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Ellipsometric Characterization of Ethylene Oxide-Butylene Oxide Diblock Copolymer Adsorption at the Air-Water Interface B. Rippner Blomqvist,*,†,‡ J.-W. Benjamins,§ T. Nylander,§ and T. Arnebrant| Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden, Department of Chemistry, Surface Chemistry, Royal Institute of Technology, Drottning Kristinas va¨ g 51, SE-100 44 Stockholm, Sweden, Physical Chemistry 1, Lund University, Box 124, SE-221 00 Lund, Sweden, and Health and Society, Malmo¨ University, SE-205 06 Malmo¨ , Sweden Received December 23, 2004. In Final Form: February 14, 2005 Ellipsometry was used to determine the adsorbed layer thickness (d) and the surface excess (adsorbed amount, Γ) of a nonionic diblock copolymer, E106B16, of poly(ethylene oxide) (E) and poly(butylene oxide) (B) at the air-water interface. The results were obtained (i) by the conventional ellipsometric evaluation procedure using the change of both ellipsometric angles Ψ and ∆ and (ii) by using the change of ∆ only and assuming values of the layer thickness. It was demonstrated that the calculated surface excesses from the different methods were in close agreement, independent of the evaluation procedure, with a plateau adsorption of about 2.5 mg/m2 (400 Å2/molecule). Furthermore, the amount of E106B16 adsorbed at the air-water interface was found to be almost identical to that adsorbed from aqueous solution onto a hydrophobic solid surface. In addition, the possibility to use combined measurements with H2O or D2O as substrates to calculate values of d and Γ was investigated and discussed. We also briefly discuss within which limits the Gibbs equation can be used to determine the surface excess of polydisperse block copolymers.
Introduction The block copolymers used in the present paper consist of poly(ethylene oxide) (PEO or E) and poly(butylene oxide) (PBO or B) and belong to the same family as the widely used triblock copolymers of ethylene oxide and propylene oxide (PEO-PPO-PEO).1 The latter are known by the generic name poloxamers and are available under the trade names Synperonics or Pluronics. The PEO-PBO type polymers have been used as interesting model systems2 and are commercially available for use in a number of industrial applications. The effectiveness of block copolymers as surface-active agents at solid-liquid, air-liquid, and liquid-liquid interfaces is connected to their adsorption behavior, which therefore is of basic interest. The surface excess of adsorbed surfactants at the airwater interface can be quantitatively determined indirectly from equilibrium surface tension data by the Gibbs’ method3 or with techniques such as radioactive-labeling methods, ellipsometry, and X-ray and neutron reflection. Information about the thickness of surface layers can be obtained using ellipsometry, neutron reflectivity, and the thin-film pressure balance (TFPB or TFB) techniques. From neutron or X-ray reflection measurements, a density profile normal to the surface can be constructed, and * Corresponding author. Address: Brita Rippner Blomqvist, Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden. E-mail:
[email protected]. † Institute for Surface Chemistry. ‡ Royal Institute of Technology. § Lund University. | Malmo ¨ University. (1) Alexandridis, P.; Lindman, B. Amphiphilic Block Copolymers: Self-Assembly and Applications; Elsevier Science: Amsterdam, 2000. (2) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501527. (3) Gibbs, J. W. The Collected Works of J. W. Gibbs; Longmans, Green: New York, 1931; Vol. 1.
spectroscopic methods such as second harmonic generation (SHG) and sum frequency vibrational generation (SFG) are particularly sensitive to the orientation and conformation of surfactant and polymer molecules adsorbed at the air-water interface.4,5 In addition, infrared reflectionabsorption spectroscopy (IRRAS) has recently been used to determine the surface excess6 and for tracing conformational changes of proteins upon adsorption.7 However, many of these techniques require additional information, including modeling of the layer structure, to directly give the adsorbed amount and/or thickness, while others require access to large-scale facilities. The principal application of ellipsometry is to characterize thin films at solid substrates.8 However, there have been relatively fewer reports on the use of ellipsometry to study polymer and surfactant adsorption at the air-water interface.9-13 Apart from the flexibility of the fluid interface, another challenge with measurements on very thin, transparent films at the interface between nonabsorbing media such as water, air, or oil is that the formation of the film will mainly be observed as a change of ∆ (phase shift),5,14 while the changes in Ψ (amplitude ratio) relative to the bare (4) Lu, J. R.; Thomas, R. K.; Penfold, J. Adv. Colloid Interface Sci. 2000, 84, 143-304. (5) Bain, C. D. Curr. Opin. Colloid Interface Sci. 1998, 3, 287-292. (6) Walsh, C. B.; Wen, X. Y.; Franses, E. I. J. Colloid Interface Sci. 2001, 233, 295-305. (7) Martin, A. H.; Meinders, M. B. J.; Bos, M. A.; Stuart, M. A. C.; van Vliet, T. Langmuir 2003, 19, 2922-2928. (8) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1989. (9) ManningBenson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109-116. (10) Battal, T.; Shearman, G. C.; Valkovska, D.; Bain, C. D. Langmuir 2003, 19, 1244-1248. (11) Manning-Benson, S.; Parker, S. R. W.; Bain, C. D.; Penfold, J. 1998, 14, 990-996. (12) Reiter, R.; Motschmann, H.; Orendi, H.; Nemetz, A.; Knoll, W. Langmuir 1992, 8, 1784-1788. (13) Teppner, R.; Haage, K.; Wantke, D.; Motschmann, H. J. J. Phys. Chem. B 2000, 104, 11489-11496.
