Dynamics of polymers in ultra-thin films

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Dynamics of polymers in ultra-thin films

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magniﬁcus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op woensdag 29 november 2006 om 10.00 uur

door

Veronica Raluca LUPAŞCU

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Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. S. J. Picken and Prof. dr. M. Wübbenhorst Samenstelling van de promotiecommissie:

Rector Magniﬁcus, voorzitter

Prof. dr. S. J. Picken Technische Universiteit Delft, promotor Prof. dr. M. Wübbenhorst Katholieke Universiteit Leuven, promotor

Prof. dr. J. -U. Sommer Leibniz Institut für Polymerforschung Dresden e.V., Duitsland

Prof. dr. G. Frens Technische Universiteit Delft Prof. dr. L. D. A. Siebbeles Technische Universiteit Delft

Priv.-Doz. dr. A. Schönhals Bundesanstalt für Materialforschung und -prüfung, Duitsland

Dr. N. Willard Philips Research

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Preface

Before I started to write this preface, I stopped for a moment and I travelled back in time trying to picture in my mind the most important moments during the years that led to this thesis. At the end of 2001, following a few discussions with Prof. G. Frens, I was accepted as a PhD student, working on a project aimed at understanding the properties of thin polymer ﬁlms. The project was intended as a collaboration between the Physical Chemistry group in DelftChemTech and Philips NatLab. I still remember my ﬁrst day in NatLab, 2nd_{of January 2002, and}

the days that followed. In NatLab I had the opportunity to learn how to work in a clean room and to prepare the ultra-thin ﬁlms, knowledge that proved to be very useful during my PhD research. For this I am grateful to Amar Mavinkurve who guided my ﬁrst steps as a researcher. I want to mention Bart-Hendrik Huisman who introduced me to the world of conductive polymers, as well as Rifat, Tis, Călina, Dimitri and Mustapha for making my stay in Philips very pleasant.

I would like to thank Professor Frens, who accepted me as a PhD student in DelftChemTech. I highly appreciate his intuition and the way in which he can convince his students that things are easier in the end than it looks like in the beginning.

This thesis would have not been possible without the help of Professor Michael Wübbenhorst. I would like to thank him for the supervision he kindly oﬀered me. I highly beneﬁted from the many discussions we had, ranging from the experiments to the interpretation of the results.

In am grateful to Professor Stephen Picken, who accepted to be my promotor and gave me the possibility to work in the Polymer Materials and Engineering group. I appreciate a lot his prompt reaction anytime I needed his help.

Working in the Polymer group was very enjoyable and all the group members treated me as I was part of the group. I would like to thank everyone in this group and especially Ben Norder for his help with the calorimetric measurements and Otto van den Berg for sharing some of his lab experience with me. During the organization of BDS 2004, I enjoyed very much working with Tony and Karin. Very special thanks to Piet Droppert, who not only helped me with the

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vi Preface

electric measurements, but was also always ready to listen to my problems and to give me strength in the diﬃcult moments during my PhD. I thank him as well for translating my propositions into Dutch.

Now, coming to my group, Polymer Chemistry and Molecular Thermody-namics, I will start by expressing my appreciation for the scientiﬁc, as well as non-scientiﬁc discussions I had with Mieke van der Leeden. Thank you Mieke for your continuous support and for writing the Dutch translation of my summary.

I will never forget Lianjie, my roommate and my friend, and I would like to thank her for being there for me any time I needed. I should not forget to thank Nico for being so nice to me all these years: he even let me call him Nicolino.

During these years I enjoyed very much the numerous discussions I had with Anees and Antonia and I appreciate their good advice and the continuous support they oﬀered me.

I would like to thank Mieke, Nico, Lianjie, Christophe, Sander, Pilar, Sue, Ger, Anees, Antonia, Wang, Raghu, Alexei, Charlie, Coos, Urijan, Stephen, Dana, Johan, Djoffie, Rachid, Krishna, Andreea, Camelia and Matias for unforgettable over lunch or coffee brakes discussions. I am thankful to Krishna who helped me with some of the thesis arrangements. To Alexei, Djoffie and Rachid I would like to thank for being such good friends.

I am very grateful to Joke Orsel for her help in a diﬃcult moment of my PhD. Before ending, I would like to acknowledge two special friends, Adriana and Simone, who gave me both friendly and scientiﬁc advices during the last year of my PhD. Thank you both for being there for me.

Finally I would like to thank Adrian for convincing me to do a PhD, for the help he gave me in preparing the thesis and for his continuous support throughout these years.

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Chapter 1 Introduction

Since the earliest stages of human existence, people are making use of natural polymers. Fur, wood, wool and cotton are just a few examples of natural polymers that exist in the nature from the beginning of time. Natural polymers were used by our ancestors for clothing, shelter and decoration and constituted goods on which trading was based, helping to the rise of great civilizations. There would be no Bible, no Greek epics and tragedies and basically no written history without papyrus and parchment. Without canvas and polymerizing oils we would not admire today the paintings of Leonardo, Vermeer, or Rembrandt. In fact our life would have not been possible without polymers, since DNA and RNA are polymers as well.

Since our daily life depended and still depends so much on the use of polymers, there is no wonder scientists have always been attracted by the properties of these materials.

Though the fascinating phenomena of threads spinning by spiders and silk-worms caused early speculations in China about making artiﬁcial silk, even before suggested by Robert Hook in 1664, the ﬁrst man-made polymer start to be stud-ied only in the early 19th _century.

Today, the polymer industry has grown to be larger than the aluminum, cop-per and steel industries combined. Polymers already have a range of applications that far exceeds that of any other class of material available to man. Current applications extend from adhesives, coatings, foams, and packaging materials to textile and industrial ﬁbers, composites, electronic devices, biomedical devices, optical devices, and precursors for many newly developed high-tech ceramics.

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2 Chapter 1. Introduction

1.1 General introduction to polymers

1.1.1 Polymers

Polymers, sometimes also referred to as ’macromolecules’, are built up of a large number of molecular units, which are linked together by covalent bonds. Their structure consists of constitutional repeating units that can be identical (homo-polymer) or diﬀerent (co(homo-polymer).

There are two fundamental characteristics of polymers: their chemical

struc-ture and their molecular mass distribution, which determine all the properties of

a particular polymer. The chemical structure of polymers comprises: the nature of the repeating units, the nature of the end groups, the composition of possible branches and cross-links, and the nature of defects in the structural sequence. The molecular mass distribution contains information about the average molec-ular size and describes how regmolec-ular or irregmolec-ular the molecule size is.

Inside the polymer chains the atoms can adopt two diﬀerent types of

geomet-rical arrangements:

1) Arrangements fixed by the chemical bonds, known as configurations. The configurations of a chain can be altered only if chemical bonds are broken or reformed. Examples of configuration are cis- and trans-isomers.

2) Arrangements arising from rotation about single bonds, known as confor-mations.

1.1.2 Stereoregularity

Stereoregularity describes the isomeric arrangements of functional groups on the backbone of carbon chains.

Isotactic chains are deﬁned as having constituent functional groups aligned in one direction. This enables them to line up close to each other, creating crystalline areas and resulting in highly rigid polymers.

Syndiotactic constituent groups alternate regularly in opposite directions. Be-cause of this regularity, syndiotactic chains can position themselves close to each other, though not as close as isotactic polymers. They do have better impact strength than isotactic polymers because of the higher ﬂexibility resulting from their weaker intermolecular forces.

