Structure an d Molecular D y namics of Thin Film s of
Homopol ymers and Mis cible Po lymer Blends

Vorgelegt von
M.Sc.
Sherif A. Madk our
geb. in Kair o , Ägy p ten

von der Fa kultät III - Proze sswissen s chafte n
der Techn ischen Uni v ersitä t Berlin
zur Erlang ung des akadem ischen Grades

Doktor der I ngenieur wissenschaften
Dr. – In g.

genehm i gte Dissertati on

Prom otionsaussch u ss:
Vorsitzender : Prof. Dr. rer. nat . W al ter Re im ers (TU Berlin)
Gutachter : Prof. Dr.-Ing. Di etm ar Auh l (TU Berlin)
Gutachter : Prof. Dr. r er. n at. Andreas S chönhals (BAM)

Tag der w issenscha ftlichen A ussprache : 24 .11 .2017

Berlin 2 018

I
T A BLE OF CONT ENTS
ACKN OW LE DGM ENTS ..................................................................................................... V
ZUSAMM ENFASSUN G .................................................................................................... VII
ABSTRAC T ....................................................................................................................... XI
CHAP T ER 1 – Introduc t ion ................................................................................................ . 1
CHAP T ER 2 – Glass Transition and G lassy Dynamics ....................................................... 6
2.1. Glass T ransition ............................................................................................................ 6
2.2. M olecular Dynamics ...................................................................................................... 7
2.3. M odels Relating Segmental Dy namics to Gl ass Tr ansi t ion ......................................... 11
2.3.1. Ada m-Gibbs Theo r y .......................................................................................... 11
2.3.2. Free Vol ume Theory ......................................................................................... 12
CHAP T ER 3 – Poly mer Blends ......................................................................................... 16
3.1. M iscibility of Binary Poly mer Blends ............................................................................ 16
3.2. Asy mmetric M iscible Polymer Blends ................................................................ ......... 18
3.3. Se g mental Dy namics o f Misci ble Polymer Blends ....................................................... 18
3.3.1. Dy namic Hete rogeneity ..................................................................................... 19
3.3.2. Symme tr ic Broade ning ...................................................................................... 21
3.4. Surface En richment .................................................................................................... 23
CHAP T ER 4 – 1D Con f inement ( Thin Films ) .................................................................... 26
4.1. E ffect of 1D Con f inement on the Glass transition ........................................................ 26
4.1.1. Three Lay er M odel ............................................................................................ 27
4.1.2. Free Vol ume under Con f inement (Pac k in g Frustration) .................................... 28
4.1.3. Adso r bed Layer ................................................................ ................................ 30
4.2. E ffect of Thin Fil m Con f inement on Segment al Dynamics ........................................... 32
CHAP T ER 5 – The Idea Behind This W o rk ........................................................................ 38
CHAP T ER 6 - Experime ntal Techniques (Pri nciples and P reparation) .............................. 44
6.1. Principl es of t he M ain Experimental Techniqu es ......................................................... 44
6.1.1. Broadb and Diel ectric Spect r oscopy .................................................................. 45
6.1.2. Speci f ic Heat Spectroscopy .............................................................................. 52
6.2. M ethods and Experimental Te chniques ...................................................................... 54
6.2.1. Broadb and Diel ectric Spect r oscopy (BD S) ........................................................ 54
6.2.2. Speci f ic Heat Spectroscopy ( SHS) .................................................................... 54
6.2.3. Di f ferential Scan ning Cal orimetry (DS C) ................................ ........................... 55
6.2.4. Elli psometry ...................................................................................................... 55
6.2.5. Atomic Force Mi cr oscopy .................................................................................. 57
6.2.6. Con t act An g le Measuremen ts (CAM ) ................................................................ 57
6.2.7. X-ray Photoelect ron Spect r oscopy (XPS) ......................................................... 57

II
6.3. Sample P reparation .................................................................................................... 57
6.3.1. M ater ials ........................................................................................................... 58
6.3.2. Sa mple Prepa ration .......................................................................................... 59
CHAP T ER 7 - Cal orimetri c E vi dence f or a M obile Surface Lay er in Ultrathi n Poly meric Film s:
Poly (2- vinyl py r idine) ................................................................................................ ........ 65
Abstract ............................................................................................................................. 65
7.1 Introduction ................................................................................................ .................. 66
7. 2. Experi mental Sectio n ................................................................................................ . 68
7.2.1. M ethods ............................................................................................................ 68
7.2.2. M ater ials and Sa mple Preparation .................................................................... 70
7.3. Results an d Discussion ............................................................................................... 71
7.3.1. Conv entional Analy sis of Specific Hea t Spectros copy Data .............................. 73
7.3.2. Con t act Angle M e asurements ........................................................................... 76
7.3.3. Deriv ative Analysis o f Specific Heat Spec t roscopy Data ................................... 79
7.4. Conclusi on ................................................................ .................................................. 86
CHAP T ER 8 - Unveil ing t he Dynamics of Sel f -As sembled Layers of Thin Films of PVM E by
Nanosiz ed Relaxation Spectros copy ................................................................................. 90
Abstract ............................................................................................................................. 90
8.1. Introduc t ion ................................................................................................................. 91
8.2. Ex perimental Sec t ion .................................................................................................. 93
8.3. Results an d Discussion ............................................................................................... 99
8.4. Conclusi on ................................................................ ................................................ 113
CHAP T ER 9 - Unexpected Behavior of Ultra- Thin Films of Blends of Pol ystyrene/Poly (vinyl
methyl ethe r ) studied by Specific Heat Spec t rosc opy ...................................................... 117
Abstract ........................................................................................................................... 117
9.I. Introduction ................................................................................................ ................ 118
9.2. M ethods ................................ .................................................................................... 121
9.3. Results an d Discussion ............................................................................................. 124
9.4. Conclusi on ................................................................ ................................................ 134
CHAP T ER 10 - Decoup ling of Dy namic and Thermal Glass Transition in Thin Films of
PVM E/PS Blen ds ............................................................................................................. 138
Abstract ........................................................................................................................... 138
10.1. Introduc t ion ............................................................................................................. 139
10.2. Ex perimental Methods ............................................................................................ 141
10.3. Resul ts and Discus sion ........................................................................................... 141
10.4. Concl usion .............................................................................................................. 1 47
CHAP T ER 11 - Unraveli ng t he Dyna mics of Nanoscopi cally Confined PVM E in T hin Films of
a Mi scib le PVM E/PS Blend .............................................................................................. 151
Abstract ........................................................................................................................... 151

III
11.1. Introduc t ion ............................................................................................................. 152
11.2. Ex perimental Section .............................................................................................. 154
11.3. Resul ts and Discus sion ........................................................................................... 157
11.4. Concl usion .............................................................................................................. 174
CHAP T ER 12- Conclusi on & Outlook .............................................................................. 179
12.1. Concl usion .............................................................................................................. 179
12.2. Outloo k ................................................................................................................... 183
Appendi x I. - Supporting In formation for Chap ter 8 .............................................................. I
Appendi x II – Supportin g Information f or Chapte r 10 ........................................................ VII
Appendi x III – Supporting Information for Chapter 11 ...................................................... XIX
Appendi x IV ................................................................................................................. XXVII
List of Abbrev iations, Symbols and Constant ................................................................ XXVI I
List of Abbrev iations .............................................................................................. XX VII
List of Sy m bols ..................................................................................................... XXVI II
List of Constan t s ................................................................................................... XXVI II
List of Publi cations ......................................................................................................... XX IX
List of Aw ards ......................................................................................................... XXIX
Other Publicatio ns ................................................................................................... XXX
Conference Contribu t ions ............................................................................................... XXX

IV

V
A C KN OWLEDG MENTS
I would like to express my heartfelt gratitude to Prof. Dr . Andreas Schönhals for giving me
the opportunity to join his research group and fini shing m y PhD at BAM Bundesanstalt für
Materialfor schun g und -prüfung. His fl exibili ty , support, encouragement, and guidance
have been m y guiding stones throughout this work. During the past 4 y e ars, he has been
empowering me to become a b etter s cientist and above all a better person. In addition, I
would like to thank him for his continuous sincerity and honest y in conve y ing his knowledge
to m y colleagues and m yself. I would also want to acknowledge th e financial support from
the German Sc ience Foundation (DFG SCHO-470/20 -2).
Moreover, I would like to ex press my sincere app erception to Prof. Dr. Di etmar Auhl and
Prof. Dr. Manfred H. Wagner at the Te chnical U niversity of B erlin (TU Berlin) for their
continuous support, understanding and valuable suggestions.
I would also like to take this opportunity to thank Prof. Dr. Friedrich Kremer (Universität
Le ipzig), and Dr. Martin Tr ess (Universit y of Te nnessee) for th e e xperimental assistance
and the m an y fruitful dis cussions. In addition, I th ank Prof. Dr. Heinz Sturm (BAM), Prof.
Dr. Christoph Schick (Universität Rostock), Dr. Heiko Huth (Universität Rostock), for all
the guidance and h elp. Th ey have provided me with a lot of useful suggestion s and guidance
that he lped me overcome many dif ficulties in the ex perimental work. Additionally, I would
like to send s pecial thanks to Prof. Dr. Simone Napolitano (Université L ibr e de Bruxelles),
Prof. Dr. Regine von Klit zing (TU Darmstadt), D r. Andrea s Hertwig ( BAM), Dr. Radnik
Jörg (BAM), and Prof. Dr. Zahraa Fakhraai (Universit y of Penns y lv ania) for the valuable
discussions, which have enriched m y scientific knowledge as well as t he pleasant and
successful c ollaborations .
Furthermore, I would li ke to t hank all the prof essors, facult y during th e course of m y
education for giving me such valuable knowled ge. Especial thanks to P rof. Dr. Wei-H eng
Shih (Drexel Unive rsity , PA ) for introducing me to the world of research and
nanotechnology a nd believing that I could one day become a scientist.
La st but not least, I would like to thank all the expe rts of BAM who kindly participated in
this work. Mr. D. Neubert for his help with all the DSC measurements and Ms. Hidde and
Mr. F. Mil czewski for th eir help with th e dail y problems faced in the lab. I am also in d ebt
to other labs that allowed me to use their facilit ies in m y research. Moreo ver, I would like
to thank all m y colleagues in BAM, MSc. Paulina S z y moniak, MSc. Arda Yildirim, MSc.

VI
Marce l G awek, MSc. S hereen Omara , Dr. Huajie Yin, and Dr. Nora Konnertz for all the
help with the da y - to -da y issues in the lab as we ll as the countless laughs and priceless
memories though out the y ea rs.
At the end, I would like t o thank m y family and fr iends around the world for t heir love and
support throughout my years of studying. Most importantl y , I would like to thank my
fiancée, Fairouz Gaber, whom I found throu gh the motivation and strength. She patientl y
supported me to achieve m y goals and b rought me so much happin ess, lov e, coura ge and
streng th. Finall y, I woul d like to send m y sinc ere thanks and gra ti tude to m y parents, Al y
Madkour and Salwa Taha, as well as m y broth er, K arim Madkour, for all their financial and
incorporeal support throughout the years. There are no words th at could possi bly describe
what the y have done for me. The success of this work , and wh ere I am to day, is the result
of their love, patience, trust, and encourage ment throughout m y entire life.

VII
ZUS A M MENF ASSUNG
In den letzten Jahren hat die Forschun g auf d em Gebiet des Confinements auf der
Nanometerskala zu vielen Versuchen geführt, die Eigenschaften von Poly m eren für
spezielle Anwendunge n zu verändern. Eines de r am häufigsten untersuchten S y steme mit
Confinement im Nanometerber eich sind dünne Filme, bei dem ein 1-dimensionales
Confinement aus der V erringerung der Filmdicke resultiert. Fü r de rartige S y steme ist es
wichtig zu verstehen, wie das Confinement den Glasübergang und d ie dazugehörige
Glasdy namik im Vergleich zu einer räumlich aus gedehnten P robe b ee influsst. So kann es
bei dünnen Filmen mit einige n N anometern Dick e sein, d ass innere und die Luft/Pol y mer
Grenzfläche z u einer Än derung des Glasübe rgangs und der Glasd y namik führen, welche s
letztlich zu einer Veränderung von makroskopischen Eigenschaften wie z.B. Adhäsion,
Biokompabilität oder/und Entnetzung führ en kann.
Die Untersuchunge n, die in dieser Dissertation dargestellt sind, konzentriere n sich auf das
Verständnis, wie das Confinement in dünnen Filmen (200 nm - 7 nm) die
Glasüberga ngstemperatur ( T g therm ) und die zugehörig e Segmentd y namik (  -Relaxation,
chara kterisiert durch eine d y namisch e Glasübergangstemperatur, T g dyn ) bei
Homopolymeren und mischbare n Pol ymerblends beeinflussen. Die Ergebnisse wurden über
das 3-Layer-Modell hinaus diskutiert, wobei weit ere Parameter wie das Molekulargewicht,
die He iz rate, die kompositionelle Heterogenität, geometrische Frustration, etc. mit
einbezoge n worden. Sich ergänzende e xperimentelle Methoden wie die s pektroskopische
Ellipsometrie, dielektrische Spektroskopie (BDS), auch unter Nutzung neuartiger
Probengeometrien welche die Messung von dünnen Filmen mit freier Oberflä che erlauben,
und der spezifischen Wärmespektroskopie (SHS) wurden angewandt, um den Glasübergang
dünner Pol y m erfilme s owohl vom thermod ynamischen als auch vo m kinetischen
Standpunkt zu untersuchen.
Im ersten Teil der Dissertation wurden dünne Filme aus Pol y(2- vin y l p yridine) (P2VP) mit
hohem Molekulargewicht mi ttels der S HS untersucht, um die in der L it eratur lang
andauernde Diskussion der Unabhän gig keit von T g dyn von der Schichtdicke dünner Filme
von Homopolymeren un d ihre Ursachen zu verifizieren. Mittels einer neu entwickelten
Analy semethode wurde ge zeigt, dass die Messdat en neue Einsichten übe r den Einfluss der
Pol y mer/ Luft- und der Poly mer/Substrat-Grenzfläche auf die D yna mi k des g es amten Films

VIII
liefern. Diese neu entwickelte Methode wurde dan n angewandt, um alle SHS-Messdaten die
in der Dissertationen darge stellt sind, z u anal y sier en.
Obwohl die Ergebnisse de r Messungen von dünnen Filmen vo n P2VP einen leichten
Confinement-Effekt zeigen, konnte dennoch nicht bestätigt werden, ob dieser Effekt auf die
höhere molekul are B eweglichkeit an der Polymeroberfläche (d.h. die Pol y me r/Luft-
Grenzfläche) oder eine r Erhöhun g des freien Volumens an der Pol y mer-Subst rat-
Grenzfläche auf Grund der ge ringeren Konditionierungszeit im Vergleic h zu r terminalen
Relaxationszeit des Pol y mers zurückzuführen ist. Aus diesem Grund wurde der Fokus auf
die Untersuchung dünner Filme von Poly (vin yl methy l ether) (PVME) mit niedr igem
Molekulargewic ht gelegt. Dünne Filme von PVME wurden sowohl mi t der SHS als auch
mit der BDS untersucht. Mittels ang epasster Probenanordnungen wu rden di e Ergebnisse der
Messungen von B DS un d SHS quantitativ verglichen. Mit der BDS wurden zwei Proz esse
beobachtet. Der erste Prozess wurde den kooperativen Segmentfluktuationen der  -
Relaxation zugeordne t, v erursacht durch die volumea rtige Schicht. Diese s Erg ebnis ist in
übereinstimmung mit den Erge bnissen der SHS. Der zweite Prozess dagegen, wurde
lo kalisierten se gmentellen Fluktuationen innerhalb einer irreversibel am Substrat
adsorbierten Schicht z ugeordnet, Di ese konnt e fü r dünne Filmen erstmalig in dieser Arbeit
untersucht wurde.
Die Ergebnisse der Untersuchungen dünner Filme von P2VP und P VME wei sen darauf hin,
dass der Effekt de r Schicht an der Pol y me r/Lu ft -Grenzfläche auf die segmentelle D y namik
des ge s amten Films schwierig zu untersuc hen bzw. zu verifizie ren ist. Dies lässt sich damit
begründen, dass oberhalb von T g therm , die seg mente lle Dyna mi k der Oberflächenschicht sich
an die Segmentd y namik rä umlich ausgedehnter P roben angleicht. I nd em eine
asy mmetrische Pol y mermi schung ausgewählt w urde, bei der es zur An reicherung einer
Pol y merkomponente an d er Oberfläche kommt, konnte der Einfluss der Obe rflächenschicht
auf die segmentelle Dynamik de gesamten F ilms geuntersucht werden.
Im z weiten Teil der Di ssertation wurde das g l eiche PVME, we lch es bere its oben als
Homopolymer untersucht wurde , mit P oly st y rol (P S) in zwei Ge wichtsanteilen (50:50 wt%
und 25:75 wt%) gemischt. Untersuchungen dü nner Filme dieser Pol ymermischungen
mittels der S HS z eigten zum ersten Mal eine d eutliche Dickenabhän gigkeit von T g dyn .
Während Filme der 50:50 wt%-Probe eine monotone Verringerung von T g dyn mit
abnehmender Filmdicke zeigen, weisen Filme der 25:75 wt% -Probe ein nicht -monotones
Verhalte n von T g dyn auf, welche bei 30 nm ein M aximum hat. Die Abnah me von T g d yn für

IX
kleinere Schichtdicken als 30 nm wurde auf die Anreicherung von PVME an der
Oberflächensc hicht z urückgeführ t, wel che bei filmdicken unter 30 nm das Verha lten des
ge samten Filmes dominiert.
Da rüber hinaus lieferten die S HS und Ellipsometrie w eiter Möglichkeiten, sowohl den
Glasüberga ng als auch die Glasd y n amik für dünne Filme der 25:75 wt% Mischung zu
untersuchen. Untersuchungen d er Schichtdickenabhängigkeit von T g therm und der Vogel-
Tempera tur (T 0 ) fü r di e Mischung 25:75 wt % ergaben, d ass beide letztgena nnten
Tempera turen im Unterschied zu T g dyn einen s y st emati schen Anstieg mi t abn ehmender
Filmdicke Größen. Dieses wurde im Rahmen verschiedene r Kooperations- Längenskalen für
jede Temperatur diskutiert, welche in verschiedenen Empfindlichkeiten bzgl. der
Zusa mmensetzung und der Dicke re sultieren. Üb erraschenderweise konnte gezeigt werd en,
dass die Schichtdickenabhäng igkeit von T g dyn tatsächlich die Dicken abhängigkeit von T g therm
und T 0 bei Fre quenzen die für T 0 charakteristisch sind, abbilden konnte.
Des weiteren wurde die Röntgen-Photoele ktrone n-Spektroskopie (XPS) a ngewandt, um die
Existenz einer PVME -angereicherten Schi cht na chzuweisen und ihre Zusammensetzung
abzuschätzen. Dadurch wurde die dickenabhängige komposit ionelle Heteroge nität bestätigt.
Abschließend wurden dü nne Filme des 50:50 wt % S ystems mit der BDS untersucht. Die
Ergebnisse wu rden qu antit ativ sowohl mi t den SHS -Ergebnissen sowie mit den Ergebnissen
von Messung en reinen dünnen PVME-Filme diskutiert. Die Kombination von BDS und
SHS bietet dabei ein leistungsfähiges Werkzeug, um die verschieden en Aspekte der
Glasdy namik und ihre Beziehung z u den kompositionellen He terogenitäten zu betrachten.
Bei dünnen Filmen von PVME/PS-Blends ist die BDS aufgrund der starken As y mm etrie
der Dipolmomente von PVME und PS nur empfindlich auf die Segmentdy namik von
PVME, die durch das PS beeinflusst wird. Währenddessen ist die SHS auf mobile Segmente
von P VME und P S empfindlich. Der Vergleich d er Daten aus beider Met hoden z eigte die
kompositionelle Heterogenität innerhalb des Pol y m erblends. Zusätzlich z eigten die
Ergebnisse der BDS eine schichtdickenabhängige Veränderun g der ko mpositionellen
Heteroge nität (in molek ularen Größenordnungen) auf. Diese Ände rungen beeinflussen
direkt die Moleküld y namik des gesamten Films und sollten als zusätzlicher Parameter
betrachtet werden, wenn der Confinement-Effekt auf d en Glasübergan g und die
Glasdynamik von dünnen Filmen a us mischbaren Pol ymerblends diskuti ert wird. Darüber
hinaus wurde, ähnlich wie be i den dünnen Filmen aus reinen PVME, ein vollständig
unabhängiger thermisch aktivierter R elaxationsprozess beobachtet Dieser Proz ess wird

X
Fluktuationen innerhalb der adsorbierten Schicht molekular z u geortnet. Es wurde der
Schluss gezogen, dass dieser Prozess z usätzlich zu der Dickenverminderung z wei
zusätzliche Confinementeffekte er fährt. I ) Confinement zwischen einem stark gebundenen
Teil in der adsorbierten Schicht und d er volumenartigen Sc hicht. II) Confinement aufgrund
immobiler PS -Segmente innerhalb der adsorbierten Schicht.

XI
A B S TR A C T
In recent years, r esearch on nanoscale confinement of polymers has witnessed topical
investigations in attempt to tune pol y mer properties on demand. One o f the most studi ed
forms of nanoconfinement are thin films, where 1D confinement results from the reduc tion
of the film thickness. For these s y stems, it is cruc i al to unde rstand how confinement a ffects
the glass transition phenomenon and the associated glass y d ynamics, compared to the bulk
behavior. This is due to the direct impact of these phenomena on m an y thin film -based
technolog ies. For instanc e, for films of few nanometers in thickn ess, solid interfaces and
free surf aces could alter glass transition and glassy dynamics, which co uld, in return, cha nge
macroscopic propertie s like adhesion, biocompatibil it y and dewetting.
The research wo rk presented in this dissertatio n is focused on understanding ho w the
confinement in thi n films (200 nm – 7 nm) influences the glass transition temperature
( 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ) and the related segmental d y namics (α -relaxation proc ess, rel ated to a so - called
dyna mic glass tr ansition temperature 𝑇 𝑔 𝑑𝑦𝑛 ) in both homopol y m ers and miscibl e pol y mer
blends. The results were discussed be yond the idealized three-la y e r model, taking int o
account othe r parameters like molecular weight, annealing ti me, compositional
heteroge neities, packing frustra tion, etc. This goa l is achieve d through careful choosing of
the polymeric s y stems as well as combining different charact erization methods with
differe nt s ensitivities and frequency windows. Complementary experimental techniques
including S pectroscopic ellipsometry, Broadband Dielectric Spectr oscopy (BDS),
employing a novel sample ge ometr y that allows the measurement of sup p orted films, and
Specific Heat S pectroscop y (SHS) were used to investigate the glass transition phenomena
of thin poly m er films, from the thermod y n amic and the kinetic point of views.
First, thin films of hig h mol ecular wei ght P oly(2-vinyl pyridine) were studi ed b y S HS to
confirm the long-standing discussion in literature regarding th e thi ckness i ndependenc y of
𝑇 𝑔 𝑑𝑦𝑛 of thin homopol y m er film and molecular r easons behind it. Through a newly
developed anal ysis method, a sli ght de crease in 𝑇 𝑔 𝑑𝑦𝑛 with decreasing the film thickness
was eviden ced for the firs t time. I t was shown that SHS data, if anal ysis errors were avoided,
could indeed be an insightful tool to stud y confinement effects on the overall d y namics of
the film. This new analysis method was then employ ed to an al y ze the SHS data for the entir e
work presented in this dissertation.

