Langmuir 2001, 17, 7529-7534
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Simultaneous Thickness and Refractive Index Determination of Monolayers Deposited on an Aqueous Subphase by Null Ellipsometry Daniel Ducharme,† Alain Tessier,*,† and Stoyan C. Russev‡ De´ partement de Chimie-Biologie, GREIB, Universite´ du Que´ bec a` Trois-Rivie` res, Trois-Rivie` res, Quebec G9A 5H7, Canada, and Department of Solid State Physics, Faculty of Physics, Sofia University, Sofia, Bulgaria, 1164 Received October 31, 2000. In Final Form: August 23, 2001 For the first time, the thickness and refractive index of monolayers at the air/water interface have simultaneously been determined by null ellipsometry. Separation of refractive index from film thickness has been achieved by highly precise measurements of the two ellipsometric angles Ψ and ∆. In the solid state, film thicknesses of arachidic acid and valine gramicidin A obtained by ellipsometry are comparable with those obtained by the X-ray techniques. For arachidic acid in the condensed state, our results suggest that only the thickness of the hydrophobic moiety is measured. When highly hydrated, the thickness of the polar headgroup is not detected. This is presumably due to its refractive index being the same as that of the bulk water; hence, the calculated film thickness corresponds to the thickness of the hydrophobic part only. As molecular area is reduced, the polar headgroup gradually loses hydration water molecules causing its refractive index profile to become different from that of the bulk water. Our results suggest that the measurable thickness of the film-forming molecules increases as the degree of dehydration of the headgroup increases.
Introduction Reflection ellipsometry is used to monitor the optical properties of surfaces. At a fixed angle of incidence (φ) and wavelength (λ), ellipsometry measures simultaneously two parameters, i.e., the angles Ψ (tangent of the angle of the ratio between the modulus of the p and s reflection coefficients) and ∆ (phase difference between the arguments of the p and s reflection coefficients). Determination of Ψ and ∆ can provide information on the refractive index (n1) and thickness (d1) of a monolayer deposited at the air/water interface.1 Although ellipsometry is a very sensitive, nondestructive method suited for the investigation of transparent monolayers on water, its use is rather limited. A plausible cause to this could be due to the classical problem of the separation of film thickness from refractive index. Both angles, Ψ and ∆, are dependent on the same parameters (n0, n1, n2, d1, φ, and λ) where n0 and n2 are the refractive indices of the ambient and subphase, respectively. Assuming that the other parameters are known, the determination of n1 and d1 requires that both Ψ and ∆ be measured. Unfortunately, for ultrathin films, ∆ is the only sensitive parameter while Ψ is sensitive only to the second order in thickness. As a monolayer is spread on an aqueous surface and compressed, the values of n1 and d1 change causing changes in Ψ and ∆. However, because of the lack of sensitivity of most ellipsometers, only changes in ∆ can be determined; variation in Ψ is too small to be measured. At the air/water interface, because the thickness of monolayers on water rarely exceeds 30 Å, which is small as compared to the wavelength of light, it has been a common practice to use the Drude approximation.2,3 † ‡
Universite´ du Que´bec a` Trois-Rivie`res. Sofia University.
(1) Azzam, R. M. N.; Bashara, N. M. Ellipsometry and Polarized Light, 1st ed.; North-Holland: Amsterdam, 1977. (2) den Engelsen, D.; de Koning, B. J. Chem. Soc., Faraday Trans. 1 1974, 70, 1603. (3) Bootsma, G. A.; Meyer, F. Surf. Sci. 1969, 14, 52.