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1.1 General introduction to polymers 3

density and tensile strength, but a high degree of ﬂexibility.

An example of polymer that can exist in all the three forms described above depending on the process chosen for synthesis is polystyrene (PS).

1.1.3 Morphology and thermodynamics of polymers

Molecular shape and the way molecules are arranged in a material are important factors in determining the properties of polymers. From polymers that crumble to the touch to those used in bullet proof vests, the molecular structure, conforma-tion and orientaconforma-tion of the polymers can have a major eﬀect on the macroscopic properties of the material.

The general concept of self-assembly enters into the organization of molecules on the microscopic and macroscopic scales as they aggregate into more ordered structures (i.e crystals). The physical properties of a polymer depend to quite an extent on whether the polymer is (a) completely amorphous or (b) partially crystalline.

In an amorphous polymer material the molecular chains are all tangled up in a disordered way and, since the chains are mostly in a randomly coiled confor-mation, the solid is elastic. If some crystallinity is present the material becomes stiﬀer. Amorphous polymers may be glassy or rubbery depending on the tem-perature. At low temperatures amorphous polymers are in a glassy state. As the temperature is raised up to a certain temperature, which is characteristic to a speciﬁc polymer and named "glass transition temperature" (Tg), a transition

from the glassy to the rubbery state takes place.

Below Tg even amorphous polymers are rigid and brittle. The atoms or small

group of atoms can vibrate about their mean positions, but it is not possible for molecular segments to slide over each other.

Above Tg an amorphous polymer becomes rubbery, or elastic, and a

semi-crystalline polymer becomes more ﬂexible or less brittle. In amorphous polymers large molecular segments are able to slide over each other, and the characteristic plastic properties are obtained. The glass transition temperature depends in particular on the rate at which the system is heated (cooled). For both amorphous and semi-crystalline polymers the rate of change of density with temperature is greater above Tg than below because of the increase in molecular motion.

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T

V

T

_g

T

_K

T

_m glass crystal liquid

T

V

T

_g

T

_K

T

V

T

_g

T

_K

T

Figure 1.1: The transition temperatures characterizing a polymer.

Polymers form crystals, but not in any circumstances - like most of the low molecular mass compounds. For polymers to form crystals the cooling from the molten state has to be slow enough to enable the necessary rearrangements of the chains. As a basic requirement, chains must adopt a straight, perfectly ordered form. Then a lattice can be constructed by orienting the chains uniformly in one direction and packing them laterally in a regular manner. The thus obtained lattice with three-dimensional order has the monomeric units as structure units. However, this type of crystallization is never complete and crystallites are always surrounded by amorphous regions. Of course not all polymers can crystallize and the degree of crystallinity can vary as well from one polymer to another. Therefore, if the chain elements are small, simple and equal in size, as in linear polyethylene, a large portion of the material will crystallize: one speaks of a high degree of crystallinity. In contrast, if the chain elements are complex, containing bulky side groups, as in polystyrene, the material can crystallize only if these groups are arranged in an ordered conﬁguration (i.e. isotactic or syndiotactic). The melting point characterized by the melting temperature (Tm) is theoretically

the highest temperature at which polymer crystallites can exist.

In the case of amorphous polymers above Tg, the material softens and the

polymer can relax. This type of structural relaxation is called α-relaxation and is directly related to the cooperative movement of chain segments. The material below Tg is not completely frozen either. Examples attesting to some remaining

molecular mobility are the secondary relaxations at low temperatures, such as

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1.2 Dielectric properties of amorphous polymers 5

with time.

1.2 Dielectric properties of amorphous polymers

Since Debye [1] established the theory of dipolar relaxation, dielectric spec-troscopy has proven to be very useful for studying the conformation and dynamics of amorphous polymers. An exceptionally broad frequency range ( 10−6 Hz to 1013 _{Hz) is accessible with this method, which makes it an ideal tool to follow the}

α-relaxation dynamics during its many decades change from Tg, deep into the

liquid state. Moreover, all the additional contributions below the α-relaxation such as the secondary β-relaxation processes (or γ, δ,.. relaxations if there are more than one) can be detected in dielectric spectra of glass forming materials.

1.2.1 Dipole moments in polymers and basic relations

Dielectric spectroscopy deals with the influence of an alternating electric field E(ω) on matter. Application of an electric field E results in the appearance of a polarization P of the medium. For small electric-field strengths, a linear relationship holds between E and P [2]:

P(ω) = (ε(ω) − 1)εvacE(ω), (1.1)

with

ε(ω) = ε(ω) − iε(ω), (1.2)

where εvac denotes the permittivity in vacuum. The quantity ε is called the

complex dielectric function, with ε the real part and ε the imaginary or loss part.

From a microscopic point of view, the macroscopic observable polarization P is related to the dipole density of N permanent molecular dipoles, µi, in a volume

V . For low molecular weight molecules, the dipole moment can be represented

by a single rigid vector, while for macromolecules there are diﬀerent geometric possibilities for the orientation of molecular dipole vectors with respect to the polymer backbone. Depending on this orientation, polymers belong to three diﬀerent categories:

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6 Chapter 1. Introduction CH2 C C CH3 CH2 CH2 H cis-1,4-polyisoprene

Figure 1.2: Type A polymers; ex cis-1,4 poly-isoprene

poly(vinyl chloride)

CH

2

C

Cl

C

CH

2

H

Cl

Figure 1.3: Type B polymers; ex poly(vinyl chloride)

2) type B polymers, which have the dipole moment rigidly attached perpen-dicularly to the chain skeleton (see ﬁg 1.3)

3) type C polymers, with chain molecules having the dipoles in the side chain (see ﬁg 1.4).

The net dipole moment per unit volume (polarization) of a polymer system is given as a vector summation over all molecular dipole types in the repeating unit, the polymer chain, and over all chains in the system:

P= 1 V all chains chain repeating unit µi. (1.3)

Due to the fact that molecular motion in dense amorphous polymer systems is determined by very different time and length scales, different parts of the net dipole moment can be reoriented by different motional processes. Thus, the dielectric spectrum of an amorphous polymer generally shows multiple relaxation behavior, where each process is indicated by a peak in ε and a step-like decrease in ε versus frequency at a fixed temperature.

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char-1.2 Dielectric properties of amorphous polymers 7 PMMA CH2 C CH3 C CH2 C CH3 O O CH3 C O O CH3 poly(mhetyl methacrylate)

Figure 1.4: Type C polymers; ex poly(methyl methacrylate)

acterized by its frequency position, determined by the frequency of maximal loss

fp. From the loss peak diﬀerent characteristic parameters can be obtained, such

as relaxation time τ = 1/(2πfp), relaxation strength ∆ε, and shape properties

such as width and symmetry.

The Debye theory of dielectric relaxation [1], as improved by Onsager, Fröh-lich and Kirkwood gives the temperature dependence of∆ε of N independently relaxing dipoles [2, 3]: ∆ε = εs− ε∞= 1 3ε₀F g µ2N kT V , (1.4) with F = 1 3 εs(ε∞+ 2)2 (2εs+ ε_∞) , (1.5)

where µ is the moment of the moving unit, T is the temperature, k is the Boltz-mann constant, F is the correction factor for internal ﬁeld eﬀects, g is the cor-relation factor which models the interaction between dipoles with respect to the ideal case of non-interacting dipoles, and ε_∞ and εs denote the permittivities

at high and at low frequencies with respect to fp of the relaxation region under

investigation.

