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Molecular Ordering in Thin Liquid Films of Polydimethylsiloxanes G. Evmenenko,* S. W. Dugan, J. Kmetko, and P. Dutta Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208-3112 Received December 19, 2000. In Final Form: April 19, 2001 X-ray reflectivity has been used for investigations of molecular ordering in thin liquid films of polydimethylsiloxanes (PDMS) of low molecular weights deposited on a polished silicon wafer. The liquid films we studied were ∼40-90 Å thick. Evidence of molecular layering induced by geometrical confinement by a hard wall is obtained for thin films of lowest molecular weight PDMS. The positions of the secondary maxima in the Patterson functions, P(z), for these samples reveal a periodicity of about 10 Å, consistent with the size of PDMS molecules. Further increasing the molecular weight leads to suppression of P(z) oscillations, causing the electron density profile to become more uniform. For higher molecular weight PDMS, a flatlike conformation of molecules absorbed on a solid surface is observed.
Introduction The physical properties of confined liquids are different from those of the same liquids in the bulk.1 The effect of confinement on the dynamical properties of thin liquid films has been explored in the last two decades using atomic-scale measurement techniques as well as computer simulations and theoretical models.2 It has been shown that these films undergo an abrupt transition from liquidlike to solidlike behavior below a critical thickness corresponding to several molecular layers of the liquid. For example, the effective viscosity of octamethylcyclotetrasiloxane increases by 7 orders of magnitude upon confinement.3 The first surface forces apparatus (SFA) experiments established that confined fluids are strongly inhomogeneous in the vicinity of the confining surfaces, for systems both of small molecules4,5 and of long polymers.6,7 This inhomogeneity results in strong density variations normal to the wall smoothed on a molecular scale. The “wall-induced layering” (oscillatory density profile near the confining surfaces) has the same physical origin as the oscillations in the radial distribution function of simple liquids.8 The necessity of these finite-size molecules to organize in a restricted geometry diminishes the number of possible configurations in the liquid state and gives preference to more ordered structures.9 For oligomers and polymers, it can be manifested by an extended, flat conformation of the physisorbed molecules at the solid surface, as was seen for thin liquid films of fluorocarbon polymers of 5000 g/mol and higher molecular weight by atomic force microscopy and angle resolved X-ray photoelectron spectroscopy.10 * To whom correspondence should be addressed: G. Evmenenko, Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112. Phone: 847-4913477. Fax: 847-491-9982. E-mail:
[email protected]. (1) Henniker, J. C. Rev. Mod. Phys. 1949, 21, 322. (2) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607 and references therein. (3) Klein, J.; Kumacheva, E. Physica A 1998, 249, 207. (4) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. (5) Christenson, H. K. J. Chem. Phys. 1983, 78, 6906. (6) Horn, R. G.; Israelachvili, J. N. Macromolecules 1988, 21, 2836. (7) Horn, R. G.; Hirz, S. J.; Hadziioannou, G.; Frank, C. W.; Catala, J. M. J. Chem. Phys. 1989, 90, 6767. (8) Bitsanis, I.; Hadziioannou, G. J. Chem. Phys. 1990, 92, 3827. (9) Weinstein, A.; Safran, S. A. Europhys. Lett. 1998, 42, 61. (10) Mathew Mate, C.; Novotny, V. J. J. Chem. Phys. 1991, 94, 8420.
