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On the Analysis of Ellipsometric Measurements of Adsorption Layers at Fluid Interfaces R. Teppner, S. Bae, K. Haage, and H. Motschmann* Max-Planck Institute of Colloids and Interfaces, Am Mu¨ hlenberg, Haus 2, D-15576 Golm, Germany Received March 1, 1999. In Final Form: May 24, 1999 Ellipsometry is a well-established, nondestructive optical method for the characterization of thin films. An ellipsometric experiment yields in the thin film limit only a single parameter η, which is related to changes in the state of polarization caused by reflection. The ellipsometric quantity is only subject to certain conditions proportional to the adsorbed amount Γ. The necessary requirements leading to the proportionably are not met for adsorption layers of soluble surfactants at the air-water interface since the dielectric constants of all media are very similar. It is not possible to establish from first principles (Maxwells equations) a unique relation between state of the monolayer and η. The derived expression cannot be inverted, and it is not justified to assume a linear relation between η and the surface excess Γ. The aim of this contribution is to obtain an understanding what η represents for soluble surfactants at the air-water interface. For the purpose of this study a soluble surfactant was designed which possesses a sufficiently high hyperpolarizability to enable surface second harmonic generation (SHG) in reflection mode to be performed. Polarization dependent SHG measurements were used to determine the orientation, the surface excess, and the symmetry of the interface. These data were used to assess the meaning of ellipsometric measurements. The comparison reveals that the relation between surface coverage and ellipsometric signal is nonlinear. The ellipsometric isotherm increases at low concentration and possesses a maximum at an intermediate coverage and then even decreases with increasing surface excess. These features can be understood in terms of changes in the orientation of the aliphatic tails of the amphiphile and by the prevailing ion distribution at the interface. Ellipsometry is therefore not a suitable alternative to surface tension measurements, neutron reflectometry, or nonlinear optical investigations for the determination of the surface excess of soluble surfactants although it is convenient technique to characterize qualitatively local and temporal variations of the molecular density at fluid interfaces.
Introduction Ellipsometry is a well-established nondestructive optical method for the characterization of thin films and surfaces.1 It uses the fact that the state of polarization of the incident light is changed upon reflection at a film-covered surface. An ellipsometric measurement yields two quantities ∆ and Ψ which are sensitive to the interfacial architecture. The basic equation of ellipsometry relates both quantities with the complex reflectivity coefficient rp and rs for pˆ and sˆ-polarized light.
tan Ψei∆ ) rp/rs
(1)
The calculation of reflectivity coefficients of stratified media is straightforward and well documented in the literature. Sophisticated algorithms exist which can be easily translated into computer programs. A sound description, which also covers anisotropic media, can be found in the book of Lekner.2 The inverse problem, namely the evaluation of the film parameters such as the refractive index n or the film thickness t, is not trivial and quite frequently leads to inherent ambiguities. In favorable cases it is possible to determine the refractive index n and the layer thickness t. The accuracy which can be achieved is about 1 Å, which is rather fascinating since the wavelength of light is of the order of 5000 Å. In unfavorable cases n and t remain strongly coupled and a variety of * Corresponding author: electronic mail, Hubert.Motschmann@ mpikg-golm.mpg.de. (1) Azzam, R. M.; Bashara, N. M. Ellipsometry and Polarized Light; North Holland Publication: Amsterdam, 1979. (2) Lekner, J. Theory of Reflection; Martinus Nijhoff Publishers: Boston, 1987.
(n, t)-combinations are in complete agreement with the measurement. Hence a careful error analysis is always required. Optical techniques can be applied to a great variety of different interfaces, and they possess properties which make them appealing for the investigation of liquid-liquid or liquid-air interfaces. A recent review which discusses the potential of optical techniques is given in refs 3 and 4. Many established powerful surface analytical techniques such as high resolution electron loss spectroscopy (HREELS) rely on the scattering of charged particles and cannot be used for the investigation of the liquid-liquid or liquid-air interface for obvious reasons. As a result many investigations in this area of science5 still rely on the interpretation of surface tension measurements. For instance the surface excess of soluble surfactants is given by the Gibbs equation as the derivative of the recorded isotherm σe(c) (equilibrium surface tension σe versus bulk concentration c).6
Γ)-
∂σe 1 mRT ∂ ln c
(2)
Other quantities as for example elasticity require derivatives of higher order, which leads to increasing and inherent uncertainties. Hence the development of methods which directly measure the surface excess and layer thickness is desireable for further progress in this field. (3) Bain, C. D. Curr. Opin. Colloid Interface Sci. 1998, 3, 287. (4) Mobius, D. Curr. Opin. Colloid Interface Sci. 1996, 1, 250. (5) Mo¨hwald, H. Rep. Prog. Phys. 1993, 56, 653. (6) Adamson, A. W. Physical Chemistry of Surfaces; Wiley & Sons: New York, 1993.