XII
Although the re sult s of the P2VP thin films showed a slight confinement effec t, it could not
be confirmed whe ther the e videnced c onfinement effec t was due to a free surface (the la y er
at the poly m er/air interface) or an increase in the free volume, at the pol ymer /s ubstrate
interface, due to the lower annealing time , compared to the terminal relaxati on time of the
polymer . Therefore, the attention was switched to a low mol ecular weight Pol y (vin y l methy l
ether) PVME thi n films, to insure good annealing conditions within a reasonable time.
PVME thin films were then investi ga ted b y b oth S HS and BDS. Through adapting a new
sample arrangement that allows the measuring supported films, the results from BDS and
SHS were quantitatively compare d. This stud y revealed that the mole cular dynamics of the
thin films had two dielec tricall y active process es . The first process was assig ned to the
coopera tive se gmental fl uctuations of the  -relaxation, originating from a bulk -like lay er ,
also confirmed b y S HS. However, the second process was assi gned to localiz ed segmenta l
dyna mics within an irreversibly a dsorb ed la y er, reporting the first probing of the molecular
dyna mics of an adsorbed la y er within thin films.
The results of both studi es on P2VP and PVME t hin films suggested that t he e ffect of the
layer at the pol y mer/substrate interface on the ov erall segmental d y namic s would be ver y
difficult to probe and/or confirm. This is due to the fact that above 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , which is the
temperature ra nge at which the seg mental d y nami cs are probe d, the se gmental d y namics of
the free surface la y er bec ome indistinguishable from that of the bulk. However, b y ca refully
choosing an as y mmetric pol ymer blend s y stem, the effect of the free sur face la yer on th e
overall se gmental d y na mics could be probed. This is due to the surface enrichment
phenomenon, which results in a different com position at the pol y mer/air interface,
compared to the bulk.
Consequently, in the second part of this dissertati on, an identical PVME, to the one studied
above, was then blended with the well-studied Pol y st y rene (PS ) in two weight fractions
50:50 wt% and 25:75 wt%. SHS investigations of the thin films of the two blends revealed
for the first time an un expected thickness d ependence of 𝑇 𝑔 𝑑𝑦𝑛 (relate d to the  -r elaxation).
While thin films of the 50:50 wt% blend showed a systematic decrease in 𝑇 𝑔 𝑑𝑦𝑛 with
decreasing film thickness, thin films of the 25:7 5 wt% blend show ed a non-monotonous
behavior, which peaks at 30 nm. For the former blend, the s ystema tic decrease was traced
to a PVME-rich la y er at t he pol y me r/air interface, which becomes dominant with decreasing
the film thickness. On the other ha nd, the non-monotonous behavior of the latter blend was
traced b ack to compositional heteroge neities, which is thi ckness depende nt and results in an

XIII
increase in 𝑇 𝑔 𝑑𝑦𝑛 to 30 nm, followed b y a drop in the 𝑇 𝑔 𝑑𝑦𝑛 down to 10 nm. The d rop in
𝑇 𝑔 𝑑𝑦𝑛 was trac ed back to the effect of a PVME -rich la y er at the polymer/air interfac e ,
becoming dominate for thicknesses below 30 nm.
Furthermore, combin g SHS and spec troscopic ellipsometr y provided a w indow to stud y
both the glass t ransition and the g lass y d y namics of the thin films of the 2 5:75 wt% blend.
Investigations of the thickness dependence o f 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 and the Vogel temperature (T 0 ) for
the 25:75 wt% blend revealed that the latter temp eratures show ed a s y st ematic increase with
decreasing film thickness, in diffe rence to that of 𝑇 𝑔 𝑑𝑦𝑛 . This was discussed throug h
elaborating the different cooperativit y length sc ales corresponding to each temperature ,
which would result in di fferent sensitiviti es to composition and thickness. Surprisingl y, it
was shown that the thickness dependence of 𝑇 𝑔 𝑑𝑦𝑛 could indeed recover the thickness
dependence of bo th 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 and T 0, at frequencies related to T 0 .
X-ray photoele ctron spectroscop y (XPS) was then uti lized to affirm the ex istence and
estimate the composition of the PVME -rich interfaces. In addition, it confirmed the
thickness dependent composit ional heterogeneity and suppo rt ed the above mentioned
findings.
Finally , thin films of th e 50:50 wt% blend were investigated by BDS. The results were
quantitatively dis cussed with the SHS ones as well as that of pure PVME thi n films. The
combination of BDS and S HS provides a powerful tool to look at the different asp ects of
the glassy d y n amics and its relationship to th e dy n amic heterogeneities . For PVME/PS
blends, BDS is onl y sensitive to the se gmental d ynamics of PVME, as affe ct b y PS, due to
the strong as y mm etr y in the dipole moment s of P VME and PS. Whereas, S HS is sensit ive
to all the mobile segments of PVME and PS. Comparing that data from both methods
elaborated the d ynamics heterogeneity within the blend samples. I n addition, BDS results
evidence d thicknesses depende nt changes in the compositional heterogeneities (at a
molecular level) within the films. These changes direc tl y affect the molecular d ynamics of
the overall film and should be considered as an extra paramete r, when discussing the
confinement effe ct on the glass tra nsit ion and glassy d y namics of miscible poly m er blends .
Moreover, similar to the pure PVME thin film s, a completely ind ependent ther mall y
activated relaxation process, re lated to the molecular fluctuations within the adsorbed layer,
was observ ed for films belo w 30 nm. For the latter process it was concluded that this process
undergoes two extra confinement effects, in addition to the thickness reduction. I )

XIV
Confinement between a s trongl y bounded part in t he adsorbed lay er and the bulk-like lay er.
II ) Confinement due to froz en PS segments within the adsorbe d la y e r.

1
CH A P TER 1 – Introduction
Humankind has been pro ducing and d eveloping glasses for a f ew millennia. Throughout the
y e ars, glasses have been extremel y versatile; from hunti ng tools to stained glass windows,
to thin films in smart phones screens. Under th e genetic n ame “glasses”, this class of
materials ex hibits a solid-like response, though la cking th e lon g-ran ge order of crystals. I n
ge neral, rapid cooling of a glass-forming liquid (e.g . amorphous polymer s, which is the
focus of this work) induces the decrease of the molecular mobilit y of the s y stem .
Subsequently, the molecules lose their abilit y to r earrange themselves in a thermodynamic
equilibrium. This transition fr om a liquid-like equ ilibrium state to a non-equilibrium g lass y
state is called glass transition. This transition takes place over a certain temperature r ange,
which is character ized b y the so-called thermal glass transition temperature ( 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ).
For more than a centur y n ow, glass transition has been considered on e of the most interesting
phenomena in soft matter physics.

1

-

7

De spite the wealth of knowle dge present on thi s top ic ,
a complete and unified understandin g of the ph enomena sti ll remains. For instance, to thi s
date, it is not understood why the viscosity of a glas s-forming li quid, which cannot crystalize,
increases by almost 10-orders of magnitude, with in a limited temperature range, while the
density varies only by 5%.

8

For amorphous pol ymers, the glass transition is a ccompanied b y
an increase in the shear modul us with decre asin g temperature, related to the segmental
dyna mics (  -relaxation), which makes it a very im portant phenomenon for pol y me rs
processing.

9

Furthermore, the pa st thr ee de cades have witness ed an increasin g interest in glass tra nsition
and the related  -relaxation for confined pol ymers at the nanoscale. Now adays, thin
polymer films (<100 nm) have b een attracting the most attention due to the ir high demand
in functional c oatings, batte ries, innovative or ganic electronics, and h ybrid materials.
Advance s in these fields depend strongl y on organic a nd/or poly m eric materials confined in
thin films or adsorbed at surfaces. 6,

10

For thin films of few nanometers in thickness, solid
interfaces and free surfaces could alter for instance entanglements, se gmental d y namics, and
𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , compar ed to their bulk va lues. Consequently, this could change macroscopic
quantities of thin films like adhesion, wettability, fr iction, and reactivity, which are, for
instance, essential properties for h ybrid materials.

11

Therefore, for optimized innovative
applications of thin polymer films, an understanding of the molecular reasons for th e

2
possible de viations of the prope rties of confined polymers from that of the ir bulk is
essential. 10
Th e aim of this work is to achieve a deeper understanding of how the surfaces, the interfaces
(espec iall y the pol ymer/substrate interface), and th e film thickness influence 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 and the
segmental d y namics of t he whole film. In addition, it aims to understand the mol ecular
mechanism behind the possible deviations fr om the bulk properties, bey ond a trivial
surface/volume ratio parameter. Th e research work presented in this di ssertati on, considers
especially selected s y stems, including thin films of homopol y mer and miscible polymer
blends, as well as their bulk films . Th is g oal is approache d b y attempting to simplify th e
topic through two parallel methodologies I ) careful choosing of the polymeric systems,
which allows the enhancement of the effect of a certain parameter ( e.g. optimi zing M w and
annealing times affects t he thickness of the la y er at the pol y m er/substrate i nterface) on the
glass transition and glass y d y namics of the whole film. II) Com bining diff erent
character ization methods with different s ensitivities and fr equency windo ws, which could
allow selective probing o f a polymer (in the case of polymer blends) and/or a propert y (glass
transition versus se gment al d y namics) o f the measured systems. A detailed discussion of
the idea and the line of thoug ht behind this work is presented in chapter 5.
To investiga te the thi n polymer films , a combination of surface anal ytica l techniques and
volume sensitive methods was utiliz ed. The surfac e analytica l techniques, concluded in
Atomic Force Microscop y (AFM), ellipsometr y, and X-ra y photoelectron spectroscopy
(XPS) were emplo y ed to control the qualit y and thicknesses of the films, a s well as their
chemical composition. Whereas the volume sensitive methods, concluded in Broadban d
Dielectric Spectroscop y (BDS), Specific Heat Spectrosc op y (SHS), and spectroscopic
ellipsometry, were used to investigate the influe nce of the film thickness on the glass y
dyna mics and the glass tr ansition behavior of the poly mer thi n films , from both the kinetic
and the thermodyna mic point of views.
This dissertation is arra n ged as follows. Chapter 1 gives a short introduction to the g lass
transition phenomena as well as the motivation behind the research on glass transition and
thin poly mer films. This is then followed b y an overvie w of the glass transition and the
related relaxation behavior in amorphous pol y mers , as presented in C hapter 2 . I t begins with
the discussion of bulk polymer s, covering the topi cs of the glass transition temperature, the
segmental dy namics, and some models uti lized to relate the glass transition phenomena to
the seg mental d ynamic s.

3
Chapter 3 provides fund amental information on miscible pol y me r blends. It discusses the
mi scibilit y of pol ymer blend , covering the topics of the glass transition temperature, the
segmental d ynamics, the dynamic heterogeneit y, and some models describing the intrinsic
features and anomalies found for these especial sy s tems.
Chapter 4 provides a litera tur e review, theories and suggested mod el to discuss the glass
transition and glass y d ynamics of thin pol ymer fil ms and the possible deviation from the ir
bulk values. This is confe rr ed in the framework of the three-la y er mode l as well as the
packing frustration, which is built on the free volu me concepts. It also pa ys attention to the
rece nt research on of the so-called irreversi ble adsorbed l a y ers (the la y er at the
polymer /substrate interface).
Chapter 5 provides the idea behind all the experimental w ork presented here. I t starts with
the core aim of this work and how the idea behind this work was developed. I t explains why
the investigated s y stems where o f choosing and w h y the employed ch aracterization methods
were used, in the exact combination. This chapter connects all the experimental work that
follows. Afterwards, C hapter 6 provides fundamental principles about the main
experimental techniques used in thi s work. Moreover, it briefly introduces all the materials
used in the study as well as all the methods and co nditions used to prepare and characterize
the samples.
The results and dis cussion are then pre sented in an accumulative manner , in cha pte rs 7
through 11. Chapter 7 p resents and discusses the re sults of homopoly mers poly(2-vin y l
pyridine) ( P2 VP ), where a new anal ysis method wa s developed, resulting in an enhanced
sensitivit y of the SHS data, in addition to evide ncing the first confinement effect on the
segmental d ynamic s o f homopol y mer thi n films.

13

Th is anal ysis method wa s then emplo yed
to anal y ze all S HS data presented in this dissertati on . Chapter 8 presents a stud y on the
dyna mics of pol y(vinyl methyl ether) (PVME) thin films, from both the thermal and
dielectric pe rspectives.

14

This was carr ied out usi ng SHS and BDS. For the latter method, a
rece ntl y d eveloped nano structured electrode c apacitors was uti lized to measure supported
polymer films .

15

Further, PVME wa s then blended with the well-st udied P olystyre ne ( PS ) in an as y mmetric
miscible- in -bulk blend with two different concertation; P VME/PS 50:50 wt% and
PVME/PS 25:75 wt%. Multiple studies were carr ied out to stud y the glassy dynamics and
glass transition of the blends . Chapter 9 presents a calorimetric investi gation on thin films
of PVME/P S with a conce ntration of 25 :75 wt%, emplo y in g SHS.

16

Furthermore, the results

4
were further quantitatively compared to those of the 50:50 wt% blend.

17

Chapter 10 presents
a study on the decoupling phenomena of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 (obtained by spectroscopic ellipsometry ),
𝑇 𝑔 𝑑𝑦𝑛 , and the so-called Voge l temperature (T 0 ), for th e 25:75 wt% blend.

18

The results and
conclusions were supported b y X-ra y photoelectron spectroscop y (XPS) stud y o f the
interfaces of the thin films.
La st but not least, Chapter 11 presents a studies on the dielectric response of the segmental
dyna mics of PVME/PS blend with a concentration of 50:50 wt%.

19

The se results were
further quantit at ivel y compared to that of pure P VME thin films , chapter 7. 14 Finally,
Chapter 12 gives a short summary to the r esearch work presented, connecting all the a bov e-
mentioned studi es, follo wed b y a short outl ook on the next int eresting challenges in the
field.

5
References

1

Debenedetti, P.; Stillinger, F. Natu re 2001 , 410, 259 – 267 .

2

Anderson, P . W. Science 1 995 , 267, 1617 .

3

Ediger, M. ; Horro w ell, P. J. Chem. P hys. 2012 , 137 , 080901.

4

Sastry , S.; Debendetti, PG. ; Stillinger , FH. Na tur e 199 8 , 393, 554-557.

5

Y i n, H.; Mad kour , S.; Schö nhals, A . Dynamics in confine ment: P rogress in Dielec trics , Spr inger vol. 2 . 2014 ,
Kre m er , F . (Ed .) .

6

McKenna, G.; S imon, S. Mac romolecules 2017 , 50 , 6333 – 6361.

7

Russell, T .; Chai, Y. Macrom olecu les 2017 , 50, 4597 -4609.

8

Napolitano, S.; Glynos, E.; T ito, N. Rep orts on Progress in Physics 201 7 , 80, 036602.

9

Young, R.; Lovell, P. T he Amorphous State in I ntroductio n to P olymers, CRC press 20 11 , 3 rd eds, Florida.

10

Ediger, M. ; Forrest, J . A. Macromo lecules 2014 , 47, 47 1-478.

11

Napolitano, S.; Pilleri, A.; Rolla, P .; Wübbenhorst, M. ACS Nano 2010 , 4, 841 - 848.

12

Anderson, P . Through the Glass Lightly. Scien ce 1995 , 267, 1615- 1616.

13

Madkour, S.; Yin, H.; F üllbra ndt, M.; Schön hals, A. Soft Ma tter 2015 , 11, 79 42 - 7952.

14

Mad kour, S.; Sz ymoniak, P .; Heidari, M.; von Klitzing, R.; A. Schö nhals. ACS Ap pl. Mater. In terfaces .
2017 , 9, 7535- 7546.

15

Tr ess, M.; Mapesa, E. U.; Kossack, W.; Kipnusu, W . K .; Reiche, M.; Krem er , F. Science 201 3 , 341,
1371−137 4.

16

Madkour, S.; Sz ymoniak, P.; Schic k, C.; Schön hals. A. J. Chem. Phys . 2 017 , 146, 2033 21.

17

Yin, H.; Madkour, Sc hönhals, A. Macro molecules 2015 , 48, 4936.

18

Madkour, S.; Sz ymoniak, P.; Her twig, A.; Heidari, M.; vo n Klitzing, R.; Napo litan o , S.; S ferrazza, M.; A.
Schönhals. A CS Macro Letter s 2017 , 6, 1156 -1161.

19

Madkour, S.; Sz ymoniak, P .; Radnik, J.; A . Schönhals. A CS Appl. Mater. Interface s . 2017, 9, 3 7289 -27299.

6
CH A P TER 2 – Glass Tra nsition and Glass y D y n amics
2.1. Glass Trans ition
Cooling a glass-forming liqui d or polymer, without crystallizing, induces an increase in their
density and viscosit y. Consequently, the molecular motions slowdown with decre asing
temperature. W ithin a certain temperature r ange, the characteristic time required fo r the
molecules to structurally rea rrange themselves into a ther modynamic e quilibrium wil l
become much longer th a n the timescale of the experiment. Conseque ntly, the system will
fall out of equilibrium a nd freeze in to a non-equilibrium glassy st ate. This continues to
temperatures, at which th e viscosity is exceedingly high and the m aterial can be considered
as glass.

1

This process takes place ove r a given t emperature range, called t he glass transition
region, which is chara cterized by the thermal glass transition temperature ( 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ). I t is
worth to note that 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 could be deter mined by differe nt methods , 1 for ex ample
𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 could be taken as the midpoint temperature of the glass transition region . For
instance, t he g lass transition shows no abrupt chang e in the volume, but ra ther a c onti nuous
change in the t emperature dependence of the sp ecific volume , see figure 2 .1 . I t shifts from
higher v alues in the rubber y state to lower ones in the glassy stat e. It is important to point
out that due to the continuit y of this ch ange, glass transition is not a phase transition of an y
order. In fac t, the glass transition is considered as a thermo-kinetic phenomenon.

2

Figure 2.1. A sch ematic of the tempera ture depend ence of specific vo lume or enthalp y for an amorpho us
polymer, ex posed to different coolin g rates. Ta ken and modified from reference [3 ].

7
Furthermore, 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 is cooling-r ate dependent. The hi gher the cooling rate, the higher th e
temperature range at which the s y stem falls out of equilibrium, see figure. 2.1. Thus,
resulting in a higher 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 with increasing cooling rate. In the followin g discussio n, 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚
defines the thermodynamic point of view of the glass transition phenomenon measure d b y
the so-called static methods. These m ethods in clude Differential Scanning Calorimetr y
(DSC), spectroscopic ellipsometr y,

4

fluorescence spectroscop y,

5

Capacitive S canning
Dilatometry (CSD),

6

,

7

etc. These techniques m easure the temperature d ependence of a
physica l property (heat capacit y , volum e, e tc.), which under goe s a change as a function of
temperature, at 𝑇 𝑔 𝑡 ℎ𝑒𝑟 𝑚 .
It is important to note that 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 is different from the so-ca lled d y namic g lass transition
temperature 𝑇 𝑔 𝑑𝑦𝑛 , which is directly related to the se gmental dynamics of pol ymers , discussed
in the following section.
2.2. Molecular Dy namics
Amorphous poly mers are well known to have complex mechanica l behavior. This be havior
is partially a result of a n umber of different motional proc esses within the system, o ccurring
at the molecular and intermolecular lev el.

8

Due to the complex chemical structures of the
polymer chains, i.e. for isolated chains, a large n umber of confor mational -c hanges could
take place within. Th ese mol ecular pro cesses i nvolve localized fluctua tions, segmental
dyna mics, which are related to the glass transiti on, and ev en collective chain motions
encompassing the whole macromolecule. The for mer two molecular processes are the focus
of this work. From the phy sical point of view, the aforementioned mol ecular d y n amics
depends on the structural units, henc e their sizes, involved in the proce ss , see figure 2.2. The
differe nt size-scales with in the pol y m er result in different relax ation times (reorientation
times), which is related to the different modes of motion (mobilit y ). These m odes reflect the
relaxation behavior (the dy namics) of specific parts within t he poly me r.

8

Figure 2. 2 . Schema tic representa tion o f the characteristi c leng th scales and relaxation times for th e
relaxation processes in p olymeric systems. Taken from reference 9

The above mentioned act ive molecular dynamics could be probe d by applying an external
disturbance (e.g. small oscillating electric field), given the ri ght frequency and temperature
window. In principle, a bove 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , the segmental d ynamics are active and the whole
system is in a the rmodynamic equilibrium. In this temperature rang e, the segmental
relaxation times decrease with increasing temperature and the glass transitio n phenomena is
regarded as a d ynamic phe nomenon in an equilibrium state. Where as, b elow 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , the
segmental d ynamic s a re more or less frozen. Though, othe r localized fluctuations might still
be thermall y active. It is worth to note that , from the kinetics point of view, th e empirical
value of 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 is often found in a good agreement wi th the temperature at w hich the
segmental relaxation time is τ = 10 2 s, figures 2.4A and B.

10

Various methods, introducing a wide range of frequenc y windows, a re used to probe the
molecular d y namics of amorphous polymers; for instance, D y namic Mechanical Anal y sis
(DMA),

11

neutron scattering,

12

light scattering,

13

,

14

Broadband Diel ectric Spe ctrosc opy
(BDS),

15

and S pecific Hea t Spectroscopy (SHS).

16

The latter two methods were the main
character ization techniques used in this work.
To understand the diffe rent relaxation time scale, resulting from the r elaxation of the
differe nt structural units, the dielectric loss spectra obtained fr om BDS, of an amorphous
polymer, is considered, see fi gure 2.3. I n general, BDS shows two co mmon molecular
motions for most amorphous poly m ers I) the lo calized mot ions, i.e. fluctuations of side
group(s) of the se gments II ) the fluctu ations of the segments themselves (i.e.  -relaxation),
which are t ypica ll y co rrelated to cooperative rearrangement with respect to their
environment, see fi gure s 2.2 and 2.3. For most amorphous pol y mer, the dielectric spectra
show a peak at hi gh frequencies (low temper atures), which is related to the β -relaxation
process. At lower fr equencies (high temp eratures), the α -re l ax ation can be observed as an
asy mmetric broad peak. It is important to note that the sha pe of the  -relaxation peak is not
related to the distribution of the relaxation times, due to local spatial heterogeneities,
discussed below. Therefore, the sha pe of the peak is consider ed to be an intrinsic fe ature of
the segmenta l d y namics of glass-forming s y stem.

17

This is contrar y to the case of the β -
relaxation.

9

 -relaxation (Localized
fluctuations )

log 
log(f [Hz])
 relaxation (coop erative segmenta l motion)
T1 < T2
f p
1 < f p
2

Figure 2.3. Schema tic rep resentation of a ty pica l dielec tric lo ss spectra in a b road freq uency r ange for tw o
temperatures T 1 – black solid line - a nd T 2 – red solid line. Two relaxation proce sses, th e α -rela xation
(dynamic glass transition) and the β -relaxation, are indicated. Figure was ta ke n and adapted from
Reference [ 21 ].

Throug h analyzing the relaxation peaks in the die lec tric spectra , the frequency at which the
loss is maximum is related to the relaxation proc ess and is defined as the relaxation rate f p
or re lax ation time τ p = 1/(2  f p ) of the process. Through quantitative analy sis of the
temperature dependencies of thes e r elaxation ti mes (rat es), information about the natur e of
the dielectric process es can be obtained. This is commonly pr esented in a relaxation map
(also called a ctivation plot ); where the relaxation times are plotted as a function of reciprocal
temperature, fi gure 2.4 A. The temperature de pendences of localized and segmental
dyna mics are discussed in detail in the next two subsections.

10

Figure 2. 4. ( A ) Relaxa tion map of typica l segmen tal times
𝜏
p versus inver se temperature as obtain ed by
BDS sho wing the α and β relaxa tion for Po ly(2-vinyl Pyridin e) (P2VP). Th e so lid black and blu e lines are
VFT A rrhenius fit s to the data , respectively. The blu e dashed dotted lin e mark the segmental dyn amics at
100 secs, which correspo nds to 𝑇 𝑔 𝑡 ℎ𝑒𝑟𝑚 ( B ) DSC thermo gram o f P2VP, measured at 10 K/min. The dashed
dotted arrow marks 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . The data are taken and adap ted from reference [ 18 ] .

2.2.1. Loca l Fluctuations
Localized fluctuations refer to the motions (chang e of conformation) of structural units,
which does not result in a chan ge in conformation o f the “ environment ” arou nd it. T herefore,
the motion is localized (isolated) from the neighboring unit s. An example for localized
fluctuations is the β -re laxation proc ess, which arises from int ramolecular fluctuations or
localized rotational fluctuations of side gr oups or parts of them.

19

In g eneral, th e temperature d ependence of the r elaxation rates of an y lo calized process
𝑓 𝑝 ,𝑙𝑜𝑐 is expected to follow an Arrhenius-t y pe equation

20

𝑓 𝑝 ,𝑙𝑜𝑐 = 𝑓 ∞ ,𝑙𝑜𝑐 exp [ −𝐸 𝑎
𝑘 𝐵 𝑇 ]

(2.1)

where E a is the activation energy and k B is the Boltzmann constant. T he value of th e
activation energy depend s on both internal rotational barriers and the “ environment ” of the
fluctuating unit. For instance, the t ypica l values of E a for β -relaxations are in the range of
20-50 kJ/mol.