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1.2.2 α-relaxation in amorphous polymers

The α-relaxation is related to the glass transition of the system and for that rea-son this relaxation process is also called dynamic glass transition. The dynamic glass transition is deﬁned, in the case of dielectric measurements, as the temper-ature of the maximum loss at a selected frequency [5]. The glass transition is a cooperative phenomenon [6] and for polymers the α-process corresponds to the micro-Brownian motion of the segments that form the chain. For bulk polymers, this motional process takes place in dense environments, built by other chains; intermolecular interactions contribute to this relaxation process in addition to the intramolecular ones.

For most amorphous polymers the α-relaxation has the following characteris-tics: relaxation rate, shape of the loss curve, and relaxation strength.

Relaxation rate

The relaxation rate of the α-process, fp,α, has a temperature dependence well

described by the Vogel-Fulcher-Tamman-Hesse (VFT) [7, 8, 9] equation:

fp,α = f∞,αexp A T − T₀ , (1.6)

where A and f_∞,α are constants, and T₀ is the so-called ideal glass transition, or Vogel temperature. Since the α-relaxation is related to the glass transition,

fp,α shows the same dependence on molecular weight and chain architecture as

Tg [10, 11]. For linear chains and stars, fp,α increases slightly with molecular

weight (Mw) below the critical value Mc (where Mc is of the order of104g/mol)

and is independent of Mw above Mc. For networks, fp,α generally increases with

increasing cross-linking density.

Shape of the loss peak

Generally, the α-process is well deﬁned in the frequency domain and shows a relatively broad asymmetric peak. Its width depends on polymer structure and can range from 2 to 6 decades. The function used to describe the broad loss peak of the α-relaxation in the frequency domain, is the model function of Havriliak and Nagami [12, 13] known as HN-function:

ε(ω) − ε_∞= ∆ε

(1 + (iωτHN)βHN)γHN

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1.2 Dielectric properties of amorphous polymers 9

τHN is a characteristic relaxation time related to the peak frequency fp [14] and

βHN and γHN are fractional shape parameters. βHN (βHN > 0) and βHNγHN

(βHNγHN <1) are related to the limiting low and high frequency slopes of log ε

versus log ω: ∂log ε ∂log ω = βHN = m, ω << 1 τHN (1.8) and ∂log ε ∂log ω = −βHNγHN = n, ω >> 1 τHN . (1.9)

The two parameters m and n above have a diﬀerent dependence on temperature, crystallization, and cross-linking density. For polymeric materials n is found to be in the range0 < n ≤ 0.5. Experimentally was found that the width of the α-peak depends on factors as temperature or cross-linking density (it becomes narrower with increasing temperature and broadens dramatically with cross-linking) [15].

Relaxation strength

For the α-process, ∆εα increases with decreasing temperature. However, it is

observed for several polymers, that this increase is much stronger than the tem-perature dependence predicted by the equation 1.4 [5].

1.2.3 β-relaxation in amorphous polymers

Below Tg, the material is not completely frozen and some remaining molecular

mobility exists, proved by the existence of secondary relaxation processes at low temperatures. The β-relaxation originates from localized fluctuation of the dipole vector. According to the nomenclature developed by Heijboer [16], fluctuations of localized parts of the main chain or the rotational fluctuation of side groups or parts of them are assigned as the molecular mechanism for this relaxation process. The β-process is usually an Arrhenius process and has the following properties: relaxation rate, shape of the loss peak, and relaxation strength.

Relaxation rate

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10 Chapter 1. Introduction fp,β = f∞,βexp −Ea kT . (1.10)

The activation energy Ea is related to the slope of log f∞,β versus 1/T , and

depends on both the internal rotation barriers and the environment of the moving unit.

Shape of the loss peak

In the frequency domain the dielectric β-relaxation displays a broad and usu-ally symmetric loss peak with half width between 4 and 6 decades. Extract-ing information on the basic mechanism of motion is diﬃcult from such broad peaks. The width of the β-peak is often explained in terms of distribution of both the activation energy and the preexponential factor, caused by a distribu-tion of molecular environments in which the molecular modistribu-tion of the β-relaxadistribu-tion can take place [17]. Generally the width of the β-peak decreases with increasing temperature.

Relaxation strength

For many amorphous polymers with a dipole moment rigidly attached to the main chain such as polyvinyl chloride [18], polychloroprene [19] or polycarbonate [20] ∆εβ << ∆εα holds for the relaxation strength of the β-process, while polymers

containing ﬂexible dipolar side groups, such as poly(methyl acrylate) [21], show ∆εβ < ∆εα. The conventional poly(n-alkyl-methacrylate) [22, 23] make an

ex-ception and they show ∆εβ >∆εα. ∆εβ increases usually with the temperature.

1.3 Length scales of motion in polymers

Atactic, ﬂexible, long macromolecules chains are usually good glass formers, with-out tendency to crystallize. In comparison to small-molecule glass formers, in polymers two additional length scales exist: the entanglement spacing de and

the average chain end-to-end distance REE. As an example, vinyl polymers have

a REE ∼ 0.7

√

N for N > 20, where N is the number of monomeric units. A

schematic representation of the length scales motions in polymers is given in ﬁgure 1.5.

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1.4 Principle of dielectric measurements 11

R

_EE

x

a

d

e

x

b

Figure 1.5: Length scales of motion in polymers.

polymer films. Foremost, among the advantages of this sample geometry is that the confining dimension, the film thickness, can be continuously varied over many orders of magnitude, from nanometers to micrometers. Furthermore there are a large number of polymers, which will readily vitrify rather than crystallize, and this feature, combined with many substrate materials and treatments, allows a range of interfacial interactions to be investigated.

1.4 Principle of dielectric measurements

Most dielectric measurements are conducted by applying a voltage to the elec-trode interface and measuring the amplitude and the phase shift of the resulting current. During the dielectric spectroscopy experiments, the dielectric data of the materials under study are generally extracted in terms of the frequency depen-dence of impedance Z or admittance Y . Since both the amplitude and the phase angle of the output may change with respect to the input values the impedance is expressed as a complex number

Z = Z+ iZ, (1.11)

where Z and Z are the real and the imaginary components of the impedance respectively.

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12 Chapter 1. Introduction Sample holder Sample capacitor Sample

U

₀

I

₀ Generator Analyzer Current Channel Analyzer Voltage Channel Sample holder Sample capacitor Sample

U

₀

I

₀ Generator Analyzer Current Channel Analyzer Voltage Channel

Figure 1.6: Principle of a dielectric or impedance measurement.

The sample material is usually mounted in a sample cell between two elec-trodes forming a sample capacitor. The most commonly used type of elecelec-trodes are parallel plates and comb. For good quantitative analysis the electrodes area and the spacing between them must be determined accurately. For ultra-thin films, sample capacitors are usually used, where the polymer material is clamped between two aluminum evaporated electrodes with a fixed geometry. Typical arrangement of sample capacitors for thin films is given in figure 1.7.

A voltage U₀ with a ﬁxed frequency ω/2π is applied to the sample capacitor.