10.1021/la990232f CCC: $15.00 © 1999 American Chemical Society Published on Web 08/07/1999
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The desired information can be obtained by neutron reflectometry,7 but a fancy instrumentation (neutron source) is needed. Optical experiments such as ellipsometry require only a compact laboratory setup and are easy to handle. However, the characterization of monolayers leads to some ambiguities. The presence of an organic monolayer (refractive index 1.38-1.6) with a thickness below 2.5 nm does not change the reflectivity |ri|2, and hence there are no detectable changes in Ψ. In the thin film limit the data analysis relies on a single parameter, and unfortunately there is no way to increase the number of independent measured quantities. No independent information is gained by spectroscopic ellipsometry or by a scan of the angle of incidence. Spectroscopic ellipsometric measurements yield only an estimate of the magnitude of the dispersion of the adsorption layer, which is not useful for the determination of the surface excess. The measured quantities remain strongly coupled. A sound treatment of this problem especially dedicated to monolayers at fluid interfaces is given in ref 8. If the layer thickness t is much smaller than the wavelength λ of light, it is justified to expand the complex reflectivity coefficients in a power series in terms of t/λ. The first term in this expansion describes the reflectivity properties of thin films and is also known as Drude’s equation. In the thin film it is possible to describe the reflectivity properties in terms of integral invariants. A sound description of this concept can be found in the book of Lekner.2 A uniform homogeneous layer can be completely characterized by the integral η of the dielectric constant across the interface. An ellipsometric experiment in the vicinity of the Brewster angle measures a quantity which is directly proportional to η.
η)
∫
( - 1) ( - 2) dz
(3)
A further simplification of eq 3 reveals its physical meaning. Quite often, as for example in the case of adsorption of organic compounds onto solid supports,9 2 exceeds of the monolayer while ≈ 1. Under these assumptions Drude’s equation can be further simplified:
1 - 2 η) 1
∫ ( - 1) dz
(4)
A linear relationship between and the prevailing concentration c of amphiphile within the adsorption layer are well established10
) 1 + c
d dc
(5)
This relation yields a direct proportionality between the quantity η and the adsorbed amount Γ.
η)
1 - 2 d 1 dc
∫ c dz )
1 - 2 d Γ 1 dc
(6)
(7) Purcell, I. P.; Lu, J. R.; Thomas, R. K.; Howe, A. M.; Penfold, J. Langmuir 1998, 14, 1637. (8) Reiter, R.; Motschmann, H.; Orendi, H.; Nemetz, A.; Knoll, W. Langmuir 1992, 8, 1784. (9) Kull, T.; Nylander, T.; Tiberg, F.; Wahlgren, N. Langmuir 1997, 13, 5141. (10) Motschmann, H.; Stamm, M.; Toprakcioglu, C. Macromolecules 1991, 24, 3681.
Figure 1. Chemical structure of the cationic amphiphile used for the study. Different chain lengths have been synthesized, and C12 was used as a soluble amphiphile and C20 as a waterinsoluble compound.