11
2.2.2. Se gmental Dy namics (  -Rela xation)
 he segmental d y n amics  -relaxation) refers to the motions of the segments, which re s ult
in a change in the confor mation of the seg ment s within the environment around it. For
example, it is directly r elated to conformational changes , like gauche-trans transitions . The
α -re lax ation process controls the diffusion, the viscosit y and the rotation of segments.

21

.
This molecular motion is , for inst ance, the main structural relaxation in most amorphous
polymer, as probe d b y BDS .
For these confo rmational changes, the temperatur e dependence of their relax ation rates f p, 
cannot be well described wit h the Arrhenius equation (equation 2.1) , as the y are curved
when plotted versus 1/T. The temperature dependence of f p,  could be described b y the
empirical Voge l/Fulcher/ Tammann (VFT) formula

22

,

23

,

24

𝑓 𝑝, 𝛼 ( 𝑇 ) = 1
2𝜋 𝜏 𝑝, 𝛼 (𝑇 ) = 𝑓 ∞ exp (− 𝐷𝑇 0
𝑇 − 𝑇 0 )

(2 .2)

where f ∞ is the frequency in the hi gh temperature limit and T 0 denotes the Vog el
temperature, which is found 30 -70 K b elow 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . 20 D is the so-called fragilit y para meter
and provides a w a y to classif y glass-forming s y stems into fragile and strong glasses. This
classification depends on how stron g ly the tempe rature dependence of the relaxation rates
deviates from the Arrhenius-t ype beh avior. It is worth to note that this equation is valid only
in the temperature ra nge of 𝑇 𝑔 𝑡 ℎ𝑒𝑟𝑚 . to 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 +100 K.

25

,

26

2.3. Models Relat i ng Seg mental Dy namics to Glass Trans ition
A number of models have been proposed in the past [

27

-

34

] to explain the molecula r reasons
behind the glass transition phenomenon. Nonetheless, to this date, n o model could
univocally describe all facts of the glass transition phenomenon. The empiric al VFT
dependence could be just ified b y differe nt theoretical approaches. However , t he followin g
subsection presents only two possible theoretical approaches to describe the scaling of the
dyna mics in amorphous polymer s. For a detailed review on this topic, the rea der is referred
to refe rences [20 and

35

].
2.3.1. Adam-Gibbs Theor y
The core idea of Adam and Gibbs model is based on defi ning a cooperatively rearranging
region (CRR), which is the smallest volume that could change its configuration
independently from its neig hborin g environment. 31 Brie fl y , the model concluded that the

12
temperature-dependence of the  -relaxation process and that of the size of a CRR are
related. It assumes that the length of the cooperative d y namic length scale would increase
with dec r easing temperature (T). Ther efore, t he seg mental relaxation time at a given
temperature 𝜏 ( 𝑇 ) of a number of segments z (T) per CRR can be de scribed as

1
𝜏 (𝑇 ) ~ 𝑒𝑥𝑝 (− 𝑧 ( 𝑇 ) Δ 𝐸
𝑘 𝐵 𝑇 )

(2.3)

Where 𝑧 ( T) = 𝑆 𝐶
𝑁𝑘 𝐵 ln 2 and S c is the total configurational entrop y . N is the tot al number of
particles and k B ln2 is the mi nimum entrop y of a CRR. Δ 𝐸 is the f ree ener gy barrier for a
segment to change its conformation. S c can b e relat ed to the change in specific heat capacit y
Δ𝑐 𝑝 , at the g lass transition with t he following e quation

𝑆 𝑐 ( 𝑇 ) = ∫ Δ 𝑐 𝑝
𝑇
𝑇
𝑇 2 𝑑𝑇

(2.4)

At T 2 =T 0 and ∆ c p ≈ C/T, equations 2.4 result s in a VFT dependence. At T 0 , the
config urational entrop y b ecomes zero and the size of the CRR diverges as 𝑧 (T) ≈ 1
𝐶 (𝑇 −𝑇 0 ) .
Neverthe less, the Adam-Gibbs model does not provide information about the ab solut e size
of a CRR at 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 .
The Adam-Gibbs mode l was further extended b y Donth [

36

-

37

], with the so-called
fluctuations approach presented in equation 2.5, where the correlation length ξ was related
to the step height of c p an d the temperature fluctuati ons 𝛿𝑇 of a CRR at T g ( 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ) through
equation 2.3.

𝜉 3 ~𝑉 𝐶𝑅𝑅 = 𝑘 𝐵 𝑇 𝑔 2 Δ 1
𝑐 𝑝
𝜌𝛿𝑇

(2.5)

where 𝜌 is the density, Δ 1
𝑐 𝑝 is the step of the reciprocal specific heat capacit y where c v ≈ c p
was assumed. Experimen tally, the 𝛿𝑇 can b e ex tracted from th e width of the g l ass transition.
It is worth to note that the size of the CRR was estimated for several pol ymer s to be in the
range of 1-3 nm, corresponding to ca. 100 se gments.

38

2.3.2. Fre e Volume Theory
In p arallel to the Adams -Gibbs model, Doolit tle and Cohen [21,

39

,

40

] deve loped a
theoretica l fr ee volume model with no charac teristic length. This model is based on the idea

13
that in amorphous polymers, insufficie nt packing of disord ered s egments would result in
free volume. T he y defined the free volume (V f ) concept by

𝑉 𝑓 = 𝑉 − 𝑉 0

(2.6)

where V is the actual volume and V 0 is the theo retical volume based on the actual ch emical
structure and the van der Waals radii of the seg me nts. Doolittle then related the fr ee volume
to the viscosity of the poly m er as follows [ 39 ]:

𝜂 = 𝐴 exp[ 𝐵 ( 𝑉 − 𝑉 𝑓 )
𝑉 𝑓 ]

(2.7)

where A and B are fitting parameters an d η is viscosit y . Further assuming that the fre e
volume increases linearly with temperature, the fractional free volume f would then read

𝑓 = 𝑓 𝑔 + Δ𝛼 (𝑇 − 𝑇 𝑔 )

(2.8)

where f=V f /(V f +V 0 ) , f g is the fractional f ree volume at T g ( 𝑇 𝑔 𝑡 ℎ𝑒𝑟 𝑚 ) and Δα is the d iffere nce
in thermal expansion coefficients above and below 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . The Doolitt le Equation (equa ti on
2.7 ) could then be employed to r ationalize the so -called WLF-equation, which is a nalogous
to the VFT e quation described above, in the frame of the free volume theory:

log ( 𝛼 𝑇 ) = log [ < 𝜏 ( 𝑇 ) >
< 𝜏 (𝑇 𝑅 ) > ] ≈ l og [ 𝜂 ( 𝑇 )
< 𝜂 ( 𝑇 𝑔 ) > ] = 𝐵
( 1
log ( 𝑒 ) ) ( 1
𝑓 − 1
𝑓 𝑔 )
= −𝐶 1 (𝑇 − 𝑇 𝑔 )
𝐶 2 + (𝑇 − 𝑇 𝑔 )

(2.9)

where C 1 = B/2.303f g and C 2 =f g /Δα.
Generally , the free volum e model could also be used to describe the tempe rature dependence
of α - relaxation time s. Nevertheless, the fr actional free volume cannot be determined
foreha nd.
Furthermore, the relationship between free volu me and the g lass tra nsition was rec entl y
reviewe d in detail in references [

41

,

42

]. The reviews provide a thoroug h survey on th e
modern applications of free volume in ex periment al, theoretical, a nd simulation
investigations. White et al.

43

rece ntl y reviewed thi s topic, where 50 diff erent polymers,
systematically- studied in literature, were correlate d in terms of the e ffec t of the fr ee volume
to 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 . There, it was shown that for eve r y pol ymer, a critica l free volum e value exists,
at which the pol y m er becomes glass y . These crit ical free volume values follow a master

14
curve across the 50 pol y m ers considered, reveali ng a close correlation/dependence on
𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , see figure 2.5.
0 100 200 300 400 500 600
0
5
10
15
20
Free voulme % at T g
T g, DSC [K]
PDMS
PE
PS
PMMA
PES

Figure 2. 5. F ree volume perce n tage computed at T = T g ( 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ) in the “loca lly - correlated la ttice” (LCL)
model, p lotted as a function o f 𝑇 𝑔 𝑡ℎ 𝑒𝑟 𝑚 , f o r 5 0 d ifferent p olymer melts. Da ta for selected p olymers a re
labeled in the figure. Adapted from reference [ 43 ].

15
References

1

Young, R.; Lovell, P. T he Amorphous State in I ntroductio n to P olymers. CR C pres s, 2011 , 3 rd eds, Florida.

2

Kanaya, T.; Rintar o, I .; Kazuk o, K. ; T sukasa, M.; I taru, T .; K aoru, S.; Go , M.; Koji, N.; Masahiro, H. Journal
of the P hysical Society o f Japan 2 009 , 78, 04100 4.

3

Donth, E.-J. Glas überga ng . Aka demie-V erlag , 1981 , B erlin.

4

Keddie, J.L.; Jones, R. A.L .; Cor y, R.A . Euro. Phys. Lett. 1994 , 27, 59 - 64.

5

Ellison, C.J.; T or kelson, J.M. Nat. Mater. 2003 , 2, 695 - 700.

6

Napolitano, S.; Pilleri, A.; Rolla, P .; Wübbenhorst, M. ACS Nano 2010 , 4, 841- 848.

7

Lupaşcu, V.; Picke n, SJ.; W ü bb enhorst, M. Jo urnal o f Non -Crystalline So lids 20 06 , 352, 559 4 -5600.

8

Schönhals, A . , Molecular D ynamics in P olymer Mo del S ystems in Broad band Dielectric Spec troscopy.
Kre m er, F.; Schö nhals, A., ed s., Spring er : Ber lin, 2002 , p. 226.

9

Schönhals, A. Novoco ntr ol, A pplicatio n Note Dielectrics. 1998 ,1.

10

Debenedetti, P.; Stillinger, F. Natu re , 2001 , 410: 259 – 267.

11

Mijo vić, J., Lee, H., Kenny, J., Mays, J. Macromolecules 2 006 , 39, 2172 -2182.

12

Frick, B., Richter, D. S cience , 1995 , 267, 1939 -1945.

13

Fitz, B. D. , Mijovic, J . Macromolecules , 1999 , 32, 4134 -4140.

14

Frick, B.; Richter, D. Scien ce , 1995 , 267, 193 9-1945.

15

Sch ö nhals, A.; Kre mer, F. Theor y of D ielectric Relaxatio n and Broadband Dielectric Measu r eme nt
Tec hniques . In Br oadb and Dielectric Spectro scopy; Kre mer, F.; Sch ö nhals, A., E ds.; 1 st ed; Springer : Ber lin,
2002 ; 01- 57.

16

Birge, N. O., Nagel, S. R. Physica l Review Lette rs 1985 , 54, 26 74- 267.

17

Yin, H., Schön hals, A., Die l ectric P roperties o f Polymer Blends in P ol ymer Blend Handbo ok. W ilkie,
Charles A.; Utracki, L. A., ed s., Spring er , 2014.

18

Madkour, S.; Yin, H.; F üllbra ndt, M.; Schön hals, A. Soft Ma tter 2015 , 11, 7942- 7952.

19

Heijb oer, J. Molecular b asis of transitions and r elaxation. In : Meier DJ , Ed. Gordon and B reach, 1978 .

20

Sch ö nhals, A .; Kr emer, F. T he Scaling of the Dynamics of Glass e s and S uperco oled Liquid s. In Bro adband
Dielectric Spectro scopy; Kremer, F.; Sch ö nhals, A., Eds.; S pringer , Ber lin, 2002 , 99 - 137 .

21

Cohen, M.; T urnbull, D. Journ al of Chemic al Physics 1959 , 3 1, 1164 -1169.

22

Vogel, H. Physikalische Zeits chrift 1919 , 22, 645-64 6.

23

Fulcher, G. S. Jou rnal of th e American Ceramic Society , 1 925 , 8 , 339- 355.

24

T amm a nn, G.; Hesse, W. Zeitsch rift für ano rganische und allgemeine Chemie , 1926 , 156, 245- 257.

25

Ferry, J. D. , Viscoelastic pr operties o f polymers. 3d ed.; W iley : Ne w York, 1980.

26

Jing, Z.; Simon, S.; Mc kenna, G. Natu re Communica tions 2013 , 4, 41783.

27

Fox, T. ; Flory, T. Journal o f Applied P hysics 1 950 , 21, 581 .

28

Fox, T .; Flory, T. Journal o f Physical Chemist ry 1951 , 55 , 221.

29

Fox, T .; Flory, T. Journal o f Polymer Scien ce 1954, 14, 315.

30

T urnbull, D.; Cohen, M. Journ al of Chemic al Physics 19 58, 29, 1049.

31

Adam, G.; Gibb s, J. Journa l of Chemical Ph ysics 1965 , 46:139.

32

Leutheuser, E. Physical R eview A , 1984 , 29 , 2765.

33

Dyre, J. C.; Niels, B .; T age, C. Phys. Rev. B 1 996 , 53:2171 – 2174.

34

Dyre, J. C. Colloq uium. Rev. Mod. Phys . 2006 , 78:953 – 972.

35

Ngai, K.; Capaccio li, S. J. Chem. Ph ys. 2 013 ,138, 05490 3.

36

Donth, E. T he glass transition: relaxatio n d ynamic s in liq uids and disordered m a terials. S pringer : Berlin,
2001.

37

Donth, E. Relaxatio n and t hermodynamic s in po lymers: glass trans ition. 1st ed.; Aka demie Verlag : B erlin,
1992 .

38

Schönhals, A.; Kr emer, F., Amorphous Polymers in Po ly mer Scie nce: A Comprehe nsive Re ference,
Volume 1. Mat y jasze wski, K.; M öller, M. , eds., Elsevier, 2012 , 201- 226.

39

Doolittle, A. Jo urnal o f App lied Physics 1 951, 2 2, 1471-1475.

40

Cohen, M.; Gres t, G. Physical Rev iew B 1979, 20, 1077 -1098.

41

White, R. P . & Lipson, J. E. G. Macromolecu les 2016 , 49, 3987 -4007.

42

Napolitano, S.; Glynos, E.; T ito, N. B . Rep . Prog. Ph ys. 2017 , 80 , 036602.

43

White, R. P .; Lipson, J. E. G. ACS Macro Letters 2 015 , 4 , 588 – 592 .

16
CH A P TER 3 – P ol y mer Blen ds
For the past century, o btaining new mat erials b y blending two homopolymers has been an
active topi c, not only from a scientific point of view, but also for technolo gical applications.
Due to the understanda ble diff iculti es in re gularly commercializing n ew poly m ers, industr y
has thrived to blend po lymers with different p roperties for tailor-mad e materials with
optimized end-use properties (e.g. mech anical and rheological). Nevertheless, most
polymer s do not favor miscible blending, as it often comes at the expense of the tot al entropy
of the whole s ystem. Therefore, achieving mi scible blending requires understanding o f the
thermody namics of blending as w ell as th e glassy d ynamics o f the blend at the molecular
level.
3.1. Miscibi lity of Binary Pol y mer Blend s
Despite the wealth of knowledge about the thermod y namics and structure of bulk binary
miscible pol y mer blends

1

-

13

, a number of questions regarding the molecular mobility
remain; i.e. how the segmental dynamics of ea ch component of the blend is affected b y
blending and by changing the composition ?
In principle, the macroscopic miscible blending is governed b y th e thermod y namic Gibbs
free energ y o f mix ing ∆ G M .

∆𝐺 𝑀 = ∆𝐻 𝑀 − 𝑇 ∆𝑆 𝑀

(3.1)

where ∆ H M is the enthalpy and ∆S M is the entrop y of mi xing. Fo r polymer blends, the
contribution of the the entropy of mix ing to the free enthalpy of mi xing is small . In the
framew ork of the lattice model of Flory / Huggins free ener gy [

14

], the Gibbs free ener g y for
a polymer blends with A and B c omponents is given as

∆𝐺 𝑀
𝑅𝑇 = ϕ 𝐴
𝑁 𝐴 ln ϕ 𝐴 + ϕ 𝐵
𝑁 𝐵 ln ϕ 𝐵 + 𝜒𝜙 𝐴 𝜙 𝐵

(3.2)

where R is the universal gas constant. ϕ A and ϕ B are th e pa rtial composition (volume)
frac tions of the components and χ is the interaction parameter between component A and
B. N A and N B and the deg rees of polymerization of both components, respec tivel y.
Accordingly, t o achieve thermod y namic mi scibilit y of both homopol ymers, the followin g
criterion have to be maintained:

Δ𝐺 𝑀
𝑅𝑇 < 0

(3.3)

17

𝜕 2 Δ𝐺 𝑀
𝜕 𝜙 𝐴
2 = 𝜕 2 Δ𝐺 𝑀
𝜕 𝜙 𝐵
2 = 𝑅𝑇 [ 1
ϕ 𝐴 𝑁 𝐴 + 1
ϕ 𝐵 𝑁 𝐵 − 2𝜒] > 0

(3.4)

In ge neral th e Flor y /Hu ggins theo r y could onl y b e used to des cribe sy st e ms with an upp er
critical solution temperature. This means that above a critical tempera tures, T C , the two
components are miscible on a mol ecular level , whereas b elow T c , phase separation occurs.
This sugge sts that the composition of the separa ted phases is bim odal. In other words, for
these s y st ems, ev en in th e phase separated state th ere will still be a certain degre e of mixing
resulting in two e nriched phases of the two components of the blend.
The characterization of the miscibil it y of poly me r blends is often carried out by Dif ferential
Scanning Calorime tr y (D SC). For a n immiscible polymer blend, two transitions, hence two
𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 s, corresponding to both components of the blend is observed. On the contrary, for
miscible pol y me r blends, a single glass transition ex tending over the whole glass transition
regions of both component is detected, he nce single 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 , see figure 3.1.

15

Figure 3 .1. DSC trace (second h eating run ; rate: 10 K/min) fo r PVME (dash ed), PS (dashed dotted ),
PVME/PS (50: 50 wt%, red solid), all take n from reference [ 16 ] a nd PVME/PS 25:75 wt%, blue solid . Figure
wa s taken an d adapted from reference [ 15 ].

It is also important to note that the sin gle 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 for miscible blends is an intrinsic feature
of these systems. In fact, for bulk samples, the composition dependence of the 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 of
miscible poly m er blends could be described, for instance, by the Fox equation

17

1
𝑇 𝑔, 𝐵𝑙𝑒 𝑛𝑑 = (1 − 𝑤 𝐵 )
𝑇 𝑔,𝐴 + 𝑤 𝐵
𝑇 𝑔,𝐵

(3.5)

200 250 300 350 400 450
PVME/PS
25/75wt% Exother m

PVME/PS
50/50wt% PS
PVME
Heat Flow [a.u.]
T [K]

18
where w B is the we i ght fraction of component B.
3. 2 . A s y m metric Miscible Po ly mer Blends
Asymmetric miscible blends, in which the difference b etween the glass tr ansition
temperatures of the two components is large , ha ve attra cted a lar ge number of studies in the
past few decades. In this case, the pol ymer with the lower mobi lit y , at temp eratures below
its glass transition temperature, strongl y affects t he dynamics of the component with the
higher mobilit y . This has been elaborated for Pol y (Meth yl Ethyl Ether)
(PVME)/Polysty rene (PS) blends . 12 , 13 ,

18

-

20

Here the m ain anomalies and intrinsic features of
miscible pol ymer blends are sho rtl y discussed, from the dy n amics and kinet ic point of view.
For a detailed discussion on the anomalies of th e glass transition and g lass y dynamics of the
components of the blend, the rea der is referred to references [

21

and 22].
3. 3 . Segmenta l D yn ami cs of Miscible Poly mer Blends
It is well accepted that th e mol ecular composition of a miscible A/B pol y m er blend, is not
completely random. I t is more likel y that a se gment of component A is surrounded b y
se g ments of the same k ind , than b y segments of component B. This means that on a
molecular scale, the effective composition of a bi nary miscible blend is different from the
macroscopic one, which would reflect on the s egmental d y namics of th e p olymer bl ends . 1-
13
In general, the segmental dy n amics of miscible pol y mer blends is affected in two major
ways.

22

I) Unlike the sing le 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 obtained for miscible blends, mea sured b y DSC, the
molecular dyna mics are known to be spatial ly dynamically heteroge n eous .
II ) Symmetric broadening of the relaxation function s in the f requenc y domain with
respec t to the corresponding homopolymers is observed.
It is worth to note that there is no unified theo r y tha t can explain these experimental findings
in poly mer blends. Nevertheless, the c urrent understanding of these findings is often
explained through th e combi ned effect of chain c onnecti vit y , whic h results in a self-
concentration mechanism, 7 and thermally driven concentration fluctuations . 22 These
mechanisms give rise to spatial regions, which h ave different local composit ions t han the
mean one with their own local relaxation behavior, and subsequentl y local 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 , as
discussed in the upcoming subsections.

19
3.3.1. D y namic He terogeneity
For an ide al mol ecularl y homogenous blend s ystem, one would ex pect a single averaged
relaxation process, muc h like the single averaged 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , obtained f rom t he DSC
measurements for miscible blends. Nonetheless, probing the segmental dynamics of a
polymer blend b y B D S with dielectrically visi ble components, have shown that ev en for
miscible blend s y stems, t wo processes are detected. This m eans that at the molecular level,
their segmental d ynamics is heterogeneous. Figure 3. 2 elucidates thi s behavior through th e
dielectric loss spec tra for Pol y (Vin yl Ether) /P ol y(isoprene) PVE/PI of 50:50 wt%.
-4 -2 0 2 4 6 8
Blend
PVE/PI (50% / 50%)
PI

 ´´ [a.u.]
log(f [Hz])
PVE

Figure 3 .2. Dielec tric loss ve rsus frequ ency at 27 0 K fo r the PVE/PI blen d at a compo sition of PVE /PI
50: 50 wt %. Circles – p ure PVE; S quares – pure PI; stares – blend PVE/PI. Lines a r e HN - function fits to
the active processes in the dielectric spectra . Figure was tak en and adapted from reference [ 28 ].
In addition, it is im portan t to note that the ex istence of the two proc esses in the loss spectrum
is independe nt from the α - peak broadenin g discuss ed below. This hete rogeneity phenomena
could be clearl y elaborated from the combination of DSC and Thermal S imulated Currents
measurement (TSC), figure 3.3. There, 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of pure PVME and P VME/PS blend were
depicted; keeping in min d that PVME has a much strong er dipole mom ent, compared to that
of PS. 22 Consequently , s i nce DSC is sensitive to th e molecular d ynamic s of t he whole bl end,
while TSC is onl y sensitive to the polar component of the blend as influenced b y P S,
comparing the data of the two mea surements could elucidate the compositional
heteroge neit y phenomena. A closer look on f i gu r e 3.3, reveal s that 𝑇 𝑔 𝑡 ℎ 𝑒𝑟𝑚 fr om TSC i s
observed a t a low er tempera ture compared to that obtained fr om DS C. 23 I n other words, the
local 𝑇 𝑔 𝑡ℎ 𝑒 𝑟𝑚 due to the polar P VME segments is observed a t much low er temperatures than

20
the overall 𝑇 𝑔 𝑡 ℎ𝑒𝑟 𝑚 , which proves that 𝑇 𝑔 ,𝑒𝑓𝑓
𝑡ℎ𝑒𝑟𝑚 is differe nt from the mean 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 .

200 220 240 260 280 300 320 340
Blend
PVME/PS
TSC

c p [a.u.]
DSC
 T g
PVME
Blend
PVME/PS
PVME

I Depo / I Max
T [K]
Dynamic Heterog eneity

Figure 3. 3 . Compa rison o f DSC and TSC measurements for p ure PVME (dashed lines) and a PV ME/PS
(solid lin es) at a comp osition o f PVME/PS 50 : 50 wt %. Dotted vertical lines ind icate the g lass tra nsition
temperatures. Fig ure was taken and adapted from reference [ 28 ]

A similar conclusion could be drawn from figure 3.4, whe re the tempe rature de pendence of
the segmental relaxation rate of the PVME/PS ble nd and that of the PVM E, measured b y
BDS and SHS are depict ed. I t is worth to note th a t, similar to TSC, for PVME/P S, BDS is
only be sensitive to the mol ecular d yna mics of PVME (as affect b y PS), due to the negligible
dipole moment of PS compared to that of PVME. Ne vertheless, SHS is sensitive to the
entropy fluctuations result ing from the mobile segments of both PVME and PS . Therefore ,
combing both methods could provide dee p insights into the d y namic hetero ge neit y .
For PVME/PS 50:50 wt%, despite the fact that both SHS and BDS probe the segmental
dyna mics, the re lax ation rates measured b y SHS are shifted by 13 K to hig h er temperatures,

21
compared to the dielectric data. This is contrary to the case of pure PVME, where both data
coincide, within the experimental error. I n other words, this shift in the rates of the
segmental d y namics of t he polymer blend , measured b y the two dif ferent methods, is an
expression of the dy namic heterogeneit y within the bulk blend sample.

