Download - Distribution of Segmental Mobility in Ultrathin Polymer Films

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ISBN 978-90-8649-495-8 Wettelijk depot D/2012/10.109/12

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II

Contents

Preface

Abstract

1. Dynamics in Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 The glass transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The -relaxation process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Non exponential behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 Non-Arrhenius temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . .7

1.3 Phenomenological models of the glass transition . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.1 Free volume approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 8

1.3.2 Adam-Gibbs model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 The energy landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5 Random first order transition theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2. Ultrathin Polymer Films: Confinement Effects Modulated by Interfaces . . 16

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Tg of ultrathin polymer films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Supported ultrathin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.2 Free surfaces: Tg reductions in freely-standing ultrathin films . . . . . . . . 20

2.2.3 Characterization of free surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.4 Heterogeneous dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Non-equilibrium nature of thin polymer films . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.1 Spincoating process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

2.3.2 Out of equilibrium glassy thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4 Adsorption and chains conformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3. Segmental Mobility and Glass Transition Temperature of Freely Suspended

Ultrathin Polymer Membranes (Article) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

III

4. Distribution of Segmental Mobility in Ultrathin Polymer Films (Article) . . 49

5. Probing interfacial mobility profiles via the impact of nanoscopic

confinement on the strength of the dynamic glass transition (Article) . . . . . . . .73

6. Adsorption Kinetics of Ultrathin Polymer Films in the Melt Probed by

Dielectric Spectroscopy and Second-Harmonic Generation (Article) . . . . . . . . .99

7. Is the Reduction in Tracer Diffusivity under Nanoscopic Confinement

Related to a Frustrated Segmental Mobility? (Article) . . . . . . . . . . . . . . . . . . . 118

8. General Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

9. Appendix .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

A1. Dielectric spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138A2. Dielectric relaxation . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A3. Dielectric spectroscopy on the dynamics of polymers. . . . . . . . . . . . . . . . . . . .140A4. Principle of dielectric measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

IV

Preface

The form of this doctoral thesis titled “Ultrathin Polymer Films Probed by Dielectric

Relaxation Spectroscopy: Interfacial Effects” is based on publications. The structure

has been organized in accordance with the regulations of the Arenberg doctoral

school (see below) in the following way. The first chapter gives a short overview

about the glass transition and the associated -relaxation process. In the second

chapter we provide a review of the most relevant literature studies related to the

dynamics of ultrathin films, serving as a framework where we locate our work. To

ease the readability of this chapter we highlighted the contributions of our

publications to the research field between text dividers. The publications constitute

the main body of the thesis and are organized in five chapters: from Chapter 3 to

Chapter 7. Finally, we present our general conclusions along with some opportunities

for future works. We added in Appendix 1 some additional information on the

dielectric spectroscopy technique.

Doctoral thesis based on publications

Candidates who have written international publications may bundle these into a

collection which serves as a PhD thesis in accordance with these guidelines:

a. The PhD needs to include a sufficient number of high-quality articles which form a

coherent body of work. The PhD candidate must be the main author of at least four

accepted publications in international journals or equivalent. This number may vary

depending on the scientific domain;

b. Approximately six months prior to the expected submission date of the PhD thesis,

the candidate needs to inform the SC about his intention to compose his PhD thesis in

the form of publications;

c. During the preliminary defence, the EC will assess the scope and quality of these

V

publications (and thus of the PhD thesis itself);

d. The PhD candidate must include an extensive introduction: this should describe

the research field, situate the submitted publications, indicate the candidate’s own

contribution to the field and make clear what the innovative aspects are. The

introduction may include an extensive review of relevant literature (either published

or not);

e. In case of a co-authored article, the PhD candidate must specify his own

contribution on a separate page preceding the article. This may be verified by the

EC;

f. Corrections, possibly suggested during the discussion during the preliminary

defence, need to be added on a separate page following each publication;

g. The thesis should contain an extensive conclusion indicating possible directions for

future research in the field;

h. The candidate must determine whether the publisher allows public availability and

in which form via the webpage Romeo/Sherpa.

VI

Samenvatting

Deze doctoraatsthesis heeft als doel de invloed te onderzoeken van interfase

interacties op de dynamische eigenschappen van ultradunne polymeerfilmen.

Hiervoor gebruikten we meerlagige systemen van polymeren met een specifieke

chemische structuur, dewelke specifieke interacties aan de interfase opleveren. De

experimenten werden uitgevoerd door middel van diëlektrische relaxatie

spectroscopie.

Het eerste deel van de thesis is toegewijd aan onderzoek op de beweging van

polymeer-segmenten in vrijstaande ultradunne filmen. Deze studie omvat de

implementatie van een nieuwe experimentele methode gebaseerd op drie-

dimensionale electrodes (geintegreerde kam-electroden). De analyse van de

dielectrische spectra toont aan dat de glastransitietemperatuur van polymeerfilmen

die niet interageren met een vast oppervlak daalt bij het reduceren van de dikte van de

film. Deze daling wordt geassocierd met relaxatietijden die veel korter zijn dan in

bulk.

Het tweede deel behandelt de dynamische eigenschappen van dunne filmen bestaande

uit ongelabelde en gelabelde polystyreen die interageren met een vast oppervlak. We

ontdekten dat de dynamiek van het ongelabelde polystyreen niet beïnvloed wordt

door een reductie in dikte van de film. De filmen van gelabeld polystyreen

daarentegen vertonen een tragere dynamiek en een lagere dielectrische sterkte in

vergelijking met de bulk. Vervolgens bestudeerden we de ruimtelijke dynamiek door

een dunne laag gelabeled polystyreen te verwerken op verschillende afstanden tot het

oppervlak. Indien de gelabelde laag niet interageert met het oppervlak, gedragen de

glastransitietemperatuur (Tg) ) zich hetzelfde als in

bulk. Indien dezelfde gelabelde laag interageert met het vaste oppervlak, ontstaan er

afwijkingen t.o.v. het bulkgedrag. Deze afwijkingen zijn het resultaat van de

specifieke interactie van het gelabelde polymeer met het vaste oppervlak. De

experimentele resultaten werden vervolgens verwerkt met een wiskundig model dat

VII

rekening houdt met een niet-mobiele polymeerlaag in de nabijheid van het vaste

oppervlak.

Verder ontdekten we dat de afwijking in Tg in vergelijking tot de bulk

veranderde in functie van de tijd voor sterk adsorberende polymeerlagen in contact

met het oppervlak. Dit effect is gerelateerd aan de progressieve immobilisatie van de

gelabelde functionele groepen aan het oppervlak en hun gemiddelde moleculaire

als de gemiddelde oriëntatie volgen twee vergelijkbare

) ten opzichte van de

tweede (oriëntatie). Dit experimenteel bewijs stelt een interpretatie voor die

gebaseerd is op adsorptie. In het begin van het adsorptieproces zijn grote lege plekken

vrij waardoor de gelabelde groepen adsorberen met als voorkeur een parallelle

oriëntatie ten opzichte van het oppervlak. Op latere tijdstippen tijdens het

adsorptieproces is er reeds een grote bezettingsgraad waardoor de gelabelde groepen

verder adsorberen met een uitlijning die voornamelijk loodrecht is ten opzichte van

het oppervlak.

VIII

Abstract

The aim of this dissertation is to investigate the influence of interfacial interactions

on the dynamic properties of ultrathin polymer films. We used multilayer systems in

conjunction with polymers of particular chemical structures, which confer them

specific interfacial activity. The experimental investigation has been carried out by

means of dielectric relaxation spectroscopy.

The first part of the thesis has been devoted to the investigation of the segmental

dynamics of freely-standing ultrathin films. The study comprised the implementation

of a new experimental method based on three-dimensional electrode structures

(Interdigitated comb electrodes, IDE). From the analysis of the dielectric spectra we

found that films with no interaction with solid surfaces show large reductions of the

glass transition temperatures upon confinement, which are associated to relaxations

times much shorter than in the bulk.

In the second part, we focused on the dynamic properties of thin films of neat and

labelled-polystyrene (PS) in contact with solid surfaces. We observed that while the

dynamics of the neat polymer is not affected by the thickness reduction, thin films of

the labelled-PS display slower dynamics and a lower dielectric strength compared to

the bulk. We then probed spatially resolved dynamics by inserting a very thin

labelled-PS layer at different positions above the substrate. When the labelled layer

has no contact with the substrate, the local glass transition temperature, Tg, and

, are bulk like. If the same layer is placed in contact with the

solid surface, deviations from the bulk behaviour arise. These deviations are the result

of the specific interaction of the labelled polymer with the solid surface. This

experimental results are rationalized with a mathematical model that takes into

account an immobile layer located in the vicinity of the solid surface.

Furthermore, for strongly adsorbing polymer layers in contact with the surface, we

observed that deviations from the bulk of Tg vary as a function of time. This

effect is associated to the progressive immobilization of the labelling moieties on the

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solid surface, and to a change of the average molecular orientation of the labelling

and the mean orientation follow two comparable kinetics

regimes, being the first faster than the second. These experimental evidences

suggested the following interpretation based on adsorption. At the beginning, large

bare spots are available for adsorption and the labelling moieties adsorb with a

parallel orientation. At later times, the surface coverage is high and adsorption

develops via an alignment of the dye moieties normal to the surface.

X

Dynamics in Amorphous Materials 1

Chapter 1

Dynamics in Amorphous Materials

1.1 The glass transition

Systems such as metallic, polymeric, colloidal, and biomolecular materials may be

subjected to the glass transition. A glass is obtained at a temperature Tg, by cooling a

liquid fast enough to avoid crystallization (or possibly by compressing it).

When considering the mechanical properties, the glass transition is a liquid - solid

transition. In fact, the shear modulus of a rubber above the glass transition is about 1

MPa while the modulus of a glassy solid is about 1 GPa (Fig. 1(a)). Note that for

molecular liquids the rubbery zone does not exist. In any case, the variation of the

modulus is modest as compared to the variation of the viscosity that can vary by 13

orders of magnitude. Since the viscosity is related to the shear rate, this very large

variation is linked to important changes of the relaxation times of the system. In

general a glassy system has a viscosity of 1013 Pa s, corresponding to a relaxation

time = 100s. This value of is the criteria used in this thesis to define Tg. One of the

most characteristic feature of a glassy solid is a lack of the long range structural order

(or translational symmetry) that is usually associated to high mechanical properties.

Indeed, as shown in Fig. 1(c) the static structure factor S(Q) of a polymer does not

vary with temperature from above to below the glass transition temperature.1

This thermal transition has other common points with liquid – solid transitions (such

as first order melting transition) since the thermal expansivity P of the (solid) glass

is lower than the liquid (Fig. 1 b). However, contrarily to first order transitions, the

reduction of the volume under cooling is not discontinuous at Tg, a feature

characteristic of a second order transition. Hence, in the Ehrenfest classification, the


glass transition contains ingredients typical of both first and second order transitions :

it is neither one nor the other.

Moreover, the glass transition temperature is not an intrinsic temperature of the

system since it depends on external parameters such as the cooling rate. As seen in

Fig. 1 (b), the Tg increases with cooling rate, thereby the glass transition is a kinetic

phenomenon.

(c)

Figure 1.1 (a) Schematic temperature dependence of the shear modulus G for a polymer; (b) Temperature dependence of the volume, V, of a liquid at constant pressure. Tm is the melting temperature. A slow cooling rate produces a glass transition at Tg2, a faster cooling rate leads to a glass transition at Tg1. The thermal expansion coefficient p p changes abruptly at Tg. (c) Temperature dependence of the static structure factor for deuterated polybutadiene (Tg =186 K).

Log (G)glass-likebehavior

G 109 Pa

simpleglassformer

viscoelasticbehavior

liquid likebehavior

Temperature(a)

Tg

G 106 Pa

Tg

melt

Tg1

V

T

glass 1

glass 2

crystal

supercooledliquid

Tg2 Tm

p

p

(b)


Additionally, the state reached after the transition is not stable and glasses are known

to age toward denser states that can be reached at lower cooling rates. In fact, close to

Tg the characteristic equilibration timescale exceeds the laboratory timescale and the

rate of “molecular” rearrangements undergoes a dramatic slowing down. These

molecular rearrangement are referred to as the -process, and for polymers they

occur at the segmental scale.

1.2 The -relaxation process

In glass forming systems different types of atomic or molecular movements exist

above and below Tg. It is possible to probe the dynamics of such motions by

oscillatory drive. The corresponding temporal response of an intensive variable (such

as (t)) to an extensive perturbation (such as (t)) is called relaxation.2 By various

experiments the characteristic relaxation times (or the relaxation rates ~1/ ) of

these movements are measured as a function of the temperature. Fig. 1.2 shows a

typical relaxation map, that is the variation of as a function of 1/T, for different

motions.3 Between T0 and Tg, at longest time scales the dynamics is controlled by the

-process, that is the cooperative motions of groups of molecules or polymer

segments. This is the process associated to the glass transition. At shorter time scales

secondary processes take place that are called -process (often assigned to

intramolecular fluctuations), - process etc.

The -process and the secondary -process merge together above a critical

temperature T* whose value for most systems is about 100°C above Tg. This cross-

over corresponds to a relaxation rate * that for both simple liquids and polymers is

about 107-109 Hz, as illustrated in Fig. 1.2.

-process is related to segmental motion and is based on the idea of

a “damped diffusion” of conformational changes (such as gauche-trans transition)

along the chain.4 For an isolated chain these conformational changes disturb the bond

length and also the angles, and enhance the probability that a neighboring segment

will also undergo a conformational transition.


Figure 1.2 Relaxation map: frequencies m of the different molecular motions of glass forming materials as function of the inverse of the temperature, process, and secondary processes. The and processes merge together at cross-over point ( *,T*).3

Therefore, this process is supposed to be cooperative to some extent, i.e. the

conformational rearrangement of the segments are not independent.

This idea may be extended also to dense polymer systems composed by a collection

of chains, with the difference that the correlation between conformation transitions

arises from both intra-molecular (due to the connectivity of monomers) and

intermolecular (due to the dense packing) cooperativity.

The -relaxation process is the process that slows down more rapidly on approaching

the glass transition, and it is the more affected by vitrification. Therefore, the glass

-relaxation motions occur on the

time scale of the order of 102 s. The most prominent features of the process close to

Tg are the non-exponentiality and the non-Arrhenius temperature dependence of the

relaxation time . These constitute some general signatures of glassy systems.

1.2.1 Non-exponential behavior

The dielectric response of molecular liquids at high temperature is characterized by

an exponential decay of the autocorrelation function (t) of the polarization P :


2

( ) (0)( )

P t Pt

P (1.1)

where ( ) ( )P t P t P . In the frequency domain, this corresponds to the Debye

shape of the dielectric loss peak.4 However in polymers and in general at low

temperatures, some interactions between dipoles become important and deviations of

the Debye behaviour are commonly observed. Correspondingly, t -relaxation

process of a typical supercooled liquid slows down with decreasing temperature and

becomes non-exponential near the glass transition. The autocorrelation function is

usually described by a stretched exponential, or Kohlraush-Williams-Watt (KWW)

function:

( ) exp[ ( / ) ]KWWt t (1.2)

where is the stretching parameter whose value is generally in the range between 0

and 1 and KWW is the relaxation time. When is near 0 the distribution of relaxation

times is very broad. To the contrary, for values close to 1 the distribution of

relaxation times is characterized by a simple exponential (Debye relaxation), that is

the time behaviour of liquids above the melting point.

The reason why the time correlation function at low temperatures shows a non-Debye

is still a matter of debate. There are two possible extreme

scenarios able to describe this phenomenon: heterogeneous and homogeneous

scenario, see Fig. 1.3.5

In the heterogeneous scenario, the dynamics in one region of a supercooled liquid

can be orders of magnitude faster than the dynamics in another region only a few

nanometers away. In this case, the relaxation in each region is locally exponential, but

the typical relaxation timescale varies spatially. Hence, the response function (t)

becomes non-exponential upon spatial averaging over this spatial distribution of

relaxation times.

In an homogeneous scenario, it is possible to imagine that supercooled liquids are

homogeneous and that each domain relaxes nearly identically and in an intrinsically

non-exponential manner.


Figure 1.3 Heterogeneous and homogeneous scenarios for a non-exponential relaxation function (t). Different locations in the figure represent different locations in the sample. Observation of only the ensemble averaged relaxation function cannot distinguish between these scenarios.5

Dynamic heterogeneity has been observed experimentally by dielectric

spectroscopy,6 nuclear magnetic resonance,7 and other techniques. The concepts and

experimental evidences for dynamic heterogeneity in glass-forming systems have

been reviewed by Ediger.8 Experiments indicate that the characteristic size of these

regions is on the order of few nanometer at Tg and that their lifetime is on the order of

the average relaxation time.5

The existence of dynamic heterogeneity has been used to explain the difference in the

temperature dependence of translational and rotational diffusion as the glass

transition is approached ( for T 1.2 Tg).8 In fact, it is found that the translational

diffusion has a weaker temperature dependence than the rotational one. This

decoupling could be due to the different way in which rotational and translational

experiments average over the regions of slower and faster mobility.9 In particular, the

rotational time provides information about regions of slower mobility while the time

translational diffusion coefficient emphasizes regions of high mobility. Therefore, if

-

relaxation, the wider is the distribution the stronger is the decoupling.

heterogeneous scenario homogeneous scenario

time

average signal

Log (t)


Another manifestation of heterogeneous dynamics can be seen in the peak narrowing

observed for probe relaxation at high temperatures or high frequencies, when

dielectric probes are used to dope apolar polymers.10

1.2.2 Non-Arrhenius temperature dependence

Experimentally it is found that the increase of the -relaxation time during cooling

significantly deviates from a thermally activated behaviour that would be described

by an Arrhenius law : kBT). The majority of glass formers, in fact, show

a stronger than Arrhenius increase of , which can be parameterized by using the

empirical Vogel-Fulcher-Tammann (VFT) equation:

0

0

( )( ) exp expB

DTE TTk T T T

(1.3)

Where E(T) indicates that the activation energy must be temperature dependent.

is the high temperature limit of the relaxation time ( 10 13 s), kB the Boltzmann

constant, D a positive parameter called “strength parameter” and T0 is the Vogel

temperature at which the relaxation time diverges if extrapolated according to the

VFT law (typically, T0 is 30-70 °C below Tg).

The strength parameter D provides a way to classify glass formers according to the

deviation of (T) from the thermally activated behaviour, see Fig 1.4. Strongly non-

Arrhenius liquids are called “fragile” and are characterized by small values of D

(typically D < 10) while those closer to Arrhenius behavior are termed “strong” and

posses higher values of D ( > 10).11

Another parameter m (called the fragility or steepness index) is associated to this

classification and represent the slope of the relaxation time curve vs Tg / T at the glass

transition temperature Tg.

log

gg T T

mT T

(1.4)


Figure 1.4 Log( ) as a function of Tg/T gives a representation of how glass formers deviate from the Arrhenius behavior. Strong glasses follow the Arrhenius law, fragile glasses are non- Arrhenius.

We mentioned that the non exponentiality of the relaxation of the autocorrelation

function cited above was probably due to some interactions between dipoles. Some

fundamental mechanisms occurring in supercooled liquids may be related to some

cooperative rearrangements. In the next sections we will briefly describe the free

volume concept and the idea of cooperatively rearranging regions, both supporting

the VFT law.

1.3 Phenomenological models of the glass transition

The free-volume and the configurational-entropy models are useful to rationalize data

on liquids and polymers at a semiempirical level.

1.3.1 Free volume

The free volume approach is based on the assumption that molecular transport in

viscous fluids occurs only when voids, having a volume large enough to

accommodate a molecule, form by the redistribution of some “free volume”.12 The

last is defined as an excess volume in the system which is not occupied by the “hard

sphere” volume of the molecules. It is assumed that the redistribution of the free

Tg/T 1

Log( (s))

Strong glasses

1

Fragile glasses

Log( (s))

Tg/T


volume in the system is not controlled by an activation energy. Accordingly, the

slowdown of the molecular transport in supercooled liquids is attributed to a decrease

of free volume rather than to the existence of energy barriers.

The average free volume /f fv V N where Vf is the total free volume and N is the

number of molecules. The fundamental hypothesis from Cohen and Turnbull lies in

the linear dependence of the average free volume on the temperature:

0( ) ( )f P mv T v T T (1.5)

where T0 is the temperature at which the average free volume is zero, p is the

thermal expansion coefficient and mv is the mean molecular volume. Therefore, the

free volume model predicts that when the temperature approaches T0, vf vanishes and

the molecular diffusion is arrested.

The distribution of v , the free volume of a given molecule, is given by:

( ) ( / ) exp( / )f fp v v v v (1.6)

The rate of molecular transport is determined by the probability of finding a free

volume above a critical value, *,v corresponding to a void of critical size. Hence, for

the rate of transport 1/ one finds:

1/ exp( * / )fv v (1.7)

In the case of a constant thermal expansion coefficient, the insertion of equation (1.5)

for the average mean free volume vf in equation (1.7) yields to the VFT expression.

1.3.2 Adams-Gibbs model

The Adams-Gibbs approach explains the slowing down of the relaxation behaviour of

glass forming systems in terms of a decrease of “configurational entropy”.13

Relaxation is assumed to take place through cooperative rearrangements of groups of

molecules (or polymer segments). Any of these groups, called cooperative

rearranging regions (CRR’s), can relax independently from the others. The size of the

CRR’s is related to z, the number of segments inside a CRR. When decreasing the


temperature the cooperativity increases, leading to an increase of the size of the

CRR's.

In the model the average cooperative transition probability W(T) is given by:*

( ) expB

zW T Ak T

(1.8)

Where A is a temperature independent factor, z* is the critical lowest number of

molecules or polymer segments inside a CRR that can yield a non zero value of

W(T), and is the potential energy (per segment) hindering the cooperative

rearrangement.

The value of z* can be related to a critical configurational entropy of the macroscopic

system by:* *

c A cz S N s (1.9)

Where *cs is the critical configuration entropy corresponding to a CRR of z* number

of molecules, Sc is the molar configuration entropy of the macroscopic sample and NA

is the Avogadro’s number. Equation (1.8) becomes

( ) expc

CW T ATS

(1.10)

With C a constant. The relaxation time is reciprocally related to the transition

probability 0( ) expc

CTTS

. Using thermodynamic considerations Sc(T) can be

connected to the change of the heat capacitance pc 1/T giving Sc(T) (T-T0)/TT0

that leads to the VFT equation.

Although in the Adam and Gibbs model the heterogeneous dynamics are not

discussed, it may be possible to correlate the length scale of the dynamic

heterogeneities het to that of the cooperatively rearranging regions. Ediger has

proposed to assume that het is an upper limit for the length scale of the CRR’s.8


1.4 The energy landscape

In the energy landscape scenario the potential energy of a glass forming liquid can be

written as a function of degrees of liberty of the N particles present in it. The shape of

the free energy as a function of the configurational coordinates is illustrated in Fig.

1.5.14 It is characterized by a number of energy minima and saddle points separating

neighbouring minima. The temperature controls the way in which a system samples

its landscape, which in turn provides information on its dynamic behaviour. At high

temperatures the system has enough energy to sample the whole energy landscape,

exhibiting a temperature-independent activation energy for relaxation. With

decreasing the temperature, the system is unable to jump the high energy barriers, and

therefore it will mainly sample the deeper minima. Under this condition, the kinetics

of the structural relaxation changes from exponential to stretched exponential, and the

activation energy increases with decreasing temperature (super-Arrhenius behaviour).

In the landscape scenario the glass transition is reached when the temperature is low

enough that the system is stacked in a single minimum.

A main point in the theory of the glass transition is to understand how the transition

between different states is achieved.

Figure 1.5 Schematic illustration of the landscape scenario. The potential energy is plotted as a function of the configurational coordinates.14


1.5 Random first order transition theory

One possibility to describe the behaviour of structural glasses is to consider them as

aperiodic crystals. In this case, a theory of glass transition would be similar to a first

order transition (for example the melt-crystal transition) but resulting in a non-

crystalline system.15,16 At a given temperature, there are many possible aperiodic

structures, and describing the solid nature of glasses relies on explaining why it is not

easy to switch from one configuration to another.

In a periodic crystalline system, the solid state corresponds to a state where atoms

cannot move to a distance larger than 1/10 the interparticle spacing (Lindemann

criterium). A similar phenomenon could be expected also in a glassy system, for

which the Lindemann criterium can be obtained with a density functional approach.

The free energy is written as:

F[ (r)] = Fentr + Fint + Fliq (1.11)

The first term, Fentr, describes the entropic cost for localizing a group of atoms in

specific regions, Fint is the contribution resulting from the interaction between such

localizations, and Fliq is the free energy of the uniform liquid. While for an ordinary

crystal the density (r) can be described with simple periodic functions, for an

aperiodic crystal the density is chosen to have the shape of a sum of Gaussians that

are centered around random lattice sites so that:

3/22( ) exp[ ( ) ]i

ir r r (1.12)

displacement from the lattice

sites, ri . The free energy has the shape shown in Fig. 1.6.


Figure 1.6 Schematic graph of the free energy of an aperiodic lattice as a function of

Fentr, Fint and Fliq are the different contributions to the free

energy.16

that corresponds to the liquid phase. By lowering the temperature down to a

temperature called TA a second minimum appears in the free energy, which

corresponds to a glassy state. Similarly to a first order transition this second minimum

L (see Fig. 1.5). The free energy difference between

the liquid and glassy state is TSc(T), that approaches zero at the Kauzmann

temperature TK.