10.1021/la0468040 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/28/2005
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surface are minor. This means that the two unknown parameters, the film thickness d and its refractive index n, should be calculated from only one measured quantity (∆), which is clearly insufficient. Hence, conventional procedures for data evaluation are not obviously applicable. The aim of the present study was to characterize the adsorption of a block copolymer (E106B16) at the air-water interface by ellipsometry and to evaluate the ellipsometric method for the determination of the surface excess at the air-water interface. In this article we report on different approaches to circumvent the difficulties involved in measurements at air-aqueous interfaces. The adsorbed amount and thickness were calculated (i) by the standard ellipsometric evaluation procedure, using the measured values of ∆ and Ψ (despite small changes in Ψ), and (ii) by making assumptions about the layer thickness. An alternative approach, which we have used, is to follow, in two separate experiments, the adsorption at two substrates (H2O and D2O) of different refractive indices to obtain complementary data. In addition we discuss the interpretation of surface tension isotherms for this class of polymers at the air-aqueous interface. Experimental Section Material. The diblock copolymer E106B16 (Mw, 5990 g/mol; 80 wt % EO)15 was kindly provided by Professor Colin Booth and co-workers (University of Manchester, U.K.). The polymer was synthesized by polymerization of ethylene oxide followed by addition of 1,2-butylene oxide and polymerization to completion. The purity was analyzed with 13C NMR, and the width of the chain length distribution was analyzed by gel permeation chromatography. The molar mass ratio, Mw/Mn (polydispersity index), was 1.03.15 The critical micelle concentration (cmc) is 100-150 ppm (17-25 µM).16 The polymer sample was stored at -20 °C until used for preparation of solutions for this study. Ultrapure H2O (water) was obtained by deionization and purification by a Millipore system (Millipore Corp., Bedford, MA). D2O (heavy water) (batch no. 116A51), 99.8 at. % D, was purchased from Dr. Glaser AG, Basel, Switzerland. D2O was filtered through Sartorius MinisartN SM 17597 sterile filters (0.2 µm) to remove particles and placed under vacuum for 20 min to avoid formation of gas bubbles, which could give rise to erratic reflections. All glassware was washed with Decon90 and rinsed thoroughly with water. Stock solutions were prepared by dissolving the polymer in H2O or D2O at least 1 day before the measurement and were stored under nitrogen at room temperature until use (at most 3 days). Ellipsometry Method. Ellipsometry is an optical method that measures the change in polarization of elliptically polarized light upon reflection at a planar interface between two media. The light wave may be resolved into components parallel and normal to the plane of incidence, and the reflection causes a phase shift, ∆, between these two components, as well as a relative change in amplitude by a factor tan Ψ. Ψ and ∆ are sensitive to the presence of a surface film at the interface. In the present study, we assume that the system consists of stratified isotropic planar structures, i.e., the adsorbed molecules form a planar and parallel homogeneous film at the air-aqueous interface. The measured parameters Ψ and ∆ can be related to the overall Fresnel reflectivity coefficients8 of the parallel and perpendicular components, Rp and Rs, respectively:
F)
Rp ) tan Ψei∆ ) tan Ψ(cos ∆ + i sin ∆) Rs
(1)
Rp and Rs are functions of the wavelength of the light, λ, the (14) Antippa, A. F.; Leblanc, R. M.; Ducharme, D. J. Opt. Soc. Am. A 1986, 3, 1794-1802. (15) Kelarakis, A.; Havredaki, V.; Derici, L.; Yu, G.-E.; Booth, C.; Hamley, I. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3639-3647.
