Analysis of the Asymmetric Synergy in the Adsorption of Zwitterionic

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Analysis of the Asymmetric Synergy in the Adsorption of Zwitterionic--Ionic Surfactant Mixtures at the Air--Water Interface Below and Above the Critical Micelle Concentration Peixun Li, Kun Ma, Robert K. Thomas, and Jeffrey Penfold J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00762 • Publication Date (Web): 30 Mar 2016 Downloaded from http://pubs.acs.org on April 5, 2016

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The Journal of Physical Chemistry

Analysis of the Asymmetric Synergy in the Adsorption of Zwitterionic–Ionic Surfactant Mixtures at the Air–Water Interface Below and Above the Critical Micelle Concentration Peixun Li,† Kun Ma,† Robert K.Thomas,∗,† and Jeffrey Penfold‡,¶ †Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, UK. ‡Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon ¶Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, UK. E-mail: [email protected]

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Abstract Surface tension (ST) and neutron reflection (NR) measurements have been made on a series of mixtures of two ionic surfactants, one anionic (SDS) and one cationic (C12 TAB), with the two zwitterionic surfactants dodecyldimethylammonium propanesulfonate (C12 SB) and dodecyldimethylammonium acetate C12 CB. The anionic surfactant SDS interacts equally strongly with both zwitterionics and the C12 TAB less strongly. For the SDS-C12 SB mixtures simultaneous fitting of ST and NR data made it possible to use the pseudophase approximation with an expansion of the excess free energy, GE , up to and including the quartic term. GE is asymmetric for the adsorbed layer and the minimum occurs at a surface mole fraction, xSDS , of 0.38 with a depth of −2.8RT . NR was also used to follow the adsorption above the CMC and the changes showed that the intramicellar interaction is more asymmetric, but weaker than the surface interaction with a depth of GE of −2.2RT at the minimum of xSDS = 0.23. A strong synergy in the total surface excess was observed above the mixed CMC with an enhancement over the adsorption of the pure components of about 45%, which appears to result from a sharp variation of the packing with surface composition coupled with the effects of the strongly asymmetric micellization. NR data on SDS–C12 CB showed that GE for both surface and micelles was similarly asymmetric to those for SDS-C12 SB, but there is no strong synergy in adsorption. This is attributed to the more rigid head group. C12 TAB–C12 SB has an asymmetric GE for both surface and micelle similar to those for SDS-C12 SB but the depths are smaller at −0.6RT and −0.5RT respectively and there is no synergy in the total adsorption.

Keywords: surfactant mixing, surfactant synergy, adsorption above CMC, synergy above CMC, zwitterionic surfactants.

INTRODUCTION Zwitterionic surfactants are an interesting class of surfactants. 1 Many carry no nett charge at the natural pH with no added electrolyte. This lack of overall charge makes their interactions 2 ACS Paragon Plus Environment

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with biosystems weaker than those of ionic surfactants and they are therefore widely used in biological applications 2 and in formulations for personal care. 3 The presence of charges within the overall neutral molecule generally makes them highly water soluble, 4 and the potentially strong interaction of their separate charged groups with ionic surfactants often leads to strong synergy, which is of great importance in formulations, but is not easy to understand. There are two limiting approaches to the understanding of surfactant mixing. One is to interpret experimental measurements of ST and/or surface coverage data in terms of a thermodynamic framework, rigorous or approximate, and the other is to use statistical mechanics to relate models of the molecular interactions to the same sort of data. The former approach sub-divides into two. Thus zwitterionic–ionic surfactant mixtures have been studied using the pseudophase approximation (PPA) on its own 5 and by using the PPA in combination with the regular solution approximation. 6–9 As an example of the other limiting approach, often called the molecular thermodynamic approach, Mulqueen and Blankschtein modelled the molecular interactions in the dodecyldimethylammonium acetate (C12 CB)– SDS system directly and showed that the results obtained by Hines et al. 8 could be well accounted for in terms of the electrostatic interactions in the system. 10 Danov et al. have used an intermediate between these two limits, which also included a treatment of the double layer, and applied it to the zwitterionic surfactant dodecylamidopropylbetaine mixed with SDS in electrolyte. 11 In this paper we present surface tension and neutron reflection results on mixtures of one anionic surfactant, SDS, and one cationic, dodecyltrimethylammonium bromide (C12 TAB), with each of the two commonly used zwitterionics, dodecyldimethylammonium propanesulfonate (C12 SB) and C12 CB, for which the structures are shown in Figure 1. The individual behaviour of three of the four surfactants has been characterized previously by both ST and NR measurements. The ST behaviour of the remaining one, C12 SB, has been characterized 12–14 but there are no corresponding NR measurements. Although ST measurements



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in principle give the surface coverage of individual surfactants by application of the Gibbs equation, this is often fraught with error, 15–17 and more reliable values of surface coverage are obtained from the less model dependent NR. For mixtures, the determination of coverage and composition using ST is expected to be even less reliable. However, for mixtures these composition measurements are then used in thermodynamic models of surface tension or micellization to try to understand the mixing. The apparent self-consistency of such fitting is difficult to assess without information that is independent of the ST. Compositions and coverages from NR can be used either to test or to be incorporated into the ST model. There are already ST measurements in the literature for each of the possible zwitterionic– ionic combinations of this set of surfactants 5,8,9 but there are only NR measurements for one combination. 8

Figure 1: The structures of the two zwitterionics studied. The spacer is 3 methylene groups in C12 SB above and one methylene in C12 CB below. The short spacer in C12 CB makes the carboxylate group a strong electrolyte.

EXPERIMENTAL DETAILS For three of the four surfactants used the details of the preparation of the deuterated surfactant needed for the NR measurements and the corresponding protonated species have been given in full elsewhere, dSDS, 18 dC12 TAB, 19 and C12 CB. 8 The remaining surfactant, C12 SB, was prepared following the procedure described by Qu et al. 13 1,3-propanesultone 4 ACS Paragon Plus Environment

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(0.25 ml) was dissolved in 50 ml acetone and added to a stirred solution of dimethyldodecan1-amine(0.05 mol) in 50 ml acetone over a period of 15 min and the mixture refluxed at 60◦ C overnight. The crude C12 SB was produced as a white solid, which was filtered and washed with acetone. Recrystallization from mixtures of acetone and methanol was repeated until there was no minimum in the ST-ln c curve. Alkyl chain deuterated dodecyldimethylamine was prepared from bromododecane and dimethylamine as described previously. 20 Neutron reflection (NR) measurements were performed on the reflectometers INTER and SURF at the Rutherford-Appleton Laboratory (Didcot, U.K.). The instruments and the procedure for making the measurements have been described fully elsewhere. 21,22 Measurements were made at an incident angle of 1.5◦ , which gives a range of momentum transfer, κ ( = (4π sin θ)/λ, where θ is the glancing angle of incidence), from 0.05 to 0.35 ˚ A−1 , and a flat incoherent scattering background was subtracted. The conversion of measured signal to absolute intensity was made by calibration with D2 O and the direct beam. Since the main aim of this work was to determine coverage and composition rather than structure, all the measurements were made in null reflecting water (NRW) with one or other component of the mixture, or both, containing perdeuterated alkyl chains. Under these circumstances the reflected signal is entirely from the surfactant layer and the two surfactants can be distinguished easily. The surface coverage of surfactant can then either be determined independently of the structure of the layer from the intercept of a linear plot of log(κ2 R) against κ2 23 or by fitting the NR data with a simple slab model using the standard optical matrix method to calculate the reflectivity. 24 Although the individual determinations of layer thickness, layer roughness and layer density in the second method are to some extent coupled under these circumstances, the surface coverage is given by a combination of these terms that is not affected by the coupling. It is therefore also model independent and its absolute accuracy is typically better than ±7%. 25