U₀ causes a current I₀at the same frequency in the sample. In addition, there will generally be a phase shift between the current and the voltage described by the phase angle ϕ. The ratio between U₀ and I₀ and the phase angle ϕ are determined by the sample material electric properties (permittivity and conductivity) and the sample geometry.

For a sample with a linear electromagnetic response the measured impedance of the sample capacitor is connected with the dielectric function of the sample material by

ε= ε− iε = −i ωZ(ω)

1

C₀, (1.12)

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1.5 Thesis layout 13 Top electrode Polymer film Lower electrode Substrate Top electrode Polymer film Lower electrode Substrate

Figure 1.7: Arrangements of sample capacitors used for the studies of ultra-thin ﬁlms.

1.5 Thesis layout

In chapter 2 of this thesis a short introduction to ultra-thin polymer ﬁlms is given.

In the following chapter, we present experiments on the eﬀect of thickness reductions on the glass transition dynamics in ultra-thin ﬁlms of polystyrene, studied by dielectric spectroscopy (DS) and capacitive dilatometry (CD).

Chapter 4 contains a comparative study on the same system, polystyrene, between dielectric spectroscopy and ultra-thin film calorimetry. The influence of the annealing temperature used in the preparation of the films on the resulting films properties is discussed.

In chapter 5 experimental results that prove the existence of T₂G₂ helices in bulk atactic PS are presented. For comparison, syndiotactic polystyrene was measured as well.

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References

[1] P. Debye, Polar molecules, Dover, 1929.

[2] C. Böttcher and P. Bordewijk, Theory of Dielectric Polarization vol 2, El-sevier, 1973.

[3] F. Kremer and A. Schönhals, Broadband Dielectric Spectroscopy, Springer, 2003.

[4] W. Stockmayer, Pure. Appl. Chem 15, 539 (1967).

[5] J. Runt and J. Fitzgerald, Dielectric Spectroscopy of Polymeric Materials, American Chemical Society, 1997.

[6] G. Adam and J. H. Gibbs, Journal of Chemical Physics 43, 139 (1965). [7] H. Z. Vogel, Physica 22, 645 (1921).

[8] G. S. Fulcher, J. Am. Ceram. Soc. 8, 339 (1925).

[9] G. Tammann and G. Z. Hesse, Anorg. Alleg. Chem. 156, 245 (1926). [10] E. Donth, Glasübergang, Akademie Verlag, Berlin, 1981.

[11] J. Ferry, Viscoelastic properties of polymers, Wiley New York, 1980. [12] S. Havriliak and S. Negami, J. Polym. Sci , 99 (1966).

[13] S. Havriliak and S. Negami, Polymer 8, 161 (1967). [14] E. Schlosser, Polymer Bulletin 8, 461 (1982).

[15] A. Schönhals, F. Kremer, and E. Schlosser, Phys. Rev. Lett. 67, 999 (1991). [16] J. Heijboer, Molecular Basis of Transitions and Relaxations, Gordon and

Breach Science Publishers, New York , 75 (1978). [17] L. Wu, Physical review B 43, 9906 (1991).

[18] J. Colmenero, Physica A 201, 38 (1993).

[19] M. Matsuo, Y. Ishida, K. Yamafuji, M. Takayanagi, and F. Irie, Colloid & Polymer Science 201, 89 (1965).

[20] G. Katana, F. Kremer, E. Fischer, and R. Plaetschke, Macromolecules 26, 3075 (1993).

[21] G. Williams, D. Watts, S. Dev, and A. North, Transactions of the Faraday Society 67, 1323 (1971).

[22] N. G. McCrum, B. E. Read, and G. Williams, (1967).

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Chapter 2 Thin polymer films

Many aspects of the behavior of polymers in thin films or close to interfaces are not well understood. Observations related to structural and dynamic behavior indicate that the properties of the polymer thin films differ from the ones we know for the bulk state. There are still questions concerning the glass transition temperature, Tg, the conformation of the chains and their relaxation, density and

diffusion coefficient that are highly debated. In this chapter the experimental data concerning the anomalous behavior of the glass transition temperature in thin polymer films are briefly reviewed. The effect of the polymer-substrate interaction on the measured behavior is also considered, together with measurements on the polymer mobility. Finally, measurements of polymers relaxation at the surface and their Tg values are investigated, with the aim of differentiating between the

properties of the polymer surface and the bulk polymer.

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16 Chapter2. Thin polymer films

2.1 Introduction

2.1.1 Why study thin polymer films?

Nowadays, numerous technological applications involve the use of thin polymer ﬁlms. Polymers have an advantage over non-polymeric materials, since they are synthesized in a very large range of chemistries, providing opportunities to "tailor" many physical properties of the material as well as being cheap and easy to handle. Some applications require polymers to meet speciﬁc performance criteria that range from adhesive and mechanical performances, to electronic and optical ones.

In applications as coatings, synthetic membranes, optical devices, or struc-tured composite materials, polymers need to be processed into very thin films or other types of confined geometries. Ultra-thin films are incorporated as resists and inter-layer dielectrics in microelectronics fabrication, as alignment layers in liquid crystal displays, and as lubricants in magnetic information storage devices. In each of these applications, the polymer chain orientation and the state of or-ganization play important roles in determining the final properties.

As the degree of miniaturization increases continuously such confinement ef-fects become increasingly important. Together with the influence of the interfaces they play a crucial role in determining the behavior of the whole system. All these effects can help reaching a given goal by controlling the properties of the material. Therefore a good understanding of how such factors affect the morphology and the dynamic behavior of polymers is very important.

A more detailed knowledge of the polymer interfaces could also be helpful in the design of surface modiﬁcation procedures, with further applications to such areas as bio-compatibility. Some nanocomposites are layered structures where the polymer serves as a substrate for further deposition of thin layers. Knowledge of the surface properties of polymer ﬁlms in comparison to their bulk analogues may be an important factor in the achievement of better physical parameters of such composites.

2.2 The glass transition in thin supported

poly-mer ﬁlms

In bulk materials the glass transition temperature, Tg, is usually described in

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2.2 The glass transition in thin supported polymer films 17

to a predeﬁned value (usually 100 s). The common technique used to measure glass transition temperature for bulk polymers is calorimetry.

In the case of thin polymer ﬁlms the most used measurement techniques are those that probe, directly or indirectly, the thermal expansion of the sample, such as ellipsometry or X-ray diﬀraction [1].

For a simple isotropic ﬁlm the quantities measured by ellipsometry can be related in a straightforward manner to the refractive index n and the thickness h of the thin ﬁlm [2]. Small changes in the sample thickness were shown to be lin-early related to small changes in the ellipsometric measurable angles [2]. These quantities vary with the density of the sample so they exhibit a ’kink’ at the glass transition temperature Tg. The way to determine the Tg from

ellipsomet-ric measurements is by selecting two linear regions of the data and ﬁnding the intersection point between the extrapolated lines. This method is generally sat-isfactory, but in some cases due to an excessive broadening of the glass transition region this type of Tg evaluation can prove to be less accurate.

A second technique, which has been successfully used to measure Tg in thin

supported films, is X-ray reflectivity. This technique is also able to provide a sufficiently accurate measure of film thickness.