incident angle, φ, the refractive indices of the bulk media on both sides of the interface, n1 (upper medium) and n0 (substrate), and if a film is present, also the refractive index, n, and the thickness, d, of the film. Thus, by using the experimental values of Ψ and ∆ to solve the Fresnel equations, the refractive index and the thickness of a surface film can be calculated according to McCrackin et al.17 An Optrel Multiskop Ellipsometer (Optrel, Berlin, Germany), which has been described in detail elsewhere,18 was used. The instrument consists of two adjustable arms: the laser arm with the light source, a quarter wave plate, a polarizer, and a compensator; and the detector arm with an analyzer and a photo detector. The instrument was mounted on a damped optical table (High Performance Laminar Flow Isolator, RS4000, Newport, Irvine, CA) to counteract mechanical disturbances of the liquid interface caused by ambient vibrations. The wavelength of the laser beam (Nd:YAG) was 5320 Å, and the angle of incidence was set to 50.0°, which is close to the Brewster angle (53.12°, 23 °C, tan Φb ) nH2O/nair). An average of two zones was used for the determination of the ellipsometric angles ∆ and Ψ. Each reported set of ∆ and Ψ is the mean of two two-zone measurements following immediately after each other. The cell containing the solution under investigation was made of a circular glass ring (diameter ) 55 mm) mounted on a steel plate. To ensure a planar liquid interface, an assembly of a Teflon ring (hydrophobic) and a stainless steel rim (wetted by the aqueous solution) were mounted on top of the glass ring.19 To avoid problems due to evaporation of solvent, i.e., that the lightbeam diverges from the analyzer opening, a Plexiglas lid covered the measuring cell. There were apertures in the lid to allow the incident and reflected laser beam to pass. Adsorption measurements were conducted at room temperature (22.5 °C). Before each experiment, the cell was filled with an excess volume of H2O or D2O (the substrate). After 30 min the ellipsometric angles were measured, and then the surface layer was removed by using a pipet tip connected to a suction device. This cleaning procedure was repeated until the measured ∆ angle was stable and close to 180°. The ∆ and Ψ angles at the bare water surface were ∆ ) 179.846 (standard deviation (SD) ) 0.0148) and Ψ ) 5.121 (SD ) 0.0094), respectively. The corresponding values at the bare heavy water surface were ∆ ) 179.951 (SD ) 0.0564) and Ψ ) 4.978 (SD ) 0.0091). Here we note that the interface will be roughened by thermal capillary waves. Under some conditions, this effect can be measured by ellipsometry.20-22 Capillary waves depend on the interfacial tension, and in the limiting case of an interface without rigidity they will add to the Im F obtained from ellipsometry measurements, by Im Fcw as discussed by Meunier23 and Schulz et al.24
Im Fcw )
2 2 3π (n0 - nair ) 2λ xn02 + nair2
xπkT 6γ
(2)
Here n0 is the refractive index of water or D2O, λ is the wavelength of the light, k is the Boltzmann constant, T is the absolute temperature, and γ is the surface tension (nH2O ) 1.3348, nD2O ) 1.3298 and γ ) 72 mN/m at 298 K, k ) 1.381 × 10-23 J/K and λ ) 5320 Å). This will result in a calculated value of Im Fcw of 0.0007182 and 0.0007077 for H2O and D2O, respectively. This should be compared with the value of Im F obtained from ellipsometry measurements of the bare air-aqueous interface, (16) Rippner, B.; Boschkova, K.; Claesson, P. M.; Arnebrant, T. Langmuir 2002, 18, 5213-5221. (17) McCrackin, F. L.; Passaglia, E.; Stromberg, R. R.; Steinberg, H. L. J. Res. Natl. Bur. Stand., Sect. A 1963, 67, 363-377. (18) Harke, M.; Teppner, R.; Schulz, O.; Motschmann, H.; Orendi, H. Rev. Sci. Instrum. 1997, 68, 3130-3134. (19) Benjamins, J. W.; Jonsson, B.; Thuresson, K.; Nylander, T. Langmuir 2002, 18, 6437-6444. (20) Beagelhole, D. Phys. Rev. Lett. 1987, 58, 1434-1436. (21) Beagelhole, D. J. J. Phys. Chem. 1987, 91, 5091-5092. (22) Braslau, A.; Pershan, P. S.; Swislow, G.; Ocko, B. M.; Als-Nielsen, J. Phys. Rev. A 1988, 38, 2457-2470. (23) Meunier, J. J. Phys. (Paris) 1987, 48, 1819-1831. (24) Schulz, J.; Hirtz, A.; Findenegg, G. H. Physica A 1997, 244, 334-343.