Microstructure near the surface and in thin films has played an important role in industrial applications, chemical engineering, and so forth. Information about this structure can be obtained by X-ray reflectivity measurements (XRR), which provide electron density profiles normal to the surface.11,12 The first evidence of layering in thin films induced by geometrical confinement by a hard wall obtained by XRR have been reported recently for liquid metals13,14 and normal liquids.15,16 In this work, we have used XRR to study molecular layering in thin films of polydimethylsiloxanes (PDMS) of low molecular weight. XRR data have been analyzed using a Fourier method, which is useful for analysis of reflectivity data from low-contrast layer systems.15,17-18 Experimental Section Materials. The PDMS, trimethylsiloxy terminated samples used were a commercial product of Gelest, Inc. Co. and used as received. The molecular weights Mw of the samples were 550 (DMS-TO3), 770 (DMS-TO5), and 2000 g/mol (DMS-TO12). The substrates (3 in. × 1 in. × 0.1 in.), silicon (111) with native oxide, were purchased from Semiconductor Processing, Inc. They were cleaned in a strong oxidizer, a mixture of 70% sulfuric acid and 30% hydrogen peroxide (70:30 v/v), for 45 min at 90 °C, rinsed with copious amounts of pure water (1018 MΩ cm), and stored under distilled water before use. Prior to preparation of the films, the wafers were removed from the water and blown dry under a stream of nitrogen. We spread thin films by making dilute solutions of PDMS in hexane (3-20 g/L), dipping the substrates in the solutions, and withdrawing them at a constant speed of (11) X-ray and neutron reflectivity: principles and applications; Daillant, J., Gibaud, A., Eds.; Springer: Berlin, 1999. (12) Tolan, M. X-ray Scattering from soft-matter thin films: materials science and basic research; Springer Tracts in Modern Physics, Vol. 148; Springer: Berlin, 1999. (13) Huisman, W. J.; Peters, J. F.; Zwanenburg, M. J.; de Vries, S. A.; Derry, T. E.; Abernathy, D.; van der Veen, J. F. Nature 1997, 390, 379. (14) DiMasi, E.; Tostmann, H.; Shpyrko, O. G.; Deutsch, M.; Pershan, P. S.; Ocko, B. M. J. Phys.: Condens. Matter 2000, 12, A209. (15) Doerr, A. K.; Tolan, M.; Seydel, T.; Press, W. Physica B 1998, 248, 263. (16) Yu, C.-J.; Richter, A. G.; Datta, A.; Durbin, M. K.; Dutta, P. Phys. Rev. Lett. 1999, 82, 2326. (17) Tidswell, I. M.; Osko, B. M.; Pershan, P. S.; Wasserman, S. R.; Whitesides, G. M.; Axe, J. D. Phys. Rev. B 1990, 41, 1111. (18) Seeck, O. H.; Kaendler, I. D.; Tolan, M.; Shin, K.; Rafailovich, M. H.; Sokolov, J.; Kolb, R. Appl. Phys. Lett. 2000, 76, 2713.
10.1021/la0017734 CCC: $20.00 © 2001 American Chemical Society Published on Web 06/02/2001
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1.5 mm/s to get uniform film thickness. The liquid films we studied were ∼50-90 Å thick. Methods. XRR studies were performed at the beam line ×18A (MATRIX) of the National Synchrotron Light Source using a Huber four-circle diffractometer in the specular reflection mode (i.e., incident angle is equal to exit angle). X-rays of energy E ) 10 keV (λ ) 1.24 Å) were used for these measurements. The beam size was 0.4 mm vertically and 1.5 mm horizontally. The samples were placed under helium during the measurements to reduce the background scattering from the ambient gas and radiation damage. The experiments were performed at room temperature. The off-specular background was measured and subtracted from the specular counts.
Results and Discussion X-ray specular reflectivity is determined by the density profile F(z) perpendicular to the sample surface.19 In the Born approximation, the normalized reflectivity is20
R(qz)
∫
1 ∂F(z) -izqz )| e dz|2 FSi ∂z RF(qz)
(1)
where the wave vector transfer |q| ) qz ) (4π/λ) sin θ is along the surface normal, FSi is the electron density of the semi-infinite silicon substrate, and F(z) is the electron density distribution inside the film averaged over the inplane coherence length of the X-rays. RF(qz) is the Fresnel reflectivity for an ideally flat surface of the substrate:
RF(qz) )
qz - xqz2 - qc2 qz + xqz2 - qc2
Figure 1. Patterson functions calculated from theoretical XRR data for the variable-density profiles (shown in the inset) with different oscillation amplitudes: ∆F ) 0.03 (curve 1), 0.015 (2), 0.005 (3), 0.0025 (4), and 0 (5).
(2)
where qc is the critical wave vector for total external reflection (qc ) 0.0316 Å-1 for silicon). Equation 1 is valid for angles greater than approximately twice the critical angle, where refraction effects are negligible. The refraction correction is also included by replacing qz by (qz2 qc2)1/2 in eq 1. Because of the “phase problem” of X-ray scattering, the electron density profile cannot be calculated directly from the reflectivity. However, because eq 1 can also be written in terms of a Fourier transform of a “density derivative auto-correlation”,11 the inverse Fourier transform on the normalized reflectivity is related to the corresponding onedimensional Patterson function:
( )
TF-1
R(qz)
RF(qz)
) P(z) ∝
∫
∂F(z + s) ∂F(s) ds ∂s ∂(s)
(3)
The positions of peaks in P(z) correspond to the distances between regions where the density is changing rapidly. The Patterson functions are sensitive to the relative positions of interfaces in the electron density distribution. Even a low-contrast variation in a thin liquid film leads to the appearance of small peaks in P(z). The insets of Figures 1 and 2 show different model electron density profiles assumed in 80 Å films, consisting of a single slab of average density of 〈F〉/FSi ) 0.41 except at error-function-broadened interfaces,21 plus electron density oscillations. The period of oscillations was always 10 Å. The amplitude of oscillations, ∆F ) F(z) - 〈F〉, was either constant within the film (Figure 1) or decayed according (19) Parratt, L. G. Phys. Rev. 1954, 95, 359. (20) Als-Nielsen, J. Physica 1986, 140A, 376. (21) We chose error-function-broadened interfaces such that its derivative is a Gaussian: (d〈F〉/dz) ) (-∆F/x2πσ2)e-z2/2σ2, where ∆F is the density contrast and σ is the width of the interface or root-meansquare roughness.