3.0 3.2 3.4 3.6 3.8 4.0
0
2
4
6
PVME/PS
(BDS)

log(f p [Hz])
1000/T [K]
13 K
Dy namic
Heterogeneity
Pure PVME
(BDS)
PVME/PS
(SHS)
Pure PVME
(SHS)

Figure 3. 4 . R elaxation map for bulk PV ME/PS 50:50 wt% : red circles -

- relaxation ; blue sq uares - bu lk
PVME/PS measured b y S HS, 43 gree n stars -

- relaxation pu re PVME measured by BDS and SHS – black
square s 24 Th e solid lines a re VFT fits to the data. Figure was taken and adapted from refere nce [ 25 ].
The Self - concentration (SC) mod el is usuall y used to discuss the d ynamic heterogeneit y . 26
In short, the SC model considers the segments of each component in its loca l environment,
contrary to the TCF model, which onl y takes in to ac count the local composition of certain
volume. The SC model assumes that every se gment is enriche d b y t he same kind of
segments in its environment, due to chains connectivit y. This would lead to an average d
local composition, thus l o cal glass transition tem peratures . Subsequentl y , it would lead to
average relaxation times for seg ments of both c omponents . Furthe r, this g ives rise to the
double peaks of the d y nami c het ero geneit y , s een in figure 3. 2.
3.3.2 . Sy mmetric Broadening
As mentioned above, the segmental relaxation proce ss measured for mi scible blends shows
notable broadening com pared to that of the hom opol y mer components. T he dielectric loss
spectrum for PVME/PS 65: 35 wt% versus pure PVME elucidates this behavior, see fi gure
3.5. I n general the broadening of the loss pe ak of the blend is temperature dependent in two
main w a ys .

22
I) The broadenin g of the loss peaks d ecreases wit h increasing temperature, as depicted i n
figure 3.5.
II ) Th e broadening of the loss peaks increases with increasing the difference betwee n 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚
of both components.
This broadening phenom enon can be described by the Tempe rature dri ven concentration
fluctuations (TCF) model .

27

.

-2 0 2 4 6 8 10
-2 0 2 4 6 8 10

 ´´ [a.u.]
Increasing Te mp
A
PVME/PS
B

 ´´ [a.u.]
log(  [ rad s -1 ])
PVME

Figure 3. 5. Dielectric loss fo r the PV ME/PS blen d 65:35 wt%. (A) Dielect ric loss ver su s frequency fo r
PVME/PS blend: (T=263, 273, 2 83, 293, 308, 3 18, 338, and 368 K) ( B) Dielectric loss versus frequen cy
for pure PVME: (T=253, 258, 2 63 , 268 , 2 78 , 288, 298, 3 08, 328,and 348 K) . Figure w as taken and
adap ted from reference [ 28 ].

The Temperature driven concentration fluctuations (TCF) model assumes that the sample
consists of i subcells of volume V with composition ϕ i and thus a local glass transition 𝑇 𝑔 𝑖 ( ϕ i ).

23
On the molecular level, local concentration of the se sub cells, which is different from the
macroscopic concentration, will lead to differe n t local glass transition 𝑇 𝑔 𝑖 ( ϕ i ). Consequently,
this will g ive rise to local relaxation ti mes, whic h is also diff er ent fr om th e mean rel axation
time. Eventually , the statistical distribution of these different relaxation times , see figure
3.6, yields the br oadening of the loss peak, se e fi gure 3.5.

Figure 3 . 6 . Scheme
of the temperature driven con centration fluctuatio n approach to binary miscible blen ds.

Figure was take n and ad apted from reference [ 28 ].
3. 4 . Surface Enr i chmen t
Pol y mer blends undergo another special phenomenon due to the different surface tensions
of the blend components. This is especiall y si gnificant for as ymme tric polymer blends. A
part of the c omponent with lower surfa ce tension wil l diffuse to the surf ace to minimize the
free ener gy of the s y s tem, which is thermodynamically f avorable . 29 There fore, the
composition at the interfac es is different than that of the bulk .
Distribution
P(  i )
Low T g
Component

log ( Relax ati on ra te)
Temperature
High T g
Component

24

Figure 3 .7. Schema tic diagram of the surface comp osition profile in a bina ry polymer blend. Figure taken
and adapted from reference [ 29 ].

The composit ion differenc e of the surface composit ion 𝜙 0 to the bulk composition 𝜙 ∞ is
described b y the composition profile 𝜙 ( 𝑧) . This composition profile is ex tended throug hout
a characteristic leng th 𝜆 , in the order of magnitude of 10 nm, figure 3.7. Equation 3.6
describes the surface excess (Z *), by integrating t he composition profile when the sy stem is
at a thermod y namic equilibrium.

𝑍 ∗ = ∫ [∅ ( 𝑧 ) − ∅ ∞ ]
∞
0 𝑑𝑧

(3.6)

At Z*=0, there is no s egregation, where as at Z* >0 would indicate pr eferential segregation
to the surface. I n fact, this phenomenon is more or less negligible for bulk samples.
However, it becomes o f g r eat importance with co nfining the pol y mer blend films into thi n
films, where the interf aces can no longer be ignored. This will be discussed in detail in the
next chapter.

25
References

1

Alegria, A.; Colmenero, J.; Ngai, K.; Rola nd, C. Macromolecu les 1994 , 27, 4486.

2

Cendo y a, I. Alegria, A. Alb erdi, J. M. Colmenero, J . Gri mm, H. Ric hter, D. Fric k, B. Macro molecules 1999,
32 4065.

3

T akeno, H.; Kob ayashi, M.; Aikawa, T. Macromolecu les 2006 , 39 , 2183.

4

Watanabe, H.; Uraka wa, O. Korean -Australia n Rheol. J. 2009 , 21 , 235 .

5

Green, P .; Adolf, D.; Gillio m, L. Macromolecu les 1991 , 24 , 3377 .

6

Colb y, R.; Lipson, J. Macromolecu les 2005 , 38 , 4919 .

7

Urakawa, O. ; Fuse, Y.; Hori, H.; T ran-Cong, Q.; Yano, O. Polymer 2001 , 42, 765 .

8

Chung, G.; Kor nfield, J .; S m ith, S. Macromolecu les 1994 , 27 , 5729 .

9

Wang, D.; Ishid a, H. Macromol. Chem. Phys. 2 007 , 208 , 2222.

10

Dionisio, M.; Fernandes, A.; Mano, J .; Correia, N.; So usa, R. Macromo lecules 2000 , 33 , 1002 .

11

Wang, J.; Roland, C. Polymer 2005 , 46 , 4160.

12

Alvarez, F.; A. Alegria, A.; Col menero, J. Macromolecu les 1997 , 30 , 597

13

Arbe, A.; Alegria, A.; Col menero, J.; Ho ffmann, S.; W ill ner, L.; Richter, D. Macro mo lecules 1999 , 32,
7572.

14

Sperling, L.H. Introdu ction to Physica l Polymer S cience , 1986 , John Wiley & Sons , Ne w Yo rk.

15

Madkour, S.; Szymoniak, P.; Schic k, C.; Sc hönhals. A. J. Chem . Phys . 2 017 , 146, 2033 21.

16

Yin, H.; Madkour, S.; Sc hönhals, A. Macromolecu les 2015 , 48 , 4936.

17

Hiemenz, P .; Lodge, T . Polymer Chemistry (second Edition ) . ( CRC Press, B oca Raton, Florid a, 200 7 ).

18

Sc hwartz, G. A.; Col menero, J. ; Alegria, A. Macro molecule s 2007 , 40 , 3246.

19

He, Y.; Lutz, T. R.; Ed iger, M. D. J. Chem. Phys. 2003 , 119 , 9956.

20

Gotzen, N.- A.; Huth, H.; Schi ck, C.; Van Assche, G.; Ne us, C.; Van Mele, B . Polymer 2010, 51, 647.

21

Ngai, K.; Capaccio li, S. J. Chem. Ph ys. 2 013, 138 , 054903.

22

Colmenero; J .; Arbe, A. S oft Matter , 2007 , 3, 1474-14 80.

23

Leroy, E.; Alegria, A.; Col menero , J . Macromo lecules , 2002 , 35, 5587.

24

Madkour, S.; Sz ymoniak, P.; Heid ari, M. ; von Klitzing, R.; A. Schönhals. ACS Appl. Mater. Interfaces .
2017 , 9, 7535- 7546.

25

Madkour, S.; Sz ymoniak, P.; Rad nik, J.; A. Sc hönhals. ACS Ap pl. Mater. I nterfaces . 2017, 9 , 37289-
27299.

26

Lodge, T .P.; Mcleish, T. Macromolecules , 2000 , 33, 6332 .

27

Wetton, R.E. ; Macknight, W.J .; Fried , J.R.; Karasz, F.E. Macro molecules , 1978 , 11, 158-164 .

28

Yin, H.; Schönhals, A. Bro adban d Dielectric Spec troscopy of Polymer Blends in Polymer Blen ds
Handb ook , 2014 , L.A. Utrac ki, Ch., Wilkie, (Ed s.), S pringer .

29

Jones, R. A. L.; Kramer, J . Po lymer 1993 , 3 4, 115- 118.

26
CH A P TER 4 – 1D Co nfinement (T hi n Films )
Nowadays, modern technolog y frequentl y employs pol y me rs and/or their blends confined
at the nanoscale. In general, confinement can take place in 1D (thin films), 2D ( c y li ndrical
nanopores), or 3D (nanop orous glasses). At the pr esent time, thin pol y m er film s (<200 nm),
have been attracting a lot of attention due to their high demand in thin -film based
technolog ies.

1

-

6

I n prin ciple, thi n films could have three diff erent confi gura ti ons , supporte d,
capped and freestanding films. However, thi s work onl y focuses on the former two
config urations. I n the capped sample geometr y, the substrate has two polymer /subs trate
interfaces, while for supported films; the samples are allowed a free surface at the
polymer /air interface, in addition to the one at the poly mer/substrate interface.
4.1. Effect of 1D Co nfinement on the Glass t r ans ition
Two de cades ag o, the pioneering wo rk of K eddie et a l.

7

,

8

showe d that the thic kness
dependence of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of suppor ted PS (figure 4.1) and P oly(methyl meth acrylate) PMMA
films deviates from their bulk values depe nding o n their supporting substrates. Since then,
the int erest in this topic has been on the rise, exponentiall y. In fact, despite the wealth of
knowledge present on this topic now, there are still a lot of open questions. For instance,
what are the molecular reasons behind the possi ble deviations in the properties (e.g. glass
transition) of confined polyme rs, compared to that of the bulk?
In general, the discussion on this topic is still controversial, where divergent results were
published, even for the same pol y mer/substrate s ystems.

9

,

10

These results show both a
depression

11

-

14

or a n increase in 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 ,

15

-

17

with dec reasing film thickness. Furthermore , a
similar behavior w as als o reported for capped fil ms. For instance, Al -capped Pol y st y rene
films experience a 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 depression, with decreasing film thickness. 10 Nevertheless, for
Al -capped PC films, an elevation of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 with decreasing film thickness, was observed. 9
This was related to the fact that the fact that the in terfacial en ergy of PS/Al is much hi gher
than that of PC/Al.

27

Figure 4 .1. 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 - green circles and 𝑇 𝑔 𝑑𝑦𝑛 - red triang les as a functio n of film thickn ess for thin PS films
suppo rted on silicon wafer. The b lack dashed a nd solid lines are g uides fo r the ey es. The Blue solid line
marks the limit o f the deviation from the bulk value, which is observed for free standing PS films . The figure
and data were taken and ada pted from reference [ 18 ] .

In a perspective review by Edi ger et al.,

19

the progress made in the last y ears was thorou ghly
discussed, the reader is also referre d to references [

20

-

28

] for a deepe r insight in this topic.
4.1.1 . Three Lay e r Model
Nowadays, the thickness depe ndence of 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 of supported thin films is usually d iscussed
in the framework of an idealized three-la yer model. This model elaborates a sensitive
balance between the eff ects of a spatial d yna mically hetero gene ous stru cture across the
whole film, see figure 4. 2. For supported films, this structure is composed of a free surface
layer (polymer/air interface), a bulk-like la y er w ith bulk properties (in the mi ddle of the
film), and a layer a dsorbed at the substrate (pol ymer/substrate interfac e ).

Figure 4.2. Sch ematic representation of the idealized three-layer model of thin films. Figure was taken and
modified from reference [ 21 ].

28
Upon decreasing the total film thickness, the thickne ss of the bulk -like lay er d ecreases. 15
However, at the pol ymer/air int erface, due to th e missing se gment-segment interactions,
compared to the bulk, a mobi le surface la y er will always be formed. Consequently , for a
repulsive pol y mer/substrate interactions, th e free surf ace la y er becomes more dominant,
y i eldin g a reduction in 𝑇 𝑔
𝑡ℎ𝑒𝑟𝑚 . For non-repulsive pol y m er/substrate int eractions, segments
can get adsorb ed at the pol ymer /substrate int erface. W ithin this adsorbed la yer, the segments
have a r educed mobilit y and ma y result in an elevation of 𝑇 𝑔 𝑡 ℎ𝑒𝑟𝑚 , compared to that of the
bulk. Consequentl y , the measured 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 is a complicated average reflecting the effect of
the aforementioned layers.
Furthermore, r ecent studies on linear

29

,

30

and star shap ed pol y m ers

31

revealed tha t the thre e-
layer model and inter facial int eractions are not adequate to univocally describe the
deviations of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , form its bulk value, observed for pol ymer und er confinement. Thus,
suggesting that more parameters should also be taken into accoun t.
For instance, one has to b ear in mind that the diffu sive mobili ty of a pol y m er chain depends
on molecular weight (M w ). The high er the M w , the longer the time needed for the chains to
reac h an equilibrate confi rmation. This process (annealing) is necessary to form an adsorbed
lay er . Th erefore, the fo rmation of the adso rbed layer (at the pol y m er/sub strate interface)
requires a given time (longer th an the terminal relaxation time). Conseque ntl y, this
insinuates that the effect of the adsorbe d layer, an d thus the possible de crease or incr e ase of
𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 of a thin film, is also influenced b y the ann ealing condition, which is a function of
the M w . 32 This was con cluded from inv estigations b y ellipsom etry on p ol y st y rene thin
films

32

,

33

as we ll as broa dband dielectric spectroscopy (BDS) of isolated, semi -isolated, 28
and brushes of high M w poly(2- vin yl pyridine) (P2VP) films.

34

In addition , Burroughs e t al. have confirmed a correlation between the change of 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚
and the thickness of the adsorbe d l a yer. Their data was quantitatively rationalized through
the free volume hole diffusion model, see references [

35

,

36

]. The shift in 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 wa s
explained as a result of the diffusion of fr ee volume sit es toward interfacial “ sinks ” , c ausing
packing frustration at the pol y mer/substrat e interface. This concept is explained in the
following subsection.
4. 1.2. Free Volume under Confinement (Packing Frustration)
The relationship between the free volum e and th e glass transition has been an active topic
not onl y for bulk pol ymers, as discussed in section 2.3.2, but also for confined polymeric

29
films. I n recent y ears, th e concept of p acking frustration , which is due to the cha nge in the
free volum e within the s ystem, has g ained popul arit y in explaining th e effect of confin ement
on the glass transition phenomenon. I n general, the increase of the free volume sites would
translate into a reduction in 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . For thin films, the free surface and the ad sor bed la y er
could act as a source and/or sink of free volume sites.
The mechanism of how the free surf a ce could introduce fr ee volume sit es to the system was
first propose d by deGennes.

37

-

39

Throug h the suggested model, deGennes theo rized that at
the free su rface, kinks al ong the pol y mer chains could generate a free vol ume site, which
could then diffuse into the films along the cha in back bone. Since the radius of g y r ation of
the pol ymer chains is related to the molecular wei ght of the chains, this mode l would then
impl y that the free volume sites would be able to diffuse deep er into the film, for polymer s
with higher M W . Nevertheless, investigations on the local distributions of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 in
free standing films

40

disagre es with this model. Where as , 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 of thin supported films o f
poly(  - meth y l st y ren e), PaMS, showed no confine ment effects on 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 for shortest chains
(1.3 kg/mol),

41

contrary to a 20 K drop in 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 for 420 kg/mol samples, in agreement with
the model. A sim ilar behavior was observed for different molecular w eights o f PS supported
films. 10 Furthe r explanation for these contradicting results could be deduce d fr om reference
[

42

] . There, it w as discuss ed that for short chains, the excess in free volu me could be
promptly suppl ied b y the ir relativel y abundant ch ain ends. Nonetheless, fo r longer chains
the excess must be created, which would r esult in the reduction of 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . Nevertheless, to
verify this conce pt this model, further investi gations are necessar y due to the controversial
results in literature.
In reference [

43

], this behavior w as further discussed in the framework of the Gibbs -Di
Marzio Model. This mod el introduc ed the c hain rigidity a s factor in determining the impact
of the free volume on 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 . If k B 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 > E conf applies, conformational chan ge s of the
chains will take place, where E c onf is the energy barrier related to a conformational cha nge
possible via free volume. In the li ght of this model, polymer with rigid backbones, would
not evidence a reduction in 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 unless their k B 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 is higher than E conf . Consequently ,
this behavior would not a ppl y for shorter chains, due to their low 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 . For instance, this
trend is in a g ood agreement with the results obtained for PMMA thin films.

44

Alternatively, excess free volume sit es could al so be introduced in the vicinit y of an
adsorbing interface, for instance in poorl y annealed pol y mer films supported on non-

30
repulsive substrates. There, packing frustration re sults in the reduction of the local densit y
of the seg ments at the interface; between the adsorbed and the non -a dsorbed la y er. As
expected, this packing frustration would get enhance s in the presence of bulk y side groups.
This was shown for the c ase o f pol y ( 4-tertbutyl styrene) films, with bulky tertbut y l
moieties. 11 This is in agreement with re ference [45], where it was shown , for freestanding
films, that the yielded packing frustration could b e quantitatively recovered, as the excess
in fre e volume.

45

Furthe r more, Cangialosi and Na politano evidenced a p rop ortionality of
𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 with the excess in interfacial free volume. 36
In the lig ht of these findings, the aforementioned consideration should all be taken into
account when discussin g 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 re ductions in the vicinity o f free surfaces and weakl y
adsorbing interfaces.
4.1. 3. A dsorbe d La y e r
Pol y mer s y stems with non-repulsive pol y mer/substrate int erfacial interactions , present
further c hallenges to the understanding of the deviations of 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 from its bulk value. For
a well annea l ed polymer thin films with non-repulsive pol y mer/substrate interactions, it was
shown that an adsorbed la y e r is expected to fo rm. In this la y e r, the ch ains get trapped into
non-equilibrium conformations, which reduces their effective viscosit y . To achieve
equilibrated conformations, the reptation model

46

predicted that the annealing times should
be longer than the terminal relaxation time. This was found fo r PS

47

, PMMA, and PVAc .

48

Rotella et al .

49

show ed tha t onl y the mol ecules in direct contact with an adsorbing surface
are influ enced, resulting in cha nges in the loc al 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 . I t was further su ggested in r eference
[49] that at the molecular level, these alterations have a finite lifetime. Furthe rmore, th ese
changes c orrespond to metastable conformations of the poly m er chain corresponding to
local minima in the free energ y lands cape rather than a global one.
The current understanding of the behavior and growth kinetic of the adsorbed la y er was
rece ntl y concluded f rom solvent leaching (also called Guiselin brushes ) experiments, 29
where the free surface and the bulk -like layers are removed. Through combing spectroscopic
ellipsometry and A FM im aging, it was recently shown that for a well-annealed sample, an
irreversibly adso rbed thin la y e r is formed at the pol y m er/substrate interface , with a thi ckness
compared to the radius of g y r ation (R g ) o f the po l y mer . This was shown for a number o f
polymer s, as reported in references [

50

,

51

], where the seg m ent/surface interaction energ ies
are in the order of k B T. The connectivit y o f the chains further stabili zes this layer, as th e

31
detachment would require cooperative r earrangement of a larger se t of the adsorbed
segments.

52

Housmans et al. showed that for well annealed atactic PS supported films, the adsorption
process takes place in two different regimes having different time dependencies , figure
4.3A. 32 At short times, the pol y mer chains thrive to pin as man y segments as possible to the
substrate, lowering it s free e ne rg y . The growth kin etics of this adsorption p rocess follows a
linear time dependence and the poly me r segments are directl y adsorbed at the substrate
forming a dense stron gly bounded adsorbed layer.

53

,

54

This la y er is mainl y fo rmed of trai ns
strongly boun ded to the substrate, hence , it is assumed to be completely im mobili zed (dead
layer). This part of the adsorbed la y er is referred to as “strongly bound ed layer” in th e
following discussion.
However, at longer times, the adsorption grow th kinetics is character iz ed b y lo garithmic
time dependence. The adsorbed la y er further grows by the diffusion of segments throu gh
the alread y existing lay e r, on the expense of their entr opy. The structure of thi s part of the
adsorbed la y e r is less den se, c ompar ed to the stron gl y bounde d layer, as it is mainly formed
out of loops and tails. Theses loops and tails allow for some molecular mob ilit y, compared
to the trains of the s trongly bound ed la y er, see figur e 4.3A and B. This par t of the adsorbed
layer is r eferred to in the following discussion as “loosel y bounded la y e r”. For further
details, see references [

55

,

56

].

