Limitations in the Use of Surface Tension and the Gibbs Equation To

May 22, 2014 - Measurements using ring, plate, and bubble shape analyses indicate .... plate measurements on the K11 typically took 10 min for tempera...
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Limitations in the Use of Surface Tension and the Gibbs Equation To Determine Surface Excesses of Cationic Surfactants Pei Xun Li,† Robert K. Thomas,*,† and Jeffrey Penfold†,‡ †

Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, United Kingdom ISIS, Rutherford−Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom

‡

S Supporting Information *

ABSTRACT: Neutron reflection (NR) and surface tension (ST) are used to show that there are serious limitations in applying the Gibbs equation accurately to ST data of cationic surfactants to obtain the limiting surface excess, ΓCMC, at the critical micelle concentration (CMC). Nonionic impurities in C12TABr and C16TABr have been eliminated by extensive purification to give ST − ln(concentration) (σ − ln c) curves that are convex with respect to the ln c axis around the CMC, which is characteristic of a finite micellization width. Because NR shows that the surface excess often continues to increase at and above the CMC, this finite width makes it impossible to apply the Gibbs equation to obtain ΓCMC without knowledge of the effect of aggregation on the activity. NR data made it possible to apply the integrated Gibbs equation to the ST below the onset of the convex region of the σ − ln c curve and show that for C12TABr the micellization width causes the ST to underestimate ΓCMC by 12%. Hexadecyltrimethylammonium (C16TA) sulfate is used to show that divalent ion impurities are not a significant problem. For cationic surfactants, further errors are associated with ST methods that rely on complete wetting. Measurements using ring, plate, and bubble shape analyses indicate that with ring and plate incomplete wetting occurs at or above the CMC and may extend to lower concentrations and also causes the ST-Gibbs analysis to underestimate the surface excess. In combination with ion association and preaggregation in cationic gemini surfactants, this can cause errors as large as 100% in ΓCMC. Comparison of ellipsometry and NR for C16TAX in 0.1 M KX (X = F or Cl) shows that ellipsometry cannot, as yet, be quantitatively modeled accurately enough for surface excess determination independent of NR calibration.

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INTRODUCTION Recent papers by Menger et al.1−4 have questioned the use of the Gibbs equation for analyzing surface tension (ST) data to obtain the surface excess. There have been two attempts to refute these papers, one by Laven and de With5 and one by Bermudez-Salguero and Gracia-Fadrique,6 with some further discussion by Mukherjee et al.7 The key issue is whether surface saturation occurs at the critical micelle concentration (CMC). The value of the limiting surface excess at the CMC, ΓCMC, requires the determination of the limiting slope of the ST curve (σ − ln a or approximately σ − ln c), which becomes difficult as the approximate discontinuity of the CMC is approached. If saturation occurs at or above the CMC, then the analysis is difficult and may be inaccurate (the view of Menger et al.1−4), whereas if saturation is reached before the CMC, then the ST curve becomes linear and the analysis is straightforward. Neutron reflectometry (NR) can be used to resolve this question by determining surface excesses above the CMC. We have therefore used NR to explore the issue of saturation for nonionic surfactants (Paper I8) and anionic surfactants (Paper II9). Paper I8 showed that for nonionic surfactants the layer becomes saturated sufficiently below the CMC that ΓCMC can be reliably determined by ST-Gibbs. In contrast, Paper II9 showed that saturation is not reached at the CMC for sodium © 2014 American Chemical Society

dodecyl sulfate (SDS) and that it also varies up to the CMC for some other anionic surfactants. Comparison of NR data with earlier ST results on SDS by Elworthy and Mysels10 brought to light the further problem of the effect of a finite width of micellization on the ST-Gibbs analysis. The combination of this finite width, about ±25% of the CMC for SDS, with the directly observed increase in surface excess beyond the onset of micellization makes it exceedingly difficult to apply the Gibbs equation in the important range just below the CMC, thus confirming that the analysis of Menger et al. applies to anionic surfactants. Here, we extend the measurements to cationic surfactants where the many disagreements between ST-Gibbs and NR in the literature suggest that the doubts of Menger et al.1−4 may be even more justified. Examples where there are significant mismatches between ST and other methods, mainly NR, are the gemini cationics (NR and ST),12,14,15 alkyltrimethylammonium (CnTA−) salts with fluorocarboxylate counterions (NR and ST),11 partially fluorinated CTABr (NR and ST),16 and C16TACl and C16TAF in the presence of 0.1 M electrolyte (ellipsometry Received: April 5, 2014 Revised: May 22, 2014 Published: May 22, 2014 6739

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necessary to obtain a limiting σ − ln c curve. The same procedure of six recrystallizations was used for the deuterated C12TABr for the NR experiments. Four recrystallizations were found to be necessary for the C16TABr, and this was again done for both protonated and deuterated samples. ST measurements were made using a Kruss K11 tensiometer using a Pt−Ir ring or Pt plate and an IT Concepts Tracker Drop Shape Analysis instrument using bubble shape analysis. The cleaning procedures were performed as described previously.11 The ring and plate measurements on the K11 typically took 10 min for temperature equilibration and completion of the first set of repeated measurements, and these were followed by subsequent cleaning of the ring and further measurements. For the CnTAB measurements from about CMC/3 upward, equilibration was largely complete in the first 10 min. For the IT bubble shape experiments, the measurements were averaged over the first 20 min, and equilibration was complete early in the cycle. Equilibration was slower for the gemini surfactants. The NR measurements were made on the reflectometers SURF and INTER at ISIS28 using Teflon troughs in sealed containers and varying equilibration times, all longer than 20 min. The general method of measurement of surface excess using deuterated surfactants in null reflecting water (NRW), where the reflected signal is entirely from the adsorbed layer, has been described previously, as has the method of the analysis of the data.29