Recently, a number of other techniques have been used to measure Tg in thin

ﬁlms. Such techniques include positron annihilation lifetime spectroscopy [3] a technique also used in bulk polymers, optical wave-guide spectroscopy [4], capacitance measurements [5, 7] and ultra-thin ﬁlm calorimetry [8].

First systematic investigation of the glass transition in thin polymer ﬁlms was done by Keddie at al. [9] and involved ellipsometric measurements of Tg in ﬁlms

of polystyrene (PS) supported on hydrogen passivated Si(111) wafers. The ﬁlm thickness, h, was varied from 3000 Å, down to ∼ 100 Å. This study revealed that the Tg values for ﬁlms with h <400 Å, were reduced below the bulk value

of 100 ℃. This reduction in Tg was found to increase as the ﬁlm thickness was

lowered. The lowest measured Tg was 25 K below the bulk Tg and was observed

for a ﬁlm thickness of 100 Å. Films composed of PS with Mw values ranging

from 120 x 103 g/mol to 2900 x 103 g/mol (REE from ∼ 200 to 1000 Å) were

studied in order to investigate the importance of polymer chain conﬁnement. For all samples considered, the measured Tg values were independent of Mw and the

data were collectively described by the empirical relation:

Tg = Tgbulk 1 −a h δ , (2.1) where Tbulk

g is the value of Tg for bulk PS. The best ﬁt to the measured Tg

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18 Chapter2. Thin polymer films 3 10 100 400 L [nm] 40 60 80 100 120 T_g[°C]

Figure 2.1: Compilation of most of the measured Tg values reported in literature as

Tg reductions in supported PS ﬁlms. The values are from references [5, 6, 9, 11, 12].

dominated by the existence of a liquid-like layer near the free surface with a char-acteristic size, which increased as the temperature was raised and diverging at

Tg. The intuitive idea of a surface layer with higher mobility is still incorporated

into more recent attempts at modelling. However, the idea of a length scale of mobility, which increases with temperature is in contrast with the temperature dependence predicted and observed in simulations for the length scale of cooper-ative motion. There is also no evidence for a length scale, which diverges with increasing temperature from other experiments or simulations.

In order to gain an understanding of the glass transition in more general terms, it is important that finite size effects in polymer films are not restricted to a single polymer material, and instead exhibits some degree of universality. Reported measurements confirmed that the Tg anomalies are not peculiar to polystyrene.

Using optical waveguide spectroscopy, Prucker et al. [4] measured poly(methyl methacrylate)(PMMA) ﬁlms supported on hydrophobic glass substrates treated with HMDS (hexamethyldisilazane) and showed that the measured Tg values

decrease with decreasing ﬁlm thickness. For describing the data he used equation 2.1 as well, and found that the parameters were a = 3.5 Å, and δ = 0.8, which were diﬀerent from those for PS.

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2.2 The glass transition in thin supported polymer films 19

3

10

100

400 L [nm]

-40

-20

0

20

40 T

_g

- T

_g

(bulk) [K]

Figure 2.2: Compilation of most of the measured Tg values reported in literature as

Tg reductions in supported PS ﬁlms. The values are from references [5, 6, 9, 11, 12].

physical meaning to either of the parameters.

Finally, it is worth noting that very similar behavior in Tg versus h has also

been observed for thin polycarbonate ﬁlms as well as ﬁlms of poly(α-methyl styrene) and polysulfone [14].

Since the initial investigations of Keddie et al. [9], there have been many other studies for PS on a variety of different substrates, and employing a number of experimental techniques. Researchers using ellipsometry [15], X-ray reflectivity, positron annihilation [3], and dielectric [16] techniques have all reached the same conclusion, that the Tg value of thin PS films is reduced below the bulk value,

and this effect becomes more pronounced for films with smaller thickness. Fig-ure 2.1 presents the experimental results from these different studies and shows most of the measured Tg for PS thin films supported on substrates found in the

literature [5, 6, 9, 11, 12]. For reasons of clarity, we have not distinguished the results of diﬀerent studies.

While there is some scatter in the quantitative values shown in ﬁgure 2.2, the qualitative trend mentioned above is obvious. Despite the large number of experimental studies of the Tg value in thin supported ﬁlms, very few ideas have

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and Dalnoky-Veress [17] that the most likely reason for this is the scatter between the results from the different studies in figure 2.2, which suggests that the details of the interaction between the polymer and the substrate are important to get quantitative agreement between different studies.

The importance of the polymer-substrate interaction was recognized early and this has resulted in a number of studies aimed directly to analyze this eﬀect. One such study was an extension of the ellipsometric experiments of Keddie et

al. to ultra-thin ﬁlms, which were physically grafted to the substrate [18]. For

such thin films, it may be argued that the polymer substrate interaction will dominate the behavior, and it was observed that for sufficiently thin films the trend of Tg decreasing with h is actually reversed, and for films with 50 Å< h <

100 Å, the measured Tg values increase with decreasing ﬁlm thickness. As an

alternative to grafting, when the focus is on the eﬀect of the polymer-substrate interaction, one can also study systems where a much stronger attractive inter-action is present. One example of this is the study by van Zanten et al. [19] for poly(2-vinylpyridine)(P2VP) on oxide-coated Si substrates. In this system the measured Tg value was observed to increase above the bulk Tg, with a maximum

increase of 50 ℃ for a 77 Å ﬁlm.

The most extensive studies concerning the inﬂuence of the polymer-substrate interaction on the measured Tgvalue was done by Keddie et al. [20] for poly(methyl

methacrylate). It was shown that the nature of this interaction could qualita-tively change the thickness dependence of the Tg value. For PMMA ﬁlms on

Au-coated glass substrates, the measured Tg value was found to decrease with

decreasing ﬁlm thickness. For the same polymer on SiOx, when the ﬁlm thickness

is low enough, the Tg value was found to increase above the bulk Tg. Later studies

by Grohens et al. [21] using PMMA with diﬀerent tacticity were able to show a direct correlation between the density of polymer-substrate interaction and the measured Tg value.

While the Tg value of many polymers has been shown to be sensitive to the

substrate used, it does not appear to be sensitive to the method of preparing the thin ﬁlm. For the case of PS, Keddie et al. showed that spin-coated ﬁlms behaved quantitatively similar to grafted ones. For PMMA, Prucker et al. observed similar

Tg reductions for ﬁlms, which were grafted, spin-coated, or prepared using the

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2.3 The controversy in thin polymer films studies 21

2.3 The controversy in thin polymer ﬁlms studies

The discussion above demonstrates the importance of the strength of interaction between the polymer and substrates on measured Tg values. In contrast, ﬁgure

2.1 clearly shows that for the case of PS, this interaction does not appear to dominate the behavior as there is a large body of experimental evidence, which demonstrates that the Tg values are only weakly sensitive to the properties of the

substrate. However a similar study on the same system using X-ray reﬂectivity [22] claimed that the Tg value for PS ﬁlms on hydrogen-passivated Si substrates

was increased to a value at least 40 K higher than their measured bulk Tg for

ﬁlm thicknesses lower than 40 nm. The contradiction with the results of Keddie

et al. was suggested to be due to a strong sensitivity to slight diﬀerences in the

substrate properties.

