5960
Langmuir 2003, 19, 5960-5962
Measurement of the Dynamic Surface Excess of the Nonionic Surfactant C8E4OMe by Neutron Reflection and Ellipsometry Dimitrina Valkovska, Katherine M. Wilkinson, Richard A. Campbell, and Colin D. Bain* Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom Ray Wat and Julian Eastoe School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom Received January 13, 2003. In Final Form: May 15, 2003
Introduction Ellipsometry is a powerful experimental technique for studying surfaces of surfactant solutions under both static and dynamic conditions: it is fast, local, noninvasive, and precise. Although the ellipsometric parameters are determined by the properties of the adsorbed surfactant monolayer, there is a priori no direct relationship between these parameters and the surface excess, Γ, of a surfactant at the air-water interface. In particular, the ellipsometric parameters are sensitive to the packing density and orientation of hydrocarbon chains in the surfactant. Consequently, to determine the surface excess by ellipsometry, the ellipsometric parameters need to be calibrated against values of Γ determined in a separate experiment. The best-established methods for measuring the surface excess are tensiometry and neutron reflection (NR). For a nonionic surfactant, the surface excess is given by the Gibbs equation in the form Γ ) (RT)-1dσ/d ln c, where σ is the surface tension and c is the bulk concentration (assuming the activity coefficient is unity). For nonionic surfactants, the determination of adsorption isotherms from the Gibbs equation generally requires accurate measurements at very low concentrations, where trace impurities, long adsorption times, and depletion of surfactant in solution can seriously compromise accuracy. Neutron reflection is a direct and accurate method for determining the surface excess,1 but it requires a large, flat surface and it is not a practical tool for laboratorybased studies. In previous papers,2,3 we have reported NR, tensiometric, and ellipsometric measurements on the family of alkyltrimethylammonium bromide surfactants, CnTAB (n ) 12, 14, 16, 18), and demonstrated that the coefficient of ellipticity, Fj, is linearly proportional to the amount of adsorbed surfactant, Γ. These results raised the question of whether this linear relationship is peculiar to single-chain cationics or whether it is a general result that holds for a wide range of simple surfactants. In this note, we report analogous measurements for a nonionic surfactant, C8H17(OC2H4)4OCH3 (abbreviated C8E4OMe), by ellipsometry and NR. We chose this surfactant since the chain-deuterated compound, which is required for the NR experiment, can be prepared by a * Corresponding author. E-mail:
[email protected]. (1) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143. (2) Manning-Benson, S.; Parker, S. R. W.; Bain, C. D. Langmuir 1998, 14, 990. (3) Battal, T.; Shearman, G.; Valkovska, D. S.; Bain, C. D.; Darton, R. C.; Eastoe, J. Langmuir 2003, 19, 1244.