and ST).17 The extent of the problem is illustrated by the selection of results in Table 1. The large discrepancies, all in the Table 1. Areas Per Molecule of Cationic Single-Chain Surfactants11 and Gemini Surfactants12,13 at Their CMC Using NR and STa surfactant fC4hC11TABr fC5hC10TABr fC6hC8TABr fC8hC6TABr average discrepancy C12−C3−C12 C12−C4−C12 C12−C6−C12 C12−C10−C12 C12−C12−C12 average discrepancy

ANR

AST

Å2 ± 6%

Å2 ± 6%

%

39 42 39 43

58 53 47 50

66 82 104 112 140

98 (105) 114 (116) 143 (143) 220 (220) 224 (226)

+48 +26 +21 +16 +28 +48 +39 +38 +96 +60 +61

discrepancy

a fCnhCm indicates CnF2n+1CmH2m and Cn−Cm−Cn indicates CnH2n+1N(CH3)2Br−CmH2m−N(CH3)2BrCnH2n+1.

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RESULTS AND DISCUSSION All NR measurements were done with materials in which the alkyl chain was perdeuterated (normally 98% D) and in null reflecting water (NRW) (i.e., after subtraction of a flat background, the reflected signal is entirely from the adsorbed surfactant layer). The procedure, the analysis of the data, and the possible sources of error have been fully described elsewhere.8,9,29 If there is appreciable small-angle scattering from micelles in the bulk solution, then this may generate a scattered background that is not flat and that can make analysis of the data impossible. This depends on the incident wavelength of the neutrons and on the angle of incidence. In general, it is not a significant problem unless the bulk concentration of surfactant in the form of micelles is greater than about 50 mM. Thus, it is straightforward to determine the surface excess of C16TABr up to about 50× CMC, but data for C12TABr in the absence of NaBr could be analyzed reliably only up to 3× CMC. The new results obtained in this work are given in Table 2 and will be discussed below. Divalent Ionic Contamination of a Cationic Surfactant: (C 16 TA) 2 SO 4 . It was shown in Paper II 9 that contamination by divalent ions is a serious problem for anionic surfactants. It has been suggested that a parallel problem could occur for cationic surfactants C16TACl and C16TAF with contaminating ions such as carbonate and silicate and that this could be the cause of discrepancies between ST and ellipsometry.17 In the typical range of pH used for surface measurements, carbonate ions are largely hydrolyzed to the monovalent HCO−3 ion, and this should have no anomalous effect. The natural level of silicates (typically from washing glassware with alkaline detergents) would generally be expected to be lower than that of Ca2+ because of the lower solubility of silicates in comparison with that of calcium carbonate. In addition, the charge on possible oxyacid anions is more diffuse than on the divalent metal cations that are the problem for anionic surfactants; therefore, the tight packing induced in anionic surfactants by divalent metal ions is unlikely to be induced by oxyacid anions. We have tested the hypothesis experimentally here by examining the surface characteristics of

same direction, and the difference in the average from different groups of surfactant types are very striking and can be associated only with a major systematic error in one or the other technique. However, the possible causes of these discrepancies differ in a number of ways from those for anionic surfactants. First, the problems associated with impurities are totally different for cationic surfactants. Second, there is no experimental data showing any effect of the width of micellization on ST for cationics, although Al-Soufi et al. have shown by conductivity that micellization of C12TABr has a finite width.18 Third, there are many experimental observations of association below the CMC in cationic systems (e.g., refs 19−23 and 24). Fourth, similar to that for SDS, NR has been used to show that the surface excess for one cationic, C14TABr, continues to increase above the CMC,25 which means that the rapid variation in the ST-Gibbs slope near the CMC may also be difficult to analyze for cationics. Finally, and this is known to be a particular problem for cationic surfactants, the actual measurement of the ST may be compromised by incomplete wetting if the method of ST measurement relies on complete wetting. We have made a number of new NR and ST measurements to examine all of these problems.

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EXPERIMENTAL DETAILS

The CnTABr were prepared from the reaction of bromoalkane (protonated or deuterated) and trimethylamine, pure or in methanol or ethanol, to give the bromide as described previously.26 For the preparation of (C16TA)2SO4, C16TACl, and C16TAF, the bromide was treated with ion-exchange resin to remove the anion to create a solution of the hydroxide, to which the appropriate dilute acid was added to neutralize the solution. The solid was obtained by freezedrying. This was not found to be satisfactory in the case of the fluoride, and an alternative method, making use of the solubility of silver fluoride in methanol, was also used, in which C16TABr was reacted with AgF in methanol and the AgBr precipitate was removed by precipitation.27 C16TAF was obtained by evaporation of the methanol. All crude products were recrystallized from acetone with varying amounts of ethanol. Typically, this was done three times. However, higher purity, as demonstrated by ST measurements, was obtained by further recrystallizations using distilled acetone. In the case of C12TABr, three further recrystallizations using pure acetone were 6740