Almost ten years later than Wallace and coworkers, Efremov et al. [8] used a new technique, thin-films differential scanning calorimetry (TDSC), to observe the glass transition in thin spin-cast films of polystyrene, poly (2-vinylpyridine) and poly (methyl methacrylate) on a platinum surface. A pronounced glass transition was observed even at a thickness as small as 3 nm and no appreciable dependence of the glass transition temperature over the thickness range from hundreds of nanometers down to 3 nm thick film was measured. Due to the high heating rate used for the measurements (20-200 K/ms) their results were highly criticized at the time. One year later Efremov et al. [23, 24], using a much slower heating rate came to the conclusion that, regardless of more than 3 orders of magnitude difference between the time scales of the regular and modified TDSC technique, the annealing measurements gave essentially the same results as regular TDSC. No appreciable dependence of Tg on film thickness from hundreds

of nanometers down to 3 nm could be found for all investigated polymers. A second area of controversy regards the structure that polymer chains adopt when they are conﬁned in a space of the order of their unperturbed dimension (bulk radius of gyration (Rg)). One expects this conformation to be modiﬁed

by the presence of limiting surfaces [25, 26] and in particular chains should have a ﬂatter conformation [27, 28]. It was reported by Shuto et al., that when the ﬁlm thickness becomes lower than 2Rg, the radius of gyration of a chain along

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down to 2Rg [32, 33].

One more issue is the density that polymer chains have in a thin film. Do they maintain their bulk density or not? Early studies using positron annihilation lifetime spectroscopy (PALS), which is sensitive to the amount of voids present in between polymer chains, reported no increase of this free volume close to the free surface of polystyrene films [34]. Neutron reflectivity measurements have shown that polystyrene films deposited on silicon wafers keep their bulk density for thicknesses down to 6.5 nm [35]. Later PALS measurements detected an increase in the PS free volume close to the free surface [36].

A fourth area of controversy when studying glass transition of thin films in-volves attempts to measure the dynamics more directly. A straightforward way to probe dynamics in thin films is to look at the diffusion of entire chains. Such studies have been performed and a somewhat surprising result was found, that the diffusion of PS chains both in the plane of the film [37] as well as normal to the film plane [38], are reduced for films having a thickness lower than 100 nm compared to thick films or bulk samples. The observation of slower chain motion seems to disagree with the idea of lower Tg values in thin films, which would

suggest an enhanced mobility.

The last area of controversy is the glass transition temperature value of the surface layer. Many authors agreed that a surface layer with different properties than the rest of the polymer films does exist and, if the Tg of the whole film

decreases below the bulk value this is a direct consequence of the drastically reduced Tg of the surface layer. As a result, many researchers were interested to

measure such Tg values. While some reported a reduced surface Tg [3, 39] others

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References 23

References

[1] R. Jones and R. Richards, Polymers at Surfaces and Interfaces, Cambridge University Press, 1999.

[2] R. Azzam and N. Bashara, Ellipsometry and polarized light, North-Holland, 1977.

[3] G. DeMaggio et al., Physical Review Letters 78, 1524 (1997).

[4] O. Prucker et al., Macromolecular Chemistry and Physics 199, 1435 (1998). [5] K. Fukao and Y. Miyamoto, Physical Review E 61, 1743 (2000).

[6] S. Kawana and R. A. L. Jones, Physical Review E 63, 021501 (2001). [7] A. Serghei and F. Kremer, Physical Review Letters 91, 165702 (2003). [8] M. Y. Efremov, E. A. Olson, M. Zhang, Z. Zhang, and L. H. Allen, Physical

Review Letters 91, 085703 (2003).

[9] J. L. Keddie, R. A. L. Jones, and R. A. Cory, Europhysics Letters 27, 59 (1994).

[10] J. A. Forrest, K. Dalnoki-Veress, J. R. Stevens, and J. R. Dutcher, Physical Review Letters 77, 2002 (1996).

[11] J. S. Sharp and J. A. Forrest, Physical Review Letters 91, 235701 (2003). [12] K. Fukao and Y. Miyamoto, Physical Review E 64, 011803-1 (2001). [13] E. Dalnoki-Veress, J. A. Forrest, C. Murray, C. Gigault, and J. R. Dutcher,

Physical Review E 63, 031801-1 (2001).

[14] J. Kim, J. Jang, and W. Zin, Langmuir 16, 4064 (2000).

[15] J. A. Forrest, K. Dalnoki-Veress, and J. R. Dutcher, Physical Review E 56, 5705 (1997).

[16] K. Fukao and Y. Miyamoto, Europhysics Letters 46, 649 (1999).

[17] J. A. Forrest and K. Dalnoki-Veress, Advances in Colloid and Interface Science 94, 167 (2001).

[18] J. Keddie and R. Jones, Chem. Soc 35, 21 (1995).

[19] J. van Zanten, W. Wallace, and W. Wu, Physical Review E 53, 2053 (1996). [20] J. Keddie, R. Jones, and R. Cory, Faraday Discussions 98, 219 (1994). [21] Y. Grohens, M. Brogly, C. Labbe, M. David, and J. Schultz, Langmuir 14,

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[22] W. E. Wallace, J. H. van Zanten, and W. L. Wu, Physical Review E 52, 3329 (1995).

[23] M. Y. Efremov, E. A. Olson, M. Zhang, Z. S. Zhang, and L. H. Allen, Macromolecules 37, 4607 (2004).

[24] M. Y. Efremov et al., Thermochimica Acta 412, 13 (2004). [25] C. W. Frank et al., Science 273, 912 (1996).

[26] A. Brulet, F. Boue, A. Menelle, and J. P. Cotton, Macromolecules 33, 997 (2000).

[27] J. Baschnagel and K. Binder, Macromolecules 28, 6808 (1995).

[28] C. Mischler, J. Baschnagel, and K. Binder, Advances in Colloid and Interface Science 94, 197 (2001).

[29] K. Shuto, Y. Oishi, T. Kajiyama, and C. H. Han, Macromolecules 26, 6589 (1993).

[30] K. Shuto, Y. Oishi, and T. Kajiyamaf, Polymer 36, 549 (1995). [31] M. Daoud and P. de Gennes, J. Physique 38, 85 (1977).

[32] H. Cao et al., Applied Surface Science 149, 116 (1999).

[33] R. L. Jones, S. K. Kumar, D. L. Ho, R. M. Briber, and T. P. Russell, Nature 400, 146 (1999).

[34] L. Xie et al., Physical Review Letters 74, 4947 (1995).

[35] W. E. Wallace, N. C. B. Tan, W. L. Wu, and S. Satija, Journal of Chemical Physics 108, 3798 (1998).

[36] J. Algers, R. Suzukib, T. Ohdairab, and F. H. J. Maurera, Polymer 45, 4533 (2004).

[37] B. Frank, A. P. Gast, T. P. Russell, H. R. Brown, and C. Hawker, Macro-molecules 29, 6531 (1996).

[38] X. Zheng et al., Physical Review Letters 79, 241 (1997). [39] Y. C. Jean et al., Physical Review B 56, R8459 (1997). [40] H. Fischer, Macromolecules 38, 844 (2005).

