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Langmuir 2003, 19, 1244-1248
Determination of the Dynamic Surface Excess of a Homologous Series of Cationic Surfactants by Ellipsometry Turgut Battal, Gemma C. Shearman, Dimitrina Valkovska, and Colin D. Bain* Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
Richard C. Darton Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom
Julian Eastoe School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom Received September 17, 2002. In Final Form: December 12, 2002 Ellipsometry is a powerful experimental technique for studying the surfaces of surfactant solutions both at and away from equilibrium. From a theoretical perspective, there is no simple relationship between ellipsometric parameters at the air-water interface and the surface excess, Γ, of the surfactant. Here we report neutron reflection measurements of the dynamic surface excess, Γdyn, of the cationic surfactants CnTAB (n ) 14, 18) in an overflowing cylinder (OFC) as a function of the bulk surfactant concentration, to complement earlier measurements on C16TAB. These results are compared with ellipsometric measurement of the coefficient of ellipticity, Fj, of the surfactant solutions in an OFC in order to generate a calibration curve Fj(Γ). For each surfactant, Fj was found to be a linear function of surface excess. For the shorter homologue, n ) 12, surface tension measurements on equilibrium solutions have been used to determine the adsorption isotherm and the surface excess was then compared with the coefficient of ellipticity. Again, the relationship between Fj and Γ is linear. A protocol is described for determining surface excesses ellipsometrically in this class of surfactants, and the errors in the procedure are quantified.
Introduction Surfactants are universally used to control the properties of liquid interfaces in man-made systems and in the natural world.1 These interfaces are frequently far from equilibrium. The behavior of surfactant solutions away from equilibrium plays a crucial role in many technological processes, including foaming, emulsification, two-phase flow, and coating.2,3 Nonequilibrium phenomena also occur in natural systems, such as lung surfactants.4 The addition of a surfactant to an aqueous solution lowers the equilibrium surface tension of the solution due to adsorption of the surfactant at the air-water interface. At thermal and chemical equilibrium, the surface tension is constant everywhere and no surface tension gradients exist. If the surface of the liquid is expanding or contracting, the surface excess of the surfactant departs from its equilibrium value, resulting in a dynamic surface tension, σdyn, that differs from the equilibrium surface tension, σe. Several techniques have been developed for the measurement of σdyn1,5,6 of which the most widely used is the * To whom correspondence should be addressed. Fax: 44 1865 275 410. E-mail:
[email protected]. (1) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990. (2) Clint, J. H. Surfactant Aggregation; Blackie: Glasgow, U.K., 1992. (3) Foam and Foam Films: Theory, Experiment, Application; Exerowa, D., Kruglyakov, P. M., Eds.; Elsevier: Amsterdam, 1997. (4) Lunkenheimer, K.; Winsel, K.; Fruhner, H.; Fang, J.; Wantke, K. D.; Siegler, K. Colloids Surf., A 1996, 114, 199. (5) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interface Transport Processes and Rheology; Butterworth-Heinemann: Boston, 1991. (6) Dunkin, S. S.; Kretzschmar, G.; Miller, R. Dynamics of Adsorption at Liquid Interfaces; Elsevier: Amsterdam, 1995.
maximum bubble pressure (MBP) method. The dynamic surface excess, Γdyn, is difficult to measure directly. Γdyn can be inferred from σdyn, but only in single-component systems and only if one assumes that Γdyn(σ) ) Γe(σ) where Γe is the surface excess at equilibrium. In this paper, we seek to develop a simple and accurate approach for determining Γdyn by ellipsometry. Ellipsometry is powerful tool for studying liquid interfaces away from equilibrium: it is sensitive, fast, noninvasive, and remote and has excellent spatial resolution. The ellipsometric parameters are determined by the structure of the adsorbed surfactant layer but are not simply related to the surface excess of a surfactant at the air-water interface; they need to be calibrated against the surface excess determined in a separate experiment. The most accurate and direct method for the quantitative determination of surface excess is neutron reflection (NR),7 but neutron reflection places stringent restrictions on the sample environment and is in any case not a practical tool for laboratory-based studies. An overflowing cylinder (OFC), however, provides a platform on which both neutron reflection and ellipsometry measurements can be conducted on an expanding liquid surface. In an OFC,8-17 the liquid is pumped vertically upward through a cylinder and allowed to flow over the horizontal rim. (7) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143. (8) Bain, C. D.; Manning-Benson, S.; Darton, R. C. J. Colloid Interface Sci. 2000, 229, 247. (9) Bergink-Martens, D. J. M.; Bisperink, C. G. J.; Bos, H. J.; Prins, A.; Zuidberg, A. F. Colloids Surf. 1992, 65, 191. (10) Bergink-Martens, D. J. M.; Bos, H. J.; Prins, A. J. Colloid Interface Sci. 1994, 165, 221.