However, none of the used assumptions which lead to eq 6 applies for adsorption layers at the liquid-air interface. Drudes equation cannot be further simplified, and the relationship between monolayer data and recorded changes remains obscure with no further simplifications possible on the basis of first principles (solutions of Maxwell’s equations). The aim of this contribution is an investigation of the underlying relationship between the state of the monolayer and ellipsometric response for soluble surfactants at the air-water interface. The purpose of this study requires a suitable model system which can be completely characterized by independent means. We used second harmonic generation (SHG) as an independent technique to characterize the adsorption layer. SHG is a nonlinear optical technique, and as a χ(2) process it provides an inherent surface specificity.11 The SHG light is only generated within the interfacial region, and centrosymmetric media such as the bulk of a fluid do not contribute to the signal. In the case of soluble surfactants the signal is only generated by the topmost monolayer. Analysis of polarization-dependent SHG measurements yields the symmetry of the interface, the orientation, and the number density N of the amphiphile within the adsorption layer. SHG is meanwhile a well-established and powerful surface analytical tool. However, only certain molecules are suitable for SHG, and a sophisticated and expensive instrumentation is required. The experimental task therefore requires the synthesis of an amphiphile which resembles all characteristic features of soluble surfactants and in addition possesses a sufficiently high hyperpolarizability to enable SHG. Experimental Section Materials. The chemical formula of the soluble cationic amphiphile 1-dodecyl-4-dimethylaminopyridinium bromide used in this study is presented in Figure 1. The SHG activity is provided by the cationic headgroup with the dimethylamino group N(CH3)2 acting as an electron donor. Details about the synthesis, analysis, and various physical properties and can be found in ref 12. Sample Preparation. An aqueous solution of the surfactant at a concentration close to the critical micelle concentration (cmc) was prepared using bidistilled water. This solution was then purified using a fully automated device described in ref 13. The applied purification scheme ensures complete removal of any surface-active impurities by repeated cycles of (a) compression of the surface layer, (b) its removal with the aid of a capillary, (c) dilation to an increased surface area, and (d) again a formation of a new adsorption layer. These cycles are repeated until the equilibrium surface tension σe in between subsequent cycles remains constant. All trace impurities which might have an impact on the measurements are then completely removed. Solutions of different concentrations were prepared by a dilution of the stock solution. Surface Tension Measurement. Surface tension was determined by a ring tensiometer (model K10, Kru¨ss, FRG) with (11) Shen, Y. R. Annu. Rev. Phys. Chem. 1989, 40, 327. (12) Bae, S.; Haage, K.; Wantke, K.; Motschmann, H. J. Phys. Chem. B 1999, 103, 1049. (13) Lunkenheimer, K.; Pergande, H. J.; Kru¨ger, H. Rev. Sci. Instrum. 1987, 58, 2313.
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a slightly modified arrangement in order to meet the requirement imposed by surfactant solutions.14 Surface tension was recorded until a constant equilibrium value, σe, was established. The cmc was determined on the basis of the adsorption isotherm. The cmc values of the member of the homologous series follow strictly the Stauff-Klevens equation and the cmc of the C12 compound is 4.31 × 10-3 mol/L. Second Harmonic Generation. Second harmonic generation experiments were carried out in reflection mode at a fixed angle of incidence of 53°. The fundamental (λ ) 1064 nm) of an activepassive mode-locked Nd-YAG laser (PY-61, Continuum), with a pulse width of τ ) 30 ps and a repetition rate of 12.5 Hz, was used as a light source. All spurious SHG created by the optical components were removed by a visible cutoff filter (RG630, Schott) placed just in front of the sample. The frequency-doubled light generated at the interface was separated from the fundamental using an IR-cutoff filter (BG39, Schott) in conjunction with a narrow band interference filter (532 BP, Instruments S.A.) and subsequently detected by a photomultiplier (C83068, Burle) with a quantum efficiency of 15%. The signal was amplified (V5D, Fa. Seefelder Metechnik) and processed by a 500 MHz, 2 Gs/s digitizing oscilloscope (HP 54522 A, Hewlett Packard). A computer controls all vital elements of the experiment and performs also the integration of the waveform. The SHG signal of a quartz crystal was used as a reference in order to eliminate experimental errors due to intensity fluctuations. The plane of polarization of the incident beam can be rotated by a Glan laser polarizer (extinction ratio 10-6, PGL, Halle) and a low order quartz half-wave plate (∆λ ) 0.001, RLQ Halle) mounted on motordriven, computer-controlled rotary stages (M-445.21, Physik Instruments). The polarization of the reflected SHG light is analyzed using a Glan-Thomson prism (extinction ratio 10-6, Typ K, Fa. Steeg & Reuter). Ellipsometry. All relevant design features of the ellipsometer (Multiskop, Optrel, Germany) are discussed in detail in ref 15. We used the Nullellipsometer mode of the ellipsometer module in a laser, polarizer, compensator, sample, analyzer arrangement. The corresponding imaging module was used for a direct visualization of the morphology of the adsorption layer.