The transition from one supercooled state to another is allowed by saddle points of

the potential landscape scenario, in which a droplet 0 forms in

region. The free energy at these saddle points takes the form of a nucleation process:

3 24( ) 43 cF r Ts r r (1.13)

Where is the surface tension, r is the radius of the droplet (not to be confused with

the spatial coordinates) and sc is the configurational entropy density. The maximum

of F(r) gives a transition barrier of the type: F* = 16/3 3/( T sc )2. This barrier

Fint

Fentr

Fliq


differs from the one suggested by Adam and Gibbs: F* = sc* / sc where is the

bulk activation energy that in the model it is assumed to be constant for different

substances without an apparent reason. To the contrary, the random first order

transition theory provides an explanation for the universality of based on the

L-1/2/ r0 ( r0 is the mean lattice spacing). Indeed,

for temperatures between TK and TA the surface tension is:2

00 0

3 ln4

LB

rnr k Te

. The universality of the Lindemann ratio means that

/nr0kBT is universal and this provides a microscopic explanation for the slowdown

of the dynamics below TA.

For temperatures close to TK the surface tension depends on the radius of the droplet.

At TK the following expression holds:

1/20 0( ) /r r r (1.14)

When this is substituted into Equation (1.13) for F(r) one finds a simple expression

for the activation barrier, which scales with sc-1 and leads to the VFT law:

2 2* 0 03 3o o K K

Bc p K K

r r TT TF k TDTs T c T T T T

(1.15)

Where D is the liquid’s fragility and can be expressed in terms of the heat capacity

jump at the transition, D~1/ cp , which varies from different substances.

Combining Equation (1.13) and Equation (1.15) we obtain a characteristic size of the

droplet that is related to the relaxation time:2/32/3

0 0

lnK

K

DTr T T

. At the

laboratory glass transition temperature: / r0 ~ 4.5.

One topic underpinning the research on glassy materials in confined geometry is the

possibility of showing new physics at the scale of the CRR, when the size of the


system is close to it.2 However such studies must rely on an extensive understanding

of the effects of interfaces that play a major role on the dynamics of confined

systems. We study this aspect in the next chapter.

References

1. Frick, B.; Richter, D., Science 1995, 267 (5206), 1939-1945.

2. Donth, E., The Glass Transition, Relaxation Dynamics in Liquids and Disordered

Materials. Springer-Verlag: New York, 2001.

3. Rault J., Journal of Non-Crystalline Solids 2000, 271, 177-217

4. Kremer, F.; Schoenhals, A.; (editors), Broadband dielectric spectroscopy.

Springer: Berlin, 2003.

5. Richert, R., Journal of Physics-Condensed Matter 2002, 14 (23), R703-R738.

6. Russell, E.V.; Israeloff N. E., Nature 2000, 408, 695

7. Tracht, U.; Wilhelm, M.; Heuer, A.; Feng, H.; Schmidt-Rohr, K. and Spiess, H.

W., Physical Review Letters, 1998, 81, 2727

8. Ediger, M. D., Annual Review of Physical Chemistry 2000, 51, 99-128.

9. Tarjus G, Kivelson D.. J. Chem. Phys. 1995, 103, 3071–73

10. Kessairi,K.; Napolitano, S,; Capaccioli,S.; Rolla, P. and Wübbenhorst M.;

Macromolecules 2007, 40, 1786-1788

11. Angell, C. A., Science 1995, 267 (5206), 1924-1935.

12. Cohen, M. H.; Turnbull, D., Journal of Chemical Physics 1959, 31 (5), 1164-

1169.

13. Adam, G.; Gibbs, J. H., J. Chem. Phys. 1965, 43 (1), 139.

14. Debenedetti, P. G.; Stillinger, F. H., Nature 2001, 410, 259-267.

15. Lubchenko, V.; Wolynes, P. G., Annual Review of Physical Chemistry 2007, 58,

235-266.

16. Xia, X. Y.; Wolynes, P. G., Proceedings of the National Academy of Sciences of the United States of America 2000, 97, 2990-2994.

Ultrathin Polymer Films: Confinement Effects Modulated by Interfaces 17

Chapter 2

2.1 Introduction

Surfaces and interfaces play a major role in friction, adhesion, electronic transport

and catalysis. However the structural properties of surfaces and interfaces are

different from the bulk and understanding the behaviour of interfaces from “structure

- properties relationships” is not straightforward. In crystals the lattice parameters at

the surface are not equivalent to the bulk values, due to the asymmetry of the number

of neighbours between the inner and outer atoms.1 In simple liquids close to solid

surfaces, it is known that the density is not homogenous and varies in a discrete

manner away from the surface.2 In both crystals and simple liquids, the spatial

extension of the perturbations induced by surfaces and interfaces is on the order of 1

nm. In systems of small dimensions (such as Micro-Electro-Mechanical-Systems, or

MEMS, for example), the effect of interfaces is more important than in macroscopic

systems because of the high surface to volume ratio. Therefore some “size effects”

arise when considering the material properties of small systems, which is referred to

as “confinement effects”.

Interfaces have a large influence on the structure and the properties of solid

amorphous (polymers, colloidal suspension etc.) materials, but with a different

characteristic length scale with respect to simple liquids or crystalline solids. For

example, the extension of the influence of an interface is about from 10 nm to several

microns, of the order of the size of the basic constituents. Therefore, size effects

appear for “larger” systems in solid amorphous materials. For polymers, that are the

Ultrathin Polymer Films: Confinement Effects Modulated by Interfaces


topic of interest in this thesis, the size of radius of gyration of macromolecules (Rg) is

about 10 to 50 nm and confinement effects are observed at this scale.

We study polymer thin films, which is a particular example of systems of high

surface to volume ratio. Polymers thin films are used in many technological and

industrial applications such as electronic packaging materials, dielectric coatings,

resist layers for lithography and adhesion and lubrication as already mentioned. Thin

films can be either free standing (two free surfaces), supported (one free surface) or

capped (no free surfaces), the different configurations are illustrated in Fig 2.1.

Figure 2.1: Three configurations commonly employed in the study of polymer films: freely-standing, supported and capped films. These configurations differ by the number of polymer-air and polymer-substrate interface.

In these thin films the size effect is expected since the film thickness can be smaller

than the unperturbed size of the macromolecules, which may result in the distortion

of the chains themselves.

The effect of confinement on the properties of polymers, with particular emphasis on

the global glass transition temperature and its likely distribution is discussed in 2.2.

Other important topics of interest such as non-equilibrium aspects of thin films are

mentioned in 2.3, in order to situate our work in the research field. Furthermore, 2.4

is focused on the kinetic aspects of chains-solid interactions, from the segmental to

the molecular scale.


2.2 Tg of ultrathin polymer films

2.2.1 Supported ultrathin films

The first direct evidence of the thickness dependence of the chain mobility of

polymer films confined at the nanoscale was spotted by Reiter. He found that

supported polystyrene (PS) films with thickness below 10 nm could dewet at

temperatures inferior to the bulk Tg.3

Then, Keddie and co-workers measured systematically the glass transition

temperature of thin films as a function of the film thickness.4 This study revealed that

PS films deposited on silicon substrates show a substantial depression of Tg for film

thicknesses below 40 nm, with quantitatively similar results for all the molecular

weights investigated (120 2900 kg/mol). The Tg scales such as Tg (h)

Tg( )[1 (A/h) ] where h is the thickness and A 3 nm and 2 are fitting parameters.

A further work from the same group, emphasised the role of specific interactions

between polymer and substrate in determining whether the Tg increases or decreases

with the thickness reduction. Keddie et al. showed that poly(methyl methacrylate)

(PMMA) on a gold substrate displays depressions in Tg, while the same polymer on a

silicon oxide substrate showed a small increase of Tg.5 It was proposed that a strongly

attractive interaction between PMMA and the Si native oxide due to hydrogen

bonding was responsible for the increase of Tg with decreasing film thickness. The

PMMA-Au interaction is much weaker, corresponding to a decrease in Tg with

decreasing film thickness. This qualitative difference in the thickness dependence of

Tg for the two substrates revealed the strong influence of the polymer-substrate

interaction on the deviation from bulk Tg.

During the years that followed, many others works have confirmed the importance of

the polymer-substrate interaction by studying either the Tg averaged along the whole

film thickness6-12 or within individual layers inserted into multilayer films of different

polymer species.13, 14


Mainly, the effect of the substrate has been parameterized with the interfacial energy

between the polymer and the substrate SL,12 which in vacuum correspond to half of

the adhesion energy W, see Fig 2.2.

Figure 2.2 Plot of the difference between the Tg of thin films and the bulk Tg for various PS and PMMA samples, as a function of the interfacial energy.

The glass transition temperatures of thin films of PS and PMMA can be tuned by

changing the value of SL. For low values of SL, the Tg’s are lower than the bulk

values of the polymers. To the contrary, for high values of SL, the Tg’s are higher

than the bulk and increase “linearly” with increasing SL. Moreover, the deviations of

the Tg values of the films from the bulk increased upon confinement for constant

interfacial energies.

It is worth mentioning that there are controversial opinions regarding confinements

and interfacial effects on thin films. For example, in a recent study by Kremer et al.,

where the effect of the substrate on the Tg of PMMA films has been investigated, no

shift of Tg is detected neither by decreasing the film thickness nor by changing the

kind of substrate interaction from strong attractive interactions for covalently bonded

PMMA brushes with high grafting density and for native silicon oxide (Si/SiOx) to

weak and strong repulsive interactions.15

T g(fil

m)- T

g(bu

lk)

Interfacial energy (mJ/m2)

PMMA - 20 nm PMMA - 30 nm PMMA - 172 nm PS - 22 nm PS - 38 nm PS - 124 nm


The controversy regarding this topic is still under debate. Factors such as the

specificity of the techniques used to investigate the Tg and the effects induced by the

sample preparation may be at the origin of these contradictory results.

Note that the Tg of supported thin films is influenced by the free surface as well.

Indeed, Keddie et al. interpreted the Tg reduction observed for samples of PS mainly

in terms of a liquid-like layer at the free surface. This layer is supposed to have a

higher mobility and a lower Tg than the bulk, which changes the overall Tg of the

film. The thinner the film, the higher the effect of the surface layer, whose thickness

has been estimated to be on the order of 10 nm.4,16 It is likely that the glass

transition temperature of the film will be a result of the interplay between the effects

of the solid and free surfaces.

Recently a local dielectric spectroscopy technique has been implemented to study

-relaxation process of ultrathin poly(vinyl acetate)

films.17 Measurements revealed that thin films with one upper free surface show a

faster relaxation compared to the bulk. In particular for the thinnest film investigated

( ~ 18 nm) an increase by a factor of 2 in relaxation rate compared to the thickest one

was detected. These results highlight the importance of the free surface in

determining the dynamic behaviour of thin polymer films.

In the next two sections we describe in more details the effects induced by the free

surface.

2.2.2 Free surface: Tg reductions in freely-standing ultrathin films

The influence of the free surface on the average glass transition temperature of thin

films can be appreciated by studying freely-standing films, see Fig 2.1. First

measurements on the Tg of freely-standing films were conducted by Forrest and

Dalnoki-Verres by using Brillouin light scattering and transmission ellipsometry on

PS samples of various thickness and molecular weight,18-21 see Fig 2.3.

The most striking feature of the data in Fig. 2.3 is that the reductions of Tg with film

thickness are much larger for freely-standing films than for supported films. For

instance, the Tg of a 20 nm thick film is reduced by more than 70 °C relative to the


bulk, while only a variation of 10 °C is observed, at a similar thickness, for supported

PS films.9

Moreover, Tg(h) showed two different behaviours with respect to the molecular

weight (Mw) dependence, a feature that is not observed for supported films. For

moderate Mw (below 350 kg/mol), similarly to supported films, there is not visible

dependence of Tg(h) on the molecular weight. On the contrary, at higher Mw

kg/mol) the Tg values decrease linearly with decreasing the film thickness below a

threshold value h0. The linear dependence has been described very well by the

following equation: 0( ) ( )g gT h T bulk h h for 0h h and ( )gT bulk for 0h h

where is the slope that describes the linear reduction of Tg, and increases with

increasing Mw.

Figure 2.3 Measured Tg values for free-standing polymer films. The solid symbols are obtained with ellipsometry and taken from ref [19]. The empty symbols are obtained using BLS, with a vertical bar indicating the data from ref [20] and a bar indicating data from ref [21].

This strong molecular weight dependence of Tg is reminiscent of some chain

confinement since it is not observed in bulk samples.

Qualitatively the same results were found for other systems by Dutcher et al.,22 and

by other techniques.23

Tg

h[Å]


The fact that the molecular weight dependence is different for freely standing and

supported thin films is still not understood. It is possible that the interaction with the

substrate, which takes place via formation of loops and trains (see 2.4 ), may

annihilate the effect of the molecular weight on the glass transition dynamics of

confined polymer chains.

Note that the reduction of Tg in freely-standing films is accompanied by lower values

of the fragility index m with respect to the bulk (~ 130), i.e. the fragility of 40 nm PS

films approaches the monomer limit value (~ 60).24 This finding has been related to

the effect of the two free surfaces for which lower fragility than the value assumed by

the bulk of the same materials could be expected. 25

Among the contradictory results about Tg variation with film thickness is the effect of

the interfaces. In dielectric spectroscopy the technique itself impose the use of capped

films, which limits the comparison of the dielectric data with other data from the

literature. To assess the dynamics of freely-standing ultrathin films via DS without

altering the free surfaces, a new experimental approach based on three-dimensional

electrode structures (Interdigitated comb electrodes, IDE) was implemented (Chapter

3).13 By our new experimental method we found that the Tg of PS films of various

thicknesses and molecular weights is reduced upon confinement, in good agreement

with studies from other groups20,23,26 and comparable with the scaling law proposed

by Dalnoki-Verres for high molecular weights Mw16. We showed that

the Tg reductions in thin films are associated to relaxation times much shorter than

in the bulk. In more detail, the ratio between of the thin film and the one of the

bulk approaches the value of ~ 10-7 at the bulk Tg.

We proved that the variation of Tg in free standing films is robust whatever the

technique used to look at it. At this stage it is then useful to provide a literature study

on the structure of the supposedly liquid like layer that resides at the top of the thin


films. If the surface layer with enhanced mobility is responsible for the Tg reductions

in supported films, it is natural to expect that the reductions are greater in freely-

supported films because of the presence of two free surfaces. However the fact that

the mobility is enhanced is challenged by several works that probe directly the

surface dynamics.

2.2.3 Characterization of free surfaces

Several groups studied the dynamics of polymers at or near the free surface. This

provides essential information on the possible link between the nature of the free

surface and its influence on the Tg of thin films. Many different techniques have been

developed and used to probe the mobility of polymer molecules near a free surface.

These experiments measure: the diffusion of polymer chains27, the damping due to

the interaction with an AFM tip,28 the relaxation of molecular alignment,29, 30 the

local volumetric glass transition temperature31 and the relaxation of a mechanical

strain achieved with nanometric indenters.25 In this last work Frakhraai et al.

observed that nanoscale indentations on the surface of polymer glass relax much

faster than comparable relaxation processes in bulk. This evidence suggests the

presence of a highly mobile surface layer of few nanometers. Furthermore, the

surface relaxation process has an almost temperature independent activation process,

a feature that may explain the low value of fragility obtained for ultrathin freely-

standing films.

Despite the large amount of studies, results are contradictory and the experimental

proof that the free surface is liquid-like is still under debate. As a consequence, a

clear explanation for the large reductions of Tg observed in freely standing films is

still missing.

We showed that the interfaces (free or solid) have a large influence on the Tg of thin

films. The influence of the interfaces may extend into the film, creating a gradient of

glass transition temperatures, reflecting heterogeneous dynamics.


2.2.4 Heterogeneous dynamics

As discussed in the first chapter, polymers at temperatures close to Tg are

characterized by non-exponential relaxations and heterogeneous dynamics. A further

complexity when studying ultrathin films is the gradient of mobility induced by

interfaces. In this case, the nature of the heterogeneity is directional and normal to the

surface.

Evidences of heterogeneous dynamics of thin films arise from the broadening of the

relaxation process under confinement24, 32 and from the increase of the width of the

glass transition as measured by ellipsometry.33

Ellison and Torkelson were the first to measure the depth-dependent Tg. By placing

fluorescent labels in only one layer at a specific position inside multilayer PS films

they determined a volumetric glass transition temperature averaged over a depth

region of typically 15 nm. They found that the local Tg of PS was smaller than the

bulk value at the free surface, but continuously approached the bulk Tg over several

tens of nm into the film.31

The same experimental method was later applied to freely-standing PS films and, also

in this case, confirmed the existence of a Tg gradient along the film thickness.34

Interestingly, when the total thickness of the freely standing film is reduced below

60 nm no gradient of glass transition temperature is observed. In fact, in this case, the

Tg of a 15 nm labeled layer does not vary whether it is located on the surface or in the

middle of the film, and agrees with the averaged Tg of a single layer freely standing

film of similar thickness. The authors hypothesized that the suppression of the Tg

gradient is due to the effect of the two surfaces propagating into the film and

impacting the average dynamics in the interior of the sample. When films are too thin

they cannot support the full gradient of Tg observed in thick samples. This leads to an

apparent suppression of the mobility gradient and to the measurement of an averaged

Tg across the whole film. This interpretation is in line with an analysis by Napolitano

et al. on the dielectric spectra of freely standing ultrathin films of PS. They showed

an asymmetric broadening of the structural relaxation peak toward lower

temperatures and that the broadening increases with the film thickness because of the


presence of two free surfaces. Freely standing films thinner than a certain threshold

should not contain any bulk component.

In this thesis (see Chapter 4),35 we expanded the multilayer approach to dielectric

spectroscopy. By using multilayer films capped between aluminum layers we have

been able to map, at different distances from the metallic surfaces, not only the Tg but

also the relaxation time distribution over a broad frequency range. Measurements

proved that the metallic surfaces influence the Tg of the interfacial layers. The

variations of the relaxation time distribution confirmed our picture.

To model such heterogeneities, it may be possible to divide the film into various

discrete layers of different mobility. Indeed, experimental results on the Tg of

supported ultrathin films have been generally explained in terms of a bi- or three-

layer models,32, 33, 36 the last one originally proposed by DeMaggio et al.37 These

models assume that the dynamics of the material and thus the glass transition

temperature of each layer is different. The bi-layer model consists of a free surface

layer with enhanced mobility and reduced Tg compared to the bulk and a rest of the

film with a bulk like behavior. The three layer model accounts also for a layer in

contact with the substrate where the polymer dynamics is slower than in the bulk.

This substrate-interface layer is considered to be “immobile”, showing no Tg over the

temperature range of interest or characterized by a reduced mobility layer and an

higher Tg compared to the bulk. Already 40 years ago, NMR measurements on

carbon black filled polymers demonstrated the presence of different regions of

mobility around the fillers: a region of unbound material with bulk mobility, an outer

shell with less mobility and an inner shell of tightly bounded chains with almost no

mobility.38

It is likely that interfaces perturb the segmental dynamics of the interfacial layer and

that this perturbation extends to the adjoining layers, albeit with a lower strength, see

Fig 2.4. This implies that the dynamic behavior will vary smoothly with the distance

from the interfaces and not in a sharp way as predicted by simplified layer models.


Hence, to take in account layers with different mobility it is more appropriate to use

multilayer models.39 Moreover, multilayer models avoid misleading due to the use of

very sharp mobility profiles in the estimation of the dimension of the dead layer.

Figure 2.4 Illustration representing the effect of the substrate and the free surface on the distribution of glass transition temperature in supported thin films.

As summarized in a recent review, simulation works on confined polymers support

the view of an interface-induced gradient in relaxation dynamics.40 These works

reveal a complex relaxation behaviour of confined systems on approaching the glass

transition. They also report deviations of Tg which are in qualitative agreement with

the trends observed in experiments. The propagation of enhanced or reduced mobility

from the boundary toward the interior of the film has been observed in both freely-

standing and supported polymer films. These studies carried out analysis of highly

mobile monomers in the case of the freely-standing film and of immobile monomers

for the supported film. In both cases, it was found that clusters of these monomers

originate at the interface and penetrate into the bulk of the film. Other simulations

showed that for a given interface, as the temperature is lowered, the perturbation

introduced by the walls on the mobility increases and persists further into the bulk

material. These works further justify the use of multilayer approach to model the

dynamic behavior of thin film.

Polymer-substrate interface

Free surface


In this thesis we introduced a multilayer model able to describe the dielectric data of

different polymers confined between two attractive walls (Chapter 5).41 The model

provided information about the penetration depth of the surface induced perturbations

along with the thickness of the immobile (or reduced) mobility layer at the polymer-

substrate interface. For films of dye-labelled polystyrene it was possible to determine

the temperature evolution of the interfacial mobility profile. The results showed a

trend similar to previous molecular dynamics simulations,42 and showed that the

influence of interfaces on the mobility of thin films increases upon cooling. One of

the outcome of the model is that the spatial extension of interfacial effects is limited

by the gyration radius at temperatures much larger than Tg, while increases

significantly with approaching Tg .

2.3 Non-equilibrium Nature of Thin Polymer Films

2.3.1 Spin coating process

In this thesis, we prepared thin polymer films by spin coating, which allows obtaining

uniform films with a well-defined thickness. When discussing about dynamic

properties of thin polymer films we need to consider if the sample preparation is a

possible cause for the anomalous behavior observed in such systems. The spin-

coating process consists in depositing a drop of a dilute polymer solution onto a

substrate and then spin at high angular velocity to spread the solution and to

evaporate the solvent. During the solvent evaporation the glass transition temperature

of the system increases until it equals the ambient temperature and the system

vitrifies.43 At this point the film still contains a significant amount of solvent,

typically volume fraction of 10-20 %.44 The solvent loss proceeds also in the glassy

state although at a much slower rate compared to the first stage of spin-coating,45 and

depends on the complex structure of the film during evaporation.43 It is a common


practice to anneal the films at high temperatures for a long time in order to facilitate

the evaporation of the solvent stuck in the polymer after the preparation.

In a recent work Perlich et al. studied the presence of residual solvent in spin-coated

films of various thickness by neutron reflectometry.46 Experiments were carried out

on a model system such as polystyrene spin-coated from toluene onto silicon

substrates. Films of different thicknesses were prepared by changing the

concentration of the polymer in the solutions. Measurements on films probed directly

after spin-coating revealed that the remaining solvent content increases with

increasing film thickness, varying from the 10 to the 20 % vol. Although thinner

films are prepared starting from solutions with a higher concentration of solvent

compared to thicker films, it is likely that during the spin-coating process the solvent

evaporation is more efficient for the thinner ones. In fact, the solvent evaporates at

the free surface giving rise to a gradient of concentration that is the driving force for

the diffusion of solvent molecules toward the polymer/air interface. A crust forms on

the surface and for high thicknesses the diffusion path for the solvent molecules is

longer and less solvent can reach the free surface to evaporate at a given time. This

would explain the higher solvent concentration found in thick samples just after the

spin-coating process. Thermal treatments above Tg decreased the quantity of solvent,

however they were not suitable for removing all remaining solvent. The authors

observed that even after an annealing of 8 h under vacuum at T = Tg + 60 °C

polymer films retain a significant amount of solvent, 10% vol.

An area of controversy when studying the glassy dynamics of thin films is the

potential effect of the solvent molecules trapped in the films. It has been argued that

the observed Tg reduction in ultrathin polymer films can be traced back to the

presence of solvent after a non appropriate annealing procedure.47 The solvent

molecules may reduce the Tg because of plasticization effect without necessarily

invoking interfacial or size effects. However, the results by Perlich contradict the idea

that the reduction of glass transition temperature is imputable to the solvent retention

because the largest deviations of Tg are observed for thinner films where the solvent

content is lower than in thicker films.


2.3.2 Out of equilibrium glassy thin film

Whatever the effect of the solvent content on the measured Tg is, thin films obtained

by solvent quench (spin coating) are “out of equilibrium” in the sense that during

ageing the solvent should evaporate and the film should relax toward the state that

would be obtained by thermal quench. Note that films obtained by thermal quench

are as well out of equilibrium, a feature that they share with bulk glasses in general.

Thin films obtained by spin coating are therefore in a very complex state because

additionally, the conformation of the chains is frozen in a different state that what

obtained by quenching from the melt. In solution (before spin coating), the chains are

isolated one from the other while in melt they are entangled. Therefore during spin

coating the entanglement density must increase toward the melt value. However this

process may not have time to be fully accomplished during the preparation because

the spin coating proceeds in a very short time. Annealing above Tg could promote

chains re-entanglement. This process have been invoked in order to explain dewetting

experiments48 and the changes of viscosity observed upon annealing thin films.49

Note that when thin films are deposited on a strongly attractive surface, annealing

above the bulk Tg promotes adsorption of the chain segments onto the surface. This

can have an influence on the dynamics as shown in the next paragraph.

2.4 Adsorption and Chain Conformations

A deeper understanding of the dynamic and structural properties of thin polymer

films may be reached by studying the adsorption process and the conformation of

chains in contact a with solid surface. This study is also relevant to technological

applications, because the deposition of polymer thin films controls important

processes such as adhesion and friction.

