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Langmuir 1996, 12, 2446-2453
Apparent Anomalies in Surface Excesses Determined from Neutron Reflection and the Gibbs Equation in Anionic Surfactants with Particular Reference to Perfluorooctanoates at the Air/Water Interface S. W. An, J. R. Lu, and R. K. Thomas* Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, U.K.
J. Penfold DRAL, Chilton, Didcot, Oxon, OX11 0QX, U.K. Received October 10, 1995. In Final Form: January 16, 1996X The surface tension and neutron reflectivity of several perfluorooctanoic acid salts with monovalent metal cations have been investigated over a wide range of surfactant, counterion, and co-ion concentrations. Previous interpretations of similar surface tension data have indicated that there is significant dissociation of the counterions from the surfactant layer, leading to a prefactor less than 2 in the Gibbs equation for the surfactant in the absence of electrolyte, which could be interpreted in terms of a depletion layer of surfactant in the region underneath the surfactant ion monolayer. We show that this result is an artifact resulting from the presence of small amounts of divalent cation impurity. Once the divalent ions are removed, we obtain complete consistency between the neutron and surface tension results using a Gibbs prefactor of 2 with no significant subsurface depletion. It is concluded that contamination of anionic surfactants by divalent ions may be the most common cause of inaccurate determination of adsorption isotherms of these materials at the air/solution interface.
Introduction There have been a number of experimental observations in the literature concerning the surface excess of counterions in a charged surfactant layer which seem to indicate that there is not necessarily a 1:1 correspondence between surfactant ion and counterion, a particularly large one being observed by Shinoda et al.1,2 for the monovalent metal salts of the perfluorooctanoates. Shinoda et al. used surface tension measurements in conjunction with the Gibbs equation, varying the counterion concentration in different ways, and found that typically only just over half the expected amount of counterion was adsorbed at the surface. Hall et al.3,4 reanalyzed these and other results and also found that they are consistent with a nonzero degree of dissociation of the surfactant layer resulting in a surface excess of counterion less than that of surfactant ion. A degree of dissociation greater than zero has the consequence that when the Gibbs equation is applied to a simple mono-monovalent ionic surfactant solution, the prefactor in the equation is less than the usual value of 2. Hall et al. tabulated the results from several anionic surfactants, and in each case there was some discrepancy, although it was largest for the perfluorooctanoates. It has been suggested that one contribution to such a discrepancy could be a depletion layer of surfactant ion in the region below the monolayer, which, because of electroneutrality, causes a parallel deficit in the total amount of adsorbed counterion. While such an explanation may be consistent with the results and analysis of the surface tension measurements, it is difficult to test experimentally. Several attempts to test this hypothesis have been made using radiotracer measure* To whom all correspondence should be addressed. X Abstract published in Advance ACS Abstracts, April 1, 1996. (1) Shinoda, K.; Nakayama, H. J. Colloid Interface Sci., 1963, 18, 705. (2) Shinoda, K.; Hato, M.; Hayashi, T. J. Phys. Chem. 1972, 76, 909. (3) Hall, D. G. Colloids Surf., A 1994, 90, 285. (4) Hall, D. G.; Pethica, B. A.; Shinoba, K. Bull. Chem. Soc. Jpn. 1975, 48, 324.
