Impact of Electrolyte on Adsorption at the Air–Water Interface for

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The Impact of Electrolyte on Adsorption at the Air-Water Interface for Ternary Surfactant Mixtures above the Critical Micelle Concentration Jessica Liley, Robert K. Thomas, Jeffrey Penfold, Ian M. Tucker, Jordan T. Petkov, Paul Stevenson, and John Robert Peter Webster Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b00904 • Publication Date (Web): 12 Apr 2017 Downloaded from http://pubs.acs.org on April 18, 2017

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The Impact of Electrolyte on Adsorption at the Air–Water Interface for Ternary Surfactant Mixtures above the Critical Micelle Concentration Jessica R. Liley,†,k Robert K.Thomas,∗,† Jeffrey Penfold,‡,⊥ Ian M. Tucker,¶ Jordan T. Petkov,¶,# Paul Stevenson,¶ and John R. P. Webster§ †Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, United Kingdom ‡Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0RA, United Kingdom ¶Unilever Research and Development Laboratory, Port Sunlight, Quarry Road East, Bebington, Wirral CH63 3JW, United Kingdom §STFC, Rutherford-Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0RA, United Kingdom kCurrent address: LGC, Queens Road, Teddington, Middlesex, TW11 0LY, United Kingdom ⊥Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, United Kingdom #Current address: Lonza UK, GB-Blackley, Manchester, Lancs., M9 8ES, United Kingdom E-mail: [email protected]

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Abstract The composition of the air–water adsorbed layer of the ternary surfactant mixture, octaethylene monododecyl ether, C12 E8 , sodium dodecyl 6-benzene sulfonate, LAS, and sodium dioxyethylene glycol monododecyl sulphate, SLES, and of each of the binary mixtures, with varying amounts of electrolyte, has been studied by neutron reflectivity. The measurements were made above the mixed critical micelle concentration. In the absence of electrolyte adsorption is dominated by the nonionic component C12 E8 but addition of electrolyte gradually changes this so that SLES and LAS dominate at higher electrolyte concentrations. The composition of the adsorbed layer in both binary and ternary mixtures can be quantitatively described using the pseudo–phase approximation with quadratic and cubic interactions in the excess free energy of mixing (GE ) at both the surface and in the micelles. A single set of parameters fits all the experimental data. A similar analysis is effective for a mixture in which SDS replaces SLES. Addition of electrolyte weakens the synergistic SLES–C12 E8 and LAS–C12 E8 interactions, consistent with them being dominated by electrostatic interactions. The SLES–LAS (and SDS–LAS) interaction is moderately strong at the surface and is little affected by addition of electrolyte, suggesting that it is controlled by structural or packing factors. Most of the significant interactions in the mixtures are unsymmetrical with respect to composition, with the minimum in GE at the 1:2 or 2:1 composition. There is a small structural contribution to the LAS-C12 E8 interaction that leads to a minimum intermediate in composition between 1:2 and 1:1 (LAS:C12 E8 ) and to a significant residual GE in strong electrolyte.

Introduction Owing to the reduction in headgroup electrostatic interactions, the addition of electrolyte reduces the critical micelle concentration, CMC, 1,2 promotes micellar growth, 3 and enhances

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the adsorption 4 in ionic surfactants. Thus, anionic surfactants are affected to varying degrees by the addition of electrolytes such as NaCl, CaCl2 , or AlCl3 , with the strong binding associated with multivalent ions often rapidly leading to precipitation. In applications, strategies are adopted to minimise the effects of electrolyte on ionic surfactants, 5–7 e.g. differently structured surfactants such as the alkyl benzene sulphonate and the oligoethylene glycol monoalkyl sulphate surfactants are often added to alkyl sulphate anionic surfactants to give a greater tolerance to the addition of multivalent ions. 6 The blending of ionic surfactants with non-ionic surfactants also minimises the onset of precipitation. The properties of such mixtures are generally non-ideal, and the non-ionic surfactants have intrinsically lower CMC values than ionic surfactants. However, the addition of electrolyte reduces the CMC and enhances adsorption of the ionic surfactant components, which results in significant changes in micellar and surface composition and hence affects the functionality of a surfactant blend. Although mixing at surfaces has been extensively studied, the effects of electrolyte on the surface composition of the more complex mixtures that are used in formulations have been relatively little studied. Recently we have used neutron reflection, NR, and surface tension, ST, to investigate the surface adsorption properties at the air-water interface of the ternary surfactant mixture of C12 E8 –LAS–SLES, 8 which is the basis of formulations extensively used in a wide range of home and personal care products. 9 In that paper, the range of solution concentrations above the mixed CMC the surface mixing was found to be highly non-ideal. Although the surface composition reaches a constant limiting value with increasing solution concentration it remains significantly different from the solution composition. The adsorption is dominated by the C12 E8 and LAS, and there is little SLES at the interface, i.e. the relative adsorption is in the order C12 E8 >LAS >SLES. In this paper we explore the role of the added electrolytes, NaCl and CaCl2 , on the surface properties of the ternary surfactant mixture, and the impact of replacing the SLES with SDS. The electrolytes greatly reduce the mixed CMC so that the measurements of surface coverage are at concentrations much higher than the mixed CMC.