Figure 2. Patterson functions calculated from theoretical XRR data for the variable-density profiles (shown in the inset) with constant oscillation amplitude (∆F ) 0.03) and different decay constants: R ) 0 (1), 0.1 (2), 0.2 (3), 0.4 (4), and 0.6 (5).
to ∆F ) ∆F0 exp(-Rz) (Figure 2). The parameters describing the Si-film and film-air interfaces are identical for all density profiles: σSi-film ) 2.5 Å, σfilm-air ) 4 Å. The theoretical XRR curves for these model density profiles were calculated up to qz,max ) 4 Å-1 according to eq 1. The corresponding one-dimensional Patterson functions calculated from XRR data are presented in Figures 1 and 2. As one can see from these figures, the oscillations of P(z) corresponding to oscillations of electron density are easily visible for films with only 0.3% contrast variations about the average bulk density.22 Experimentally, in thin (∼4590 Å) liquid films of nearly spherical molecules of tetrakis-
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Figure 4. Patterson functions from the observed XRR data presented in Figure 3, shifted vertically for clarity. Figure 3. X-ray reflectivity data for thin films of different PDMS samples: filled circles, measured XRR curves; dashed lines, best fits assuming a uniform electron density film; solid lines, best fits using a variable electron density within the film.
(2-ethylhexoxy)-silane (TEHOS) on a substrate with surface roughness of 2.5 Å, density fluctuations of ∼1.5% of the average liquid density have been observed by synchrotron XRR.16 Molecular dynamics simulations predict in some cases oscillations of up to ∼50% and more for point particles at smooth surfaces.23 So, we can state that analysis of XRR data based on Fourier transformation is a very sensitive method to obtain evidence of variations in the density profile F(z) perpendicular to the sample surface. Figure 3 shows normalized reflectivity data (R/RF) from typical scans of different PDMS films. Before Fourier transforming R/RF and obtaining P(z), the experimental data were extrapolated to 4 Å-1 using a Gaussian in order to smooth the electron density profile. In addition, a Blackman window24 has been used to reduce the parasitic oscillations due to the cutoff window of the dataset, that is, qz,max - qz,min. The Patterson functions P(z) for some PDMS films are shown in Figure 4. The large primary maximum is due to the solid-liquid and liquid-gas interfaces; that is, its position indicates the overall thickness of the film. The existence of secondary maxima shows, without any model-dependent assumptions, that there are density variations inside the liquid films. The positions of the secondary maxima in the Patterson functions reveal a periodicity of 9-10 Å (samples DMSTO3 and DMS-TO5) that is consistent with the sizes of these PDMS molecules. For DMS-TO5, there is a characteristic small increase in the period of P(z) oscillations as a function of z that can be related to the larger conformational freedom in packing of molecules with (22) This value was evaluated as 〈F(z) - 〈F〉〉/〈F〉 involving all density fluctuations about 〈F〉 in the film. (23) Henderson, J. R.; van Swol, F. Mol. Phys. 1984, 51, 991. (24) Using appropriate window functions other than the rectangular window can enhance the spectrum resolution during Fourier transform. We used a Blackman window: w[n] ) 0.42 - 0.5 cos(2πn/(N - 1)) + 0.08 cos(4πn/(N - 1)), where N is a number of input data points and n is the index for a dataset. For more information, see: Elliott, D. F.; Rao, K. R. Fast transforms: algorithms, analyses, applications; Academic Press: Orlando, 1982.