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these can be eliminated by distilling the acetone before use. Bromoalkane is, therefore, the main nonionic impurity. The best studied nonionic impurity in any ionic surfactant is dodecanol in SDS, and, although SDS is anionic, the existing understanding of this system is equally appropriate for nonionic impurities in cationics and can be used to give an approximate estimate of the maximum level of nonionic impurity that can be tolerated in a given ionic surfactant (see Supporting Information). The key parameter in assessing the impurity is its water solubility because when the total concentration of impurity reaches saturation, it will often form a complete monolayer with an ST much lower than that of the surfactant. If this occurs below the CMC of the surfactant (as shown for dodecanol in SDS in Figure 1 of the Supporting Information), then the effect of the impurity may be dominant. To eliminate the effect of the impurity, its total concentration must not exceed saturation until well above the CMC of the surfactant, typically at least 10× CMC, when the residues will be solubilized into surfactant micelles. The water solubility of bromoalkanes is much lower than that of alkanols and is too small to measure for bromododecane. However, the solubility of bromooctane is about 2000 times smaller than that of octanol33,34 and, making the very approximate assumptions that this ratio also holds for bromododecane and dodecanol and that the ST of a monolayer bromide is comparable with that of the alkanol, suggests that a concentration of bromododecane of 2.5 × 10−4 wt % has an effect on the ST of C12TABr that is comparable with that of 0.5 wt % dodecanol on SDS. Thus, the ST curve of the bromide at 2.5 × 10−4 wt % is likely to have a comparable effect to that for 0.5 wt % dodecanol in SDS (shown in Figure 1b of the Supporting Information), and the bromododecane would therefore need to be reduced to at least 2 × 10−5 wt %. Although bromododecane is rapidly removed by recrystallization, reducing it to this level requires more than the usual pattern of recrystallizations (the effects of the early stages of recrystallization on the NR measurement have been shown for C14TABr in Figure 1a of Simister et al.35). We have indeed found that not less than six recrystallizations with the use of redistilled acetone in the later recrystallizations, as described in the Experimental Details, gives a product of sufficient purity to start to show a convex region of the σ − ln c plot through the CMC. Figure 1 compares the ST of this sample and of an equivalent sample of C16TABr, both determined by bubble shape analysis, with the SDS measurements of Elworthy and Mysels,10 each plotted on approximately the same reduced concentration scale to make the comparison easier. The convex region (convex with respect to the ln c axis) around the CMC is evident in all three samples and is most clearly seen in the expanded section of the full-scale plot shown in the inset to Figure 1a. Above the CMC, the ST of all three samples has been fitted with a simple straight line (as a function of ln c) to show the differing variation of ST with ln c in this region. As discussed in Paper II,9 the slope above the CMC is dominated by the combination of the law of mass action and the degree of dissociation of the micelles, which is higher for SDS and one of the reasons for the greater slope for SDS. For C12TABr, the region below the CMC has been fitted with the integrated Gibbs equation using the line fitted to the surface excesses of C12TABr shown in Figure 1b. The concentrations were changed to activities using the Debye−Huckel limiting law (ln γ± = −Ac1/2 for a 1:1 electrolyte). The fit of the calculated ST curve is excellent in

Table 2. Areas Per Molecule of Cationic Surfactants Determined in the Present Worka surfactant (CMC/mM) C12TABr (16 mM)

C16TABr (0.9 mM)

c

A

CMC

Å2 ± 6%

0.1

93

0.3 0.5 0.9b 1

63 51 48b 44

3 0.1

43 85

0.3 0.5

59 51

1.0 1.0 1.5 3.0

(C16TA)2SO4 (0.6 mM)

42 b

10.0 1

(CMC/mM) C12TABr/NaBr (4.7 mM)

C16TABr/NaBr (0.036 mM)

C16TABr/KBr (0.036 mM) C16TACl/KCl (0.09 mM)

b

44 42 42 40 98

c

A

CMC

Å2 ± 6%

0.85b

44b

1.5 3 10 1.0

44 42 40 42

1.5 3.0

42 41

10 1.5

40 41

1

46

1.5 3 1

46 47 50

1.5 3

47 48

surfactant

C16TAF/KF (0.23 mM)

a

The concentrations are given relative to the respective CMCs, which are given in brackets. The C16 experiments were done at 30 °C, and C12, at 25 °C. bValues are from previous NR measurements.30,31

(C16TA)2SO4 as a model divalent compound to compare with those of C16TABr. The CMC of C16TABr was found to be 0.9 mM, and the limiting ST, about 39 mN m−1. For the sulfate, the CMC was lower, 0.6 mM, but the limiting ST was higher, 44 mN m−1. This behavior is totally different from sodium and calcium AOT (bis-diethyl-hexyl sulfosuccinate), where the Ca2+ ion strongly affects the ST behavior and leads to both a much lower CMC and a much lower limiting ST (see Figure 2 of Paper II9). Para et al. similarly found that the hydrogen sulfate ion (HSO−4 ), which is expected to be partly dissociated into the sulfate, has a lower CMC than bromide but a higher limiting ST.32 The higher ST for the sulfate suggests a greater exposure of water at the surface (i.e., a higher area per surfactant chain). NR confirmed this, giving a value of 49 ± 3 Å2 at the CMC, compared with the value of 44 ± 2 Å2 for C16TABr31 or 42 ± 3 Å2 (Table 2). Although the combination of the values of CMC and limiting ST makes the sulfate more surface active than bromide in the crucial concentration range from about 0.6 to 0.9 mM, the difference is small, and the sulfate will have only a negligible effect at impurity-level concentrations. This suggests that cationic surfactants are not prone to the same ion impurity effects as anionic surfactants. Nonionic Impurities and the Surface Tension of C12TABr and C16TABr. The main nonionic impurities in the most common cationic surfactants, the CnTABr, are the bromoalkane used in the preparation and impurities in the solvent used for recrystallization. Acetone is normally used for recrystallization, and this typically contains impurities with surface properties comparable with those of nonionic surfactants in the hexaethylene glycol monododecyl ether (C12E6) range, as judged from their presence as colored impurities in the flash columning of C12E6. We have found that 6741