ments of the surface excess and some of them have found unexplained discrepancies5 and others have obtained results apparently consistent with the prefactor of 2.6-8 However, when, for example, the overall results for the anionic surfactant sodium dodecyl sulfate (SDS) are examined,9 it is apparent that radiotracer measurements generally obtain a higher coverage at concentrations below the critical micelle concentration (cmc) than surface tension measurements and the Gibbs equation. Recently, SDS solutions have been reexamined with radiotracer measurements and again the discrepancy was found to be a higher coverage from radiotracers than from surface tension, especially in the region of about one-third of the cmc.10 However, the authors found that this could be attributed to the presence of Ca2+ ions rather than any depletion layer. This is an important result and we will discuss it in full below. We have recently shown in a number of papers that neutron reflection is an extremely accurate method for determining surface excess.11 The neutron reflection signal depends on the square of the scattering length density in the surface region and, in the way the experiment is usually done, essentially determines the amount of surfactant ion in the monolayer at the surface of a dilute surfactant solution. The technique is not at all sensitive to the absence of surfactant ion or counterion in the rest of the interfacial region, except in very special circumstances. The combination of neutron reflection and surface tension measurement should therefore be able to (5) Salley, D. J.; Weith, A. J., Jr.; Argyle, A. A.; Dixon, J. K. Proc. R. Soc. London 1950, A203, 42. (6) Tajima, K.; Muramatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1970, 43, 1991. (7) Tajima, K. Bull. Chem. Soc. Jpn. 1971, 44, 1767. (8) Muramatsu, M. Surface and Colloid Science; Matijevic, E., Ed.; Wiley-Interscience: New York, 1973; Vol. 6. (9) Lu, J. R.; Purcell, I. P.; Lee, E. M.; Simister, E. A.; Thomas, R. K.; Rennie, A. R.; Penfold, J. J. Colloid Interface Sci. 1995, 174, 471. (10) Cross, A. W.; Jayson, J. J. J. Colloid Interface Sci. 1994, 162, 45. (11) Lu, J. R.; Lee, E. M.; Thomas, R. K.; Penfold, J.; Flitsch, S. Langmuir 1993, 9, 1352.
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test whether the discrepancy really comes from an underlying depletion layer. We have chosen the perfluorooctanoates partly because of the large discrepancy observed by Shinoda, partly because they are suitable for study with neutron reflection, and partly because they are part of an important class of surfactants, which needs to be well understood.12 Some measurements have already been made using X-ray reflection13 and neutron reflectivity,14 but neither of these set out to explore the problem of the anomalous surface excess. Experimental Details Perfluorooctanoic acid of stated purity >99% was obtained from Fluorochem, converted into the appropriate metal salt by reaction with the stoichiometric amount of hydroxide, and purified by recrystallization at least twice from a mixture of ethanol and propanol (1:1). Water from an Elgastat was used for all experiments and all salts were roasted in air before use. It will become clear in the results section that the purity of the hydroxide in terms of metal ions will be of great importance. Initially, we used standard reagent grade sodium hydroxide, later semiconductor grade (99.99%). The cesium hydroxide was 99.9% from Aldrich. The surface tension measurements were made on a Kru¨ss K10 tensiometer using a Pt/Ir ring using procedures described previously.15 Neutron reflection measurements were made on the reflectometers CRISP and SURF at ISIS, U.K., as described elsewhere.16,17 The instrument was calibrated using D2O (K & K Greeff).
Determination of Coverage: Theory (a) Neutron Reflection. The simplest possible model of an adsorbed monolayer of surfactant is that it forms a layer of uniform refractive index which is different from the refractive index of the underlying solution. While this is not a realistic model, it is convenient and accurate for discussing neutron reflection results from surfactant solutions. The neutron reflective index is close to unity and it is convenient to discuss reflection in terms of the scattering length density, related to the refractive index by
η2 ) 1 -
λ2 F π
(1)
where η is the refractive index, λ the wavelength, and F is the scattering length density given by
F(z) )
∑j bjnj(z)
(2)
where bj is the scattering length and nj is the number density of atomic species j. For surfactant solutions the difference between the scattering of the isotopes of hydrogen for which bH ) -3.74 × 10-5 Å and bD ) 6.67 × 10-5 Å is important because some materials, including water, have negative scattering length densities. Thus it is possible to choose the isotopic composition of water so that its scattering length density is the same as that of air, i.e., zero. There is no reflection at all from the air/ (12) Kissa, E. Fluorinated Surfactants; Surfactant Science Series 50; Marcel Dekker: New York, 1994. (13) Pershan, P. S. J. Phys. (Colloque) 1989, C-7, 1. (14) Simister, E. A.; Lee, E. M.; Lu, J. R.; Thomas, R. K.; Ottewill, R. H.; Rennie, A. R.; Penfold, J. J. Chem. Soc., Faraday Trans. 1992, 88, 3033. (15) Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1992, 96, 1373. (16) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381. (17) Bucknall, D. G.; Penfold, J.; Webster, J. R. P.; Zarbakhsh, A.; Richardson, R. M.; Rennie, A. R.; Higgins, J. S.; Jones, R. A. L.; Pletcher, P. D. A.; Thomas, R. K.; Roser, S. J.; Dickinson, E. ICANS XIII, in press.