32

Figure 4.3 . ( A ) Kinetics of irrever sible chain ad sorption of melts of PS of consta nt M w and different
temperatures. Figure regen erated from the reference [ 32 ] . ( B ) A schema tic cartoon of a two - layer structure
(ads orbed layer and a bulk - like layer) as deduce d fro m the data a nd litera ture, taken from reference [ 57 ] .
The picture of the heterogeneous structure withi n the irreversibly adsorbed la y er suggests
that the number of the adsorbed segments is also depende nt on the annealing ti me. H ence,
the more adsorbed se gments, the hi gher t he thickness of the adsorbed la yer (h ads ) , where a
plateau is reached at h ads ≈  R g . This would mean t hat at short annea ling times/low number
of adsorbed segments, the system is comparable to the pol y mer/subst rate repulsive s y stem,
explained in the previous section. Consequentl y , o ne could conclude that even for capped
films with non - repulsive pol ymer/substrate int erfaces, if the film is not well annealed, a
reduction in 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 could be evidence d. This is in a good agreement with studi es on
lin ear 29 , 30 and star - shaped poly mers. 31
4.2. Effect of Thi n Film Confin ement o n Segmental D y namics
T he segmental dynamics an d the related 𝑇 𝑔 𝑑𝑦 𝑛 of most homopol y mers confine d into thin
films show no thickness dependency, see fi gure 4 .1. This is considered to be a combined
effect of a number of reasons with different origins. First, a s discussed in c hapter 2, 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚
is measure d at lower temperatures (lower frequencies), compa red to the 𝑇 𝑔 𝑑𝑦𝑛 , where the
system is not in a thermod y namic equilibrium. Whereas at 𝑇 𝑔 𝑑𝑦𝑛 (higher frequencies) th e
system is already in equilibrium. At both temperatures, the correlatio n length scales are
differe nt and so are the ir sensitivities to thickness changes. Secondly, dyna mic glass
transition is measured at te mperatures above 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , where it was found that the se gmental
dyna mics of the mobile surface layer becomes similar to that of the bulk - like layer. 22 Thus,
the influe nce of the sur face la y er on 𝑇 𝑔 𝑑𝑦 𝑛 be comes less pronounced with increa sin g
temperature abov e 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 . This effect could be the reason wh y d yna mic m ethods show no
thickness dependenc y of 𝑇 𝑔 𝑑𝑦 𝑛 , while 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 deviate s from its bulk value, with decreasing

33
film thickness. This su ggests that if a thickness dependence is obs erved for the 𝑇 𝑔 𝑑𝑦𝑛 , it is
more likel y that thi s confinement effect would be due to the effect of the adsorbed la y e r on
the overall segmental dynamics. Therefore, underst anding of the molecular dynamics of the
adsorbed la yer is essential for understandin g th e effect o f confinement on the ove rall
segmental dy n amics of the whole film .
Despite the existing evidence for the irreversible adsorbed layer in well-annealed polymer
films, little is known about t he ir glass y d y namics, due to the hard accessibil it y of this la yer
and their low intensity. 57 Nevertheless, experiments on s y stems related to thin films , for
instance polymer nanocomposit es of P 2VP,

58

PVAc

59

, and PDMS

60

with embedded silic a
nanoparticles, successfully probed the glass y d ynamics of the adsorbed la yer. In general, it
was found that the adsor bed la y er s howed slowed down segmental d ynamics, compared to
that of the bulk.
Further, it was r ecently found that the coopera tivit y o f the segmental dynamics of the
adsorbed la y er in these s ystem could also b e M w dependent. For instance, for PDMS with
embedded sil ica nanoparticles 60 the segmental d ynamics of PDMS in the adsorbed la y er
loses its cooperative nature with d ecreasing the M W . Where the temperatur e dependence of
the segmental rates switc hes from a VFT behavio ur to an Arrhenius one, with decreasing
the M W below the entanglement M W (M c ). This could be rationalized b y tak ing into a ccount
that with dec reasing the M W , h ads would ha ve to de crease, due to the lower R g . The decrease
in the h ads would have to take plac e first on the ex pense of the loosel y bounded la y er.
Consequently, a t a certain thickness (estimated to be 1 nm i n this work), the a dsorbed la yer
would be m ainly formed out of the stron gly bound ed la y e r, whi ch is mainl y formed out of
trains with very low mobility . Therefore, the se gmental d y n amics be comes localized an d
lose their cooperative nat ure. The localization of the segmental d ynamics (degeneration of
their cooperative nature) wa s also obse rved for other s ystems confined within a hard or
frozen host.
For inst ance, PDMS confined into nonporous glass

61

,

62

showed the dege neration of the
segmental d ynamics of PDMS (  -relaxation) with decreasing the po re si zes to a simil ar
length scale to that of V CRR . For pore sizes >> V CRR , the segmental d y namics are
coopera tive , wh ereas fo r pore sizes ≈ V CRR (or smaller), the y are locali zed. This was
evidence d b y the tra nsiti on of the temperature d ependence of th e rel axation rates of the
segmental d yna mi cs f rom a VFT to an Arrhenius behavior, upon decreasing the re aching a
similar length scale compared to that of the V CRR , s ee fi gure 4.4A. Consequently , the glassy

34
dyna mics w as assi gned to a degenerated  - re lax ation of the PDMS seg men ts. I nter estingly,
probing the glassy d y na mics of the same s y stem emplo y ing temperature modulated DSC
(TMDSC), which is a SHS technique, show ed a decrease in  c p with decreasing the pore
size. Further,  c p wa s f ound to be zero exactly at the pore size ,where the temperature
dependence of th e se gmental dynamics ch ang es from a VFT to an Arrhenius behavior, see
figure 4.4 B. This suggests that SHS is not sensitive to loca lized mol ecular d y namics and
could onl y p robe the coo perative mobili ty o f the pol ymer se gments. This is in agree m ent
with referenc e [57 ].

1 10 100 1000
0.0
0.1
0.2
0.3
0.4
>> V CRR
Pore
size
PMP S in nanoporous glass

 c p [J g -1 K -1 ] / weight Polym er
Pore size [nm]
Transition f rom VFT
to Arrhenius
Pore
size  V CRR

35

Figure 4 .4. (A) R elaxation map of segment al dynamics of PDMS co nfined into nanoporous gla ss. Inset:
cartoon representa tion of polymer segmen t confin ed in to a ho st, suc h as nanop ores. Fig ure adap ted from
the Reference s [ 61 , 62 ] . (B)
∆
c p (measured by TMSDC) o f PMPS confin ed in to n anoporous glass as a
function of the po re sizes. The dashed red line represents the p ore size at which the tran sition fro m VFT to
Arrhenius occurs. The solid black like is a g uide for th e eyes. Figu re ta ken a n d a dapted fro m the references
[ 61 , 62 ].

36
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Napolitano, S.; Pilleri, A.; Rolla, P .; Wübbenhorst, M. ACS Nano 2010 , 4, 841 - 848.

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8

Keddie, J.L.; Jones, R. A.L.; Cor y , R.A. Euro. Phys. Lett. 1994 , 27, 59 - 64

9

Yin, H.; Napo litano, S.; Schönhals, A. Macro molecules 201 2, 45 , 1652 -1662.

10

Yin, H.; Cangialo si, D.; Sc hönhals, A. Thermoch imica Acta 2013 , 566, 186 - 192 .

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Dalnoki -Veress, K.; Forrest, J . A.; Murra y, C.; Gi gault, C.; Dutcher, J. R. Phys. Rev. E 2001 , 6 3, 0 31801 -
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Lupaşcu, V.; Picke n, SJ.; W übbenhorst, M. Jo urnal o f Non -Crystalline So lids 20 06 , 352, 559 4 -5600.

13

Fakhraai, Z.; Forrest, J. A. Phys. R ev. Lett. 2005 , 95, 0257 01-025 705.

14

Sh arp, J . S.; Forrest, J. A. Ph ys. Rev. Lett. 2003 , 91, 235701 -235705.

15

Paeng, K.; Ric hert, R.; Eidger , M.D. Soft Ma tter 2012 , 8, 8 19- 826.

16

Qi, D.; Ilto n, M.; Forrest, J . A. Eur. P hys. J. E 2 011 , 34, 56 - 63.

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Qi, D.; Dale y, C. R.; Chai, Y.; Fo rrest, J . A. Soft Ma tter 2013 , 9, 8958 − 8964.

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Paeng, K.; S wallen, S. F.; Ediger, M. D. J. Am. Chem. S oc. 201 1 , 133, 8444 – 8447.

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38
CH A P TER 5 – The Idea Behind This W ork
As discussed in chapters 1 and 4 , since the pion eering work of Keddie et al. [

1

,

2

], the
thickness dependence of the g lass tra nsition temperature has been controversiall y discussed
in the literature.

3

-

12

The current understanding behind the deviations of the glass transition
temperature for pol y mer thin films, from their bulk values, is commonl y discussed in the
framew ork of an idealized three-l a y er model. N evertheless, it was recentl y sho wn that
parameters like M w , annealing time, interfacial interaction and packing f rustration could
directly influen ce the overall glass transition and the glass y d y n amics of the thi n films, as
discussed in chapter 4. Consequentl y , it was concluded that the effects of nanoconfinement
on the glass transition and g lass y d y namics go be yond an idealized thre e-layer model, which
mainly considers the surface to volume ratio effect s.
The aim of this work is t o achieve a deeper understanding of the nanoconfinement effects
on the glass transition and the glass y dynamics of poly mer films and the molecular
mechanism behind the p ossible deviations from t he bulk properties. This goal is achieved
by simplif y ing the topic t hrough two main p arallel approaches I) carefully chosen pol y meric
systems, whi ch allows th e enhancement of th e effect of a certain parameter (e.g. M w and
annealing times effec t on the growth to the adsorbed lay er) on the glass trans ition and glassy
dyna mics of the whole film. II) Combining diff erent characterization metho ds with different
sensitivities and frequency windows, whi ch could allow selective probin g o f a pol ymer (in
the case of polymer blends) or a propert y (glass transition versus segmental d y namics) of
the mea s ured s y stems. A schematic summarizing the especiall y selected sy st em and the
differe nt characterization methods employed to study them is given in figure 5.1.

39

Figure 5.1. A schematic summa rizing th e e specially sel ected systems studied in th is d issertation. I n
additio n, the selected comb ination of the characeterizatio n meth ods u sed for every system are g iven.
T he ex perimental wo rk presented here starts with a SHS stud y on thi n films of high
Molecular we ight ( M w ) Pol y (2 - vinl y p y r idine) (P2VP ), Chapter 7 . 13 This stud y w as carried
out to confirm what has been controversially discussed in literature regardi ng the thickness
independency of 𝑇 𝑔 𝑑𝑦𝑛 of thi n polymer film and mol ecular reasons behind it. Throu gh
developing a new derivative - based anal y sis method, which r educes the analy sis error, a
slight deviation , fr om t he bulk value , of 𝑇 𝑔 𝑑𝑦𝑛 with decreasing the film thickness w as
surprisingly eviden ced for the first time. A closer look on the data revealed that the
temperature dependence of the heat capacity in the g lass y and li quid states chan ge s with
film thickness, which was conside red as a c onfinement effect. Although the de creas e in
𝑇 𝑔 𝑑𝑦𝑛 with dec reasing the film thickness was relate d to the effect of the fr e e surf a ce, it c ould
not be e xcluded that this tempera ture dependence could also be a re sult of an incr ease in the
free volume at the polymer/substrate interface, as explai ned in 4.1.2. T his could also be
expected, as the annealing ti me required to equi librate segments for a high M w pol ymer,
which is necessary to for m an adsorbed la y e r, coul d be much longer than th e annealing time
used for this work (48 hrs).
Consequently, to ex clude the latter possibilit y, the attention was directed to a low er M w
polymer , n amel y Pol y ( Vin yl meth y l ethe r) ( PVME ) . The annealing ti me was increased to
72 hrs, which is expected to be lon ger than the terminal relax ation ti mes, as suggested b y
the reptation model. Therefore, ensuring th e pr esence of an adsorbed la y e r and eliminating
the effec t o f an increased free volume at the pol y mer/substr ate int erface. C hapter 8 then

40
presents a detailed SHS and BDS study on thi n films of PVME.

14

First, to avoid the long-
standing argument on the effect o f the different sa mple arrangements and s ubstrates on the
glassy d yna mics, measu re by BDS and SHS, the following approach w as followed. First,
the rece ntl y developed Nanostructured Capacitor (NSC) was adapted and employed.

15

Thi s
sample arrangement allowed BDS mea sur ements of supporte d films with a free pol ymer/air
interface, rather than capped one, commonly m easured by Crossed Electrode Cap acitor
(CEC). B y comparin g id entically prepared films measured by both arrangements, it was
concluded that for thi s s ystem, the free surface la yer has no effect on the overall segmental
dyna mics. On the other h and, due to the strong er interfacial interaction of PVME with S iO 2
compared to AlO x (as confirmed b y Conta ct Angle Measurements (CAM)), a thicker PVME
adsorbed la y e r at the pol y m er/substrate int erface was evidenced. Utiliz ing NSC, the glass y
dyna mics of this adsorbed la ye r, within the thin f ilms, was reported for th e first time and
was found to be c ompletel y indep endent from tha t of the bulk-like la y er.
The results of the homopolymer thin films, prese nted in chapters 7 and 8, sugge st ed that the
effect of the fr ee surface lay e r on the over all segmental d y namics cannot be probed with
dyna mic methods, due to the measurement condit io ns. This is in line with reference [

16

],
where it wa s shown that the segmenta l d y n ami cs of the free surface laye r becom es
indistinguishable from that of the bulk -like la y e r, at t emperatures above 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 .
Neverthe less, b y carefully choosing a polymer blend s ystem, a contra st in the segmental
dyna mics between the free surface and bulk -like layer could be created, utilizing the so -
called surface enrichment phenomenon.
Therefore, the se cond part of this work focus es o n pol y mer blends. An ide ntical PV ME , to
the one used in the a bove mentioned study , w as blended with the well-studied PS to form a
blend miscible- in -bulk, with a composition of PVME/PS 50:50 wt% and 2 5:75 wt%. These
asy mmetric polymer ble nds experience an enhanced surface enrichment phenomenon, due
to the large difference between in th e surface tensions of PVME and PS . This results in t he
segrega tion of PVME at the free surface, forming a PVME rich-la yer at the poly m er/air
interface. Since large di fferences in surface ten sions is related to lar ge differences in
viscosity, which translates int o large differences in the segmental d ynamics, having a
PVME-rich layer at the free surface would in duce enough contrast in the segmental
dyna mics, with respect to that of the bulk-like la y e r. Subsequently, allowing the probing of
the effect of the free su rface la y e r on the overall s egmental dy namics, as a function of the
film thi ckness. It is wo rth to note that for th ese bl end s ystems, there is no unified theor y to

41
explain molecular mec h anism behind the composit ional he terogene ities even for bulk
samples, see chapter 3. I n addition, the glassy dynamics of thin poly mer ble nd films and the
effect of thi n film confinement on the compositional heterogeneities an d the segmental
dyna mics is considered rare in literature.
The thickness depende nce of the glassy d y namics and glass transition of t hin films of
PVME/PS blends we re studied by BDS, SHS, spectroscopic ellipsometr y as well as X-r a y
Photoelectron S pectroscopy (XPS ), AF M in Chapters 9 through 11 .

17

-

19

The choosing o f
these s ystems as well as the exact combination s of the characterization methods were
carefully selected based on a number of reasons.
I) These pol y mer blends are as ymme tric with respect of the 𝑇 𝑔 𝑡 ℎ𝑒𝑟𝑚 s of both components
( ∆ 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 =130 K) and M w (1:50 folds), which enhances the compositional
heteroge neities as w ell as the preferential s egregation of the PVME at the interfaces,

20

see sec tion 3.4.
II ) For these pol ymer blends, the re is an additional asymmetr y with respect to the dipole
moments of both components. F or BDS measurements, this feature allows th e
selective p robing of the P VME d ynamics as affected b y PS . This is due to the f act that
PS has a ne glig ibl e dipole moment, compared to P VME. Therefore, b y comparing the
glassy d y namics of the blend to that o f pure P VME, as a fun ction of film thi ckness,
differe nt aspects of the nanoconfinement effect on the compositional hete rogeneities
within the pol ymer blend film, and the mole cu lar me chanism behind it, was
elaborated. For instance, this methodology helped in deciding whether a confinement
effect was due to frozen P S segments or PVME adsorbed at the substrate.
III ) C ombing BDS and SHS provide d a powerful tool to look at th e diff erent aspects o f
the glassy d ynamics and its relationship to the dy namic heterogeneities.

21

While BDS
would only b e sensitive to the PVME segments, as affect b y PS, SHS measures the
entropy fluctuations all mobile segments of both PVME and PS. By comparing the
te mpera ture dep endence of the se gmental relax ation rates, various aspects of th e
nanoconfinement effec ts on the glassy d y namics as well as the com positional
heteroge neit y was displayed.
IV) In addition, the combination of BDS measure ments using NSC and S HS allowed the
studying of the influence of the mobile surface la yer as well as the surface e nrichment
phenomena on th e segmental d y namics , which could not be probed for thin films of
homopoly m ers, as discus sed above.

42
V) Combi ning ellipsometr y (Ellip.) with SHS provides a window to look at the g lass
transition and the related segmental dynamics in a large frequency spectrum. C hoosing
this s y stem, which shows a thickness dependence of 𝑇 𝑔 𝑑𝑦𝑛 , allows for the comparison
with the thickness dependence of 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 . Utilizing this behavior, a direct evidence was
provided on th e coupling/decoupling phenom ena of 𝑇 𝑔 𝑑𝑦𝑛 and 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 , which
withstands a two-decade controversia l discussion.
VI) Finally, XPS measure me nts on the free surface as well as the leac hed adsorbed laye r
(utilizing recentl y developed solvent leaching experiments), provided fo r th e first time
direct evidence of the compositional heterog eneiti es at the interfa ces. Due to the mass
conserva tion of the measured film, educated a ssumptions about the overall
compositional heterogeneities was then con cluded. B y combing the XPS results to that
of the BDS, the molecular mechanism behind the effect of the com positional
heteroge neities on the glassy d ynamics of the poly mer bl end were discussed .

43
References

1

Keddie, J.L.; Jones, R. A.L .; Cor y, R.A. Farad ay Discussio ns 1994 , 98, 219- 230.

2

Keddie, J.L.; Jones, R. A.L .; Cor y, R.A. Euro. Phys. Lett. 1994 , 27, 59 - 64 .

3

Ediger, M. ; Forrest, J . A. Macromolecu les 2014 , 47, 47 1-478.

4

Forrest, J. ; Dalnoki-Veress, K . ACS Ma cro Letters 2 014 , 3, 310 −314

5

O’Connell, P . A.; McKenna, G. B. Science 2005 , 307, 1760 – 17 63.

6

Paeng, K.; S wallen, S. F.; Ediger, M. D. J. Am. Chem. S oc. 2011 , 133, 8444 – 8447.

7

Forrest, J . A.; Dalnoki -Veress, K.; Coll. ; J. Int. Sci . 2001 , 9 4, 167 – 1 95.

8

Forrest, J . A.; Eu r. Phys. J. E 2002 , 8, 261 – 266.

9

Fakhraai, Z.; Forrest, J. A. Scien ce 2008 , 319, 600 -604 .

10

Chai, Y.; Salez, T .; McGr aw, J. D.; Benzaq uen, M.; Dalnoki -Veres s, K.; Raphaël, E. ; Forrest, J . A.
Science 2014 , 343, 9 94- 999.

11

Tress, M.; E rber, M. ; Mapesa, E. U.; H uth, H.; Müller, J .; Serghei, A.; Schic k, C.; Eic hhorn, K. -J.; Voit,
B.; Kremer, F. Macromolecu les 2010 , 43, 9937−9944 .

12

Tress, M.; Map esa, E. U. ; Kossack, W.; Kip nusu, W. K.; R eiche, M.; Kre mer, F. Science 2013 , 341,
1371−137 4.

13

Madkour, S.; Yin, H.; F üllbra ndt, M.; Schön hals, A. Soft Ma tter 2015 , 11, 7942- 7952.

14

Mad kour, S.; Sz ymoniak, P .; Heidari, M.; von Klitzing, R.; A. Schönhals. ACS Appl. Mater. Interfaces .
2017 , 9, 7535- 7546.

15

Tr ess, M.; Mapesa, E. U.; Kossack, W.; Kipnusu, W . K .; Reiche, M.; Krem er , F. Science 201 3 , 341,
1371−137 4.

16

Paeng, K.; S wallen, S. F.; Ediger, M. D. J. Am. Chem. So c. 201 1 , 133, 8444 – 8447.

17

Madkour, S.; Sz ymoniak, P.; Schic k, C.; Schön hals. A. J. Chem. Phys . 2 017 , 146, 2033 21.

18

Madkour, S.; Sz ymoniak, P.; Her twig, A.; Heidari, M.; vo n Klitzing, R.; Napo litano, S.; Sferrazza , M.; A.
Schönhals. A CS Macro Letters 2017 , 6, 1 156 -1161.

19

Madkour, S.; Sz ymoniak, P .; Radnik, J.; A . Schönhals. A CS Appl. Mater. Interface s . 2017, 9, 3 7289 -27299.

20

Jones, R. A. L.; Kramer, J. P olymer 1993 , 34 , 115-118.

21

Yin, H.; Madkour, S.; Schönh als. A. Macro molecules 2015 , 48, 4936 -4941.

44
CH A P TER 6 - Experime ntal Tec hniques (Principles and
Preparation)
The idea behind the characterization t echniques used in this work is co mbing diffe rent
volume sensitive methods with surfac e analytical techniques. The main volum e sensitive
methods employe d here were Broadband Dielectric S pectroscopy ( BDS), Specific Heat
Spectroscopy (SHS) and spectroscopic ellipsometry . These dif ferent techniques reveal the
differe nt aspe cts o f the glass transition a nd the rela ted glass y d y n amics, as il lustrated in this
section. As for the surface anal y tical techniques, Atomic Forc e Mic roscop y (AFM), Contact
Angle Measurements (CAM), and X-ra y P hotoelectron Spe ctroscopy (XP S) were carried
out to control and affirm the quality, the thicknes s, and the molecular co mpositi on of the
prepared thin films. This chapter is arra nged as f ollows. First, the principles of the main
character ization methods (BDS and SHS) used in this work are briefl y int roduced. This is
then followed b y a brief description of all the oth er complementary techni ques used in thi s
work. Finall y , a short summary of the sample preparation a nd the diffe r ent samples
arra ngements is given.
6.1. Princ iples of th e Main Exp erimental Techniqu es
Broa dband Dielectric Spec troscop y ( BDS) and Specific Heat Spe ctroscop y (SHS) were the
two main ch aracterization methods used. Both methods follow the linear response theor y
(L RT).

1

,

2

In general, L RT states that if an outer dist urbance x (t) (applied perturbation) acts
on a s y stem , a response y(t) may be caused. If the observed response o f the s y stem is
proportional to the applied perturbation, the line ar response theo r y

3

ca n be applied. I n that
case, the time -dependent response of the s ystem, following an applied dist urbance, can be
described b y a li near equation. B y appl y in g for in stance a small ex ternal disturbance to the
system under investi gation, the time -de pendent response of the s ystem, e.g. mol ecular
fluctuations alread y present in the system, can b e probed. The applied disturbance can b e
for example modulations of temperature, electric field, shear force, etc. B y changing the
source of the external di sturbance, the y i elded the proportional response will also differ.
Consequently, allowing t o probe dif ferent aspects of the same process. This is for inst ance
one of the advantage s of combing BDS and SHS in a complementary manner, figure 6.1.

45

Figure 6 .1 . A schematic of th e a pplied externa l disturbance an d the yielded prop ortional response o f the
system in the case of Br oadband Diel ectr ic Spectr oscopy (BDS ) – up per panel - an d Sp ecific Hea t
Spectr oscopy (S HS ) – bo ttom panel.
6 .1.1. Broadband Dielectric Spectroscopy
B roa dband D ielectric Spectroscopy (BDS) r efers to the measurement of a sample using
electromag netic fields , in the fre quen c y range from 10 -4 Hz to 10 12 Hz . The int eractions of
these elect romagnetic fi elds with the matter are based on different process es , such as
restricted mol ecular an d/ or cooperative fluctuati ons, as well as charge transport and
polariza tion effects at the interf aces. For pol y me ric s y s t em, different d ynamic processes
occur ove r an extremel y broad time and tempe rature scales . The r efore, BDS is a useful and
efficie nt tool to probe the different molecular dynamics of pol y m ers . The section is based
on references [ 3-6 ].
6 .1.1.1. Elec trostatics
In an isotropic s y stem, f or small electric field strength E, the dielectric displacement D can
be expressed as:
𝐷 = 𝜀 ∗ 𝜀 0 𝐸 (6.1)
where 𝜀 0 is the dielectric permittivit y of v acuum ( 𝜀 0 = 8. 854 10 − 12 𝐴𝑠 𝑉 −1 𝑚 −1 ) . When a
time - depe ndent process is present, the time dependenc ies of the applied electric field and
the resulting dielectric displ acemen t are phase shifted .
I n th e case of a periodic electric field E (t) with small streng th, 𝐸 ( 𝑡 ) = 𝐸 0 𝑒𝑥𝑝 (− 𝑖 𝜔 𝑡 ) ;
where 𝜔 = 2 𝜋𝑓 and 𝑖 = √ −1 s y mboliz es an imaginary unit, this phase shift can be
described by the comple x dielectric function
𝜀 ∗ ( 𝜔 ) = 𝜀 ′ ( 𝜔 ) − 𝑖 𝜀 ′′ ( 𝜔 ) (6.2)

46
where 𝜀 ′ ( 𝜔 ) is the real part and 𝜀 ′′ ( 𝜔 ) is the imag inar y (loss) p art of the complex dielectric
function.
Polarization 𝑃 is the part of the dielectric displacement , which is specifically attributed to
the reaction of the material under study

𝑃 = 𝐷 − 𝐷 0 = ( 𝜀 ∗ − 1 ) 𝜀 0 𝐸 with 𝜒 ∗ = ( 𝜀 ∗ − 1 )

(6.3)

where 𝜒 ∗ defines the die lectric susceptibilit y
In ge neral, the macroscopic Polarization 𝑃 is a y i eld of microscopic dipole moments 𝑝 𝑖 in
the volume V . S ince 𝑝 𝑖 could have a permanent o r i nduced cha racter. The latter is due to a
local field E loc , which dis turbs the neutral char ge distribution. For small field strengths, the
linear relation 𝑃 =  .E loc ; where  denotes the polarizabilit y. The polarization effects that
occur on very short time scales are induced polarization P ∞ , which are ty pi cally
I ) Electronic polarization : resonant process occu rring when the electron cloud of an atom
(or molecule) is shifted with respect to the positive nucleus.
II) Atomic polarization : This proc ess is observed when an agg lom eration of positi ve a nd
negative ions is deformed under the force of the applied field.
Additionally, due to the chemical structure, ma ny molecules carr y a permanent dipole
moment µ  . If there is onl y one t y pe of N permanent dipol es in the sy stem, with the mean
dipole moment 〈 µ  〉 , 𝑃 then reads

𝑃 = 1
𝑉 ∑ µ 𝑖 + 𝑝 ∞ = N/V 〈 µ 𝑖 〉 + 𝑃 ∞

(6.4)

where 𝜇 𝑖 defines the dipole moment of the re peating unit and N/V denotes the number
density of the dipoles involved in the time -dependent process present.
Assuming that the dipoles do not in teract with ea c h other (isolated dipoles) and the E loc ( at
the permeant dipoles) is equal to the outer electric field, one can derive th e contribution of
the orientational polarization originating from the electric field

7

-

9

as

Δ𝜀 = Δ𝜀 𝑠 − Δ𝜀 ∞ = 1
3𝜀 0 𝜇 2
𝑘 𝐵 𝑇 𝑁
𝑉

(6.5)

where 𝜀 𝑠 = lim
𝜔 →0 𝜀 ′ (𝜔 ) . 𝜀 ∞ = lim
𝜔 →∞ 𝜀 ′ ( 𝜔 ) covers all contributi ons to the dielec tric function ,
which are due to induced polarization P ∞ and Δ𝜀 is also called the die le ctric strength. 3

47
6.1.1.2. Die l ectric Relax ation
For small applied e lectric field strength, the dielectric relaxation theor y c an be described in
the framework of the linear re spons e theor y. In dielectric spectroscop y, the external electric
field E(t) corresponds to the perturbation, and th e polarization P (t ) is the response of the
system and they are linked together as follows, 1

𝑃 ( 𝑡 ) = 𝑃 ∞ + 𝜀 0 ∫ 𝜀 ( 𝑡 − 𝑡 ′ ) 𝑑𝐸 ( 𝑡 ′ )
𝑑 𝑡 ′
𝑡
−∞ 𝑑𝑡 ′

(6.6)

where 𝜀 (𝑡 ) is the time depende nt dielec tric function. Consequently, the ti me-dependent
dielectric function can be directl y measured as a response of the s ystem exposed to a step-
like change o f the external electric field 𝑑𝐸 ( 𝑡 )
𝑑𝑡 = 𝐸 0 𝛿 (𝑡 )  as shown in the figure 6.2. Thus,
according to equation 6 .6, the response of th e s y st em can be des cribed b y 𝜀 (𝑡 ) , where 𝜀 ( 𝑡 ) =
𝑃 ( 𝑡 ) −𝑃 ∞
𝐸 0 𝜀 0 .