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RESULTS Results for Pure C12 SB Surface tension measurements at 298 K gave a CMC value of 2.2 ± 0.2 mM and a limiting surface tension at the CMC of 38.9 ± 0.5 mN m−2 . Analysis of the ST curve with the Gibbs equation using a prefactor of 1 and fitting a quadratic in ln c gave the limiting coverages given in Table 1. NR measurements on the chain deuterated form, whose interpretation does not depend on any assumptions about either the Gibbs prefactor or the shape of the ST-ln c curve, gave closely similar surface coverage results as shown in Table 1 (the data and their fits are shown in Figure S4 of the Supporting Information). The close agreement establishes that the Gibbs prefactor is 1 and therefore that C12 SB carries no nett charge in solution at its natural pH. The value of the area per molecule at the CMC from NR was found to be 46 ± 3 ˚ A2 . Zhao et al. have recently obtained the values of 1.383 mM for the CMC, 38.64 mN m−1 for the limiting surface tension and 63.57 ˚ A2 for the area per molecule (no errors given, but unlikely to be less than about ±20% in area per molecule) for a purified commercial sample of C12 SB. 12 There is a large discrepancy between this value of the limiting area and ours in Table 1. We have discussed this problem in detail elsewhere 15,16 and it probably lies with an inappropriate determination of the limiting slope of the ST-ln c plot by Zhao et al. In general, the only chance of obtaining a correct value of the limiting slope is to fit the curve to a quadratic in ln c, but Zhao et al. do not give the details of their analysis. Yaseen et al. 26 made a very full analysis of their ST and NR results for the zwitterionic dodecylphosphocholine (C12 PC) and found limiting areas of 65, 53 and 52 ˚ A2 from ST analysis with a simple linear plot, ST analysis with a quadratic, and direct measurement with NR respectively. These values suggest that Zhao et al. may have used a linear plot to analyse their ST data and this could account for the surprisingly high value ˚2 is much of A they obtained. To reinforce this conclusion, we note that our A value of 46 A ˚2 for C12 PC and 50 A ˚2 for C12 CB. 8 Qu et al. 13 closer to the corresponding values of 52 A


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˚2 for CMC, limiting ST and area per obtained values of 1.6 mM, 32.8 mN m−1 and 105 A molecule respectively, but here the large discrepancy in the limiting ST suggests that there is something faulty in their calibration of the tensiometer (drop volume method), since the limiting value of the ST for other zwitterionics tends to be closer to 40 mN m−1 . Graciani et al. obtained 2.7 mM for the CMC of C12 SB at 298 K, 14 giving a mean value of 1.9 mM for these three previous measurements, within error of our value. A further point of interest in Table 1 is that the thicknesses of the layer are significantly smaller than for ionic surfactants with the C12 chain. Thus, SDS and dC12 hTAB (C12 chain deuterated, quaternary methyl groups protonated) have layer thicknesses at the CMC of 18 and 17.5 ˚ A at limiting areas of ˚2 respectively, about 20% higher than for C12 SB. This suggests that the alkyl 44 and 48 A chains in the C12 SB layer are more strongly tilted than in the two ionic surfactants. Strong tilting of this magnitude is usually associated with a significantly larger A but here it may be associated with the long head group taking up a vertical orientation in the water and forcing the alkyl chain to tilt. Table 1: Surface excesses and areas per molecule for C12 SB from NR and ST measurements at 298 K. concentration τ Γ(NR) mM ±20% ˚ A ±7% µmol/m2 0.22(0.1CMC) 11 2.8 0.66(0.3CMC) 13 3.3 2.2(CMC) 14 3.7

A(NR) ±7% ˚ A2 60 50 45

Γ(ST) ±20% µmol/m2 3.1 3.3 3.5

A(ST) ±20% ˚ A2 54 50 48

Mixtures: the CMC The strong synergy between the zwitterionics and the ionic surfactants is immediately noticeable in the mixed CMC, determined from the ST curves done at fixed compositions of the binary mixtures. For both zwitterionics the interaction is significantly stronger with SDS than with C12 TAB as is shown by the much lower values of the mixed CMC relative to the two pure compounds, no doubt because of the larger size of the TAB head group. The 7 ACS Paragon Plus Environment


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Figure 2: The variation of the CMC (points) with composition for mixtures of (a) SDS with C12 SB (black) and C12 CB (red, triangles) and (b) C12 TAB with C12 SB (black) and C12 CB (red, triangles). The thin lines show the variation of the CMC for ideal mixing of the surfactants and the heavy lines show fits using the regular solution model with values of the interaction parameter Bm of (a) −10 and −9.4, and (b) −2.4 and −0.7 for C12 SB and C12 CB respectively.


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results for the 4 mixtures studied are given in Table 2 and the actual data for three of them in Figures S1, S2 and S3 in the Supporting Information. We compare our ST measurements with those of others 5,9 below. Table 2: Measured CMC (mM) for SDS and C12 TAB with the zwitterionic surfactants, C12 SB and C12 CB. Measurements were at 298 K except for C12 CB with SDS, which was done at 313 K, because the strong interaction leads to a raised Krafft point for the mixed system . Since the CMC is determined from a lnc plot the error is approximately a constant additive error in lnc and therefore a fractional error in c, estimated to be about ±20%. SDS:Z 0:100 25:75 50:50 75:25 100:0

C12 SB mM 2.2 0.25 0.3 0.8 7.0

C12 CB mM 1.9 0.2 0.3 0.8 7.0

C12 TAB:Z 0:100 25:75 50:50 75:25 100:0

C12 SB mM 2.2 2.0 2.7 3.2 14.1

C12 CB mM 1.9 2.0 2.8 4.9 14.1

The pseudophase approximation gives for a mixed micelle consisting only of two nonionic 27–29 surfactants the following equation at the mixed CMC (cm mix ),

α2 1 α1 + = m m m f 1 c1 f 2 c2 cmix

(1)

where αi are the fractions of surfactant relative to total surfactant in the bulk solution and cm i are the pure CMCs. The activity coefficients, fi , in the micelle are determined by the excess free energy of mixing, GE , and in the regular solution approximation this is assumed to be a single quadratic term, i.e.

GE = RT Bm x1 x2

(2)

which gives the activity coefficients as

ln fi = Bm x2j 9 ACS Paragon Plus Environment

(3)


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where xi is the concentration of species i in the micelles and Bm is a constant. For a binary mixture of nonionic surfactants the pseudophase approximation in combination with the regular solution approximation gives the result that the minimum in the plot of CMC against bulk concentration occurs when αi = xi , 30 i.e. the micelle and bulk solution composition are identical at the CMC at the minimum in the CMC. If we assume that this applies approximately to the SDS-C12 SB mixture then the experimental points in Figure 2 suggest that the minimum occurs well below xSDS = 1/2 in the micelle. Because the regular solution model eq 2 is symmetrical in the micelle composition it constrains the minimum in the CMC to be closer to xSDS = 1/2 for the observed CMC ratio of about 3.5 and requires there to be a very strong attractive interaction (large negative value of Bm ). There is insufficient information to improve such a simple fit but, as we will show below, the surface adsorption above the CMC is extremely sensitive to any fractionation of the composition of the micelles relative to the bulk composition and this information can make it possible to fit the CMC behaviour with a better model. The procedure for applying the regular solution approximation is to make an iterative fit of eq 1 to a set of CMC data to give a value of Bm and the composition of the micelle, x1 . The use of the function ln(f2 /f1 ) reduces the degree of the polynomial to be solved by 1 (basically because x1 + x2 = 1) and makes the iteration easier. Thus, using eq 3 gives 31,32 ln

f2 f1

x 1 cm 1 α2 = Bm (x1 − x2 ) = ln x 2 cm 2 α1

(4)

Iteration of x 1 cm 1 α2 Bm (x1 − x2 ) − ln =0 x 2 cm 2 α1

(5)

can be done using the simplest iteration method, the sector method. 33 The solutions are stable and the equation is easily extended to more complicated forms of GE . In Figure 2 the results are compared with calculations of both ideal and non-ideal mixing where the latter uses the regular solution model with a single interaction parameter, i.e.


