
1 a l-a -=c * flC1 f2C2 where f i are activity coefficients that are related in the regular solution approximation to the mole fraction ( x ) of surfactant [il in the mixed micelle and an interaction parameter /3 that represents the excess free energy of mixing within the micelle
fl = exp[B(1-
(3)
f2 =exp[~(x)~~ (4) Using this approach, it is possible to evaluate B 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 B for monomers in a mixed micelle are then obtained by iterative solution of the following
(5) and (9) Corkhill, J. M.;Goodman, J. F.; T a b , J. R. Trons. Furuday SOC. 1966,62, 979.
where C* is the cmc of the mixed micelle, C1 and C2 are the cmc's of pure surfactants 1and 2, and a is the mole fraction of surfactant 1 in the total mixed solute. The supra-cmc micelle composition was derived by iterative solution of -(C - D)+ ((C - 0 ) 2 + 4aCD)1'2 (7) 20 where D = f2C2 - flC1, and C is the total surfactant concentration, from which the monomer concentrations CMl, CM2 can be derived, where x=
"flc,
(8)
= (1- ")f2c2
(9)
cM1 = cM2
Holland3extended 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 an interaction parameter was used to described excess free energy of mixing at the airwater 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 and surface composition are derived from iterative solution of
as
os
RT In fixi ?rlmax =(10) .~ Ai fsPm where A is the area/molecule of surfactant i, aimax is the surface pressure of surfactant i above the cmc, 7r is the surface pressure of mixed surfactant and f~ = exp(/3$,i2). ?r
+
Neutron Reflectivity The specular reflection of neutrons has now been extensively applied to a range of problems in surface chemistry'O and especially to the study of surfactant adsorption at the air-solution interface.11J2 In a neutron reflection experiment the specular reflection is measured as a function of wave vector transfer Q (where Q = 4a sin O/A, B is the grazing angle of incidence and X the neutron wavelength) perpendicular to the reflecting surface. This is simply related to the neutron refractive index profiie normal to the surface and provides information about the neutron scattering length density profile (and hence composition and density gradient) at the interface. A particular advantage for neutron reflectivity is that isotopic substitution can be used to produce largecontrasts in scatteringlength densities. For problems in surface chemistry this stems from the large difference in scattering powers between hydrogen and deuterium, and selective deuteration can be used to manipulate refractive index profiles. Not only can the amount adsorbed be determined for single and multicomponent systems but the detailed surfacestructure can be obtained. This approach has now been applied to a range of surfactant systems adsorbed at the air-water interface.1°J2J3 By choosingthe appropriate hydrogeddeuterium ratio the refractive index of an (10) Penfold, J.; Thomae R. K. J. Phys.: Condens. Matter lS90,2, 1369. (11) Simister, E.A.;Lee, E.M.;Thomas, R. K.; Penfold, J. J. Phys. Chem. 1992,26, 1373. (12) Crowley,T.L.;Lee,E.M.;Simister,E.A.;Thomas,R.K.;Penfold, J.; Rennie, A. R. Colloids Surf. 1990, 52, 85. (13) Penfold, J.; Thomas, R. K.; Simiater, E. A.; Lee,E.M.;Rennie, A. R. J. Phys.: Condens. Matter 1990,2, SA 411.
Surface Composition of Mixed Surfactant Monolayers
Langmuir, Vol. 9, No. 7, 1993 1653
aqueous solvent can be matched to air. If the surfactant is deuterated, then any reflectivity results entirely from the surface adsorbed layer of surfactant and is related directly to the surface excess, l?, or area per molecule, Furthermore, by selective deuteration of each component,it is straightforward to determine the surface excess of each individual component at the surface.13 If the reflectivity measured in such a way is modeled by a single uniform layer, then the area per molecule is given by15 ab = (Zb)/d, Nb, (11) where Zb is the total scattering length of the deuterated surfactant molecule and &and Nbfare the fitted surfactant layer thickness and scattering length density. It is important to note that in the determination of the excess, it is the product dfNbfwhich is used, and hence surface excesses can be determined to good accuracy even when the reflectivity is such that the thickness and density of the layer cannot be uniquely separated in the data. Based on the kinematic approximation there is an alternative approach which will be more appropriate to the system studied in this paper. For the situation of a thin deuterated layer at an interface index matched to air, the reflectivity can be written in the kinematic approximation,16 as
where
the excess scattering length density at the interface and h(Q)isthe normalized form factor for the interfacial profile. In the Guinier approximation h(Q)can be expressed as
-
h(Q) 1 - Q2u2 (13) and u is the standard deviation of ~(2). If Q a 4 X 10-3 mol dm-3). In Figure 6 the data are presented as the proportion of SDS in the adsorbed layer and are compared to the theoretical results obtained through regular solution theory. At low concentrations the results (not shown in the figure) are distorted by the dodecanol impurity in the deuterated SDS, but at intermediate and high concentrations a good agreement is obtained. The statistical ~
~~~~~
(21)Aveyard, R.;Binlre, B. P.; Mead, J.; Clint,J. H.J. Chem. Soc., Faraday T r c l n ~1. 1988,84,676. (22)Aveyard, R.;Binke, B. P.;Mead, J. J. Chem.Soc.,Faraday n a m . 1 1986,82,1766.