Characterization of Diblock Copolymer Adsorption which amounts to 0.000241 and 0.000074 for H2O and D2O, respectively. The scattering and deviation from the theoretical ∆ of 180.000° are therefore the combined effects of capillary waves, small optical imperfections of the instrument, and infinitesimal changes of the angle of incidence (air cushion table not being perfectly horizontal). Just before starting a measurement, the volume in the cell was adjusted to obtain a planar surface and the purity of the bare substrate was checked by calculating the refractive index, n0, of the aqueous phase from the measured values of Ψ and ∆. Deviations from the theoretical values of the refractive indices of up to (0.0004 as a maximum were accepted. Then a volume of the substrate was removed, equal to the volume of polymer stock solution to be added. A measurement was started by adding the polymer (at time t ) 0) close to the bottom of the cell using a pipet and then stirring with a magnetic stirrer for 1 min. The surface was allowed to come to rest, and the first Ψ and ∆ could be recorded about 1.5-2 min after polymer addition. Investigated polymer concentrations were 5, 50, and 100 ppm (corresponding to 0.8, 8, and 17 µM). Evaluation of Ellipsometric Data. The density of the film is likely to be somewhat inhomogeneous normal to the interface.25 Since no independent information about the layer’s density profile is available, a stratified layer model with perfectly smooth interfaces and a plane parallel homogeneous film was used. Hence, the calculated thickness and refractive indices represent average values. Three approaches were used to calculate adsorbed amounts and the thickness of the adsorbed layer from the ellipsometric data. Approach 1. Values of thickness (d) and refractive index (n) of the adsorbed layer were calculated by a conventional iterative procedure26 using the measured set of both Ψ and ∆. The evaluation of data was performed by using a computer program (Ellipsometry version 1.3.1 1994-1995, based on an algorithm by McCrackin et al.17). Approach 2. A computer program (Elli version 5.2, Optrel, Germany) was used for calculation of the refractive index from the parameter δ∆ by assuming values of the layer thickness. The procedure involved entering the experimentally determined δ∆ and changing the refractive index of the film until the calculated thickness was equal to the predetermined one. The data were fitted to give a layer thickness of d ) 5, 10, or 17.5 nm. Approach 3. The thin-film approximation14 described in the Appendix was used to evaluate the data with an assumed layer thickness. Two measurements of δ∆ were available, using H2O or D2O, respectively, as substrates. In an earlier study, it was demonstrated that it is possible to combine measurements from different aqueous phases, H2O and D2O, utilizing their different refractive indices, to evaluate ellipsometry data for surfactant and polymer adsorption at the oil/aqueous interface.27 This procedure will be further analyzed in the discussion section. The simulations were performed with Mathematica 5.0 (Wolfram Research Inc., Champaign, IL) using eq 1 in the Appendix and the full expression for the reflection coefficients. The data used were n0 ) 1.3348, n1 ) 1, φ ) 50°, λ ) 5320 Å and r ) 0.255 g/mL, ν ) 0.84 mL/g. Once the thickness and the refractive index of the adsorbed layer had been determined, the adsorbed amount of E106B16 per unit area (Γ) was calculated by using Cuypers’s formula28 (see Appendix, eq 5) by using values of ν and M/A of 0.84 mL/g29 and 0.255 g/mL,30 respectively. For the purpose of comparison, we also applied De Feijter’s expression31 (see Appendix, eq 6) using a refractive index increment of 0.133 mL/mg.32 (25) Vieira, J. B.; Li, Z. X.; Thomas, R. K.; Penfold, J. J. Phys. Chem. B 2002, 106, 10641-10648. (26) McCrackin, F. L.; Colson, J. P. Natl. Bur. Stand. Publ. 1964, Publ. 256, 61-82. (27) Benjamins, J. W.; Thuresson, K.; Nylander, T. Langmuir 2004, 21, 149-159. (28) Cuypers, P. A.; Corsel, J. W.; Janssen, M. P.; Kop, J. M. M.; Hermens, W. T.; Hemker, H. C. J. Biol. Chem. 1983, 258, 2426-2431. (29) Armstrong, J. K.; Parsonage, J.; Chowdhry, B.; Leharne, S.; Mitchell, J.; Beezer, A.; Lohner, K.; Laggner, P. J. Phys. Chem. 1993, 97, 3904-3909.
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Figure 1. The increase with time of the ellipsometric angles, δ∆ (δ∆ ) ∆ - ∆bare substrate) and δΨ (δΨ ) Ψ - Ψbare substrate), during adsorption of the block copolymer E106B16 at the airwater interface. E106B16 was added at t ) 0.
Results E106B16 was adsorbed from bulk solutions of concentrations 5, 50, and 100 ppm by weight ()0.8, 8, and 17 µM), which is below or in the vicinity of the critical micelle concentration. The ellipsometric angles were measured for 3-5 h after addition of polymer to pure water (H2O). The time dependence of the changes in ∆ and Ψ with respect to their values at the bare interface (δ∆ and δΨ) is given in Figure 1. As the polymer adsorbs at the air-water interface, δ∆ increases rapidly with time and reaches a plateau within 20-30 min for the two higher concentrations. The plateau value of δ∆ was about 3.5°. As expected for the combination of a nonadsorbing thin film between nonadsorbing ambient media and substrate, δΨ is small with an increase of only 0.02-0.05°. Although the changes in Ψ are small, the effect of polymer adsorption is significant. This is inferred from the similar time dependence of δΨ and δ∆, which is particularly evident at the lowest bulk concentration (5 ppm). The experimental data were evaluated using three different methods. Refractive indices and layer thicknesses at t ) 200 min, obtained by an evaluation based on both Ψ and ∆ values, are in the range n ) 1.38-1.44 and d ) 3-10 nm, respectively (approach 1). Results obtained at the highest concentration, 100 ppm, deviate by showing lower thickness and higher refractive index of the adsorbed layer than at the other concentrations, possibly owing to lower changes and less stability in Ψ. From these results, the adsorbed amount of E106B16 per unit area (Γ) was calculated by Cuypers’s formula as illustrated in Figure 2b. The adsorption is characterized by an initial rapid change of Γ with time, when the main part of the adsorption takes place, followed by a slower adsorption rate with increasing time and surface coverage. The calculated plateau surface excess was 2.2 and 2.4 mg/m2 for the two lower concentrations and slightly lower at the highest bulk concentration. At the lowest concentration (5 ppm), which is well below cmc, the rapid initial adsorption is followed by a gradually slower increase of Γ with time. (30) Batsanov, S. S. Refractometry and Chemical Structure; Consultants Bureau: New York, 1961. (31) De Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1759-1772. (32) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Heatly, F.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1235-1242.