We can mention different kind of adsorption on the basis of the interaction with the

surface. If the sticking energy between the segment and the surface is high (formation

of covalent bonds), the adsorption process is chemisorption, while for low energies it


is called physisorption. In this last case, we can have weak physisorption for

interactions on the order of kBT (van der Waals interactions) or strong physisorption

for interaction of about 10 kBT (hydrogen bonding). Strong physisorption is relevant

to some common polymers (PDMS, PMMA..) deposited on oxidized metal and

silicon surfaces. Adsorbing polymer chains generally contain sequences of surface-

bound monomers, called trains, and loops and tails extending away from the

surface,50 see Fig 2.5.

Figure 2.5 First arriving chains adopt a flat configuration forming trains; later arriving chains assume a loosely configurations with more loops and tails.

The importance of polymer adsorption has motivated extensive experimental and

theoretical investigations.51 The main physics governing polymer adsorption are

based on the competition between the energy gain per segmental adsorption and the

corresponding lost of conformational entropy of the chain. As a result, the thickness

of an adsorbed layer depends on the ratio (a/ , where a is the size of the Kuhn

segment and is an adsorption energy scale close to kBT.52 However in real cases,

even when heated well above Tg, the time required to reach the equilibrium thickness

can be much longer than the typical experimental time scale and the chains are

trapped in non-equilibrium conformations. As a result, dynamic and structural

properties of adsorbed layers are time dependent.

In particular, the chain conformations can change with time and surface coverage:

chains arriving first at the surface find space and adsorb with a relatively flat

conformation while those arriving later, finding less available space, adsorb with a

loosely bound conformation.53 In other words, a given chain in the adsorbed layer,


either belongs to the surface-bound part with more trains (high bound fraction) or to

the outer layer with more loops and tails (low bound fraction), as depicted in Fig 2.5.

The specific chemical structure of polymer chains selects among the possible

conformations (train, loops, tails) through the specific interaction of the segments to

the surface. Polymers containing end-functionalized groups are irreversibly adsorbed

(grafted) onto the surface forming the so called “polymer brushes”, where chains are

uniformly stretched away from the substrate to avoid the overlapping,54 see Fig 2.6

(a).

An alternative way for obtaining irreversibly adsorbed layers (with a controlled

thickness) is the protocol proposed by Guiselin.55 When a polymer melt is exposed to

an attractive surface, chains adsorb irreversibly. After annealing for a sufficient time,

if then the system is immersed in a good solvent, chains which are not adsorbed will

be washed away and the remaining layer will contain only the chains the most

strongly adsorbed onto the surface. Adsorbed layers obtained with this procedure are

called Guiselin’s brushes or “pseudo-brushes”, see Fig 2.6 (b).

Figure 2.6 a) Polymer brush, b) Polymer pseudo-brush (Guiselin’s brush), c) Density profile (z) of a pseudo brush, where z is the distance from the solid surface

Using scaling arguments, Guiselin derived the thickness of the polymer layer h and

its density profile (z) where z is the distance to the solid surface. For chains made of

N monomers with a Kuhn monomer size a, the thickness scales such as h aN5/6,

while (z) (a/z)2/5, where a < z < h. Near the polymer-solid interface, the

concentration of monomers is very high and the layer is very dense. Away from the

0,5 1,0

20

40

(z)

z [n

m]

c) density profile pseudo-brushb) pseudo-brusha) polymer brush


solid surface adsorbed layer is fluffier, as shown in Fig 2.6 (c) for polystyrene (a =

1.8 nm).

In this thesis (Chapter 6)56 we studied the adsorption process of a thin layer of dye-

labeled-PS deposited onto two different substrates: a PS Guiselin’s brush and a metal

surface. The Guiselin’s brush has been used to ensure that no interaction of the

labeled polymer can take place with the metal because of the high density of the

brush near the solid surface, limiting diffusion. When the labeled layer is in contact

with the metal surface there is a first stage where the dye-moieties are oriented

parallel to the solid surface and adsorb progressively following a power law regime.

Then, the adsorption kinetics slows down, following a logarithmic law, while the

dye-moieties orient preferentially perpendicular to the surface. These results were

compared with changes of chain conformation observed in other systems (see above).

Furthermore, the study of the film deposited on the pseudo-brush provided a strong

evidence that the phenomena observed for the labeled layer on the metal surface are

indeed related to the adsorption process and not to other processes such as stress

relaxations, evaporation of residual solvent.

The characteristic (out of plane) diffusion time of labeled polymer chains through

polymer layers of different structure and thickness has been the subject of another

study by our group. Parts of the results are presented in Chapter 7.57

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Segmental Mobility and Glass Transition Temperature of Freely Suspended Ultrathin Polymer Membranes

38

Chapter 3

Segmental Mobility and Glass Transition

Temperature of Freely Suspended Ultrathin

Polymer Membranes

Cinzia Rotella, Simone Napolitano* and Michael Wübbenhorst*

Department of Physics and Astronomy, Katholieke Universiteit Leuven Laboratory for Acoustics and Thermal Physics, Celestijnenlaan 200D, B-3001 Leuven, Belgium

* corresponding author

Adapted with permission from

Macromolecules, 2009, 42 (5), pp 1415–1417Copyright © 2009, American Chemical Society


39

Abstract

The segmental dynamics of freely standing films of high molecular weight atactic

polystyrene (PS) was studied by dielectric spectroscopy at frequencies between 1 and

106 Hz. To probe the dynamics of the films without altering their two free surfaces,

we applied an in-plane electrical field to samples suspended over m-spaced,

elevated, interdigitated comb electrodes. The analysis of the frequency and

temperature dependent complex electrical capacitance revealed tremendous

reductions in the glass transition temperature (Tg), up to 60 C compared to bulk, in

line with previous literature data based on optical techniques.

Segmental Mobility and Glass Transition Temperature of Freely

Suspended Ultrathin Polymer Membranes

Extensive investigation of polymer layers confined in nanometer sized geometries

revealed that the presence of an absorbing substrate or a free surface alters properties

of polymers such as biaxial creep behaviour,1 flow and intermolecular

entanglements,2 diffusion of small molecules inside the matrix,3 crystallization

kinetics,4, 5 physical aging,6 the glass transition temperature (Tg),7 and thus local chain

(segmental) mobility.8-12 In bulk, the local chain mobility can be investigated by

means of several experimental approaches.13 On the contrary, due to obvious

instrumental difficulties, a technique probing the local chain dynamics of freely

standing ultrathin polymer films was not available so far.

In this Communication, we introduce a novel experimental method taking advantage

of the sensitivity of dielectric spectroscopy (DS) and being able to probe the

segmental dynamics of freely standing ultrathin polymer over a broad frequency

range (1 Hz – 1 MHz) without altering or eliminating14 their two free surfaces. The

glass transition temperatures assigned by the approach described in this

Communication are in excellent agreement with data from the literature.


40

In our approach, polymer films are suspended over interdigitated comb electrodes,

IDE.15 The electric signal is measured by applying an AC voltage to elevated metallic

electrodes made up by the two interdigitated comb structures deposited on a highly

insulating substrate, see Figure 1a. For films of thickness D much smaller than the

separation between two neighbored finger electrodes (~10 m), the electric field lines

penetrate inside the layer with a direction parallel to the surface. Consequently, the

individual complex electric capacitances of all sublayers (of thickness Di) constituting

the membrane add-up to the total capacitance according to * *( , , ) ( , , )TOT i ii

C T D C T D , an expression that holds for any angular frequency

and temperature T.16 Under these conditions, the different contributions to the

relaxation spectra are linearly superimposed. The comb electrode geometry, in fact,

avoids ambiguities arising from spectra of ultrathin films probed by an electric field

orthogonal to the surface, as in the parallel plates geometry10 where capacitances

enter in a series model, 1* 1 *( , , ) ( , , )TOT i iiC T D C T D . To prove the feasibility

of our technique, we investigated the structural relaxation dynamics of atactic

polystyrene, PS, a system widely explored in both supported and freely standing

geometry.17-19

Because of the micrometer spacing between the electrodes, IDE allow the employing

of higher voltages compared to the parallel plate geometry, ensuring a better

signal/noise ratio. In fact, keeping constant the electric field, the maximum voltage

applicable in the IDE is larger than the one in the parallel plate geometry by a factor

equal to the ratio between the distance separating the fingers (~10 m) and the film

thickness (~10-100 nm). The low intensity of the applied electric field (~105 V/m)

does not alter the properties of the investigated materials but acts a perturbation in the 6 V/m).

Atactic polystyrene of three different molecular weights (Mw = 932, 1200, and 3000

kg/mol, PDI < 1.3) was used as received from Polymer Source Inc. Because of the

low value of the intrinsic dipole moment of PS, the polymer was doped with a small

fraction (0.5 wt%) of 4,4’-(N,N-dibutylamino)-(E)-nitrostilbene, (DBANS), an

organic molecule with a high dipole moment acting as “dielectric probe”. The


41

feasibility of this approach has been already tested successfully in bulk and confined

polymer layers by means of both dielectric20, 21 and fluorescent probes.6, 22-24 Here,

the addition of DBANS solely increases the sensitivity of our measurements and does

not alter the segmental mobility. Exact amounts of the polymer and the probe were

mixed together and dissolved in chloroform; ultrathin films of PS with different

thicknesses were prepared by spin coating drops of solutions of different

concentrations on freshly cleaved mica substrates. Film thicknesses were determined

by ellipsometry on reference samples prepared under the same spin coating

conditions (same concentration, spin speed and time) and deposited on Si wafer.

Freely-standing films were obtained by a standard water transfer technique.19 Well-

dried and equilibrated films were transferred to the top of the IDE comb electrodes

for the dielectric measurements. Consecutively repeated thermal ramps in heating and

cooling resulted in annealing of the film for a minimum of 3 up to 6 hr above bulk Tg

(see Supporting information).

Measurements of the complex electric capacitance of PS were performed under high

vacuum in the temperature region from above the bulk glass transition down to room

temperature in the frequency range from 1 Hz to 1 MHz using a high-resolution

dielectric analyzer (Alpha Analyzer, Novocontrol Technologies). The response of the

material originates from the correlated fluctuations of permanent dipole moments

which provide the physical link between the molecular motion and the interactions

with an external electric field.

IDE structures were purchased from Xensor Integration. Each metal comb structure

(finger) is 5 m wide and 0.8 m high and the mean distance between two

consecutive oppositely charged finger is 8 m, see Figure 1a. Contributions of the

empty chip to the dielectric response were subtracted. A detailed report on the

dielectric characterization of the IDE chips and on the related issues regarding to the

measurements is in preparation.

Atomic Force Microscopy was used in order to verify the stability of the freely-

standing ultrathin layers after repeated dielectric measurements cycles. Samples were

imaged using a MultiModeTM (Digital Instruments) operating in tapping mode at

room temperature with high aspect ratio silicon tips. Figure 1b displays a 20 m 20


42

m AFM topographic image of a 65 nm-tick film of PS (Mw=3´ 106 g/mol) deposited

on the top of IDE after a complete thermal measurement cycle where the sample was

brought up to 70 C above the film Tg. The polymer membrane was found to be

suspended over the substrate, laying 150 nm from the top of the electrodes and its

root-mean-square roughness was on the order of 1 nm. This proves that the film, even

after the measurement, remains intact and freely-standing. Refer to the supporting

information for an image at a larger scanning area (50 m 50 m).

(a)

(b)

Figure 1 (a) Schematic representation of the IDE chip, the red and blue fingers are at opposite potential. The height of the structures is 0.8 m, the width of each finger is 5

m and the mean distance between two neighbored fingers is 8 m. The black arrows represent the direction of the E-field inside the film. (b) AFM image 20 m 20 m(topography) of a 65 nm-thick film of PS after annealing at 70 C above its Tg (see the text). The white dashed lines reproduce the structure of the empty chip. The peaks at the edge of the electrodes metal build-ups already present in the empty chip.


43

The response of the film is dominated by a peak which shifts in temperature and

frequency following a super-Arrhenius activation law. The peak is attributed to the

structural (or ) relaxation of polystyrene, the dielectric manifestation of the glass

transition dynamics, and it originated from the correlated motion of several repeating

units belonging to the same or different macromolecules. The experimental data were

analyzed by means of model independent parameters, relating the traces of the -

modes to those couples of values of frequency and temperature (fmax, Tmax) identifying

the maximum of the structural relaxation peak.13

The -relaxation time, , was calculated from fmax, via the relation 2 fmax =1, and

its temperature dependence was fitted by means of the Vogel-Fulcher-Tammann

(VFT) equation

0

0

exp BTTT T

(1)

which describes a thermally activated process with an apparent activation energy 1

0 0app BE T k T BT T T that increases upon cooling.25 Following a common

convention, the glass transition temperatures of the samples were obtained by

extrapolating Eq.1 to Tg = T( = 100s). In Figure 2a we compare the Tg values of

films of different thickness and different molecular weight with the scaling law

proposed by Dalnoki-Veress et al.19 for freely standing ultrathin films of high

molecular weight PS (Mw 514 kg/mol). The data obtained via our new experimental

approach are in excellent agreement with those obtained by Brillouin Light

Scattering,18, 26 ellipsometry19, 26 and recently also by fluorescent methods.24

This new finding proves that the tremendous Tg reductions in freely standing films of

PS as previously observed on the basis of discontinuities in the volume thermal

expansivity are truly related to a correspondingly huge shift in the time scale of the

structural relaxation. This shift, expressed by the ratio between the relaxation time of

the film and the one in bulk at a given temperature, approaches the value of 10-6 (i.e,

the relaxation peaks are separated by 7 decades in frequency) at bulk Tg and further

increases upon cooling, see Figure 2b. Such temperature dependence is in agreement


44

with our previous work on supported films10, 27, 28 and with several other experimental

observations6, 29 and computer simulations.30

(a) (b)

Figure 2 (a) Thickness dependence of Tg of freely standing membranes of high molecular weight PS. The colored lines are readapted from the scaling law proposed in ref 19 (b) Relaxation map of the local chain mobility for a film of PS (932k) of 40 nm. The dashed line is a VFT fit to the experimental points. The solid line is a VFT fit for a PS bulk sample, from ref 20

Acknowledgments

CR acknowledges financial support from the Research Council of the K.U.Leuven, project no. OT/30/06. SN acknowledges financial support from the European Community's 'Marie-Curie Actions' under contract MRTN-CT-2004-504052 [POLYFILM] and f.w.o. (Fonds Wetenschappelijk Onderzoek - Vlaanderen) for a postdoctoral scholarship.


45

References

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(2) Shin, K.; Obukhov, S.; Chen, J. T.; Huh, J.; Hwang, Y.; Mok, S.; Dobriyal, P.;

Thiyagarajan, P.; Russell, T. P. Nature Materials 2007, 6, 961-965.

(3) Pu, Y.; White, H.; Rafailovich, M. H.; Sokolov, J.; Patel, A.; White, C.; Wu, W.

L.; Zaitsev, V.; Schwarz, S. A. Macromolecules 2001, 34, 8518-8522.

(4) Capitan, M. J.; Rueda, D. R.; Ezquerra, T. A. Macromolecules 2004, 37, 5653-

5659.

(5) Napolitano, S.; Wubbenhorst, M. Macromolecules 2006, 39, 5967-5970.

(6) Priestley, R. D.; Ellison, C. J.; Broadbelt, L. J.; Torkelson, J. M. Science 2005,

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Letters 1996, 77, 2002-2005.

(8) Fakhraai, Z.; Forrest, J. A. Science 2008, 319, 600-604.

(9) Fukao, K.; Miyamoto, Y. Physical Review E 2000, 61, 1743-1754.

(10) Napolitano, S.; Lupascu, V.; Wübbenhorst, M. Macromolecules 2008, 41,

1061-1063.

(11) Serghei, A.; Kremer, F. Physical Review Letters 2003, 91.

(12) Qi, D.; Fakhraai, Z.; Forrest, J. A. Physical Review Letters 2008, 101, 4.

(13) Donth, E., The Glass Transition, Relaxation Dynamics in Liquids and

Disordered Materials. Springer-Verlag: New York, 2001.

(14) Sharp, J. S.; Forrest, J. A. Phys. Rev. Lett. 2003, 91, 235701-1.

(15) den Otter, M. W. Sensors and Actuators a-Physical 2002, 96, 140-144.

(16) Peter, S.; Napolitano, S.; Meyer, H.; Wubbenhorst, M.; Baschnagel, J.


(17) Forrest, J. A.; Dalnoki-Veress, K.; Dutcher, J. R. Physical Review E 1998, 58,

6109-6114.

(18) Mattsson, J.; Forrest, J. A.; Borjesson, L. Phys. Rev. E 2000, 62, 5187-5200.

(19) Dalnoki-Veress, E.; Forrest, J. A.; Murray, C.; Gigault, C.; Dutcher, J. R.

Physical Review E 2001, 6303, 1801.


46

(20) van den Berg, O.; Sengers, W. G. F.; Jager, W. F.; Picken, S. J.; Wubbenhorst,

M. Macromolecules 2004, 37, 2460-2470.

(21) Priestley, R. D.; Broadbelt, L. J.; Torkelson, J. M.; Fukao, K. Physical Review

E 2007, 75.

(22) Ellison, C. J.; Torkelson, J. M. Nature Materials 2003, 2, 695-700.

(23) Rittigstein, P.; Priestley, R. D.; Broadbelt, L. J.; Torkelson, J. M. Nature

Materials 2007, 6, 278-282.

(24) Kim, S.; Roth, C. B.; Torkelson, J. M. Journal of Polymer Science, part B:

Physics 2008, 46, 2754-2764.

(25) Dyre, J. C. Reviews of Modern Physics 2006, 78, 953-972.

(26) Forrest, J. A.; Dalnoki-Veress, K.; Dutcher, J. R. Physical Review E 1997, 56,

5705-5716.

(27) Napolitano, S.; Wubbenhorst, M. Journal of Physical Chemistry B 2007, 111,

5775-5780.


9197-9199.

(29) Fakhraai, Z.; Forrest, J. A. Physical Review Letters 2005, 95.

(30) Peter, S.; Meyer, H.; Baschnagel, J. Journal of Polymer Science Part B-

Polymer Physics 2006, 44, 2951-2967.


47

Supporting information

1) To further prove that the film remains stable after the measurements cycles, we

added a larger topography AFM image (50 m 50 m) of a 65 nm-thick film of PS

after annealing at 70 C above its Tg

2) Scheme of the typical thermal cycle used for the measurements

0 200 400 600 800 1000 1200 1400 1600 180020

40

60

80

100

120

T [C

]

time [min]

TgBULK

-

Distribution of Segmental Mobility in Ultrathin Polymer Films 49

Chapter 4

Distribution of Segmental Mobility in Ultrathin

Polymer Films

Cinzia Rotella†, Simone Napolitano*†, Lieven De Cremer‡, Guy Koeckelberghs‡,

and Michael Wübbenhorst†

† Katholieke Universiteit Leuven, Laboratory of Acoustic and Thermal Physics, Department of Physics and Astronomy, Celestijnenlaan 200D, B-3001 Leuven, Belgium‡ Katholieke Universiteit Leuven, Laboratory of Molecular Electronics and Photonics, Department of Chemistry, Celestijnenlaan 200F, B-3001 Leuven, Belgium

*corresponding author

Adapted with permission from Macromolecules, 2010, 43 (20), pp 8686–8691

Copyright © 2010, American Chemical Society

‡ Lieven De Cremer and Guy Koeckelberghs synthesized and characterized the

Chromophore-Functionalized Polymer


Abstract

We investigated by dielectric relaxation spectroscopy the distribution of glass

transition temperatures and dielectric relaxation strength inside ultrathin polymer

films capped between metallic layers. Measurements of the local dielectric properties

were achieved by selectively placing layers of dye-labeled polystyrene at different

depth inside films of neat polystyrene of different thickness. We show experimental

evidence for an interfacial nature of the deviations from bulk behavior; in particular,

the value of the dielectric strength and the glass transition temperature strongly

depend on the distance from the solid interface. These peculiar profiles of static and

dynamic dielectric properties are discussed in terms of a physical picture based on

competition between chain adsorption and packing frustration at different annealing

conditions. Such a picture was able to rationalize common features observed in

properties of ultrathin films like reduction of the relaxation strength, broadening of

the dynamic glass transition process and finally a shift of the structural relaxation

time.

1. Introduction

The physical properties of polymers in the proximity of surfaces and interfaces have

been widely investigated in the last years. The interest for polymer surfaces and

ultrathin films arises from the development of nanofabrication processes, where the

knowledge about the structure and dynamics of interfacial layers has significant

implications.1 Numerous experimental works have established that properties of

confined polymers such as viscoelasticity,2, 3 crystallization kinetics,4-7 diffusion 8, 9

and glass transition temperature (Tg) 10-12 display significant deviations from their

bulk values. Substantial evidence supports the idea that the origin of those deviations

is mainly related to interfacial interactions rather than to solely size effects. It was

shown, for instance, that the presence of a free surface typically results in enhanced

mobility of the chain segments near the surface, which effectively yields a surface


layer with a reduced Tg, extending over a few nanometers inside the film.3, 13, 14 The

global mobility in ultrathin polymer films can also be affected by the presence of

solid surfaces like for supported films (having both a free surface and an interface

with a solid substrate) or capped films (layers embedded between two solid surfaces).

Increases in Tg upon thickness reduction are commonly reported for polymers

showing a strong chemical affinity with the substrate.15, 16 In this case, chain

segments in proximity of the interface are adsorbed and their mobility is seriously

hindered, leading to an increase of Tg.17-19 In contrast, small variations of Tg are

observed in case of weak or slightly repulsive interactions between the polymer and

the substrate.16 It is generally assumed that interfacial properties are directly governed

by the strength of intermolecular interactions. Nevertheless, even in case of favorable

polymer/substrate interactions, a reduction in Tg has been noticed and explained in

terms of packing frustration of chain segments adsorbed at the solid interfaces.20

Hence, it is reasonable to assume that the interplay between chain adsorption and

packing frustration gives rise to a profile of mobility and thus to a distribution of

glass transition temperatures across the film thickness.21-25 Despite substantial efforts

to study the effect interfaces on the polymer dynamics, it remains unclear how these

perturbations propagate inside the film. A successful approach to achieve depth

resolution for the glass transition temperature in ultrathin polymer films was

proposed and exploited by Torkelson and coworkers using fluorescence techniques.26-

28 By placing a (fluorescent) dye-labeled polymer layer at a specific position within a

stack of unlabeled polymer layers it was possible to determine a volumetric glass

transition temperature averaged over a depth region of typically 15 nm.26

In our experiment, we adopted the multilayer approach by taking advantage of the

sensitivity of dielectric spectroscopy to determine the profile of the structural

relaxation time resolved along the thickness. In fact, this technique, in contrast to

dilatometric measurements, is able to investigate the relaxation processes and thus the

relaxation time distribution over a broad frequency range for temperatures extending

from above to below the bulk glass transition. In addition to the information achieved

on a depth profile of Tg, the investigation of the structural relaxation allowed us to

map the molecular mobility also by means of the dielectric strength, a quantity


proportional to the amount of mobile molecules relaxing on the time- and the

lengthscale of the dynamic glass transition.

The determination of the actual mobility depth profile via the multilayer approach is

of crucial importance to test theoretical models and predictions of materials

performances at the nanoscale, but it is also challenging from the experimental point

of view. The study required the synthesis of a labeled polymer with specific

properties such as a sufficient content of dye molecules that ensured an enhanced

dielectric strength relative to the neat polymer and a high molecular weight, in order

to reduce the inter-diffusion depth between consecutive layers.

In this study, we first describe the synthesis and the dielectric properties of high

molecular weight (Mw) dye-labeled polystyrene (chromophore: disperse red one,

DR1). Subsequently we focus on the dynamics of bi- and trilayers of labeled PS (l-

PS) and neat PS of similar Mw, discussing the impact of layer thickness and annealing

conditions at different depth positions. Finally, we study the effect of annealing on

the evolution of the profile of molecular mobility providing a solid physical picture of

the changes of Tg in proximity of an interface.

2. Experimental section

2.1 Synthesis of the chromophore-functionalized polymer

Styrene (5.97 mL; 51.9 mmol), 3-(ethynyl)benzoic acid (222 mg; 1.50 mmol) and

benzoylperoxide (BPO) (2.1 mg) were mixed, purged with argon and then stirred for

3 days at 70 °C. The polymer was dissolved in chloroform (100 mL) and precipitated

in methanol and dried. This procedure was repeated twice. Oxalyl chloride (3.00 mL)

was added to an argon-purged solution of the product (1.04 g) in dry toluene (200

mL). The mixture was stirred at 40 °C and the reaction was followed with infra-red

spectroscopy. After completeness of the reaction (typically 5h), the excess of oxalyl

chloride was removed at reduced pressure. The chromophore was synthesized

according to literature procedures.29 To a solution of the polymer, bearing the acid

chloride functionalities, in toluene was added 4-dimethyl aminopyridine (DMAP)

(855 mg; 7.00 mmol) and chromophore (2.59 g; 7.00 mmol) and the mixture was


stirred overnight at 40 °C. After concentrating, the labeled polymer was precipitated

in methanol and rinsed with methanol. The polymer was dissolved in toluene and

successively precipitated in methanol, rinsed with methanol and dried. This procedure

was repeated three times.

Gel permeation chromatography (GPC) measurements were done with a Shimadzu

10A apparatus with a tunable absorbance detector and a differential refractometer in

tetrahydrofurane (THF) as eluent toward polystyrene standards. The labeled PS used

in this study had Mn = 619 kg mol-1 and Mw = 819 kg mol-1. The structure of the

precursor polymers and the chromophore-functionalized PS was verified by 1H

nuclear magnetic resonance (NMR) measurements and were carried out with a Bruker

Avance 300 MHz. The content of chromophore in the labeled PS (1.25%) was

measured with UV-vis spectroscopy using a Varian Cary 400 apparatus. Atactic

polystyrene (Mw= 932 kg/mol) was used as received from Polymer Source Inc.