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eq 2. For the more strongly interacting systems, SDS–Z, the fit of this single parameter model is poor. An alternative empirical way of dealing with this is to use a different value of the parameter Bm to fit each composition, in which case the magnitude of B decreases significantly with bulk mole fraction of zitterionic. This was done by Hines for SDS–C12 CB, 8 by Lopez-Diaz et al. 9 for SDS–C12 SB and C12 TAB–C12 SB, and by Li et al. for sodium dodecyl sulfonate–C12 SB (at 313 K). 34 Our values for SDS-C12 SB using this method were −11, −10 and −7 for mole fractions of SDS of 0.25, 0.50 and 0.75 respectively. Remarkably, the values of the mixed CMC are almost identical for the C12 SB and C12 CB mixtures. Thus, although a sulfonate group generally ionizes much more strongly than a carboxylate, this difference is reduced when the carboxylate is close to the permanent positive charge of the quaternary ammonium group in the zwitterionic. 35 As shown by Hines et al. asymmetry in the regular solution model may result from either the ionization of the micelle or a less symmetrical excess free energy than given by just a quadratic term in GE and we return to this below. For the C12 TAB systems the interaction parameter is much lower, probably because the head groups are of comparable size so that the charge on the cationic head group cannot discriminate well between the two charged groups on the zwitterionic. It is possible to fit the data to a single set of parameters if a more extended expansion of GE is used rather than the regular solution approximation. However, given that there are some weaknesses in the model itself, such an extension of the fit preferably requires additional experimental information. The most valuable information would be the composition of the micelle but this is not generally available in the vicinity of the CMC. The situation changes completely when we examine the surface behaviour.

Mixtures: Surface Tension and Composition at and below the CMC There are two distinct situations where the pseudophase approximation can be applied to analyse the surface tension and/or surface excess of a surfactant mixture. Below the CMC the interpretation is relatively simple using either NR or surface tension measurements. 11 ACS Paragon Plus Environment


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However, NR also offers the interesting possibility of being able to measure the surface excess above the CMC, which is the concentration range where surfactant formulations are mostly used in practice. Below the CMC eqs 4 and 5 can be applied to the ST behaviour π π if the cm i are replaced by ci where ci is the concentration at which the surface pressure, π,

reaches a particular value. Such a set of measurements of cπi for different compositions at a fixed surface pressure can be fitted in terms of a parameter Bs using an iterative procedure to solve eq 5. It should be noted that Bs is not the same as Bm for micelle formation and that Bs also depends on the surface pressure because the values of cπi depend on π through cπi = cπ=0 exp i

πω i

RT

(6)

is a measure of its binding to the where ωi is the molecular area of surfactant i and cπ=0 i surface at zero pressure. 36,37 Below the CMC it is possible to collect a set of measurements at constant π, whose variation is independent of π and to which the simpler model can be applied. Such a set of data is assembled in Table 3 based on the surface tension curves given in the Supporting Information. The cπ in Table 3 were obtained by interpolation of the surface tension curves using fitted quadratics in ln c at the highest possible surface pressure in each case, i.e. close to the limiting ST at the CMC of the less surface active component. An important difference from the analysis of the CMC data is that the concentration of the individual surfactants at the surface, i.e. the xi in eq 5, can be determined using NR both above and below the CMC. As an example, Figure 3 shows the NR profiles for 50:50 mixtures for each of SDS–C12 SB and C12 TAB–C12 SB at a concentration of 0.66 mM plotted in the form of logκ2 R against κ2 for three isotopic compositions, two where one of the components has a deuterated chain, and the third where both chains are deuterated. The scattering lengths of the components here are such that the intercepts of the profiles are to a high level of accuracy respectively dependent only on the surface coverage of each of the individual components and on the total surface coverage, apart from the known values


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Figure 3: Neutron reflectivity data from 50:50 mixtures of (a) C12 TAB–C12 SB and (b) SDS– C12 SB at a concentration of 0.66 mM (below the mixed CMC for C12 TAB–C12 SB and above the mixed CMC for SDS–C12 SB) plotted in the form of log(κ2 R) against κ2 . In such plots the combination of the known scattering length of the molecule and the intercept gives the surface coverage directly without any assumption about the structure of the layer. 23 The scattering lengths of the protonated molecules here are approximately zero and those of the deuterated molecules are very similar to each other.



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of the scattering lengths of the molecules. Thus in Figure 3a it is immediately obvious that in 50:50 C12 TAB–C12 SB there is only a small difference between the total adsorbed amount and that of just C12 SB, and this is consistent with the low level of adsorption of C12 TAB. In Figure 3 the fraction of SDS in the layer is higher but still less than that of C12 SB. Finally, since the scattering lengths of the three molecules involved are almost the same, the total adsorption in SDS–C12 SB is higher than in C12 TAB–C12 SB. The set of three isotopic profiles give independent measures of the total coverage and of the individual coverages and the complete set of results is given in Table 4. Ideally, the sum of the individual coverages should equal the measured total but, as shown in Table 4, there are discrepancies and the final composition will then depend on the way the results are combined. Here we have first determined the total coverage from the average of the total measurement and the sum of the individual measurements to give the result in the last column in Table 4. We have then used this to determine the individual fractions and finally normalized the sum of these fractions to unity. The NR values used in Table 3 are averages of the values below the mixed CMC from Table 4. Strictly these should be corrected for the surface pressure term in eq 6 but the correction is small here and there appears to be no systematic change in the fractional coverages over the concentrations studied, although Hines et al. observed changes in the SDS–C12 CB system at concentrations well below the CMC. In addition, we reanalysed the NR data of Hines et al. using the same method as used here and this gave different values of x from the original paper, especially at the two lower compositions (the details are given in the Supporting Information). Since the regular solution model used in the original paper did not fit the data at all well these changes do not affect the original conclusions significantly. The pseudophase assumption is normally applied just to the cπ data using the regular solution model and not to coverage data. This often leads to the problem identified above for micellization, that Bs varies with coverage, and, if coverage data are available, to discrepancies between the values of Bs needed to fit the two different types of data. In particular, Hines et al. found that Bs = −8 for the cπ data on the SDS–C12 CB system whereas it was


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Table 3: Measured cπ (mM) for SDS and C12 TAB with the zwitterionic surfactant (C12 SB and C12 CB) and surface compositions, x1 , below the mixed CMC from NR, all at 298 K except C12 CB-SDS at 313 K. The measurements were made at an ST of 40 mN m−1 . The superscript a denotes an average over values at total concentrations of 0.22 and 0.66 mM, b denotes an average over 0.22, 0.66 and 2.2 mM (full details of the NR measurements are given in Table 4), and c denotes results recalculated from the reflectivity data of Hines et al. 8 The errors in cπ are the same as for the CMC measurements in Table 2. SDS:Z 0:100 20:80 25:75 50:50 75:25 80:20 100:0 C12 TAB:Z 0:100 25:75 50:50 75:25 100:0