Results and Discussion Special care was devoted to the preparation of the samples. Due to the peculiarities of surfactant synthesis, all surfactants contain trace impurities with a stronger surface activity than the main component. These trace impurities have no impact on any of the bulk properties. However, at the air-water interface they are enriched and may dominate the properties of the interfacial region. This was first recognized by Mysels,16 and there is experimental evidence that some pecularities as for instance the frequently reported linear dependence of σe versus ln c is simply caused by impurities (see ref 17 and references therein). The purpose of our study requires the complete removal of all impurities. This was achieved by applying the above mentioned purification scheme. About 400 cycles and a total time of about 4 days were required until the desired degree of purity was achieved. All solutions were then prepared by diluting the stock solution. The equilibrium surface tension versus the bulk concentration is shown in Figure 2, and a detailed discussion of the isotherm can be found in ref 12. The model system shows all characteristic features of soluble surfactants and possesses a critical micelle concentration. The adsorption layer was further characterized by imaging ellipsometry. Imaging ellipsometry combines the high vertical sensitivity of ellipsometry with the lateral resolu(14) Lunkenheimer, K.; Miller, R. J. Colloid Interface Sci. 1989, 131, 580. (15) Harke, M.; Teppner, R.; Schulz, O.; Orendi, H.; Motschmann, H. Rev. Sci. Instrum. 1997, 68(8). (16) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 331. (17) Lunkenheimer, K.; Wedler, Ch. Tenside, Surfactants, Deterg. 1993, 30, 342.
Teppner et al.
Figure 2. Equilibrium surface tension σe of a purified aqueous solution of 1-dodecyl-4-dimethylaminopyridinium bromide as a function of the bulk concentration c. The cmc is at 4.1 × 10-3 mol/L.
tion of a light microscope and provides the means to obtain information about the morphology. The adsorption layer was homogeneous at all concentrations. The model system behaves in any respect as a classical soluble amphiphile. The headgroup of the surfactant possesses a sufficiently high hyperpolarizability to enable SHG measurements. A high value of the hyperpolarizability is observed in organic π system with electron donor or acceptor. The aliphatic chain does not contribute to the nonlinear susceptibility, and our SHG experiment is only sensitive toward the state of the headgroup. Surface second harmonic generation is a powerful method with an intrinsic surface specificity. The SHG signal is only generated within the interfacial region, and all contributions arising from the bulk are suppressed. This was also experimentally verified by the following experiments which clearly indicates that terms of higher order of the nonlinear polarization such as the quadrupolar contribution of the bulk can be neglected. The solubility of our amphiphile varies with the length of the alkyl chain. The C20-compound of the homologous series is insoluble in water and can be processed as a Langmuir layer. A monolayer of the insoluble compound was prepared using two different subphases: water and an aqueous solution of the soluble surfactants C12 slightly below the cmc. The measured SHG response turned out to be independent of the presence of the soluble C12 compound in the subphase. This demonstates that only the topmost layer contributes to the signal. A significant quadrupolar contribution to the nonlinear polarization wave would lead to major deviation since it does not obey the same selection rules as the dipolar contribution. Soluble and insoluble compound possesses the very same moiety responsible for the generation of SHG light. The insoluble compound can also be used for a proper calibration of the SHG signal to avoid complications arising from local fields. Our SHG experiment can be described in the framework of dipole approximation and combinations of various elements of the macroscopic susceptibility tensor χ(2) are measured in reflection mode. The relation between individual elements of the susceptibility tensor χ(2) and the corresponding molecular quantities is provided by the oriented gas model18,19 (18) Prasad, P.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (19) Motschmann, H.; Penner, T.; Armstrong, N.; Enzenyilimba, M. J. Phys. Chem. 1993, 97, 3933.