{
tan Ψ exp(i∆) ) tan Ψ h exp(i∆ h) 1 + i
[
]}
4πd1 cos φ sin2 φ n22 G
λ (n22 - n20) (n20 sin2 φ - n22 cos2 φ)
(1)
where i ) x-1 and Ψ h and ∆ h are the values for Ψ and ∆ of the pure subphase. In the case of an isotropic nonabsorbing monolayer, G is written as
G ) n20 + n22 - n21 -
n20 n22
(2)
n21
Separating the real and imaginary parts at both sides of eq 1 leads to
δ∆ ) ∆ - ∆ h )B
[
n20
+
n22
-
n21
-
]
n20 n22 n21
(3)
where
B)
4πd1 cos φ sin2 φ n22 λ (n22 - n20) (n20 sin 2 φ - n22 cos2 φ)
(4)
and
δΨ ) Ψ - Ψ h )0
(5)
The sole measurement of δ∆ makes the separation of n1 from d1 impossible, and information relative to the optical properties of the film is lost. A common practice is to assume a value of n1 and then use the equation for δ∆ to calculate d1. However, this approach may lead to serious errors. Simulations and model calculations have also been used to explain ellipsometric film characterization.4,5 These procedures have the drawback of having too many
10.1021/la001528k CCC: $20.00 © 2001 American Chemical Society Published on Web 10/23/2001
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Langmuir, Vol. 17, No. 24, 2001
a priori model assumptions. Other envisaged solutions to characterize the film optically are to combine ellipsometry with other methods, which can provide one of the missing parameters such as surface plasmon resonance and X-ray reflectivity.6,7 However, in that perspective, ellipsometry is not that appealing. Highly precise measurements however show that the Drude approximation is not valid. Experimental results clearly show that δΨ * 0. It has been shown8,9 by a numerical inversion procedure that n1 can be separated from d1 provided precise absolute Ψ and ∆ be obtained. In addition, φ must be precisely known. The angle of incidence is one of the most important parameters and must be determined to a precision at least as good as that of the Ψ angle since film thickness is heavily dependent on φ. The inversion procedure uses the ellipsometrically measured ratios of the reflection coefficients to find unknown optical properties, i.e., film thickness and refractive index. It must be strongly emphasized that the optical constants (n1 and d1) so obtained are not adjustable parameters. Film thickness is directly obtained without any a priori model assumptions of the film under measurement. In the numerical inversion approach, film thickness and refractive index, considered as isotropic, are obtained by finding the roots of a fifth degree polynomial. The coefficients of the polynomial are determined by the angle of incidence, the refractive indices of the incident medium and subphase, and the experimental ellipsometric ratio, F (F ) tan Ψ exp(i∆). The derivation of the fifth degree polynomial equation includes the restriction that only roots with real values in both film thickness and refractive index are a physical solution. This approach to the problem gives directly the solution (n1 and d1) without the need for initial guesses or ranges. In that regard, we have constructed a highly precise automated conventional null ellipsometer capable of tracking the azimuth angles with a precision of 0.000 34°. Highly precise Ψ, ∆, and φ angles used in conjunction with the inversion equation allow us to obtain, simultaneously, the film thickness and refractive index of monolayers at the air/water interface. The best way to ensure correct calibration of the ellipsometer (methods not discussed here) and understand what is ellipsometrically measured is to compare the calculated film thickness to that reported from the wellestablished synchrotron X-ray reflectivity and surface X-ray reflectometry. For that purpose, arachidic acid10 and valine gramicidin A (VGA)7 were used. In the solid state (S state), where the polar headgroup is mainly dehydrated, film thicknesses of arachidic acid and VGA obtained by ellipsometry are similar to those obtained by the X-ray techniques. However, at a large molecular area where the polar headgroup is expected to be highly hydrated, our results relative to film thickness of arachidic acid differ from those obtained by synchrotron X-ray reflectivity. In such a case, the refractive index of the headgroup is presumably identical to that of the bulk water; hence, its thickness is not detected by ellipsometry. Limitations and sources of errors will be discussed. (4) Ishino, Y.; Ishida, H. Langmuir 1988, 4, 1341. (5) Ducharme, D.; Max, J. J.; Salesse, C.; Leblanc, R. M. J. Phys. Chem. 1990, 94, 1925. (6) Schildkraut, J. S. Appl. Opt. 1988, 27, 3329. (7) Ducharme, D.; Vaknin, D.; Paudler, M.; Salesse, C.; Riegler, H.; Mo¨hwald, H. Thin Solid Films 1996, 284-285, 90. (8) Lekner, J. Appl. Opt. 1994, 33, 5159. (9) Drolet, J. P.; Russev, S. C.; Boyanov, M. I.; Leblanc, R. M. JOSA A 1994, 11, 3284. (10) Kjaer, K.; Als-Nielsen, J.; Helm, C. A.; Tippman-Krayer, P.; Mo¨hwald, H. J. Phys. Chem. 1989, 93, 3200.
Ducharme et al.