water interface for water of this composition (0.088 mole fraction of D2O), which we refer to as null reflecting water (NRW). For a solution of perfluorinated surfactant in NRW, reflection can only occur from the surfactant monolayer formed at the surface; i.e., the technique is then surface specific. A typical signal from a perfluorinated surfactant monolayer may be as much as 1000 times the residual background signal and, unlike radiotracer measurements, there are no ambiguities in the calibration of the signal or in the determination of the background level. The surface coverage is most conveniently determined by fitting the model of a uniform monolayer to the reflectivity using standard formulas for the reflected intensity.18 The two fitted parameters F and τ (the thickness of the layer) combine to give the surface coverage Γm using
Γm )
1 Fτ ) NaA Nab
(3)
where A is the area per molecule, Na is Avogadro’s number, and Γm is the surface coverage. When the contrast situation is as described above, i.e., deuterated surfactant in NRW, the reflection experiment is extremely sensitive to Γm because of the quadratic dependence of R on Γm. Exactly what Γm signifies will be discussed below. The thickness τ of the layer depends on the choice of model for the distribution of surfactant along the surface normal but the derived coverage is not at all model dependent. The reason is that, although a range of τ will usually fit a given profile especially at lower coverages, the corresponding best fitted values of F exactly compensate, i.e., Fτ is model independent. Thus, a quite different shape for the scattering length density profile normal to the surface is a Gaussian
( )
F ) F0 exp -
4z2 σ2
(4)
where σ is the full width at 1/e of the maximum for which the reflectivity is
πσ2Fm2κ2 κ R= exp(-κ2σ2) 4 4
(5)
where Fm is the maximum value of the scattering length density of the layer and the approximation sign refers only to values of κ, the momentum transfer ()(4πsinθ)/λ), lower than being considered here. The surface coverage is now given by
Γm )
xπσFm 2Na
(6)
Even though the Gaussian distribution is completely different from the uniform monolayer, the value of Γm obtained is not affected at all by the choice of model. Another way of demonstrating the model independence is to take logs in eq 5 to obtain
ln(κ2R) = Γm2 - κ2σ2
(7)
which shows that it is the limiting value of the reflectivity as κ f 0 that is determined by Γm. At low κ the reflectivity is independent of the shape of the distribution and hence so is the derived value of Γm. (18) Born, M.; Wolf, E. Principles of Optics; Pergamon: Oxford, 1970.