straightforward synthesis with a well-defined number of ethylene oxide (EO) groups. In addition, its critical micelle concentration (cmc) (7.4 mM) is appropriate for measurements in an overflowing cylinder (see below) and its cloud point is well above room temperature. We show below that a linear relationship between Fj and Γ also holds for this nonionic surfactant. Direct measurements on equilibrium solutions of nonionic surfactants of the general structure CH3(CH2)n-1(OC2H4)mOH (abbreviated CnEm) have been carried out before by ellipsometry4,5 and by neutron reflection.6 These measurements share some of the limitations of tensiometry, namely, that significant adsorption occurs at inconveniently low bulk concentrations. For example, in the lowest concentration of C12E5 studied by Binks et al.,5 a surface excess of 0.7 × 10-6 mol m-2 was deduced for a bulk concentration, c, of 1.0 × 10-7 mol dm-3. The depletion depth in this case, Γ/c, is 7 mm, and the diffusion time under stagnant conditions, (Γ/c)2/D, is ∼2 days, where D is the diffusion coefficient. Making measurements under such conditions demands extreme care, pure materials, and patience. One way of circumventing these problems is to make measurements on a continually expanding surface. At steady-state, loss of surfactant from the surface by convection is balanced by diffusion of surfactant to the surface from the bulk. For surface expansion rates of the order of 10 s-1, very low surface concentrations are observed for relatively high bulk concentrations (g10-4 mol dm-3 for typical small-molecule surfactants). The overflowing cylinder (OFC) provides a convenient experimental platform for generating a flat expanding surface with expansion rates in the range of 1-10 s-1. Since both neutron reflection and ellipsometry are determined by the local structure of the interface, which equilibrates rapidly on the time scale of the OFC (0.1-1 s), the calibration curve Fj(Γ) determined on the OFC is valid under both equilibrium and dynamic conditions. Experimental Section C8H17(OC2H4)4OCH3 (abbreviated C8E4OMe) and C8D17(OC2H4)4OCH3 (abbreviated dC8E4OMe) were synthesized according to the method of Selve et al.7,8 Triethyleneglycol monomethyl ether (1.4 equiv, Fluka, 97%) dissolved in anhydrous THF (100 mL, Sigma) was mixed with aqueous sodium hydroxide (5 mol dm-3, 100 mL, 2.0 equiv, BDH Aristar). The mixture was cooled to 0 °C in an ice-bath. Tosyl chloride (1.3 equiv, Sigma) in THF (100 mL) was added dropwise with constant stirring, maintaining a temperature below 5 °C. Once addition was complete, the reaction mixture was stirred for a further 30 min at 0 °C and then poured over ice water (500 mL). This solution was divided into two, and each half was extracted with dichloromethane (3 × 100 mL). The organic phase was washed with water (2 × 150 mL) and a saturated aqueous solution of sodium chloride (1 × 150 mL, BDH) and then dried over magnesium sulfate (BDH). Rotary evaporation of the solvent gave tosyl-triethyleneglycol monomethyl ether as a colorless oil. Tosyl-triethyleneglycol monomethyl ether (1.0 equiv), 1,4-dioxane (400 mL, BDH), and n-octanol (1.2 equiv, either C8H17OH (BDH, >99%) or C8D17OH (CDN Isotopes), both vacuum distilled before (4) Goates, S. R.; Schofield, D. A.; Bain, C. D. Langmuir 1999, 15, 1400. (5) Binks, B. P.; Fletcher, P. D. I.; Paunov, V. N.; Segal, D. Langmuir 2000, 16, 8926. (6) Lu, J. R.; Su, T. J.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Tucker, I.; Penfold, J. J. Phys. Chem. B 1997, 101, 10332. (7) Selve, C.; Achilefu, S. J. Chem. Soc., Chem. Commun. 1990, 911. (8) Selve, C.; Achilefu, S.; Stebe, M. J.; Ravey, J. C.; Delpeuch, J. J. Langmuir 1994, 10, 2131.