C12 SB cπ 1.55 0.1 0.2 0.4 7.0 C12 SB cπ 1.6 1.8 2.8 3.0 14.9

C12 CB x1 ± 0.04 cπ 0.0 1.4 0.32 0.1 0.32 0.15 0.39a 0.4 1.0 7.0 C12 CB x1 cπ 0.0 1.4 a 0.25 1.55 0.30b 2.1 b 0.33 4.1 1.0 14.9


x1 ± 0.04 0.0 0.26c 0.32c 0.39c 1.0 x1 -


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only -1.6 for the coverage data obtained by neutrons. This large discrepancy has a simple explanation, which can be illustrated using our SDS–C12 SB data as follows. Where the minimum in cπ occurs, the regular solution approximation requires the composition of bulk solution and surface layer to be identical and the surface version of eq 5 can be used to relate this surface composition, x1min and Bs directly by

x1min

1 1 ln = + 2 2Bs

cπ1 cπ2

(7)

The behaviour of x1min as a function of negative values of Bs for the value of cπ1 /cπ2 for SDS–C12 SB is shown in Figure 4, where x1 designates xSDS . For the large magnitude of Bs observed for this system x1min is between 0.4 and 0.5, i.e. the strong attraction between the surfactants causes the surface to tend towards being equimolar even though SDS is much less surface active than C12 SB. The mixed cπ is obtained directly by substituting the value of x1min from eq 7 into the surface version of eq 1

cπ1

x1min 1 − x1min 1 + π = π 2 2 exp (−Bs x2min ) c2 exp(−Bs x1min ) cmin

(8)

where the cπi refer to the pure components. The resulting value of cπmin relative to the cπ of C12 SB is also plotted in Figure 4 and shows that a value of x1min of about 0.25 correlates with a weak interaction of Bs of about -2, while low values of cπmin in the range 0.05–0.08 correspond to values of x1min of about 0.45. The experimental values of x1min for all the SDS systems in Table 2 therefore require −Bs to be small, while the corresponding cπmin values require −Bs to be large. Thus the coverage and cπ data cannot even be approximately reconciled in the regular solution model. There are several possible explanations for this failure of the regular solution model, all of which have been discussed previously by many authors 38 and which were discussed explicitly for the SDS–C12 CB system by Hines et al. First, leaving aside the important question of whether or not the pseudophase approximation is applicable, 38–40 the model strictly only 16 ACS Paragon Plus Environment

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Figure 4: The behaviour of the minimum value of cπ at a mixed surface and of the surface composition of the less surface active component (component with the higher cπ ) as a function of the interaction parameter, Bs , calculated using the exact solution of the regular solution approximation, eqs 7 and 8, and the observed cπ1 /cπ2 ratio.



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Figure 5: (a) Fitting of the values of cπ from surface tension (red) and of xi from NR (black) for SDS-C12 SB mixtures below the CMC and (b) the excess free energy of mixing at the surface plotted against the surface composition over the range accessible to the surface tension and neutron experiments. In (a) thin lines use the regular solution approximation and thick lines use the full excess free energy of Eqn (9) using the values of the parameters in the Figure. In (b) the surface compositions corresponding to the three bulk concentrations of the measurements are marked with vertical lines.


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applies to nonionic surfactants. Secondly, the representation of the excess free energy as a simple quadratic may not be realistic, and thirdly, the extent of hydration of the layer may well change on mixing and this affects the assumption that the layer consists only of the two surfactants. One common solution for the first of these has been to use swamping electrolyte, but this is likely to affect the interaction, which is the main point of interest in ionic-zwitterionic mixtures. Hines et al. showed that the dissociation can in principle be treated quantitatively if its variation with composition is known, and the second factor above is analysable using a more extensive expansion of GE , but there are no models for the change in hydration, the third factor above, although Hines et al. used NR to determine the structure of the layer, from which they showed that the mixing of SDS and C12 CB was indeed associated with large hydration changes. They also showed that the first two factors can have similar effects on the apparent GE but they are to some extent mutually exclusive. 8 Since the GE expansion requires less a priori information we have chosen to use this route to fit the data. Holland and Rubingh 37 in their original treatment of the nonideal mixing of surfactants used an expansion for GE that is well established for bulk binary mixtures, 31,41,42 which is GE = RT x1 x2 Bs + Cs (x1 − x2 ) + Ds (x1 − x2 )2 + ...

(9)

where Bs , Cs and Ds are constants appropriate to the surface layer. This conforms with the requirement that a true phase obeys the Gibbs-Duhem equation, i.e. it applies as a consequence of the pseudophase approximation. There are alternative formulae for GE that also fulfil the requirement of satisfying the Gibbs-Duhem equation, e.g. ref, 43 but most bulk liquid mixtures can be explained with the series above without going beyond the quartic D term. 42 The use of this fuller expression in eq 9 does not change the procedure for solving eqn 1 but the activity coefficients are now 41,42

ln f1 = Bs x22 + x22 (3 − 4x2 )Cs + x22 (5 − 16x2 + 12x22 )Ds 19 ACS Paragon Plus Environment

(10)


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Table 4: Surface excesses and fraction of ionic surfactant at the surface (xs ) measured by NR for three isotopic compositions of the systems SDS-C12 SB and C12 TAB–C12 SB. Sets of figures in italics are measurements at or below the mixed CMC. system (composition)

c/mM

SDS–C12 SB (25:75)

0.22 0.66 2.2 6.6 0.22 0.66 2.2 6.6 0.22 0.66 2.2 6.6 0.22 0.66 2.2 6.6 0.22 0.66 2.2 6.6 0.22 0.66 2.2 6.6

SDS–C12 SB (50:50)

SDS–C12 SB (75:25)

C12 TAB–C12 SB (25:75)

C12 TAB–C12 SB (50:50)

C12 TAB–C12 SB (75:25)

Γ (d–d) ±0.25 4.3 4.7 5.0 5.2 4.9 5.2 5.2 5.6 4.3 5.0 5.3 5.4 2.9 3.3 3.9 4.2 2.6 3.0 3.9 4.3 2.2 2.6 3.5 3.9

Γ (d–h) ±0.15 1.4 1.7 1.8 2.1 1.4 2.0 2.0 2.3 1.7 1.9 2.2 2.5 0.8 0.8 1.1 1.4 0.7 0.9 1.3 1.7 0.75 0.9 1.2 1.4

Γ (h–d) xs (ionic) ±0.2 ±0.03 3.0 0.32 3.3 0.34 3.3 0.35 3.3 0.39 3.0 0.32 3.0 0.40 3.3 0.38 3.3 0.41 2.7 0.39 2.9 0.40 3.0 0.42 3.0 0.45 2.2 0.27 2.7 0.23 3.1 0.26 2.9 0.33 2.0 0.26 2.1 0.30 2.4 0.35 2.7 0.39 1.5 0.33 1.8 0.33 2.4 0.33 2.7 0.34


Γtotal ±0.2 4.35 4.85 5.05 5.3 4.65 5.1 5.25 5.6 4.35 4.9 5.25 5.45 2.95 3.4 4.05 4.25 2.65 3.0 3.8 4.35 2.25 2.65 3.55 4.35