Experimental Section The ellipsometer is a conventional PCSA null ellipsometer setup. Essentially, unpolarized light passes through a polarizer, set at angle P, that produces in-phase p and s incident waves. The light then passes through a quarter-wave plate set at angle C where the incoming components are resolved along the fast (F) and slow (S) axis of the plate. Upon reflection on the surface, both components are altered in amplitude and phase. The reflected light passes through the analyzer set at angle A before reaching the detector. The light intensity measured by the detector is the result of the combination of the p and s components and contains information about the relative phases (∆) and the reflection amplitudes (Ψ) of these components. The azimuths P and A at null are directly related to ∆ and Ψ, respectively. Each P and A azimuth is read by a hollow shaft absolute optical encoder 21 bits resolution (RCN 220, from Heidenhain Co.). Arachidic acid from Sigma, used as received, was dissolved in a 3:1 mixture of chloroform and methanol. Both solvents were of high-performance liquid chromatography grade. VGA, a gift from J. Morrel (Department of Health and Human Services, NIH, Bethesda, MD), was dissolved in chloroform. The experiments were performed on a self-made Teflon trough (70 cm × 10.4 cm × 0.5 cm) covered with stainless steel and placed on a thermostatically controlled metal base plate. The subphase temperature was regulated by a Lauda K-2/R circulator bath equipped with a PTR electronic controller (R20/2) that keeps the variation of temperature within the bath to better than (0.05 °C. Prior to each run, the trough was cleaned with a mixture of chloroform and methanol. Ultrapure water (resistivity g 18.2 MΩ cm), used as subphase, was obtained from a Barnstead NANOpure system fed with reverse osmosis water. The NANOpure system comprises an UV chamber (Pura Modular System, U.S.A.), an EPCB carbon filter, and the D3807 Barnstead cartridge combination kit, ca., one macroreticular and organic removal resin, one high capacity separate bed resin, one ultrapure mixed bed resin, and one organic scavenger followed by a 0.2 µm final filter. Glassware used for the experiments was regularly soaked in Hellmanex solutions and thoroughly rinsed with ultrapure water. Isotherms. Using an automated data acquisition system, surface pressure, and surface potential, Polarizer and Analyzer azimuths were recorded simultaneously as a function of the molecular area. The surface pressure of the monolayer was measured by the Wilhelmy hanging plate method, using a filter paper (Whatman No. 4) attached to a sensitive force transducer (R&K, Mainz, Germany). Surface potentials were measured with a 241Am radioactive electrode placed at approximately 1-2 mm above the subphase and a grounded Pt reference electrode (25 mm × 25 mm × 0.25 mm) fastened on the bottom of the trough. Prior to each run, the Pt electrode was flamed dull red. All isotherms were run at least twice with two different stock solutions. Each run was performed with a freshly prepared subphase. The water surface was suction cleaned until no rise in surface pressure was recorded on compression and the surface potential had reached a constant value. The standard spreading conditions were as follows: the solutions were spread with a microsyringe and equilibrated for 10 min before they were compressed. The monolayer area was reduced at a rate of 0.3 and 5 Å2/molecule/min for arachidic acid and VGA, respectively. Under optimum conditions, the isotherms were completely superimposable; however, typical error values were (0.5 mN/m for the surface pressure and (10 mV for the surface potential. Measurements of absolute Ψ and ∆ angles were performed in two zones, namely, zones 2 and 4.1 Compression was stopped during the measurements. Features of the ellipsometer and methods of calibration will be described in details elsewhere.
Results and Discussion The accuracy of an ellipsometer is difficult to establish. Although commercially available samples with certification data may be used, this does not ensure accuracy of the measurements. It is well-known that Ψ and ∆ (particularly Ψ) are a strong function of φ, and errors in φ will, in turn, produce errors in Ψ and ∆. The angle of incidence is usually considered as an external parameter
Thickness and Refractive Index Determination
Langmuir, Vol. 17, No. 24, 2001 7531 Table 1. Roots of the 5th Degree Polynomial Obtained for Arachidic Acid from the Ψ and ∆ Angles Measured 25 Å2/Moleculea Ψ (°)
∆ (°)
12.7958
-1.4329
roots n1
d1 (Å)
0.0187 + 0.0000i 1.5071 + 0.0000i 1.3323 + 0.0091i 1.3323 - 0.0091i 1.0419 - 0.0000i
0.2 - 0.0i 19.0 + 0.0i 886.5 + 7227.6i 13.2 - 347.4i -97.3 + 0.0i
a The parameters are φ ) 61.1910°, λ ) 6328 Å, n ) 1.0, and 0 n2 ) 1.3320.