10.1021/la034053g CCC: $25.00 © 2003 American Chemical Society Published on Web 06/10/2003
Notes
Langmuir, Vol. 19, No. 14, 2003 5961
use) were mixed, and finely ground potassium hydroxide (4.0 equiv, Fluka, >85%) was added with stirring. The mixture was refluxed with vigorous stirring for 24 h. The solvent was removed on a rotary evaporator, and the resulting slurry was dissolved in a minimum amount of water (∼100 mL). The aqueous solution was divided into two portions, each of which was extracted with diethyl ether (3 × 100 mL). The organic phase was washed once with a small amount of water, and the combined extracts were dried over magnesium sulfate. Removal of the solvent gave crude surfactant, which was purified by column chromatography (Si60 silica 40-63 µm, and ethyl acetate, BDH) and vacuum distillation to yield colorless liquids, which gave single spots by thin-layer chromatography (TLC) (Si60 F254, Merck). Elemental analysis and 1H and 13C NMR were consistent with the desired products. Mass spectroscopy gave no peaks for higher/lower chain homologues, confirming the surfactants were single molecular weight compounds. Ultrahigh-purity H2O (Elga UHQ) was used throughout. D2O (Aldrich, 99.9%) was used as received. The overflowing cylinder has been described in detail previously.2,9,10 The OFC in these experiments was 8 cm in diameter and fabricated from stainless steel. The flow rate of 17 cm3 s-1 was in the range where the surface expansion rate is independent of bulk flow rate.9 The volume of the OFC and pumping system was 1.6 dm3. Neutron reflection experiments were performed on the reflectometer SURF at the neutron spallation source “ISIS” (Rutherford Appleton Laboratory, Didcot, U.K.). A pulsed beam of neutrons with wavelength λ ) 0.5-6.7 Å was reflected from the flowing surface of the OFC at an angle of incidence θ ) 1.5° and detected by a time-of-flight detector. The footprint of the neutron beam on the surface of the OFC was 20 × 20 mm. Technical details may be found elsewhere.2,11 Solutions of dC8E4OMe were prepared in null reflecting water (nrw; 91.1% H2O, 8.9% D2O by weight), and all experiments were carried out at T ) 25 °C. Reflectivity profiles, R(Qz) (where Qz ) 4π sin θ/λ is the momentum transfer), were fitted with a three-layer model (air-monolayer-nrw). The thickness of the layer, τ, the scattering length density of the monolayer, ω, and the background level were free parameters. The surface excess was calculated through the relationship
Γ)
ωτ
∑c b
(1)
i i
where bi is the scattering length of atom i and ci is the number of atoms of type i in the surfactant molecule. In calculating Σcibi, we assumed an isotopic purity of 98% D. Pure D2O was used as a calibration standard in the OFC in order to determine the scale factor of the reflectometer. (D2O is a strong scatterer with a well-established reflectivity curve.) Independent measurements of the scale factor before and after the surfactant experiments agreed to within 5%. To conserve deuterated surfactant, stock solutions were diluted successively up to a maximum of 4 times. The concentration ranges prepared by successive dilution of different stock solutions were chosen to overlap in order to minimize systematic errors. Acquisition times varied from 1 h at the highest concentrations to 3 h at the lowest concentrations. Ellipsometric measurements on the OFC were carried out in Oxford on a Picometer ellipsometer (Beaglehole Instruments, Wellington, NZ) with C8E4OMe in H2O. The reported parameter is the coefficient of ellipticity, Fj, defined as the imaginary part of rp/rs at the Brewster angle, where rp and rs are the reflection coefficients for p- and s-polarized light, respectively. Ellipsometric measurements were made at the center of the OFC. Previous experiments with C16TAB suggest that the average surface excess over the central 20 mm of the cylinder differs from the value at the center by less than 1% of a monolayer.2,12 Further experimental details may be found elsewhere.2,9,10,12 (9) Manning-Benson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109. (10) Manning-Benson, S.; Bain, C. D.; Darton, R. C.; Sharpe, D.; Eastoe, J.; Reynolds, P. Langmuir 1997, 13, 5808. (11) Eastoe, J.; Rankin, A.; Wat, R.; Bain, C. D.; Styrkas, D.; Penfold, J. Langmuir, in press.
Figure 1. Surface excess, Γ, determined by neutron reflection plotted as a function of the bulk concentration, c, of dC8E4OMe. A linear fit to the data is shown: Γ/10-6 mol m-2 ) 0.93 ln(c/M) + 9.68.
