Cooperative and Non Cooperative Dynamics in Ultra-thin Films.pdf

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Cooperative and non-cooperative dynamics in ultra-thin filmsof polystyrene studied by dielectric spectroscopy and

capacitive dilatometry

Veronica Lupascu a, Stephen J. Picken a, Michael Wubbenhorst b,*

a Department of Chemical Technology, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlandsb Department of Physics and Astronomy, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium

Received 16 June 2006; received in revised form 29 August 2006Available online 19 October 2006

Abstract

The effect of thickness reductions on the glass transition dynamics in ultrathin films of polystyrene has been studied by dielectric spec-troscopy (DS) and capacitive dilatometry (CD). Upon reduction of the film thickness, a systematic decrease in the dilatometric glasstransition temperatures, Tg (dil), was observed via CD, while DS revealed a continuous speed-up and broadening of the a-process,accompanied by only minor reductions in the fragility index. A good agreement between spectroscopic and the dilatometric glasstransition temperatures was found for films thicker than 20 nm, while for thinner films both quantities diverge increasingly. A likelyexplanation for this discrepancy is the presence of another dynamic process showing Arrhenius-behavior ( Ea72 kJ/mol) with a pre-exponential factor of 1012 s being indicative for non-cooperative dynamics. Such a new process might be assigned to distinct surfacedynamics in polystyrene films as suggested in recent papers. 2006 Elsevier B.V. All rights reserved.

PACS: 61.30.v; 77.22.Gm; 64.70.Pf

Keywords: Dielectric properties; Relaxation; Electric modulus; Films and coatings; Glass transition; Fragility; Structural relaxation

1. Introduction

Since the pioneering work of Keddie and Jones [1] in1994, who observed substantial reductions in the glass tran-sition temperature Tgcompared to the bulk value in ultra-thin films of polystyrene (PS), glass transition effects in

ultrathin polymer films have been studied by manyresearch groups with the aim to improve our understandingof the glass transition as a general phenomenon in con-densed matter physics [28]. Starting from ellipsometricmeasurements on polystyrene in the original work by Ked-die et al. [1], systematic investigations comprising variouspolymer systems (e.g., PS, PMMA, P2VP), different samplegeometries (freely-standing films, supported and capped

films) and various measurement techniques were performedin the last decade. Though most of the studies in the earlierdays were based on density related methods such as ellips-ometry[1,9], X-ray reflectivity[2,10], Brillouin light scatter-ing [11] and positron annihilation lifetime spectroscopy(PALS) [12], recent studies utilise more and more tech-

niques that are directly sensitive to molecular fluctuations,such as dielectric spectroscopy[1317], calorimetric meth-ods[7,18,19], and shear-modulated scanning force micros-copy[8].

Despite the diversity in the experimental approachesand, sometimes, contradicting results, one can identifysome clear trends from the experimental work:

1. Polymers having weak interactions with the substrate,e.g., atactic polystyrene (a-PS) on Si, show typically areduction in the glass transition temperatures below a

0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2006.09.004

* Corresponding author. Tel.: +32 16 327148; fax: +32 16 327984.E-mail address:[email protected](M. Wubbenhorst).

www.elsevier.com/locate/jnoncrysol

Journal of Non-Crystalline Solids 352 (2006) 55945600
mailto:[email protected]:[email protected]


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thickness of roughly 40 nm, regardless to the chemicalnature of the substrate (e.g., SiOx, H-passivatedSi(11 1), glass, aluminium oxide). For PS, these Tg-reductions are also maintained in the absence of a freesurface (capped vs. uncapped films)[1,4], and have beenconfirmed consistently by different experimental tech-

niques, (ellipsometry, positron annihilation and X-rayreflectivity).2. In contrast, polymers with strong specific interactions to

the substrate like poly(methyl methacrylate) (PMMA)on SiOx might show either depressions or elevations inthe glass transition temperature, however, the specificTg(L) trends depends often on subtle details in the poly-mer (micro)structure such as the stereoregularity of thepolymer.

Dielectric relaxation spectroscopy (DRS) is particularlyuseful to assess the dynamics of ultra-thin polymer filmsin a wide dynamic range and thus provides detailed spectral

information about the dynamic glass transition and otherrelaxation processes present in both the glassy and the meltstate. DRS measurements have been performed on cappedand supported layers of PS[14,19,20], PVAc[21], PMMA[1517,21], cis-polyisoprene [22] and Poly(2-vinylpyridine)P2VP[23,24], and have provided detailed insights into theglass transition dynamics, secondary relaxation linked tolocal conformations[16,25], and even whole chain mobility[22]by virtue of dielectric normal process. Regarding DRSresults on ultrathin PS films, Fukao was the first one whostudied capped thin polystyrene films supported on an alu-minium (Al) coated glass substrate using Dielectric Spec-

troscopy [14,26]. His results are largely consistent withresults obtained with the other methods in view of the trendthat the observed Tg decreases with decreasing the samplethickness. In his experiments, glass transition temperatureswere determined using the temperature change in the high-frequency permittivity, a technique known as capacitivedilatometry (CD). It was also shown that the thicknessdependence in Tg is directly correlated to the width of thea-process in the temperature representation and thus tothe distribution of relaxation times of the a-process.