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This is the range where surfactants are typically used in practice, but where measurements of total coverage and composition are inaccessible except with NR.

Experimental Details The surfactants used were exactly the same samples as used by Liley et al. 8 and, rather than repeat their description, details of the synthesis and characterization are given in the Supporting Information. The measurements differed only in that electrolyte, either 100 mM NaCl or 2 mM CaCl2 , was included in the surfactant mixtures, which were otherwise at the same compositions and concentration apart from the set being slightly less complete than in the previous work. The compositions studied were a slightly reduced set of those displayed on a triangular composition diagram by Liley et al., which is reproduced as Figure S1 in the Supporting Information. Neutron reflection measurements were made on the SURF and INTER reflectometers at ISIS 10,11 and on FIGARO at the ILL 12 using a fixed glancing angle of incidence θ and a range of wavelengths λ. The reflectivity R was calibrated by reference to the reflectivity from the surface of D2 O. The samples were contained in sealed Teflon troughs held at 298K and containing a sample volume of ≈ 25 mL. All the measurements of adsorption were based on deuterated surfactants in null reflecting water, in which case R is given exactly by 4 64π 2 2 2 R(κ) = 4 ρ sin κ



κd 2

 (1)

where κ = (4π sin θ)/λ and d and ρ are the thickness and scattering length density of the adsorbed layer, which are obtained by fitting R. Although the individual quantities d and ρ are model dependent, the product is not. Hence for a single surfactant species at the interface, the surface adsorbed amount Γ, which is related to ρd through the sum of the

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P known scattering lengths ( b), is also model independent.

Γ=

ρd P

Na

b

(2)

A series of NR measurements with each of the three components deuterium labelled in turn, leads to a set of simultaneous equations, which can be solved to determine the adsorbed amounts of each component. For the binary and ternary mixtures measurements were made for the isotopic combinations of dd, dh, and hd and for ddd, dhh, hdh, and hhd respectively in NRW, where d and h refer to the deuterium labelled and hydrogeneous surfactant components. In both cases the system is over determined and the sets of 3 or 4 simultaneous equations were solved using the subroutine MB11a from the Harwell subroutine library, 13 which uses a simplex algorithm to solve a series of over-determined linear equations. An example of the fitting of the data for the same set of surfactants in a ternary mixture as used here, but without electrolyte, was given by Liley et al. and is shown in Figure S2 of the Supporting Information. There is no additional signal from the levels of electrolyte used in the present measurements. The compositions of the mixtures were analysed using the pseudophase approximation, which treats micelles and adsorbed layers as thermodynamic phases. The assumption means that the chemical potentials of the components of micelle, solution, and surface layer are equal. Equating the chemical potentials of a surfactant in the bulk solution to that in the micelles 14–17 gives the fundamental equation,

xi =

cmon i fiµ cµi

(3)

where xi is the mole fraction of component i in the micelle, cmon the monomer concentration i of i in the bulk solution, fiµ its activity coefficient in the micelle (the mean activity coefficient in the bulk is taken to be 1), and cµi its CMC. The way that this is used for a binary mixture has been given many times and here we therefore outline only how it is used for a ternary 5 ACS Paragon Plus Environment