48

0 20 40 60
0
1
2

orientational pol arization
Induced polarization
 =  S -  
 S
 
 (t)= ( P(t) - P  ) /  E  
Time

 E
E (t)

Figure 6 .2 . Schema tic represen tation of the pola rization, and the time -dep endent diele ctric relaxation
function (right panel) as well as the time dep endence o f the electric field ( inset ). R eproduced and adapted
from the reference [3] .

When the applied electric field is periodic in a stationar y state, the induc ed polariz ation from
equation 6.6. becomes

𝑃 ∗ ( 𝜔 ) = 𝜀 0 (𝜀 ∗ ( 𝜔 ) − 1)𝐸 ∗ ( 𝜔 )

(6.7)

where 𝜀 ∗ ( 𝜔 ) is related to 𝜀 ( 𝑡 ) with the following equation

𝜀 ∗ ( 𝜔 ) = 𝜀 ′ ( 𝜔 ) − 𝑖 𝜀 " ( 𝜔 ) = 𝜀 ∞ − ∫ 𝑑𝜀 (𝑡 )
𝑑𝑡 𝑒𝑥 𝑝 ( −𝑖𝜔 𝑡 ) 𝑑𝑡
∞
0 ,

(6.8)

49
6.1.1.3. A nal y s is of th e Dielectric Spe ctra
In principle, the anal y sis of the dielectric relax ation processes is usu all y done usin g model
functions. Starting with the theoreticall y we ll-fou nded Debye function, sev eral formulas for
both the freque nc y and ti me domain, which were suggested to des cribed the ex perimentally
observed dielectric spectra. Here, only the important approaches are discussed.
Deby e Beha vior
Debye relaxation is a theoretically well-grounded model for dielectric relaxation. I t assumes
that the change in polarization is proportional to its actual v alue. 9,

10

The time dependence of
a dielectric process, where 𝜏 𝐷 is the relaxation time of the process, is given as follows

𝑑𝑃 (𝑡 )
𝑑𝑡 = − 1
𝜏 𝐷 𝑃 (𝑡 )

(6.9)

This model was firstl y derived b y Deb ye, leading to a dielectric function i n the frequ ency
domain, which rea ds

𝜀 ∗ ( 𝜔 ) = 𝜀 ′ ( 𝜔 ) − 𝑖 𝜀 " ( 𝜔 ) = 𝜀 ∞ + ∆𝜀
1 + 𝑖𝜔 𝜏 𝐷

(6.10)

With real and imaginary parts, figure 6.3, given as

𝜀 ′ ( 𝜔 ) = 𝜀 ∞ + ∆𝜀
1 + (𝜔 𝜏 𝐷 ) 2
𝜀 ′′ ( 𝜔 ) = ∆ 𝜀𝜔 𝜏 𝐷
1 + ( 𝜔 𝜏 𝐷 ) 2

(6.11 a)

(6.11 b)

In the f requenc y domain, the real part shows a stepwise decrease, with increasing frequency,
while the imag inar y p art shows a symmetric loss peak. The maximal loss position provides
an information about the relaxation rate 𝑓 𝑝 = 𝜔 𝑝
2𝜋 or relaxation time 𝜏 𝐷 = 1
2𝜋𝑓 𝑝 = 1
𝜔 𝑝 . In
addition, the step hei ght of the r eal part of the relax ation process or the area under the loss
peak gives the dielectric streng th ∆𝜀 .

50

0
log (  /  p )
log  ''
 p = 2  f p

 
 S
 =  S -  
 ´

Figure 6.3. Frequency d ependence of the real part and th e im agina ry part of th e comp lex dielectric function
accordin g to the Deb ye functio n. Figure rep roduced from referen ce [ 5 ] .

6.1.1.4. Non-D eby e Behavior
In practice, the Deby e function is not sufficient to describe the experimental results obtained
from complex sy stems li ke amorphous pol y mers. I n most cases, the mea sured loss peaks
have a half width that is much broader than what is pred icted b y equation 6.10. Moreover,
their shapes are a s y mmetric with a high frequenc y tail. This is called non-Debye behavior.
The broadening of the s y mmetric relaxation peak i s described b y Cole/Col e (CC) function

11

𝜀 ∗ ( 𝜔 ) = 𝜀 ∞ + ∆𝜀
(1 + 𝑖𝜔 𝜏 𝐶𝐶 ) 𝛽

(6.12)

where 𝛽 va lue characterizes the s y mm etric broadening of the relaxation peaks withi n the
boundary conditions of (0< 𝛽 ≤1) and 𝜏 𝐶𝐶 is the characteristic relaxation time.
The relaxation peaks can also have an as y mmetric broadening, which can be described b y
the Cole/Davidson (CD) function

12

,

13

𝜀 ∗ ( 𝜔 ) = 𝜀 ∞ + ∆𝜀
(1 + 𝑖𝜔 𝜏 𝐶𝐷 ) γ

(6.13)

where 𝛾 value characterizes the as ymmetric broadening of the relaxation peaks within the
boundary conditions of (0< 𝛾 ≤1) and 𝜏 𝐶𝐷 is the characteristic relaxation time.

51
In general, most non-Deby e relaxation process es ca n be well described b y H avrilian/ Negami
(HN) function developed , which is the most g eneralized form of the Deb ye function, takin g
into account both the asymmetry a nd th e broadening of the peak.

𝜀 ∗ ( 𝜔 ) = 𝜀 ∞ + ∆𝜀
((1 + 𝑖𝜔 𝜏 𝐶𝐷 ) β ) 𝛾

(6.14)

where and 𝜏 𝐻𝑁 is the cha racteristic relaxation time. The fractional shape par ameters 𝛽 and
 (0 < 𝛽 , 𝛽  ≤ 1) determine the devi ation from the Deb ye function. Their effect on the
dielectric r elaxation spectra is illustrated in figure 6.4. From the ex perimental point of view,
all of the re levant parameters, such as dielectri c streng th, re laxation time and the shap e
parameters ca n be estimated b y fitt ing the HN function to the obtained data. 16

-4 -2 0 2 4
-4
-2
0
1.2
1.6
2.0
1.2
1.6
2.0
-4 -2 0 2 4
-4
-2
0
 '' ~  
 '' ~  - 

log (  HN )

 '
A
 '' ~  
 HN =1.0
 HN =0.8
 HN =0.6
 HN =0.4
 HN =0.2
 '
D

C
 HN =1.0
 HN =0.8
 HN =0.6
 HN =0.4
 HN =0.2
B

log  ''
 '' ~  - 
log  ''
log (  HN )

Figure 6 .4 . Complex dielectric permittivity fo r the HN-function with fixed β =1 and γ =1 a nd decreasing till
before 0 (0< β , βγ =<1 .). Figure was taken and adap ted from reference [ 5 ] .

6.1.1.5. Fitt i ng HN Func t ion to Experimenta l Data
From the experimental po int of view, the di electric spectra of a complex s y st em do not show
isolated loss peaks. In addition to the relaxation process es (one or more could be
dielectrica ll y active), other parasitic cont ributions are often observed, such as the

52
conductivity contributio ns due to the conductivity of the elect rode. The conductivity
contribution to the dielectric loss can be described as ε ´´ = σ/(ω s ε 0 ) , where σ is connected to
the DC conductivity , s is a parameter to model non-Ohmic effects, s = 1 for Ohmic contacts,
and s<1 holds for a non -Ohmic beh avior. It is worth to note that t he condu ctivit y
contribution is taken int o account during the data anal y sis , in addition to the relaxation
processes, which can be well-described by the HN -function. For bulk samples, t he following
equation was obtained for the whole fit function 5

0
* * ) (
 

  
s
HN F it i  

(6.15)

6.1.2. Specific Heat Spectroscop y
In the frame work of the LRT, 1,2 analog ousl y to B DS, in Specific Heat Spectrosc op y (SHS)
the complex he at capacity function can be regarded as the response of the sy stem to an
external periodic disturbance (te mpe rature modul ations), figure 6.1.
6.1.2.1. Comp lex Heat Cap acity
Many thermal processes are related to the time -de pendent entrop y/enthalpy changes, e.g.
glass transition. If the applied disturbance is also t ime-dependent and adequatel y small , the
resultant time -de pend ent heat capacity C(t) can b e considered as the response of the s y stem,
within the framework of the linear response theory .

14

The time depende nt enthalp y and temperature is described as follows

𝜕𝐻 ( 𝑡 ) = ∫ 𝑑𝐶 (𝑡 − 𝑡 ′ )
𝑑𝑡
𝑡
−∞ 𝜕𝑇 (𝑡 ′ ) 𝑑 𝑡 ′

(6.16)

If this equation is then Fourier tra nsfo rmed, it would yield

𝐻 ( 𝜔 ) = 𝐶 ∗ ( 𝜔 ) 𝑇 (𝜔 )

(6.17)

where 𝐶 ∗ ( 𝜔 ) = 𝐶 ′ ( 𝜔 ) − 𝑖 𝐶 " ( 𝜔 ) , with a real and imaginary part.
The time- dependent complex heat capacity C* (ω) could then be related to a time -depe ndent
relaxation process,

15

as

𝐶 ∗ ( 𝜔 ) = 𝐶 ∞ + 𝑖𝜔 ∫ 𝑑𝐶 (𝑡 )
𝑑𝑡 𝑒𝑥 𝑝 ( −𝑖 𝜔𝑡 ) 𝑑𝑡
𝑡
0

(6.18)

53
6.1.2.2. Di f ferentia l A C- Chip Calori metry
The basic principle of this method is based on utilizing a commerc iall y av ailable AC -chip
calorimeter in a different ial set-up, which result i n a boost in the sensitivity b y two orders
of magnitude. B y appl y ing an alternating cur rent (AC) with frequenc y ν , throug h a small
heating area, where the sy s tem under investi gation is placed , a small periodic hea t flow with
freque nc y ω is measured, where ω = 2 ν .
For the differential AC-C hip calorimetry, calorimetric chip XEN 39390 (Xensor I nte gration,
NI) was used as measuring cell, see figure 6.5. I t has optimized heater and thermometer on
a sub-micrometer -thick s ilicon nitride membra ne, which dramaticall y reduces the addenda
heat capacity, allowing accurate measurements of ng samples. Th e sen sor h as a heater
located in the center of a freestanding thi n silicon nitride membrane (thickness 1 µm)
supported b y a Si-fr ame with a window. It has a theoretical heated hot spot area of about 30
x 30 µm 2 , with an integrated 6-couple thermopiles and two-four-wire h eaters (bias and guard
heater), as shown in r eference [

16

]. Please note that in addition to the 30 x 30 µm 2 hot spot,
the heater strips also contribute to the heated area. A SiO 2 la yer with a thickness of 0.5 - 1
µm protects the heaters and thermopiles. The thi n films are spin coated over the whole
sensor, but only the smal l heated ar ea is sensed, th us considered as a point heat sourc e. For
further de tails, the reader is referred to references [

17

-

20

].

Figure 6.5 . Pictures of ( left ) XEN 39390A C-ch ip sensor ( middle ) Silicon nitride membra ne fixed on a
rectangu lar silicon e substrate. Pictures were a dapted from reference [5] ( right ) SEM images of the 30
X 30 µm 2 heating area.

In the di fferential approach to AC -chip calorimetry , the contribution of the heat capacity of
the empt y s ensor to the measured si gnal is mi nimi zed. This approach boosts t he sensitivit y
of the measurement to reach pJ /K . In the approximation of thin films (submicron), the heat
capacity of the sample C S is then given by

21

,

22

(6.19)

0 0
2 / ) ( SP U U C i C S    


54
where  is the an gular f requenc y . describes the eff ective heat capacity of
the empt y sensor (C 0 – heat capacity of the sensor; G/i  is the heat loss through the
surrounding atmosphere), S is the sensitivity of the thermopile, P 0 is the applied heatin g
power, and ∆U is the complex diffe rential therm opile signal for an empt y refere n ce sensor
and a chip with a sample, where ∆U 0 is the complex differe ntial voltage measured for two
empty s ensors. A more detailed description of the ca lorimetric chip, its di ffere ntial s etup
and the ex perimental method can be found in refere nc e [ 21]. Absolute values of the hea t
capacity can be obtained b y calibration procedures . 22
6.2. Method s and Exp e rimental T ech niques
6.2.1. Broadband Dielectric Spectroscopy ( BDS )
The dielectric prop erties of samples were measured by a high-resolution ALPHA analyzer
(Novocontrol) in cluding a sample hold er with an a ctive head. Diele ctric m easurements wer e
carr ied out, employing a small sinusoidal changing electric fi eld, where the voltag e is in the
linear reg ime for all film thicknesses (0.1 V), in a broad frequency range (10 -2 -10 7 Hz). A
Quatro cr yosystem (No vocontrol) was int erfaced to the c r y ostat to control the sam ple
temperature with a temp erature stabilit y better than 0.1 K. The impenden ce 𝑍 ∗ (𝜔 ) of the
sample wa s mea sured, which is dire ctly related to the complex dielectric f unction with the
following equation

𝜀 ∗ ( 𝜔 ) = 1
𝑖𝜔 𝑍 ∗ ( 𝜔 )𝐶 0

(6.20)

where C 0 is the capacitance of an empt y capacitor . C 0 for a parallel plate capacitor with a
dielectric material in between can be represented as

𝐶 0 = 𝜀 0 𝜖 𝑟 𝐴
𝑑

(6.21)

where A is the area of t he cap acitor (area between the two electrode plates) and d is the
distance b etween the two electrodes. I t is also impo rtant to note that all samples were purged
with dr y nitro gen durin g the course of the m easurement. For more experimental details the
reader is referred to ref [5 ].
6.2.2. Specific Heat Spectroscopy (SHS)
SHS was emplo ye d utilizing differential AC chip calori metry. The experiments were carried
out in the temperature scan mode, which means that the frequenc y was in creased step-wise ,


i G C C /
0  

55
while the temper ature was ramped throu ghout the whole temperature ran ge , for ever y
freque nc y st ep. To ensure stationary conditions during the measurement, the scanning rate
was varied in the ra n ge fr om 1 K/min to 2.0 K/min , depending on the programmed
freque nc y. The po wer fo r temperature modulation was kept const ant at abo ut 25 µ W . This
value ensures that the maximum amplitude of the temperature oscillation is smaller than
0.25 K and so the re sponse takes place in the linear regime.
It is worth to n ote that b efore th e measurement, the PT-100 of the th ermostat chamber w as
calibrated b y measurin g the phase transition temperatures for five diff erent calibration
substances, covering the whole temperature range o f the calorimeter (173 -573 K). The
calibration equation obtained was then used to c orrect all the collec ted temperature data.
Due to the lag betw een the cry ostat temperature and the temperature at the chip m embrane,
an additional tempe rature c orrection was a ppli ed to the collected data. With the assumption
of symmetric conditions for heating and c ooli ng, the temperature lag w as determined as  T,
with the 2  T, being the tempe rature difference for same resistance at heating and cooling at
the same ra te [

23

].
6.2.3. Differential Scanning Calorimetr y (D SC)
The glass tr ansition temperature of all bulk samples were d etermined b y DSC .
Measurements were carried out on a Seiko Instrument DSC 220C attached to a liquid -
nitroge n cooling s y stem. All measurements were run at heating/cooling rate of 10 K/min,
with nitrogen a s the purging gas. The glass tra nsition temperature of the samples was taken
as the inflection point of the heat flow of the second heating run.
6.2.4. Ellipsometry
Ellipsometry is an optical technique for investigating the dielectric properties (complex
refractive index also related to the dielectric function) of thin films. Ellipsometry measures
the change of polarization upon reflection or transmission and compares it to a model.
The measured si gnal is the change in polarization of the incident be am, in a k nown polarized
state, a fter it intera cts (e.g. reflected, absorbe d, e tc.) with the structure of the materia l under
investigation. The polarization change is quantified by th e amplitude ratio, Ψ, and the phase
differe nce, Δ.
Upon the anal y sis of the change in polarization of lig ht, given the right model, the thickness
of the thin fil ms can be estimated with gre at accurac y . I n thi s work, the analy sis model
employe d a simplified multila y er model, consisting of air/polymer film/ SiO 2 /Si-substrate.

56
To reduce the number of free fit parameters, the thickness of the natural SiO 2 la y er was
determined and this value (1.7 nm) was kept constant during the data anal ysis of the pol y m er
film.
Furthermore, for a pol y mer thin film, if the tempe rature is ramped during the mea surement,
the temperature dep endence of the thickness (relat ed to the thermal expansion coefficient of
the film) can be determined. At 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , the temperature dep en dence of the th ickness
changes. 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 is defined as the intersection of the li near dependencies o f the thickness in
the supercooled and glassy regimes in ac co rdance with lit era ture procedure s.

24

During the course o f thi s work, two ellipsometry machines we re used, whi ch are discuss ed
below. The lase r ellipsometry was used to measure 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of thin films in the ran ge of 0 K
< 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 < 373 K. Howe ver, for films with lowe r 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 , a spectroscopic e llipsometer
allowing measure ments in the temperature range of 173 K - 373 K was utilized.
Laser Ellipso metry
To measure the film thi ckness as well as 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of thin films , an ellipsometer with p olarizer-
compensator sample analyzer (PC SA) (Op trel Gb R, Sinzing, Germany) was utilized. This
ellipsometer has a laser light with an average wavelength λ = 632.8 nm. The samples were
measured at a set angle of incidence of 70 degre es . The analy sis of the raw data was done
employing the a bov e-menti oned analy sis model.
For the temperature measurements, the films were mounted onto a he ating stage in ambient
atmosphere. Water was used as the heating liqui d, hence the limited hea ting/cooling range
of 0 K < 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 < 373 K, while the heating/cooling rate was fixed to 1 K/mi n.
Spectroscopic Ellipsometry
Secondly , the spe ctroscopic ellipsometer used is this work was M-2000 VI , J. A. W ollam .
The raw ellipsometric angles Ψ and Δ data were fitted to a Cauch y mod el (n (λ) =A + B/λ 2
+ C/λ 4 , K ≅ 0). Where n and K are the real and imaginar y p arts of the compl ex index of
refraction. For 10 nm (±1 nm) films , B was also fix ed to 0 due to the short path length of
the light passing through the sample and reduced resol ution. The anal y sis of the
measurements e mplo ye d the mult ilaye r model discussed above.
For the temperature mea surements, the films were mount ed onto a he ating sta ge, inside a
chamber, connected to a liquid nitrogen cooling system interfaced with the ellips ometer.
The closed chamber with the heating sta ge was purged with dry nitrogen ga s throug hout the
experiment. The heating/cooling r ate was fix ed to1 K/min.

57
6.2.5 . A tomic Force Microscopy
Atomic forces microscopy (A FM) - C y pher (As y l um Research, Santa Barb ara, CA, USA,
Silicon cantileve rs with a r eflective co ating of aluminum (AC160TS, Ox ford I nstruments)
were used to control th e qualit y , topograph y an d thickness of the film. In ge neral, the
thickness of the films we re determined b y estimating the step height of a scratch across the
film. For all films considered here in thi s work, AFM pictures showed low roughness and
no dewettin g, down to th e lowest film thicknesses. I t is worth to note that the thicknesses
were further confirmed by ellipsometr y.
6.2.6. Contact A ngle Measure ments (CA M)
The measurements w ere carried out usin g th e a utomated contact angle system OCA20
(Dataphysics, German y ), equipped with halogen lamps to ensure a homogeneous back
lighting , a six -fold power zoom lens and a CCD camera. The contact angle (CA) was
determined usin g the tang ent fitting method. The used test liquids were Gl y ce rol, n -
hexadecane , n-tetradecane, and polyeth y l ene gly c ol with a mol ecular weight of 200 g/mol .
The measurements were carried out in an atmosphere saturated b y the vapor of the test
liquid. To insure the complete saturation of the atmosphere , samples were place in cuvette
with the test liquid for 15 mi ns prior to the measurements. 3 drops with a volume of 4 μl
were dropped onto the surface of a w ell-annealed 200 nm thi ck pol y mer film. Mean c onta ct
ang les were calculated from averaging the an gles of both sides o f the drop over 10 minutes.
The data f or SiO 2 and AlO x were taken from references [

25

and

26

], respectively .
6.2.7 . X -ray P hotoelectron Spectroscopy (XPS)
XPS investigations were carried out with an ESC AL AB 220iX L (ThermoFisher) using
monochromatic Al K α radiation (1486.6 eV). The samples were fix ed with a double
adhesive Carbon tape on a stainless stee l sample holder. The peaks we re fitted b y
Gaussian−Lorentz ian curves after Shirley background subtraction. The electron bindin g
energy was referenced to the Ti 2p3/2 peak of TiO 2 at 458.8 eV. The areas of the peaks were
determined from the Gaussi an−Lore ntzian fits and divided by the element-specific Scofield
factor and the analy s ator- depending transmission function.
6.3. Sample Preparation

58
6.3.1. Materials
The g lass tra nsition and glassy d y namics of different homopolymer s and th eir blends in the
thin film geometr y was investiga ted b y the different characterization methods, discussed
above. The mate rials use d in this work described in the following subsectio ns. The chemical
structure of all the homopol y mers used ar e giv en in figure 6.6, as well as their DSC
thermograms are shown in figure 6.7 and its inset.

Figure 6.6. Chemical structu re of ( left ) Poly (2 vin yl pyridin e) (P2VP) ( middle ) poly(vinyl meth yl
ether)(PVME ) ( right ) po lystyrene (PS).

200 250 300 350 400 450
360 380 400 420
PVME/PS
25/75wt%
Exotherm

PVME/PS
50/50wt%
PS
PVME
Heat Flow [a.u.]
T [K]
Heat Flow [a.u.]
T [K]
P2VP

Figure 6 .7 . DS C Thermog rams (second heating run; rate : 10 K/min) fo r PV ME – d ash ed, PS -dashed
dotted , PVME/P S 50:5 0 wt% - red solid , and P VME/PS 25: 75 wt% - blue solid . Inset : D SC thermog rams
of P2V P – Purple solid line.

