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Polymer film dynamics using X-ray photon correlation spectroscopy
Materials Science and Engineering C 24 (2004) 11 – 14 www.elsevier.com/locate/msec
Polymer film dynamics using X-ray photon correlation spectroscopy Hyunjung Kim a,*, A. Ru¨hm b, L.B. Lurio c, J.K. Basu d, J. Lal e, S.G.J. Mochrie f, S.K. Sinha g,h a
Department of Physics, Sogang University, Seoul 121-742, South Korea b Max-Planck-Institut fu¨r Metallforschung, Stuttgart, Germany c Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA d Materials Research Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USA e Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, IL 60439, USA f Departments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USA g Department of Physics, University of California San Diego, La Jolla, CA 92093, USA h LANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract A new method of X-ray photon correlation spectroscopy (XPCS) is applied for probing the dynamics of surface height fluctuations as a function of lateral length scale in supported polymer films. The short wavelength and slow time scales characteristic of XPCS extend the phase space accessible to scattering studies beyond some restrictions by light and neutron. Measurements were carried out on polystyrene films of thicknesses ranging from 84 to 333 nm at temperatures above the PS glass transition temperature. We present the experimental verification of the theoretical predictions for the thickness, wave vector and temperature dependence of the capillary wave relaxation times for supported polymeric films above the glass transition temperature. D 2003 Elsevier B.V. All rights reserved. Keywords: X-ray photon correlation spectroscopy; X-ray scattering; Polymer films; Dynamics
1. Introduction The glass transition is one of the least-well-understood phenomena in physics. Many experimental and theoretical investigations [1] have turned to polymers to study this transition. Many aspects of the conformation and dynamics of polymer chains in thin polymer films are also not well understood from a basic point of view. In this work, we applied a new method of X-ray photon correlation spectroscopy (XPCS) [2] for probing the dynamics of surface height fluctuations as a function of lateral length scale. This emerging technique applies the principles of dynamic light scattering in the X-ray regime. The short wavelength and slow time scales characteristic of XPCS extend the phase space accessible to scattering studies beyond some restrictions by light and neutron. The motivation of this work was the fact although the surface modes of viscoelastic liquid films were predicted [3,4] to be strongly overdamped modes with relaxation times
* Corresponding author. Tel.: +82-2-705-8431; fax: +82-2-701-8431. E-mail address: [email protected] (H. Kim). 0928-4931/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msec.2003.09.038
determined by viscosity, surface tension, film thickness and wave number, there had been no experimental tests of how these theories might apply to thin films, and particularly to thin polymer films. This question is especially interesting in the context of recent experiments indicating that the glass transition temperature near surface is lower than in the bulk [5]. Among the proposed explanations for this effect is the notion that a surface layer having low viscosity exists even at temperatures below glass transitions of bulk [6– 11]. We also studied the question of viscosity inhomogeneities in polymer films using our experimental techniques.
2. Experimental Polystyrene (PS) films were prepared by spin-casting onto optically-flat silicon substrates, which were previously cleaned by Pirhana etch for removing residual organics. Molecular weight (Mw) of PS is 123 kg/mol (Mw/Mn) = 1.08. The samples were then annealed in vacuum for 12 h at 150 jC to ensure complete solvent removal. The thicknesses of the PS films were from 84
12
H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
Fig. 1. The schematic diagram of the experimental setup for XPCS in reflectivity.