2.2 Preparation of Ultrathin polymer films and Multilayers

Ultrathin single layers of labeled PS (l-PS) and neat PS were prepared by spincoating

filtered solutions of the polymer in chloroform on glass slides onto which a 50 nm

thick layer of aluminum was previously deposited by thermal evaporation in a high

vacuum (p 10-6 mbar). Films of different thickness were obtained by changing the

concentration of the polymer in the solution. After deposition, all samples were

annealed at 120 °C for 2 hours on a hotplate in order to remove residual solvent and

to reduce the mechanical stresses induced by the spincoating procedure.30

Subsequently, the samples were kept under high vacuum for 1 hour at room

temperature. On completion, a second layer of patterned aluminum electrodes was

evaporated on top of the polymer film, resulting in individual capacitors with an area

of 4 mm2. A fast evaporation rate ( 10 nm/s) was used to obtain sharp polymer/metal

interfaces. Bilayer and trilayer films were prepared by spin-coating individual layers

on mica sheets and subsequently floating them from a water reservoir onto the blank

substrate or onto a previously deposited and annealed polymer layer. Water

occasionally trapped between consecutive layers was allowed to evaporate at ambient


conditions for a couple of days before the deposition of the next layer. After

assembling, the multilayer films were further annealed at 110 C for 1 hour. Sample

capacitors were obtained following the same procedure used for the single layer

films. The annealing conditions and the high molecular weights used in this work

permitted to obtain continuous films with labeled chains present only at particular

depth within the film, in particular interdiffusion between neighboring layers was

limited at 3 nm in the first heating run and reached 10 nm during the subsequent

cooling rate. 31

2.3 Dielectric relaxation spectroscopy

Dielectric measurements were recorded in the frequency range from 10-1 to 106 Hz

using a high- resolution dielectric analyzer (Alpha Analyzer, Novocontrol

Technologies). All measurements were performed under N2 in a closed cell to prevent

any possible oxidation or degradation. The thickness h of the samples was evaluated

from the value of the capacitance at room temperature using the relation for the

electrical capacitance in the geometry of parallel plates, C 0(S/h), where is the

permittivity of the vacuum, ttivity of the polymer and S is the effective

area of the capacitor (4 mm2).

For a quantitative analysis of the dielectric spectra in the frequency domain the -

peak was fitted with the empirical Havriliak-Negami (HN) function:

0

" Im1

baHNi

(1)

where HN is the mean relaxation time, is the relaxation strength, a and b shape

parameters which describe the symmetric and asymmetric broadening of the -peak,

while the last term accounts for ohmic conduction. For a more detailed description of

the fit procedure see ref 32. The dielectric strength proportional to both the mean

square dipole moment and the density of dipoles provides a measure of the amount of

mobile chains involved in the structural relaxation.


The structural relaxation times , calculated from HN, a and b,33 were fitted in terms

of the empirical Vogel-Fulcher-Tammann equation (VFT), which describes the

temperature dependence of supercooled liquid in the temperature range between Tg

and the melting point, Tm:

exp( )

V

V

ER T T

(2)

here, EV is the activation energy in the high temperature limit, TV is the Vogel

temperature, and denotes the ultimate relaxation time at T .34 From the VFT

parameters we can evaluate an operationally defined glass transition temperature

using the criterion Tg = T ( = 100s).

Multilayer films were modeled as a series of capacitance where *totC is given by

* * *tot labeled PS neat PS

1 1 1C C C

and *labeled PSC and *

neat PSC are the complex capacitance relative

to the l-PS and to the neat PS, respectively. From the knowledge of the intrinsic

contribution of neat PS, it was possible to extract the contribution of the labeled layer

from the total response of the multilayer film.

3. Results and discussion

3.1 Effect of confinement on the dynamics of single layers of neat and labeled PS

Polystyrene has a low intrinsic dielectric activity due to the presence of weakly polar

C-phenyl side-group that gives rise to the dielectric -relaxation. This dielectric

activity, expressed by the dielectric strength , however, can be facilitated by the

addition of a small amount of dipolar molecules.35 The idea of enhancing the

dielectric response of a nearly apolar polymer by doping with molecular dipoles that

are either dispersed (probes) or covalently attached to the polymer chain (labels) was

recently extended to ultrathin polymer films.36, 37 For example, dispersion of 1%

-(N,N-dibutylamino)-(E)-nitrostilbene (DBANS) increases the dielectric


strength of PS by a factor of 5,35, 38 while the dielectric loss of PS (Mw=13kg/mol)

was shown to be enhanced 65 times after covalently attaching DR1 (3% w/w)

directly onto the backbone.37

The inset in Figure 1 displays the imaginary component of the complex dielectric

function, ”(T), measured upon cooling at 1kHz for bulk samples of neat PS and l-PS

of comparable thickness (~100 nm). For the two different polymers, a peak

corresponding to the structural relaxation process ( -process), the dielectric signature

of the dynamic glass transition, is present. Compared to neat PS, the dielectric loss of

l-PS increased by a factor of 15 (for thick films). Analysis of the segmental mobility

provided that the labeling with DR1 probe molecules of 1.25% of the aromatic rings

does not alter the glass transition temperature ( = 100.3 10), or the dynamic fragility

m ( = 131 10), i.e. the steepness of the temperature dependence of the structural

relaxation, of polystyrene. A complete relaxation map of the two polymers is

provided in the Supporting Information.

Reduction of the thickness strongly affected the gain in the dielectric strength. Figure

1a shows the isochronal representation of the dielectric loss at 1 kHz for films of

various thicknesses, ranging from 10 nm to 106 nm, revealing a systematic decrease

of the intensity of the -peak. For comparison, the dielectric loss of single layers of

neat PS is reported in Figure 1b. It is noteworthy that for the neat polymer, the -peak

does not show any significant alteration down to a thickness of 25 nm, even after

severe annealing, see supporting information. In addition to the reduction of , two

other main features characterizing the thickness dependence on the -process of

several other polymers are present for l-PS. Upon reduction of the thickness, the

maximum of the -peak (T ) shifts (here towards higher temperatures), which is

indicative for a slowing down of the molecular dynamics, while the width of the -

peak increases due to a broadening of the distribution of the dynamic glass transition

process.


Figure 1: Temperature dependence of the imaginary part of the complex dielectric function " (frequency f = 1 kHz, cooling) for films of (a) labeled PS and (b) neat PS of different thickness. The inset in (b) shows the comparison between " (f = 1 kHz,cooling) for thick samples of labeled PS (h = 106 nm) and neat PS (h = 130 nm). Schemes of the repeating units are given.

On the basis of these findings, we reasoned that the different behavior between the

neat PS and l-PS arises from a specific interaction of the chromophore with the

substrate. We can argue that due to the presence of polar groups in the dye moiety

(DR1) the l-PS can establish a large number of contact points (forming H-bonds) with

the OH sites of the Al surface.

In an attempt to explore this hypothesis and to determine the actual depth profile of

the glass transition dynamics, we prepared multilayer films of l-PS and neat PS,

placing the chains with higher dielectric signal at specific positions inside films of

neat PS. Regardless of the reduction of , even at 15 nm, the l-PS is well-suited for

this study because of a sufficient contrast in dielectric signal over neat PS.

0.00

0.05

0.10

0.15

0.20

40 60 80 100 120 1400.000

0.005

0.010

0.015

80 100 120 140 0.00

0.05

0.10

0.15CH2 CH

n

CH2 CH CH2 CHn1-x x

ON N

N NO2

O

19nm15nm10nm

106 nm75nm36nm

"

(a)

(b)

130 nm 45 nm 25 nm

"

T [ C]

A


Values of the glass transition temperature measured in different geometries are

plotted as function of the film thickness in Figure 2 (geometry 1). A continuous

increase of Tg up to 4 C at 19 nm is observed for single layers of l-PS. The increase

of Tg upon thickness reduction can be explained in terms of a reduction of mobility in

proximity of the metallic interface, as already discussed in previous work.18, 39

Because of strong favorable polymer-substrate interactions, polymer chains in

intimate contact with the solid interface are partially absorbed and consequently

exhibit a slower dynamics compared to their behavior in bulk.40 The resulting

perturbations in the dynamics and structure (local packing) propagate into the depth

of the film and decay after a characteristic distance, rationalized by a reduced

mobility layer (RML) after which bulk mobility is largely recovered.18 The RML

would correspond to a layer of chains physisorbed at the interface where a certain

fraction of its monomers is bound onto the surface and have almost zero mobility.

The extension of the RML depends on various parameters such as the substrate

polymer interaction and on the flexibility of the polymer chains. At higher surface to

volume ratios (reduction of the thickness), due to the reduction of the bulk

component, interfacial layers have a larger impact on the film properties.

Under those conditions, we can rationalize the tremendous drop by merely 85% of

compared to the bulk value observed for the thinnest samples (see Figure 2

(geometry 1)). A reduction of the dielectric strength corresponds, in fact, to a

decrease of the density of the fluctuating dipoles, contributing to the dielectric signal.

In amorphous ultrathin polymer films, this trend can be explained by considering that

due to the reduced mobility, interfacial chains have a lower or almost zero value of

. For l-PS the reduction of scales with the inverse of the thickness, in line with

data reported for other polymers.41-43 This trend corresponds to a profile of molecular

mobility sketched by the step-like function of the inset of Figure 2b, related to a

bilayer model system where a bulk-like core is sandwiched between two dead layers

(DL), i.e. a fraction of molecules where the structural relaxation is inhibited over the

whole experimental temperature range. The dimension of DL was estimated

= 0 is achieved. From our

results we evaluated a DLPS-DR1 6nm, a value larger than the one reported for a


strongly adsorbing polymer like poly (2-vinylpyridine) on Al ( 3nm),44 and in

agreement with the one extrapolated for a low molecular weight l-PS on Al ( 7

nm).37

3.2 Impact of annealing on the distributions of Tg and dielectric strength

To investigate the influence of annealing on the behavior of chains at the interface,

we measured the response of multilayer films both during heating (RT 150 C)

and cooling scans (150 C RT), a condition which corresponds to respectively

short and long annealing times. In fact, changes in the properties of ultrathin films

held above Tg scale with the same activation energy as the structural relaxation, i.e.

annealing at higher temperatures compare to longer annealing times at lower

temperature provided that time-temperature superposition is fulfilled.

We first analyzed the total dielectric signal of multilayer films obtained by

assembling layers of 45 nm thick layers of PS neat and 15 nm thick layers of labeled

PS, see Figure 3.

Comparing the signal in heating and cooling we observed a reduction of the peak

height as the result of annealing only when the l-PS layer was in direct contact with

the metal. On the contrary, no relevant changes of the dielectric loss curve have been

found for the trilayer film, where the labeled layer was placed between two thick

layers of neat PS. These findings clearly support our picture that this reduction of

originates from a specific interaction between the polymer and the substrate, which,

in this specific case, is physisorption of dye moieties at the metallic interface. This is

further in line with the idea that deviations from bulk behavior originates from

conformations assumed by the absorbed chains at the interfaces.44

Extracting the response of the labeled layer from the total dielectric function of the

multilayer film, we were able to quantify the segmental dynamics and the dielectric

strength at different distances from the interface and check their evolutions upon

annealing. Such a procedure is facilitated by the difference in dielectric strength

between the two different layers and justified by our previous work on averaging of

the dielectric signal in ultrathin polymer films.18,24


Figure 2: Values of glass transition temperature, Tg, (a) and dielectric strength, ,(b) are reported for different thickness and sample configurations. Colors of thesymbols correspond to the color chosen for the different geometries sketched on the right. Open symbols are used for the values measured in heating and solid symbolsfor those in cooling. Sketch of the profiles of Tg (a) and (b) along the film thickness in heating (red) and in cooling (blue) are given as insets.

Figure 3: Temperature dependence of the imaginary part of the total dielectric function at 1 kHz in heating (open symbol) and cooling scans (full symbol) for: (a)bilayer films in geometries 3 and 4 ; (b) trilayer film, geometry 2.

10 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

10 100

96

100

104

108 heating top middle bottom

T g [C

]

cooling top middle bottom capped films

h [nm]h [nm]

x

0

(b)

Tg

0

x

(a)

60 80 100 120 1400.000

0.005

0.010

0.015

0.020

0.025

0.030

60 80 100 120 1400.000

0.005

0.010

0.015

0.020

0.025

0.030

heating cooling

heating cooling

45 nm PSN

15 nm PSL15 nm PSL15 nm PSL

15 nm PSL

"

T [ C]

45 nm PSN

15 nm PSL

45 nm PSN45 nm PSN

15 nm PSL45 nm PSN

(a)

1 kHz 1 kHz

"

T [ C]

heating cooling

(b)


In particular, considering the identical values of Tg and the same fragility values, the

dynamics of the doped polymer in contact with neat PS corresponds to the dynamics

of l-PS enslaved to its own gradient of mobility.26,27A 15 nm thick layer of l-PS

placed in between two 45 nm layers of neat PS (geometry 2) exhibits a bulk Tg over

does not show any reduction

either compared to the bulk value or as a consequence of the annealing.45

On the contrary, the dielectric strength of layers of labeled polymer of the same

thickness placed in direct contact with the metallic interfaces (geometry 3 and 4) was

reduced by roughly one third already during the heating scan. After reaching 150°C

and successive cooling, dropped further till reaching ~ 30% of its bulk value. It is

worth reminding that the sample preparation of the layers in the two geometries is

rather different. Soon after assembling of the multilayers, the conformations adopted

by polymer chains in geometries 3 and 4 are intrinsically dissimilar: at the lower

interface (geometry 3) chains adsorption starts already during spincoating of dilute

solutions on the metal, while at the upper electrode (geometry 4), molecules facing a

free surface are finally covered by metal atoms thermally evaporated in high vacuum.

The asymmetry in the sample preparation is probably erased within the times scale of

the structural relaxation time, i.e. considering our slow scanning rates (~ 0.5 °C/min)

differences between the two interfaces disappear soon after holding the multilayers

above Tg.

The segmental dynamics showed a dependence on the thermal cycles implying a

metastable character of the chain conformations. One of the criteria to identify

thermodynamic equilibrium is in fact stability against annealing.46 In particular, the

layer placed in the top position of the film (geometry 4) displayed an enhancement of

Tg compared to the bulk during the heating scan (short annealing) and an increased Tg

upon cooling (long annealing).

Similar results were found for films of neat PS of lower molecular weight (Mw =160

kg/mol)47 where it was possible to tune Tg within 45 °C by varying the annealing

temperature.39 Samples annealed at 100°C for 12 h exhibited a glass transition

temperature lower than in bulk and could be schemed as trilayers composed by a dead


layer in contact with the lower electrode, a free surface stacked underneath the upper

electrode and a bulk-like layer embedded in between. On the contrary, an increase of

Tg was measured for films annealed for the same time at 120°C, and analysis of the

thermal expansivity proved that the free surface was transformed into a dead layer. In

this experiment, it was not possible to discriminate between an enhancement of

molecular mobility due to the presence of a free surface and an overall reduction of

the segmental mobility imputable to the presence of residual solvent. The multilayer

approach allowed us to disentangle these two effects.

An enhancement of segmental mobili due to

adsorption of polymer chains at the interface, may however appear contradictory.

Nevertheless, the behavior we found for interfacial chains during heating scans is in

line with a recent study on the confinement effects on thermal expansivity and Tg of

ultrathin films of poly(tert-butylstyrene) capped between aluminum layers.20 The

non-intuitive decrease of Tg appearing simultaneously with a reduction of the thermal

expansivity was explained in terms of a conformation-density coupling of rigid

chains at the interface. Polymer segments at the very interface are anchored to the

metal surface and form a dead layer with a reduced thermal expansivity. At longer

distances from the substrate the presence of a bulky group in the PTBS chains

reduces the packing efficiency of the polymer segments and thus leads to an increase

of free volume and a corresponding reduction of Tg.48 The same arguments can be

taken in consideration to explain how 15 nm thick layers of labeled PS at the

interface can mimic the behavior of a free surface with a reduced Tg (in the heating

ramp) even if the polymer segments are already adsorbed.

Because of a longer annealing (cooling ramp), the Tg increased up to 8 °C and the

dielectric strength was further reduced (see Figure 2). These findings can be readily

interpreted in terms of a growth and evolution of the adsorbed polymer layer at the

interface. Annealing would lead to a state where the initially adsorbed polymer chains

endure internal relaxation processes and become progressively more attached to the

surface.49 This process needs rearrangement and deformation of already adsorbed

chain segments and brings to a larger surface coverage or higher concentration of the


adsorbed layer. The resulting improved packing causes a reduction of the free volume

and a consequent increase of Tg.

This hypothesis is confirmed by the impact of interfaces on the distribution of

relaxation times, L( ) ( see Figure 4).50 By means of the HN-parameters obtained by

fitting isothermal spectra via Eq (1) we calculated the distribution relaxation times for

a 106 nm thick film of labeled PS in the capped configuration (geometry 1) and for a

15 nm thick layer of the same polymer placed in the upper position (geometry 4).

Figure 4: The distribution relaxation times L( ) of the -process at 130 C for layers of labeled PS for a thick sample (106 nm) in geometry 1 (dot) and a 15 nm thicklayer in geometry 3 during heating (dash dot) and cooling (solid).

Compared to the thicker film, the peak maximum of the interfacial layer is shifted

towards shorter times in heating and longer times in cooling following the trend

observed for the glass transition temperature. In the proximity of the attractive

interface, L( ) broadens manifesting a more heterogeneous character of the relaxation

mechanism, in line with the broadening observed for the -peak of ultrathin polymer

films. At the upper interface, the distribution of relaxation times of layers heated from

RT to 130°C shows an enrichment towards short timescales, confirming the faster

dynamics mimicking the free surface effect. More rigorous annealing (130°C

10-10 10-8 10-6 10-4 10-2 100 1020.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

L(

) [a.u

.]

[s]

15 nm heating 15 nm cooling 106 nm


150°C 130°C) leads to a further broadening of the peak, due to the appearance of

slower relaxation modes, related to the reduced mobility in the mature adsorbed

layers. These findings support the physical pictures described above.

Thicker layer of l-PS placed at the bottom of the film (40 and 80 nm in geometry 3,

Fig 2) did not show any deviation from the bulk behavior suggesting that the

perturbations on the mobility and the chains conformation decay at a few tens of nm

from the bounding interface. The drop of in the physiosorbed layer, however,

reduces the weight of those interfacial chains assuming conformations different from

the bulk and generating the perturbation in Tg. As a consequence, the profile in

molecular mobility might appear sharper than in the case of those obtained by

measuring quantities constant all over the film thickness.

4. Conclusions

We have developed a multilayer approach by exploiting the advantages of dielectric

relaxation spectroscopy that allowed us to access the actual depth profile of the

cooperative segmental mobility in ultrathin polymer films capped between aluminum

layers. Selectively placing layers of dye-labeled PS at different distances from the

metallic interfaces, we have been able to map the values of the glass transition

temperature and the dielectric strength inside the film. We observed local changes in

Tg and exclusively when the labeled polymer was in direct contact with the Al

surface. Polymer properties recovered bulk values at a distance from each interface

smaller than 45 nm. On the other hand, in the proximity of bounding interfaces we

observed a drop in chain pinning) already at short annealing times in conjunction

with an unexpected reduction of Tg (packing frustration), which cannot be explained

in terms of the effect of a free surface. A further decrease of upon annealing was

finally accompanied by an increase of Tg. We explained these experimental findings

considering the evolution of an “imperfect” adsorbed layer, characteristic of short

annealing times into more mature physisorbed chains where an improvement of

chains packing inhibits chain mobility and consequently increases Tg.


Universal features observed for the dielectric behavior of ultrathin films, i.e.

reduction of the dielectric strength, broadening of the -peak and shift of the

structural relaxation time, are finally rationalized by the physical picture here

proposed. Out of our experimental results, we conclude that chain organization and

its evolution upon annealing are key parameters in rationalizing the thermal

properties of polymer layers at interfaces and should be included in future models on

the deviation on bulk behavior.

Acknowledgements

CR acknowledges financial support from the Research Council of the K.U.Leuven, project no. OT/30/06. SN acknowledges FWO (Fonds Wetenschappelijk Onderzoeks - Vlaanderen) for a postdoctoral scholarship.

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(40) vanZanten, J. H.; Wallace, W. E.; Wu, W. L. Physical Review E 1996, 53,

R2053-R2056.

(41) Labahn, D.; Mix, R.; Schonhals, A. Physical Review E 2009, 79, 9.

(42) Fukao, K.; Uno, S.; Miyamoto, Y.; Hoshino, A.; Miyaji, H. Physical Review E

2001, 6405.

(43) Serghei, A.; Tress, M.; Kremer, F. Macromolecules 2006, 39, 9385-9387.

(44) Napolitano, S.; Lupascu, V.; Wubbenhorst, M. Macromolecules 2008, 41,

1061-1063.

(45) The experimental evidence that both the dielectric strength and the glass

transition temperature of a layer of l-PS placed in between layers of neat PS are


not altered compared to their bulk values further proves the validity of our

substraction procedure.

(46) Reiter, G.; Napolitano, S. submitted as a Perspective to Journal of Polymer

Science Part B-Polymer Physics 2010.

(47) Owing to diffusion coefficients three orders of magnitudes smaller, the kinetics

of adsorption of this lower Mw is expected to be several orders of magnitude

faster than the one used in this work

(48) Ellison, C. J.; Mundra, M. K.; Torkelson, J. M. Macromolecules 2005, 38,

1767-1778.

(49) Schneider, H. M.; Frantz, P.; Granick, S. Langmuir 1996, 12, 994-996.

(50) Runt, J.; Fitzgerald, J. J., Dielectric Spectroscopy of Polymeric materials:

Fundamental and Applications; American Chemical Sosiety: Washington, DC

1997.


Supporting information

1) Relaxation map for bulk films of labeled and neat polystyrene of high molecular

weight

2) Variation of the dielectric strength for a 25 nm thick layer of labeled PS and a 30

nm thick film of neat PS during annealing in nitrogen and in a dark environment at

140 C

2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70

-6

-4

-2

0

2

l-PS 50 ml-PS 106 nm neat PS 130 nm

log(

)

1000/T [K-1]

Tg [°C] mneat PS 99.9 ± 1.0 131 ± 10

labeled-PS 100.4 ± 1.0 125 ± 7

0 500 1000 15000.00

0.05

0.10

0.15

0.20

0.25

0.30labeled PSneat PS

annealing time [min]


3) Syntactical schemes of the chromophore/functionalized polystyrene

Chromophore: 6-[N-ethyl-N-[4-[(4-nitrophenyl)azo]phenyl]amino]hexanol

Polymer:

x ~ 1.25% (measured with UV-vis spectroscopy)

Synthetical scheme:

HON N

N NO2

CH2 CH CH2 CH

O

ON N

N NO2

1-x x n

CH2 CH CH2 CH

O

ON N

N NO2

1-x x n

HON N

N NO2

CH2 CH CH2 CH

O

OH

1-x x nCH2 CH CH2 CH

O

Cl

1-x x nCH2 CH CH2 CH

O

OH

BPOCl

O

Cl

O

Toluene

DMAP

Precursor copolymer A Precursor copolymer B


4 ) Characterization of the chromophore/functionalized polystyrene

IR spectra of the precursor copolymers and of the chromophore-functionalized PS

1H-NMR spectrum of chromophore-functionalized PS

UV-vis spectra of chromophore-functionalized PS

4000 3000 2000 1000

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Tran

smitt

ance

(%)

Wavenumber (cm-1)

Precursor copolymer A Precursor copolymer B Chromophore-functionalized PS

(ppm)0.00.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.0

300 400 500 600 700 800 9000,0

0,2

0,4

0,6

0,8

1,0

1,2

Abso

rban

ce

Wavelength (nm)

chrom in CHCl3 (c = 1 x 10-5 g/mL) chrom-funct PS in CHCl3 (c = 2,8 x 10-4 g/mL)

Probing interfacial mobility profiles via the impact of nanoscopic confinement on the strength of the dynamic glass transition

73

Chapter 5

Probing interfacial mobility profiles via the

impact of nanoscopic confinement on the strength

of the dynamic glass transition

Cinzia Rotella, Michael Wübbenhorst and Simone Napolitano*

Katholieke Universiteit Leuven, Laboratory of Acoustic and Thermal Physics, Department of Physics and Astronomy, Celestijnenlaan 200D, B-3001 Leuven, Belgium


Reproduced by permission of The Royal Society of Chemistry

Soft Matter, 2011, 7, 5260-5266http://pubs.rsc.org/en/content/articlelanding/2011/sm/c1sm05430a

Temperature dependence of the local dielectric strength (x,T) for an 80 nm film


74

Abstract

Dielectric measurements of ultrathin polymer layers capped between metallic

electrodes revealed, besides controversial deviations in the dielectric glass transition

temperature, a universal and continuous decrease of the dielectric strength which

scales with the surface/volume ratio. In an attempt to describe the thickness

dependence of this last quantity, proportional to the number of segments relaxing on

the time and length scale of the dynamic glass transition and being a unique probe of

the deviations from bulk behavior, we propose a model based on the impact of

adsorption on the segmental dynamics and on the assumption of a smooth distribution

of mobility inside the film. Differently to simplified bilayer and trilayer-models

already described in literature, our approach is able to reproduce the behavior of all

the polymer systems so far investigated. Moreover, our calculations allow

determining the penetration depth of the surface induced perturbations along with the

thickness of the dead (or reduced) mobility layer where motions of polymer segments

are highly inhibited (or partially reduced) on the time scale of the glassy dynamics.