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mixture. All our measurements were made above the CMC. There are then two steps to the analysis, the calculation of the surfactant monomer concentrations, followed by the use of the monomer concentrations to calculate the composition of the adsorbed layer. The first step uses a combination of mass balance combined with Eqn (3), followed by elimination of x3 by x3 = 1 − x1 − x2 . This results in two independent equations for a tenary mixture 14 (f3 cµ3 − f1 cµ1 )x21 + (f3 cµ3 − f2 cµ2 )x1 x2 + (c + f1 cµ1 − f3 cµ3 )x1 − α1 c = 0 (f3 cµ3 − f2 cµ2 )x22 + (f3 cµ3 − f1 cµ1 )x1 x2 + (c + f2 cµ2 − f3 cµ3 )x2 − α2 c = 0

(4)

where αi are the overall compositions of each component and c is the total concentration. Writing A31 = f3 cµ3 − f1 cµ1 and A32 = f3 cµ3 − f2 cµ2 these reduce to A31 x21 + A32 x1 x2 + (c − A31 )x1 − α1 c = 0 A32 x22 + A31 x1 x2 + (c − A32 )x2 − α2 c = 0

(5)

Aji = fj cµj − fi cµi

(6)

where

The solution of these equations to obtain the three xi requires an expression relating the activity coefficients and the micellar compositions. For a phase in a ternary mixture obeying the Gibbs–Duhem equation a well used expression for the excess free energy of mixing, GE , 18 leads to two contributions to the activity coefficients. The first depends on the quadratic terms in xi and is 16,19 RT ln f1 = x22 B12 + x2 x3 (B12 − B23 + B31 ) + x23 B31 RT ln f2 = x23 B23 + x3 x1 (B23 − B31 + B12 ) + x21 B12 RT ln f3 = x21 B31 + x1 x2 (B31 − B12 + B23 ) + x22 B23 6 ACS Paragon Plus Environment

(7)

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where the Bi j are constants. The second depends on the cubic terms 20,21   2x1 x2 (1 − x1 + x2 ) − x22 C12 + 2x2 x3 (x3 − x2 )C23   − 2x3 x1 (1 − x1 + x3 ) − x23 C31   = 2x2 x3 (1 − x2 + x3 ) − x23 C23 + 2x3 x1 (x1 − x3 )C31   − 2x1 x2 (1 − x2 + x1 ) − x21 C12   = 2x3 x1 (1 − x3 + x1 ) − x21 C31 + 2x1 x2 (x2 − x1 )C12   − 2x2 x3 (1 − x3 + x2 ) − x22 C23

RT ln f1 =

RT ln f2

RT ln f3

(8)

The total activity coefficient fi is the product of the quadratic and cubic contributions to fi and the C parameters become zero in a regular solution. Eqns (5), (7) and (8) are solved , the iteratively to obtain values of xi , which are then substituted into Eqn (3) to give cmon i monomer concentrations above the CMC. There are several ways of doing the iteration and here we used the method recently described by Liley et al. 8 The key equation for the calculation of the adsorbed is Eqn (3), with cmon as calculated i in step one above, xi now becoming the compositions in the adsorbed layer, and cπi replacing cµi . 14–17 The cπi are to adsorption what cµi is to micellization, i.e. a low cπi indicates that adsorption occurs at a lower concentration. In the Holland approximation, 15 the assumption is made that a complete monolayer is adsorbed at the CMC, i.e. the CMC is the major determinant of the adsorption but it is modified by a surface pressure factor given by

cπi

=

cµi exp



(π mix − πi )Acmc i RT

 (9)

where πj and π mix are respectively the surface pressures of the pure monomer and the mixture above the CMC, and Acmc is the limiting molecular area of i at the CMC. All of i these quantities are determined experimentally. The composition of the adsorbed layer is then determined by iterative solution of the modified Eqn (3) with Eqns (7) and (8). Again,

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there are several ways of doing this iteration and we used the method described by Liley et al.