to 333 nm. Films were mounted in a temperature controlled sample chamber whose vacuum space (~10-3) was integrated with the vacuum of the X-ray beamline. The XPCS experiments were performed at Sector 8-ID at the Advanced Photon Source (APS) and employed monochromatic radiation with an X-ray energy of 7.66 keV. The experimental geometry is illustrated schematically in Fig. 1. By arranging for the X-ray incidence angle (0.14j) to lie below the critical angle for total external reflection (0.16j), we were able to restrict the X-ray penetration into the film to a depth of f 9 nm, far thinner than any of the films studied here. Thus, scattering from the film – substrate interface is negligible, and only fluctuations at the polymer/vacuum interface are probed. Moreover, with X-rays it is possible to access larger in-plane wave vectors (out to 10-2 nm-1 in these experiments) than can be easily achieved with optical methods. The off-specular diffuse scattering of the rough polymer surface was recorded with a direct-illumination charge-coupled device (CCD) camera located 3545 mm downstream of the sample. The beam dimensions were 20 20 Am2, comparable to the X-ray coherence lengths of 7 and 90 Am in the horizontal and vertical directions, respectively. As a result, the polymer surface is partially coherently illuminated, giving rise to a speckled scattering pattern, which varies in time as the surface modes experience random thermal fluctuations. The normalized intensity –intensity time autocorrelation function, g2, is calculated by g2 ðq; tÞ ¼
hIðq; tVÞIðq; t þ tVÞi hIðq; tVÞi2
3. Results and discussions The relaxation data that were collected were consistent with the single-exponential decay of strongly overdamped surface capillary waves. Figs. 2(a) and (b) show the best fit relaxation time constants (shown in symbols) a function of in-plane wave vector ( qO) at three different temperatures for the 177-nm-thick film and at T = 160 jC for films of thickness 84, 177 and 333 nm. The lines correspond to least-squares fits based on the theory below. From the theory
ð1Þ
where I(q, tV) is the scattering intensity at wave vector transfer q at time tV. The angular brackets in Eq. (1) refer to averages over time tV and t denotes delay time. The relaxation time constant can be extracted from the intensity correlation function of speckled pattern. We calculate the normalized intensity autocorrelation of sequential two-dimensional scattering patterns pixel-by-pixel. This is followed by an appropriate averaging over all pixels corresponding to the same narrow range of qO . To avoid X-ray sample damage, the X-ray exposure of any position on the sample was limited to about 10 min, after which time the sample was shifted to illuminate a fresh area.
Fig. 2. Measured time constant (s) vs. in-plane wave vector ( qN) (a) for 177 nm-thick films at different temperatures and (b) at T = 160 jC for films of thickness 84, 177 and 333 nm. The lines correspond to least-squares fits shown in Eq. (2).
H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
[4] of the dynamics of capillary waves on the thin viscous liquid films, we have earlier deduced [12] the following expression for the relaxation time s for capillary waves in the overdamped regime: sc2gðcosh2 ðqN hÞ þ ðqN hÞ2 ÞÞ=½cqN ðsinhðqN hÞÞ coshðqN hÞ ðqN hÞ
ð2Þ
where g is the viscosity, c is the surface tension and h is the thickness. In Eq. (2), s/h is solely a function of qNh and directly proportional to the ratio g/c. In Fig. 3, we plotted the quantity s/h as a function of qNh for different film thicknesses at 150 jC shown as symbols. The data from different samples collapse form a single curve, confirming the anticipated scaling with film thicknesses. This scaling were also confirmed at 160 and 170 jC. From the excellent agreement between the experimental data and theory (shown as line (1)), the ratio g/c can be determined. Using the known (bulk) surface tension of PS [13] at each temperature, we obtained the viscosity of PS supported films. The values of the viscosity obtained at different temperatures show good agreement with those of bulk PS [14] within the accuracy of the measurements [12]. It was also possible to set the limits on the extent to which viscosity inhomogeneities in the film were present. A
13
Navier-Stokes model was used to calculate relaxation times for a film with two layers having different viscosities but the same density and no interfacial tension. We calculated the s/h as a function of qNh for two-layer model with a surface layer of thickness 10 nm having 10 times less than the bulk viscosity (line (2) in Fig. 3) and 1000 times less than that (line (3)). This comparison represents the limit of accuracy of our measurements and thus, we were able to rule out a surface layer thicker than 10 nm having one-tenth of the bulk viscosity.
4. Conclusions We have measured the relaxation times of overdamped capillary waves for thin polystyrene films of molecular weight 123,000 at various temperatures above the glass transition using XPCS technique. We also verified scaling relations for s as a function of wave vector and film thickness as predicted from the theory of such capillary waves. We have obtained the values of viscosity in supported films using the results and bulk surface tensions. They are in good agreement with the measured bulk values interpolated to the molecular weight of 123,000. The calculation of the capillary wave relaxation times for inhomogeneous thin films with two-layer model gives the limit of existence of surface layer with a viscosity less than the bulk viscosity. The polymer surface dynamics
Fig. 3. Comparison between the data at 150 jC (circles) and various model curves. The solid line (1) corresponds to Eq. (2). The inset shows the schematic diagram for each calculation curve for inhomogeneous films according to the two-layer model described in the text. The total film thickness is 80 nm. Line (1) (solid line) was calculated as homogeneous film. Line (2) (dashed line) was calculated with a surface layer of thickness 10 nm having 10 times less than the measured viscosity and line (3) (dotted line) was with a surface layer 1000 times less than the measured one.
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H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
data provide a starting point for investigating even thinner films and temperatures closer to the glass transition temperature.