Figure 1. Surface pressure (a) and surface potential (b) of arachidic acid on water: pH ) 5.6; t ) 20.00 ( 0.05 °C; compression speed ) 0.3 Å2/molecule/min.
to the ellipsometric measurements. Consequently, provided the certification data of the standards are correct, the tested ellipsometer will give zero error only if the ellipsometric parameters are measured with no errors and φ is precisely set to the specified value. In the investigation involving ultrathin films where ∆ is the only sensitive parameter while Ψ is sensitive only to the second order of thickness, the precise determination of φ is of paramount importance. Decoupling n1 from d1 requires almost no error in Ψ, which implies very precise determination of φ. We have found that this can be achieved if the angle of incidence is considered as an internal parameter (determined from Ψ and ∆ on water) rather than an external one (measured with goniometers). Clearly, there is a transition layer on water as shown by the nonzero ∆ value obtained on the pure subphase. However, it is unclear at this stage whether this layer affects the φ value. Arachidic Acid. Arachidic acid was spread on pure water. The surface pressure-area (π-A) isotherm shown in Figure 1a is given as a reference only. We will first discuss ellipsometric measurements performed at 25 Å2/molecule (the onset of the surface pressure) and 20 Å2/molecule (πs = 26 mN/m), respectively. Discussion relative to measurements carried out at a larger molecular area will follow. Table 1 shows the roots of the fifth degree polynomial obtained at 25 Å2/molecule. As mentioned earlier, the polynomial approach gives directly the solution without initial guesses or ranges. Only the root with real values in both d1 and n1 (n1 > 1.0) is a physical solution. The other roots will make the polynomial equal to zero but are not of physical interest. As seen in the table, there is only one n1 and d1 couple with real values (1.5071 + 0.000 0i, 19.0 + 0.0i) that satisfy the restriction imposed on the roots of the polynomial. Thus, the film thickness, d1,
calculated from the experimental Ψ, ∆, and φ values, is 19.0 Å with a refractive index of n1 ) 1.5071. The question that arises is what is ellipsometrically measured? Does the calculated thickness correspond to the total length of the molecule, or only to the hydrophobic tail, or to some combination of the hydrophilic headgroup and the hydrophobic tail? To help answer this question, our data are compared with those reported in ref 10. The total reported length of the molecule (headgroup (lH) + tail group (lT)) at 11.0 mN/m (22.7 Å2/molecule) is 25.63 Å (lH ) 4.43 Å; lT ) 21.2 Å). Although direct comparison under the same experimental conditions is not possible, film thickness obtained by ellipsometry appears smaller (19.0 ( 1.0 Å) than that obtained by the synchrotron X-ray (25.63 Å). How can we explain this difference? The difference can be ascribed either to changes in orientation of the film-forming molecules or to the hydration of the headgroup, which renders the refractive index of this moiety equal to that of the bulk water and thus not detectable by ellipsometry, or to some combination of both. It has been shown10 that between 11.0 and 25.0 mN/m the thickness of the tail region increases with decreasing area (increasing surface pressure) whereas that of the headgroup decreases. This compensation generates an overall increase in the film thickness less than 2 Å. Should a similar behavior exist between 0 and 11.0 mN/m, it is doubtful that changes in orientation of the film-forming molecules alone can explain the difference of 7 Å cited above. Furthermore, if the difference of 7 Å could be attributed to changes in orientation alone, this would imply that the total length of the molecules should be measured regardless of the hydration of the headgroup; that is, the degree of hydration would have no effect on the refractive index of that moiety. The refractive index, which is a macroscopic concept that depends on the ability of individual atoms to polarize in response to an external field, is to our knowledge still valid for submonolayer films.11 The headgroup region is known to be hydrated with a degree of hydration that varies as a function of the molecular area: more hydrated in the condensed state than in the S state.10 Then, because refractive index varies according to concentration of solution, we have no reason to believe that the headgroup of the monolayer would behave differently in the presence of varying bound water molecules. Increasing the surface pressure doubtlessly causes the thickness of the hydrocarbon tail to increase; however, the discrepancy cannot be explained only by the fact that the tail length is shorter at the onset of the surface pressure than at 11 mN/m. Hydration of the headgroup is believed to play an important role: if the polar headgroup is highly hydrated and its refractive index is equal to that of the bulk water, then its thickness will not be measured. Should (11) Bennett, H. E.; Burge, K.; Peck, L.; Bennett, J. M. J. Opt. Soc. Am. 1969, 59, 675.