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with a parallel expression for f2 except that the sign changes for the Cs term. The simultaneous solution of eq 1 can still be done accurately by the iteration method described above. The thick lines in Figure 5a show the best fit of the pseudophase model to SDS–C12 SB using the full expression, eq 9, for the excess free energy, and thin lines for the regular solution model. The reason that the extra parameters in GE , i.e. Cs and Ds , give a much improved fit to the composition of the surface is that these parameters shift the minimum in GE so that it matches the observed compositions, as is shown in Figure 5b, where the corresponding excess free energies are plotted over the restricted range of surface composition accessible between the solution composition limits of 0.001 and 0.999. This suggests that a GE parameterized in terms of just depth (Gmin ) and composition at the minimum (xmin ) would be a physically more transparent way to quantify GE . However, there is no obvious way of rewriting eq 9 in terms of these two parameters. Others have tried to introduce asymmetry, for example, by using a value of Bs/m that varies with surface composition, 44 but this was not in a form that is consistent with the pseudophase approximation, i.e. one that obeys the Gibbs-Duhem equation. It is nevertheless clear that Gmin and xmin are the two important parameters. Therefore, in the fits to the data for all six systems given in Table 5 we include the derived values of Gmin and xmin with the results of fitting B alone, and the result of fitting the set of Bs , Cs and Ds at the same depth of GE . Thus we are effectively fitting the asymmetry in terms of its depth and composition at the minimum but in a way that is thermodynamically consistent with the pseudophase approximation. However, the doubts over the validity of the pseudophase approximation and the limited range of surface concentration probed might allow a more flexible choice of expressions for GE than those from bulk liquid mixtures. The most obvious causes of the asymmetry in GE are different lateral dimensions for the two surfactants and the optimization of electrostatic screening. For example, a 1:2 lattice is particularly stable for a regular two dimensional lattice of one charged and one uncharged component, and local structures with this conformation will persist in a liquid-like layer. 45



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Figure 6: (a) Fitting of the values of cπ from surface tension (red) and of xi from NR (black) for C12 TAB-C12 SB mixtures below the CMC and (b) the excess free energy of mixing at the surface plotted against the surface composition over the range accessible to the surface tension and neutron experiments. In (a) thin lines use the regular solution approximation and thick lines use the full excess free energy of eq 9 using the values of the parameters in the Figure. In (b) the surface compositions corresponding to the three bulk concentrations of the measurements are marked with vertical lines.


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The fitting of the combination of NR coverage and ST data to a single model using a fuller expansion of GE overcomes the commonly stated limitation that the Rubingh model 29 of mixing assumes the regular solution approximation for GE . The second common criticism of the model is that it neglects dissociation, i.e. it only applies to mixtures of nonionic surfactants. Hines et al. 8 applied a dissociation model based on the theoretical work of Hall 46,47 to neutron and surface tension data data on SDS–C12 CB and found that it was similar to the use of the fuller expansion of GE . The advantage of using the latter is that it parameterises the interaction more accurately without the need to introduce an explicit model for the dissociation. Hines et al. noted the further difficulty that the expansion of GE in eq 9 cannot be used in conjunction with the dissociation model. Hence the successful simultaneous fitting of cπ and surface composition with the implicit inclusion of dissociation into the higher coefficients of eq 1 for nonionic mixing therefore seems to be a more practicable option. We return to the question of dissociation in connection with adsorption and micellization above the CMC in the next section. The interactions in the C12 TAB–C12 SB system are weaker versions of those discussed above for SDS–C12 SB and the parallel calculations and data are shown in Figure 6, where it can be seen that the maximum depth of GE is much reduced compared with SDS–C12 SB. The fitting parameters are given in Table 5. In some cases the extrapolation of eq 9 to regions outside those explored within the 0.001–0.999 bulk composition range indicates that there might be phase separation. However, since this involves extrapolation outside the normal range of bulk concentrations, we do not consider them further. Such a result suggests that an exploration of very low or very high fractions (e.g. < 0.001 or > 0.999) would be useful. However, measurements in these regions would be vulnerable to surface contamination, surface depletion and slow equilibration. In Table 5 we also include values of GEmin and xmin obtained by Wydro and Paluch 5 and of Bs obtained by Lopez–Dias et al. 9 There are some uncertainties in using the values from Wydro and Paluch. First, their SDS–C12 SB surfactants have the sulfate and sulfonate labelled the opposite way round to ours, although



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the properties and surface tension behaviour match ours. In particular the CMC of their “sodium dodecylsulfonate” is 8.1 mM, i.e. the same as SDS, whereas that of the true sulfonate is higher at about 11 mM, 48 and this is confirmed by reference to two SDS papers. Also the Krafft temperature of the true sulfonate is high, 48 which would make experiments without precipitation at room temperature difficult. 34 There is a further uncertainty in that their values of G are quoted in kJ mol−1 but seem to be in units of RT . We have assumed the latter, in which case their values of GEmin for C12 SB with both SDS and C12 TAB, though not their values of x1min , are in reasonable agreement with ours. The values of Bs obtained by Lopez–Dias et al. are, on the other hand, somewhat low in comparison to ours. We discuss the methods by which the Wydsro and Paluch results were obtained in more detail below. Table 5: Two sets of parameters characterizing the excess free energy of mixing, GE (units of RT ). Columns 3 and 4 are the interaction parameter for the regular solution model, B, and the composition of the minimum energy mixture, xmin , which refers to the first component of the mixture. Columns 5 and 6 give the corresponding parameters for a free energy of mixing with quadratic (B), cubic (C) and quartic (D). The calculation of the two sets of parameters were constrained to have the same depth Gmin . a Values obtained by Wydro and Paluch 5 at a surface tension of 45 mN m−1 and b approximate average values obtained by Lopez-Dias et al. 9 also at 45 mN m−1 . Note that the values of B in Figure 2 may be slightly different because they were not constrained. system

state

B

B, C, D

xmin Gmin ±0.03 ±0.3 SDS–C12 SB surface -11.2 -10.2, 7.5, 2.5 0.38 -2.8 SDS–C12 SB micelle -8.8 -5.0, 8.5, -10.0 0.23 -2.2 SDS–C12 CB surface -10.9 -10.8, 3.8, -4.5 0.38 -2.8 SDS–C12 CB micelle -9.6 -8.6, 3.5, - 9.0 0.30 -2.4 C12 TAB–C12 SB surface -2.3 -1.8, 3.8, 5.0 0.38 -0.6 C12 TAB–C12 SB micelle -2.1 -1.0, 1.8, -2.2 0.23 -0.5 C12 TAB–C12 CB surface - 1.0 0.5 -0.25 C12 TAB–C12 CB micelle - 0.8 0.5 -0.2


xmin (Gmin )a

Bsb

0.5(-2.7) 0.47(-2.6) 0.22 (-0.3) 0.24(-0.6) -

- 5.5 0- 0.45 -

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Mixtures: Surface Composition above the CMC NR can also measure the composition of the surface above the CMC and most of the values of surface excess given in Table 4 are in this region. Although the changes are comparable with the experimental error, there is a systematic increase of the SDS fraction in the layer from below to above the CMC for the SDS–C12 SB system and a weaker increase for the C12 TAB– C12 SB system. There is no reason for the interaction between the surfactants in the layer to change above the CMC and this leaves two factors that might affect the adsorption. The first is that the surface pressure above the CMC is significantly different from that used for the determination of GE in Figure 5, which was limited to the surface pressure at the CMC of the pure components. To do the same calculation at the higher surface pressure of the mixed CMCs a correction has to be made to the cπ of the two pure components. This is given by c