6.3.1.1. Poly (2 Viny l Pyri dine) (P2VP)
P2VP was purchased from Pol y mer Standards Services GmbH (Germany) with a M w of
1020 kg /m ol and a pol y dispersit y index (PDI) of 1.33. 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 was found to be 373 K,
estimated b y DSC. Chloroform (≥ 99.9%) was use d as a solvent to prepare a master polymer

59
solution. This solution was further dil uted b y Chloroform to pre par e different
co ncentrations, used to attune the films thicknesses.
6.3.1.2. Poly (Vinyl Methy l Ether) ( PVME)
PVME was purchased (Aldrich, Inc.) as an aqueous solution (50 wt% ) with a M w of 10
kg/mol, which is lower than the entanglement M w , a nd a PDI of 3. To obtain the d ried
PVME, the aqueous pol ymer solution was dried a nd annealed in an oil free vacuum for 72
h at 303 K, then for another 96 h at 323 K. 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of the dried PVME was estimated by DSC
and found to be 246 K. A conc entrated solution of the drie d PVME in tol uene was prepared
as a master solution. This solution was further dil uted b y Toluene to p repare different
concentrations, used to attune the films thicknesses.
6.3.1.3. Poly styrene (PS)
PS was purchased from Aldrich I nc. with a M w of 524 kg/mol and a P DI of 1.04. 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of
the bulk PS estimated by DSC, was found to be to be 376 K.
6.3.1.4. PVME/PS Blend
A concentrated pol ymer solution of the dried P VME and PS with the weight ratio of the
polymer s o f 50:50 wt% and 25:75 wt% was pr epared as master solut ion using toluene. A
bulk film was prepared by castin g from the master solution. This solution was further diluted
by Toluene to prepare different concentrations, used to attune the films thicknesses. The
films were then dried and annealed in an oil f ree va cuum for 72 h at 313 K, then for another
96 h at 343 K. The 𝑇 𝑔 𝑡ℎ 𝑒𝑟𝑚 of th e bulk materials w ere det ermined b y DSC to be 273 K and
293 K for the 50:50 wt% and 25:75 wt% blends, respective ly.
6.3.2. Sample Preparation
6.3.2.1. Spin Coating
In t his work, all thin polymer fil ms were pre pared by spin -coating (SPI N150, SPS-Europe). The
spin coater was placed i n a laminar flow box during the sample preparation to avoid a ny possible
contamination. Attuned film thickness es were prepared from vary in g conc entrations of the
solution, after filtration (Minipore, 0.2 µm). Meanwhile, both rotation speed and time (3000
rpm, 60 s) were kept constant. It is worth to note that spin coating is an eff icient approach to
form unif orm thin polymer films, with well-controll e d thicknesses.

60
6.3.2.2 A nnealing
After the spin coating p roc ess, the samples w ere annealed at temperatures T ann > T g,Bu lk for
time t ann . Table 6.1 il lustrates the annealing conditions for all the samples prepared in this
work. This annealing procedure insures two main points: I) the removal of the solvent, II )
the relea se of the induced stress during spin coating.

27

Table 6. 1. 𝑇 𝑔 𝑡ℎ𝑒𝑟𝑚 measured by DSC an d ann ealing co ndition - temperatures (T ann ) an d time (t ann ) emp loyed
for all po lymer thin films mea sured in th is work.

Polymers

𝐓 𝐠 𝐭𝐡𝐞𝐫𝐦 [K]

T ann [K]

t ann [hr]

P2VP

373

398

48

PVME

246

313

72

PS

376

423

72

PVME/PS 50:5 0 wt%

273

323

72

PVME/PS 25:7 5 wt%

293

338

72

6.3.2.3 P lasma Oven
The surfac e of all the Silicon wafers and AC -chi p sensors (explained below) used in this
work were activated, except for the work don e on thin films of P2VP. Sam ples we re placed
in a plasma oven in a pure ox yge n atmosphere (20 W, 300 sec). This p rocess insures the
removal of an y organic c ontaminations and further activate the na tural silica. I t is important
to note that this process wa s the main cleaning proce dure for the AC-chip sensors, whereas,
for the silicon wafers, it was a step within a longer clea nin g protocol, as discussed below.
6.3.2.4. Solv ent Leaching (Guiselin brushes experimen ts)
Prepara tion of the irreversibl y adsorbed layer (PVME, PS, PVME/PS blends) wa s done
employing solvent-leaching experiments. Toluene was used as the leaching- solvent, for all
samples. First, all samples we re dipped into separate toluen e baths for 20 mins. This was
then followed b y a two -step proc ess I) resining with toluene II) fast dr y in g wi th dry nitrogen.
Finally , the sample s were anne aled fo r 20 mins at T = T g + 50 K. For a more detailed
explanation, the reader is referre d to reference [

28

]. The y i elded adso rbed la yers were then
checked by AFM, where no sign of dewetting was observe d. Th e thickness of this lay er was
found to be ca. 4 nm for PVME and PVME/PS blend, wherea s it was found to be ca. 9 nm
for PS.

61
6 .3.2.4. Broad band D i electric Spe ctroscopy
6 .3.2.4.1. Bulk Sample
Bulk sample was prepared by melting the pol y mer on a gold plated brass elec trode. The
thickness was controlled by emplo ying fused silica spacers with fixed diamete r of 50 μ m.
After that, the pol y m er was covered with a smaller top gold electrode. A rea of the molten
polymer on the bottom elec trode has to b e la rger than the upp er electrode t o avoid air gaps
between the capacitor pla tes. A schematic re presentation of the bulk sample is shown in the
figure 6 .8.

Figure 6 .8 . Schema tic of a bulk sample capp ed between two go ld plated electrodes with 5 0µm fused silica
spac ers.
6 .3 .2.4.2. Cro ssed Ele ctrod es Capacitors
In this work, Crossed Electrodes Capacitors (CEC) were used to measure thin films A
schematic r epresentation of a CEC is given in figure 6 .9. H ere, th e pol y mer film is capped
between two thin aluminum electrode s. Glass sub strates (10 x 10 mm) were cleaned in an
ultrasonic alkaline bath a t 333 K for 15 min. Subsequently , glass subst rates were washed
with ultrahig h purified w ater (Millipore, resistivity > 18 MΩ/cm ), rinsed with acetone and
dried in an inert gas flow. First, an aluminum electrode (2 mm width, ca. 60 nm thickness)
was deposited on the glass substrate via ther mal evaporation in ultrahigh vacuum (10 − 5
mbar). To minimize the risk of c reating electrical shortcuts, a so - called flash evaporation
was emplo y ed (> 30 n m/s), which allows for a smooth and defined metal/pol y mer
int erface. 29 , 30 After spin - coating and annea li ng of the film, the second aluminum strip w a s
evapora ted perpendicularl y to the bottom electrode. This means that the capacitor was at the
cross - section of the two strips.

62

Figure 6 .9 . Schematic representation of a Crossed Electrodes Ca pacitor samp le.

6.3.2.4.3. Nanost ructured Capacitors
In the case of Nanostructured Capacitors (NSC),

31

both electrodes consist of highly doped
conductive silicon wafers with a sp ecific resistance  < 0.003 Ωcm and 0.23 nm rou ghness
of RMS. On the backside of the electrodes a 200 nm Al -electrode w as deposi ted. Bottom
electrode additionall y consis ts of a native ox ide layer of ca. 2 nm. The sizes of the electrodes
are 4 x 10 mm and 1 x 1 mm for the bottom and top electrode , respectivel y . The top electrode
consists of an arra y o f hi ghl y insulating silica spa cers with the h eight of 3 5 or 70 nm and a
cross-section of 5 x 5 µm and a fix ed separation. Figure 6.10 represents a schematic of the
NSC and an AFM image of the top nanostructured electrode . The preparation of thi n films
was carried out as follows . Silicon wafers were initiall y rinsed with acetone to remove the
photoresist lay er and dried with an inert gas flow (N 2 ). S ubsequently , th e substrates were
cleane d and activated in O 2 plasma , as discussed above. As a final stage of the wafers
cleaning, a snow jet g un was used (30 Gunjet Spray in g S ystems CO., Wheaton, USA),
which pur ge s supe r critical C O 2 through a nozzle, generating a jet flow of CO 2 . This
procedure w as don e while heating the substr ate, t o insure th e subli mation of the solid CO 2
into gas, and thus polishing the surface with CO 2 solid particles and removing of an y
contaminating particles.
Pol y mer films were spi n -coated on a these thoroughl y cl eaned bottom electrodes and
thermally annealed as d escribed in th e section 6.3.2.2. I n the last step, the top electrode was
assembled on the counter planar wafer. 31
In this sample geometry , thin films remain in contact with air, a llowing polymer/air
interaction at the free surface. It is important to note that the spacer heights must be ca. twice
as lar ge as the film thickness, to allow a free surface, even in the case spa cers sinking i nto
the film.

63

Fig ure 6 .10 . AFM picture of the top electrode with 70nm spacers (up per panel), side view schematic of the
nano structured capa citor (bottom p anel) .
6 .3.2.5. A C- Chip Calorimetry
AC -C hip sensors were c leaned b y exposing them to ox y gen plasm a , see section 6 .3.2.3.
Afterwards, poly me r solutions were spin coated and annealed according to the protocol
described in sections 6 .3.2.1 and 6 .3.2.2. Thickn ess of the films could n ot be mea sured
directly on the sensor, d ue to the siz e li mitations. Therefore, spin coated films (pr epared
under identical conditions) on silicon substrates with sim ilar surface properties to the sensor
were used to estimate the film thicknesses by ellipsometr y and/or AFM.

64
References

1

Landau, L. D,; Lifschitz, E. M., Course of Theoretical P hysics, vol. 5. Statis tical Ph ysics. Akade mie-
Verlag: Berlin, 1979 .

2

Kubo, R. Reports on Progress in Ph ysics 1966, 29, 255.

3

Sch ö nhals, A.; Kre mer, F. B roadband Dielec tric Measure ment Techniques and Theo ry of Dielectric
Relaxation. In B roadb and Dielectr ic Spectr oscopy; Kr emer, F.; Sch ö nhals, A ., Ed s.; 1 st ed ; S pringer : B erlin,
2002 ; 01- 34.

4

Sch ö nhals, A.; Kre mer, F. Br oadband Dielectric Measure ment Techniques. In B roadb and Dielectric
Spectrosco py; Kremer, F.; Sch ö n hals, A., Eds.; 1 st ed ; Springer : B erlin, 2002 ; 35 - 57 .

5

Sch ö nhals, A.; Kremer, F. Analysis of D ielectric Spec tra I n B roadb and Dielectric Spectrosco py; Kre mer,
F.; Sch ö nhals, A., Eds.; Spring er , Ber lin, 2002 ; 59 - 96 .

6

Sch ö nhals, A.; Kre mer, F. T he Scaling of t he Dynamics o f Glasse s and Super cooled Liquids. In
Broadband Dielectric Spectr oscopy; Kremer, F.; Sch ö nhals, A., Ed s.; Sp ringer , B erlin, 20 02 , 99 -127.

7

Kirkwood, J. G. The Jou rnal of Chemical Physics 1939 , 7, 911 - 919.

8

Kirkwood, J. G. Annals of the New York Aca demy of S ciences 1940, 40, 315 -320.

9

Fröhlich, H., T heory of dielectrics: d ielectric co nstant and d ielectric loss. 2d ed.; Clarend on Press: Oxford ,
1958 .

10

Debye, P. J . W., Polar mo lecules . T he Chemical Catalog C ompany, I nc.: Ne w York, 1929 .

11

Cole, K. S.; Co le, R. H. T he Journal of Chemical P hysics 1941 , 9, 341- 351 .

12

Davidson, D. W. ; Cole, R. H. The Jo urnal of Chemica l Physics 1950, 1 8, 1417-1417.

13

Davidson, D. W. ; Cole, R. H. The Jo urnal of Chemica l Physics 1951, 1 9, 1484-1490.

14

H. Y in, S. Madkour and A. Schönhals, Glass transitio n of ul tra -thin pol ym er films: A co mbination of
relaxation spectro scop y with surface analytics i n Dynamics in co nfinemen t: Pr ogr ess in Dielectrics, Kre mer ,
F . (Ed.) Springer , Berlin 2 014 , pp1 7- 59

15

Haase, R., T hermodynamics o f irreversible pro cesses. Dover : New York, 1990 .

16

van Her waade n, S.; Applicatio n note for Xsensor ’ s ca lorimeter chips o f XE N -39390 ser ies
http://www . xensor .nl/pdffiles/sheets/nanogas3 939. pdf

17

Huth, H.; Minakov, A . A.; Ser ghei, A.; Kre mer, F.; Schic k, C. The Eu ropea n Physica l Jou rnal Special
Topics 2007 , 141, 153 - 160.

18

Efrem ov, M. Y.; Warren, J. T.; Olson, E. A.; Zhang, M.; Kwan, A. T.; A llen, L. H. Macromo lecules 2002,
35, 148 1-1483.

19

Yin, H.; Sc hönhals, A. Soft M atter 2012 , 8, 9132 -9139.

20

Madkour, S.; Yin, H.; F üllbra ndt, M.; Schön hals, A. Soft Ma tter 2015 , 11, 7942- 7952.

21

H. Huth, A . Mina kov and C. Schic k, J. Polym. Sci. B: Polym. Phys . 2 006 , 44, 299 6-3005 .

22

D.S. Zhou, H. Hut h, Y . Gao, G. Xue and C. Sc hick, Macr omo lecules, 2008 , 41,7662 -7666.

23

Huth, H.; Schic k, C. Perso nal Commu nicatio n .

24

Glor, R.; Co mposto, J.; Fakhr aai, Z. Macromo lecules , 2015 , 48 , 6682 – 6689 .

25

Madkour, S.; Yin, H.; F üllbra ndt, M.; Schön hals, A. Soft Ma tter 2015 , 11, 7942- 7952 .

26

Yin, H.; Napo litano, S.; Sc hönhals, A. Macromolecu les 2012 , 4 5, 1652 -1662.

27

Reiter, G.; Hamieh, M.; Damm an, P.; Sclavon s, S.; Gabriele, S.; Vilm i n, T.; Raphael, E. Nat. Mater . 2 005,
4 , 754- 758.

28

Napolitano, S.; Wubbenhorst, M. Natu re Communica tions 201 1 , 2, 260 .

29

Amarandei , G.; Clancy, I.; O’Dwyer, C.; Arshak, A.; Corco ran, D. ACS A ppl. Mater. In terface s 2014 , 6,
20758- 20766.

30

Zaporoj tchenko, V.; Strunsk us, T .; Erichsen, J.; Faupel, F. Macromo lecules 2001 , 34 , 1125 – 1127 .

31

T ress, M.; Mapesa, E.; Kossack, W .; Kipnusu , W.; Reiche, M.; Kremer, F. Science 2013 , 341 , 1371−1374.

65
CH A P TER 7 - C alorimetric Evidence f or a Mo bile Surface
La y er in Ultra thin P ol y m eric Fi lms: P ol y(2- v in y l p yridine)
This chapter is reproduced b y permiss ion of The Royal Society of Chemistr y from
(Madkour, S.; Yin, H.; Füllbrandt, M.; Schönhals , A. Calorimetric Eviden ce for A Mobile
Surface Layer in Ultrathin Polymeric Films: Poly(2-vinyl pyridine). Soft Matter 2015, 11,
7942-7952. DOI:10.1039/C5SM01558H). Cop yright (2015) R o y al Ch emical S ociety
(RCS).
DOI: http://dx.doi.org/10.1039/C5SM01558H

A bstract
Specific heat spe ctroscopy was us ed to study the dynamic glass transition of ultrathin
poly(2- vin yl p yridine) films (thic knesses: 405 - 10 nm). The amplitude and the phase angle
of the differential voltage were obtained as a measure of the c omplex heat capacity. I n a
traditional data analysis, the dynamic g lass transition tempera ture T g is estimated from the
phase angle. These data showed no thickness dep endenc y on T g down to 22 nm (err o r of the
measurement of  3 K). A derivative-based meth od was established, evide ncing a decrease
in T g with decre asing thickness up to 7 K, which can be explained by a su rface la yer. For
ultrathin films, data showed broadening at the lowe r tempe rature side of the spectra,
supporting the ex istence of a surface la yer. Finall y, tempe rature dependence o f the hea t
capacity in the glass y and liquid states chan ges with film thickness, which can be considered
as a confinement effec t.

66
7.1 Introduction
The characterization of the glass transition temperature, T g , of ultrathin pol ymer films has
been of g r eat interest due to their numerous applications in fields li ke coatings, membranes,
and innovative organic electronics. Scientifically, ultrathin films provide ideal sample
ge ometr y for stud y ing the confin ement effects on the glass transition of p olymers; as film
thicknesses c an be easil y tun ed b y spin coating .

1

Genera ll y, g lass transition is a topic al
problem of soft matter research (see fo r inst ance [

2

-

7

]). I nvestigations on highl y confined
systems may h elp to evidence the ex isting of a d y namical length scale

8

corresponding to the
glass tra nsition, which is difficult to measure b y other approaches.
Since the pioneering work of Keddie et al.,

9

,

10

the thickness dependence of the glas s
transition temperature h as been controversiall y discussed in the literature. For the same
polymer /substrate s ystems, divergent results have be en published. I n a recent perspective
discussion b y Ediger et al. ,

11

the pro gre ss mad e in the last years was disc ussed (see for
instance [

12

-

20

]). For pol ymers supported b y a non - attractive substrate (see for instance
[10,

21

-

27

]) a de pression of the thermal g lass tra nsition tempera tur e T g with decreasing film
thickness is widel y observed. This T g dep ression is discussed to originate as a result of a
free pol y mer/air surface having a higher mol ecular mobili ty than the bulk due to missing
polymer-poly mer s egment interactions and also due to structur al differ ences . 19 , 23 Recently,
optical photobleaching experiments, 22 ,

28

as well as the e mbedding of gold nanospheres into
a polymer surface ,

29

,

30

provided some evidence for a highl y mobile surface la y er.
For pol y mers having a strong int eraction with t he substrate, T g ma y in crease with the
reduction of the film thickness.

31

-

33

These experime ntal results were explained b y the
formation of an adsorbed boundary la yer, in which the pol y mer segments have a lower
molecular mobilit y ; hen ce a higher glass transitio n temperature.

34

For that reason, attempt s
are made to correlate de pression or increase of the glass transition tempera tur e with the
interaction energ y betwe en the surf ace of the subs trate and the pol ymer  SP .

35

A depression
of T g should be observe d for values of  SP smaller than a critica l value  c , bec ause the
influence of the mobile s urface la yer should be do minant in thi s case. For  SP >  c the reduced
mobilit y layer at the substrate will dominate a nd a n incre ase of T g should be e xpected. This
concept was criticall y considered b y Tsui et al. ,

36

with the conclusion that the interaction
energy between the pol y m er s egments and the surface of the substrate is not the onl y
relevant pa rameter. Also the packing of the segments at the interfac e mi ght play a rol e. In
ge neral, no co rrelation between  SP and the change of T g with the film thi ckness was found. 7

67
Nowadays, the re is growing cons ensus that the T g shifts observed in ultrathin films
compared to the bulk are re lated to the combined influence o f the fre e surfa ce (pol ymer-air)
and the polymer-substrate interfacial interaction. 19 Even though the fre e surface is assumed
to speed up the seg mental dynamics, at temper atures near T g , the effect of the pol y m er-
substrate interaction ca n either increase or decrease the dyna mi cs, a nd consequently the
relaxation times of the adjac ent pol y m er segments.
Generally , ther e a re two d ifferent experim ental approaches to investi gate the glass tr ansition
of ultrathin pol y mer fil ms. I n the first appro ach (also called static e xperiments), the
temperature is ramped and a thermod y namic propert y (or an associated quantity) is
measured. A c hange in the temperature dependence of this quantity is interpreted as the rmal
glass transition, where a corresponding thermal glass transition temperature (T g ) can be
extracted. Examples for these methods are elli psometr y, 10 , 23 DSC 43 or Flash DSC , 26
fluoresce nce spectroscopy ,

37

dielec tric ex pansion d il atometry , 12 , 32 or X-ray reflectivity,

38

just to mention a few. I n the second approach, techniques that directl y explore the seg ment al
mobilit y , like diele ctric (see for instance [19, 32,33]) or specific hea t spectroscop y 27 ,

39

-

42

have been emplo y ed. In these cases, a d ynamic glass transition temperature is measured
which is hi gher than the thermal one. So far, all investigations carried out b y specific heat
spectroscopy did not show a thickness dependence of the dynamic glass transition
temperature, even in cases where sim ultaneous dilatometric experiments evidenced a
decrease o f the thermal g l ass transition temperature .

43

A possible reason for that is discussed
in reference [ 19]. Moreover by emplo y ing co oling rate dependent ex periments like
ellipsometric, 23 , 25 photoblea chin g 22 or Flash DSC 26 experiments it was evidenc ed that there
is a limiti ng cooling for the depression of the thermal T g . For instance, for polystyre ne the
value of this limiting cooling rate was found to be higher than 90 K/min . 25
This stud y focuses on the investigation of the dyna mic glass t ransition of thin films of
poly(2- vin yl p y ridine) (P 2VP), as c ontradicting results exist in the literature. I n an X -ra y
reflectivity stud y of P 2VP films on acid cleaned SiO 2 surface, the thermal glass transition
temperature T g increases with decreasing fil m thi ckness up to 20 – 50 K compared to the
bulk value. 38 These results are also consistent with more recent d ata

44

,

45

and were explaine d
assuming strong inter actions of the poly mer segments with surface of the s ubstrates.
Moreover, a similar behavior was observed for thin P2VP films capped between alumin um
layers in a dielectric study .

46

Moll and Kumar found only a small shift in T g for P2VP/ sil ic a
nanocomposites.

47

. Holt et al.

48

re port also a study on P2VP filled with silica na noparticles .

68
An adsorbed bounda r y layer a round the nanoparticles with a thickness of ca. 4 nm was found
having a two-ord er of magnitude reduced mobili ty compared to the bulk P2VP, hence a
higher glass transition temperature consistent with findings discussed above. A sim ilar result
was reported for pol y ( vin y l a cetate) filled with si lica nanopa rticles .

49

These results are in
contradiction to an invest igation of P2VP films spin coated on a highl y doped Si wafe r b y
broadband di electric spe ctrosco py

50

where the d y n amic glass transition was found to be
independent of th e film thickness. Also semi -isolated P2VP chains adsorbed on a doped S i
wafer seem to resemble bulk like dyna mics. 28 These results are als o consistent with data
obtained b y high speed chip calorimetry where also a thickness independent T g v alue for
ultrathin P2VP films was found.

51

Paeng et al. e mployed photoble aching techniques to
explore the d ynamics of t hin P2VP films on the c leaned native surface of a SiO 2 wa fer.

52

A
highly mobile surf ace layer at the pol ymer/air interface was evidenced. However,
indications for a reduce d mobilit y la yer at the surface of the substrate were also reported.
Here sp ecific h eat spectroscop y is employ ed utili zing AC -chip c alorimetry 39 to investigate
the d yna mi c glass transition of thin P 2VP fil ms. These measurements are accompanied b y
contact angle measurements in orde r to quantif y the int eraction of the P 2VP segment w ith
a SiO 2 surface used as su bstrate. Additionally, broadband diele ct ric spectroscopy is used to
measure the molecular dynamics of the bulk material for comparison.
7 . 2. Experimenta l Section
7.2.1. Methods
Specific heat spectroscopy: Specific heat spectroscopy is emplo y ed using differe ntial AC -
chip calorimetry [ 39 ] . The ca lorim etric chip XEN 39390 (Xe nsor Integration, NI ) w as used
as measuring cell. The heater is lo cated in th e ce nter of a fr eestanding thi n sil icon nitride
membrane (thickness 1 µm) supported b y a Si -frame with a window. This nanocalorimeter
chip has a th eoretical heated hot spot area of about 30 x 30 µm 2 , with an integrated 6- couple
thermopiles and two-four -wire h eaters (bias and guard heater), as shown in refere nce [

53

] .
Please note that in additi on to the 30 x 30 µm 2 hot spot , the heater strips also contribute to
the heated area. A SiO 2 la y er with a thickness of 0.5 - 1 µm protects the heaters and
thermopiles. The thin films are spin co ated over the whole chip area, but onl y the small
heated area was sensed and considered as a point heat source. Pictures of the sensor can be
found in reference [41 ].