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Ducharme et al. Table 2. Comparison between Synchrotron X-ray Reflectivity and Null Ellipsometry for Film Thickness of Arachidic Acid Measured at πs ) 26 mN/m ellipsometrya
synchrotron X-ray reflectivity Å 27.3 ( 0.3
Å 29.6 (
n 1.6b
1.4461 ( 0.0056
λ ) 6328 Å and t ) 20.00 ( 0.05 °C. b The standard deviation was calculated on seven different measurements made with three different stock solutions. The individual values were as follows: 30.1, 28.3, and 27.2 Å for φ ) 61.1910 and 31.3, 29.3, 31.9, and 28.8 Å for φ ) 61.2807. a
Figure 2. Variation of n1 and d1 values for arachidic acid as a function of the refractive index of the polar headgroup. The nT and dT values shown in the upper shaded slab are those obtained at 25 Å2/molecule whereas the dH value in the lower shaded slab was taken from ref 10. The angle of incidence used for the calculation is 61.2807°. Calculations with the parameters shown in the two-layer system generate Ψ and ∆ values, which are inverted to yield the n1 and d1 values in the single-layer system.
that be the case, our calculated thickness would correspond to the thickness of the hydrophobic tail, and our value of 19.0 ( 1.0 Å obtained at the onset of the surface pressure compares very well with the lT value of 21.2 Å obtained by synchrotron X-ray at 11 mN/m. Unpublished data on ellipsometric investigation of a phospholipid (dimyristoylphosphatidylcholine) show exactly the same phenomenon: the agreement beween ellipsometry and synchroton X-ray increases as the surface pressure increases. This was particularly evident through the liquid expanded state and at the onset of the S state where water molecules are squeezed out, allowing ellipsometry to measure both the tail and the headgroup. To further be convinced that the refractive index of the headgroup may strongly influence the measurable length of the molecule, let us consider the following case. From the ellipsometric point of view, a molecule made up of a hydrophobic tail and a hydrophilic headgroup corresponds to a two-layer system embedded between air and water. Assuming the refractive indices of the ambient (air) and subphase (water) are known, this two-layer system contains four unknown parameters; two of them are associated with the hydrophobic tail (nT and dT), and two others characterize the optical response of the headgroup (nH and dH). As only two independent quantities are measured (Ψ and ∆), the two-layer system cannot be treated analytically since it contains four unknown parameters. Values (n1 and d1) obtained from the fifth degree polynomial are some average quantities of the optical contribution of the headgroup and the hydrophobic tail. By using a two-layer model, we can calculate Ψ and ∆ for any value of nT, dT, nH, and dH by using ellipsometric equations. Calculation was done for nH increasing from 1.3320 to 1.5071 while keeping nT, dT, and dH at constant values of 1.507, 19, and 4.4 Å, respectively. From these calculated Ψ and ∆, we obtained n1 and d1 from solution of the fifth degree polynomial as we usually do for experimental data. Results are plotted in Figure 2. As can be seen, the calculated thickness increases as the refractive index of the polar headgroup increases. With
nH ) 1.3320, i.e., the refractive index of the bulk water, the thickness of the monolayer is 19 Å. The polar headgroup is not detected. Should the headgroup have a refractive index equal to that of the tail, the two-layer model predicts that the total thickness of the monolayer (dT + dH ) 23.4 Å) would be measured by ellipsometry. A complete interpretation of the refractive indices data obtained at this surface pressure will require more exprimental and analytical work. Measurements were then performed at =20 Å2/molecule (πs = 26 mN/m). The n1 and d1 values obtained under this condition are shown in Table 2 along with film thickness obtained by synchrotron X-ray from ref 10. An average value of 29.6 ( 1.6 Å was obtained for seven different freshly prepared monolayers. As reported,10 the total length of arachidic acid at πs is 27.3 ( 0.3 Å (lH ) 3.07 Å; lT ) 24.2 Å). At πs, the polar headgroup is associated with only one molecule of water.10 The above results (at 25 and 20 Å2/molecule) suggest that the agreement in film thickness between ellipsometry and synchrotron X-ray increases as the degree of dehydration of the headgroup increases. At this point, it is not clear why in the S state, film thickness measured by ellipsometry is slightly higher than that measured with synchrotron X-ray. Variation in angle of incidence caused by, among others, surface roughness and laser beam pointing stability could explain the discrepancy between the two methods. Film thickness is heavily dependent on the angle of incidence, e.g., a change of 0.0001° in φ can vary film thickness of arachidic acid by as much as 0.5 Å. The scattering of the data shown in Table 2 can easily be explained by the extremely high effect of the angle of incidence over film thickness