Physica B 336 (2003) 211–215

X-ray photon correlation spectroscopy on polymer films withmolecular weight dependence

Hyunjung Kima,b,c,d,*, A. R .uhme,f, L.B. Luriof,g, J.K. Basuc,h, J. Lali,S.G.J. Mochriej, S.K. Sinhaa,b,c

aDepartment of Physics, University of California San Diego, La Jolla, CA 92093, USAbLANSCE, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

cArgonne National Laboratory, Advanced Photon Source, Argonne, IL 60439, USAdDepartment of Physics, Sogang University, Seoul 121-742, South Korea

eMax-Planck-Institut f .ur Metallforschung, Stuttgart, GermanyfCenter for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

gDepartment of Physics, Northern Illinois University, DeKalb, IL 60115, USAhMaterials Research Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USAiArgonne National Laboratory, Intense Pulsed Neutron Source, Argonne, IL 60439, USA

jDepartments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USA

Received 26 September 2002; accepted 9 March 2003

Abstract

We have applied X-ray photon correlation spectroscopy (XPCS) to study the dynamics of surface fluctuations in thin

supported polystyrene films as a function of wave vector, temperature, film thickness, and molecular weight. Molecular

weights, ranging from 30 to 650 kg/mol, were used in the study. Lateral length scales probed are at least ten times

smaller than those accessible in conventional dynamic light scattering. Good agreement between the experimental

results and conventional theory permits us to determine the film viscosity. The viscosity obtained in thin films with a

higher molecular weight shows lower viscosity than the one obtained from bulk polystyrene of corresponding molecular

weight.

r 2003 Elsevier Science B.V. All rights reserved.

Keywords: X-ray photon correlation spectroscopy; X-ray reflectivity; Polymer films

1. Introduction

Thin polymer films continue to attract consider-able attention [1], in part, because of a wide varietyof technological applications, ranging from the

creation of bio-compatible surfaces for medicalimplants (see, for example Ref. [2]) to expandingthe limits of computer disk drive technology (see,for example, Ref. [3]). The physical properties ofpolymers in thin films can be expected to differ ininteresting and important respects from those ofbulk polymers [4].Many aspects of the conformation and dy-

namics of polymer chains in thin polymer films are

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*Corresponding author. Department of Physics, Sogang

University, C.P.O. Box 1142, Seoul 100-611, South Korea.

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

0921-4526/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0921-4526(03)00291-6

still not well understood from a basic point ofview. This is even more true for the dynamicalbehavior of free polymer surfaces and polymericthin films near the glass transition (and the natureof the glass transition itself). There are sometheoretical predictions for the dynamical behaviorof viscoelastic liquid films [5,6] that the slowmodes are strongly overdamped capillary waveswhere the relaxation times are determined by theviscosity, the surface tension, the film thickness,and the wave vector of the capillary wave.Recently, we have reported [7] the first experi-mental verification of the theories in supportedpolymer films using X-ray photon correlationspectroscopy (XPCS) as a means to studydynamics of small scale surface height fluctuations.The measurements were performed on polystyrene(PS) films of molecular weight (Mw) 123 kg/moland of thicknesses varying from 84 to 333 nm attemperatures above the PS glass transition tem-perature. Within a range of wave vectors spanning10�3 to 10�2 nm�1, good agreement was foundbetween the measured surface dynamics and thetheory of overdamped thermal capillary waves onthin films. Quantitatively, the data for films ofMw ¼ 123 kg/mol can be accounted for using theviscosity of bulk PS.In this paper, we extend these measurements to

a wider range of Mw in order to test whether thepolymer radius of gyration (Rg) is the dominatinglength scale controlling the surface dynamics. Ifthe depth over which the packing density of chainsegments [8] changes near the free surface is muchsmaller than Rg; then there should not be muchdifference between the bulk viscosity and theviscosity obtained for the film.

2. Materials and methods

Our films were prepared by dissolving polystyr-ene (PS) in toluene and then spin-casting ontooptically flat silicon substrates, which were pre-viously cleaned by Pirhana etch solution to removeresidual organics. PS films of Mw ranging from 30to 650 kg/mol were used in this study. Thesesamples were then annealed in vacuum for 12 h at150�C to ensure complete solvent removal. The

thicknesses of the PS films were kept between 160and 180 nm for all the molecular weights forcomparison.The XPCS experiments were performed at

Sector 8-ID at the Advanced Photon Source(APS) and employed monochromatic radiationwith an X-ray energy of 7.66 keV. The experi-mental geometry is illustrated schematically in Fig.1. By arranging for the X-ray incidence angle(0.14�) to lie below the critical angle for totalexternal reflection (0.16�), we were able to restrictthe X-ray penetration into the film to a depth ofB9 nm, far thinner than any of the films studiedhere. Thus, scattering from the film-substrateinterface is negligible, and only fluctuations atthe polymer/vacuum interface are probed. More-over, with X-rays it is possible to access larger in-plane wave vectors (out to 10�2 nm�1 in theseexperiments) than can be easily achieved withoptical methods. This makes it possible to avoidcomplications due to the van der Waals interactionwith the substrate for thin films [9]. The off-specular diffuse scattering of the rough polymersurface was recorded with a direct-illuminationcharge-coupled device (CCD) camera, located3545mm downstream of the sample. The beamdimensions were 20� 20 mm2, comparable to theX-ray coherence lengths of 7 and 90 mm in thehorizontal and vertical directions, respectively. Asa result, the polymer surface is partially coherentlyilluminated, giving rise to a speckled scatteringpattern, which varies in time as the surface modesexperience random thermal fluctuations. Thenormalized intensity–intensity time autocorrela-tion function, g2; then yields the sample’s surface

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Fig. 1. The experimental setup for XPCS in reflectivity

geometry.