Results and Discussion Binary Mixtures An important part of understanding ternary mixing of surfactants is to establish whether or not the ternary behaviour can be accounted for as the sum of the three sets of binary interactions in a given system. For molecular interactions there is good reason to expect that this is the case. However, for mixtures involving ionic surfactants variation of, for example, incomplete ionization of any one of them could change the pairwise interactions so as to give an apparent three body interaction. Since the addition of different electrolytes will greatly change the interactions between the surfactant species it might be expected to show up weaknesses in the additivity assumption. The main aim was therefore to obtain experimental results for the effects of added electrolyte on the systems studied by Liley et al. 8 NR measurements of the adsorbed fraction of the components in C12 E8 –SLES and LAS– SLES were made at a total surfactant concentration of 2 mM and in 100 mM NaCl and 6 mM CaCl2 and the results analysed as described in the Experimental Details to give the set of results in Table 1. Measurements on LAS–C12 E8 had previously been made by Penfold et al. for the different NaCl concentration of 6 mM and are also included in the table, 22 as are the total adsorbed amounts in the absence of electrolyte. The previous composition behaviour is included graphically in Figure 1. The total adsorbed amount increases substantially at all compositions for the two mixtures SLES–LAS and C12 E8 –SLES on addition of both 100 mM NaCl and 2 mM CaCl2 , which indicates a strongly enhanced adsorption of one or both components and/or a significant attraction between the two components. However, there is no corresponding significant change for the LAS–C12 E8 mixture with 2 mM CaCl2 (the comparison with the effect of NaCl cannot be made because of the lower concentration). 8 ACS Paragon Plus Environment

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These results taken together then suggest that it is SLES that is most affected by the electrostatic screening. Table 1: Variation in surface composition and total adsorption at a total concentration of 2 mM for SLES–LAS, LAS–C12 E8 (data from Penfold et al. 22 ) and C12 E8 –SLES in the presence of NaCl and of CaCl2 . Values for the total coverage without electrolyte from 8 are given in brackets and the equivalent changes in composition are shown graphically in Figure 1. system

mole fraction SLES SLES–LAS 0.25 100 mM NaCl 0.50 (no salt) 0.75 SLES–LAS 0.25 2 mM CaCl2 0.50 0.75 LAS LAS–C12 E8 0.20 6 mM NaCl 0.40 (no salt) 0.60 0.80 0.90 0.95 LAS–C12 E8 0.20 2 mM CaCl2 0.40 0.60 0.80 C12 E8 C12 E8 –SLES 0.25 100mM NaCl 0.50 (no salt) 0.75 C12 E8 –SLES 0.25 2mM CaCl2 0.50

surface mole fraction SLES 0.26 0.40 0.61 0.30 0.46 0.77 LAS 0.41 0.45 0.60 0.85 0.80 0.84 0.41 0.56 0.63 0.74 C12 E8 0.28 0.54 0.74 0.25 0.48

106 × Γtotal ±0.05 mol m−2 3.78 (3.68) 3.82 (3.31) 4.16 (3.23) 3.75 3.86 3.98 3.00 (3.00) 2.90 (2.70) 2.80 (2.90) 3.20 (2.90) 3.10 (3.20) 3.20 (3.10) 3.00 3.10 3.30 4.00 3.61 (2.65) 3.58 (2.59) 3.57 (2.50) 3.83 3.64

The fitting of the data proceeded in two steps as described in the Experimental Details and by Liley et al. 8 The general limitations of the assumptions of this method have been extensively discussed in the literature and we revisit this in the Discussion section. The experimental inputs to the fitting are the characteristic concentrations cπi defined in Eqn (9), which depend on the known limiting areas at the CMC, A, and the STs of the individual components and of the mixture. The limiting values of A for the individual components 9 ACS Paragon Plus Environment

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adsorbed mole fraction SLES

1.0

(a) SLES-LAS

100 mM NaCl 100 mM NaCl no electrolyte 2 mM CaCl2

0.8

0.6

0.4

0.2 adsorbed mole fraction SLES

0.0

no electrolyte 6 mM NaCl 6 mM NaCl 2 mM CaCl2

total mole fractionLAS

0.8

(b) LAS-C12E8

0.6

0.4

0.2 adsorbed mole fraction LAS

0.0

(c) C12E8-SLES

100 mM NaCl 100 mM NaCl no electrolyte CaCl2 (experiment)

0.8 total mole fraction C12E8

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0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

adsorbed mole fraction C 12E8

Figure 1: Variation of adsorbed mole fraction with bulk mole fraction for the three binary mixtures (a) SLES–LAS, (b) LAS–C12 E8 and (c) C12 E8 –SLS. The experimental and fitted points for 100mM NaCl are shown in red in (a) and (c) and the original fitted points for the electrolyte free solution are shown in black. The experimental points for calcium are shown as blue triangles but the fitted curves are not shown. 10 ACS Paragon Plus Environment