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Figure 2. (a) The average thickness (d) and the average refractive index (n) of the polymer film, at bulk solution concentrations of 5, 50, and 100 ppm of E106B16, as calculated from the measured values of Ψ and ∆. (b) Adsorbed amounts (Γ) of E106B16 as calculated using the n and d values from panel a.
For the purpose of comparison, we also applied De Feijter’s expression,31 which led to similar results, though the amounts adsorbed differed by ≈10%. As an example, Γ at the adsorption plateau at 50 ppm was 2.4 and 2.7 mg/m2 as obtained by Cuypers’s and De Feijter’s formulas, respectively. The differences between these approaches to calculate the amount adsorbed from ellipsometry data have been discussed by Engstro¨m and Ba¨ckstro¨m.33 Values of the film refractive indices were also calculated from the experimental δ∆ values under assumptions of the film thickness (approach 2). The data were fitted to give d ) 5, 10, or 17.5 nm, taking 17.5 nm as a possible higher limit of the layer thickness, i.e., the maximum extension of the polymer chains, based on results from a previous thin-film balance study.16 Moreover, ellipsometric characterization of an E106B16 layer at a hydrophobic (nonpolar) solid surface indicated a thickness of 5-10 nm in the concentration interval 20-50 ppm,16 which was the reason to fit the data also to 5 and 10 nm. At 50 and 100 ppm and plateau adsorption, the refractive indices computed in this way are 1.40, 1.37, and 1.36 (at adsorbed layer thicknesses of 5, 10, or 17.5 nm, respectively), while slightly lower values were obtained at 5 ppm (Figure 3ac). The evaluation procedure of ellipsometry data leads to an inverse covariance of the calculated n and d values (Appendix). This is clearly observed in Figure 3a-c, where a thicker polymer film corresponds to a lower calculated refractive index and vice versa. Applying the values calculated by this procedure to the equation derived by (33) Engstro¨m, S.; Ba¨ckstro¨m, K. Langmuir 1987, 3, 568-574.
Figure 3. The average refractive indices (n) and adsorbed amounts (Γ) calculated by using the measured δ∆ only and assuming layer thicknesses of 5, 10, or 17.5 nm for bulk solution concentrations of 5 ppm (a), 50 ppm (b), and 100 ppm (c) of E106B16.
Cuypers et al.28 gives plateau adsorbed amounts between 2.2 and 2.55 mg/m2 (Figure 3a-c). The thin-film approximation (Appendix) was also applied to calculate the amount adsorbed from δ∆ for the two substrates, H2O and D2O (approach 3). In a recent study,27 a new method was introduced to evaluate ellipsometry data for thin films at aqueous-oil interfaces based on measurements on both water and D2O and utilizing the refractive index difference between these two aqueous phases. In this approach, it was assumed either that the thickness d and the adsorbed amount or that d and the refractive index of the film were the same for the two systems (for details see ref 27). The aim here was to investigate if this method could be applied to the airaqueous interface to resolve both the thickness and the mass of the adsorbed layer in order to avoid uncertainties
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Figure 4. The amount of E106B16 adsorbed (Γ) from aqueous (H2O) solution with 5, 50, and 100 ppm of polymer. Γ was calculated from δ∆, using the thin-film approximation and assuming a film thickness of 10 nm.