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Apart from impurities there are three possible sources of difficulty in determining the coverage from neutron reflection, none of which has yet been definitely identified in an experiment. The first is that if the layer breaks up into islands and the dimensions of these are comparable with the coherence length for the experiment, then the reflectivity will depend on the coverage differently from a uniform layer.19 The number density of surfactant n is the average number density over the whole surface and the reflectivity is proportional to n2. If the adsorbed layer breaks up into islands which cover only a fraction θ of the surface, the experiment will observe the average reflectivity, which will be proportional to θ(n/θ)2. In interpretation of the reflection from islands in terms of a uniform layer, the coverage would be overestimated by a factor (1/xθ). The changeover between the two reflection regimes should occur when the dimensions of the islands are of the order of micrometers, depending on the resolution of the experiment, and it should be identifiable because it should be associated with enhanced off-specular scattering. This effect has not been observed with any certainty, even for insoluble monolayers. It has been suggested that, at very low coverage, a surfactant layer in equilibrium with the subphase does undergo a phase change from a liquid expanded phase to a gaseous phase (e.g., ref 20), which could lead to misinterpretation of the neutron reflectivity. However, such a transition is not expected at the higher coverages being considered here. The second possible ambiguity in the neutron experiment is whether or not equilibrium has been established. Diffusion to the surface is generally fast enough to establish a monolayer in a few seconds or minutes depending on the concentration. However, at low coverages (less than about 150 Å2) we have sometimes observed erratic time effects on the signal over periods of hours when the surface is completely undisturbed, suggesting that the establishment of equilibrium is not always rapid. While such effects are most likely to be associated with impurities, they could be associated with the system becoming locked into one or other of the phases mentioned above with convection currents possibly favoring one or other phase. It should be emphasized that the establishment of equilibrium is not at all a problem at areas per molecule below about 100 Å2. The final possible error in interpretation is that damping effects may reduce the signal below what is expected.21,22 Such effects have also not been observed with certainty and they would be unlikely to affect a layer of surfactant ion. What is actually being measured in the experiment depends on the labeling scheme used. In principle, if the surfactant ion is perfluorinated, NRW is the solvent, and the surfactant concentration is at sub-cmc levels, the signal is from the total surfactant excess, including counterion, at the interface. In practice, the counterion usually has such a relatively small scattering length that its contribution is negligible, and therefore it is the surfactant ion excess that is being measured. The surfactant ion excess may consist of two parts, surfactant adsorbed in a monolayer, Γm, and a negative excess in the region below the monolayer, Γd, so that the overall excess is3
Γ ) Γm + Γd
(8)
The effect on the reflectivity of any surfactant ion desorbed from the sub-monolayer region of the interface is negligible (19) Roser, S. J.; Richardson, R. M. Langmuir 1991, 7, 1458. (20) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (21) Pershan, P. S. J. Phys. Condens. Matter 1994, 23A, 37. (22) Lu, J. R.; Lee, E. M.; Thomas, R. K. Acta Crystallogr., in press.
and therefore the coverage measured in a neutron experiment is Γm. Since it is Γ that is determined by the application of the Gibbs equation to surface tension data, the two experiments may give different results. (b) Surface Tension. To make the comparison between the two different methods of determining the surface coverage somewhat clearer, we review Hall’s formulation of the Gibb’s equation for ionic surfactants3,4 but simplify the treatment to consider only uni-univalent charged surfactant systems. The Gibbs equation for an ionic surfactant in the presence of co-ion is
-dγ ) Γ1 dµ1 + Γ2 dµ2 + Γ3 dµ3 RT
(9)
where the subscripts 1, 2, and 3 refer to surfactant, counterion, and co-ion, respectively, γ is the surface tension, Γi are the surface excesses defined with respect to Γsolvent ) 0, and the µi are the chemical potentials. The electroneutrality conditions are for the bulk
c1 + c3 - c2 ) 0
(10)
and, for the interface
Γ1 + Γ3 - Γ2 ) 0
(11)
and when these are combined with the Gibbs equation we obtain
-dγ ) Γ1(d ln c1f1 + d ln c2f2) + RT Γ3(d ln c3f3 + d ln c2f2) (12) where fi are the mean activity coefficients of electrically neutral surfactant and supporting electrolyte. Further manipulation gives the set of equations
( ) [
-1 ∂γ RT ∂c1
)
c3
( )
Γ1 Γ1 + Γ3 ∂ ln f1 + + Γ1 c1 c1 + c3 ∂c1
+
c3
( )]
Γ3
( ) [
-1 ∂γ RT ∂c2
)
c1
( )
Γ3 Γ1 + Γ3 ∂ ln f1 + + Γ1 c3 c1 + c3 ∂c3
( ) [ )
c2
( )
Γ1 Γ3 ∂ ln f1 - Γ1 c1 c3 ∂c1
c2
(13)
c3
+
c1
( )]
(14)
( )]
(15)
Γ3 -1 ∂γ RT ∂c1
∂ ln f3 ∂c1
∂ ln f3 ∂c3
c1
+
Γ3
∂ ln f3 ∂c1
c2
Because the monolayer repels co-ions we can expect Γ3 to be negative. As suggested above, in connection with eq 8 there will be a negative contribution, Γd, to Γ1 for the same reason; i.e., surfactant ions will be repelled from the region just below the monolayer because of the charge on the surfactant layer. Hall has defined a surface degree of dissociation, R, which is
R ) -2
Γd + Γ3 Γm
where Γm is as defined in eq 8.