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˚2 for SLES (based on the 10% effect of electrolyte in 100 mM NaCl were taken to be 42 A ˚2 for LAS (assumed from a similar 10% reduction from the value of 57 on SLE1 S 23 ), 52 A ˚2 for C12 E8 . 24 The corresponding measured limiting STs determined using NR) and 62 A are 37 and 36 mN m−1 for SLES and C12 E8 . Ma et al. have measured the surface tension for LAS in the absence of electrolyte at 298 K and in 100 mM NaCl at 323 K. 25 For the latter they obtained a limiting ST of 25 mN m−1 . Making an arbitrary small correction for the difference in temperature we use 27 mN m−1 in the analysis that follows. Finally, the surface tension of the mixtures has been taken to have a constant value of 34 mN m−1 to be compared with 39 mN m−1 used for the mixtures without electrolyte. Two approximations are involved in this assumption, first that the ST is constant for a given mixture and second that it does not change between mixtures of different composition. In practice the fitting of the data is generally relatively insensitive to variations in the ST, which suggests that the assumption of a constant value is unlikely to be problematic. For the calculation of the monomer composition above the mixed CMC the CMCs in the presence of electrolyte are required. These are 0.3 mM at 298 K and 0.25 mM at 323 K for SLES and LAS respectively, but in the fitting we found it necessary to reduce both of these by 0.05 mM, although this is probably within the experimental error. The CMC of C12 E8 was not significantly affected by 100 mM NaCl and its value is taken to be 0.09 mM. The data in Table 1 were fitted with the pseudophase approximation and an excess free energy of mixing that includes both quadratic and cubic terms as described in the Experimental Details. The binary fits shown in Figure 1 and the ternary fits shown later used the same set of fitting parameters. Given that the simple regular solution model (quadratic terms only) could not be fitted to the whole set of data without electrolyte and that composition asymmetry of the excess free energy of mixing, GE , was found to be a key contribution to the successful fitting, we have not included the best fits of the regular solution model. The best fits to the three sets of data for 100 mM NaCl are shown as red lines in Figure 1 and the fitting parameters used are given in Table 2. For reference the final

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fits for each system without electrolyte are shown as black lines using the analysis of Liley et al. However, it is important to realize that the change between no electrolyte and 100 mM NaCl results from changes in both the interaction parameters and the relative CMCs. The surface interactions of C12 E8 with SLES and with LAS are both substantially reduced by the addition of 100 mM NaCl. Originally the C12 E8 –SLES and C12 E8 –LAS interactions were respectively moderately and strongly attractive. In 100 mM NaCl the former is reduced almost to nothing and the latter has become only moderately attractive. This behaviour is consistent with an attractive electrostatic interaction that is reduced by the screening of the additional electrolyte. Surprisingly, the SLES–LAS attraction is almost unchanged from its value without electrolyte, although its shape is slightly changed. Liley et al. speculated that this particular interaction could be a mix of electrostatic and packing effects. That it is not affected by addition of electrolyte indicates that it results entirely from packing effects and we discuss this further below. The interactions in the micelle were moderate in the absence of electrolyte but in 100 mM NaCl all are weak with values not very different from zero, i.e. the micellar mixing in the ternary system with electrolyte is close to ideal (all B and C parameters in Eqns (7) and (8) equal to zero). It is also clear from Figure 1 that, apart from one experimental point for CaCl2 (the SLES–LAS mixture at high SLES), the effects of 2 mM CaCl2 and 100 mM NaCl are indistinguishable. However, the calculated fit for 6 mM NaCl, which is the same ionic strength as 2 mM CaCl2 , also fits the data for C12 E8 –LAS as well as the fit for 100 mM NaCl, i.e. there is little change between 6 and 100 mM NaCl. This is confirmed directly from the effect of salt on the adsorption in a following section.