Results and Discussion Relationship between Ellipticity and Surface Excess. In Figure 1, we plot experimental values of the dynamic surface excess, Γdyn, obtained by NR, as a function of surfactant concentration, c. The highest concentration (6 mM) was determined by the amount of deuterated surfactant available. Although this concentration is less than the cmc of C8E4OMe (7.4 mM), ellipsometric measurements suggest that the dynamic surface excess at 6 mM is close to the limiting surface excess at the cmc in equilibrium solutions. Near the cmc, where mass transport of the surfactant to the surface is sufficiently fast, the dynamic surface excess is close to the equilibrium value at the same bulk concentration (as deduced from ellipsometry). At low concentrations, however, the surface is far from equilibrium. Consequently, the surface excess can be varied by a factor of 5 through variation in c from 0.1 to 6 mM. For equilibrium measurements over the same range of surface excess, the bulk concentration needs to be varied by 4 orders of magnitude. The lower limit to the measurable surface excess is dictated by the reflectivity of the surfactant layer: R ∝ Γ2. dC8E4OMe has a relatively low scattering length, and the reflected signals were too weak to analyze for Γ < 1 × 10-6 mol m-2. Over the concentration range studied, the experimental values of Γ can be fitted to a straight line with high precision. The best fit parameters for Γ(c) are given in the caption to Figure 1. Ellipsometric measurements were performed on the OFC over the same range of concentrations as those studied by NR. The experimental data set, Fjdyn(c), together with the relationship Γ(c) from Figure 1, can be used to create a calibration curve, Fj(Γ), which is shown in Figure 2. The data lie on a good straight line with an intercept that nearly coincides with our measured value for the coefficient of ellipticity of pure water, Fj ) 0.38 × 10-3. Two-Layer Model. Binks et al. and Bell et al.5,13 have argued for nonionic and cationic surfactants, respectively, at the air-water interface that ellipsometric data can be explained by a two-layer model in which the polar headgroups are solvated in the aqueous phase and the hydrophobic tail groups form an isotropic layer with the (12) Bain, C. D.; Manning-Benson, S.; Darton, R. C. J. Colloid Interface Sci. 2000, 229, 247. (13) Bell, G. R.; Manning-Benson, S.; Bain, C. D. J. Phys. Chem. B 1998, 102, 218.
5962
Langmuir, Vol. 19, No. 14, 2003
Figure 2. Relationship between the coefficient of ellipticity, Fj, and the surface excess, Γ, for C8E4OMe. A linear fit to the data (excluding Γ ) 0) is shown: Fj/10-3 ) -0.29Γ/10-6 mol m-2 + 0.40.
density of bulk oil. This model generates a very nearly linear relationship between Fj and Γ.14 To check whether C8E4OMe conforms to the same model, we have estimated the coefficient of ellipticity at the highest value of surface excess measured, Γ ) 4.9 × 10-6 mol m-2. The general method of calculation has been described elsewhere.4,16,17 The dielectric constant of the hydrophobic layer ( ) 1.96) is found from the Clausius-Mossotti equation with the molar refractivity Rm ) 38.3 cm3 mol-1 and the molar volume Vm ) 156 cm3 mol-1. These values were obtained from the respective values of Rm ) 39.2 cm3 mol-1 and Vm ) 162 cm3 mol-1 for octane, derived from literature values of the refractive index and density.18 The small corrections arise from the difference in the molar volumes of a CH2 and CH3 group19 and in the molar refractivities of C-H and C-O bonds.20 The dielectric constant of the aqueous layer was found from the LorentzLorenz effective medium approximation, with the volume fraction of water φH2O ) 0.4 and the volume fraction of the polar headgroup φE4OMe ) 0.6. The results are not very sensitive to the choice of φ.4 To estimate the dielectric constant of the polar headgroup -(OC2H4)4OCH3 ( ) 2.05), we first calculated the values of Rm ) 57.5 cm3 mol-1 and Vm ) 221 cm3 mol-1 for tetraglyme [CH3(OC2H4)4OCH3] from literature data18 and then corrected these values for the molar volume (21 cm3 mol-1)19 and molar refractivity (5.6 cm3 mol-1)20 of a methyl group. The contributions of