Adsorption Layers at Fluid Interfaces
χ(2) ∝
β ∝ N〈β〉 ∑ mol
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(7)
It states that the susceptibility χ(2) is the sum of the hyperpolarizabilities β of all molecules. This can also be expressed in terms of the number density of the SHG active molecules, N, and their corresponding orientational average. A discussion of eq 7 reveals precisely what the term surface specific means. The amphiphiles dissolved in the bulk phase are randomly distributed, and hence the orientational average leads to a vanishing susceptibility tensor. However, the amphiphiles adsorbed at the interface possess a polar ordering which leads to a nonvanishing susceptibility tensor. SHG experiments do not provide information about the geometrical dimension of the interfacial phase. In our case it was also experimentally verified that only the topmost layer is detected. SHG theory in reflection mode and data analysis is described in detail in ref 20. The general equations21 which related the SHG intensity with the properties of the sample are simplified by our experimental arrangement. The experiments reveal that the amphiphile adopts an azimuthal isotropic arrangement within the adsorption layer. The symmetry of the interface belongs to the point group C∞v. As a result most of the 27 elements of the susceptibility tensor vanish and only two numerically independent elements χ(2) remain. Furthermore the hyperpolarizability tensor of the SHG active headgroup is dominated by its βzzz component, which further simplifies the resulting equations. For our experimental situation the following relation between the intensity I2ω and Iω can be derived. For an analyzer setting at pˆ the following equation holds:
Figure 3. Polar diagram of the SHG intensity I2ω versus the plane of polarization of the linear polarized fundamental beam. The squares represent the SHG data as measured; the solid line refers to a model fit according to eq 8 and eq 9 yielding the unknown elements of the susceptibility tensor. Part a was measured at a fixed analyzer setting of A ) sˆ . Part b shows the corresponding measurement for an analyzer setting of A ) pˆ . The concentration of the solution was 4.16 × 10-3 mol/L.
The most accurate determination of the susceptibility elements is obtained by polarization-dependent measurements. The plane of polarization of the linear polarized
fundamental beam is continuously rotated, and the SHG response is measured at fixed setting of the analyzer. Figure 3 shows a representative measurement of the SHG intensity I2ω of an aqueous surfactant solution at a concentration of 4.16 × 10-3 mol/L. The squares represent the SHG data as measured; the solid line refers to a fit with the unknown elements of the susceptibility tensor being fit parameter. Figure 3a refers to an analyzer setting of A ) sˆ . The absence of sˆ-polarized second harmonic light irrespective of incident sˆ or pˆ polarization of the fundamental is in agreement with an isotropic azimuthal distribution of the molecules. Figure 3b shows the corresponding data together with the model fit for an analyzer setting at pˆpolarization. Measurements at different bulk concentrations c possess the very same features, and the analysis reveals unambiguously that the orientation of the headgroup remains nearly constant for all bulk concentrations. This implies that the orientation of the headgroup is fairly independent of the packing of the aliphatic tails. The orientation is determined by the local environment as for instance the charge distribution. The tilt angle θ was determined to be 49° being defined in a way that θ ) 0 denotes an orientation parallel to the surface normal. A careful error analysis suggests an accuracy to within (2 degrees. However, we would like to point out that this refers to the determination of absolute angles and the reader should not mix this up with the sensitivity in recording slight relative changes. A constant tilt angle over a wide range of surface concentrations appears to be peculiar but has also been reported for other soluble surfactants22 as well as for some insoluble monolayers.23 The experimental fact that there is no change in the orientational order simplifies the determination of the number density N of the surfactant within the adsorbed layer. SHG measurements with an analyzer setting at A ) sˆ depend only on the tensor element χyzy as can be
(20) Harke, M.; Ibn Elhaj, M.; Mo¨hwald, H.; Motschmann, H. Phys. Rev. E 1998, 57, 1806. (21) Hirose, C.; Akamatsu, N.; Domen, K. Appl. Spectros. 1992, 6, 1051.
(22) Hicks, J. M.; Kemnitz, K.; Eisenthal, K. B.; Heinz, T. F. J. Phys. Chem. 1986, 90, 560. (23) Berkovic, G.; Rasing, T.; Shen, Y. R. J. Opt. Soc. Am. B 1987, 4, 945.