Ternary Mixtures The results from four isotopic species ddd, dhh, hdh, hhd were used to give an overdetermined set of measurements for the two independent surface mole fractions at the fixed total composition of 2 mM (see Experimental Details). The adsorbed layer compositions and total adsorption are given as a function of overall composition in Table 3 for the solutions con-

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Table 2: Parameters determining the excess free energy of mixing for the three binary pairs of surfactants and C12 E8 –SDS in 100 mM NaCl, 6 mM NaCl and 2 mM CaCl2 , which were used for all the calculated profiles in Figures 1, 2 and 3. The values in brackets are those for no electrolyte from Liley et al. 8 The primary parameters are Bij and Cij , from which Gmin and xmin are derived. The CMCs are included because they contribute to the fitted profiles in Figure 2. The CMCs for 100 mM NaCl and 6 mM CaCl2 have been taken to be the same, that for LAS in 6mM NaCl, which was used for the LAS–C12 E8 mixture, is included in brackets. The units are RT except for x, which is a mole fraction. system micelle/surface SLES–LAS–m SLES–LAS–s LAS–C12 E8 –m LAS–C12 E8 –s C12 E8 –SLES–m C12 E8 –SLES–s SDS–LAS–m SDS–LAS–s C12 E8 –SDS–m C12 E8 –SDS–s

Bij Cij RT RT −0.3 (0) 0.3 (0) −2.2 (−2.2) −2.0 (−1.2) −0.6 (−2.6) 0.6 (1.8) −2.2 (−4.0) 1.0 (0.8) 0.0 (−1.8) 0.0 (−1.8) −0.3 (−2.0) 0.3 (−2.0) −0.7 (0) 0.7 (0) −1.4 (−2.2) −1.4 (−1.2) −1.0 (−1.0) −1.0 (−1.0) −1.0 (−3.0) 1.0 (−3.0)

Gmin RT -0.09 −0.64 −0.18 −0.58 −0.09 −0.21 −0.41 −0.3 −0.3

xBC 0.33 0.66 0.33 0.40 0.33 0.33 0.67 0.67 0.33

cµ1 mM 0.24 0.20 (0.5) 0.09 1.0 0.09 -

cµ2 mM 0.20 0.09 0.24 0.20 1.0 -

taining 100 mM NaCl and those containing 6 mM CaCl2 . The bulk fractional compositions of the solutions studied are marked on the ternary composition diagram in Figure S1 of the Supporting Information. The total coverages from the electrolyte free solutions are included in brackets in the Table for comparison. The effects of the two added electrolytes on the total coverage are large, causing an increase of around 25%, for all the mixtures. There is little difference between the effects of 100 mM NaCl and 6 mM CaCl2 . The compositions of the adsorbed mixtures are plotted in Figure 2 together with the fits using the calculations described in the Experimental Details for independent pairwise interactions with GE containing both quadratic (B parameters) and cubic terms (C parameters). The final parameters are given in Table 2 and the same set was used for the fits in Figure 2 as for those in Figure 1, as well as those to be discussed below in connection with measurements with varying NaCl concentration. Since there seemed to be negligible difference in the adsorption between the solutions in 100 mM NaCl and 2 mM CaCl2 , apart from a greater

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Table 3: Surface composition and total adsorbed amount for C12 E8 –LAS–SLES mixtures at a total concentration of 2 mM in 100 mM NaCl and 2 mM CaCl2 . Values of the total adsorbed amount without electrolyte are given in brackets. surface mole fraction 1010 × Γtotal ±0.05 ±0.1 mol m−2 xC12E8 = xLAS (100 mM NaCl) SLES C12 E8 LAS SLES 0.90 0.05 0.14 0.81 4.07 (3.00) 0.75 0.11 0.29 0.60 3.78 (2.86) 0.60 0.18 0.35 0.46 3.59 (2.85) 0.33 0.27 0.45 0.28 3.45 (2.81) 0.25 0.30 0.49 0.20 3.42 (2.72) xC12E8 = xSLES (100 mM NaCl) 0.125 0.10 0.73 0.17 3.56 (2.80) 0.20 0.18 0.66 0.16 3.31 (2.88) 0.33 0.27 0.45 0.28 3.45 (2.81) 0.375 0.34 0.37 0.29 3.59 (2.84) xSLES = xLAS (100 mM NaCl) 0.125 0.68 0.16 0.16 3.46 (2.60) 0.20 0.56 0.30 0.14 3.19 (2.80) 0.33 0.27 0.45 0.28 3.45 (2.81) 0.375 0.20 0.51 0.27 3.47 (2.75) xC12E8 = xLAS (2 mM CaCl2 ) SLES C12 E8 LAS SLES 0.90 0.05 0.18 0.77 4.12 0.75 0.13 0.28 0.59 3.88 0.60 0.14 0.38 0.48 3.75 0.33 0.26 0.48 0.26 3.52 0.25 0.24 0.68 0.08 3.48 xC12E8 = xSLES (2 mM CaCl2 ) 0.125 0.12 0.73 0.15 3.40 0.20 0.19 0.61 0.20 3.51 0.33 0.26 0.28 0.46 3.52 0.375 0.29 0.40 0.31 3.59 xSLES = xLAS (2 mM CaCl2 ) 0.125 0.63 0.24 0.13 3.69 0.33 0.26 0.28 0.46 3.52 0.375 0.19 0.51 0.30 3.61