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Chapter 3 Cooperative and non-cooperative

dynamics in ultra-thin films of polystyrene

studied by dielectric spectroscopy and

capacitive dilatometry

Veronica Lupaşcu, Stephen J. Picken, and Michael Wübbenhorst

The effect of thickness reduction on the glass transition dynamics in ultra-thin films of polystyrene has been studied by dielectric spectroscopy (DS) and ca-pacitive dilatometry (CD). Upon reduction of the film thickness, a systematic decrease in the dilatometric glass transition temperatures, Tg, was observed via

CD, while DS revealed a continuous speed-up and broadening of the α-process, accompanied by only minor reductions in the fragility index. A good agreement between the dynamic glass transition temperature and the dilatometric glass transition temperature was found for ﬁlms thicker than 20 nm, while for thinner ﬁlms both quantities diverge increasingly. A likely explanation for this discrep-ancy is the presence of another dynamic process showing Arrhenius-behaviour (Ea ∼ 72 kJ/mol) with a pre-exponential factor of 10−12 s being indicative for

non-cooperative dynamics.

This chapter was accepted for publication in Journal of Non-Crystalline Solids.

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26

Chapter 3. Cooperative and non-cooperative dynamics in ultra-thin films of polystyrene studied by dielectric spectroscopy and capacitive dilatometry

3.1 Introduction

Since the pioneering work of Keddie and Jones [1] in 1994, who observed substan-tial reductions in the glass transition temperature Tg compared to the bulk value

in ultra-thin films of polystyrene (PS), glass transition effects in ultra-thin poly-mer films have been studied by many research groups with the aim to improve the understanding of the glass transition as a general phenomenon in condensed matter physics [2, 3, 4, 5, 6, 7, 8]. Starting from ellipsometric measurements on polystyrene in the original work by Keddie et al. [1], systematic investigations comprising various polymer systems (e.g. PS, PMMA, P2VP), different sam-ple geometries (freely-standing films, supported and capped films) and various measurement techniques were performed in the last decade. Though most of the studies in the earlier days were based on density related methods such as ellipsom-etry [1, 9] , X-ray reflectivity [2, 10] , Brillouin light scattering [11] and positron annihilation lifetime spectroscopy (PALS) [12], recent studies utilize more and more techniques that are directly sensitive to molecular fluctuations, such as di-electric spectroscopy [13, 14, 15, 16, 17, 18], calorimetric methods [7, 18, 19], and shear-modulated scanning force microscopy [8].

Despite the diversity in the experimental approaches and, sometimes, contra-dicting results, one can identify some clear trends from the experimental work: 1) Polymers having weak interactions with the substrate, e.g. atactic poly-styrene (a-PS) on Si, show typically a reduction in the glass transition temper-atures below a thickness of roughly 40 nm, regardless to the chemical nature of the substrate (e.g. SiOx, H-passivated Si(111), glass, aluminium oxide). For PS,

these Tg-reductions are also maintained in the absence of a free surface (capped

vs. uncapped films) [1, 20], and have been confirmed consistently by different experimental techniques, (ellipsometry, positron annihilation and X-ray reflectiv-ity).

2) In contrast, polymers with strong speciﬁc interactions to the substrate like poly(methyl methacrylate) (PMMA) on SiOx might show either depressions or

elevations in the glass transition temperature, however, the speciﬁc Tg(L) trends

depends often on subtle details in the polymer (micro)structure such as the stere-oregularity of the polymer.

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Poly(2-3.1 Introduction 27

vinylpyridine) P2VP [24, 25], and have provided detailed insights into the glass transition dynamics, secondary relaxation linked to local conformations [16, 26], and even whole chain mobility [23] by virtue of dielectric normal process.

Regarding DS results on ultra-thin PS films, Fukao was the first one who studied capped thin polystyrene films supported on an aluminium (Al) coated glass substrate using dielectric spectroscopy [14, 27]. His results are largely con-sistent with results obtained with the other methods in view of the trend that the observed Tg decreases with decreasing the sample thickness. In his

exper-iments, glass transition temperatures were determined using the temperature change in the high-frequency dielectric permittivity, a technique known as capac-itive dilatometry (CD). It was also shown that the thickness dependence of Tg is

directly correlated to the width of the α-process in the temperature representa-tion and thus to the distriburepresenta-tion of relaxarepresenta-tion times of the α-process. Another, interesting ﬁnding was the observation of a second, weak relaxation peak (la-belled αl) at temperature below the main transition [14]. Though the authors

could not determine the thermal activation parameters of this process, a link was suggested between the observed αl-peak and possibly distinct surface dynamics

in PS films in the context of a three-layer model. Such layer model assumes that a thin film having one free surface (supported film) likely consists of three thickness regions, a dead layer of immobilized polymer chains at the substrate, a bulk like core layer and a surface layer next to the free surface, each of which characterized by specific dynamics. In this picture, the α-process described the cooperative dynamics in the core layer, which become broadened upon thickness reduction 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 transition dynamics could be rationalized by an asymmetric effect of the outer layers on the overall dynamics.

Though such a layer model is a useful aid for the interpretation of averaged mobility data (like peak shape and position of the α-relaxation), one has to realize the actual mobility profile in ultra-thin films might be more complicated as shown recently by a Ellison et al. by using multi-layer PS samples labelled with fluorescent probes [24].

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28

3.2 Experimental methods

Atactic polystyrene (Pressure Chemical Company) with a weight average molec-ular mass of 160 kg/mol and low polydispersity (<1.06) was used in this study. Ultra-thin PS-ﬁlms were prepared by spin coating of the polymer-toluene solu-tion on aluminium deposited glass slides (DS samples) for 20 s at a rotasolu-tion speed of 3000 rotations per minute (r.p.m.). The resulting ﬁlms were annealed for 12 hours at Tann = 100 ℃ in order to remove residual solvent and to allow

for the relaxation of internal stresses. After this annealing procedure, a pat-terned top electrode was deposited by "flash" evaporation (deposition time < 5 seconds) of purified aluminum from a tungsten filament, a process that resulted in ultra-smooth Al-layers between 50 and 100 nm in thickness. Polymer films of different thickness were obtained by varying the concentration of the polymer in solution, while all other parameters (spin coating) were kept constant. In this study, (semi)-dilute PS solutions between 0.22 and 5 wt% yielded samples in the thickness range from 8.7 to 285 nm. Dielectric measurements were performed in the frequency range from 10−1 to 107 Hz using a high-resolution dielectric analyzer (ALPHA Analyzer, Novocontrol Technologies). The thin-film samples were first heated to 150 ℃, annealed for 1 h and subsequently measured upon cooling to -20 ℃ at an effective rate of 0.5 K/min. All measurements were done under a N₂ atmosphere that prevented moisture uptake and possible oxidation during the experiments. The thickness of the films was evaluated from the value of capacitance at room temperature using the relation for the capacitance (C) of a parallel-plate capacitor, C= εεo S/L, were ε, ε₀, S and L are the permittivity

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

3.3 Results and discussion

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3.3 Results and discussion 29

0

50

100

150 T [°C]

0.95

1.00

1.05 e

'(T)/

e

'(0

°C)

+

D

bulk 285 nm 20 nm 15 nm 8.7 nm

Figure 3.1: Temperature dependence of the normalized permittivity for bulk-PS and for four ﬁlms with thicknesses from 8.7 nm to 285 nm. For clarity, all curves have been normalized and vertically shifted by a constant= n x 0.01 (n: 0, 1, 2, 3, 5).

temperature Tg(dil) can be obtained [19]. The second way is the evaluation of

the "spectroscopic" Tg from the temperature dependent shift of the α relaxation

peak. This method requires a full analysis of complete dielectric loss spectra at diﬀerent temperatures; the details will be discussed later in this chapter.