Analysis of the temperature dependence of this quantity confirmed that the gradient

of mobility is limited by the gyration radius at temperatures much larger than Tg

while in deeply supercooled melts the penetration of the interfacial interactions

exceeds the dimension of the single polymer chain.

1. Introduction

Upon confinement in restricted geometries and in the presence of interfaces, polymer

chains tend to minimize their free energy adopting different molecular configurations,

which might result in a perturbation of their dynamics with respect to the bulk

behavior.1, 2 Ultrathin films (thickness < 200 nm) provide an ideal sample geometry

to study the confinement effects on polymer properties which are of interest in a large

number of appealing technological applications such as coatings, adhesives,

controlled drug-release carriers and smart packaging materials. In fact, this geometry

allows an easy control of the level of nanoconfinement and permits a straightforward


75

tunability of the interfacial interactions between polymer and substrate. Numerous

experimental and simulations works have shown that in thin films crystallization

kinetics,3-6 diffusion mechanism,7, 8 viscoelastic behavior 9, 10 and the glass transition

process11-15 are substantially different from those in bulk. Recently, we verified that

the shifts in the glass transition temperature, Tg, are related to non-equilibrium

conformations assumed by polymer chains at the interface.16 Upon annealing, Tg

obtained from dilatometric experiments (capacitive dilatometry) evolves following

the same kinetics of the growth of an irreversibly adsorbed layer, a process showing

strong molecular weight dependence. In particular, in the case of ultrathin films of

polystyrene (PS) on aluminum, completion of the adsorbed layer requires 6 h at Tg +

50K for chains containing ~ 100 monomers, while an increase by 1.6 of the molecular

weight demands more than 6 weeks of annealing at the same temperature. Properties

of ultrathin films can thus be related to both the thickness of the irreversible adsorbed

layer and the ratio between the time scale of adsorption and the annealing time,

t*= ads/tANN. Consequently, at constant annealing, a condition commonly fulfilled in

the preparation of ultrathin films, deviations from bulk behavior are principally

governed by the ratio of the surface of the interface to the volume of confinement.

For this reason, properties of ultrathin films are very often described by linear

relationships scaling with the inverse of the thickness, h-1, corresponding for this

geometry to the surface/volume ratio.17

Perturbations originating at the interfaces affect the dynamics of the neighboring

layers inside the film for a finite depth, albeit with a reduced strength.18-20 Interfaces,

thus, generate a smooth distribution of mobility (and of glass transition temperature,

Tg) covering distances that depend both on polymer structure and on the nature and

entity of the surface interactions. Validity of models providing the position

dependence of Tg has been recently tested both in supported thin films (one free

surface) via fluorescent measurements21-23 and in capped thin films (polymer

embedded between two solid surfaces) by means of dielectric relaxation spectroscopy

(DRS).24

This last technique is a powerful tool to investigate the molecular dynamics of

ultrathin films since its sensitivity increases with the reduction of the thickness of the


76

sample, i.e. the electrical capacitance of the film grows with the surface/volume ratio.

Differently from approaches based on the temperature dependence of density related

quantities (e.g. thickness, refractive index for ellipsometry), DRS can detect a

dynamic glass transition temperature, following the reduction in the segmental

mobility ( relaxation) upon cooling. Comparison with calorimetric measurements

in bulk supports the conventional assignment of Tg to the temperature where the

characteristic relaxation time of the structural process, , is 100 s.25 Investigation

performed via DRS on different polymer systems24, 26-32 revealed however that, when

confinement effects are observed, T (the dynamic glass transition temperature at a

given frequency) remains constant down to a critical thickness hc below which, it

scales linearly with h-1, see Fig.1 (top panel). The onset thickness of the changes in

the dielectric glass transition (15 20 nm) is usually smaller than that observed via

other techniques. Besides these deviations, another feature generally observed in the

thickness dependence of the dielectric spectra is the reduction of the dielectric

strength of the -relaxation process, ,33 with an onset at thicknesses on the order of

a few hundreds of nanometers. This quantity, related to the integral of the -peak in

logarithmic of the frequency or similarly to the correspondent step in the dielectric

constant, is proportional to the amount of dipoles relaxing on the length and time

scale of the dynamic glass transition and is consequently linked to the distribution of

molecular mobility in the film.33 We verified that the dielectric strength is a suitable

parameter to monitor adsorption and thus to evaluate the lifetime of the deviations

from bulk behavior.16 Therefore, to understand the changes in the performance of

macromolecular materials in close proximity to an interface a detailed investigation

of the distribution of dielectric strength is required. Because it is not possible to map

the values assumed by with a resolution smaller than 15 nm,24 in the attempt to

(h) permitted obtaining profiles of molecular mobility, based on the number of

molecules participating to the glass transition process.


77

Fig.1 Normalized variation of T or Tg ( T at 1.6 mHz) (top panel) and at the temperature indicated (bottom panel) vs. the surface/volume ratio (inverse of thickness) for poly(vinylacetate), PVAc (�) [T (100 Hz), De(333 K), Fukao et al., 2001]26; poly(vinylacetate), PVAc ( ) [T (38Hz), De(322 K), Serghei et al.,2006]27; labeled polystyrene, PS-DR1 [Tg, De(421 K)]24; poly(2-vinylpyridine), P2VP [Tg, De(403 K)]29; polysulfone, PSF [Tg, De(485 K)]30; hyperbranched polyester, POHOAc [T (0.3 Hz), De(500 K)]31; poly(ethylene terephthalate), PET [Tg, De(363 K)]32 and new experimental points collected following the same procedure described in Napolitano et al. Langmuir 2007; polystyrene, PS [T ]28.Continuous and dotted lines in the panels are guides for the eyes.

At constant annealing, upon thickness reduction, gets continuously reduced with

decreasing the thickness, see Fig. 1 (bottom panel), indicating larger deviations from

bulk behavior in the thinnest films. The reduction of this parameter can be explained

in terms of adsorption of polymer chains, whose immobilization, in analogy to a cold

crystallization process, leads to a decrease of the density of the fluctuating dipoles

contributing to the dielectric signal.4, 29, 34 For various polymer systems, the decay of

vs. h-1 in isothermal conditions was described by a linear relationship, which

implies a sharp mobility profile at the two interfaces (Heaviside function, no

broadening).26, 27, 30 Linear fits of the type (h) = bulk(1 L/h) reproduce this

trend, by means of a step-like function consisting of a bulk layer sandwiched between


78

L where = 0 at each interface. This definition

reflects the consideration that the interfacial regions are composed by adsorbed

molecules whose structural relaxation is inhibited at the time scales investigated over

the whole experimental temperature range.35 Although this simplified model was able

to reproduce qualitatively the trends observed in the dielectric spectra upon

confinement, investigation of several polymers revealed also exotic scaling like

h,31 together with several cases where the reduction in the dielectric strength cannot

be satisfactorily reproduced by a linear dependence of the type 1 const/h.30, 32

This evidence hints at the existence of more complex and broader mobility profiles.

Therefore, it is reasonable that the incorporation of a continuous distribution of

mobility across the film would bring to a more realistic scenario. On the basis of

these considerations we have developed a new molecular-based model, able to

reproduce the thickness dependence of the dielectric strength ranging from the h-1

to the h decay behavior and to provide profiles of mobility for a wide class of

polymers.

2. A profile of molecular mobility based on the thickness dependence

of the dielectric strength

We modeled the mobility profile of the density of fluctuating dipoles ( ) in

ultrathin polymer films, readapting a smooth profile derived from a Landau-Ginsburg

free energy functional theory.36 Such a profile was developed to describe the density

distribution of a polymer melt in contact with solid walls. The analytical equation, in

the case of a reduction of density at the interface (neutral or repulsive wall), reads:

2( ) tanh

2bxx A (1)

where b is the bulk density, is the correlation length describing the decay length

for the surface profile, and A is a shift parameter incorporating the boundary


79

conditions. The profile in Eq (1) identifies an interfacial layer with a lower density

extending for a thickness on the order of 3 2 , where the bulk value is recovered.

, justifying the

reduction of dielectric strength in ultrathin films capped between two non-repulsive

solid surfaces. The correspondence between the behavior of the two properties was

possible considering a surface- interface <

bulk) and under the assumption of a smooth distribution of segmental mobility.24 In

, we considered the sample configuration most commonly used to

measure ultrathin films via dielectric spectroscopy, where the polymer layer is capped

in between two solid surfaces (metallic electrodes) kept at a distance h (film

thickness):

2 2( ) tanh 3 tanh 3bulk

x x x h c (2)

where is here the penetration depth of the reduction of the dielectric strength and

at the very interface is reduced to a fraction

corresponding to tanh2( interface bulk. The symmetry of the profile with respect

to the center of the film is ensured by subtracting the constant c tanh2(3h/ + ). The

advantage of Eq (2) is the straightforward determination of two fit parameters and

corresponding to material properties.

Assuming that the segmental mobility (and thus Tg) is a function of the distance

normal to the interface, we reproduced the total dielectric response of a film applying

a layer resolved approach, as suggested in a previous simulation work on the

dielectric relaxation at the nanoscale.19 The method employs the subdivision of the

whole thickness h into nl = h/l sub-layers, each of thickness l (= 1 nm) at which we

attributed a dielectric function and thus a complex capacitance. The dielectric

response of each layer was reproduced by the Havriliak-Negami (HN) function:37

*( , )1

HNHN

j

HN

ji

(3)


80

where is the angular frequency, is the high frequencies limit of the dielectric

constant, HN the mean relaxation time and HN and HN the shape parameters

describing the symmetric and asymmetric broadening of the relaxation peak. We

considered a capped geometry where the electric field is applied perpendicular to the

plane of the film. In this configuration the total capacitance C*( ,T) of the film is

calculated by summing up the individual capacitance of each sub-layer in a series-

model, 1 11

( , ) ( , )lnTOT ii

C T C T and the corresponding total dielectric function is thus

given by:

* *1

1 1 1( , ) ( , )

ln

il ih n h (4)

We kept constant the position and the shape parameters of the -peak in each sub-

layer, an approximation valid considering the large frequency range (18 orders of

magnitude) that we used to integrate the relaxation spectra to obtain . Such a

frequency range is much broader than the experimental window normally accessible

during dielectric experiments at the nanoscale (1 Hz- 105 Hz) and moreover

significantly larger than the frequency range where shifts due to confinement are

commonly detected (< 3 frequency decades). Having defined the mobility profile for

(x) and calculated the dielectric spectra via the HN function, we applied our model

to the data sets available in literature for the thickness dependence of for different

polymer systems.

We generated a matrix of couples ( i, i) centered around physically reasonable

starting parameters, and found the best fitting values for each system, minimizing the

sum of squared deviations:

exp2model exp

exp1exp

1 ni i

i i

En (5)

where imodel indicate the value provided by the model, i

exp are the experimental

values and nexp is the number of data points. Values of and


81

were then inserted in Eq (2) to obtain the corresponding profile of mobility which

finally yielded the thickness dependence of the dielectric strength.

In addition to this numeric approach, we derived the solution of the inverse problem

related to the thickness dependence of the dielectric strength for the special case of

zero residual polarization at the interface, and neglecting the effects of the direction

of the electric field. Under these assumptions, applying the mean value theorem, we

obtained an approximate expression of the form:

( ) tanh( )1bulk

h hh (6)

Regardless of the approximations used, this scaling reproduces analytically the

experimental and numerically calculated trends for the drop of . For films much

thicker than the penetration depth of the dielectric strength, where the condition h/

>> 1 is satisfied, (h) bulk (1-

const/h) ; at a critical thickness h a bending in the thickness dependence of

(h), slows down its reduction. In Fig. 3 we reported analytical curves obtained from

Eq (6) at different values of . With this trend in mind, we point out that Eq (2)

cannot be applied to (nor the bending in (h) can be observed in) data sets limited to

films much thicker than .

3. Results and Discussion

The values of (h) obtained by a computation of the dielectric function at discrete

thicknesses via Eq(3) and Eq(4), are presented for different polymers together with

the correspondent experimental points normalized to the bulk values in Fig. 2. Two

limiting behaviors corresponding to extreme mobility profiles can be recognized in

the reduction of (h), i.e. the case in which drops with h-1 (PVAC27 and

P2VP) and the less common decay h (hyper-branched polyester). The first

behavior exemplifies a sharp mobility profile while the second is representative of a

very broad interfacial layer, see top right panel in Fig. 3.


82

Fig. 2 Variation of the normalized dielectric strength vs. the different polymers: PVAc,26, 27 PET,32 P2VP,29 PS-DR1,24 PSF,30 POHOAc.31 The continuous curves are fits, obtained from Eq(2) and Eq(4), through the corresponding experimental data points. The dashed and the dotted-dashed lines represent respectively the h-1 and the h drops of the dielectric strength. The inset shows the deviation of the experimental and calculated trends for samples of PVAc from the linear fit 1 cost/h. Because the value of tads is unknown, it was not possible to assign a t* for the reported systems.

The drop of for other polymers (PET, PSF, PS-DR1) shows intermediate trends

between the two limiting cases. It is noteworthy that the agreement between the

experimental data points and the modeled curves is considerably good for all the

systems investigated, which supports the general validity of our model. Values of

and tanh2( ) for the polymers investigated are given in Table 1. In Fig. 3, we compare

in detail the mobility profiles of the various samples; considering the striking

correlations we recently discussed (ref NC),16 Fig. 3 can be interpreted as a map of

the deviations from bulk behavior. For sack of simplicity we considered films thick

enough to avoid the reciprocal influence of the two interfaces (h > 2 ).


83

Fig. 3 Thickness dependence of obtained by the expression in Eq(6) at different values of (top left panel); Mobility profiles of (x) plotted imposing in Eq(2) the same values of used in the previous graph and considering 0 (top right panel); Mobility profiles at one interface for thick samples of various polymers, continuous curves were obtained from Eq(2) using the corresponding best fit values of and (bottom panel).

[nm] tanh2( )DL [nm]

poly(vinylacetate)27 7.5 0.7 0 0.9 0.1poly(2-vinylpyridine)29 11.7 1.2 0 1 0.1hyperbranched polyester31 153 15 0 18.7 2

[nm] tanh2( ) RML [nm]labeled-polystyrene24 (421 K) 27.6 3 0.05 2.7 0.2labeled-polystyrene24 (403 K) 43 4 0.12 3.4 0.2polysulfone 30 38 4 0.2 2.2 0.4poly(vinylacetate)34 43 4 0.18 2.7 0.4poly(ethylene terephthalate)32 68 7 0.3 3.6 0.8

Table 1. Values of the fit parameters (penetration depth of the dielectric strength) and of tanh2( ) = interface/ bulk. Polymers were divided into two classes depending on the value of the residual polarization at the interface: DL (= dead layer) and RML (= reduced mobility layer) are respectively the thicknesses of the interfacial layer with zero and constant (> 0) residual polarization, evaluated as min(x) (x)> 0.1·[1+9tanh2( )].

1 10 1000,0

0,5

1,0

0 10

1

0,0 0,20

1

PSFPOHOAcP2vP

PS-DR1 (421 K) PS-DR1 (403 K)PVAcPETPVAc

hbu

lk

xbu

lkx

bulk

x [nm]

x/hh-1


84

For all polymers, three main thickness ranges can be observed, a first layer of few

nanometers characterized by a constant value of and a transition zone extending

for distances x ( 10 100 nm), where the bulk behavior is finally recovered.

Differently from the critical dimension where a shift of the

observed (< 20 nm), the larger order of magnitude of the penetration depth of the

proves that the deviations from bulk behavior affect the dielectric spectra

at thicknesses comparable with those reported by other techniques. The transition

is manifested by an

increase of , a broadening parameter38 sensitive to the different chain architectures.

It is not a case that in this study the most pronounced broadening is observed for

POHOAc, an hyper-branched polyester with a complex tridimensional molecular

structure.

The value of we found for the this polymer, 160 nm, is in line with its

tremendously large onset thickness of the confinement effects in the glass transition,

300 nm, being on the order of 2 .

Regardless of the broadening parameter, we can further divide the systems plotted in

Figure 3 into two groups, depending on th at the walls (=

tanh2( ) bulk), i.e. a measurement of the residual degree of mobility inside the

interfacial layer with respect to the bulk. For some polymers, like PVAc27 and P2VP

the extrapolations of the model suggest that drops to negligible values in

proximity of the metallic surface (DL).35, 39 In other systems such as, PET, PS-DR1

and PSF, becomes independent on the distance from the interface, and thus

assumes constant values at thicknesses below a threshold value (reduced mobility

layer, RML) on the order of a few nm, see Figure 3 and Table 1.32, 40

The size of this interfacial layer obtained via our computation (1 3.6 nm, with

exception of POHOAc where DL 19 nm) is comparable with the thickness of dead

layers obtained by dilatometric investigations of different ultrathin polymer films, 35,

39, 41 e.g. 2.5 5 nm for polystyrene and 4 13 nm for polycarbonate.

In the next paragraphs we discuss these results revising the current interpretation

based on a reduction of cooperativity at the interface. The reduction of in capped


85

ultrathin films has been interpreted, similarly as for polymer nanocomposites, in

terms of change in the cooperativity motions of the structural relaxation.26 The

dielectric strength is classically described by 20 3 BN k T where N is the dipole

number density, μ0 is the dipole moment of the relaxing unit, kB is the Boltzmann

constant and T is the temperature. When n neighboring dipoles relax cooperatively,

the effective density number drops to ~N/n while the dipole moment rises to ~nμ0;

under those conditions the dielectric strength scales as 20 3 BnN k T . The number of

the cooperative units n at the interfaces gets smaller due to the break in the symmetry,

consequently interface/ bulk<1.

Under these hypotheses, averaging the different contributions in volume (thus as in a

parallel-model for the electric capacitance) one obtains an expression for a sharp

profile, (h)= bulk[1 (1 bulk / interface) 1/h] where is the dimension of the

interfacial layer. This analysis relies on the assumption that the total response

obtained averaging the different contributions either in parallel or in series is

identical, an approximation valid only for weakly polar systems like for polystyrene.

In fact, exclusively for this limited class of polymers, the condition / << 1 is

satisfied and the electrical capacitance of the whole film can be considered as the sum

of the different contributions participating to the dielectric signal. Moreover, the

physical considerations based on the hypothesis that the cooperativity is reduced at

the interfaces hold solely in the case of a reduction of Tg,42 which is not always

verified. Reductions of versus thickness are actually observed regardless the sign

of the variation of the glass transition temperature Tg(h), [Tg(h) Tg(bulk)], see

Figure1.

As a further argument to refute the cooperativity argument we consider our recent

work on the distribution of mobility in ultrathin films where we highlighted that the

reduction of is mainly related to the interaction with the metallic electrodes.24 By

using a multilayer approach we selectively placed 15 nm thick layers of dye-labeled

PS (PS-DR1) at different distances from the metallic surfaces and verified that

drops exclusively when the polymer chains are in direct contact with the metal. On

the contrary, no reduction is observed when the same layer is embedded between

layers of neat PS, i.e. no interface with the metal. Furthermore we verified that the


86

reduction in

up from room temperature to 50 K above Tg showed a reduction of of one-third,

compared to the bulk; a successive cooling down to room temperature doubled the

. In view of the correspondence between heating and cooling scan with

respectively short and long annealing times, we observed that the decrease of

takes place on time scales of a few hours, exceeding by several orders of magnitude

the time scale of the cooperative segmental motions which is on the order of the

relaxation time ( s).

On the basis of this evidence, we interpret the reduction of at larger

surface/volume ratios in the framework of polymer adsorption. Molecules in the

region adjacent to the electrodes are physically bonded with the surface for either via

a topological affinity or due to specific interactions with the substrate. Pinning of the

polymer segments restricts the rotational fluctuations of the dipoles and leads to a

respective reduction of the effective dipole moment and thus of the dielectric

strength. Following this physical picture, the constant value assumed by at the

interface might be considered as a signature of a residual mobility, supporting the

non-equilibrium character of the irreversibly adsorbed interfacial layer.43 The kinetics

of polymer adsorption is a sluggish process evolving trough different stages: (i)

diffusion of the chains towards the bare interface, which starts already during

spincoating; (ii) attachment of the chain segments onto the available adsorption sites;

(iii) structural rearrangements of the attached interfacial layer and thus relaxation

towards the equilibrium conformation.44, 45 This last step, which normally results in a

densification of the interfacial layer (packing optimization), can involve timescales

exceeding by several orders of magnitude the reptation time ( >> ). As a result, the

adsorbed layer can be kinetically metastable on the time scale of the measurements,

because the attainment of an equilibrium (or steady) state could occur in several

hours or weeks, depending on molecular weight and the nature of the interfacial

interactions,46 e.g. the growth of an adsorbed layer of relatively low molecular weight

chains of PS ( = 44.1 kg/mol) on hydrogen-passivated silicon requires 50 h at Tg +

50K.47 may be rationalized assuming that the

structure of the adsorbed interfacial layer is still “imperfect’ as it consists of polymer


87

chains trapped in non equilibrium conformations. In other words, the adsorbed layer

endures a low-density state that contains a certain fraction of free volume, where

some residual degree of orientational mobility is still present. We provided

experimental evidence supporting this physical picture in a recent work on nanolayers

of PS-DR1, where we observed a drop in already at short annealing times in

conjunction with an unexpected reduction of Tg. A further decrease of upon

annealing was finally accompanied by an increase of Tg, probably related to the

densification of the adsorbed layer. A similar argument has been already taken in

consideration to explain the coexistence of an immobilized interfacial layer with a

reduction of thermal expansivity and a lower Tg, observed in capped thin films of

poly(tert-butylstyrene) (PTBS).48 Although polymer segments are adsorbed at the

solid surface, the presence of a bulky group in the PTBS chains significantly hinders

the chains packing efficiency, leading to an increase of free volume and a

corresponding reduction of Tg compared to the bulk value.

Moreover, an analysis of the energy landscape scenario of adsorbed chains revealed

that in the latest stages of adsorption, due to a lack of available pinning sites, chains

tend to align perpendicularly to the surface.49 We speculate that due to a better

alignment with the direction of the electric field, in case of dipole moments having a

non-zero component parallel to the backbone, the dielectric signal would not decay to

zero values at the interface. The increase in the orientational order parameter would

make the interfacial chains more “visible” to the dielectric experiment even if the

mobility in the layer is seriously hindered.19

To further understand the behavior of chains in the reduced mobility and dead layers,

we analyzed the impact of supercooling on the mobility profiles of PS-DR1, a system

for which we measured the thickness dependence of the dielectric strength at different

temperatures upon cooling from Tg + 50K down to the glassy state.24 Considering the

strong correlation between the structural relaxation and the adsorption kinetics,16

reduction of the temperature significantly slowed down the insertion of new chains at

the interface within the time scale of the experiments, i.e. the value of t* can be

considered temperature independent.


88

The results of the computations, summarized in Figure 4, revealed an increase of the

penetration depth of the interfacial interactions upon cooling, manifesting as larger

values of and when the temperature of the polymer melt is reduced. In the limit of

high temperatures, T > 1.15 Tg, approaches the gyration radius while extrapolation

at Tg confirmed that in a deeply supercooled melt the Rg is not the largest length scale

characterizing the size of the interfacial region.

Fig. 4 Temperature dependence of the penetration depth of the dielectric strength ,normalized to the radius of gyration Rg ( 25 nm), for PS-DR1(top panel); the red curve is a smooth function used as guide for the eyes. The same smooth function was used to obtain the temperature dependence of the local dielectric strength (x,T) for an 80 nm thick film (bottom panel).

Our results are in line with previous molecular dynamics simulations of dense

polymer melts confined between two hard walls,50, 51 predicting an exponential

growth of the length scale of the perturbations in the dynamics introduced by an

interface upon cooling, (T), weaker than the increase of . Analysis of this

quantity with an Arrhenius formulism provided, in fact, that the thermal activation

barrier of is 35 2 kJ/mol, i.e. 6 7 folds smaller than the activation energy of the

structural relaxation time in the same temperature range.24 Moreover, the temperature

dependence pictured in Figure 4 is in agreement with the scaling we proposed for the


89

29 confirming a reduction of the

confinement effects on the glass transition dynamics upon heating.

This trend is thus probably a feature common to a large class of polymers and might

be particularly relevant in rigid and semi-rigid systems. For the specific case of PS-

DR1, whose chains are decorated with highly polar azobenzene groups, the results of

the model suggest that the dipole moments of the rigid aromatic moieties tend to

orient perpendicularly to the interface and that the solid angle covered during their

fluctuations (and thus the local ) gets reduced upon cooling, due to the increase in

viscosity approaching Tg. The reduction of the preferential orientation upon heating

brings to a randomization of the average direction of the aromatic rings, which results

in a virtual thinning of the adsorbed layer at higher temperatures.