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ST data in the literature are commonly drawn with a linear σ − ln c plot or one that is concave to the ln c axis, which makes the CMC appear to be a true discontinuity. In the case of C12TABr, Al-Soufi et al. have shown that conductivity data are best fitted with a finite width of micellization.18 The sharpness of a CMC measured by conductivity should be affected only by concentrations of surface-active impurity large enough to affect the micellization process, whereas the discussion above indicates that traces are sufficient to affect the ST curve. The width of micellization derived from the ST of SDS and that derived for C12TABr from conductivity by Al-Soufi et al. are both more than double the effect that we estimate here. This may be a consequence of traces of impurity still present in our C12TABr. Figure 1b and Table 2 show that the directly measured surface excesses for C12TABr, C14TABr, and C16TABr all increase through and above the CMC. There is no plateau, even though the increase in activity above the CMC must be relatively small. The line below the CMC was obtained using the data for C12TABr only, but the line for the data above the CMC used the data for all three surfactants. The use of separate fitting to the two branches of the σ − ln c curve generates an artificial discontinuity at the CMC. As was discussed in Paper II,9 there has to be a significant difference between the slopes of the two curves above and below the CMC but there will be a smooth variation through the CMC because the switch between the two activity regimes is separated by a smooth variation of the activity. The cluster of points at about 0.1× CMC do not fit the line for the data below the CMC. There is no reason why the linear variation of surface excess with ln c should be maintained at low concentration, but because our main concern here is ΓCMC, we do not pursue this question. A least-squares fit of a quadratic in ln a (using the Debye− Huckel limiting law for the activity coefficient) to the data from an ST of about 50 mN m−1 to just below the CMC fits the data well and gives a surface excess of 3.4 μmol m−2, about 12% lower than the value of 3.8 obtained directly from NR. The same plot using just ln c gives 3.1 μmol m−2, more than 20% lower. The variation with ln c or ln a is suggested by the linear ln c dependence of the excess often observed by NR and by the original SDS experiment of Elworthy and Mysels.10 The significant range of flattening of the σ − ln c curve caused by the micellization width causes these errors and prevents the accurate use of the Gibbs equation. The fits of the integrated Gibbs equation given in Figures 1 and 2 and based on the NR data also use assumptions that reduce their validity. Thus, although NR can be used to determine the value and dependence of Γ on concentration up to and through the CMC, this cannot be used in the integrated Gibbs equation without a knowledge of the activity variation introduced by the finite width of micellization. Any fits of the integrated Gibbs equation, therefore, also do not have a sound quantitative basis. Incomplete Wetting in Ring and Plate Methods. It is well-known that the ST of solutions of cationic surfactant is difficult to measure with ring and plate methods,36,37 and this was the reason for choosing the bubble shape method here. Nevertheless, many measurements in the literature have determined ΓCMC by these two methods, and the reproducibility appears to be good. Thus, the measurements in Table 1 were made using a Pt−Ir ring, and the measurements on the gemini surfactants are in excellent agreement, even though they were done by different groups, on different samples, and using different makes of instrument. However, Figure 2a shows that

Figure 1. (a) Comparison of the ST for specially purified C12TABr and C16TABr measured by bubble shape analysis and the SDS results of Elworthy and Mysels.10 The curve fitted through the ST points for C12TABr below the CMC was determined using the integrated Gibbs equation. The surface excess measurements were those fitted by the straight line in panel b with Debye−Huckel limiting law activity coefficients. Empirically fitted straight lines are drawn through each set of data above the CMC. The inset shows an expanded region of the larger plot in the figure. (b) Surface excesses of purified C12TABr and C16TABr with perdeuterated alkyl chains measured by NR (Table 2). Data from earlier measurements on C14TABr are also included25 as well as a single point just below the CMC for C12TABr.30 The line below the CMC is the best linear fit (in ln c) to the C12 data. The line above the CMC is a linear fit to the combined data for C12TABr, C14TABr, and C16TABr.

the region from 0.5× to about 0.9× CMC. However, as discussed previously in Paper II,9 the additional variation of activity associated with the significant width of the CMC means that the Gibbs equation cannot be applied to the ST data right up to the CMC without some quantitative knowledge of how this activity is affected by micellization. This would not matter if adsorption reached a plateau at a concentration below about 0.9× CMC because that would allow a linear extrapolation of the Gibbs plot to the CMC. However, as found by Elworthy and Mysels as well as here, the surface excess increases linearly with ln c from about 0.5× CMC (i.e., in the absence of any micellization width, the ST would vary quadratically with ln c up to the CMC). This makes it impossible to extrapolate ST data accurately through the micellar width region to obtain the limiting excess. 6742