total mole fraction

C12 E8 0.05 0.125 0.20 0.33 0.375

LAS 0.05 0.125 0.20 0.33 0.375

0.125 0.20 0.33 0.375

0.75 0.60 0.33 0.25

0.75 0.60 0.33 0.25

0.125 0.20 0.33 0.375

C12 E8 0.05 0.125 0.20 0.33 0.375

LAS 0.05 0.125 0.20 0.33 0.375

0.125 0.20 0.33 0.375

0.75 0.60 0.33 0.25

0.75 0.33 0.25

0.125 0.33 0.375

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scatter in the points for CaCl2 , the experimental measurements for both are on the same plots. We also note that the change between 100 mM and 6 mM NaCl is negligible and this is elaborated in the next section. It is difficult to find an effective objective criterion for the optimum fit, mainly because the range of composition covered means that some points are very sensitive to some parameters and not at all to others. The poorest fit is of the SLES and LAS compositions at high C12 E8 in Figure 2(a) and this can be adjusted by small changes in the micellar mixing parameters but these cause poorer fits in the other two diagrams, which suggests that there may be some genuine ternary interaction in the micelles. However, as for the fits in the absence of electrolyte the fits are consistently reasonable and show that the assumption that only binary interactions are required to fit the ternary mixing in these mixtures is sound. Liley et al. included an attempt to fit the simpler regular solution model to a similar set of data, but without electrolyte, which was not successful, and we have not attempted that here. Table 2 shows that none of the GE for the pairwise interactions in either micelle or at the surface have their minima at the 50:50 composition required in the regular solution model and it is therefore unlikely to be useful to attempt such a fit. We emphasize that the choice of bulk compositions allows these data to be represented in a conventional 2D graph but the calculation of the interactions involves an extra variable, i.e. the data can be collected as if the solution were a pseudo-binary mixture with one pair of surfactants as a pseudocomponent 26 but this assumption can not be used in the calculation of the behaviour of such a mixture. The corresponding calculated fraction of the principal component for each of the three parts of Figure 2 is also shown for no electrolyte. The substantial difference results mainly from the change in the CMCs of the components, with SLES and LAS becoming relatively much more surface active. The principal changes in the surface interaction parameters are a strong decrease in the magnitude of the minima in GE for LAS–C12 E8 and C12 E8 –SLES, which would be expected for a predominantly electrostatic interaction. However, the surface interaction between the two anionic surfactants SLES and LAS is more or less unchanged

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Langmuir

1.0

(a) equimolar SLES-LAS

bulk mole fraction C12E8

0.8

C12E8 (no electrolyte)

0.6

0.4

0.2 mole fraction C12E8 0.0 LAS (NaCl) C12E8 (NaCl)

bulk mole fraction LAS

(b) equimolar C12E8 -SLES

SLES (NaCl)

0.8

LAS (no electrolyte) LAS (CaCl2) SLES (CaCl2)

0.6

C12E8 (CaCl2)

0.4

0.2 mole fraction LAS 0.0

(c) equimolar LAS- C12E8 SLES (no electrolyte)

0.8

bulk mole fraction SLES

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0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

mole fraction SLES

Figure 2: Fits of the calculated composition of the adsorbed layer of three different ternary mixtures of SLES–LAS–C12 E8 to data above the CMC at 2 mM CaCl2 (filled in points) and 100 mM NaCl. In each set of data one surfactant, (a) C12 E8 , (b) LAS and (c) SLES, varies while the other two form an equimolar pair. The set of 6 B and C parameters in Table 2 was used to fit the data with the ST fixed at 34 mN m−1 . The key to the plotted data in given in (b).