Regardless of its physical origin, the main consequence of the lower value assumed

by

arise from the chains in the middle of the film. This consideration is exemplified by

the experimental observations that gets reduced already at hundreds of nanometers

while the relaxation time , linked to dynamic properties, either remains constant or

varies at much higher degree of confinement, see Figure 1. In fact, differently from

, the relaxation time obtained by dielectric spectroscopy is not additive, i.e. the

contribution of each sub-layer is not weighted over its volume percentage (due to

both the series-model sum required for the dielectric functions and the asymmetric

broadening of the -peak), leading to a reduction of the confinement effects on the

dynamic properties, in comparison with the shift in Tg reported by other techniques.

The use of the model we introduced might help overcoming this averaging issue:

investigation of confinement effects in ultrathin films cannot simply be limited to the

apparent (lack of)28 changes of the relaxation time and thus of the glass transition

temperature, but to the more complex variations of properties like the dielectric

strength.


90

5. ConclusionsIn addition to minor changes in the glass transition temperature, the thickness

dependence of the dielectric relaxation spectra of several polymers revealed a

universal reduction of dielectric strength upon increase of the surface/volume ratio.

Bearing in mind this finding and considering the proportionality between and the

number of molecules taking part in the dynamic glass transition process and the

sensitivity of this parameter to the deviations from bulk behavior,16 we chose the

dielectric strength as a probe of the mobility distribution in ultrathin films.

We proposed a model able to reproduce the variegated thickness dependence of

for all the polymers investigated, which we explained in terms of chain adsorption at

the solid interface. The model provides the penetration depth of the polymer/metal

interactions together with the thickness of the interfacial dead (or reduced mobility)

layer where the orientational polarization assumes zero (or constant) values. Mobility

profiles based on the sum of a finite number of Heaviside functions cannot take

properly into account for interfacial broadening, which brings to an overestimation of

the interfacial layer. The temperature dependence of the penetration depth of the

interfacial interactions obtained via our computation is in line with predictions of

simulations of polymer melts confined between hard walls. Analysis of the trends

observed for a large number of polymer systems prompts to the conclusion that,

because of averaging issues,51 modeling of the mobility profile in ultrathin films

cannot be simply related to the thickness dependence of the glass transition but to a

more adequate parameter such as the dielectric strength.

Acknowledgments

C.R. acknowledges financial support from the Research Council of the K.U. Leuven, project no. OT/30/06. S.N. acknowledges FWO (Fonds Wetenschappelijk Onderzoeks-Vlaanderen) for a postdoctoral scholarship.


91

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94

Additional comments following the suggestions of the Examination Committee

In order to reproduce the evolution of the dielectric strength along the thickness of

capped polymer films we chose an ad hoc profile, indicated by the following

equation:

2 2( ) tanh 3 tanh 3bulk

x x x h c (c1)

This is a symmetric profile that allows describing the growth of the dielectric strength

from the interfaces into the film (of thickness h) in a continuous way. and are

fitting parameters related to the distance over which the dielectric strength is

disturbed by the interfaces and the value of assumed at the interfaces, respectively.

This profile takes in account the possibility to have a constant value of ( = bulk

value) in the core of the film, a condition that is verified for films thicker than two

times the value of . Figure (1C) displays mobility profiles of (x)/ (bulk) for a

given couple of and values, and for various thicknesses h.

Figure 1C: mobility profiles obtained by the Eq(1C) for given values of and and for different thicknesses h

0 20 40 60 80 100 120 140 160

0,2

0,4

0,6

0,8

1,0

150 nm100 nm75 nm50 nm30 nm20 nm(x

)/bu

lk

x [nm]

h


95

In the Figure (2C) we plot the mobility profile for the thickest sample (h=150 nm) at

one interface. is the dimension of the interfacial layer and tanh2 ( ) is the value of

(x)/ (bulk) at the interface.

Figure 2C: mobility profile for a thick film

We used the mobility profile expressed by Eq(c1) to deduce numerically the

reduction of as a function of the film thickness. First, the mobility profiles,

corresponding to different thicknesses, are divided in sub-layers 1 nm thick. We

assign to each of these sub-layers a dielectric function j, reproduced by the

Havriliak-Negami equation (see Article, Eq(3)). For every thickness we calculate the

total dielectric function by using a series-model, i.e. the j of the different sub-layers

are summed up in series (see Article, Eq(4)). From the modeled dielectric spectra in

the frequency domain we deduce the thickness dependence of model(h).

A minimization of the sum of the squared deviations between model(h) and the

experimental values exp(h) (see Article, Eq(5)) is used to obtain the best fitting

parameters and for each polymer system.

To clarify the procedure above described we added some parts of the MatLab routine

created for the modeling. The full code is available from the authors upon request.

1 10 100

0,0

0,2

0,4

0,6

0,8

1,0

(x)/

bulk

x [nm]

h =150 nmlooking at one interface of a thick sample

tanh2( )


96

Modeling

a = 0.18; % fitting parameter b = 8.8; % fitting parameteruu = 219; % num of thicknessesll = 219; % thickness maxm1 = zeros (uu,ll); S = zeros(ll,uu);

for k = 1:210L = 220-1*k % film thicknessl = 0:L; % x axis

cost= ((tanh(a+L/b)).^2+(tanh(a))^2)-(tanh(a))^2;N = L;x = linspace(0,L,N+1);h = x(2)-x(1);f = ((tanh(l/b+a)).^2+(tanh((l-L)/b-a)).^2)-cost;

% we divide the profile in slises of area gr = [1:1:220-1*k];g(r) = (h/2)*(f(r)+ f(r+1)); bl = size (g(r));al = bl(2);

% matrix of f to save the datas = size(f);ss = s(2);S(1:ss,k)= f;

% matrix with g(r)values;m1(k,1:al)= g(r);mm1 = [m1];

figure(1) % mobility profileplot(l,f)hold onend

% making the Deps matrixc = size(mm1);f = logspace(-3,15,500)';alpha = 0.6*ones(c);beta = 0.45*ones(c);deps = mm1;

a = alpha(1,1) ;b = beta(1,1) ;

logtau = -4.7156*ones(size(mm1));tau = 10.^logtau; %tauMaxw = 1./(tau);


97

tauHN =1./w.*(sin((b*pi)./(2+2*a))).^(1./b).*(sin((b.*a*pi)./(2+2*a))).^(-1./b); %tauHNepsi = 2.5;resolution = 10^-40;[m,n] = size(mm1);omega = 2*pi*f;

hn = zeros( length( f ), m );size(hn)for jj = 1:m

hnT= zeros(length( f ), 1 );size(hnT);for ii = 1:(ll+1-1*jj)

term = 1./((deps(jj,ii).*(1./(1+(i.*omega.*tauHN(jj,ii)).^alpha(jj,ii)).^beta(jj,ii)))+ epsi);% the total dieletric function is given by summing up the dielectric function of each sub-layer in a series model

hnT = hnT + term;hnT1 = hnT./(ll+1-1*jj);hnT2 = 1./hnT1;

endhn (:,jj) = hnT2;

end

real1 = real(hn);imag1 = -imag(hn) + resolution;

% modeled peaks in the f domainfigure(3)for u=1:m%plot(log10(f),(real1(:,u)),'color', [1-u/20 0+u/40 0+u/20])plot(log10(f),(imag1(:,u)));hold onend

% EXPERIMENTAL VALUES of Depsthexp = [200 100 80 57 30];Depsexp = [ 0.92336 0.86562 0.79403 0.71903 0.48834];ErrDepsexp = [ 0.07 0.05 0.1 0.1 0.15];

% Deps from the modeled peaks in the frequency domainfigure (5)for vv = 1:uu

plot ((1./((ll+1-vv))),(real1(1,vv)-real1(end,vv)), 'ro');hold onerrorbar(1./thexp,Depsexp,ErrDepsexp, 'd') DELTA(vv) = (real1(1,vv)-real1(end,vv))*ones(1,length(vv));hold on

end

Adsorption Kinetics of Ultrathin Polymer Films in the Melt Probed by Dielectric Spectroscopy and Second-Harmonic Generation

99

Chapter 6

Adsorption Kinetics of Ultrathin Polymer Films in

the Melt Probed by Dielectric Spectroscopy and

Second Harmonic Generation

Cinzia Rotella*†, Simone Napolitano†, Stefaan Vandendriessche‡, Ventsislav K.

Valev‡, Thierry Verbiest‡, Maria Larkowska§, Stanislaw Kucharski§, and Michael

Wübbenhorst†

†Katholieke Universiteit Leuven, Laboratory of Acoustic and Thermal Physics, Department of Physics and Astronomy, Celestijnenlaan 200D, B-3001 Leuven, Belgium ‡Katholieke Universiteit Leuven, INPAC, Molecular Electronics and Photonics, Celestijnenlaan 200 D, B-3001 Leuven, Belgium §Wroclaw University of Technology, Faculty of Chemistry, Department of Polymer Engineering and Technology, Wybrze e Wyspia skiego 27, 50-370 Wroc aw, Poland *corresponding author


Langmuir, 2011, 27 (22), pp 13533–13538

Copyright © 2011, American Chemical Society

‡ Stefaan Vandendriessche, Ventsislav K. Valev and Thierry Verbiest performed the measurements of second harmonic generation.

§ Maria Larkowska and Stanislaw Kucharski provided the labeled polymer.


100

Abstract

We studied the adsorption kinetics of supported ultrathin films of dye-labeled

polystyrene (l-PS) by combining dielectric spectroscopy (DS) and the interface-

specific nonlinear optical second harmonic generation (SHG) technique. While DS is

sensitive to the fraction of mobile dye moieties (chromophores), the SHG signal

probes their anisotropic orientation. Time resolved measurements were performed

above the glass transition temperature on two different sample geometries. In one

configuration, the l-PS layer is placed in contact with the aluminum surface while, in

the other one, the deposition is done on a strongly adsorbed layer of neat PS. From

the time dependence of the dielectric strength and SHG signal of the l-PS layer in

contact with the metal, we detected two different kinetics regimes. We interpret these

regimes in terms of the interplay between adsorption and orientation of the adsorbing

labeling moieties. At early times, dye moieties get adsorbed adopting an orientation

parallel to the surface. When adsorption proceeds to completeness the kinetics slows

down and the dye moieties progressively orient normal to the surface. Conversely,

when the layer of l-PS layer is deposited on the strongly adsorbed layer of neat PS,

both the dielectric strength and the SHG signal do not show any variation with time.

This means that no adsorption takes place.

1. Introduction

Polymer adsorption is relevant in different technological fields ranging from coatings

to pharmaceutical applications and nanocomposite materials.1 For this reason, much

effort has been devoted to understanding both experimentally2 and theoretically3 the

kinetics of adsorption of polymer layers on a solid surface. At the interface, the

polymer conformation is perturbed compared to the bulk because of the interaction of

the surface and geometrical constraints. As a consequence, in ultrathin polymer films

(thickness < 200 nm), dynamical properties such as diffusion,4 crystallization

kinetics,5 and the glass transition6, 7 may substantially differ from their bulk

counterpart. Hence, for a better control of the functionality of polymer layers, the

understanding of surface - polymer interaction at a fundamental level is essential.


101

First studies of polymer adsorption were focused on predicting the adsorbed amount

and the density profile at equilibrium.8 However, recent studies revealed that

adsorbed polymer layers may not fully equilibrate on experimental time scales.9, 10

Moreover, polymer adsorption on a solid surface proceeds through various regimes of

different kinetics before equilibrium may be reached, after days or weeks, depending

on the molecular characteristics of the polymer.11, 12 In particular, the conformation of

each newly adsorbing chain changes with time and surface coverage: chains arriving

first at the surface adsorb with a relatively flat conformation, while those arriving

later adsorb with a loosely bound conformation.13-15

A number of experimental approaches such as neutron scattering,16 ellipsometry17

and IR spectroscopy18 have been employed to study the nature of polymer adsorption

onto surfaces from dilute solutions. Recently we investigated, by dielectric

spectroscopy, the effect of annealing on the dielectric response of multilayer ultrathin

films capped between aluminum electrodes.19 By selectively placing a layer of dye-

labeled polystyrene (PS) at different depths inside films of neat PS, we observed

changes of the glass transition temperature (Tg) with respect to the bulk exclusively

when the labeled layer is placed in contact with the metal. Furthermore, for ultrathin

films of neat PS we found that the variation of Tg during annealing follows the same

kinetics as the thickening of the layer irreversibly adsorbed onto the solid substrate.20

Deviations from bulk behavior would arise from non-equilibrium conformations of

the adsorbed chains, as confirmed by the evolution of the distribution of relaxation

times upon annealing. These studies motivated further investigations of the

adsorption process in order to achieve a direct experimental observation of real-time

conformational changes that occur during the formation of the adsorbed layer. For

this aim, we used dielectric spectroscopy to study the segmental mobility, in

conjunction with second-harmonic generation. This last technique is based on the

nonlinear optical response of chromophores which are arranged in a

noncentrosymmetric configuration. The SHG signal is very sensitive to any breaking

of inversion symmetry in materials, induced by e.g. internal electrical or magnetic

fields,21 surfaces and interfaces.22, 23 The symmetry at interfaces can also be broken

by molecular adsorption.24 The particular arrangement of the adsorbed molecules,


102

oriented parallel or perpendicular to the interface, can in itself constitute a source of

SHG signal. In our study, we have employed SHG active dye moieties, whose

orientation upon adsorption is probed.

2. Experimental section

2.1 Synthesis of the labelled polystyrene (l-PS)

4-aminobenzonitrille (Aldrich), 2-(methylphenylamino) ethanol (Aldrich),

methacrylic anhydride (Aldrich), styrene (Sigma-Aldrich), 2,2’-azoisobutyronitrile

(AIBN) (Fluka) were used as received. The synthesis of the chromophore 4-[(E)-[4-

(2-hydroxyethyl (methyl) amino) phenyl]azo]benzonitrile (CN) was carried out

according to literature procedures.25 The photochromic methacrylate 2-[4-[(E)-(4-

cyanophenyl)azo]-N-methyl-anilino]ethyl 2-methacrylate (MCN) was obtained

starting from azo dye (CN) and methacrylic anhydride and following the reaction

elsewhere described.26 The labeled polystyrene, poly (2-[4-[(E)-(4-cyanophenyl)azo]-

N-methyl-anilino]ethyl 2-methacrylate-co-styrene), was synthesized in bulk radical

polymerization in the presence of azobisisobutyronitrile (AIBN), used as radical

initiator. The reaction was performed in an ampoule, purged with nitrogen, where the

styrene monomer was first mixed with the methacrylic monomer (MCN) (3% mol)

and then with the AIBN initiator (0, 15 % w/w). The mixture was kept at 90 ºC in

nitrogen atmosphere for 72 h. After completion of the reaction, the copolymer was

dissolved in benzene and purified by precipitation in methanol. Gel permeation

chromatography GPC measurements revealed that the functionalized polystyrene (l-

PS) had a Mw= 20 kg/mol and PDI=2.

The labeling azobenzene organic molecule (4-[(E)-[4-(2-

hydroxyethyl(methyl)amino)phenyl]azo]benzonitrile) has both a strong permanent

dipole moment and hyperpolarisability, which make this group a suitable dielectric

label and a probe for SHG experiments.

Some experiments were conducted with atactic polystyrene (Mw = 97 kg/mol, PDI =

1.01) purchased from Scientific Polymer products and used as received.


103

2.2 Preparation of Ultrathin Polymer Films

Ultrathin single layers of labeled PS (l-PS) were prepared by spincoating filtered

solutions of the polymer in chloroform on glass slides onto which a 50 nm thick layer

of aluminum was previously deposited by thermal evaporation in a high vacuum (p

10-6 mbar). After deposition, samples were annealed at 110 °C for 20 minutes on a

hotplate in order to remove residual solvent and to reduce mechanical stresses

induced by the spincoating process. Subsequently, the samples were kept under high

vacuum at room temperature over night. Exclusively for the dielectric measurements,

a second aluminum layer was evaporated at high deposition rate ( 10 nm/s) onto the

polymer film to form a top electrode.

Bilayer films were prepared by spincoating a layer of l-PS on top of a densely

adsorbed layer of neat PS prepared following the experimental approached used by

Guiselin.27, 28 The procedure consisted in depositing a thick layer of PS onto the Al

substrate and annealing it at 150 C for 20 hours in order to promote the formation

of a strongly adsorbed layer at the metal interface.

After completion of the annealing stage, the non adsorbed chains were washed away

dipping the samples in the same good solvent used for spincoating (chloroform).

Guiselin brushes were then dried overnight in high vacuum (p 10-6 mbar) before

preparing the bilayer films.

2.2 Dielectric relaxation spectroscopy

A high- resolution dielectric analyzer (Alpha Analyzer, Novocontrol Technologies) is

used to measure the complex dielectric function *( ) = ( ) i ( ) ( is the

angular frequency, and are the real and the imaginary parts of the complex

dielectric function) in the frequency range from 10-1 to 106 Hz. All measurements

were performed under N2 in a closed cell to prevent any possible oxidation,

degradation or moisture uptake. The thickness of the samples h was evaluated from

the value of the real part of the sample capacitance (C ) outside the region of dipolar

relaxation processes, using the relation for the capacitance in the geometry of parallel

plates, which reads: C = 0 (S/h), where is dielectric constant of the polymer, 0


104

is the permittivity of the vacuum (8.85 · 10 12 F/m) and S is the effective area of the

capacitor (4 mm2).

The bilayer film was modeled as a series of capacitance where Ctot* is given by:

1/C*tot= 1/ C*PS + 1/C*l-PS where C*PS and C*l-PS are the complex capacitance relative

to the PS and to the labeled PS, respectively. From the knowledge of the intrinsic

contribution of neat PS, it was possible to extract the contribution of the labeled layer

from the total response of the bilayer film.

To obtain quantitative information from the isothermal dielectric spectra, relaxation

processes were analyzed using the empirical Havriliak–Negami (HN) function

*

1 HNi (1)

Where HN is the relaxation time, a and b are shape parameters describing the

symmetric and asymmetric broadening of the -peak and is the relaxation

strength. This last quantity is proportional to both the mean square dipole moment

and the density of dipoles ( and provides a measure of the amount of

mobile polar chain segments involved in the structural relaxation.

2.3 Second-Harmonic Generation

SHG measurements were performed using a Ti: Sapphire laser at a wavelength of 800

nm, emitting 100 fs short pulses with a repetition rate of 82 MHz. First, the beam was

polarized by a Glann-laser polarizer mounted on a motorized rotation stage, which

was alternated between s- and p-polarization. After passing a filter to exclude any 400

nm light, the beam was focused on the sample at an incidence angle of 45°. The

reflected beam was filtered to exclude any 800 nm light and subsequently the SHG

passed through a p-polarized analyzer. Finally, the SHG signal was collected by a

photomultiplier tube cooled to -20°C to improve the signal-to-noise ratio. The

resulting electrical current pulses were processed by a gated photon counter.

In the dipole approximation the optical polarization P(2 ) at the double frequency

of incident light can be written as:29 (2)(2 ) (2 : , ) ( ) ( )i ijk j kP E E (2)


105

where E( ) is the electric field of the incident light, i, j, and k are the Cartesian

coordinates and (2)ijk

is the second-order susceptibility tensor. This 3rd-rank tensor

consists of 27 elements, however, their number is considerably simplified depending

on the particular symmetry of the system at study. For instance, in the case of an in-

plane isotropic sample the susceptibility tensor becomes:

(2)

0 0 0 0 0(2 : , ) 0 0 0 0 0

0 0 0

xxz

ijk yyz

zxx zyy zzz

(3)

Where the x, y are the coordinates in the plane of incidence and z is the coordinate

normal to the plane. For this particular susceptibility tensor there are only three

independent elements: 0zxx zyy, 0xxz yyz

and 0zzz . These tensor

elements can be addressed depending on the choice of polarizer-analyzer

combination. More specifically, for incident light polarization oriented perpendicular

to the plane of incidence (SIN-polarization) and SHG polarization along the plane of

incidence (POUT-polarization) the zyy

component is addressed. This component is

attributable to molecules oriented in the plane of the sample as indicated by the y

indices. Similarly, the PIN-POUT polarizer-analyzer combination can be related to the

zxx , zzz and xxz components. Because the zzz component is attributable to

molecules oriented perpendicular to the plane of the sample, the ratio of SHG

intensity measured in the PIN-POUT versus SIN-POUT combinations constitutes a

measure for the out-of-plane anisotropy of the sample.

3. Results

Investigation of polymer adsorption via dielectric spectroscopy was performed by

monitoring changes in the structural ( -) relaxation process in real-time and

isothermal conditions. The -process is the dielectric signature of the dynamic glass

transition and appears as a peak of strength in the frequency dependence of the

imaginary part ( ) of the complex dielectric function. The dielectric strength , at a

given temperature, is related to the mean square dipole moment and provides a


106

measure of the volume fraction of molecules relaxing on the time and length scale of

the glass transition.30 Fig 1 shows the annealing time dependence of at 125 C for

a single layer film of l-PS deposited on aluminum as well as for a layer of l-PS

deposited on top of a strongly adsorbed layer of neat PS (see sketches of the two

systems in Fig 1).

Figure 1. Evolution of the dielectric strength, , upon annealing time. Open symbols correspond to a single layer of l-PS, 30 nm thick, deposited on aluminum; half filled symbols correspond to a 30 nm film l-PS deposited on a strongly absorbed layer of neat PS. The inset on the top illustrates the contribution due to reorganization of chain segments adsorbed before the measurement is started (red line), see text.

For the single layer film of l-PS in direct contact with the aluminum substrate, we

observe a drop of up to 35 % of its starting value after 105 s of annealing. This

reduction takes place through different regimes that are clearly distinguishable on a

logarithmic scale via the presence of two crossovers, at 700 s (ton) and at 1.5 105 s

(toff). The decay rate of is constant at short times, t < ton, during which some chain

segments adsorbed during spin coating, pre-annealing step, and before reaching the

set-point temperature (125°C) reorganize.20 These segments form an incomplete

adsorbed layer which is responsible for the lower dielectric strength as compared to

the bulk ( bulk = 1.2) at the start of the measurement.

100 1000 10000 1000000.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

101 102 103 104 105

1.0

(bulk)

toffton

bilayer

tANN [s]

single layer

30 nm PS-l

30 nm PS-l8 nm PS


107

The process of conformational reorganizations that occurs in this layer appears as a

linear background in the plot vs. log(t), see the red line in the inset Fig 1. New

adsorbing segments at 125 °C diffuse through the interfacial layer and after ton (first

crossover) start to get adsorbed. At toff (second crossover), the reduction rate of (t)

slows down, indicating a decrease of the adsorption kinetics. The presence of such

two crossovers in (t) was first spotted in a previous dielectric study on polymer

adsorption and is discussed elsewhere.20 Unlike to the single layer in contact with the

aluminum substrate, the dielectric strength for the film of l-PS deposited onto the

layer of strongly adsorbed PS shows a linear decrease as a function of log(t) for all

times. Moreover, in this case the value of at the start of the measurement is the

same as the bulk value, indicating that no adsorption takes place before the set-point

temperature is reached.

Subtraction of the linear background (see above) from the measured dielectric

strength for both systems allows obtaining the neat contribution corresponding to the

adsorption of new segments, defined as high. To visualize the adsorption kinetics in

a more intuitive fashion, we plotted high, which represents a quantity proportional

to the thickness of the adsorbed layer at the interface (see Fig 2).20 For the single

layer system, we observe a crossover from a power law regime at early times t < toff

to a logarithmic regime for t > toff. This is in agreement with predictions from Monte

Carlo studies on polymer adsorption.31 Differently, the dielectric strength of the l-PS

in the bilayer configuration, plotted in this way, shows essentially no variation with

time.

In an attempt to gain more insight into changes of segmental conformation in the

adsorbed layer, we performed time resolved second-harmonic generation (SHG)

experiments. The sample configurations were the same as previously investigated via

dielectric spectroscopy. The SHG measurements were carried out by recording the in-

and out-of-plane orientation specific signals from the interface.


108

Figure 2. Values of (t) of the SHG signal (blue) and the high data points (red), plotted as a function of time for: an l-PS film deposited on Al (top panel) and an l-PS film deposited onto an strongly adsorbed layer of neat PS (bottom panel).

Analysis of the data was done by plotting the ratio (t) between these in- and out-of-

plane signals, i.e the ratio of SHG intensity measured in the PIN-POUT versus SIN-POUT

combinations, as a function of time. This ratio is sensitive to the changes of

orientation upon adsorption: (t) increases with a more perpendicular alignment of

the probe moieties with respect to the surface. For the single layer system in contact

with aluminum, t shows a global reduction of about 50% at the end of the

adsorption process. We observe that the decay of (t) clearly stops at a time similar to

toff, after which (t) increases slightly until the end of the experiment. On the

contrary, (t) of the l-PS film in contact with the layer of strongly adsorbed PS

remains constant, even after 20 hours of annealing.

Hence, when the contact is established between l-PS and the metal, both high and

(t) vary significantly with time in a manner which is correlated, while it is not the

case for the contact between the l -PS and the layer of neat PS for which no variation

occurs during the whole experiment.

20

30

40

high

a.u]

-high

0.00

0.15

0.30

1000 10000 1000000

15

30

tANN [s]

-0.05

0.00

0.05

l-PS / Al

l-PS / neat PS


109

4. Discussion

Immobilization of the labeled segments leads to a decrease of the mean square dipole

moment < 2> per unit volume and thus to a reduction of the dielectric strength, , as

displayed in Fig 1 for the single layer on aluminum. Consequently, the increase of

high observed for this layer between ton and toff can be interpreted in terms of

formation of an adsorbed layer containing segments which are adsorbed via the

binding of the labeling dye moieties to the metal surface, see Fig 2.30 Simultaneously,

a decrease of the ratio (t) is observed, implying that the labeling dye moieties tend to

orient in a plane parallel to the surface while adsorbing. At this initial stage, the

parallel orientation is allowed because the surface coverage is low (few segments are

adsorbed) and large bare patches are available for adsorption.