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range of concentration, which can sometimes be approximated as a critical aggregation concentration (CAC). The CAC will be lower than the CMC if the interaction with the surface is favorable, as it is in the case of an oppositely charged surface and surfactant. However, the gain in energy through surface− aggregate interaction will be offset by the distortion of the aggregate on attachment, and the CAC is not usually much lower than the CMC. Thus, atomic force microscopy,38 surface force measurements,39 and NR40 show that cationic surfactants form layers with bilayer characteristics on the negatively charged silica and more highly negatively charged mica surfaces when adsorbed at concentrations close to the CMC. Although there are no direct structural studies of adsorbed cationic layers on flat Pt surfaces, the interaction described above suggests that these surfaces are negatively charged and therefore there will be bilayer-type adsorption close to and above the CMC. Such relatively weakly bound bilayers are susceptible to damage by shear, as shown by the procedure where mica is hydrophobized by immersing a plate in a solution of single-chain cationic surfactant above its CMC and then withdrawing it carefully.41 Mild shear evidently removes the outer layer to create a highly hydrophobic surface. Because both ring and plate measurements involve a small degree of shear, the measurement of ST at or above the CAC may itself induce the surface to become less than perfectly hydrophilic by creating a small fraction of surface that is only covered by a monolayer, and this process may also be sensitive to the exact dynamics of the particular measurement. This is the probable explanation for the observations in Figure 2 with respect to both the ST shift and its concentration dependence. The phenomenon will depend on the CAC, which will be below the CMC for a cationic, as well as on the extent to which the upper part of the bilayer can be removed by shear. For a given system, the incomplete wetting effect may be fully reproducible for similar surfactant types, as indicated for the gemini surfactants in Table 1. Anionic surfactants will generally show little tendency to adsorb on negatively charged surfaces and should therefore not be affected. The relation between the mechanism of the molecular adsorption and the outcome of the measurement is not easy to predict. The simplest interpretation suggests that incomplete wetting would lead to a decrease rather than an increase in ST (see, e.g., Lunkenheimer42,43 and Cram44), but there are a number of unusual container effects,42,43 and one manufacturer has shown how dynamical effects can lead to changes for ring and plate in the direction observed here.45 The observed changes show empirically how the ring method may underestimate the coverage. Thus, making the assumption that the ST is correctly measured at about 0.5× CMC, where wetting seems to be complete, then the shift of about 2 mN m−1, as observed for C12TAB with the ring, changes the slope of the σ − ln c curve by about 10% (i.e., the surface excess is underestimated by about 10%). For double-chain or gemini surfactants, the same argument would lead to an apparent reduction of about 25% because of the shallower slope of the σ − ln c curve. It would be useful to have an independent assessment of the differences seen in Figure 2. Notable sets of data on C12TABr and C16TABr have been obtained using the pendant drop by Para et al.,46,47 who found 38.5 and 36.6 mN m−1 for the ST of C12TABr and C16TABr, respectively, at the CMC, in good agreement with the values of 38.1 and 37.1 obtained here by the bubble shape analysis. You et al. obtained a value of 39.1

Figure 2. (a) Comparison of the ST for specially purified C12TABr with and without 0.1 M NaBr (the data with the lower CMC) measured by bubble shape analysis, Wilhelmy plate (Pt), and du Nouy ring (Pt−Ir). (b) Variation of the difference between plate or ring and the bubble shape results divided by the contact length of the two surfaces.

there are significant differences in the ST of C12TABr measured using bubble shape analysis, Pt plate, and Pt−Ir ring as well as in the ST of C12TABr with 0.1 M NaBr using bubble shape analysis and plate (a similar result for pure C16TABr is shown in Figure 2 of the Supporting Information). Above the CMC, there is a marked upward shift of the ST for the plate and an even larger one for the ring, but below the CMC, there is little difference in the measured ST. The magnitude of the shift for plate and ring in the case of C12TABr is exactly in the ratio of the length of surface contact between liquid and ring or plate (Figure 2b), which suggests that the shift is related in some way to contact angle changes with concentration. The reasonably close agreement below the CMC further suggests that the onset of the incomplete wetting effect is at or a little below the CMC. That wetting may be both incomplete and vary with concentration of cationic surfactant results from the pattern of adsorption of cationics on negatively charged solid surfaces. Adsorption at the hydrophilic/aqueous interface is driven by a combination of self-aggregation through the hydrophobic effect and the stabilization of the aggregate by interaction with the surface. The self-aggregation makes it a cooperative phenomenon, and it therefore generally occurs over a relatively narrow 6743