Acknowledgements The use of Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109ENG-38 and Sector 8-ID is supported by the DOE Facilities Initiative Program DE-FG02-96ER45593 and NSERC. Work at MIT and Yale was supported by the NSF (DMR 0071755). Work was also partly supported by NSF (DMR0209542). H.K. thanks the support from Sogang University Research Grants in 2003 and the grant from the contribution of Advanced Backbone IT Technology Development Project (IMT2000-B3-2) of the Ministry of Information and Communication.
References [1] K.L. Ngai, G.B. Wright (Eds.), Relaxations in complex systems, J. Non-Cryst. Solids 235 – 237 (1998) 1 – 799. [2] D. Lumma, L.B. Lurio, S.G.J. Mochrie, M. Sutton, Rev. Sci. Instrum. 71 (2000) 3274. [3] J.L. Harden, H. Pleiner, P.A. Pincus, J. Chem. Phys. 94 (1991) 5208. [4] J. Ja¨ckle, J. Phys., Condens. Matter 10 (1998) 7121. [5] J.A. Forrest, R.A.L. Jones, in: A. Karim, S. Kumar (Eds.), Polymer Surfaces Interfaces and Thin Films, World Scientific, Singapore, 2000, p. 251. [6] J.L. Keddie, R.A.L. Jones, R.A. Cory, Europhys. Lett. 27 (1994) 59. [7] G.B. DeMaggio, W.E. Frieze, D.W. Gidley, M. Zhu, H.A. Hristov, A.F. Yee, Phys. Rev. Lett. 78 (1997) 1524. [8] S. Kawana, R.A.L. Jones, Phys. Rev. 63 (2001) 21501. [9] A.M. Mayes, Macromolecules 27 (1994) 3114. [10] P.G. de Gennes, Eur. Phys. J. 2 (2000) 201. [11] J.D. McCoy, J.G. Curro, J. Chem. Phys. 116 (2002) 9154. [12] H. Kim, A. Ru¨hm, L.B. Lurio, J.K. Basu, J. Lal, S.G.J. Mochrie, S.K. Sinha, Phys. Rev. Lett. 90 (2003) 68302. [13] S. Wu, in: J. Brandrup, E.H. Immergut, E.A. Grulke (Eds.), Polymer Handbook, Wiley, New York, 1999, p. VI-525. [14] D.J. Plazek, V.M. O’Rourke, J. Polym. Sci., Part A-2 9 (1971) 209.
Polymer film dynamics using X-ray photon correlation spectroscopy Hyunjung Kim a,*, A. Ru¨hm b, L.B. Lurio c, J.K. Basu d, J. Lal e, S.G.J. Mochrie f, S.K. Sinha g,h a
Department of Physics, Sogang University, Seoul 121-742, South Korea b Max-Planck-Institut fu¨r Metallforschung, Stuttgart, Germany c Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA d Materials Research Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USA e Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, IL 60439, USA f Departments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USA g Department of Physics, University of California San Diego, La Jolla, CA 92093, USA h LANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract A new method of X-ray photon correlation spectroscopy (XPCS) is applied for probing the dynamics of surface height fluctuations as a function of lateral length scale in supported polymer films. The short wavelength and slow time scales characteristic of XPCS extend the phase space accessible to scattering studies beyond some restrictions by light and neutron. Measurements were carried out on polystyrene films of thicknesses ranging from 84 to 333 nm at temperatures above the PS glass transition temperature. We present the experimental verification of the theoretical predictions for the thickness, wave vector and temperature dependence of the capillary wave relaxation times for supported polymeric films above the glass transition temperature. D 2003 Elsevier B.V. All rights reserved. Keywords: X-ray photon correlation spectroscopy; X-ray scattering; Polymer films; Dynamics
1. Introduction The glass transition is one of the least-well-understood phenomena in physics. Many experimental and theoretical investigations [1] have turned to polymers to study this transition. Many aspects of the conformation and dynamics of polymer chains in thin polymer films are also not well understood from a basic point of view. In this work, we applied a new method of X-ray photon correlation spectroscopy (XPCS) [2] for probing the dynamics of surface height fluctuations as a function of lateral length scale. This emerging technique applies the principles of dynamic light scattering in the X-ray regime. The short wavelength and slow time scales characteristic of XPCS extend the phase space accessible to scattering studies beyond some restrictions by light and neutron. The motivation of this work was the fact although the surface modes of viscoelastic liquid films were predicted [3,4] to be strongly overdamped modes with relaxation times
* Corresponding author. Tel.: +82-2-705-8431; fax: +82-2-701-8431. E-mail address: [email protected] (H. Kim). 0928-4931/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msec.2003.09.038
determined by viscosity, surface tension, film thickness and wave number, there had been no experimental tests of how these theories might apply to thin films, and particularly to thin polymer films. This question is especially interesting in the context of recent experiments indicating that the glass transition temperature near surface is lower than in the bulk [5]. Among the proposed explanations for this effect is the notion that a surface layer having low viscosity exists even at temperatures below glass transitions of bulk [6– 11]. We also studied the question of viscosity inhomogeneities in polymer films using our experimental techniques.