due to the small changes of the Ψ angle. Although the δ∆ values are significantly higher (by approximately 0.2°) in D2O as compared to H2O, this method could not be utilized to calculate the thickness and adsorbed amount as will be discussed further in the discussion section. However, if a film thickness of 10 nm was assumed, the plateau values of Γ as calculated by the thin-film approximation were 2.38, 2.45, and 2.42 mg/m2 at 5, 50, and 100 ppm, respectively, in both D2O and H2O (Figure 4, showing the H2O case). Comparison between Different Evaluation Procedures. In Figure 5a,b, the adsorbed amounts of E106B16 at the air-water interface calculated by the different procedures described above are compared with the amount adsorbed of the same polymer from an aqueous solution onto a hydrophobic solid surface (data redrawn from ref 16). As in the case of the adsorption experiments on the air-water interface, the measurements on the solid surface were performed in situ by means of null ellipsometry. Having a closer look at the results for 5 ppm (Figure 5a), it is clear that the adsorbed amounts at the solid surface coincide remarkably well with those at the air-liquid interface. Furthermore, the different evaluation procedures (approach 1-3) result in similar amounts adsorbed. The comparison shows that the determination of Γ is rather insensitive to the evaluation method used. Further, the results strongly indicate that the amounts adsorbed at different nonpolar interfaces, the air-water and a hydrophobic solid-water interface in this case, are close, although the adsorbed amount on the solid surface is slightly higher. This implies that the packing density of the polymer is independent of the fluidity/penetrability of the interface. Discussion The surface excess of different proteins, notably the milk protein β-casein, adsorbed at the air-water interface has been determined by ellipsometry31,34-38 and has been (34) Benjamins, J.; De Feijter, J. A.; Evans, M. T. A.; Graham, D. E.; Phillips, M. C. Faraday Discuss. Chem. Soc. 1975, 59, 218-229. (35) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403-414. (36) Russev, S. C.; Arguirov, T. V.; Gurkov, T. D. Colloids Surf., B 2000, 19, 89-100. (37) Puff, N.; Marchal, R.; Aguie-Beghin, A.; Douillard, R. Langmuir 2001, 17, 2206-2212.
Figure 5. A comparison between the amounts adsorbed (Γ) at the air-water interface, as calculated by the different evaluation procedures, and at a nonpolar (hydrophobic) solid-water interface (adapted from ref 16 and recalculated with Cuypers’s formula), at (a) 5 ppm and (b) 50 ppm bulk solution concentration of E106B16. All data were obtained by ellipsometry.
found to be in good agreement with the surface excess determined by other methods such as surface radioactivity techniques34,39 as well as neutron and X-ray reflectivity.37 The adsorbed amount of surfactants6,40 has been measured by ellipsometry, and the thickness of spread layers of synthetic polymers has been calculated as a function of the surface pressure.41-44 However, the applicability of ellipsometry at the air-water interface is a matter of discussion, especially regarding the linearity or nonlinearity of the relation between the ellipsometric signal and the surface excess.5,45 In the present study, we have shown that the amount adsorbed of the studied polymer is indeed possible to determine accurately. To further elucidate our data, we simulated the expected changes in ∆ and Ψ for the studied system. The results (38) Grigoriev, D. O.; Fainerman, V. B.; Makievski, A. V.; Kragel, J.; Wustneck, R.; Miller, R. J. Colloid Interface Sci. 2002, 253, 257-264. (39) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 415-426. (40) Asnacios, A.; Langevin, D.; Argillier, J. F. Eur. Phys. J. B 1998, 5, 905-911. (41) Kawaguchi, M.; Tohyama, M.; Takahashi, A. Langmuir 1988, 4, 411-413. (42) Munoz, M. G.; Monroy, F.; Ortega, F.; Rubio, R. G.; Langevin, D. Langmuir 2000, 16, 1083-1093. (43) Motschmann, H.; Reiter, R.; Lawall, R.; Duda, G.; Stamm, M.; Wegner, G.; Knoll, W. Langmuir 1991, 7, 2743-2747. (44) Sauer, B. B.; Yu, H.; Yazdanian, M.; Zografi, G.; Kim, M. W. Macromolecules 1989, 22, 2332-2337. (45) Teppner, R.; Bae, S.; Haage, K.; Motschmann, H. Langmuir 1999, 15, 7002-7007.
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Figure 6. (a) Shows simulated values of δ∆ as a function of the layer thickness for several assumed adsorbed amounts of E106B16 at the air-water (H2O) interface. (b) Shows the change in Ψ, δΨ, for the same experiment. The parameters used were n0 ) 1.3348, n1 ) 1, φ ) 50°, λ ) 5320 Å and r ) 0.255 g/mL, ν ) 0.84 mL/g.