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mN m−1 for C12TABr using the ring method,22 which is close to our plate result and significantly higher than the bubble shape result of 38.1. Miyajima et al. obtained a value of 39.0 mN m−1 for C14TABr using the ring,48 which is closer to our interpolated value of 39.6 for the ring rather than to our interpolated value of 37.6 for the bubble shape analysis. Finally, Mukherjee et al.,7 using the ring method, obtained a value of 40.1 for C16TAB, which is much higher than the pendant drop and bubble shape values given above (36.6 and 37.1 mN m−1), but it is closer to our ring value of 39.1 mN m−1. The ST curve of Mukherjee et al., however, also shows a marked increase in ST as the concentration increases above the CMC from 40.1 at 1.2 mM to 40.9 mN m−1 at 3.6 mM. The ST at the CMC is too high to be caused by impurity, and our tentative explanation of the unusual ST increase and the shape of their curve is that it is associated with a change in the wetting of the ring, analogous to, but more marked than, the changes in Figure 2b. This section and the comparisons in this paragraph strongly indicate that incomplete wetting significantly impairs the accuracy of ST measurements with ring and plate to the extent that a systematic ST and contact angle study is required to resolve the problem. Effects of Electrolyte and Counterion Studied by Ellipsometry. Ellipsometry is very sensitive to materials at an interface but has been limited in its application at the air/ aqueous interface by its inability to separate thickness and composition and by difficulties in modeling the quite different effects on the signal from the hydrocarbon and ionic/ headgroup layers. Nevertheless, its high sensitivity could open up a range of applications, especially for dynamic situations, where its speed of measurement is much higher than NR, or for small area samples. Because of the difficulty of devising absolute models to account for the data, the main procedure so far used has been to calibrate the ellipsometric measurements with NR. This has proved to be straightforward and effective because there is an empirical linear relation between the signals from the two techniques for a given sample.49 Knock and Bain have further attempted to widen the scope of ellipsometry by calibrating their ellipsometric measurements using NR with C16TABr as calibrant and then using ellipsometry to determine the effect of added KBr on C16TABr and the limiting surface excesses of the two related halides, C16TACl and C16TAF,17 in the presence of KCl or KF. As with all the comparisons with ST in this article, they found larger limiting surface excesses from ellipsometry than those from ST. No NR data was available at the time to test the validity of transferring calibration data between different compounds. Using the salt-free NR value of 44 Å2 for C16TABr as calibration, Knock and Bain obtained values of 40, 53, and 78 Å2, respectively, for C16TABr in 0.1 M KBr, C16TACl in 0.1 M KCl, and C16TAF in 0.1 M KF, all at their CMC (in electrolyte). The value for C16TABr agrees within error with our result at the CMC (see Table 2). Table 2 also shows that there is no difference between NaBr and KBr. The effect of added electrolyte on the surface excess is small, indicating that the layer is already close to saturation in the absence of electrolyte. Although all the values above the CMC for C12TABr and C16TABr in Table 2 are within error, the systematic differences suggest that addition of NaBr increases the surface excess by up to about 5%, and the increase in surface excess with concentration above the CMC occurs with and without 0.1 M NaBr. The latter is different from the behavior of SDS (Paper II9). However, the differences are

small. The sum frequency results of Knock and Bain also suggested that added electrolyte has a very small or zero effect on the surface packing.17 Knock and Bain’s results for C16TACl in 0.1 M KCl and C16TAF in 0.1 M KF are unexpectedly large, especially for the fluoride, because it is difficult to see how the limiting ST of the fluoride could be so low at about 44 mN m−1 with such open packing. For example, the limiting ST of (C16TA)2SO4 is also 44 mN m−1 but with an area per chain of 49 Å−2. We have used NR to make measurements under identical conditions to those used by Knock and Bain and obtained values of 46 ± 3 and 48 ± 4 Å2, respectively, averaged over the three values each in Table 2. These new values are consistent with the limiting STs and with the sum frequency results of Knock and Bain, which indicated that there was little structural difference between the layers of the three surfactants. Our limiting area for C16TACl from ST is 56 Å2 (in the presence of 0.1 M NaCl), which is 20% higher than the NR result, similar to the discrepancies observed for other cationics. Similar to Knock and Bain, we found that the slope of the ST curve for C16TAF in 0.1 M NaF was very shallow, and, taking the Gibbs prefactor to be 1, it gave an apparent limiting area per molecule of 72 Å2, which is about 50% too high. However, HF is a weak acid (pKa = 3.2), and the dissociation of HF will be significantly suppressed in 0.1 M NaF or KF, which invalidates the assumption of 1 for the prefactor and makes it difficult to do the Gibbs analysis. The failure of the ellipsometric method to give the correct limiting surface excess must lie in the modeling of the ionic/headgroup region of the layer. Until this is solved, ellipsometric measurements will continue to require independent calibration by NR for each compound used, at least for ionic surfactants. Association, Dimerization, and Preaggregation. Dichain cationic surfactants undergo a range of association processes,50,20−2419 which should be distinguished from the natural width of the micellization process identified in earlier sections. That these phenomena have been observed mainly in cationics may reflect the fact that cationic surfactants with two chains and longer chains are in common use. However, it may be that the more hydrophobic headgroup plays a role and it may also be that the hydrogen-containing head groups are more accessible to NMR studies, which have been important in this area. When preaggregation occurs, the application of the Gibbs equation to ST data is possible only if quantitative data on the preaggregation is available, and this is generally not the case. Without this information, the value of the surface excess will be wrong. As shown in Table 1, a large discrepancy between STGibbs and NR is observed for the cationic gemini surfactants. On the basis of the pattern of this discrepancy, we previously devised a semiquantitative model for the ST behavior of surfactant series CnDABr−Cm−CnDABr, with either m = 6 and varying n or n = 12 with varying m.15 The model was partly based on observations of the conductivity by Zana et al.,20 which showed that ion association is significant for small geminis, driven by the high concentration of the CMC, and that dimerization and oligomerization are significant for large geminis. The ST measurements made by Zana and ourselves were all done using the ring method.12−14 Figure 3a shows that there is a difference between ring and bubble shape methods not only in the limiting ST of about 2.5 mN m−1 but also over much of the concentration range (i.e., incomplete wetting significantly changes the whole ST curve). Figure 3a shows that it is still necessary to invoke extensive dimerization and ion 6744