H. Kim et al. / Physica B 336 (2003) 211–215212

dynamics. To avoid X-ray sample damage, the X-ray exposure of any position on the sample waslimited to about 10min, after which time thesample was shifted to illuminate a fresh area.

3. Results and discussions

From the theory [6] of the dynamics of capillarywaves on the thin viscous liquid films, we haveearlier deduced [7] the following expression for therelaxation time t for capillary waves in theoverdamped regime:

tE 2Zðcosh2ðqjjhÞ þ ðqjjhÞ2Þ=gqjjðsinhðqjjhÞ

� coshðqjjhÞ � qjjhÞ; ð1Þ

where Z is the viscosity, g the surface tension, and h

the thickness.Fig. 2 shows the best fit relaxation time

constants (shown in symbols) as a function of in-plane wave vectors, qjj for theB170 nm-thick filmsof different molecular weights of PS (a) at 160�Cand (b) at 170�C. The time constants wereextracted from the intensity autocorrelation func-tion. In brief, we calculate the normalized intensityautocorrelation of sequential two-dimensionalscattering patterns pixel-by-pixel. This is followedby an appropriate averaging over all pixelscorresponding to the same narrow range of qjj:

1

The relaxation is faster for lower molecularweights and for higher temperature as expected.The fitted curves correspond to Eq. (1).From the excellent agreement between the

experimental data and theory, the ratio Z=g canbe determined. Using the known (bulk) surfacetension of PS [10]2 at each temperature, weobtained the viscosity of PS of different molecularweights at each temperature shown in Fig. 3. Ascan be seen in Figs. 3(a) and (b), the values of theviscosity obtained from 30 to 290 kg/molshow good agreement with those of bulk PS.(Those from 65 and 123 kg/mol also showgood agreement with bulk values.) However, theviscosity obtained from 400 kg/mol at 160�C inFig. 3(c) and those from 650 kg/mol shown inFig. 3(d) show lower values than the bulkviscosities. (The bulk viscosities were interpolatedfrom Ref. [11] for each molecular weight.) Thebehavior for higher molecular weights can beinterpreted as an indication of the existenceof a liquid surface layer having lower viscositythan bulk (it could be due to the segregation oflower Mw chains to the film surface, an effectwhich may be dominant for higher molecularweights). In this case, the effective thicknesses ofthe films should be different from the actualfilm thicknesses and the scaling relation implicitin Eq. (1) that the quantity t=h as a function of

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0.1

1

1E+1

1E+2

1E+3

τ(se

c)

1.0E-3 1.0E-2q

||(nm-1)

0.1

1

1E+1

1E+2

1E+3

1E+4

T = 160 °C

T = 170 °C

30k, h=165nm

65k, h=177nm

123k, h=177nm

650k, h=177nm

30k, h=165nm

123k, h=177nm

400k, h=168nm

290k, h=173nm

(a)

(b)

τ(se

c)

Fig. 2. Measured time constant (t) vs. in-plane wave vector (qjj)for B170nm-thick films of different molecular weights of PS:

(a) at 160�C and (b) at 170�C. The lines correspond to the

calculation shown in Eq. (1).

1The validity of this averaging procedure was checked by

verifying that pixel subregions with the same q|| but different qz

nevertheless yield the same time constant within errors.2Static diffuse scattering experiments determine the surface

tension to be independent of film thickness and, to be consistent

with the surface tension of bulk PS for Mw ¼ 123kg/mol.

H. Kim et al. / Physica B 336 (2003) 211–215 213

(qjjh) is independent of film thickness at anygiven temperature will break down, which ob-served for Mw ¼ 123 kg/mol [7]. However, it isintriguing that there does not appear to be anyclear evidence for the breakdown in scaling in ourpreliminary data with thicknesses from 85 to331 nm. The results require a new theoreticalexplanation and further investigations especiallyfor thinner films with higher molecular weights. Inthis case even longer time constants are expected.However, acquiring long time constants (>300 s)present a severe experimental challenge. We aredeveloping techniques for studying such longcorrelation time constants using exposures atspaced out intervals.

Acknowledgements

The use of Advanced Photon Source wassupported by the US Department of Energy,Office of Science, Office of Basic Energy Sciences,under Contract No. W-31-109- ENG-38 andSector 8-ID is supported by the DOE FacilitiesInitiative Program DE-FG02-96ER45593 andNSERC. Work at MIT and Yale was supportedby the NSF (DMR 0071755). J.K.B. was sup-ported by the DOE (DEFG02-91ER45439). Workwas also partly supported by NSF (DMR-0209542). H.K. thanks for support from KoreaScience & Engineering Foundation GrantNo.R01-2001-000-0042-0.

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140 150 160 170 180 1901E+5

1E+6

1E+7

1E+8

140 150 160 170 180 1901E+5

1E+6

1E+7

1E+8

T (°C)

(N

sec/

m2 )

1E+5

1E+6

1E+7

1E+8

1E+2

1E+3

1E+4

1E+5

MW = 30 k MW = 290 k

MW= 400 k MW= 650 k

(a)

(c)

(b)

(d)η

Fig. 3. Viscosity of thin-film (squares with errors) and bulk (solid symbols) PS of: (a) 30 kg/mol (b) 290 kg/mol, (c) 400 kg/mol, and (d)

650 kg/mol as a function of temperature.

H. Kim et al. / Physica B 336 (2003) 211–215214

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