(16)
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Hall now introduces two assumptions
f1 ) f3 ) f
(17)
Γd Γ3 ) c1 c3
(18)
and
which, when combined with eqs 13, 14, and 15, lead to a new set of equations
( )
-1 ∂γ RT ∂ ln c1
[
) Γm 1 c3
Rc1 2(c1 + c3)
+
(1 - R2)(c + c + c β)] (19) R -1 ∂γ ) Γ (1 - )(1 + c β) (20) [ R2 RT(∂ ln c ) 2] c1
1
1
m
3
1
2 c1
(
-1 ∂γ RT ∂ ln c1
)
(21)
) Γm
c2
where
β)
( ) ∂ ln fi ∂cj
(22)
ci
When there are no co-ions, only eq 19 applies and it reduces to
-1 dγ R ) Γm 2 - R + 1 - c1β RT d ln c1 2
[
(
) ]
(23)
The right hand side is the Gibbs surface excess, Γ. Thus
[
(
Γ ) Γm 2 - R + 1 -
) ]
R c β = Γm(2 - R) 2 1
(24)
where the approximate expression, holding when the activity coefficients are unity, identifies the prefactor in the Gibbs equation with (2 - R). The equations above suggest that it should be possible to determine both Γm and R from a suitable set of surface tension measurements. Strictly, this is not possible, but at certain concentrations which lie on two or more independent surface tension curves, the limiting slopes will be sufficiently well defined and the conditions sufficiently similar to make an approximate determination of both constants possible and this is what has been done by Shinoda et al.1,2 and Hall et al.3,4 for several perfluorooctanoic acid salts. Finally, we state the expression we will use for β
β)
(
)
-B 1 1 2(1 + xc2) xc2 1 + xc2
Figure 1. Reflectivity of fluorinated surfactants at different concentrations in NRW: (a) CsPFO (25 mM (O), 5 mM (4), 3.5 mM (+), 2 mM (×)); (b) NaPFO (20 mM (O), 7.5 mM (4), 3.5 mM (+), 2 mM (×)); (c) HPFO (10 mM (O), 3 mM (4), 1 mM (+), 0.3 mM (×)). Continuous lines are the uniform layer fits using optical matrix method and the coverages in Figure 3.
(25)
where B is the Debye-Hu¨ckel constant. Determination of Coverage: Results We denote the perfluorooctanoates by MPFO, where M refers to the counterion; thus HPFO refers to perfluorooctanoic acid. Figure 1 shows the neutron reflectivity profiles for CsPFO, NaPFO, and HPFO in NRW at various concentrations together with the best fits of a uniform monolayer to the data. The surface tension behavior of the same samples in H2O and under various conditions of added electrolyte are shown in Figure 2 with the best
fits of a polynomial to the data below the cmc. In all the surface tension plots we have used activities a where we have used eq 25 to convert concentration into activity. The surface excesses determined from the two techniques are compared in Figure 3, and it can be seen that there are large differences even at the cmc. A similar discrepancy is found at the higher temperature of 40 °C. The surface excess determined from the surface tension in Figure 3 has been determined using eq 23 with a value of exactly 0 for R. The surface tension excesses can be made to correspond with the neutron values only by taking values of R in the range of 0.3-0.5 (we here use the value of β given by eq 25). When R and β are exactly 0, eq 23 corresponds to the usual form of the Gibbs equation used for ionic surfactant with a prefactor of 2, and when R is in the range 0.3-0.5, the prefactor is in the range 1.51.7. Two sets of reflectivity profiles obtained with the counterion concentration maintained constant, at c3 ) 0.01 M, are shown in Figure 4. A similar experiment was also done at c3 ) 0.1 M. Under these conditions the application of the Gibbs equation (21) to the surface tension variation (Figure 2) should give exactly the same result as neutron reflection, and this is found to be so (Figure 5). The agreement at the lower counterion concentration is exact, and even at the higher concentration, where β may not be accurately accounted for by eq 25, the agreement is still quite good. The importance of this result is that it demonstrates that none of the possible artifacts outlined in section a above are confusing the interpretation
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Figure 2. Surface tension plots for (a) CsPFO (in pure water (O), at a constant Cs ion concentration of 0.01 M (4) and 0.1 M (+), at a constant PFO ion concentration of 1 mM (×) and 5 mM (3)), (b) NaPFO (in pure water (O), at a constant Na ion concentration of 0.01 M (4) and 0.1 M (+), (c) HPFO (in pure water (O), at a constant H ion concentration of 0.01 M (4). All measurements were made at 25 °C. The continuous lines are fits of a polynomial to second order.