2. Experimental Polystyrene (PS) films were prepared by spin-casting onto optically-flat silicon substrates, which were previously cleaned by Pirhana etch for removing residual organics. Molecular weight (Mw) of PS is 123 kg/mol (Mw/Mn) = 1.08. The samples were then annealed in vacuum for 12 h at 150 jC to ensure complete solvent removal. The thicknesses of the PS films were from 84
12
H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
Fig. 1. The schematic diagram of the experimental setup for XPCS in reflectivity.
to 333 nm. Films were mounted in a temperature controlled sample chamber whose vacuum space (~10-3) was integrated with the vacuum of the X-ray beamline. The XPCS experiments were performed at Sector 8-ID at the Advanced Photon Source (APS) and employed monochromatic radiation with an X-ray energy of 7.66 keV. The experimental geometry is illustrated schematically in Fig. 1. By arranging for the X-ray incidence angle (0.14j) to lie below the critical angle for total external reflection (0.16j), we were able to restrict the X-ray penetration into the film to a depth of f 9 nm, far thinner than any of the films studied here. Thus, scattering from the film – substrate interface is negligible, and only fluctuations at the polymer/vacuum interface are probed. Moreover, with X-rays it is possible to access larger in-plane wave vectors (out to 10-2 nm-1 in these experiments) than can be easily achieved with optical methods. The off-specular diffuse scattering of the rough polymer surface was recorded with a direct-illumination charge-coupled device (CCD) camera located 3545 mm downstream of the sample. The beam dimensions were 20 20 Am2, comparable to the X-ray coherence lengths of 7 and 90 Am in the horizontal and vertical directions, respectively. As a result, the polymer surface is partially coherently illuminated, giving rise to a speckled scattering pattern, which varies in time as the surface modes experience random thermal fluctuations. The normalized intensity –intensity time autocorrelation function, g2, is calculated by g2 ðq; tÞ ¼
hIðq; tVÞIðq; t þ tVÞi hIðq; tVÞi2
3. Results and discussions The relaxation data that were collected were consistent with the single-exponential decay of strongly overdamped surface capillary waves. Figs. 2(a) and (b) show the best fit relaxation time constants (shown in symbols) a function of in-plane wave vector ( qO) at three different temperatures for the 177-nm-thick film and at T = 160 jC for films of thickness 84, 177 and 333 nm. The lines correspond to least-squares fits based on the theory below. From the theory
ð1Þ
where I(q, tV) is the scattering intensity at wave vector transfer q at time tV. The angular brackets in Eq. (1) refer to averages over time tV and t denotes delay time. The relaxation time constant can be extracted from the intensity correlation function of speckled pattern. We calculate the normalized intensity autocorrelation of sequential two-dimensional scattering patterns pixel-by-pixel. This is followed by an appropriate averaging over all pixels corresponding to the same narrow range of qO . To avoid X-ray sample damage, the X-ray exposure of any position on the sample was limited to about 10 min, after which time the sample was shifted to illuminate a fresh area.
Fig. 2. Measured time constant (s) vs. in-plane wave vector ( qN) (a) for 177 nm-thick films at different temperatures and (b) at T = 160 jC for films of thickness 84, 177 and 333 nm. The lines correspond to least-squares fits shown in Eq. (2).