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micellization may, however, be a more acute problem for cationics because many cationics have low aggregation numbers for which the width of micellization is expected to be larger, as discussed in Paper II.9 Just as was found for SDS, extrapolation into the micellization region to obtain the limiting surface excess is not a reliable option because adsorption increases through and above the CMC. The direct measurement of NR shows that there is no plateau in the adsorption at the CMC for the three surfactants, C12TABr, C14TABr, and C16TABr. Thus, the ST cannot be easily modeled in a concentration region where it is changing significantly with coverage. The combination of these two problems presents serious obstacles to the determination of ΓCMC using the Gibbs equation and confirms that the criticism of the ST-Gibbs analysis by Menger et al.1−4 applies to all ionic surfactants. This means that the standard procedures of using either a model isotherm with the integrated Gibbs equation6 or fitting a polynomial to the ST7 cannot be used for many ionic surfactants because the change in the sign and the large change in the magnitude of curvature in the region of the onset of micellization cannot be accounted for in polynomial fits nor in model isotherms. For nonionic surfactants, the limiting coverage is reached before any micellization starts and hence the Gibbs-ST method gives the correct value. The only solution to this problem is to find a good model for the activity behavior in the sub-CMC region. The law of mass action does give such a model, but its assumptions and validity for such a purpose have not been significantly explored. The application of Gibbs-ST to situations where there are other preaggregation processes is formally the same as the problem of finite width of micellization and is well-recognized. However, it seems that in no case has there been the necessary information about the solution equilibria to be able to apply the Gibbs equation correctly, with the result that the preaggregation is ignored in the analysis. In these two situations, where activity coeffients are necessary for the Gibbs-ST analysis but are unknown, ST cannot give the correct limiting coverage. The use of the direct method of NR, which requires neither concentrations nor activities to determine surface excess, must then be the preferred alternative. Apart from the fundamental limitations of the ST-Gibbs analysis above, measurements on anionic surfactants are often badly affected by both surface-active nonionic impurities and non-surface-active cationic impurities. However, although typical nonionic impurities affect ST measurements on cationic surfactants at much lower levels than had been assumed, which therefore requires more extensive repetition of purification stages with solvents of higher purity, the effects of non-surfaceactive ionic impurities should be negligible except in special cases. A further avoidable limitation in the use of the ST-Gibbs method for cationic surfactants is something that does not seem to arise for anionics. Incomplete wetting seems to occur frequently for two of the main ST methods, the Wilhelmy plate and the du Nouy ring. This is probably a result of the negative charge on the material generally used (Pt−Ir or Pt). This combines with the other errors above to give systematic and often large underestimates of the limiting coverage of cationic surfactants to the extent that no measurement of the limiting surface excess by plate or ring can presently be considered to be reliable. Given the widespread use of these two methods, research is urgently needed to characterize and resolve this problem.

Figure 3. (a) ST of cationic gemini C12−C6−C12, as measured by ring and bubble shape methods. The data from bubble shape has been fitted by a simple least-squares straight line above the CMC and by the integrated Gibbs equation, assuming dimerization and ion association below the CMC. The model was that of Li et al.,15 with values of KD = 0.8 (dimerization) and KA = 0.4 (ion association). The limiting value of the Gibbs prefactor is close to 2.5 because there is extensive 3+ formation of the gemini dimer ions, G4+ 2 and G2X . The NR data used to calculate Γ in the integrated Gibbs equation are shown in panel b.12

association to reconcile the NR results and the ST curve, but there is a significant improvement in the fit of the integrated Gibbs equation when it is applied to the bubble shape data. In the plot shown in our original paper, for C11−C6−C11, no combination of the dimerization constant and association constant could be found to fit the data at low concentration. This would also be true for the ring data shown in Figure 3a, as can be seen by imagining the fitted curve shifted upward on to the ring data. The calculated curve is an excellent fit to the bubble shape data but deviates markedly above the ring data. We could find no reasonable combination of KD and KA that would improve the fit to the ring data. Thus, the explanation of the anomalous ST results for the geminis lies in part in the use of the ring method for the measurements and in part in the association and premicellization.

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CONCLUSIONS The application of the Gibbs equation to the analysis of ST data on cationic surfactants is limited by the effects of the finite width of micellization, just as was found for the anionic surfactant SDS, and this has been confirmed for two surfactants, C12TABr and C16TABr, by ST measurements on very pure samples. The width of the micellization process is smaller for these two surfactants than previously found for SDS, but this may result from residual traces of impurity. The finite width of 6745

