www.elsevier.com/locate/msec

Materials Science and Engineering C 24 (2004) 11–14

Polymer film dynamics using X-ray photon correlation spectroscopy

Hyunjung Kima,*, A. Ruhmb, L.B. Lurioc, J.K. Basud, J. Lale,S.G.J. Mochrief, S.K. Sinhag,h

aDepartment of Physics, Sogang University, Seoul 121-742, South KoreabMax-Planck-Institut fur Metallforschung, Stuttgart, Germany

cDepartment of Physics, Northern Illinois University, DeKalb, IL 60115, USAdMaterials Research Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USAe Intense Pulsed Neutron Source, Argonne National Laboratory, Argonne, IL 60439, USA

fDepartments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USAgDepartment of Physics, University of California San Diego, La Jolla, CA 92093, USA

hLANSCE, 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 determined by viscosity, surface tension, film thickness

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 dynam-

ics 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

0928-4931/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.msec.2003.09.038

* Corresponding author. Tel.: +82-2-705-8431; fax: +82-2-701-8431.

E-mail address: hkim@sogang.ac.kr (H. Kim).

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 sur-

face 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 previ-

ously 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

Fig. 1. The schematic diagram of the experimental setup for XPCS in reflectivity.

Fig. 2. Measured time constant (s) vs. in-plane wave vector ( qN) (a) for 177nm-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) 11–1412

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 mono-

chromatic 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 experi-

ence random thermal fluctuations. The normalized intensi-

ty–intensity time autocorrelation function, g2, is calculated

by

g2ðq; tÞ ¼hIðq; tVÞIðq; t þ tVÞi

hIðq; tVÞi2ð1Þ

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-di-

mensional scattering patterns pixel-by-pixel. This is fol-

lowed 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.

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

H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–14 13

[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:

sc2gðcosh2ðqNhÞ þ ðqNhÞ2ÞÞ=½cqNðsinhðqNhÞÞ

� coshðqNhÞ ðqNhÞ 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 thick-

nesses at 150 jC shown as symbols. The data from different

samples collapse form a single curve, confirming the antic-

ipated 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

Fig. 3. Comparison between the data at 150 jC (circles) and various model curve

diagram for each calculation curve for inhomogeneous films according to the two-

(solid line) was calculated as homogeneous film. Line (2) (dashed line) was calcu

measured viscosity and line (3) (dotted line) was with a surface layer 1000 times

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 ten-

sions. 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

s. The solid line (1) corresponds to Eq. (2). The inset shows the schematic

layer model described in the text. The total film thickness is 80 nm. Line (1)

lated with a surface layer of thickness 10 nm having 10 times less than the

less than the measured one.

H. Kim et al. / Materials Science and Engineering C 24 (2004) 11–1414

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-31-109-

ENG-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 (DMR-

0209542). 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. Jackle, 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. Ruhm, 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.