2 2 (2) 2 I2ω ) D|(A cos2 P + C sin2 P)χ(2) zxx + B cos Pχzzz| I(ω)
(8) with
A ) [Fz(2ω)Fx(ω) - 2Fx(2ω)Fz(ω)]Fx(ω) cos2 R B ) Fz(2ω)F2z (ω) sin2 R C ) Fz(2ω)Fy2(ω) D)4
() µ0 0
3/2
ω2 tan2 R
where P is the angle denoting the polarization of the fundamental with respect to the plane of incidence, R is the angle of incidence, µ0 is the permeability constant, 0 is the permittivity constant, and Fi refers to the Fresnel factor as derived by the boundary conditions at the interfaces. The value is determined by the dielectric function of the individual layer and the angle of incidence R. The corresponding equation for an analyzer setting at sˆ reads 2 2 I2ω ) DFy2(2ω) Fy2(ω)Fz2(ω) sin2 (2P)|χ(2) yzy| I(2ω) (9)
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Figure 4. Characterization of the equilibrium properties of the adsorption layer by ellipsometry and SHG. The SHG signal
xI2ω(P)45,A)90) (circles) is proportional to the surface excess and increases monotonously with the bulk concentration. The ellipsometric quantity |∆ - ∆0| (triangles) increases at low surface coverage with the concentration of the solution and shows a maximum at an intermediate concentration far below the cmc. The inset shows a plot of the corresponding quantities. A straight line should be observed if the ellipsometric signal is proportional to the adsorbed amount which is obviously not the case. read from eq 9. The susceptibility χyzy is related by the oriented gas model eq 7 with the number density N and the orientational average of the hyperpolarizability β of the adsorbed molecules. Since the orientation of the headgroup remains constant at all bulk concentrations, the intensity reading at a selected polarization setting is directly proportional to the number density
xI2ω(P)45,A)90) ∝ χyzy ∝ N.
The solutions were then measured by ellipsometry at an angle of incidence of 56° and a fixed wavelength of 632.8 nm. Null ellipsometry was used in a polarizer, compensator, sample, analyzer arrangement, and an average of zones I and III was used for the determination of the ellipsometric angles. A multizone average is the most precise algorithm for the determination of the ellipsometric angles.1 The resolution of the setting of the rotary stages is better than 5/1000 of a degree; the extinction ratio of the polarizers is better than 10-8. All solutions were measured under the very same conditions such as temperature (20 °C) and setting of the instrument. Before each measurement the sample was allowed to equilibrate for about 15 min, and then the ellipsometric angles were recorded for about 10 min. The absence of any drift in the signal indicates that equilibrium was already achieved. For further analysis an average of 100 data was taken, and the standard deviation of repeated measurements was about 0.05°. As pointed out the square root of the SHG signal recorded at a polarizer setting of P ) 45° and an analyzer setting at A ) 90° is directly proportional to the number density of the amphiphile within the adsorption layer. It can therefore be used for a comparison with the observed changes in ∆. If, as commonly assumed, the difference in ∆ between bare and film covered surface is directly proportional to the adsorbed amount, a plot of |∆ - ∆0| versus χyzy should yield a straight line and the corresponding isotherms should possess similar features. However, the analysis of the data reveal major deviations between the two quantities. Figure 4 shows the ellipsometric signal |∆ - ∆0| (triangles) versus the bulk concentration together with the SHG signal
xI
2ω
(P)45,A)90) (circles). The concentration of all so-
Teppner et al.