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(11) Jackson, A. J.; Li, Z. X.; Thomas, R. K.; Penfold, J. The Structures of Micelles of Alkytrimethylammonium Perfluorocarboxylates and of Their Adsorbed Layers at the Air/Water Interface. Phys. Chem. Chem. Phys. 2002, 4, 3022−3031. (12) Li, Z. X.; Dong, C. C.; Thomas, R. K. Neutron Reflectivity Studies of the Surface Excess of Gemini Surfactants at the Air/Water Interface. Langmuir 1999, 15, 4392−4396. (13) Alami, E.; Beinert, G.; Marie, P.; Zana, R. Alkanediyl-α,ωbis(dimethylalkylammonium bromide) Surfactants. 3. Behavior at the Air−Water Interface. Langmuir 1993, 9, 1465−1467. (14) Zana, R. Dimeric and Oligomeric Surfactants. Behaviour at Interfaces and in Aqueous Solution. A Review. Adv. Colloid Interface Sci. 2002, 97, 205−253. (15) Li, P. X.; Dong, C. C.; Thomas, R. K.; Penfold, J.; Wang, Y. L. Neutron Reflectometry of Quaternary Gemini Surfactants as a Function of Alkyl Chain Length: Anomalies Arising from Ion Association and Premicellar Aggregation. Langmuir 2011, 27, 2575− 2586. (16) Jackson, A. J.; Li, P. X.; Dong, C. C.; Thomas, R. K.; Penfold, J. Structure of Partially Fluorinated Surfactant Monolayers at the Air− Water Interface. Langmuir 2009, 25, 3957−3965. (17) Knock, M. M.; Bain, C. D. Effect of Counterion on Monolayers of Hexadecyltrimethylammonium Halides at the Air−Water Interface. Langmuir 2000, 16, 2857−2865. (18) Al-Soufi, W.; Pineiro, L.; Novo, M. A Model for Monomer and Micellar Concentrations in Surfactant Solutions: Application to Conductivity, NMR, Diffusion, and Surface Tension Data. J. Colloid Interface Sci. 2012, 370, 102−110. (19) Gillitt, N. D.; Savelli, G.; Bunton, C. A. Premicellization of Dimethyl Di-n-dodecylammonium Chloride. Langmuir 2006, 22, 5570−5571. (20) Zana, R. Dimeric (Gemini) Surfactants: Effect of the Spacer Group on the Association in Aqueous Solutions. J. Colloid Interface Sci. 2002, 248, 203−220. (21) Jiang, Y.; Chen, H.; Cui, X. H.; Mao, S. Z.; Liu, M. L.; Luo, P. Y.; Du, Y. R. 1H NMR Study on premicellization of quaternary ammonium gemini surfactants. Langmuir 2008, 24, 3118−3121. (22) You, Y.; Zhao, J. X.; Jiang, R.; Cao, J. J. Strong Effect of NaBr on Self-Assembly of Quaternary Ammonium Gemini Surfactants at Air/ Water Interface and in Aqueous Solution Studied by Surface Tension and Fluorescence Techniques. Colloid Polym. Sci. 2009, 287, 839−846. (23) Rosen, M. J.; Mathias, J. H.; Davenport, L. Aberrant Aggregation Behavior in Cationic Gemini Surfactants Investigated by Surface Tension, Interfacial Tension, and Fluorescence Methods. Langmuir 1999, 15, 7340. (24) Hattori, N.; Hirata, H.; Okabayashi, H.; O’Connor, C. J. SmallAngle Neutron-Scattering Study and Micellar Model of the Gemini (Phenylene-dimethylene)bis(n-octylammonium)dibromide Surfactant Micelles in Water. Colloid Polym. Sci. 1999, 277, 361−371. (25) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. Structure of the Surface of a Surfactant Solution above the Critical Micelle Concentration. J. Phys. Chem. 1993, 97, 13907−13913. (26) Voeks, J. F.; Tartar, H. V. The Electrical Conductance of Aqueous Solutions of Dodecyltrimethylammonium Sulfate at 25°. J. Phys. Chem. 1955, 59, 1190−1192. (27) Wolff, T.; Klaussner, B.; von Bunau, G. Multiplicity Selective Photoisomerization of 5,5-Diphenyl-1,3-hexadiene in Aqueous Micellar Solutions Containing Heavy Counterions. J. Photochem. Photobiol., A 1989, 47, 345−351. (28) ISIS Home Page. http://www.isis.stfc.ac.uk/. (29) Lu, J. R.; Thomas, R. K.; Penfold, J. Surfactant Layers at the Air/ Water Interface: Structure and Composition. Adv. Colloid Interface Sci. 2000, 84, 143−304. (30) Lyttle, D. J.; Lu, J. R.; Thomas, R. K.; Penfold, J. Structure of a Dodecyltrimethylammonium Bromide Layer at the Air−Water Interface Determined by Neutron Reflection. Langmuir 1995, 11, 1001−1008. (31) Lu, J. R.; Li, Z. X.; Smallwood, J.; Thomas, R. K.; Penfold, J. Detailed Structure of the Hydrocarbon Chain in a Surfactant

Two direct methods other than NR have been used to measure surface excess. We showed in Paper II9 that radiotracers do not give accurate and reliable results for anionic surfactants, and the technique has not been applied to cationics. Although ellipsometry has been used for sensitive measurements of surface excess of a cationic surfactant following NR calibration for that surfactant, attempts to use it as a stand-alone technique are, as yet, unreliable.

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ASSOCIATED CONTENT

* Supporting Information S

Directly measured (NR) adsorption of dodecanol and SDS at the air/water surface in a mixture containing 0.5 wt % dodecanol relative to SDS; ST behavior calculated for 0.5 wt % dodecanol in SDS from the integrated Gibbs equation; and comparison of the ST for specially purified C16TAB measured by bubble shape analysis and du Nouy ring (Pt−Ir) as well as the same comparison for the gemini surfactant, C12DAB−C6− DABC12. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank STFC for the provision of extensive neutron beam time at the ISIS facility. REFERENCES

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