and the lack of control the experimentalist may have over the above factors. However, our results clearly demonstrate the high performance of our setup. As molecular area decreases from approximately 25 to almost 20 Å2/molecule, the refractive index decreases from approximately 1.507 to 1.446. A decrease in refractive index as film density increases is certainly not an expected behavior for an isotropic film. Within this molecular area range, should the film be isotropic for a decrease in molecular area, one would expect an increase in the refractive index. However, in view of the fact that the film is in the S state and the rodlike molecules are on the average oriented close to the surface normal, the film should be considered as uniaxially anisotropic rather than isotropic as assumed in the fifth degree polynomial equation. Using our ellipsometric data (d1 ) 29.6 Å, φ ) 61.2807, n0 ) 1, and n2 ) 1.3320) and eqs 4.249 to 4.257 in ref 1 (for convenience, these equations are shown in the Appendix), calculations have been performed to obtain the refractive indices as if the monolayer were uniaxially anisotropic. We have considered the case where the optic axis is assumed to be perpendicular to the boundaries with refractive indices parallel (N1e) and perpendicular
Thickness and Refractive Index Determination
(N1o) to the optic axis. Because molecular area decreases from approximately 25 Å2/molecule at π ≈ 0-20 Å2/molecule at π ) 26 mN/m, we have assumed that as molecules are more vertically oriented N1e (perpendicular to the surface) is larger than N1o; that is, polarizability along the direction of the chain is higher than in directions normal to the chain. The film was considered isotropic at π ≈ 0. The measured n1 (1.5071) value at 25 Å2/molecule is used as the initial value (n1 ) N1o ) N1e), and then, N1o is decreased by steps of 0.0005 whereas N1e is increased by steps of 0.0005 until the generated Ψ and ∆ values become the closest possible to the experimental values of Ψ and ∆ at πs. This procedure is justified because allowance for anisotropy does not significantly change the monolayer thickness (less than 1%).12 These calculations suggest that as molecular area is reduced from 25 to 20 Å2/molecule the film-forming molecules exhibit a decrease in N1o from 1.5071 to 1.4790 and an increase in N1e from 1.5071 to 1.5358. The above N1o and N1e values are similar to the nx (1.482) and nz (1.540) values reported for the anisotropic refractive indices of arachidic acid.2 These calculations suggest that the rodlike molecules are best characterized by anisotropic refractive indices, which can be obtained from ellipsometric data alone rather than isotropic ones as directly obtained from the fifth degree polynomial. Measurements were also carried out at larger molecular areas. Between 55 and 40 Å2/molecule, the ellipsometric measurements always yielded Ψ and ∆ values identical to those measured on pure water and of course no separation of n1 from d1 was possible. The fact that ∆ is the same as on pure water is indicative of a very low surface coverage. By this, we mean that microdomains are too far apart and too diluted so that even if some of these domains are under the light beam, they are not detected because the ellipsometer does not allow spatial resolution. Light cannot resolve these particles, and the partial monolayer appears as a continuous medium with the same refractive index and density. It is interesting to compare this behavior with surface potential measurements. Figure 1b shows that upon compression ∆V remains constant and close to zero until an area is reached (= 30 Å2/molecule), after which a sudden increase in ∆V is observed. The area at which the sudden increase in ∆V occurs could correspond to the merging of the domains and has been called the critical area.13 This critical area has been claimed to occur at the packing density in which a network of hydrogen bonds is formed between the water molecules and the polar headgroup. Although not reproducible but often observed, a jump in ∆ occurred (a value different from that of water) at a molecular area close to 40 Å2/molecule. In this situation, when calculation of n1 and d1 was possible, the film thickness was approximately 20 Å and Ψ and ∆ were measured by steps of 5 down to 25 Å2/molecule. In these cases, film thickness remained constant at approximately 20 Å whereas the refractive index increased from 1.451 to 1.507. The increase in refractive index is indicative that as molecular area is decreased the fraction of covered surface increases as the closing space between domains decreases. The film has a constant thickness but an increasing density and a resultant refractive index that increases as the quantity of material in the partial monolayer changes. It is worthy to mention that in the area range the increase in refractive index as film density (12) den Engelsen, D. J. Opt. Soc. Am. 1971, 61, 1460. (13) Morgan, H.; Taylor, D. M.; Oliveira, O. N., Jr. Biochim. Biophys. Acta 1991, 1062, 149.