of the neutron data. The large discrepancy found in Figure 3 must be either attributed to a value of R different from zero or a different sort of artifact. An approximate independent value of R could be obtained at concentrations where the two curves intersect in Figure 2 but would be neither as accurate nor as valid over the whole concentration range as the neutron value. The third set of experiments is similar to that originally done by Shinoda; that is, the electrolyte is varied at a fixed surfactant ion concentration. The surface tension variation is given by eq 20 and is often thought of approximately as determining the surface excess of counterion; i.e., the Gibbs prefactor is approximately unity. In fact it is Γm that is obtained with a rather complicated prefactor which depends on R. A large discrepancy between the coverages determined by neutrons and surface tension is found at two surfactant ion concentrations (Figure 6), and once again it is necessary to invoke a large value of R in the range 0.2-0.4, depending on concentration, with the larger value obtaining at the lower concentration. All these results fit quite well with an apparent surface degree of dissociation of the counterion around 0.3. Equation 16 shows that, when there is no co-ion present, a value of R of 0.3 corresponds to a relative depletion, -Γd, of 0.15Γm. In principle, the existence of a significant
Figure 3. Comparison of surface excesses determined by neutrons (O) from data of Figure 1 and by tension (+) from data of Figure 2: (a) CsPFO, (b) NaPFO, (c) HPFO. All the data are for the surfactant only in water.
depletion of co-ion or surfactant ion from the region beneath the surface is not unacceptable and, in double layer theory, as the limit of low potential is approached the charge on the surface is counterbalanced one-half by counterion and one-half by missing co-ion.23 The difficulty here, however, is that the maximum depletion in con-
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Figure 4. Neutron reflectivities at constant counterion concentrations of 0.01 M: (a) CsPFO (PFO concentration equals 10 mM (O), 4 mM (4), 1 mM (+), 0.3 mM (×)); (b) NaPFO (PFO concentration 10 mM (O), 6 mM (4), 2 mM (+), 1 mM (×)); (c) HPFO (PFO concentation 3 mM (O), 1 mM (4), 0.3 mM (+), 0.1 mM (×).
centration that can be attained at any point in the layer can only correspond to the bulk concentration of the surfactant (or co-ion), which, for CsDS, is 25 mM at the cmc. Γm is 4.6 × 10-10 mol cm-2 at this concentration, and to satisfy the observations Γd would have to be -0.7 × 10-10 mol cm-2. To reach this value by exclusion of surfactant ion would therefore require the complete absence of surfactant ion over a depth of 2800 Å. Given that the Debye length is only about 20 Å such a depth of exclusion is physically unrealistic. It is easy to show that this becomes even more so at lower concentrations. Although the equations give by Hall have been derived for the situation when there is a co-ion, an unrealistic depth of exclusion is also obtained when co-ion is present (the results shown in Figure 6). Hall et al. did make two approximations (eqs 25 and 18), but neither of these is likely to give rise to the large effects observed here. The only other possible explanation must be that other ions are present and confusing the situation. The ion that is always present is the hydrogen ion. Although the fluorocarbon acids are strong, there is always the possibility that the dissociation constant in the layer is very different from its bulk value. Thus it is possible to envisage that, for CsPFO, some H+ displaces Cs+ from the layer leading to apparent dissociation of the layer. In these circumstances study of the variation of surface tension wth pH should reveal the H+ surface excess (eq 20). In the range of pH of most of our measurements, however, we have observed no effect of pH on the surface (23) Overbeek, J. T. G. Prog. Biophys. Biophys. Chem. 1956, 6, 57.