10.1021/la026566d CCC: $25.00 © 2003 American Chemical Society Published on Web 01/22/2003
Dynamic Surface Excess of Cationic Surfactants
The surface is static at the center of the cylinder (the stagnation point) and accelerates radially outward toward the rim. In contrast to other geometries used for the measurement of dynamic interfacial properties, the OFC has a large flat surface area that is ideally suited for a range of spectroscopic and scattering measurements. In the presence of surfactant, a radial surface tension gradient arises which greatly increases the surface velocity. The surface expansion rates can be sufficiently large to produce a surface far from equilibrium. The OFC can thus be used to study both adsorption kinetics and Marangoni effects in surfactant solutions. In a previous paper,16 we reported NR and ellipsometric measurements on a member of the family of alkyltrimethylammonium bromide surfactants (CnTABs, n ) 16) in an OFC and showed that there was a linear relationship between the coefficient of ellipticity, Fj, and the surface excess. If such a relationship is general, then ellipsometry may be used to determine surface excesses in dynamic (and equilibrium) systems without recourse to separate calibration experiments for each surfactant. In this paper, therefore, we set out to determine the relationship between Fj and Γ in the homologous series of CnTABs (n ) 12, 14, 16, 18). These cationics are well suited for such studies, since, as compared with typical anionic and nonionic surfactants, they can be obtained to a high chemical purity. In part, this purity is down to the synthetic procedure, which can be performed almost exclusively in organic solvents, thereby eliminating contamination from inorganic reagents. Cationics of this kind are also highly stable to hydrolysis. Finally, there is a significant background literature of reliable data, especially neutron reflection studies.18-24 Experimental Section The NR measurements were carried out on the reflectometer “SURF” at the neutron spallation source “ISIS” (Rutherford Appleton Laboratory, Didcot, U.K.). A pulsed beam of neutrons with wavelengths λ in the range of 0.5-6.5 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. Solutions of CD3(CD2)13N+(CH3)3Br- (dC14TAB) and CD3(CD2)17N+(CH3)3Br- (dC18TAB) were prepared in null reflecting water (nrw: 91.1% H2O, 8.9% D2O by weight). The samples dC18TAB and dC14TAB were kindly provided by Dr. R. K. Thomas. Experiments with dC18TAB were performed at 35 °C to avoid crystallization of the sample. Experiments with dC14TAB were run at 25 °C. Owing to limitations on beamtime, it was only (11) Bergink-Martens, D. J. M.; Bos, H. J.; Prins, A.; Schulte, B. C. J. Colloid Interface Sci. 1990, 138, 1. (12) Eastoe, J.; Dalton, J. S. Adv. Colloid Interface Sci. 2000, 85, 103. (13) Manning-Benson, S., D. Phil. Thesis, University of Oxford, Oxford, U.K., 1998. (14) Manning-Benson, S.; Bain, C. D.; Darton, R. C.; Sharpe, D.; Eastoe, J.; Reynolds, P. Langmuir 1997, 13, 5808. (15) Manning-Benson, S.; Bain, C. D.; Darton, R. D. J. Colloid Interface Sci. 1997, 189, 109. (16) Manning-Benson, S.; Parker, S. R. W.; Bain, C. D.; Penfold, J. Langmuir 1998, 14, 990. (17) Prins, A.; Boerboom, F. J. G.; van Kalsbeek, H. K. A. I. Colloids Surf., A 1998, 143, 395. (18) Li, Z. X.; Bain, C. D.; Thomas, R. K.; Duffy, D. C.; Penfold, J. J. Phys. Chem. B 1998, 102, 9473. (19) Lu, J. R.; Hromadova, M.; Simister, E.; Thomas, R. K.; Penfold, J. Physica B (Amsterdam) 1994, 198, 120. (20) Lu, J. R.; Hromadova, M.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1994, 98, 11519. (21) Lu, J. R.; Li, Z. X.; Smallwood, J.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1995, 99, 8233. (22) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. Prog. Colloid Polym. Sci. 1993, 93, 92. (23) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1993, 97, 13907. (24) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1993, 97, 6024.