are presented as δ∆ and δΨ as a function of the film thickness for different Γ in Figure 6a,b, respectively. To grasp the implications of these figures, it should be remembered that in a typical ellipsometry experiment, the standard deviation of the measured ∆ value at a certain point in time is often 5-10 times higher than that of Ψ. As seen in Figure 6a, at a constant Γ, δ∆ is insensitive to changes of the layer’s thickness. Thus, even the slightest error in the measured value for δ∆, due to an instrumental inaccuracy, will lead to considerable differences between the real thickness and the value that is calculated. If we then were to try and resolve both the thickness and the adsorbed amount, using a data pair obtained by measurements in both water and D2O, according to the method described in our earlier study,27 these inaccuracies would more often than not be too large to result in a meaningful solution. Therefore we could not make use of the combined measurements in D2O and H2O to determine both the thickness and the adsorbed amount. On the other hand, the fact that δ∆ does not change much with the thickness, within physically meaningful values of the thickness, means that the observed changes in ∆ reflect the changes in adsorbed amount. In fact it has been observed that the change of Im F (imaginary part of the ellipticity coefficient
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F) and hence δ∆ (F ) tan Ψi∆, Im F ) tan Ψ sin ∆) upon surfactant adsorption at liquid interfaces is basically proportional to the change in Γ.9-11,27,46 We also note that the values for δ∆ given in Figure 6 for a certain value of Γ validate the data on amounts adsorbed obtained by approaches 1-3 above. The fact that Ψ can be measured with a higher precision than ∆ means that δΨ for the formation of the polymer layer (Figure 6b) actually is of a magnitude that is possible to measure. In fact, our recorded values of δΨ are in the same range as predicted in Figure 6b. It should therefore, for a system like this, be feasible to calculate Γ and d directly from the ∆ and Ψ values. Such an evaluation (Figure 2a) did indeed give reasonable values of the thickness. However, it is clear from Figure 6b that as the surface film becomes thinner and the amount adsorbed becomes smaller, δΨ approaches the experimental detection limit. Estimating the surface excess of block copolymers at the air-water interface commonly relies on applying the Gibbs adsorption equation,2,3 although its use, defined for the chemical potential of one component and the solvent, is erroneous in strict terms, because the polymers are polydisperse (i.e., multicomponent) by nature. Surface tension isotherms reported for both PEO-PPO and PEOPBO diblock or triblock copolymers exhibit either two or more break points along the isotherm or (at higher temperatures) a wide transition region, often over a few decades of concentration, just below the cmc, instead of one sharp inflection point.16,42,47-50 It is the highconcentration inflection point or, if only one break is present, the concentration at which the surface tension becomes constant that has been assigned to the cmc.51 Linse and Hatton51 modeled a multicomponent (Mm/Mn ) 1.2) PEO-PPO-PEO system using mean-field calculations and suggested that adsorption at low concentrations causes depletion of the bulk phase, thus leading to a break of the isotherm at the concentration when depletion no longer affects the measured surface tension. In a previous study,16 it was shown that calculations based on the slope of the E106B16 isotherm below the low-concentration break overestimate the surface excess at the air-water interface. Linse and Hatton51 suggested that the part of the surface tension isotherm between this low-concentration break and the cmc is consistent with the Gibbs equation. This could therefore be used to estimate the adsorbed amount. Their idea was applied to surface tension data of E106B16, and a surface excess of approximately 3.3 mg/m2 at the cmc was obtained.16 This agrees reasonably well with the calculated adsorbed amount, about 2.5 mg/m2 (400 Å2/ molecule, adsorption time 3 h), in the present study. Hence our results can be seen as a further confirmation of the Linse and Hatton51 model. The amount adsorbed at the air-water interface was also similar to that adsorbed from an aqueous solution onto a hydrophobic solid surface.16 Γ was almost identical at the concentration 5 ppm, whereas at 50 ppm it was somewhat higher on the solid surface. Here we note that the surface-to-volume ratios for the solid-liquid and air(46) Kapilashrami, A.; Malmsten, M.; Eskilsson, K.; Benjamins, J. W.; Nylander, T. Colloids Surf., A 2003, 225, 181-192. (47) Prasad, K. N.; Luong, T. T.; Florence, A. T.; Paris, J.; Vaution, C.; Seiller, M.; Puisieux, F. J. Colloid Interface Sci. 1979, 69, 225232. (48) Wanka, G.; Hoffman, H.; Ulbricht, W. Macromolecules 1994, 27, 4145-4159. (49) Alexandridis, P.; Athanassiou, V.; Fukuda, S.; Hatton, T. A. Langmuir 1994, 10, 2604-2612. (50) Diakova, B.; Kaisheva, M.; Platikanov, D. Colloids Surf., A 2001, 190, 61-70. (51) Linse, P.; Hatton, T. A. Langmuir 1997, 13, 4066-4078.