Figure 5. Surface excesses determined at constant counterion concentration of 0.01 M from neutron reflection (O) and surface tension (+) using eq 21: (a) CsPFO; (b) NaPFO; (c) HPFO.
tension. Furthermore, the same discrepancy of a large value of R occurs for the acid form and replacement of H+ (by H+!) cannot then be invoked to explain the situation. The most likely impurities are divalent ions because the divalent perfluorooctanoates will be insoluble and therefore highly surface active. Whether or not such ions are important can be tested in three ways, by measuring
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Figure 8. Surface excesses in the presence of EDTA from neutron reflection (O) and surface tension measurements (+) for CsPFO in pure water at 25 °C.
Figure 6. Comparison of surface excesses from neutron reflection (O) and surface tension (+) at fixed surfactant ion concentration of (a) 1 mM and (b) 5 mM for CsPFO.
Figure 7. Effects of impurities on surface tension plots. The concentration of CaCl2 was fixed at 0.5 mol % to NaPFO. Surface tension of NaPFO in pure water (+) is also shown for comparison.
the effect of added divalent ion, by using highly purified metal hydroxide (from the point of view of the cation content) in the initial neutralization, or by using some means for removing traces of divalent ions from the surfactant solutions. We have done all three. Figure 7 shows the effects of a small amount of Ca2+ added to the surfactant on the surface tension curve for NaPFO. At a concentration of 0.5%, the presence of CaPFO actually produces the classical surface minimum near the cmc, normally taken to be an indication of impurity, but even when there is insufficient to generate a minimum, there is a general lowering of the surface tension. This result for the perfluorooctanoates exactly parallels that obtained for SDS by Cross and Jayson.10 The second method is to remove the divalent ion by the addition of a sequestering agent, which is itself not surface active. EDTA will sequester divalent ions, especially Ca2+,
and is not surface active, but it is an electrolyte and so will tend to increase the surfactant adsorption at a given surfactant concentration. However, if it is kept in constant ratio to the surfactant, it will only affect the prefactor through its effect on the activity coefficient of the surfactant, which can be kept to a low level, and the only effect should be a very small lowering of the cmc and the surface tension. Since the effect we are expecting is the reverse of this, it should be easy to distinguish. Figure 8 shows the effect of the tetrasodium salt of EDTA on the surface excesses determined by both methods. Both the cmc and the surface tension are increased significantly, which can only be explained by the removal of divalent cations which lower the CsPFO tension, even at the cmc. The γ-ln c plot becomes steeper and the effect on the surface excess obtained from the Gibbs equation is that it is increased. The added Na4EDTA has an even larger effect on the surface excess measured by neutrons, which is now less than in the presence of divalent ions (in principle we should have used Cs4EDTA but the effect of a small amount of sodium ion in the layer will be negligible since its surface tension is similar to that of CsPFO). The agreement between the two measurements is now seen to be excellent using the normal prefactor of 2 in the Gibbs equation (cf. Figure 3a). Finally, we have tested the effects on the surface tension alone of using different samples of sodium hydroxide of different purity. The use of semiconductor grade NaOH gives samples which increase the surface tension in the same way as addition of Na4EDTA, although we did not test them with the more sensitive neutron reflection experiment. It is not easy to estimate the level of impurity ion that causes a significant effect partly because we have not definitely identified the ion responsible and partly because the amount will vary with surfactant concentration, but it is clearly essential that a source of monovalent cation of the highest possible purity be used to prepare these anionic surfactants. Conclusions In the normal determination of the adsorption isotherm of an ionic surfactant, the Gibbs equation is applied to the surface tension data using a prefactor of 2, which arises from there being equal amounts of surfactant ion and counterion at the surface. Apart from activity coefficient corrections, all theoretical models support this value of the prefactor (see, for example, Chattoraj and Birdi24). (24) Chattoraj, D. K.; Birdi, K. S. Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984.