Another, interesting finding was the observation of asecond, weak relaxation peak (labelled al) at temperaturebelow the main transition[14]. Though the authors couldnot determine the thermal activation parameters of thisprocess, a link was suggested between the observed al-peakand a possibly distinct surface dynamics in PS films in thecontext of a three-layer model. Such layer model assumesthat a thin film having one free surface (supported film)likely consists of three thickness regions, a dead layer ofimmobilised polymer chains at the substrate, a bulk likecore layerand asurface layernext to the free surface, eachof which characterised by specific dynamics. In this picture,the a-process described the cooperative dynamics in thecore layer, which become broadened upon thickness reduc-tion due to its interconnection to a layer of enhanced

mobility (surface) and a layer of reduced mobility (dead

layer). As a consequence, a net shift in the glass transitiondynamics could be rationalised by an asymmetric effect ofthe outer layers on the overall dynamics. Though such alayer model is a useful aid for the interpretation of aver-aged mobility data (like peak shape and position of thea-relaxation), one has to realise the actual mobility profile

in ultrathin films might be more complicated as shownrecently by a Ellison et al. by using multi-layer PS sampleslabelled with fluorescent probes[23].

A systematic study by dielectric spectroscopy of theglass transition dynamics in ultra-thin atactic polystyrenefilms is presented in this paper. A specific aim is to comparethe volumetric glass transition temperature as obtained bycapacitive dilatometry, with thickness effects on the coredynamics manifested by the dielectric a-relaxation. For thispurpose, simultaneous CD and dielectric relaxation spec-troscopy (DRS) measurements on PS samples in the thick-ness range from 8


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bulk PS, the vacuum permittivity, the electrode area(S= 4 mm2) and film thickness.

3. Results

Owing to the weak dielectric activity of polystyrene,dielectric measurements on PS-films offer the determina-tion of the glass transition temperature in two ways. Thefirst method, capacitive dilatometry, relies on the analysis

of the temperature dependence of the permittivity e 0(T) asshown inFig. 2for bulk-PS and various thin-films samples.At sufficiently high frequencies, i.e. outside the appearanceof the a-relaxation, the permittivity e0(T) solely depends onthe density of the PS film and thus allows the evaluation ofthe linear thermal expansivity in the film thickness direc-

tion from the e0

(T)-curves. From the kink in the e0

(T)dependence, indicating the different volume expansivitiesin the glass state and the amorphous melt, the dilatometricglass transition temperature Tg (dil) can be obtained[19].The second way is the evaluation of the spectroscopicTg from the temperature dependent shift of the a-relaxa-tion peak. This method requires a full analysis of completedielectric loss spectra at different temperatures; the detailswill be discussed later in this paper.

Fig. 2displays the temperature dependence of the nor-malized permittivity for various film thicknesses. Asexpected, the value of Tg (dil) decreases systematicallyupon lowering the film thickness, ranging from 100C

for bulk PS and the 285 nm thick film sample to about60 C for the thinnest film. Furthermore, the glass transi-tion region for the thinnest films (15 and 8.7 nm) is tremen-dously broadened compared to the bulk sample that ischaracterized by a narrow kink in e 0(T).

The thickness dependence of the dilatometric glasstransition temperature as obtained from all experimentale

0(T)-curves is summarized inFig. 3. For comparison withprevious literature data, Tg-values from Fukao et al. [26]obtained on PS-films of two different molecular weights(1.8 106 g/mol, 2.8 105 g/mol) are shown as well (opensymbols).

Furthermore, there are two lines plotted in Fig. 3thatrepresent a best fit to Tg-data from the literature obtainedby different experimental techniques. Here, the left linerefers to glass transition values for supported films, the

Fig. 1. Three-dimensional representation of the dielectric loss e 00(f,T) of aPS film of 50 nm thickness.

0 50 100 150

T [C]

0.95

1.00

1.05

'(T)/'(0C)+

bulk285 nm20 nm15 nm8.7 nm

Fig. 2. Temperature dependence of the normalized permittivity at100 kHz for bulk-PS and for four films at various thicknesses from8.7 nm to 285 nm. For clarity, all curves have been normalized and

vertically shifted by a constant D=n 0.01 (n= 0, 1, 2, 3, 5).

0 20 40 60 80

L [nm]

40

60

80

100

Tg(d

il)[C]

Mw= 1.6105

Mw= 1.8106[14]

Mw= 2.8105[14]

Fig. 3. Thickness dependence of the dilatometric glass transition temper-ature Tg(dil) for ultrathin films of PS. The two lines represent typical Tg-trends compiled from extensive literature referring to freely standing films(right line)[38]and supported films (left line) [28]. Solid symbols show our

Tg-data for PS ofMw= 1.6 105 g/mol. For comparison, literature data

obtained by capacitive dilatometry[14]are indicated by open symbols.