Langmuir, Vol. 19, No. 4, 2003 1245 possible to study the C18, C16, and C14 analogues by neutron reflection. The high critical micelle concentration (cmc) of C12TAB (15 mM) combined with the relatively large sample volume in the OFC (typically 1.5-2 dm3) results in a requirement for prohibitive amounts of expensive chain-deuterated surfactant. This difficulty can be ameliorated to a certain extent by the addition of electrolyte, which screens repulsions between the charged headgroups and reduces the cmc. Deuterated hydrocarbon chains scatter neutrons strongly, so the specular reflection from dCnTAB solutions in nrw is assignable to the adsorbed surfactant, superimposed on a weak background signal from incoherent scattering in the subphase. The data were obtained in the form of reflectivity profiles, R(Qz), where the momentum transfer Qz ) 4π sin θ/λ, and fitted with a three-layer model (air-monolayer-nrw) in which the thickness τ and scattering length density ω of the monolayer and the background level are free parameters. (We use ω here for the scattering length density rather than the conventional symbol F to avoid confusion with the ellipticity.) The surface excess, Γ, was then calculated from Γ ) ωτ/∑cibi, where ci is the number of atoms of type i in the molecule and bi is the scattering length of atom i. Any residual hydrogen in the dCnTAB will reduce ∑cibi and lead to a systematic underestimation in Γ. In calculating ∑cibi, we assumed an isotopic purity of 98%. Pure D2O (Fluorochem) was used as a calibration standard in the OFC to determine the instrumental scale factor. To conserve dCnTAB, solutions were prepared by successive dilution of stock solutions up to three times. Ultra-high-purity H2O (Elga) was used throughout. There are two main sources of error in the NR experiments. First, errors in the alignment of the calibration sample lead to errors in the scale factor used to normalize the reflectivity profiles from the surfactant solutions. An upper error limit of (10% in the scale factor is a conservative estimate, which in turn results in an error limit of (5% in Γ. Second, the preparation of solutions by successive dilution leads to a cumulative error in the concentrations of several percent. We have prepared several stock solutions at different concentrations, forming a matrix of concentrations following dilution, so that the systematic errors caused by successive dilution could be detected. Results suggested that errors introduced by the successive dilution method were small and can be minimized by the method followed in these experiments. Ellipsometric measurements were carried out at the Brewster angle, θB, by the phase modulation technique on a Picometer ellipsometer (Beaglehole Instruments, Wellington, New Zealand). Since ellipsometry is a convenient lab-based method, it was possible to investigate all of the CnTABs by ellipsometry. Deuterated surfactants are not required for ellipsometry; all the ellipsometry experiments were carried out on commercial protonated surfactants (Aldrich, Fluka) purified by recrystallization. The parameter reported here is the coefficient of ellipticity, Fj, defined as the imaginary part of rp/rs at θB, where rp and rs are the reflection coefficients for p- and s-polarized light, respectively. Provided that the thickness, d, of the monolayer is much less than the wavelength of light, λ, Fj is determined by a single structural parameter known as the ellipsometric thickness, η.
Fj )
π x1 + 2 η λ 1 - 2
(1)
where 1 and 2 are the dielectric constants of air and water, respectively. For an optically isotropic monolayer, which is likely to be a good assumption for the disordered films formed by CnTABs,7 η can be expressed in terms of an integral of the dielectric constant, , across the interface, known as the Drude equation:
η)
∫
( - 1)( - 2) dz
(2)
Further details of the NR experiment, ellipsometry, and the operation of the OFC have been published previously.8,14-16 We note that the presence of forced convection in the OFC significantly reduces the variability in the measurement of surface
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Langmuir, Vol. 19, No. 4, 2003
Figure 1. Surface excess, Γdyn, determined by neutron reflection as a function of the concentration of (b) dC18TAB and (0) dC14TAB in the OFC. properties caused by natural convection and impurities in equilibrium systems.
Battal et al.
Figure 2. Relationship between dynamic ellipticity and dynamic surface excess for (b) C18TAB, (O) C16TAB, and (9) C14TAB and for equilibrium ellipticity and equilibrium surface excess for (0) C12TAB. Linear fits to the data are shown. Parameters may be found in the Supporting Information.
Results The NR profiles for dC14TAB and dC18TAB in the OFC were analyzed on a single-slab model of the monolayer to obtain the surface excesses, Γdyn, shown in Figure 1. Γdyn increases with increasing concentration even above the cmc because the subsurface concentration is lower than the bulk concentration under dynamic conditions. Fitting errors, alignment errors, and dilution errors all contribute to the random variation in the data shown in Figure 1, which we estimate to be 2 × 10-7 mol m-2. Errors in the scale factor used to normalize the NR profiles will lead to a systematic error in the Γdyn scale for surfactants studied on different occasions. Previous work by Thomas and coworkers7 has established that the limiting surface coverages of CnTABs with n ) 14, 16, and 18 are the same to within experimental error. The limiting concentrations that we observe at high concentrations agree to within (5% of a monolayer. Ellipsometric measurements of the dynamic coefficient of ellipticity, Fjdyn, were obtained over the same range of concentrations studied by neutron reflection.25 A smooth curve was fitted through the experimental data to obtain Fjdyn(C), where C is the bulk concentration. From the curve of Fjdyn(C) and the experimental values of Γdyn(C) in Figure 1, we constructed a plot of Γdyn(Fjdyn) for C14TAB and C18TAB, which is shown in Figure 2 together with dynamic data on C16TAB (published previously16) and data on C12TAB that were obtained as described below. Linear fits to each set of data are shown. There are no statistically significant deviations from linearity for any of the four surfactants, and the residuals all fell within the estimated experimental error. It is worth stressing at this point that both the NR profiles and ellipsometric coefficients are determined by the structure of the outermost few nanometers of the liquid surface, which should be fully relaxed on the time scale of the OFC (>0.1 s). Thus, although the calibration curves for n ) 14, 16, and 18 have been determined under dynamic conditions, they are equally valid for equilibrium systems. (25) The precision in individual measurements of Fjdyn is very high, better than (1 × 10-5. The dominant systematic error arises from the calibration of the ellipsometer. From measurements on identically prepared surfactant solutions over a period of several years, we estimate the systematic error in Fjdyn to be