Figure 3.1 displays the temperature dependence of the normalized permit-tivity for various ﬁlm thicknesses. As expected, the value of Tg(dil) decreases

systematically upon lowering the film thickness, ranging from 100 ℃ for bulk PS and the 285 nm thick film sample to about 60 ℃ for the thinnest film. Fur-thermore, the glass transition region for the thinnest films (15 and 8.7 nm) is tremendously broadened compared to the bulk sample that is characterized by a narrow kink in ε(T ).

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30

PS-films of two different molecular weights (1.8 x106 g/mol, 2.8 x105 g/mol) are shown as well (open symbols). Furthermore, there are two lines plotted in figure 3.2 that represent the best fit to Tg-data from the literature obtained by

differ-ent experimdiffer-ental techniques. Here, the full line refers to glass transition values for supported films and the dotted line represents the trend for freely standing films [1, 3, 14, 21, 27, 28]. From figure 3.2 we can make two observations: First, both our Tg(dil) values and those from reference [27] fall in between the upper

limit (supported ﬁlms) and the lower limit (freely-standing ﬁlms) despite the fact that the PS sandwich geometry has no true free surface. Secondly, it is obvious that our Tg reductions are generally higher than Fukao’s [14] values, however,

they are still close to the limit for supported ﬁlms [29]. In order to obtain the "spectral" glass transition temperature Tg(α) from the dielectric α-process of PS,

the following strategies were applied. For thick ﬁlms showing narrow loss peaks in the frequency spectra, the dielectric relaxation time τ(T ) was determined by a ﬁt of the dielectric loss spectra ε(ω) to the empirical Havriliak-Negami (HN) relaxation function (eq. 3.1) [30]:

ε = −Im{ ∆ε

(1 + (iωτ)a)b} +

σ εvω

, (3.1)

where ∆ε corresponds to the relaxation strength, while the two ’shape parame-ters’ a and b represent the logarithmic slope of the low frequency loss tail (a) and the high frequency loss tail (-ab). The second term in equation 3.1 accounts for ohmic conduction. More details about the ﬁt procedure for dielectric data are given in [32, 33].

The relaxation time data for the 285 nm thick PS sample, obtained in this way, are plotted in the activation diagram, figure 3.3. For thinner samples, where loss peaks became noisier and strongly broadened, peak relaxation time data were obtained by analyzing isochronal loss curves ε(T ) at various frequencies (cf. open triangles and open circles in figure 3.3). In the next step, these relaxation time data τ(T ) were fitted to the Vogel-Fulcher-Tammann equation

τ = τ_∞exp Ev R(T − Tv) , (3.2)

which typically describes very well the temperature dependence of the struc-tural relaxation time τα(T ) of glass forming materials. Here, EV and TV are the

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3.3 Results and discussion 31 0 20 40 60 80 L [nm] 40 60 80 100 T [°C] M_w= 1.6×105 M_w= 1.8×106_[Literature] M_w= 2.8×105_[Literature]

Figure 3.2: Thickness dependence of the dilatometric glass transition temperature Tg(dil) for ultra-thin ﬁlms of PS. The two lines represent typical Tg-trends compiled

from extensive literature referring to freely standing ﬁlms (dotted line) [31] and sup-ported ﬁlms (solid line) [29]. Solid symbols show our Tg-data for PS of Mw = 1.6 x

105 _{g/mol. For comparison, literature data obtained by capacitive dilatometry [14] are}

indicated by open symbols.

a two-dimensional fit procedure of the ε(f, T ) data to a combined HN-VFT-function [32, 33] was applied that yielded the VFT-parameters (rightmost solid line in figure 3.3) in a direct way. The knowledge of the VFT-parameter finally allows us to evaluate two other important quantities that characterize the glass transition: the steepness index m (fragility) according to a definition by Böhmer

et al. [37] (eq. 3.3), and the operationally deﬁned glass transition temperature

by assuming τ(Tg) = 100 s. m= dlog(τ) d(Tg/T) )|T=T g = Ev 2.303R Tg (Tg− Tv)2 (3.3)

The resulting Tg(α) values are displayed in ﬁgure 3.4 together with the

corre-sponding dilatometric data Tg(dil) and the steepness index (inset ﬁgure). From

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32

2.0

2.5

3.0 1000/T [K

-1

_]

-8

-6

-4

-2

0 log(

t

[s])

8.7 nm 15 nm 20 nm 286 nm

T

_g

(

t

=100s)

Figure 3.3: Activation plot of the relaxation time ταdetermined from the peak maxima

in the dielectric loss ε(T ) for a-PS films of various thickness. The lines represent fits according to the VFT equation. For the thinnest film (L = 8.7nm), a two-dimensional fit procedure of the ε(f, T ) data to a HNVFT-function [32, 33] was applied that yields the VFT-parameters (shown as solid line) instead of discrete values.

1) The dielectric α-process, which was detectable even in the thinnest PS ﬁlms, shows a systematic speed-up towards lower thicknesses.

2) While the entire cooperative dynamics is obviously affected by a thickness reduction, no substantial changes in the steepness index as seen from figure 3.4 can be noticed, a finding which is in contradiction to earlier observations by other authors [14].

3) Comparing the dilatometric Tg, [Tg(dil)] with the glass transition values

obtained from the VFT-parameters [Tg(α)] reveals a good agreement between the

two quantities for thicknesses above 20 nm, while there is an increasing discrep-ancy between Tg(dil) and Tg(α) for ﬁlms thinner than 20 nm. This discrepancy

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3.3 Results and discussion 33

5

10

100

500 L [nm]

40

50

60

70

80

90

100 T [°C]

T_g(dil) T_g(a) 5 10 _{L [nm]} 100 500 0 20 40 60 80 100 120 st e e pne ss in dex m

5

10

100

500 L [nm]

40

50

60

70

80

90

100 T [°C]

T_g(dil) T_g(a) 5 10 _{L [nm]} 100 500 0 20 40 60 80 100 120 st e e pne ss in dex m

Figure 3.4: Thickness dependence of the dilatometric glass transition temperature Tg(dil) (open circles) in comparison to Tg(α) (ﬁlled triangles), evaluated from the τα(T

)-data. The dashed line is only a guide for the eyes. The inset ﬁgure displays the corresponding thickness dependence of the steepness index m.

being 77 ℃.

Further inspection of the dielectric spectra of the sample with the lowest thick-ness reveals another peculiar feature that is clearly seen in figure 3.5. Here, the temperature dependencies of both the permittivity (left figure) and the loss (right figure) are displayed in isochronal representation for four different frequencies be-tween 0.7 Hz and 260 Hz. Besides the α-relaxation being located around 100 ℃ at these frequencies, a second relaxation process shows up at lower temperatures. This second relaxation process is characterized by both a weaker intensity and lower thermal activation than the α-process.

In order to classify this new process the data were analyzed in more detail, again by applying a two-dimensional fit procedure as mentioned before, based on loss data of different frequencies and temperatures. The result is given in figure 3.6 showing the temperature dependence of the α-process together with that of the new sub-Tg process. The τα(T )-data for the "bulk" like sample (L

Dynamics of polymers in ultra-thin films