the two layers to Fj were determined from the Drude formula: Fj ) -1.064 × 10-3η, where the ellipsometric thickness η is given by η ) -1( - 1)( - 1.778)d, and the thickness of each layer, d (in Å), is calculated from Vm and Γ. The roughness contribution to Fj was estimated from the σ-1/2 scaling of the ellipticity and the values of Fj ) 0.38 (14) At low concentrations, where the thickness of the hydrophobic layer is less than the diameter of a hydrocarbon chain, one can consider the space between the chains to be filled with either water or air. The former assumption maintains an approximately linear relationship between Fj and Γ, while the latter gives more complex behavior (refs 5 and 15). (15) Casson, B. D.; Bain, C. D. J. Am. Chem. Soc. 1999, 121, 2615. (16) Knock, M. M.; Bain, C. D. Langmuir 2000, 16, 2857. (17) McKenna, C. E.; Knock, M. M.; Bain, C. D. Langmuir 2000, 16, 5853. (18) Aldrich Catalogue: Handbook of Fine Chemicals; Aldrich Chemical Co.: Milwaukee, WI, 2000. (19) Small, D. M. Physical Chemistry of Lipids; Plenum Press: New York 1986; p 207. (20) Atkins, P. W. Physical Chemistry, 3rd ed.; Oxford University Press: Oxford, 1986; T24.3.
Notes
× 10-3 and σ ) 72 mN m-1 for pure water and σ ) 28.6 mN m-1 at the cmc. The largest term in Fj is from the polar headgroup (Fj ) -1.3 × 10-3) with contributions of Fj ) -0.8 × 10-3 from the chains and Fj ) 0.6 × 10-3 from roughness. Collecting together the three terms, the twolayer model predicts Fj ) -1.5 × 10-3, which is not in very good agreement with the measured value of Fj ) -1.0 × 10-3. The discrepancy between observed and calculated values of Fj exceeds the combined calibration errors in the neutron reflection and ellipsometry experiments. There are two plausible physical explanations for this discrepancy. First, the density of the alkyl chain region may be lower than that of octane. Fj is very sensitive to the density of the hydrocarbon layer,13 and within an effective medium approximation, only a 10% decrease in density (with a commensurate 10% increase in thickness) is sufficient to bring the calculated ellipticity into agreement with measurement. Second, the monolayer may be optically anisotropic; that is, the dielectric constant takes different values perpendicular (e) and parallel (o) to the surface. Optical anisotropy generates an additional contribution to Fj that is proportional to ∆ ) e - o. If we treat the octyl chains as rigid rods, then geometric arguments suggest a mean tilt of the chains of ∼45° at Γ ∼ 5 × 10-6 mol m-2. Using literature values for the optical properties of a monolayer of dodecanol, in which the chains are oriented vertically,21 we can estimate an anisotropy ∆ ∼ 0.03 for the octyl chains, which would account for about half the discrepancy between observed and calculated values of Fj. It is therefore likely that both a reduced density and optical anisotropy contribute to the deviation from the simple two-layer model. Conclusion This study demonstrates conclusively that the coefficient of ellipticity (and by inference other ellipsometric parameters that depend linearly on the ellipsometric thickness, η) is linearly proportional to the surface excess for the nonionic surfactant C8E4OMe. This conclusion may also be inferred from the careful study of equilibrium solutions of C12E5 by Binks et al.5 It is therefore likely that linear relationships hold for both families of nonionic surfactants, just as was found previously for the homologous series of cationic CnTABs.2,3 From a practical perspective, it would be extremely useful if calibration curves of Fj(Γ) could be deduced without the necessity for measurements by NR or tensiometry over a wide range of concentrations. This study lends support to the hypothesis that the calibration function Fj(Γ) may be approximated by a straight line connecting the data points for pure water and for the surfactant at the cmc, both of which can be determined with relative ease.3 In contrast to previous studies of C12E5 and CnTABs, a two-layer model in which the hydrocarbon region has the density of bulk oil does not give very good agreement with experiment at the highest surface coverage. A small (