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Langmuir

on addition of electrolyte. Effect of Electrolyte Concentration Table 4 gives a set of compositions for a 0.125:0.125:0.75 C12 E8 :LAS:SLES mixture at a total surfactant concentration of 2 mM for different NaCl concentrations and the results are plotted in Figure 3(c). Each set of 3 compositions was again deduced from NR measurements of 4 isotopic combinations. The CMCs of the individual components in the absence of NaCl are 0.09, 1.2 and 2.2 mM respectively and at higher electrolyte concentrations the CMCs of the two ionic surfactants decrease to 0.2 and 0.24 mM. Thus the measurements cover a range from just above the CMC (no electrolyte) to at least 10 times the CMC. Table 4: Variation in surface composition and total adsorption at an overall surfactant concentration of 2 mM for C12 E8 :LAS:SLES and C12 E8 –LAS–SDS mixtures in varying concentrations of NaCl. total mole fraction C12 E8 0.125 0.125 0.125 0.125 0.125 0.125 C12 E8 0.125 0.125 0.125 0.125 0.375 0.375

[NaCl] mM

LAS SLES 0.125 0.75 0.125 0.75 0.125 0.75 0.125 0.75 0.125 0.75 0.125 0.75 LAS SDS 0.125 0.75 0.125 0.75 0.125 0.75 0.125 0.75 0.375 0.25 0.375 0.25

0 20 40 60 80 100 20 70 150 100

surface mole fraction ±0.05 C12 E8 LAS SLES 0.41 0.34 0.25 0.17 0.30 0.53 0.14 0.27 0.59 0.12 0.27 0.61 0.12 0.27 0.61 0.11 0.29 0.60 C12 E8 LAS SDS 0.56 0.27 0.17 0.31 0.32 0.37 0.19 0.25 0.56 0.17 0.23 0.60 0.57 0.39 0.04 0.36 0.49 0.15

101 0 × Γtotal ±0.05 mol m−2 3.16 3.16 3.29 3.36 3.36 3.56 3.08 3.36 3.72 3.91 3.05 3.36

At 2 mM total surfactant and 100 mM NaCl most of the surfactant is in micellar form and therefore mass conservation constrains the micelle composition to be the same as the overall composition. Once this point has been reached the monomer composition is at a constant limiting value. The composition of the adsorbed layer is then also constant and relatively 17 ACS Paragon Plus Environment

Langmuir

1.0

monomer mole fraction

0.8 SLES LAS C12E8

0.6

0.4

(a) monomer composition

0.2

0.0

(b) micelle composition micelle mole fraction

0.8

0.6 SLES LAS C12E8

0.4

0.2

0.0 SLES LAS C12E8

(c) layer composition

0.8 adsorbed mole fraction

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0.6

0.4

0.2

0.0 0

20

40

60

80

100

[NaCl]/mM

Figure 3: The effect of varying concentration of NaCl on (a) the monomer mole fraction in solution, (b) the micellar mole fraction and (c) the adsorbed mole fraction in a 0.125:0.125:0.75 C12 E8 :LAS:SLES mixture at a total surfactant concentration of 2 mM. The CMCs and the interaction parameters at zero and 100 mM salt are those given by Liley et al. and those in Table 2 respectively. At intermediate concentrations of NaCl the mixed CMCs are assumed to follow the empirical Corrin–Harkins equation and the variation in the interaction parameters is scaled to the changes in CMC as described in the text. 18 ACS Paragon Plus Environment

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Langmuir

easily modelled. At a sufficiently high concentration all but a tiny amount of surfactant is in the micelles and hence the composition of the micelles is approximately equal to the overall composition, i.e. (xi ≈ αi ). For a binary mixture Eqn (3) then gives xmon ≈ i

αi fiµ cµi αi µ µ µ µ = αi fi ci + αj fj cj αi + αj Rf Rµ

(10)

where αi is the overall mole fraction of component i and Rf and Rµ are the ratios of the activity coefficients and of the CMCs respectively. In this concentration regime xi and R do not vary with concentration and hence neither does the monomer mole fraction. There are two easily treated limiting situations, one when the solution is ideal and Rf = 1, and the other when the CMCs are equal, when Rµ = 1. For example, for an ideal solution (Rf = 1) component j will preferentially fractionate into the micelle if it has the smaller CMC (Rµ