πmix

(πmix − π)ω = c exp RT π

(11)

where πmix and π are the surface pressures at the mixed CMC and those at the CMCs of the pure components respectively. For SDS–C12 SB π is about the same for the two pure components, at 32 mN m−1 and πmix is about the same for the three mixtures, at 40 mN m−1 and the limiting areas per molecule are 43 and 46 ˚ A2 for SDS 16 and C12 SB (Table 1) respectively. The set of cπ at the much higher surface pressure of 40 mN m−1 then becomes the three mixed CMCs in Table 2 and 3.8 and 16 mM for C12 SB and SDS respectively, for which a parallel fit to that shown in Figure 5 gives the same values of Bs , Cs and Ds within error, i.e. the surface pressure does not contribute significantly to the jump in change of adsorption at the CMC. This is not surprising because it mainly depends on the difference in the areas between the two components, which is small in this case. The other factor that might explain the consistent increase in the SDS fraction of the layer above the CMC is that the relative fraction of monomer SDS in the bulk solution also increases above the CMC. This is because the fraction of SDS in the micelles above the CMC



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Figure 7: (a) Fitting of the adsorption at the air–water surface of SDS–C12 SB mixtures as a function of total concentration at the three different fractional SDS compositions in the bulk. The surface interaction was taken to be identical to that used for the fitting in Figure 5. The mixed CMC and the monomer concentration above the mixed CMC were calculated with the parameters shown. (b) Shows the corresponding fits of the two models directly to the measured CMC. In all the calculations the depth of GE was constrained to be the same for the regular and full expressions for GE . The values of all the parameters are given in Table 5.


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Figure 8: Excess free energy for SDS–C12 SB as a function of surface or micellar composition for the regular solution model and the fuller expression, eq 9, using the parameters given in Table 5. The two vertical lines represent the approximate boundaries of the surface or micellar compositions that can be probed from the maximum range of bulk compositions.



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Figure 9: (a) Fitting of the adsorption at the air–water surface of C12 TAB–C12 SB mixtures as a function of total concentration at the three different fractional C12 TAB compositions in the bulk. The surface interaction was taken to be identical to that used for the fitting in Figure 6. The mixed CMC and the monomer concentration above the mixed CMC were calculated with the parameters shown. (b) Shows the corresponding fits of the two models directly to the measured CMC. In all the calculations the depth of GE was constrained to be the same for the regular and full expressions for GE . The values of all the parameters are given in Table 5.


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is less than its overall fraction in the solution. The argument already made in the discussion of the mixed CMC is that the fraction of SDS in the micelles is about 1/4, i.e. there is considerable enrichment of the micelles with C12 SB at 50:50 and 75:25 SDS:C12 SB but there should be a negligible effect at 25:75. If the asymmetry in the composition of the micelles parallels that found at the surface the result would be also be an enrichment at the two higher SDS compositions but not at the lower one. The further complication in this effect is that it is concentration dependent. At the CMC itself there is no effect of enrichment but the effect becomes more pronounced as the concentration increases immediately above the CMC. At very high concentrations stoichiometry requires that there is no micellar fractionation and this is well established. 49,50 The application of the pseudophase model above the CMC requires two steps, one to calculate the activity of the monomers and the second to use these activities to calculate the 29 adsorption. The monomer concentration above the CMC for a binary mixture, cm i , is

xi =

cm i fi cµi

(12)

where the activity coefficient of the monomer in solution is again assumed to be unity. Mass balance requires x1 =

α1 c − f1 x1 cm 1 m c − f 1 x 1 cm − f 2 x 2 c2 1

(13)

where c is the concentration, and this gives the following equation suitable for iteration

F = Ax21 + (c − A)x1 − α1 c

(14)

m A = f 2 cm 2 − f 1 c1

(15)

where

and the activity coefficients are as given in Eqn (10) except that the parameters are those for mixing in the micelle, not those for surface mixing. Eqn (13) is a quadratic equation and 29 ACS Paragon Plus Environment


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there is then the choice of solving either the quadratic or its root by iteration. We have found that the simple sector method of iteration works satisfactorily on the quadratic, although it is important to monitor the iteration to ensure that it is selecting the physically sensible root. The monomer fraction calculated from Eqn (13) gives the α values for calculating the surface adsorption using the same interaction parameters as already obtained below the CMC. Figure 7a shows fits of the surface composition for SDS–C12 SB as a function of overall concentration for the three fixed compositions for two alternative sets of parameters for the micelle composition. In these fits the surface interaction parameters Bs , Cs and Ds are fixed at the values determined in Figure 5 and given in Table 5. For the micellar interaction one fit uses the single parameter model and the other uses a set of Bm , Cm and Dm values with the constraint that each model has the same depth of GE , just as for the surface calculation in Figures 5 and 6. The monomer concentrations above the CMC are exceedingly sensitive to the composition of the micelles, especially at the composition 0.25 SDS. This is because this composition is close to the composition of the micelles. If the micelles contain more than 0.25 SDS monomer SDS will be depleted relative to the average and its fraction at the surface will decrease with increasing total concentration but if they contain less monomer SDS will be enhanced, which is what is observed. Since the regular solution is fixed at 0.5 SDS it therefore completely fails to account for the direction of change of the adsorption above the CMC for this composition. The pattern of adsorption requires the composition of the micelles to be less than 0.25 SDS, which demonstrates a stronger effect of the higher order parameters than for the surface. A satisfactory fit to the adsorption at all three compositions is obtained with the minimum of GE occurring at x = 0.23 and the set of Bm Cm and Dm given in Table 5. The changes in the depth of GE and the shift in the minimum are shown for surface and micelle in Figure 8. As in Figures 5 and 6 the range of the bulk concentrations reasonably accessible in the surface experiments does not encompass the full range of surface composition. A 1:2 composition should be a favourable one for the mixing of a charged and


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a nett uncharged species. 45 The significant difference in xmin between surface and micelle then suggests that some change has occurred in the packing. As can be seen from Figure 1 there is significant scope for variation in the orientation of the sulfonate group to optimize the interaction with the anionic SDS. In the absence of SDS the sulfonate group will tend to orient and move towards the cationic group, which will make the head group somewhat bulky. This is consistent with the area per molecule at the surface at the CMC, which at ˚2 is characteristic of a larger head group like the trimethylammonium between 45 and 50 A headgroup. The dielectric environment at the air–water interface is very different from that at the surface of a micelle, where there is more scope for the head group to stretch out and for a higher level of ionization of the SDS. The smaller size of the SB head group would tend to increase the number of SB molecules that are required to pack round the SDS. However, it may not be possible for the greater number of SB to shield the electrostatic repulsion between SDS as effectively in a micelle as in the surface layer because of the smaller separation of SDS molecules. Thus, xmin shifts to a lower value but GE is less deep, i.e. the surface layer is more stabilized than the micelle. Figure 9 shows the equivalent fits for the C12 TAB–C12 SB system. Figure 2 has already shown that the micelle interaction is weaker for this system than for SDS–C12 SB. In addition the higher CMC of C12 TAB makes it less surface or micelle active than SDS. As a result, at a bulk composition of 0.25 C12 TAB, the micelles contain less than 0.25 C12 TAB whether or not the full expansion or the regular mixing expression is used for GE . Hence the effects of increasing concentration above the mixed CMC do not discriminate between the two models, i.e. the supra–CMC adsorption may therefore only be useful for analysing the composition of the micelles in cases where the the ratio of the CMCs is below a certain limit. On the other hand, the weakness of the interaction is clearly responsible for making it impossible to discriminate between the two models of GE by fitting directly to the mixed CMC (Figure 9b). For the C12 TAB–C12 CB system the independent coverage information from NR is not