The time evolution of the dielectric strength corresponds to a power law regime

high t0.3. Interestingly, the power law growth yields an exponent of 0.30 0.05,

which is significantly lower than 0.5 as one would expect for diffusion-limited

processes. This value is in line with earlier neutron reflectivity studies and Monte

Carlo simulations, and can be attributed to a screening effect due to the segments that

were adsorbed before the set-point temperature was reached (see above).31, 32

The segmental adsorption mechanism provided here brings insight to other studies

assessing the conformation of the whole chain. Indeed, the orientation of the dye

moieties parallel to the surface could correspond to a flattened chain configuration, as

expected from literature.15, 33

After a certain time, we observe a transition of the adsorption kinetics, as detected by

DS. The time region (see Fig 2. hatched area, around toff) where we identify a

transition between a power law regime and a slower logarithmic growth of high

represents the beginning of a second stage of adsorption. This transition corresponds

to a minimum of t as determined by SHG followed by an increase upon annealing.

During the second stage more segments are adsorbed at the surface, leading to a

further increase of high. However, the presence of chains with some adsorbed

segments constitutes a barrier for further adsorption and very few bare patches are


110

available for new adsorption events.34 As a result, the kinetics of adsorption slows

down significantly.

At the transition (around toff), the population of dye moieties is split between some of

them that were adsorbed during the first stage with an orientation parallel to the

surface and the rest of it, with isotropic orientation. The increase of t observed

after toff indicates that new moieties, which pertained to the isotropic population,

gradually adopt an average orientation normal to the surface. The change in

orientation is a consequence of the lack of space accessible for adsorption. Although

at this stage, the surface is nearly saturated and the penetration through the adsorbed

layer is unfavorable, a labeled segment arriving from the inner part of the film still

has a certain probability to find a “hole” generated by conformational fluctuations in

the structure.35 In this condition, the adsorption is achievable only if the new

penetrating labeling moieties adopt an orientation normal to the surface.

It is possible that the perpendicular orientation of the adsorbing units observed during

this latest stage of adsorption corresponds to the formation of loops and tails

characterizing the conformation of adsorbed homopolymer chains at high surface

coverage.15, 33

Results on the bilayer system further corroborate our hypothesis. As stated in the

experimental part, the bilayer film is composed of a 30 nm thick film of PS-l

spincoated on the top of an 8 nm layer of strongly adsorbed PS. We expect that this

strongly adsorbed PS significantly retards the diffusion of the labeled segments and

prevents their adsorption onto the Al surface. In fact, as shown in a recent work,36 the

presence of a complete adsorbed layer of PS at the metallic interface leads to a

decrease of the diffusion coefficient of the labeled PS chains by 2-3 orders of

magnitude as compared to the bulk value. Concomitantly, the dielectric strength as

plotted in Fig 2 shows no time evolution, indicating that the time needed by the

labeled segments to diffuse through the dense adsorbed layer of PS is longer than the

experimental time window, and no adsorption takes place. We show with the SHG

curve Fig 2b that in this case no preferential orientation occurs; in fact (t) remains

constant during the whole experiment.


111

Hence, the changes of orientation observed for the single layer in contact with the

aluminum are not found in the case where adsorption is inhibited by the strongly

adsorbed PS layer. These results highlight the complementary role of second

harmonic generation technique and dielectric spectroscopy in assessing the

mechanisms of the adsorption process.

We do not discount the possibility that the preannealing protocol that we used for the

samples is not enough to reach the equilibrium, however this would not change the

qualitative features of the responses of the two systems and their striking differences.

To explore more in depth the kinetics of polymer adsorption, we studied labeled

polystyrene films of different molecular weights, as well as non labeled systems. As

previously shown, the adsorption can be described by a characteristic time ton < tads <

toff .20 Recently we highlighted that properties of ultrathin films are related to the

conformation of the adsorbed interfacial chains, which can be described via the ratio

between the annealing time and the time scale of adsorption, t*= tANN/ tads. If the

annealing time is much shorter, equal or much higher than tads, different regimes are

expected as confirmed by this study for the system where adsorption occurs. For

t*<<1 (tANN<<ton) and t*>>1 (tANN >> toff) polymer properties are invariant with

respect to the annealing time but the conformation of interfacial chains are different.

On the contrary, for t* 1 (ton < t < toff) the conformations within the interfacial layer

change continuously with the annealing time as well as the physical properties. By

taking advantage of the capability of dielectric spectroscopy to provide direct

information on the structural relaxation time we determined the ratio tads / for

neat and labeled polystyrene samples as a function of temperature. In agreement with

a previous work, tads/ is constant over the temperature range investigated, implying

that both processes, adsorption and the dynamic glass transition, have the same

activation energy, see Fig 3. For films of the labeled PS used in this study, the ratio

log (tads/ ) 7 implies that a measure of tads at Tg (100 s) would require annealing

times of the order of 30 years. Hence, values of tads at temperatures next to Tg can be

deduced from the temperature dependence of , a more easily accessible measurable

quantity. It is noteworthy that the nature of the surface interaction can strongly impact


112

the ratio log (tads/ ) and thus the kinetics of the adsorption process. This observation

will be studied in more detail in a further work.

Figure 3. Ratio between the characteristic adsorption time, tads, and the structural relaxation time, , for l-PS 20kg/mol used in this work (blue hexagons), labeled PS 820 kg/mol (green diamonds),19 PS 97 kg/mol (red squares),20 PS 160 kg/mol (black circle).20

5. Conclusions

We studied the adsorption kinetics of ultrathin polymer films of labeled PS supported

on aluminum substrates and on a strongly adsorbed layer of neat PS, by combining

dielectric spectroscopy (DS) and the surface-induced nonlinear optical second

harmonic generation technique (SHG).

Dielectric spectroscopy, which is sensitive to molecular dynamics, allowed us to

monitor the adsorption kinetics via the time dependence of the dielectric strength, a

quantity proportional to the amount of mobile segments involved in the structural

relaxation process. Immobilization of labeled segments during adsorption causes a

reduction of the dielectric strength and by following its evolution upon annealing we

were able to distinguish the different stages of the adsorption process.

15 20 25 30 35 40 45 50

6.0

7.5

9.0

10.5

12.0

13.5lo

g(t ad

s/)

T-Tg [K]


113

At the same time, second-harmonic generation experiments yielded information on

the average orientation of labeling dye moieties during adsorption, which provided

insight into the mechanisms of the process itself. The SHG signal was generated from

the adsorbed dye moieties, with both parallel and perpendicular orientation to the

interface. By taking the ratio between the two signals, we could determine changes in

the average orientation with respect to the surface normal.

Results on the l-PS in contact with the Al revealed a two-stage process during which

we observed a strong correlation between the kinetics of adsorption and variations in

the orientation of labeling moieties. At the beginning of the adsorption process (first

stage), the binding of the labeled segments on the surface promotes an alignment of

the labeling dye moieties parallel to it. At the end of the process (high surface

coverage, second stage), adsorption develops via an alignment of the dye moieties

normal to the surface. On the contrary, measurements on the l-PS deposited on a

strongly adsorbed layer of neat PS did not display any change with time, implying

that in this case no adsorption takes place at the metal surface.

Our results demonstrated the usefulness of second harmonic generation technique as

a complementary tool to dielectric spectroscopy in assessing the mechanisms of

segmental adsorption. Since SHG is uniquely appropriate to probe the orientation of

adsorbed dye moieties at the metal surface, we are currently expanding our approach

to other systems.

Acknowledgments

C.R. acknowledges financial support from the Research Council of the K.U. Leuven, project no. OT/30/06. S.N., S.V. and V.K.V. are grateful to the FWO (Fonds Wetenschappelijk Onderzoeks-Vlaanderen) for financial support. M.W. acknowledges financial support from FWO within the Project G.0642.08.


114

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116

Additional comments following the suggestions of the Examination Committee

1) The sample configurations used for the dielectric relaxation and the second-

harmonic generation (SHG) studies are slightly different. Polymer films characterized

by SHG are supported (one polymer/substrate interface), while samples studied by

dielectric spectroscopy are capped between two metal layers (two polymer/substrate

interfaces). In the case of a single layer capped film the adsorption process takes

place at both metal interfaces (the upper and the lower electrodes). However, the

contribution due to adsorption onto the upper electrode is logarithmic in nature and

can be subtracted from the measured dielectric strength by following the procedure

described in the text (see page 107). This procedure allowed us to focus the analysis

on the adsorption process that occur at the lower metal interface and justifies the

comparison between the dielectric and the SHG measurements.

2) We added and additional sketch to better visualize the physical picture based on

the interplay between adsorption and the orientation of the dye-moieties.

a) b)

a) For times shorter than the characteristic time toff (see text) dye moieties find large

bare spots available for adsorption. Therefore, they adsorb relatively “fast”, as

indicated by the power law growth of - t0.3, with an orientation parallel to the

surface, as seen by the decrease of (t).

b) For times larger than toff the surface coverage is high and only few spots are now

available for adsorption. As a consequence, the kinetics of adsorption slows down ( -

logt) and the adsorption is allowed only if the dye-moieties align normal to the

surface (increase of (t)).

Is the Reduction in Tracer Diffusivity under Nanoscopic Confinement Related to a Frustrated Segmental Mobility?

118 Chapter 7

Is the Reduction in Tracer Diffusivity under

Nanoscopic Confinement Related to a Frustrated

Segmental Mobility?

Simone Napolitano*, Cinzia Rotella, and Michael Wübbenhorst

Katholieke Universiteit Leuven, Laboratory of Acoustic and Thermal Physics,

Department of Physics and Astronomy, Celestijnenlaan 200D, B-3001 Leuven,

Belgium



Macromolecular Rapid Communications, Volume 32, 844–848, 2011Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Contribution to the work: Cinzia Rotella prepared the thin films and the Guiselin’s

brushes, performed the measurements and analyzed the dielectric data.


119 AbstractWe developed an experimental method for the determination of the tracer diffusivity

Dtr in ultrathin polymer films, and the changes in the segmental mobility of tracer

molecules while they diffuse through matrices of different thickness and get adsorbed

onto a target substrate. Dtr starts decreasing already at 120-150 nm and drops to 1% of

its bulk value at films as thin as 7.5 nm. We discuss the results highlighting a strong

decoupling between the reduction in mass transport at the nanoscale and the increase

in the glass transition temperature determined via capacitive dilatometry together

with a breakdown of the Stoke-Einstein relation between orientational and

translational degrees of freedom.

1. IntroductionProcessing of devices for submicro- and nanotechnological applications requires the

knowledge of the changes in the behavior of materials in restricted geometries and in

the presence of interfaces. In the case of polymer chains deposited on attractive (often

inorganic) substrates, the glass transition temperature, Tg, might show minor

deviations (both increases and reductions are reported) at thicknesses on the order of

a few tens of nanometers.[1] On the contrary, a drastic reduction of the diffusion rate

of low molecular weight components (tracer diffusivity Dtr) is observed already in

matrices as thick as hundreds of nanometers, corresponding to 4 – 6 gyration radii,

Rg.[2] These experimental evidences suggest a breakdown, at the nanoscale, of the

equivalence between translational (diffusion) and rotational (viscosity, segmental

dynamics) mobility,[3] known as Stokes-Einstein relation. This evidence has strong

fundamental implications. For example, the reduction of tracer diffusivity and

increase of crystallization time in proximity of an attractive interface,[4, 5] are often

explained in terms of increase of the glass transition temperature,[6] speculations

which have not been experimentally verified. Moreover, the perturbations in Dtr exert

a non negligible impact on the curing of polymer-based nanodevices: diffusion of

small molecules in proximity of inorganic/organic junctions is, in fact, a crucial

mechanism underlying in many processing steps like, for example, solvent

evaporation, crystallization, self-assembly and phase segregation.


120 At the state of the art, tracer diffusivity of ultrathin polymer layers (thickness < 200

nm) can be measured by studying the time evolution of the density profile of probe

molecules diffusing inside a film via neutron scattering[2] or via fluorescence

nonradiative energy transfer.[7] Such approaches, however, cannot provide the time

necessary to a molecule (solvent, diluent, etc) to diffuse through the interfacial layer

and finally reach the substrate. Molecules already adsorbed onto the metallic surface,

in fact, further retards diffusion in the polymer chains in proximity of the interface.

Furthermore, although some of the probes might couple directly to the -relaxation,[7]

those approaches do not provide direct information on the segmental mobility of the

polymer, and thus on Tg. To overcome this issue, we developed an experimental

method to measure tracer diffusivity of ultrathin polymer films (thickness < 200 nm)

via dielectric spectroscopy, a well-etablished technique to study relaxation processes

at the nanoscale. Our novel approach is based on the direct determination of the time

D needed by tracer molecules to diffuse through matrices of known thickness and get

adsorbed onto a target substrate. Adsorption, corresponding to the total or partial

inhibition of segmental mobility, is monitored via a drop of the dielectric strength,

, i.e. the intensity of the structural relaxation peak. Our analysis is justified by the

Debye relation, that in isothermal conditions reads N< 2>, with < 2> the mean

square dipole moment, and N the number density of relaxation units participating in

the orientational polarization on the time and the length scale of the dynamic glass

transition. Such proportionality justifies the use of as a parameter to monitor

adsorption; in fact, as in the case of cold crystallization,[8, 9] partial or total

immobilization of the chains limits the solid angle over which dipoles can reorient,

yielding a reduction in the dielectric strength.[10] In fact, we recently verified that the

growth of an adsorbed layer can be monitored via the correlated changes in dielectric

strength.[11]

In comparison to measurements based on neutron reflectivity, the advantages of our

method are multiple: smaller and more easily accessible instrumentation (an

impedance analyzer), and the possibility to measure the effective time needed by

tracer molecules to diffuse through the whole layer and adsorb onto the substrate,

instead of the tracer diffusivity averaged over the whole film thickness. Moreover, the


121 possibility to measure within the same experimental technique, both the diffusion and

the segmental relaxation time (connected to Tg) allowed us to verify that models

based on a slowing down of the segmental dynamics[2] are not appropriate to describe

the reduction of tracer diffusivity at the nanoscale. On the contrary, a strong

correlation is observed between the glass transition assessed by capacitive

dilatometry and the one extrapolated from the drop in tracer diffusivity.

2. Experimental Section

Polystyrene (weight-average molecular mass Mw = 97 and 640 kg/mol; PDI= 1.01

and 1.11, Tg via differential scanning calorimetry = 372 ± 2 K and 374 ± 2 K) was

purchased from Scientific Polymer Products and used as matrix without any further

treatment. The low molecular weight (Mw 20 kg/mol PDI = 2.5, Tg = 371 ± 3 K),

chromophore-functionalized polymer (l-PS), used as tracer in this study, is a random

copolymer of styrene and methyl methacrylate whose longer side chain is decorated

with the polar group {4-[(4-cyanophenyl)diazenyl]phenyl}(methyl)amino. The final

content of chromophore was ~ 2 % mol, which provided a dielectric strength ten

times larger than neat PS.

Samples containing matrices thicker than 19 nm were prepared as trilayers

(configuration A), placing the films of l-PS in between an impenetrable adsorbed

layer (“Guiselin brushes”[12] of PS97 annealed at 423 K for 20 h) and a matrix of

PS640. This configuration permitted to avoid diffusion towards the lower electrode,

protected by the brushes of PS97. Adsorbed layers with high surface coverage (8.0

nm, measured by capacitive dilatometry) were prepared by spincoating filtered

solution of the polymer in chloroform onto thermally evaporated aluminum substrates

( 50 nm of Al 99.5% Goodfellow, p < 10-6 mbar, evaporation rate 10 nm/s). The

resulting thick ( 200 nm) films of PS97 (where 97 indicates the Mw in kg/mol) were

annealed for 20 h at Tg + 50 K to favor adsorption;[11] subsequently, to remove the

unbound chains, the sample was washed in the same good solvent used for


122 spincoating.1 -6 mbar).

Films of l-PS ( 50 nm) were spincoated (chloroform) directly onto the impenetrable

adsorbed layer, which is not soluble in chlorofom. Matrices of PS640 of desired

thickness (> 19 nm) previously spincoated (chloroform) on mica and floated onto a

reservoir of ultrapure water, were finally transferred on top of the bilayer (brushes/l-

PS). Water occasionally trapped between consecutive layers was allowed to

evaporate at ambient conditions for a couple of days before the deposition of the next

layer. To facilitate the application of an electric field, the upper surface was finally

metalized following the same procedure used for the lower electrode. To avoid

perturbations in the chain conformations due to film formation at thicknesses much

smaller than the gyration radius, the thinnest film was prepared in bilayer

(configuration B) following Guiselin’s experiment.[11, 12] Thick films ( 200 nm) of

PS640, were spincoated (chloroform) and annealed at Tg+50K for 6 h. The unbound

fraction was removed as described above. Films of l-PS (20 nm) were directly

spincast on the residual film (7.5 nm) and metalized via the same procedure described

above.

Electrical capacitances of the samples were measured by applying an electric field

perpendicular to the surface of the films and measuring the current flow generated via

an impedance analyzer. Dielectric measurements were performed under inert

atmosphere (N2), in isothermal conditions in the frequency range from 10-1 to 106 Hz

using a high-resolution dielectric analyzer (Alpha Analyzer, Novocontrol

Technologies). Dielectric spectra were fitted by Havriliak-Negami (HN)

functions.[13] The temperature dependence of the structural relaxation time

(obtained from the HN fits) was analyzed by means of the Vogel-Fulcher-Tamman

equation; Tg was assigned to the temperature satisfying the condition (Tg) = 100 s.

The thickness of the different layers was evaluated via their geometrical capacitance,

using nanocapacitors of single layers obtained by the same solution used in the

multilayers under identical spincoating conditions. 1 We checked, using the bilayer configuration, that under this sample preparation, adsorption of undoped chains does not take place within the whole measuring time (56 h).


123 3. Results and discussionThe frequency dependence of the dielectric loss during diffusion of labeled PS into a

matrix (7.5 nm) of neat PS640 at 398 K is provided in figure 1. The peak centered in

the kHz region, whose intensity decays with annealing time, is the manifestation of

the structural ( ) relaxation sensed by the probe molecules. The frequency of the

maximum of the peak is related to the structural relaxation time via the relation

2 fmax =1. Regardless the higher intrinsic value of dielectric strength, the observed

reduction of is imputable to chains of l-PS only.

During annealing, the dielectric strength decreases due to both rearrangements of

chains adsorbed already during spincoating and metal evaporation (short times,

segmental time), and adsorption of new chains (long times, D).[11, 14] The two

contributions, providing different slopes in a plot of vs log(t), see inset Figure 1,

can easily be disentangled, owing to their different physical origin and a separation in

timescale by several orders of magnitude. The first logarithmic decay of the dielectric

strength, is due to local conformational rearrangement of the chains as a consequence

of the increase in the adsorbed amount on the available surface.[15] This process,

mainly related to those chains already in direct contact with the aluminum oxide (at

the non-diffusive interface), starts already before reaching the temperature at which

experiments are performed and its signature appears as a linear background in plots

of vs log(t). Chains of PS already adsorbed on the metallic surface form an

incomplete layer hindering the insertion of the labeled chains and retarding the

diffusion in the last few nanometers of the matrix.[15-17] When segments of l-PS

finally reach the substrate, the contact with the metallic layer limits the solid angle

over which dipoles can reorient, yielding an effective lower mean square dipole

moment and a lower . Consequently, we could identify the diffusion time, D, via

the adsorption of the first labeled chains hitting the substrate, i.e. the onset of the

larger reduction rate in the dielectric strength.2 2 In a plot of vs. log(t) D was assigned to the intersection of the first linear drop and of the onset of the increase in reduction of , which can be approximated with a linear term in the very early stages of adsorption.


124

Figure 1 Frequency dependence of the dielectric loss during diffusion of labeled PS into a 7.5 nm thick matrix of neat PS640 at 398 K, a scheme of the assembled multilayers in the two configurations used is provided, yellow arrows indicate diffusion of labeled PS. In the inset, time evolution of the ratio between the dielectric strength and the dielectric constant.

To avoid systematic errors arising from variation of the sample size upon adsorption,

we analyzed the time evolution of = / ( PS=0.4; PS=0.016), where is the

high frequency limit of the dielectric constant, a parameter free from uncertainties in

the film thickness and electrodes surface.3 Following a Fickian model, the tracer

diffusion coefficient Dtr was estimated as L2·(4 D)-1, where L is the thickness of the

matrix. The approximation is based on the solution of Fick’s equation in one

dimension, assuming L proportional to the diffusive length (= ), i.e. a measure

of the propagation of the concentration profile along the film thickness at the time D.

Tracer diffusivity experiments were performed at Tg + 20 K, where the adsorption

kinetics of PS is practically arrested. Due to the inverse proportionality between the

thickness of the matrix and its dielectric capacitance, reduction of the diffusive length

does not affect the sensitivity of the measurement. However, increase in the thickness

of the matrix resulted in a lower contrast between the value of the dielectric strength 3 We verified that this quantity, normalized to its value at t=0, is not affected by the capacitive contribution of the neat PS matrix.


125 before and after chain adsorption; regardless this issue, we could easily assign the

value of D for films as thick as 230 nm.

The thickness dependence of D and the corresponding variation of tracer diffusivity

are plotted in Figure 2. A clear deviation from the limiting bulk value (DtrBULK = 5 10-

15 cm2/s) is observed at thicknesses smaller than 100 - 120 nm (4-5 Rg). In analogy

with previous observations based on layers deposited on attractive interfaces,[18] we

found reduced values of diffusion coefficients for matrices thinner than 4 Rg reaching

5% of the bulk value for films of the order Rg (= 23 nm), see Figure 2.

Figure 2 Thickness dependence of the diffusion time of l-PS in matrices of PS640. The resulting tracer diffusivity is plotted in the inset. The dash-dotted line provides the value of the diffusion time in the case of position independent tracer diffusivity.

The diffusion time through this interfacial layer was 100 times longer than expected

in the case of tracer diffusivity independent on the distance from the metallic oxide

surface, i.e. Dtr decreases in proximity of the organic/inorganic interface and in the

last 7.5 nm probe molecules diffuse at a rate 2 orders of magnitude lower than in

bulk.

Attempts to ascribe the reduction of Dtr, as proposed by Zheng et al.[2] (see supporting

information) with an increase of an effective Tg, here estimated on the order of 7.5 K,

failed in view of the minor variations (< 2 K) in the “dynamic” Tg of films of neat PS


126 assigned via the temperature dependence of the segmental relaxation via dielectric

spectroscopy and AC-calorimetry.[19] The increase in effective Tg is furthermore in

disagreement with the larger drops observed for example by ellipsometry[20] and

fluorescent spectroscopy.[21, 22]

Figure 3 Comparison between the increase in “effective” Tg of PS (matrix) related to the measured reduction in tracer diffusivity, following the method proposed by Zheng et al.[2], the Tg obtained by capacitive dilatometry for single layers of PS160 cappedbetween aluminum electrodes,[23] and the “dynamic” Tg of single layers of l-PS (probe) as deduced by the temperature dependence of the segmental mobility. The shadow area indicates the variation in the “dynamic” Tg of ultrathin film of PS of different molecular weight.[19] Errors are smaller than the symbol size.

However, we noticed a strong correlation between the thickness dependence of the Tg

determined via tracer diffusivity and the glass transition temperature provided by

capacitive dilatometry,[23, 24] a technique which senses the temperature dependence of

the dielectric constant in absence of molecular mobility and thus the density

fluctuations, coupled to changes in the electric capacitance.4 4 In the approximation of parallel plates, valid for thin films tested in a capped geometry as that used in this work, the electrical capacitance is inversely proportional to the thickness of the film. The temperature dependence of the capacitance C(T), can thus be used to extract values of thermal expansivity and Tg is thus attributed to the temperature where dC/dT shows a discontinuity


127 The constant “dynamic” Tg measured for single layers of l-PS similarly disproves that

the observed reduction in mass transport are related to a frustrated intrinsic mobility

of the probe molecules in proximity of the metallic interface. However, the neat shift

of the structural peak towards lower frequencies during diffusion experiments hints to

an increase of the relaxation time of the probes as they get adsorbed, approaching the

metallic interface. With these findings in mind, we arrive to an apparent paradox: in

the layer at the interface between polystyrene and aluminum oxide, the rotational

barriers ( ) are almost unaltered while the translational mobility of probes (Dtr) is

strongly retarded and the thermally expansivity is reduced.[23] While similar

violations of the Stokes-Einstein relations are not observed in bulk systems, the

nanometer scale offers different similar examples, see for example the increase in

crystallization time accompanied by a constant[4, 25] or even lower[26] Tg.

We speculate that the origin of these apparent inconsistencies is related to the impact

of adsorption at the interface on the behavior of the whole film. The different

conformations assumed by the chains of PS in the adsorbed layer (the formation of a

“Guiselin brush” is a strong proof of chain adsorption[11, 14]) might not particularly

affect molecular relaxations on the lenghtscale of the cooperative motion (2-4 nm for

the dynamic glass transition), but lowers the probability to find available space where

diffusing in proximity of the interface (densification).[11, 24, 27] This phenomenon

results in a reduction of thermal expansivity, as experimentally verified,[23] and a less

efficient random walk, which leads to a reduction of the tracer diffusivity. Similar

ideas are in agreement with the experimental evidence that the diffusion of smaller

probes like decacyclene and lophine might be less affected (or remain constant).[28]

The specific role of the degree of adsorption on the behavior of tracer molecules at

the very interface (<10 nm) is currently under investigation.