Table 1. Electron Densities and Mean-Square Radii of Gyration for the PDMS Samples sample
Mw
d (g/cm3)
F0/FSi
〈r2g,0〉1/2 (Å)
DMS-TO3 DMS-TO5 DMS-TO12
550 770 2000
0.88 0.918 0.95
0.41 0.425 0.44
4.4 5.8 11.3
longer chains. Further increasing the molecular weight leads to suppression of P(z) oscillations (DMS-TO12) causing the electron density profile to become more uniform. This effect can be explained by the pronounced inherent conformational flexibility of completely inorganic main-chain backbones, -[Si-O]n-, for the polysiloxanes, which results in a high mobility of segments and the entire molecule.25 An increase of chain length causes a stronger interpenetration of the chains that suppresses inhomogeneities and results in a decrease in the amplitude of the density oscillations. The results we obtained based on analysis of Patterson functions were supported by fitting the XRR data. Dash lines in Figure 3 show best fits assuming a uniform electron density liquid film with error-function-broadened interfaces. The scattering length densities F0 were calculated from the chemical composition of the materials according to the equation F0 ) ∑ibidNA/M. Here, bi is the scattering amplitude for the i-th atom (the summation is carried out over all atoms), NA is the Avogadro number, M is the molar mass, and d is the physical density of the substance. Table 1 shows calculated electron densities of bulk materials that were used in this study. For convenience, the values are normalized to FSi ) 19.94 × 1010 cm-2 (at E ) 10 keV). In this table, the calculated unperturbed mean-square radii of gyration, 〈r2g,0〉1/2, for the PDMS molecules are presented as well. These values were calculated using the data given in Table 3 of ref 26. We first fitted the data using the traditional method, in which the liquid film is modeled as a single slab of uniform density, F0(z), with error-function-broadened interfaces, σSi-film and σfilm-air. The parameters were varied until the best fit to the observed R(qz)/RF(qz) was archived. (25) Bu¨yu¨ktanir, E. A.; Ku¨c¸ u¨kyavuz, Z. J. Polym. Sci., Polym. Phys. Ed. 2000, 38, 2678. (26) Edwards, C. J. C.; Stepto, R. F. T.; Semlyen, J. A. Polymer 1980, 21, 781.
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Figure 5. Electron density profiles for different PDMS films calculated from the variable-density fits.
The deviations from the experimental data are easily visible especially for DMS-TO3 and DMS-TO5 samples. Failure to fit the data well assuming a uniform density film and the presence of secondary maxima in the Patterson function imply that electron density between two interfaces should be written as F(z) ) F0(z) + ∆F(z), where F0(z) is a constant density (set to the nominal bulk value) and ∆F(z) represents small deviations from the uniform density. For fitting, we used exponentially decaying variations of ∆F(z) superimposed on an average bulk density of the corresponding samples (Table 1). The period of oscillations was about 9-10 Å as estimated from P(z), and the width of the interfaces of the density slices within the film were fixed as 2.5 Å. By varying the oscillation amplitude and decay constant, we have obtained good fits to our data (solid lines in Figure 3). Electron density distributions calculated from the variable-density fits are shown in Figure 5. All evidence of molecular layering was obtained repeatedly for DMS-TO3 and DMS-TO5 samples at different thicknesses (∼40-90 Å) showing that the results are reproducible. We can conclude that this ordering is inherent in low molecular weight PDMS thin films absorbed on flat surfaces. For better observation of
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molecular layering of the PDMS samples, the solid-liquid interface width σSi-film should not be more than 2.5-3 Å; the density variations are significantly damped at higher surface roughness, and this is consistent with what has been reported for TEHOS films.16 The polar component of the PDMS molecule, the Si-O group, has weak adhesive ability. However, one can assume that the presence of a number of such groups in a polymer chain has to result in the formation of a stable physical bond between molecules and the hydroxylated surface of the Si substrate. This interaction leads to a flatlike conformation for high molecular weight PDMS molecules perpendicular to the substrate surface. Some evidence of such ordering is obtained for DMS-TO12 films. The period of less pronounced maxima in the Patterson function for these samples is 12-15 Å, and fitting of XRR curve gives a period of 13 Å, which is less than expected from the molecular size for an unperturbed conformation of DMS-TO12 molecules (∼double the radius of gyration, see Table 1). This result indicates that the conformation of PDMS molecules closest to the substrate is compressed toward the interface. For PDMS of higher molecular weight (Mw ) 1.6 × 104 g/mol) a recent NMR study shows the uniaxial chain segments ordering in a polymer film, even in the absence of specific interactions imposed by the surfaces.27 Conclusions Evidence of molecular layering is obtained by synchrotron X-ray reflectivity for thin films of lowest molecular weight PDMS absorbed on a solid substrate. Patterson functions calculated directly from the XRR data and comparison of calculated reflectivity from different models reveal a periodicity of about 10 Å, consistent with the size of the PDMS molecules. Increasing the molecular weight leads to the suppression of density oscillations, causing the electron density profile to become more uniform. A flatlike conformation of PDMS molecules absorbed on a solid surface is observed for these samples. Acknowledgment. We are grateful to Dr. C.-J. Yu for his helpful discussion and technical assistance. This work was supported by the U.S. National Science Foundation under Grant No. DMR-9978597 and was performed at beam line X18A of the National Synchrotron Light Source, which is supported by the U.S. Department of Energy. LA0017734 (27) Rivillon, S.; Auroy, P.; Deloche, B. Phys. Rev. Lett. 2000, 84, 499.