Surface Composition of Mixed Surfactant Monolayers CONCENTRATION (M) I
I
Langmuir, Vol. 9, No. 7,1993 1655 40
SDS IN SURFACE (mole%)
35 -
I
25
20 15 -
51
t 1.OE-05
o
0.1
0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.0
I
MOLE FRACTION SDS Figure 4. cmc for SDS/C& mixtures. The line shows the predictions of regular solution theory.
I' (mole/cmA2)(~EIO)
-1
t
+
+
+
+
++
00
i n
n
1.M-06
I.O€-04
R
WE-03
WE-02
WE-0
CONCENTRATION(molell) Figure 5. Effect of concentration on adsorption from a 65/36 mole ratio Cl&/SDS mixture in 0.1 mol dm4 NaCk *, SDS; 0 , c12Ea;+, total.
errors associated with the neutron scattering experiment are small at all concentrations, being negligible at high concentration where reflectivity is greatest. Assessment of systematic errors such as those arising from the sample preparation can only be achieved through repeat experiments and this is not generally practicable in the context of a neutron scattering experiment However the smoothness of the data may be taken to be indicative of the level of systematic errors. There is some suggestion at the highest concentrations, where the relative errors are the smallest,that there is relatively more SDSadsorption than theoretically predicted. The effect is rather small and further confiiatory work is required. An effect of this sort would be expectedto originate with an increase in the totaladsorption, which, in turn reflects the inadequacyof the assumption within RST that the molecular areas of the components are the same in mixtures as in the single
, , tc,mc , , , , , , , , ,
, , ,,,,,,,
, ,
/ , , , ,
0
1.OE-05
1. o w 4 1.OE43 1.OM2 CONCENTRATION(mol@)
1.OE-Ol
Figure 6. Mole fraction of SDS in the surface as a function of concentration: (*) neutron reflection on data; (-) derived from RST; (- - -) mole fraction SDS in micelle.
surfactants. Again the data for total adsorption are consistent rather than conclusive in that a small increase is observed. Finally it is noted that in line with the invariance of the measured surface tension above the cmc (Figure 21, the RST prediction for the micellar compoeition is very close to the composition of the monolayer a t all concentrations. This is shown in Figure 6. As they stand, the results c o n f i i that neutron reflectivity has a unique capability in providing accurate detail of surfactant adsorption over a large concentration range-even in the presence of a significant amount of dispersed bulk phase. The impurities that would limit successfulcharacterization of the system by conventional means are shown to have little impact with the methodology adopted here. The current data are insufficient to constitute arigoroustest of the theory, which would require further data on this and other systems. Within the constraints of our interest in fabric washing surfactant systems, which is the stimulation for this piece of work, it is our intention progress further in this direction in the future. The present results are particularly interesting in that they show that variations in surface composition can continue to concentrations very much greater than the cmc (>102X). While this is quite consistent with the theoretical prediction, the existence of such an extensive concentration effect is certainly not generally recognized. In this particular case the variation of surface compoeition with concentration does not lead to changes in surface tension because surface and micellar compositions are similar at all concentrations. This is not universally true so that in other systems we may expect to me a concentration dependenceof surface tension over a wide range of concentration. It does not seem likely that the relatively small surface tension changes to be expected at the airlwater interface would have dramatic effecta on the properties, such as foaming, of that interface. It is however interesting to speculate on their potential impact on oil/ water interfacial phenomena where much lower tensions (23) Roeen, M. J.; Murphy, D.S.J. Colloid Interface Sci. 1986,110,
224.
1666 Langmuir, Vol. 9, No. 7, 1993 are observed and relatively small changes can lead to large variations in contact angles or efficiency of emulsification, parameters which are important in applications such as enhanced oil recovery and detergency. In summary, the present investigation has established that molecular adsorption can be measured in the presence of a microscopic disperse phase provided that allowance is made for it by a simple data manipulation. This is in contrast to earlier measurements of nonionic surfactant adsorption onto carbon where depletion from solution measurements were unable to discriminate between mo-
Staples et 01.
lecular adsorption and depoeition of the disperse phaae.9 The neutron results themselves confirm that the surface composition of 65 mol % ClzE3/35mol % SDS in 10-' mol dm4 NaCl varies with concentration in a manner consistent with regular solution theory. This is as expected for a system which has components of similar molecular area and surface tensions above the cmc. In the future it is our intension to carry out parallel measurementsfor the system Cl&/SDS/NaCl which has been shown by surfactant electrodemeasurementss not to conform to regular solution theory.