4. ConclusionsWe developed a method permitting to measure the tracer diffusivity of ultrathin

polymer films based on adsorption of the probe molecules on a target substrate. The

approach, exploiting the sensitivity of dielectric spectroscopy, allows capturing the

perturbations in the segmental dynamics (dynamic Tg) of the probes during diffusion.

For polystyrene, we observed a strong decoupling between the translational and


128 orientational degrees of freedom, which violates the Stokes-Einstein relations. We

finally verified that the effective Tg deduced from the reduction in mass transport at

the nanoscale are in line with the increase in glass transition temperature measured by

capacitive dilatometry.

Acknowledgments

SN acknowledges FWO (Fonds Wetenschappelijk Onderzoeks - Vlaanderen) for a postdoctoral scholarship. CR acknowledges financial support from the Research Council of the K.U.Leuven, project no. OT/30/06. The authors acknowledge M. Koszykowska and S. Kucharski (Department of Polymer Engineering and Technology, Wroclaw University of Technology) for synthesis of the labeled polymer.

References[1] G. Reiter, S. Napolitano, Journal of Polymer Science Part B-Polymer Physics 2010, 48, 2544. [2] X. Zheng, M. H. Rafailovich, J. Sokolov, Y. Strzhemechny, S. A. Schwarz, B. B. Sauer, M. Rubinstein, Phys Rev Lett. 1997, 79, 241. [3] P. Green, E. Kramer, Journal of Materials Research 1986, 202. [4] S. Napolitano, M. Wubbenhorst, Macromolecules 2006, 39, 5967. [5] M. J. Capitan, D. R. Rueda, T. A. Ezquerra, Macromolecules 2004, 37, 5653. [6] M. M. Despotopoulou, C. W. Frank, R. D. Miller, J. F. Rabolt, Macromolecules 1996, 29, 5797. [7] D. B. Hall, J. M. Torkelson, Abstracts of Papers of the American Chemical

Society 1998, 216, U819. [8] A. Nogales, Z. Denchev, I. Sics, T. A. Ezquerra, Macromolecules 2000, 33, 9367. [9] K. Fukao, M. Miyamoto, Phys Rev Lett. 1997, 79, 4613. [10] S. Napolitano, D. Prevosto, M. Lucchesi, P. Pingue, M. D'Acunto, P. Rolla, Langmuir 2007, 23, 2103. [11] S. Napolitano, M. Wubbenhorst, Nature Communications 2011, accepted. [12] O. Guiselin, Europh. Lett. 1991, 17, 225.


129 [13] S. Havriliak, S. Negami, Polymer 1967, 8, 161. [14] G. J. Fleer, M. A. Cohen Stuart, J. M. H. M. Scheutjens, T. Cosgrove, B. Vincent, "Polymer at interfaces", Chapman & Hall, London, 1998. [15] R. Zajac, A. Chakrabarti, Physical Review E 1995, 52, 6536. [16] C. Ligoure, L. Leibler, Journal De Physique 1990, 51, 1313. [17] J. F. Douglas, H. M. Schneider, P. Frantz, R. Lipman, S. Granick, Journal of

Physics-Condensed Matter 1997, 9, 7699. [18] E. K. Lin, W. I. Wu, S. K. Satija, Macromolecules 1997, 30, 7224. [19] M. Tress, M. Erber, E. U. Mapesa, H. Huth, J. Muller, A. Serghei, C. Schick, K. J. Eichhorn, B. Volt, F. Kremer, Macromolecules 2010, 43, 9937. [20] J. A. Forrest, K. Dalnoki-Veress, Advances in Colloid and Interface Science 2001, 94, 167. [21] C. J. Ellison, M. K. Mundra, J. M. Torkelson, Macromolecules 2005, 38, 1767. [22] C. J. Ellison, J. M. Torkelson, Nat. Mater. 2003, 2, 695. [23] S. Napolitano, M. Wubbenhorst, Journal of Physical Chemistry B 2007, 111, 9197. [24] S. Napolitano, A. Pilleri, P. Rolla, M. Wubbenhorst, Acs Nano 2010, 4, 841. [25] S. Napolitano, M. Wubbenhorst, Journal of Physical Chemistry B 2007, 111, 5775. [26] Y. Zhang, Y. L. Lu, Y. X. Duan, J. M. Zhang, S. K. Yan, D. Y. Shen, Journal of

Polymer Science Part B-Polymer Physics 2004, 42, 4440. [27] C. Rotella, S. Napolitano, L. De Cremer, G. Koeckelberghs, M. Wubbenhorst, Macromolecules 2010, 43, 8686. [28] D. B. Hall, J. M. Torkelson, Macromolecules 1998, 31, 8817.


130 Supporting information

Determination of the effective Tg from tracer diffusivity measurements

The temperature dependence of the tracer diffusivity of polystyrene can be describe

in terms of a Vogel Fulcher Tamman equation of the form

0

lnBULKtr

BULK

D BAT T T

(1)

Where A and B are constants and T0 is a reference temperature. Assuming that the

reduction of Dtr is a result in a perturbation of T0 (constant fragility) we can express

the thickness dependence of the tracer diffusivity as

0

( )ln( )

trD h BAT T T h

(2)

An expression for T0(h) can be obtained subtracting Eq(1) from Eq(2):

0

0

( )ln

( )

BULKtr

BULKtr

BT h TD BD h T T

(3)

We considered B = 710 K and T0 = 332 K as determined by Green and Kremer. [1] At

constant fragility (A and B constant) the ratio between Tg and T0 is thickness

independent,[2] and the effective Tg finally reads:

0

0

( )( ) BULKg g BULK

T hT h TT

(4)

[1] P. Green, E. Kramer, Journal of Materials Research 1986, 202

[2] S. Napolitano, M. Wubbenhorst, Journal of Physical Chemistry B 2007,111, 575

[Digitare il titolo del documento] 132

Conclusions and Future Work

Conclusions

This thesis is focused on the role of the interfacial interactions in relation with the

dynamic properties of ultrathin polymer films (thickness < 200 nm). The study has

been mainly carried out using dielectric relaxation spectroscopy in conjunction with a

fine control of the polymer – substrate interaction.

We studied by dielectric spectroscopy the -relaxation process of freely-standing

ultrathin films of various thicknesses and molecular weights (Chapter 3). The work

comprised the implementation of a new experimental configuration based on three-

dimensional electrode structures (Interdigitated comb electrodes, IDE). This

geometry allows characterizing the dielectric response of thin films regardless of the

influence of a specific polymer-solid interaction, contrarily to usual configurations

where the surfaces are covered by metallic layers. Moreover, the IDE geometry

avoids the complications arising from the interpretation of dielectric signals of films

probed by an electric field perpendicular to the surface. With these precautions we

found that the glass transition temperature is reduced upon confinement within the

same order of magnitude as that found in the literature with other methods. We

showed that the Tg reductions in thin films are associated to relaxations times

much shorter than what is observed in the bulk.

The following experimental results constitute the main body of the work and have

been achieved by specifically tuning the interfacial interactions between the polymer

and the substrate. For this purpose we used multilayer systems in combination with

polymers of specific chemical architectures which confer them useful interfacial

activity.


We studied the effect of confinement on single layer films of neat and labelled-

polystyrene capped between two metal layers, which is the common configuration

used in dielectric spectroscopy (Chapter 4). We observed that the dynamics of the

neat polymer is not affected by the thickness reduction. To the contrary, upon

confinement, films of labelled-polystyrene displayed a slower dynamics and a

reduction of the dielectric strength. We hypothesized that the contrasting behaviour of

the two systems arise from the strong interaction between the labelled polymer and

the substrate. Interfacial chains of the labelled-polystyrene show a slower dynamics

and a lower dielectric strength compared to the bulk because the chains are partially

adsorbed.

This conjecture was tested with a mathematical model developed in order to

rationalize the effects of interfacial interactions on the dielectric strength (Chapter 5).

By assuming an ad hoc profile for the evolution of the dielectric strength along the

film thickness, we deduced numerically the reduction of as a function of film

thickness. This procedure suggested a way of estimating the thickness of a

immobilized layer (or reduced mobility layer) adsorbed onto the solid surface.

To verify experimentally our hypothesis, we combined dielectric spectroscopy with

the design of multilayer systems (Chapter 4). By placing a thin layer of labelled-

polystyrene at different locations above the solid interface, we could study the

dynamics of this polymer not in contact with the solid surface. In this configuration

we were able to determine the local glass transition temperature and the local

dielectric strength, and detected no confinement effects for a 15 nm film. When the

same labelled layer was placed in contact with the surface, clear confinement effects

arose. These experiments strongly suggested that the slowing down of the dynamics

mentioned above is not an inherent property of the thin labelled-polystyrene or to an

artefact due to non equilibrium effect, but is rather the result of its specific interaction

with the solid substrate. In the same study we detected that the time spent above Tg

may have a important influence on the deviations from bulk behaviour of the labelled

polystyrene. This lead us to hypothesize that the thermal history of the labelled


polystyrene – substrate interaction may generate complex effects linked with the

adsorption kinetics.

Thus we designed specific experiments to clarify this point, by studying the

isothermal adsorption process of labeled polymer layers placed either in contact with

a metal surface or with a pseudo-brush of the neat polymer (Chapter 6). In the same

spirit as before with the multilayer systems, the pseudo-brush has been used to ensure

that no interaction of the labeled-polymer can take place with the metal, because of

the high density of the brush near the solid surface, limiting diffusion through the

layer down to the substrate (Chapter 7).

The study (Chapter 6) involved the use of dielectric spectroscopy in conjunction with

second-harmonic generation, which provided valuable information on the orientation

of the labeling moieties. When the labeled-polystyrene is in contact with the

substrate, the dielectric strength decreases with time, indicating a progressive

immobilization of the labeled moieties. We observed two stages in the temporal

evolution of the dielectric strength, the first stage being faster than the second. The

first and second stages correspond to an average orientation of the labeling moieties

parallel and normal to the surface, respectively. This suggested an interplay between

segmental adsorption and the orientation of the labeling moieties. No such

phenomena are identified when the substrate is passivated with the pseudo brush.

This lead us to the following interpretations. Because of the attractive interaction

between the polymer and the substrate, polymer segments are pinned at the solid

surface. This limits the rotational fluctuations of the dipoles and leads to a reduction

of the dielectric strength. At the initial stage, the parallel orientation is allowed

because the surface coverage is low (few segments are adsorbed) and large bare spot

are available for adsorption. The following change in orientation is a consequence of

the lack of space accessible for adsorption. In this case, the adsorption is allowed only

if the new penetrating labeling moieties adopt an orientation normal to the surface.

The work by Keddie and Jones showed that interactions stronger than purely

dispersive such as hydrogen bonds could surpass the influence of the (supposed)

liquid-like free surface layer that reduces the Tg. In this thesis, we show that the


interaction between the polymer and the surface may not be determined by solely the

energy of the segment–surface interaction. Indeed, polymers close to interfaces are

characterized by long timescales which govern the building up of the adsorbed layer

very close to the interface. This adsorbed layer reduces the average dielectric strength

and modifies the Tg of confined films.

Future work

While this work provided valuable information about the role of surfaces and

interfaces in determining the properties of polymers confined at the nanoscale, this

section will highlight a few opportunities for future works.

The dielectric study of freely-standing ultrathin polymer films provided insight on the

segmental dynamics and glass transition temperatures of such systems. However, due

to the lack of spatial resolution, imposed by dielectric technique, we could not

discriminate between the mobility of polymer chains near the free surfaces and the

global mobility averaged along the whole sample thickness. Hence, we propose to

extend the study of freely-standing films to techniques that can directly probe the

dynamics at the free surface by normal oscillations, such as scanning probe

microscopy (SPM). First measurements are on the way.

An interesting point to investigate is the effect of the surface roughness on the

dynamic behavior of the interfacial layers. We can expect that degree of surface

roughness influences the amount of segments adsorbed at the surface, thereby

modifying the local values of dielectric strength and Tg. The substrates should be

highly controlled by advanced lithographic techniques such as used in

nanotechnology by creating nano-grooves or more homogeneous rough structures.

To push the ongoing efforts regarding the determination of mobility profiles in thin

films we intend to combine the multilayer approach with polymers labeled with small

dye molecules ( 0.6 nm). These small dye molecules may behave as “free-volume”

probes offering a way to determine a depth resolved volumetric glass transition

temperature by means of dielectric experiment.


Appendix

A1. Dielectric spectroscopy

The relaxation dynamics of polymer materials is characterized by a large frequency

range. The dielectric (or impedance) spectroscopy, the measurement of dielectric

properties, comprises this frequency range, which extends over 18 orders in

magnitude: from the 10-6 Hz to the 1012 Hz range and it can be performed at different

temperatures. The technique is based on the interaction of an external field with the

electric dipole moment of the sample. The resulting dielectric response is measured

and connected to the dynamics on a molecular scale.

When an electric field is applied to a the dielectric sample placed between two

electrodes, the atomic and molecular charges in the dielectric are displaced from their

equilibrium positions and the material is said to be polarized. Different mechanisms

can induce polarization in dielectric upon the application of an E-field.

(i) Electronic/atomic polarization: the displacement of binding electrons or atoms

from their equilibrium position on a molecular level (induced dipoles). These

processes occur within times corresponding to frequencies in the UV range

(electronic polarization) and IR range (atomic polarization) and is considered

instantaneous in dielectric spectroscopy.

(ii) The reorientational motions of permanent molecular dipoles. Usually, they are

randomly oriented, but when an external E-field is applied an average orientation

parallel to the field direction is preferred.

(iii) The propagation of mobile charge carriers (translational diffusion of electrons,

ions...), and the separation of charges at interfaces. The last process can take place at

inner dielectric boundary layers (Maxwell-Wagner polarization) or at the external

electrodes contacting the sample (electrode polarization).


A.2 Dielectric relaxation

The dielectric relaxation theory for small electric fields strength is a special case of

linear response theory, where the time dependent response of the system is the

polarization P(t) and the external disturbance is the electric field E(t).1

In the hypotheses of linearity (the response of the system on two disturbances is the

sum of the two single reactions), causality (only disturbances in the past contribute to

the response at the time t), a linear equation holds between E(t) and P(t):

0( ')( ) ( ') ''

t

ordE tP t P P P t t dt

dt A.1

Where P is the contribution due to the induced polarization (electronic, atomic

polarization), and the second term Por contains the contribution due to the orientation

of permanent dipoles ( orNPV

where N is the number of permanent dipoles in a

volume V and is the mean dipole moment).

( )t is the time dependent dielectric function and 0 is the dielectric permittivity of

the vacuum ( 0 = 8.854 10-12 AsV-1m-1).

The time-dependent dielectric function can be measured as the time dependent

response to a pulse change of the outer electric field ( is the Dirac function):

00 0

( )( ) ( ) ( ) P t PdE t E t tdt E

A.2

If a stationary periodic disturbance 0( ) exp( )E t E i t is applied to the system,

where is the angular frequency ( =2 f), Eq (1.1) becomes:

*

0( )( ) ( ( ) 1) ( )( )P t E t with * "( ) '( ) ( )i A.3

Where *( ) is the complex dielectric function which is a material property

depending on frequency, temperature, pressure and structure. As an intuitive

meaning, we can define the real part ( ) as the energy stored reversibly in the

system per period of oscillation and the imaginary part ”( ) as the is the energy

which is dissipated per period.


The complex dielectric function *( ) is thus related to the time dependent dielectric

function ( )t via the one-sided Fourier transformation:

*

0

( )( ) '( ) "( ) exp( )d ti i t dtdt

A.4

Where is the value of ( ) in the limit of high frequencies.

As *( ) is a one-sided Fourier transformation and is a causal function, the real and

imaginary part are related by the Kramers/ Kronig relations (for the derivation see ref

1). Therefore, they contain the same information and the analysis can be limited to

one of the two parts.

2 2

0

2 20

2' "( )

2" '( )

xx dxx

x dxx

A.5

A.3 Dielectric spectroscopy on the dynamics of polymers

As stated before, from the microscopic point of view the macroscopic observable

polarization P is related to the permanent molecular dipoles .1 For a polymer system

the net dipole moment per unit volume is given as a vector summation over all

molecular dipoles in the repeating units, the polymer chains, and over all the chains in

the system:

all chains chain repeating unit

1iP

V A.6

In a dense polymer system the fluctuations of the net dipole moment can be driven by

various molecular motions characterized by different length and time scales, which

give rise to a multitude of relaxation processes. The relaxation is a very local

process originating from the motions of highly localized parts of the main chain or to

the rotation of side groups. At lower frequencies or higher temperature than the

relaxation, the relaxation becomes predominant. It is believed that this last process

is controlled by the segmental motion, i.e. the cooperative motion of few repeating

chain units. At larger length scales than the –relaxation, the motion of the whole


chain takes place and gives rise to the so called normal-mode (this process is

associated to macromolecules where the dipoles are parallel to the main chain).

To give a representative example of the frequency and temperature dependence of -

relaxation process we have plotted in Fig A.1 the real and the imaginary parts of the

complex dielectric function of a thick sample of labelled polystyrene. The

measurement was performed in the frequency domain, from 106 Hz to 0.3 Hz, at

temperatures ranging from 150 to 114 °C.

The process is characterized by a peak in and a step-like increase of with

decreasing frequency at isothermal conditions and is influenced at low frequencies by

a conductivity contribution.

Figure A.1 Temperature dependence of the imaginary (top panel) and real (bottom panel) parts of the complex dielectric function for a sample of labelled polystyrene. From right to left in the temperature range between 150 to 114 °C with steps of 2 °C. The frequency varies from 0.3 Hz to 106 Hz.

0,00

0,05

0,10

0,15

100 101 102 103 104 105 106

2,6

2,8

3,0

"

cooling

'

frequency [Hz]


An alternative way of representing dielectric data is the isochronal representation

where the dielectric response is plotted at a fixed frequency as a function of the

temperature. In this kind of representation exhibits a loss peak, at a temperature

depending on the selected frequency, and displays a step-like increase with the

temperature. It is worth noting that in this case lower temperatures correspond to high

frequencies while high temperatures are related to lower motional processes (for an

example see Chapter 4).

-relaxation peak can be defined by the following

features: (i) the frequency of maximal loss max = 2 fmax or relaxation time =

1/ max of the relaxation

process which can be determined either from the area under the loss peak or from

the height of the step in ,(iii) the shape of the loss peak from which the distribution

of relaxation times can be deduced.

To extract quantitative information from dielectric spectra the loss data are

commonly fitted by the Havriliak-Negami (HN) function:

*

0

1

1HNHN

s

HN baHN

ii A.7

Where the is the value of the dielectric function in absence of polarization

is the dielectric strength,

HN the relaxation time, aHN and bHN are shape parameters related to the symmetric

and asymmetric broadening of the loss peak (aHN < 1, aHN bHN < 1). Contribution to

the loss signal due to conductivity are taken into account by adding the term s

V , where is the DC-conductivity, 0 the vacuum permittivity and s is a

fitting parameter (typically 0.5 <s <1).

The most probable of the -relaxation times, , associated to maxf (the frequency of

the maximum of the loss peak), is calculated from the relaxation time obtained by the

HN-equation via the shape parameters aHN and bHN:


1/sin 2 2

sin 2 2

HNa

HN HN HNHN

HN HN

a b ba b

A.8

The temperature dependence of can be described by the VFT equation, (see

Chapter 1). The relaxation map of the -process for the sample of bulk sample of

labelled polystyrene is reported in Fig A.2. The dielectric Tg is defined by convention

as the temperature at which ( ) 100gT s (alternatively corresponds to the

temperature at which the frequency of the maximum of the loss peak is f max = 1.6

10-3 Hz).

Figure A.2 Relaxation map of the a relaxation process of a thick sample of labelled PS. The continuous line is the best VFT fit of the experimental points.

The parameters aHN and bHN are related to the limiting behaviour of the complex

dielectric function at low at high frequencies: " m for 1/ HN with HNm a ,

and " n for 1/ HN with HN HNn a b . For polymers the n varies between 0

and 0.5, differing from the behaviour of low molecular weight glass formers where n

approaches the unit (Debye relaxation) at high temperatures. It is believed that n and

m are -process.

2,40 2,48 2,56 2,64

-5

-4

-3

-2

-1

0

1

2

log(

[s])

1000/T [K-1]

Tg100 s


In bulk systems n is related to the local chain dynamics which is hindered by the

presence of other chains. At temperatures close to Tg the more densely packing of the

chains implies a more pronounced hindrance of the local chain dynamics and, as a

result, n decreases. At higher temperatures, the free volume increases leading to a

higher value of n and to the sharpening of the peak.

The low frequency parameter m (0 < m <1) is correlated to the fluctuations of the

environment of a segment, which takes place at a larger length scale than the

segmental dynamics. With increasing temperature the hindrance of the these larger

scales motions is reduced and m decreases.

Another important feature of the -

which decreases with increasing temperature. The temperature dependence of the

dielectric strength of N non-interactive molecules in a volume V is classically

described by the Onsager/Kirkwood/Fröhlich theory which gives:

213 3s Onsager

V B

NF gk T V

A.9

Here s and represent the low and high frequency limits of the dielectric

permittivity, kB is the Boltzmann constant and is the dipole moment of the rotating

unit. FOnsager is a factor which takes in account for the enhancement of the dipole

moment by the polarization of the environment and g is the Kirkwood factor which

considers the interaction between dipoles (hydrogen bonding, steric interactions...)

with respect to the ideal case of non-interacting dipoles. The Kirkwood factor is

defined by

2interact

21i j

i i jgN

A.10

Where 2 is the mean dipole moment for non-interacting isolated dipoles which can

be measured in the gas phase or in diluted solutions.

is much stronger

than the predicted T-1 dependence. The physical reason of this discrepancy is still not

clarified and the temperature dependence stronger than T-1 is considered as a general


feature of the -relaxation. It is possible that this temperature dependence results

from an increasing influence of (intermolecular) cross-correlation terms 2 with

decreasing temperatures. In other words the reorientation of a test dipole is influenced

increasingly by its environment with decreasing temperature. In the framework of the

cooperativety concept - should be related to an effective dipole

moment eff which is due to the CRR. With decreasing temperature the size of the

CRR and therefore eff increases.

A.4 Principle of dielectric measurements

Measurements of the complex dielectric function in the frequency range Hz-MHz

are based on the determination of the complex electric impedance of the sample,

Z( ). In case of a pure capacitor, the impedance is given by:

1( )( )

Zi C

A.10

The principle of the measurement is the following: a voltage with a fixed frequency

0( ) exp( )V t V i t is applied to the sample capacitor and the current generated by it,

0( ) exp( )I t I i t , is measured. The phase shift between the current and the

voltage is a frequency dependent property of the system. The ratio between the

voltage and the resulting current gives the complex impedance.

The complex dielectric function is given by the ratio between the complex

capacitance of the sample C( ) and the one of the empty cell C0. The relationship

between the dielectric function and the impedance reads:

0 0

( ) 1( ) '( ) "( )( )

CiC i C Z

A.11

In this work we used the Alpha High resolution Analyzer from Novocontrol, that can

measure the complex impedance in a frequency range from 3 Hz to 10 MHz and in


the temperature range between -170°C and 400 °C, with a resolution of "tan'<

10-5

1. Kremer, .; Schoenhals, A.; (editors), Broadband dielectric spectroscopy. Springer: Berlin, 2003.

Publications List

Publications in international journals

Adsorption kinetics of ultrathin polymer films in the melt probed by dielectric spectroscopy and second harmonic generationC. Rotella, S. Napolitano, S. Vandendriessche, V. K. Valev, T. Verbiest, M.Larkowska, S. Kucharski and M. Wübbenhorst, Langmuir, 2011, 27, 13533

Is the reduction in tracer diffusivity under nanoscopic confinement related to a frustrated segmental mobility?S. Napolitano, C. Rotella, M. Wübbenhorst, Macromolecular Rapid Communications, 2011, 32, 844

Probing interfacial mobility profiles via the impact of nanoscopic confinement on the strength of the dynamic glass transitionC. Rotella, M. Wübbenhorst and S. Napolitano, Soft Matter, 2011, 7, 5260-5266

Distribution of segmental mobility in ultrathin polymer filmsC. Rotella, S. Napolitano, L. De Cremer, G. Koeckelberghs, and M. Wübbenhorst Macromolecules (highlighted), 2010, 43, 8686

Enhanced Crystallization Kinetics in Poly(ethylene terephthalate) Thin Films Evidenced by Infrared SpectroscopyM. Bertoldo, M. Labardi, C. Rotella, S. Capaccioli, Polymer, 2010, 51, 3660

Segmental mobility and glass transition temperature of freely suspended ultrathin polymer filmsC. Rotella, S. Napolitano and M. Wübbenhorst, Macromolecules (Communication to the editor), 2009, 42, 1415-1417

Conference Proceedings

Influence of Conflnement and Substrate Interaction on the Crystallization Kinetics of PET Ultrathin Films S. Capaccioli, C. Rotella, M. Bertoldo, M. Lucchesi, P. Pingue, D.Prevosto, P.A. Rolla, , AIP Conference Proceedings, 2008, 1027,1306