Langmuir, Vol. 17, No. 24, 2001 7533
Figure 3. Surface pressure of VGA on water. pH ) 5.6; t ) 20.00 ( 0.05 °C; compression speed ) 5 Å2/molecule/min. The π-A isotherm was obtained with symmetrical compression.
increases is in agreement with an isotropic behavior. Although nonreproducible at 40 Å2/molecule, ∆ was reproducible from 30 Å2/molecule downward. VGA. VGA, a hydrophobic polypeptide consisting of 15 amino acids (HCO-L-Val-Gly-L-Ala-D-Leu-L-Ala-D-ValL-Val-D-Val-L-Try-D-Leu-L-Try-D-Leu-L-Try-D-Leu-LTry-NHCH2CH2OH) is able to form a monolayer at the air/water interface. All of the side chains of VGA are lipophilic. Only the peptide moieties and the terminal ethanolamine group may be considered polar. Its structure is very different from the typical film-forming molecules of arachidic acid, and in that regard, it is a good candidate to check the applicability of the ellipsometric measurement. Moreover, it has also been investigated by X-ray reflectometry, which allows us to compare our values in film thickness. The π-A curve, shown in Figure 3, was obtained with a Wilhelmy plate centrally mounted with symmetrical compression. The isotherm has been published by several authors7,14-16 and is given as a reference only. In the present work, Ψ and ∆ were measured at approximately the same molecular areas as those reported.7 The ellipsometric results are tabulated in Table 3 and compared with those of surface X-ray reflectometry and literature data. Before the shoulder observed in the π-A curve (e.g., at π ≈ 5 mN/m), the ellipsometrically measured film thickness is approximately 10 Å. This value is the same as that obtained by X-ray reflectometry. These results suggest that at low surface pressure the VGA molecules are essentially flat with polar headgroups immersed in the water and nonpolar moieties extending upward. In the shoulder region, film thickness measured by ellipsometry (≈ 14 Å) is similar to that extracted by visible reflectivity measurements (12.5 Å).16 However, it is smaller than that obtained by X-ray reflectometry (see Table 3). It is not clear whether the difference in thickness between X-ray and ellipsometry is due to the hydration of headgroups. However, these results are clearly incompatible with the formation of multilayers. In the closed packed region, ellipsometry, X-ray reflectometry, and reflectivity measurements all give ap(14) Davion-Van Mau, N.; Daumas, P.; Lelie`vre, D.; Trudelle, Y.; Heitz, H. Biophys. J. 1987, 51, 843. (15) Tournois, H.; Gieles, P.; Demel, R.; de Gier, J.; de Kruijff, B. Biophys. J. 1989, 55, 557. (16) Dhathathreyan, A.; Baumann, U.; Mu¨ller, A.; Mo¨bius, D. Biochim. Biophys. Acta 1988, 944, 265.