H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
[4] of the dynamics of capillary waves on the thin viscous liquid films, we have earlier deduced [12] the following expression for the relaxation time s for capillary waves in the overdamped regime: sc2gðcosh2 ðqN hÞ þ ðqN hÞ2 ÞÞ=½cqN ðsinhðqN hÞÞ coshðqN hÞ ðqN hÞ
ð2Þ
where g is the viscosity, c is the surface tension and h is the thickness. In Eq. (2), s/h is solely a function of qNh and directly proportional to the ratio g/c. In Fig. 3, we plotted the quantity s/h as a function of qNh for different film thicknesses at 150 jC shown as symbols. The data from different samples collapse form a single curve, confirming the anticipated scaling with film thicknesses. This scaling were also confirmed at 160 and 170 jC. From the excellent agreement between the experimental data and theory (shown as line (1)), the ratio g/c can be determined. Using the known (bulk) surface tension of PS [13] at each temperature, we obtained the viscosity of PS supported films. The values of the viscosity obtained at different temperatures show good agreement with those of bulk PS [14] within the accuracy of the measurements [12]. It was also possible to set the limits on the extent to which viscosity inhomogeneities in the film were present. A
13
Navier-Stokes model was used to calculate relaxation times for a film with two layers having different viscosities but the same density and no interfacial tension. We calculated the s/h as a function of qNh for two-layer model with a surface layer of thickness 10 nm having 10 times less than the bulk viscosity (line (2) in Fig. 3) and 1000 times less than that (line (3)). This comparison represents the limit of accuracy of our measurements and thus, we were able to rule out a surface layer thicker than 10 nm having one-tenth of the bulk viscosity.
4. Conclusions We have measured the relaxation times of overdamped capillary waves for thin polystyrene films of molecular weight 123,000 at various temperatures above the glass transition using XPCS technique. We also verified scaling relations for s as a function of wave vector and film thickness as predicted from the theory of such capillary waves. We have obtained the values of viscosity in supported films using the results and bulk surface tensions. They are in good agreement with the measured bulk values interpolated to the molecular weight of 123,000. The calculation of the capillary wave relaxation times for inhomogeneous thin films with two-layer model gives the limit of existence of surface layer with a viscosity less than the bulk viscosity. The polymer surface dynamics
Fig. 3. Comparison between the data at 150 jC (circles) and various model curves. The solid line (1) corresponds to Eq. (2). The inset shows the schematic diagram for each calculation curve for inhomogeneous films according to the two-layer model described in the text. The total film thickness is 80 nm. Line (1) (solid line) was calculated as homogeneous film. Line (2) (dashed line) was calculated with a surface layer of thickness 10 nm having 10 times less than the measured viscosity and line (3) (dotted line) was with a surface layer 1000 times less than the measured one.
14
H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14
data provide a starting point for investigating even thinner films and temperatures closer to the glass transition temperature.
Acknowledgements The use of Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109ENG-38 and Sector 8-ID is supported by the DOE Facilities Initiative Program DE-FG02-96ER45593 and NSERC. Work at MIT and Yale was supported by the NSF (DMR 0071755). Work was also partly supported by NSF (DMR0209542). H.K. thanks the support from Sogang University Research Grants in 2003 and the grant from the contribution of Advanced Backbone IT Technology Development Project (IMT2000-B3-2) of the Ministry of Information and Communication.
References [1] K.L. Ngai, G.B. Wright (Eds.), Relaxations in complex systems, J. Non-Cryst. Solids 235 – 237 (1998) 1 – 799. [2] D. Lumma, L.B. Lurio, S.G.J. Mochrie, M. Sutton, Rev. Sci. Instrum. 71 (2000) 3274. [3] J.L. Harden, H. Pleiner, P.A. Pincus, J. Chem. Phys. 94 (1991) 5208. [4] J. Ja¨ckle, J. Phys., Condens. Matter 10 (1998) 7121. [5] J.A. Forrest, R.A.L. Jones, in: A. Karim, S. Kumar (Eds.), Polymer Surfaces Interfaces and Thin Films, World Scientific, Singapore, 2000, p. 251. [6] J.L. Keddie, R.A.L. Jones, R.A. Cory, Europhys. Lett. 27 (1994) 59. [7] G.B. DeMaggio, W.E. Frieze, D.W. Gidley, M. Zhu, H.A. Hristov, A.F. Yee, Phys. Rev. Lett. 78 (1997) 1524. [8] S. Kawana, R.A.L. Jones, Phys. Rev. 63 (2001) 21501. [9] A.M. Mayes, Macromolecules 27 (1994) 3114. [10] P.G. de Gennes, Eur. Phys. J. 2 (2000) 201. [11] J.D. McCoy, J.G. Curro, J. Chem. Phys. 116 (2002) 9154. [12] H. Kim, A. Ru¨hm, L.B. Lurio, J.K. Basu, J. Lal, S.G.J. Mochrie, S.K. Sinha, Phys. Rev. Lett. 90 (2003) 68302. [13] S. Wu, in: J. Brandrup, E.H. Immergut, E.A. Grulke (Eds.), Polymer Handbook, Wiley, New York, 1999, p. VI-525. [14] D.J. Plazek, V.M. O’Rourke, J. Polym. Sci., Part A-2 9 (1971) 209.