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Figure 10: Fit of the excess free energy of eq 9 to the CMC of SDS–C12 CB at 313 K. Data from Hines et al. 8


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available, making the use of eq 9 less reliable for this system. However, the NR and surface tension data obtained by Hines et al. for SDS-C12 CB do allow a more complete calculation. The important point is that these authors measured the adsorption at about twice the CMC for the key low ionic composition, 20% SDS in this case. For a regular solution, i.e. symmetrical GE curve, this would show a strong depression of the SDS adsorption above the CMC, whereas the SDS adsorption is within error unchanged and possibly increases slightly. 8 This on its own shows that a full expansion of GE is needed to fit the data. Since these authors also measured more composition points for the CMC variation we have used eq 9 to fit this data for the micelles and the excellent fit, in contrast to the simple symmetrical model is shown in Figure 10. We now return to the question of the effects of dissociation. As mentioned above the 1:2 ratio for ionic to zwitterionic surfactant is a combination that in a 2-D system approximately allows a full shell of zwitterionic headgroups to screen a single ionic headgroup. This would mean that the surfactant ion is more dissociated from its counterion in comparison with the pure ionic micelle, i.e. the percentage dissociation per ionic surfactant ion is higher in the mixed micelle. The concentration where this will have most effect is just above the CMC because this is the concentration range where dissociation leads to a preferential partitioning of the surfactant ion into the micelle and of its counterion into the bulk solution. The effect of the dissociation on the 25:75 SDS–C12 SB mixture should be to decrease the concentration of monomer surfactant ion relative to the CMC. However, adsorption at the air–water interface is determined by the mean activity of the ionic surfactant because both ion and counterion adsorb and this generally makes the mean activity greater than the CMC. 16 The nett effect on the composition of the adsorbed layer should then be in the same direction as the change from the red to black curves in the lowest of the three plots in Figure 7a. However, given the relatively low proportion of SDS in the micelles, the effect is unlikely to be large enough to cause all the change observed, which requires a substantial change in composition from the regular solution model. Furthermore, the low proportion of SDS and the relatively small



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change of this proportion in the micelles over the whole range of total composition explored means that the change in dissociation with overall composition is unlikely to be significant enough to explain the variation of the adsorption pattern seen in Figure 7a. This in turn suggests that dissociation here is better handled with the flexibility of the full expansion of GE eq 9.

Figure 11: Comparison of the surface composition of SDS-C12 SB as determined by neutron reflection and by surface tension following the method of Motomura (see text). The data for the latter are from Wydro and Paluch. 5 The neutron fit is shown only as a guide to distinguish the neutron and ST data more clearly. A final interesting comparison of our results is with those of Wydro and Paluch, which were determined completely differently using a method proposed by Nguyen et al. 51 and extended by Motomura et al. to mixtures with ionic surfactants. 52,53 This method relies on the pseudophase approximation but makes no assumptions about the form of GE . It relies on the determination of the slope of plots of cm or cs at constant ST against the bulk composition. Although the method has been widely used, there appear to have been no tests of its accuracy using an independent measurement of either the surface coverage or micelle composition. We therefore compare the results of Wydro and Paluch for the surface composition at a surface tension of 45 mN m−1 with the neutron results in Figure 11. Although there is good agreement between the two methods on the magnitude of the minimum in 34 ACS Paragon Plus Environment

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GE (Table 5), there are large discrepancies in the surface composition. The accuracy of the neutron method and the failings of the surface tension method in the conventional determination of surface excess using the Gibbs equation have been discussed elsewhere. 15–17 The slope of a conventional ST-log c curve is already difficult to determine accurately unless it has reached the linear region of constant adsorption, i.e. at or close to the CMC. The slopes in the curves used in the Motomura method of analysis are evidently even more difficult to evaluate accurately, as suggested by Nikishido. 38

Synergy and Total Adsorption Rosen has described a number of measures of synergy, e.g. the reduction of the CMC itself, the reduction of the surface tension at the CMC, and the reduction in the concentration at which the surface tension drops to a given value, and given examples of correlations of these synergies with, e.g., foaming and washing performance. 54 Other than empirical measures there has, however, been little fundamental consideration of manifestations of synergy above the CMC mainly because surface tension measurements above the CMC do not lead to any quantitative measurement other than the surface tension. However, many practical applications deliberately use surfactant mixtures at concentrations above the CMC, and the activities and hence the adsorption of the surfactants can vary to a much greater extent in a mixture than those of single surfactants above the CMC. There is therefore a need to understand surface behaviour in this region. Since measurements of surface composition above the CMC with NR are just as easy as for those below the CMC, NR provides a unique tool for exploring this concentration region. The question of adsorption through the CMC is not well understood. For single surfactants it is usually assumed that adsorption reaches a plateau at the CMC and this is what is expected from, e.g., the Langmuir-Szyskowski equation. However, NR shows that this is not always the case and that, although nonionic surfactants often seem to reach a plateau below the CMC, ionic surfactants sometimes do and sometimes do not. 15–17 For mixed surfactants 35 ACS Paragon Plus Environment


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Figure 12: Total adsorption at and above the mixed CMCs (denoted cm in the figure) of SDS–C12 SB mixtures. (a) Variation of total adsorption with composition at the various cm and the empirical fit of these data to a quadratic. The individual adsorption patterns of the individual components with lines fitted using the model for surface adsorption in Table 5 are shown in red (SDS) and blue (C12 SB). (b) Variation of total adsorption with composition at a fixed concentration of 6 mM (black line), fitted by combining the Gaussian model shown in (c) with the surface compositions calculated using the data in Table 5. The red line is the cm fit from (a). (c) The Gaussian peak of adsorption obtained by fitting to the data in (b) compared with all the measured data. This is a sharp peak when plotted as a function of surface composition of SDS but resembles the observations when plotted in terms of the bulk composition (red line).


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the situation is further complicated by the phenomena that lead to the behaviour shown in Figures 7 and 9. Although this can be explained by the pseudophase approximation, the model does not give any guidance as to the behaviour of the total adsorbed amount. A recent striking example of a strong synergy leading to a maximum in the total adsorption has been found by Chen et al. in the adsorption from a ternary mixture of biosurfactant and conventional surfactant. This is both enhanced relative to the saturated layers at the CMC and passes through a strong maximum as a function of bulk composition at a fixed concentration above the CMC. 55 Furthermore this has been correlated with an improved clothes washing performance. 56 For SDS-C12 SB Table 4 shows that (i) there is a significant increase in the total adsorption in the mixtures compared with the two pure surfactants at the CMC (the limiting values are 4.1 and 3.7 µmol m−2 for pure SDS and pure C12 SB respectively), (ii) the total adsorption at the CMC increases as the mole fraction of SDS in the mixture increases, and (iii) total adsorption continues to increase with total concentration above the CMC over the whole range studied for all three mixtures. These three features appear to be driven by the coupling of three distinct effects. The first is that a significant increase in the packing in the layer must be associated with the deep minimum in GE for the mixed layer. The second is that this deep minimum is not quite reached below the mixed CMC, but occurs slightly above it. The third is that the strong asymmetry in the interaction that drives micellization ensures that the monomer concentration of the ionic species (SDS) increases with concentration over a wide concentration range, as demonstrated from the behaviour of the adsorption in Figure 7. The vertical blue lines in Figure 5b indicate that the layer just reaches the minimum of the surface GE at xSDS = 0.38 when the bulk composition is αSDS = 0.75. It is not possible to estimate the error in xmin arising from weaknesses in the assumptions made to calculate it, but is unlikely to be more than about ±0.04. That the position of the minimum could be at a slightly higher value of xSDS is suggested by two observations. First, Figure 12a shows