Characterization of Diblock Copolymer Adsorption
liquid experiments were about the same (0.4 and 0.8, respectively). Thus, effects on d and Γ due to polydispersity16,51,52 should not affect the comparison. The adsorption of nonionic polymers to hydrophobic interfaces (air, oil, or solid) is driven by hydrophobic interaction, that is an entropy-driven minimization of the water-polymer (especially the more hydrophobic PPO or PBO part) contacts. On the other hand, the plateau adsorption is limited by the adsorption barrier caused by steric repulsion between polymer molecules in the surface film. The steric repulsion is caused by loss of entropy due to increased restrictions of possible chain conformations as the area per molecule decreases. From this, there is no reason to expect the adsorption to be larger on a solid surface, but rather it could be argued that a fluid interface can harbor a larger amount because of the possibility for parts of the polymer to penetrate into the gaseous media. Indeed neutron reflection25 and mean-field calculations51 at the air-water interface have suggested a thin layer of propylene oxide from adsorbed E-P-E polymers located above the water. On the other hand, comparisons performed by force measurements (surface force apparatus and TFB) with the same nonionic block copolymer adsorbed onto a hydrophobic solid and onto the air-water interface showed a smaller range of the steric force in the latter case, which could be interpreted as an indication that Γ at the fluid interface is smaller than that at the solid.53 We should also bear in mind that the larger mobility of molecules and the surface roughness of fluid interfaces may affect the measurements. Nevertheless, our ellipsometry data indicate that the amounts adsorbed of nonionic block copolymers are independent of the penetrability of the nonpolar phase. Conclusions The present study reveals the following possibilities and limitations of ellipsometric characterization of adsorbed layers at air-aqueous interfaces: (1) Adsorbed amounts determined by two of the approaches used (determination of thickness and refractive index from changes in Ψ and ∆ and assuming a layer thickness in combination with the change of ∆) are in good agreement. (2) The determination of the adsorbed amount is rather insensitive to the assumed thickness of the layer. (3) Measurements at two air-aqueous interfaces (water and deuterated water) do not allow for the determination of both the surface excess and the thickness of the adsorbed layer with the used experimental setup and under the conditions used in the present study. Furthermore, we conclude that the ellipsometrically determined amount adsorbed corresponds well with that obtained from surface tension data applying the Gibbs equation, provided that the fitting is performed for the regime between the low-concentration inflection point nearest to the cmc and the cmc. Finally, we note that the amount adsorbed at the air-aqueous interface is in good agreement with that adsorbed at a hydrophobic solid surface. Acknowledgment. The project was financed by The Swedish Foundation for Strategic Research (SSF, The Colloid & Interface Technology program). T.A. acknowl(52) Schille´n, K.; Claesson, P. M.; Malmsten, M.; Linse, P.; Booth, C. J. Phys. Chem. B 1997, 101, 4238-4252. (53) Claesson, P. M.; Ederth, T.; Bergeron, V.; Rutland, M. W. Adv. Colloid Interface Sci. 1996, 67, 119-183.
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edges financial support from the Knowledge Foundation. T.N. acknowledges the support from the Swedish Research Council. Appendix Theory. The segment density of an adsorbed polymer film will generally decrease with distance from the interface. However, in the model the film is considered homogeneous and the calculated thickness and refractive index represent averaged values according to the expressions31
nmean )
∫0∞nx(nx - n0) dz/∫0∞(nx - n0) dz
(3)
∫0∞(nx - n0) dz/(nmean - n0)
(4)
dmean )
where n0 and nx are the refractive index of the substrate and that of the adsorbed layer, respectively. From these formulas, it follows that the average film thickness, dmean, depends on and will vary inversely with the film refractive index, nmean. Knowing the refractive index and the thickness of the film, the adsorbed amount per unit area (Γ) can be determined using different methods. The method of Cuypers et al.28 (eq 5) depends on the partial specific volume (ν) and the ratio of the molar refractivity to the molar weight (M/A ) r) of the adsorbing polymer molecules, while the expression of De Feijter et al.31 (eq 6) depends on the refractive index increment (dn/dc) for the polymer in the solvent. dn/dc is assumed linear and constant up to the concentration found in the surface film.
Γ)
0.3d(nx2 - n02) (nx2 + 2)[r(n02 + 2) - ν(n02 - 1)] Γ)
d(nx - n0) dn/dc
(5)
(6)
Because of the inverse covariation of the averaged n and d and the fact that Γ depends on the product of n and d, errors in n and d will compensate for each other in calculations of the surface excess. Thus, Γ can be determined with larger precision than n and d. For a very thin transparent film between transparent media, the formation of a film will almost entirely be reflected in a change in ∆.36 This means that only one parameter can be determined and it is difficult to establish the amount adsorbed without additional information. The problem arises when the difference between the refractive indices of the incident medium and the substrate is not large enough. Several ways to circumvent the difficulty have been proposed. Antippa et al. used multiple wavelength ellipsometry to vary the wavelength of the incident light.14 Russev et al. used different upper phases (air and oil, respectively) and calculated the refractive index and the thickness under the assumption that the adsorbed layer was not influenced by the type of hydrophobic surface.36 Walsh et al. performed the analysis with different assumptions about the layer, namely, that the layer refractive index is equal to the bulk substance index or assuming values of the maximum surface excess and
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thickness based on the molecular dimensions or on X-ray diffraction measurements.6 Another possibility is to calculate the thickness of spread layers (i.e., Γ is known) at the air-water interface by measuring δ∆ as a function of the surface concentration43,44 and by assuming values of the film refractive index.42 Evaluation Approach 3. For a thin transparent film (when d is about 100 times smaller than the wavelength, d/λ , 1), δ∆, in radians, can be expressed as a function of the light wavelength, the incident angle, the refractive indices of the media surrounding the interface, and the thickness of the interfacial film, according to eqs 7 and 8.14
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∂∆ )
4π λ
nair sin(φ) tan(φ) FX (7) nair 2 2 2 2 (nH2O - nair ) 1 tan φ nH2O
(
( ( )
2
FX ) dx nx +
nair2nH2O2 nx
2
)
)
- nair2 - nH2O2
(8)
The expression for FX (eq 8) contains all the information about the adsorbed layer. LA0468040