lutions is below the cmc, and all measurements have been carried out in at least two independent runs. The SHG response is proportional to the adsorbed amount and increases monotonously with the bulk concentration in accordance to the Gibbs model. The ellipsometric quantity |∆ - ∆0| increases at low surface coverage with the bulk concentration. At an intermediate bulk concentration |∆ - ∆0|(c) shows a maximum. A decrease in |∆ - ∆0| is observed even though there is a continuous increase of the surface excess Γ. This clearly reveals that the ellipsometric quantity is not necessarily proportional to the adsorbed amount. Significant deviations may occur as shown for adsorption layers of soluble surfactants at the air-water interface. The model system is a typical representative of soluble amphiphiles, and therefore we anticipate that these findings hold on a more general basis. There are two remarkable features of the ellipsometric measurements which should be discussed in greater detail. First there are already significant changes in ∆ at very low bulk concentrations. Even a submonolayer coverage causes pronounced changes in the optical properties. The surface excess at a bulk concentration of c ) 2.5 × 10-4 is approximately 0.1Γ∞ as determined by SHG. Nevertheless the ∆ - ∆0 amounts already for 0.6 of the ∆∞ - ∆max. Hence the relation between Γ and the ∆ - ∆0 is nonlinear and very sensitive to the presence of amphiphile. The best models for an optical description of a submonolayer coverage are given by the effective medium approximation.24 This model yields a refractive index which is in our case basically given by the volume fraction of the amphiphile within the adsorption layer. The observed changes in ∆ are much bigger than those predicted by this model. The water molecules in the interfacial area are differently bonded and oriented compared to the bulk phase. The transition layer accounts for a nonvanishing ∆ value for the neat air-water interface. The presence of amphiphiles modifies the structure of the transition layer and leads to a specific ion distribution within the interfacial area. This influences the ellipsometric angle ∆. A further quantification of this effect by adding indifferent electrolyte was not possible since the electrolyte changes also the prevailing surface coverage and the structure of the monolayer. The second surprising peculiarity of the system is a maximum in |∆ - ∆0| at an intermediate concentration range far below the cmc. First |∆ - ∆0| increases with bulk concentration and decreases at an intermediate concentration. This observation can be semiquantitatively understood in terms of anisotropy effects. The molecules within the adsorption layer possess an orientational order, and polarization dependent SHG measurements reveal a C∞v arrangement of the amphiphiles within the adsorption layer. A proper optical model is provided by a uniaxial layer on an isotropic fluid. The complex reflectivity coefficient can again be expandend in a power series in terms of (t/λ), and the following analytical expression for the change in Delta can be retrieved.25
( )
∆ - ∆0 ) -
sin φ0 tan φ0n0 4πt × λ 1 - (n /n )2 tan2 φ 0 2 0
(
n⊥2 - n22 n02 - n22
-
(
n02 n|2 - n22
))
n|2 n02 - n22
(10)
The linear optical properties of the adsorption layer are (24) Bruggeman, D. Ann. Phys. 1935, 24, 637. (25) Dignam, M.; Moskovitts, M.; Stobie, R. Trans. Faraday Soc. 1971, 67, 3306.
Adsorption Layers at Fluid Interfaces
mainly determined by the aliphatic tail of the amphiphile. The ratio of n⊥/n| depends on the orientation of the aliphatic tails. Simulations using a set of reasonable optical constants reveal that a change in tilt of an aliphatic tail of only 15° is sufficient to account for the observed |∆ - ∆0(c)| dependence. Hence further complications in the optical description of adsorption layers arise from the prevailing anisotropy within the surface layer. Slight changes in the orientational order lead to significant changes in ∆. A more quantitative analysis requires a reduction of the number of unknown parameters by independent means. Summary and Conclusion Ellipsometry is sensitive to the prevailing interfacial architecture and even a submonolayer coverage can be optically sensed. An ellipsometric experiment yields in the thin film limit only a single parameter. This parameter is only subject to certain simplifying conditions directly proportional to the adsorbed amount, and none of the underlying assumptions are fulfilled in the case of soluble surfactants at the air-water interface. It is not possible to establish from first principles a simple and unique relation between the ellipsometric parameter and monolayer data such as thickness, orientational order, and surface excess. This problem was addressed in this
Langmuir, Vol. 15, No. 20, 1999 7007
contribution. For the purpose of this study a soluble surfactant was designed which resembles all characteristic features of a classical soluble surfactant but provides in addition a sufficiently high hyperpolarizability to enable nonlinear optical investigations to be performed. Carefully purified solutions were prepared and subsequently characterized by surface tension measurements, surface second harmonic generation and ellipsometry. SHG possesses an intrinsic surface specificity and yields the surface excess without any ambiguity. These results were used for a comparison with the ellipsometric measurements. The comparison reveals that the measured ellipsometric quantity is not proportional to the adsorbed amount. The relation between surface coverage and ellipsometric signal is nonlinear, and complication arises from the subsurface layer and the prevailing orientation of the amphiphile. Ellipsometry is therefore not a suitable alternative to surface tension measurements, neutron reflectometry, or nonlinear optical investigations to determine the surface excess, although it is a convinient technique to characterize qualitatively local and temporal variations of the molecular density at fluid interfaces. Acknowledgment. The authors thank Professor H. Mo¨hwald for stimulating discussions. LA990232F