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that total adsorption is at its highest at αSDS = 0.75, i.e. total adsorption is still increasing up to that composition and may go higher. Secondly, when all the experimental data for SDS–C12 SB in Table 4 are plotted as total coverage against xSDS the pattern in Figure 12a shows that at values of xSDS (black) only slightly higher than those just below cm (blue) there are large increases in adsorption, although the errors make this difficult to quantify. However, they coincide within error with the minimum of GE and therefore indicate that a large change in packing occurs at compositions of around xSDS = 0.4 but that this is not quite reached below the mixed cm at values of αSDS ≤ 0.75. There are then two ways to reach the high adsorption conditions. One is to take αSDS higher than 0.75, which should be effective at about the mixed CMC, and the other is to increase the concentration above the CMC for a value of αSDS at or lower than 0.75. The latter is possible because xSDS increases above the CMC at all αSDS compositions above about 0.25. From the point of view of applications, where there is always a drive to reduce the load of surfactant, the second option is much to be preferred. Thus, at αSDS = 0.8 the total concentration of surfactant would need to be about 1 mM, whereas at αSDS = 0.5 it would only need to be about 0.5 mM. It is not obvious how to create a quantitative model for this behaviour because we do not know how the increase of packing relates to changes in GE . However, the following simple model describes the phenomenon well. We assume that the extra adsorption associated with the strong interaction is most closely tied to the surface composition, xSDS , and we describe it using a Gaussian distribution, as shown as a black line in Figure 12c. Its centre, width and amplitude are taken to be adjustable. We then use the results in Table 5 to calculate the surface composition as a function of composition at a fixed concentration and combine this with the Gaussian to give the total adsorption. The best fit of the constant concentration data at 6 mM, the only set that is almost completely above the CMC, is shown in Figure 12b, and the corresponding Gaussian distribution is shown in Figure 12c. It then becomes clear that the essential physical requirements are a strongly peaked function relating the


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total adsorption to the surface composition and which peaks at SDS compositions slightly higher than those at the mixed CMC, and a solution composition above the CMC that is relatively enriched in SDS compared with the overall solution. The former is required to generate the large observed increases in total coverage and the latter to drive the necessary increase in xSDS . The highly asymmetric GE of micellization means that micellization causes an increase of xSDS above the CMC for a wide range of compositions. For the fit shown in Figure 12b we had to make small alterations to the Bm , Cm , Dm parameters in Table 5 but the main features of the asymmetry were retained. Finally, Figure 12b shows that these combined effects lead to a clear maximum in the adsorption at an αSDS = 0.5, as observed, whereas a simple model of constant adsorption at the CMC would cause the adsorption to be still increasing at αSDS = 0.75, which is not observed. It is interesting to explore whether a similar synergy occurs for the other ionic-zwitterionic mixtures. Hines et al. made a set of measurements on the SDS-C12 CB system at 2CMC for 20:80, 50:50 and 80:20 mixtures, obtaining respective surface excesses of 3.8, 4.0 and 4.5 µmol m−2 . In terms of Figure 7a the effect of composition is similar to that for SDS-C12 SB but the increase of total coverage relative to the pure components is small and much less pronounced than for SDS-C12 SB at comparable concentrations. This indicates that there is no significant synergy in the total adsorption. Similarly, inspection of the data for C12 TAB in Table 4 indicates no significant synergy in the total adsorption for any of the mixtures involving C12 TAB. For this type of synergy there has to be a substantial lowering of the free energy of the layer by some rearrangement that is associated with significantly closer packing. The effect is large with the mean area per molecule dropping from about 42 ˚ A2 to less than 30 ˚ A2 for SDS-C12 SB. The dominant geometrical arrangement in a 2D system, i.e. a layer, is hexagonal and, as already noted, the mixing of similar sized ionic and nonionic species in an ordered array would be optimal in a 1:2 lattice, where each charge is surrounded by six uncharged species. Given that the zwitterionic surfactants here carry no nett charge such a structure



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might be expected in the ionic–zwitterionic mixtures. However, this would not seem to give a mechanism that would necessarily generate tighter packing, which suggests that the tighter packing must be associated with some rearrangement of the headgroup of the zwitterionic. In an isolated C12 SB molecule, the trimethylene chain separating the two charged groups should adopt a configuration that allows a moderately close approach of the two charged groups. This would create a head group more bulky than one where the separating chain is fully extended. It is then conceivable that as adsorption progresses a stage is reached where rearrangement within the head group leads to a change in conformation that leads to tighter packing and a considerable gain in free energy. This explanation would be consistent with the lack of change in the SDS-C12 CB system, where the single methylene linker group does not allow similar freedom in the relative position of the two charges.

CONCLUSIONS Neutron reflectivity and surface tension measurements have been used to analyse the interactions in four ionic–zwitterionic surfactant mixtures. The use of both coverage and surface tension below and above the CMC in models for the interactions has made it possible to study the asymmetry of the interactions in these systems in a systematic and accurate way. The analysis was based on the pseudophase approximation and the assumption of undissociated ion pairs with the further implicit assumption that any effects of ionization or other asymmetry could be accounted for by using the standard expansion of the excess free energy, GE , up to and including a quartic term, eq 9. The strong interactions in these surfactant systems are highly asymmetric and, although this can be fully characterized and parameterized by eq 9, it is easier to describe it in terms of the depth and composition of the minimum in GE for surface and micelle, rather than in terms of the individual parameters B, C and D. In all four pairs of surfactants the ionic component is the more weakly surface active


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component. The minimum in the surface GE occurs close to a surface mole fraction, xionic , of about 0.4 and, for the most strongly interacting pair, SDS–C12 SB, the depth of GE at the minimum is 2.8RT , which is equivalent to a Bs of about −11RT in the regular solution approximation. Above the CMC the surface composition proved to be sensitive to the position of the minimum in the GE of micellization. In the case of SDS–C12 SB, the monomer composition could be mapped from the composition of the adsorbed layer and hence the thermodynamics of the micellization determined using the same pattern of expansion of GE as for the surface. There is a marked shift of the position of the minimum of GE for micellization down to xionic = 0.23 with a reduced depth of 2.2RT . Similar results were found for surface and micelles in the SDS–C12 CB system. These results were different from those obtained using results from ST alone. For SDS–C12 SB a strong peak in total adsorption occurs at compositions above the CMC, indicating a strong synergy, whose origin is attributed partly to the pattern of monomer concentration above the CMC and partly to a sharp increase in the packing density of the adsorbed layer as the minimum GE is approached. This strong synergy in the total adsorption is surprisingly missing in the SDS–C12 CB system, which suggests the possibility that the large change in packing density is associated with changes in conformation of the head group in the zwitterion.

AUTHOR INFORMATION Corresponding Author Phone: +44-(0)1865-275422. Fax: +44-(0)1865-275410. Email: [email protected].

Notes The authors declare no competing financial interest.



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ACKNOWLEDGEMENTS We thank STFC for the provision of neutron beam time at the ISIS facility. KM thanks the China Scholarship Council for a scholarship to Oxford.

ASSOCIATED CONTENT Supporting Information Available The data of Hines et al. 8 is reanalysed. Figure S1‘ shows neutron reflectivity profiles for C12 SB. Figures S2, S3 and S4 show surface tension data of the mixtures SDS–C12 SB, C12 TAB– C12 SB and C12 TAB–C12 CB. This information is available free of charge via the Internet at http://pubs.acs.org.

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Analysis of the Asymmetric Synergy in the Adsorption of Zwitterionic

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