+
+
Surface Excess of Counterions
The equations of Hall et al. are thermodynamically based and, apart from minor assumptions, are independent of any model. These equations are valuable in that they show how, within a set of surface tension measurements, it is possible to determine the surface excess of surfactant ion and an approximate surface excess of the counterion independently, any discrepancies essentially being taken into the degree of dissociation R. Without such an analysis there can be no test of self-consistency of an adsorption isotherm derived from the surface tension measurements. However, even when such a thorough analysis has been made, all discrepancies are parameterized into the value of R and only an independent measurement of surface excess can be used to assess whether or not it is real. We have argued here that the values of R obtained for the fluorosurfactants are not physically sensible because they imply a depth of depletion layer of surfactant ion that is unrealistically too large. If finite values of R really were to occur for surfactant monolayers over the range of surface and bulk concentrations observed here, they would present a serious challenge to theorists because they would be in conflict with current models of the surface layer, notwithstanding the limiting result of Overbeek mentioned earlier. By using an independent method of determining the surface excess, we have shown that, for the perfluoroacid salts, a finite value of R indicates the presence of a particular kind of impurity, one which is likely to cause problems for all anionic surfactants. Using different experimental techniques and a different surfactant, SDS, Cross and Jayson10 have recently shown that the presence of Ca2+ ions causes exactly the same problem in the determination of the coverage of SDS, especially in the region below the cmc, although they did not use the rather clear surface tension formalism of Hall et al. Unlike Cross and Jayson we have not estimated the level of divalent ion that will cause an effect, and one would expect it to vary from species to species. In our results it is clear that when there is a sufficient concentration of counterion, the effects of the divalent (or trivalent?) ion are swamped and the surface tension analysis gives the correct coverage when the equations of Hall et al. are used. That both Cross and Jayson and ourselves find similar results suggests that methods of purification of all anionic surfactants, however rigorous, that do not also pay attention to contamination
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from solid surfaces during the course of measurement may not necessarily achieve the correct surface tension/ concentration curve. Although many criteria of purity have been suggested (see, for example, Lunkenheimer25) the results of the present work suggest that the material is pure either when there is complete agreement between neutron reflection (or radiotracer experiments) and surface tension coverages (using the prefactor 2) over a wide concentration range or when the effects of various added electrolyte conditions on the surface tension demonstrate that R is zero (or the Gibbs prefactor for the surfactant alone is exactly 2) within error. A further observation which is consistent with the above observations is that in doing neutron reflection experiments over a range of different types of surfactant we have usually found good agreement between surface excesses determined from neutrons and surface tension for cationic and nonionic surfactants, taking prefactors of 2 and 1, respectively, in the Gibbs equation. With all the anionic surfactants we have so far studied, not only do we nearly always fail to obtain agreement at concentrations well below the cmc but we often find the coverages as determined directly by neutron reflection rather unreproducible. For the perfluorooctanoic acid salts in the present work, this can now be attributed to varying amounts of divalent ion impurity depending either on the purity of the original hydroxide or on contamination by the glassware used. We have had similar problems with SDS and have already commented on this,9 a result explained by the work of Cross and Jayson. We have also had even more serious discrepancies with the anionic surfactant AOT, and interestingly, the first radiotracer measurements made were done on AOT5 and a similar discrepancy was observed, although it was attributed to formation of the acid form of the surfactant at the surface. Acknowledgment. We thank Professor D. G. Hall for valuable discussions concerning the formalism of the charged surfactant interface. We thank the Engineering and Physical Sciences Research Council for support of this work. LA950851Y (25) Lunkenheimer, K.; Czichocki, G. J. Colloid Interface Sci. 1993, 160, 509.