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Ducharme et al. Table 3. Film Thickness of VGAa
molecular area (Å2/molecule) b
surface pressure (mN/m)
c
290 230 185 100 d
film thickness (Å)
b
c
b
≈8 ≈12 ≈15.5 ≈55
≈5
10 8.5 18 27
≈15 ≈35
refractive index
c
b and d
9.7 ( 1.8
c 1.518 ( 0.021
13.9 ( 1.6 12.5e 24.8 ( 0.5 25e
1.487 1.531
1.518 ( 0.017 1.527 ( 0.0015
a Comparaison between surface X-ray reflectometry, ellipsometry, and literature data. b Data from ref 7. c Present investigation. Calculated from δ∆ and film thickness extracted from X-ray as presented in ref 7. e Ref 16.
proximately the same film thickness (25-27 Å). Although at low molecular area, film thickness of VGA is comparable to that of arachidic acid, its refractive index is substantially higher. This is presumably due to the presence of the highly polarizable tryptophan residues. It is worth mentioning that contrary to arachidic acid, the refractive index does not decrease as molecular area is reduced. This might suggest that due to the bulky nature of the side chains of tryptophan residues, the shape of VGA is more conducive to isotropy than the rodlike molecules of arachidic acid, which are clearly anisotropic.
where r01pp, r12pp, r01ss, and r12ss are the reflection coefficients at the 0-1 (ambient-film) and 1-2 (film-subphase) interface for the p and s polarization, respectively:
r01pp )
r12pp )
N1o N1e cos φ0 - N0(N21e - N20 sin2 φ0)1/2 N1o N1e cos φ0 + N0(N21e - N20 sin2 φ0)1/2
-N1o N1e cos φ2 + N2(N21e - N22 sin2 φ2)1/2 N1o N1e cos φ2 + N2(N21e - N22 sin2 φ2)1/2
(3)
(4)
Conclusion Applied to two different systems of monolayers, this work shows that refractive index can simultaneously be separated from film thickness by ellipsometry alone. The comparison of the results with synchrotron X-ray reflectivity and surface X-ray reflectometry indicates that ellipsometry can accurately determine film thickness of monolayers at the air/water interface. Film thickness obtained by ellipsometry appears to be dependent on the degree of hydration of the polar headgroup, which in turn is a function of the physical state of the monolayer. When film-forming molecules are dehydrated, the thicknesses of the headgroup and hydrophobic tail are measured whereas if the same molecules are highly hydrated, only the hydrophobic tail is detected. In the S state, where film-forming molecules are perpendicular to the boundaries, the rodlike molecules such as those in arachidic acid are best characterized by anisotropy of the refractive indices. The values of n1 and d1 obtained from the experimental Ψ, ∆, and φ values represent some average contribution of the polar headgroup and the hydrophobic tail that have not yet been singled out. Using a homologous series of phospholipids, work is underway to estimate the contribution of the polar group separately from the hydrophobic chains. Acknowledgment. D.D. gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada and the Fonds FCAR.
r01ss )
r12ss )
Rpp )
r01pp + r12pp e
-j2βs
r01ss + r12ss e Rss ) 1 + r01ss r12ss e-j2βs
(2)
N2 cos φ2 + (N21o - N22 sin2 φ2)1/2
( )( ) d1 λ
N1o (N21e - N20 sin2 φ0)1/2 N1e
()
βs ) 2π
(5)
(6)
d1 (N21o - N20 sin2 φ0)1/2 λ
(7)
(8)
where d1 is the film thickness and λ is the wavelength of light. The ellipsometric ratio
Rpp | ) tan Ψ exp(j∆) F)| Rss
(9)
The ellipsometric angles Ψ and ∆ are given by
(1)
1 + r01pp r12pp e
-N2 cos φ2 + (N21o - N22 sin2 φ2)1/2
βp ) 2π
-j2βp -j2β p
N0 cos φ0 + (N21o - N20 sin2 φ0)1/2
where N0 and N2 are the refractive indices of the ambient and subphase, respectively, and N1o and N1e are the ordinary and extraordinary refractive indices of the film. φ0 is the angle of incidence, and φ2 is the angle of refraction in the subphase. The phase thickness (βp and βs) that appears in eqs 1 and 2 is given by
Appendix In the case of a uniaxially anisotropic film sandwiched between two isotropic media, the following reflection coeffients apply1
N0 cos φ0 - (N21o - N20 sin2 φ0)1/2
Ψ ) tan-1 |F|
(10)
∆ ) arg(F)
(11)
The substitution of eqs 3-8 into eqs 1 and 2 allows for given φ0, d1, and λ to vary the parameters N1o and N1e in order to fit the experimental Ψ and ∆. LA001528K