5596 V. Lupascu et al. / Journal of Non-Crystalline Solids 352 (2006) 55945600


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1. The dielectric a process, which was detectable even inthe thinnest PS films, shows a systematic speed-uptowards lower thicknesses.

2. While the entire cooperative dynamics is obviouslyaffected by a thickness reduction, no substantial changesin the steepness index as seen fromFig. 5can be noticed,a finding which is in contradiction to earlier observa-tions by other authors[14].

3. Comparing the dilatometric Tg [Tg (dil)] with the glasstransition values obtained from the VFT-parameters[Tg(a)] reveals a good agreement between the two quan-tities for thicknesses above 20 nm, while there is anincreasing discrepancy between Tg (dil) and Tg (a) forfilms thinner than 20 nm. This discrepancy approachesis maximum for the thinnest sample (L= 8.7 nm), thatexhibits a difference by more than 15 C between thedilatometric Tg (61 C) and the Tg (a) being 77 C.

Further inspection of the dielectric spectra of the samplewith the lowest thickness reveals another peculiar featurethat is clearly seen in Fig. 6. Here, the temperature depen-dences of both the permittivity (left Figure) and the loss

(right figure) are displayed in isochronal representationfor four different frequencies between 0.7 Hz and 260 Hz.

Besides the a-relaxation being located around 100 C atthese frequencies, a second relaxation process shows up atlower temperatures. This second relaxation process is char-acterized by both a weaker intensity and lower thermalactivation than the a-process as indicated by the remark-able peak shift within the frequency range displayed in

Fig. 6. In order to classify this new process the data wereanalyzed in more detail, again by applying a two-dimen-sional fit procedure as mentioned before, based on lossdata of different frequencies and temperatures. The resultis given in Fig. 7 showing the temperature dependence of

Table 1VFT-parameters and steepness index for all PS film corresponding toFig. 5

L(nm) EV(kJ/mol) log s1 TV(K) Tg (sa= 100 s) (C) m

285 10.9 12.0 330.9 95.8 14620 11.4 12.0 318.3 84.6 13615 10.2 12.0 320.0 82.2 151

8.7 11.3 12.8 295.8 77.3 111

-50 0 50 100 150

T [C]

2.45

2.50

2.55

2.60

'(T)

260 Hz

16 Hz

2.8 Hz

0.7Hz

-50 0 50 100 150

T [C]

0.00

0.01

0.02

0.03

"

KK(

T)

s

s

Fig. 6. Isochronal presentation of the permittivity e0(T) (left) and the corresponding dielectric loss e 0 0(T) (right) at four frequencies for a 8.7 nm thick

polystyrene sample. The symbol asdenotes the second relaxation process.

2.0 2.5 3.0 3.5 4.0

1000/T [K-1]

-8

-6

-4

-2

0

2

log([s])

285 nm

8.7 nm

8.7 nm

s

Fig. 7. Activation plot of the relaxation time data sa(T) of bulk PS

(L= 285 nm) together with sa(T) data obtained for the 8.7 nm thick

sample (cf. Fig. 6). The dashed curve represents a VFT-fit to the bulkdata while the two solid curves show the temperature dependence of the aand as process of the ultrathin film sample according the VFT orArrhenius law.



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5. Conclusions

The effect of film thickness on the glass transitiondynamics in ultrathin polystyrene films was investigatedby both dielectric spectroscopy, yielding direct kineticinformation about the segmental dynamics (a-process),

and capacitive dilatometry, probing the volumetric glasstransition upon cooling.Systematic reductions in the dilatometric glass transition

temperatures, Tg(dil), were found, which were slightly lar-ger than those reported in earlier dielectric studies andwhich resemble quantitatively Tg-depressions known forsupported PS films.

From the dielectric spectra, a systematic speed-up of thea-process was found towards lower thicknesses, which wasaccompanied by increasing broadening of the a-peak.Despite the substantial shifts in the relaxation time, nomajor changes in the fragility (or steepness index) werefound. Comparing the spectroscopic glass transition tem-

perature Tg (a) = T(sa= 100 s) with the dilatometric glasstransition temperature reveals a good agreement betweenTg(a) andTg(dil) for films thicker than 20 nm, while below20 nm both quantities diverge increasingly. A likely expla-nation for this apparent discrepancy between volumetricresponse and the temperature dependence of the coopera-tive dynamics (a-process) is the presence of another, hid-den, dynamic process as found for the thinnest film inthis study (L= 8.7 nm). This new dielectric relaxation pro-cess shows Arrhenius-behavior (Ea72 kJ/mol), a pre-exponential factor being typical for non-cooperativedynamics (log[s

1] = 12) and might be assigned to a dis-

tinct surface dynamics in polystyrene films as discussed ear-lier[14,19].

Acknowledgement

Veronica Lupascu gratefully acknowledges the DutchOrganization for Fundamental Research on Matter(FOM) for founding this research project.

Appendix A. Supplementary data

Supplementary data associated with this article can befound, in the online version, at doi:10.1016/j.jnoncrysol.2006.09.004.

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Cooperative and Non Cooperative Dynamics in Ultra-thin Films.pdf