69
In principle the chip itself will contribute to the measured heat c apacity. I n the differential
approac h to AC-chip calorimetry, the contribution of the heat capacit y of the empt y sensor
(without a sample) to the measured signal is minimiz ed. I n the approximation of thi n films
(submicron), the heat ca pacity of the sample C S is then given b y 39 , 40

𝐶 𝑆 = 𝑖

𝐶  2 (

𝑈 −

𝑈 0 )
𝑆 𝑃 0

(7.1)

where  is t he angular frequency and i =( -1) 1/2 the imag inar y unit. describes
the e ffective heat capacity of the e mpt y sensor (C 0 – heat capa cit y of the sensor; G/i  is the
heat loss through the sur rounding atmosphere), S is the sensitivit y of the t hermopile, P 0 is
the applied heating po wer, and ∆U is the complex differential th ermopile signal for an empt y
reference s ensor and a c hip with a s ample, wh ere ∆U 0 is the complex dif ferential volta ge
measured for two empt y sensors. A more detailed description of the calorimetric chip, its
differe ntial setup and the experimental method can be found in reference [39 ]. Absolute
values of the heat ca pacity can be obtained b y c alibration procedures. 40
For the calorimetric measurement, the temperature scan mode was used. The temperature
was scanned using a he ating/cooling rate of 2.0 K/min at fix ed fr equency . After each
heating /cooling run the frequency was changed stepwise in the range of 1 Hz - 10 4 Hz. The
selected scannin g rate and the used frequenc y range ensure stationar y conditions for the
measurement.

54

The heatin g power for the modul ation was k e pt constant at about 25 μ W,
which ensures that the a mplitude of the temperature modul ation is less th an 0.5 K 39 and so
a linear reg ime. It is important to note that th e measurements a re carr ied out in the frame of
the linear response theory . The estimated glass tr ansition tempera tures are d y namic glass
transition tempera tur es and are taken in the equili brium state. As discussed in detail in the
introduction this is different form the t emperature ramping experiments carried out i n
DSC 43 , Flash DSC 26 or ellipsometric studies. 23 , 25
The PT -100 of the c r y ostat was calibrated b y me asuring phase tr ansition temperatures for
five different c alibration substances, coverin g the whole temperature range of the
calorimeter (173 -573 K). The calibration equatio n obtained was then use d to correct the
collected temperature d ata.

55

Contact angle measurements : The measurements were carried out using the automated
contact angle s ystem G2 (Krüss) emplo y ing the static sessile drop method . The used test
liquids were eth ylene gl ycol, formamide, water and diiodomethane. Usua lly , 8 drops with a


i G C C /
0  

70
volume of 3 μl were drop ped onto the surface of a thick sample film tre ated in a similar wa y
as the thin la y e rs. Th e m ean contact angles w ere calculated from the average of at le ast 6
drops. The data for SiO 2 were tak en from reference [ 41 ].
Broadband dielectric sp ectroscopy : For compa rison, the diele ctric properties of a bulk
sample (50  m ) were measured b y a hi gh r esolution Alpha anal yzer with an active sample
head ( Novocontrol GmbH). The temperature was controlled b y a Quatro c r y os y stem with a
stabilit y of 0.1 K. The s ample for the dielec tric measurements was obtained by melting
P2VP betwee n two gold plate d bra ss elec trodes (diameter 20 mm). Fused sil ica spacers
controlled its thickness to be 50 μm.
7.2.2. Materials and Sample Preparation
P2VP was purchased from Pol y mer Standards Services GmbH (Germany) with a M w of
1020 kg/mol and a PD I of 1.33. Th e thermal glass tra nsition temperature is 373 K estimated
by Differential Scannin g Calorimetry ( DSC, 10 K/mi n, second heatin g r un). The sele cted
polymer here is similar to the material used in refere nc e [ 28] and allows therefore a direct
comparison of th e dielectric data. For the AC - chip calorimetr y, the se nsors were first
mounted on the spincoat er, a few drops o f chloroform were add ed in the center, and then
spin coated to rinse dust and organic contaminations. This procedure was repea ted twi ce,
followed by an ann ealing process of the empt y chip at 473 K in vacuum for two hours to
cure the epoxy re sin completel y , whi ch is used to glue the chip to the housing.
P2VP was dissolved in chloroform with dif ferent weig ht percentages. The solutions were
spincoated (3000 rpm, 60 s) onto the central part of the sensors. The film thickness was
varied b y adjusting the c oncentration of the solution. Note that all spin coating pro cesses
were carried out in a laminar flow box to minimize an y possi ble contaminati on. Further, the
films were annealed at 3 98 K ( T ann =T g,Bulk + 25 K) in an oil-f ree vacuum f or 48 h, in ord er
to remove the residual solvent and re lax the stress induced b y the spin coa ti ng procedure .

56

The thi cknesses w ere me asured fo r films identically prepared on silicon wafers with a nativ e
SiO 2 surface, because t he film thicknesses cannot be directl y me asured at the sensor.
Assuming that the surface of the silicon wafer ha s simil ar properties as th e surface of th e
sensor, under identical spin coating and ann ealing conditions, corresponding film
thicknesses will be obtained. To pr oof this assumption in more detail a XPS study is in
preparation. The film thickness d was measured b y the step height of a s cratch across the
film down to the wafer surfa ce b y a n AFM Nanopics 2100 (see f ig u re 7.1 ).

71

Figure 7 .1 AFM ima ge of a scratch acro ss a P2VP layer with a th ickness of 50 n m on a silicon wafer.

Fig ure 7.2 gives the estimated film thicknesses ve rsus the concentration of the solution. A
linear depe ndence is observed, which goes to the point of origin as e xpected.

Figure 7. 2. Estimated film thi ckness d ve rsus the concen tration o f the solu tion. The solid line is a linear
regression to the data . The error ba r is smaller than symbols used.

Moreover, the AFM topography im age (f ig ure 7 .1) reveals no inhom ogeneities and/or
dewetting at the surface of the films. Also, a low surface roughness is obs erved. The root
mean square (rms) roughness in the central area of the empt y sensor was estimated to be
about 3.5 nm. 40 The roughness of the film spin coated onto the surfac e of th e sensor is lower
and decrease s with increasing film thickne ss. For a film thickness of ca. 10 nm, the
roughness of the f ilm on the sensor is compara ble with that of a film prepared on a wafer .

57

7.3. Results an d D i scussion
The result of an AC calorimetry measu rement yields a complex differential voltage as a
function of frequenc y and temperature, which is proportional to the complex heat capacit y

72
(C * P ) of the film. Here the rea l part of the complex differential voltage U R a nd the pha se
ang le  a re taken as measures of C * P . At the d y namic glass tr ansition, U R inc reases stepwise
with increasing tempe rature (Figu re. 7.3a) and  shows a peak (figure 7.3b).

-2
-1
0
1
2
340 360 380 400 420 440
56
58
60
62
64
T [K[
 corrected [°]
T g = 399.1K
b

Phase angle  [°]

Figure 7.3 . Rea l p art (A) and pha se a ngle (B) of th e complex differential voltag e of a thin P2V P p ol ymer
film (347 nm) measured at a frequen cy o f 160 Hz. The contribution of the un derlying step in the heat
capa city in the raw data o f the ph ase an gle (upp er panel) was sub tracted from the all over curve (lower
panel).

A dynamic glass transition tempera tur e can be determined as either the half s tep temperature
of U R or as the maximum temperature of the p eak of the corrected phas e angle. I n the raw
data of the phase an gle ( f ig ure 7.3B, upp er panel), there is an unde rlying step in the signal,

73
which is proportional to the real part. Hence, the phase angle is corrected b y subt racting this
contribution. According to equation 7 .1 and assuming that the density o f the film is the same
as in the bulk, the step hig h of the heat capacity at the glass transition is given b y 40

𝐶 𝑆,𝐿𝑖𝑞 𝑢𝑖𝑑 − 𝐶 𝑆 ,𝐺𝑙𝑎𝑠𝑠 = 𝑖

𝐶  2 (𝑈 𝑅 ,𝐿𝑖 𝑞𝑢𝑖𝑑 − 𝑈 𝑅 , 𝐺𝑙𝑎𝑠𝑠 )
𝑆 𝑃 0 ~𝑚 ~𝑑

(7.2)

where m is the mass of the film. There fo re, U R, L i quid - U R,Glass =  U R should be proportional
to the thickness of the film. In figure 7.4,  U R is plotted versus d. The expected li near
dependence is confirmed. Moreover, the data can be described by a regression line going
through the point of origin. From those results, one might conclude that the whole sample
material on the c hip takes part in the dy namic glass transition and no bound ar y la yer with a
reduce d mobilit y is pr esent.
7.3.1. Convent ional Analy sis of S pecific Heat Spectroscop y Data
Fig ure 7.5 gives the normalized phase angle versus temperature for dif ferent film
thicknesses for a f requenc y of 160 Hz. F or all values of d the data collapse into a common
curve. This means that the dy namic glass transition temperature is independent of the film
thickness. Sim ilar results were obtained b y AC- chip calorimetry for PS, 27 , 39 P MMA, 50 ,

58

poly(2,6- dimeth y l-1,5-ph enylene ox ide), 40 po l ycarbona te 41 an d also poly(vin y l meth y l
ether). 42 At the first glance the results obtained here are in accordance with the dielectric
data given in reference s [ 28,50] but disagree with findings discussed in [38,48 ].

0 100 200 300 400
0
4
8
12
16

 U R [µv]
d [nm]

74

Figure 7.4

U R versus th e film thickness d fo r a frequency of 160 Hz. The solid line is a linear
regression to the d ata. For low film thickn ess, the error is somewhat larger. Therefore, the data poin ts
for the lowest film th ickness m igh t deviate slig htly from the regression line.

Figure 7.5 . Normalized phase angle of the complex differential voltag e ve rsus temperature measured for thi n
P2VP films at a frequen cy of 160 Hz for selected thickn esses of 4 00, 347, 216, 85, 50, and 22 nm.

To anal yse th e dat a in m ore det ail, Gaussians were fitted to the normalized phase angle as
depicted in inset A of f ig ur e 7.5. 40 F rom su ch analy sis , the max imum tempera ture of the
normalized phase angle is estimated at the given f requency and the relax ation map can be
constructed (see Fig ure 7.4). Within the experimental error of  3 K, the data for all film
thicknesses collapse int o one c hart. As mentioned a bove, this is in agree ment with AC-chip
calorimetry studies on other polymers. 27 , 39 - 42 , 58
The temperature dependence o f the relaxation rates can be des cribed b y the
Vogel/Fulcher/Tammann- (VFT-) equation

59

-

61

𝑙𝑜𝑔 𝑓 𝑝 = log 𝑓 ∞ − 𝐴
𝑇 − 𝑇 0

(7.3)

where f ∞ and A are fitting parameters and T 0 is called ideal glass transition or Vogel
temperature, which is found to be 30 -70 K belo w the thermal T g . For all film thicknesses
the data can be described b y a common VFT- fit (see figure 7.4). Du e to the limited
freque nc y r ange of the specific h eat spectroscop y , th e prefactor f  was taken from the
dielectric results (see below) and kept constant during the fit procedure.

380 390 400 410 420
0.0
0.2
0.4
0.6
0.8
1.0

400 nm
347 nm
216 nm
85 nm
50 nm
22 nm
 normalized
T [K]

75

2.3 2.4 2.5 2.6
-1
0
1
2
3
4
5
2.1 2.2 2.3 2.4 2.5 2.6 2.7
-2
0
2
4
6
8
350 375 400 425 450
0.0
0.2
0.4
0.6
0.8
1.0
VFT-Line
AC-chip calorimetry
Inset B

log (f p [Hz])
1000 / T [K -1 ]
BDS thin films
with one free surface
log(f p [Hz])
1000 / T [K -1 ]
1000/T g,DSC
 normalized
T [K]
Inset A

Figure 7. 6. Relaxa tion rates ve rsus in verse tempera ture for differen t fi lm thicknesse s estimated from th e
normalized ph ase ang le (op en symbo ls): ci rcles – 405 nm, squares – 34 9 nm, up sited trian gles – 23 0 nm,
down sited triangles - 21 6 n m, stars – 1 50 nm, a sterisks – 12 0 nm, left sited triang les – 85 nm, h exagons –
50 nm, rig ht sited triangles – 22 nm, crosses – 10 n m. The solid circles are d ata from d ielectric spectroscopy
for a bulk sample. Solid lines a re fits of the VFT equation to the corresponding da ta with following
parameters. Dielectric data (dashed lin e): lo g (f

[Hz] )=12, A=779 K, T 0 =315 .4 K; Thermal da ta (solid
line): log ( f

[Hz] )=12, A=774 .6 K, T 0 =317 .8 K. The dotted lin e gives the thermal glass tran sition
temperature measured by DS C. Ins et A. gives the normalized phase ang le for a film with a t hickness of 347
nm at a frequ ency of 160 Hz (solid line). The dashed line is a fit of a Gau ssian to the data. The solid line is
the averaged value o f the giv en data p oints. Inset B . compares dielectric da ta for ultrathin P2VP films
measured with one free surf ace ta ken from reference [50 ] with th e VFT- fit ta ken from the AC -chip
calorimetry. The d ielectric da ta are averag ed data in th e thick ness range from 1 72 nm d own to 8 n m
becau se the data fo r all film thicknesses collap se into o ne chart.

In figure 7.6, the data for a bulk sample measured b y dielectric spectrosc opy are included
as well. Further, the temperature dependence of these data ca n be described by the VFT
equation where the estimated value for the Vo gel tempera tur e T 0 is close to that estimated
from the thermal d ata (s ee caption figure 7.6). Th e dielec tric and th ermal d ata overlap more
or less, whic h is a bit uncommon for most materials. The thermal and dielectric data usuall y
exhibits a sy stem atic shift, as previously found for different homopolymers, 41 , 42 and also for
low molecular c ompound s.

62

The inset B of figure 7.6 compares diel ectric d ata measured for thin films of P2VP with the
VFT fit line extracted from the specific heat spectroscop y d ata. The dielectric data are the
averaged data in the thickness range of 172 nm down to 8 nm, taken form reference [50 ].
The free surface was im plemented b y th e use of insulating colloids as sp acers. For more
details see reference [50 ]. Both sets of data, where samples have one free surface, agree
nicely with each other and both sets of relaxation have the same temperature depende nce.

76
A sim ilar behaviour should be expected for mechanical measurements, which are h ard to
conduct in the ca se of ult rathin films.
7.3.2. Contact angle measurements
To character ize the interaction of the P2VP segments with the SiO 2 surface of the substrate
contact angle measurements were carried out. It is assumed that a silicon wafer with 500 nm
native SiO 2 la y er has the same surface prope rties than the used AC -chip. The estimated
contact angles obta ined for the different test liquids are summarized in Table 7.1.
Table 7.1. Con tact a ngle valu es of th e test liq uids fo r poly( 2 - vinyl pyridine). Data for SiO 2 were ta ken from
reference [41 ] . The errors resul t from the a verage of measurements on 6 drops.

Water

Formamide

Ethylene glyc ol

Diiodomethane

P2VP

67.5°



0.9°

65.5°



0.8°

46.6°



1.1°

40.0°



0.9°

SiO 2

61.0°



1.0°

48.2°



1.0°

39.0°



0.6°

28.9°



1.2°

The total surface ener gy γ Total of a sample is ex pressed b y γ Total = γ LW +γ P where γ LW and γ P
are the dispersive and polar components of th e surface energy, respectively .

63

,

64

The
measured conta ct angles

i


for the li quid i are related b y t he Owens/Wen dt theory ,

65

,

66

which is a combination of Young's relation with Good’s equation (for d etails see [

67

]) to
the polar and dispersive components of the surface ene r gies of the solid and liquid b y

LW
S
LW
i L
p
i L
P
S
LW
i L
i L i





 
 

,
,
,
,
2
) c os 1 (

(7.4)

where 𝛾 𝑆
𝑃 and 𝛾 𝑆
𝐿𝑊 are the dispersive and pola r components of the surface energy of the
polymer or the substrate (S=P2VP, SiO 2 ). The values for the surface tension of the tes t
liquids were t aken from reference [ 63 ] . Using at least 3 test liquids, an Ow ens/Wen dt plot
according to equation 7. 4 is created and the polar and dispersive compon ents of the solid
surface energy a re estimated b y line ar regression. Results are presented in table 7.2.
Table 7.2. Tota l surface energy γ Total and its dispersive γ LW and po lar γ P co mpon ents fo r P2VP and the SiO 2
surface of th e silicon wafer.

To ta l


[mJ m -2 ]

LW


[mJ m -2 ]

P


[mJ m -2 ]

P2VP

39.5

29.8

9.7

SiO 2

47.0

44.6

2.3

77
The rule of Fowke s 64 was applied to estimate the inter fa cial energy between P2VP and
SiO 2 , which reads


𝑆𝑃 = (

𝐴 +

𝐵 ) − 2 [(

𝐴
𝐿𝑊

𝐵
𝐿𝑊 ) 1
2 + (

𝐴
𝑝

𝐵
𝑝 ) 1/2 ]

(7.5)

where A and B refer to the substrate a nd the pol y m er, respectively.
Using Equation 7.5, the total interfa cial energ y between P2VP and S iO 2 is 4.1 mJ m -2 .
According to reference [ 35] , this is a strong intera ction between the pol y m er se gments and
the surface of the subst rate. Therefore an adsorbed layer with a reduced mobi lit y should be
formed at the surf a ce of the substrate in agre ement with results published in reference [48 ].
Likew ise, for othe r pol ymers, which interact stro ngly with the subst rate, an incre as e of the
glass transition tempera tu re should be observe d. But howeve r, no change in d yna mic T g was
observed here b y specific heat sp ectroscop y . One pos sible reason for thi s result might be
the hig h molecular w eight of the used P2VP. As it was shown in r eference [ 31,71] the
formation of the reduced mobilit y la y er d ep ends on time and the diffusive mobilit y of the
polymer chains. For a high molecular wei ght, the chain mobilit y is lower than for a lower
one. I t mi ght be that under the se lected experimental c ondition the ann ealing time a bove T g
was not long enoug h to form a reduce d mobilit y at the substrate, which is thick enoug h to
influence the dy namic glass transition of the whole film.
Attempts to correlate the change in the glass tr ansition temperature wit h the interaction
energy between th e substrate and the pol y me r su rface  SP a re mad e in reference [ 35]. I n
figure 7.7, the difference of the glass tr ansition temperature for 20 nm thick films and the
bulk value v ersus the i nterfacial ener gy are pl otted for pol y st y rene and pol y(methy l
methacrylate) spin co ated on modified octadecyltrichlorosilane (OTS) surface s according
to reference [35 ]. For  SP <2 mJ m -2 a depression of the glass tra nsition temperatures should
be observed while for  SP >2 mJ m -2 an incre ase of T g should be observe d. In this figure, data
for different pol ymer substrate combinations, with comparable film thicknesses, taken from
the literature, w ere adde d. (A similar figure but with less data points is given in reference
[

68

] too). This conc ept is ab le to describe the va riatio n of the T g with interaction energy for
polystyre ne and pol y (meth y l methacr y late ) on the modified octadec y ltrichlo rosilane
surfaces. Also for some other pol y m ers li ke pol ycarbona te on S iO 2 or AlO X 32 , 41 or
poly(e th y lene terephthalate),

69

this corre lation s eems (partiall y ) valid. However, it is not
ge nericall y true for all pol ymer /subs trate combinations.

SP


78

0 1 2 3 4 5 6 7
-10
0
10
20
30 T 0
PS Films (ca. 20 nm)
PMMA Films (ca. 20 nm)
P2VP/SiO 2
PC/AlOx
PC/SiO 2
PSU/AlOx
PS/AlOx 1401 kg/mol
PS/AlOx 250 kg/mol
PS/AlOx 50 kg/mol
PVAC/Au
PVAC/AlOx
PVAC/Si
PET/AlOx

T g,film - T g,bulk [K]
 SP [mJ m -2 ]
T g
M
on OTS

Figure 7 .7. Difference of th e glass transition temperature fo r 2 0 - nm -thick films and the correspond ing bulk
value versus the interfacial energy. Th e open symbols f or poly(methyl methacrylate) (squares) a nd
polystyrene (circles ) are taken together with the (dashed) co rrelation line from reference [35] . The grey
dotted lin es gives

T g =0 and critical va lue for

c . The da ta for polyca rbonate (PC,diamo nds) are taken
from reference [32 ] (AlOx) an d [41] (SiO 2 ). The asterisks re present data for polysulfon e (PSU) taken from
reference [33 ] . The value fo r PET (left po inted trian gle) are t aken form referen ce [69] . The da ta for p oly(vinyl
acetate) (PVAC, triangels) pre pared on the indicated surfaces are take n from reference [70] . The values for
polystyrene (PS, green stars) a re drawn from [71] . P2VP (sol id circle) – this work.

For inst ance, for pol y sulf one, the interaction energy between the segments and the substrate
surface was estimated to be  SP = 5.45 mJ m -2 , taken from re ference [ 33 ]. This value is much
larger than the value of polycarbona te/AlO X , whe r e a similar increase of the glass transition
temperature of about 5 K (for a ca. 20 nm thick film) was found. How ever, th e corresponding
point for pol y sulfone is located far away from the correlation line between the pol y mer -
substrate interaction energy and the chan ge in the glass tr ansition temperature. However, b y
taking th e Vogel temperature, T 0 , as a measure for the thermal g lass transition tempe rature,
the c orrelation between the chan ge in the g lass transition temperature and the pol y m er -
substrate interaction energy 31 , 35 seems to be fulfilled.
For pol y(viny l acetate) films prepared on diff erent surf aces,

70

this corre lation is found to be
invalid as well. Data for polyst y rene samples having different molecular w eights were also
added,

71

wherea s the interaction ener gy between the AlO X surface of the su bstrate and the
polystyre ne se gments is taken from reference [31] . These data point s are located also f ar
away from the correlation line between the pol ymer / substrate int eraction energ y and the
change in the glass transition temperature . The observed dependence on the molecular
weig ht is in contradiction to the assumption that the interaction energ y between the pol y me r

79
segments a nd the surface of the substrate is the only p arameter, whi ch determines the value
of the glass transition temperature of ultrathin pol y st yrene films as well. This regards also
the observed time dependence of the depression of T g . 31 I n conc lusion, the polymer/substra te
interaction energy seems to be not the onl y parameter, which is responsible for the change
in the thermal glass transition tempera ture with the film thickness for ultrathin films .
Packing effects and/or densifications of the reduced mobi lity layer at th e surface, which can
be time and molecular weight dependent, might also pla y a role. This is discussed also in
detail in reference [31].
7.3.3. Derivativ e analysis of specific heat spectroscopy data
As discussed above, all AC -chip calorimetry studies on ultrathin films of homopol y mers,
including P 2VP used in this work concluded that t he dyna mic T g is thi ckness independent,
in man y cases, contradicting the findings of other studies us ing diff erent characterization
techniques. For P 2VP, one shall ex pect to see a rather stron g reduced mobile la y e r as
speculated from the contact an gle measurements, shown above. The reduced mobile la y er
for this polymer has also been det ected by other m ethods, e. g. X -ra y reflectivit y 38 and
differe nt BDS studi es. 46 , 48 On the other hand, also the existence of a hi gh mobile free surface
layer has b een evidenced for P2VP . 52 To resolve the systematic contradiction of AC -chip
calorimetry from the othe r characterization method , an advanced an al ysis of the calorimetric
data might be useful.
From the te chnical poin t of view, the re are a few problems with the conventional data
analy sis of AC-chip calorimetr y . Firstly, the theoretical treatment of the method assume s
that the reference and th e sample sensor are ide ntical. I n that theoretical case, one shall
expect to see a constant baseline at zero level for the differential voltage fo r all frequencies
and tempera tures. Because of the fac t that the sen sors are not complete l y identica l, an extra
contribution will be added up to the sig nal com ing from the film. This extra c ontribution to
the differential voltage is not large but depends o n both temperature and frequency. It can
be ignored for relativel y thick films (>50 nm). However, for thinner films, the difference
between the two empty sensors is in the same order of magnitude as the meas ured U R , which
might induce artifac ts.
The other problem in estimating the d y namic g lass transition temperature fr om the
maximum position of the phase angle is related t o the fact that the measured phase angl e
has also an underly ing contribution that is proportional to the step of the heat c apacit y . 39
This effect will not affect the T g peak position for thick samples. However, for ultrathin

80
films (<20 nm), the valu es of the phase angle become small and compara ble to the noise
level of the instrument. 40 Thus, the correction and estimation of the phase ang l e cannot b e
done unambig uousl y.
For these r easons here the temperature d ependen ce of the complex differ ential voltage is
analy s ed in more detail for some selected sample thi cknesses, which w as investigated with
an optimiz ed sensitivit y. First, the sensitivit y of the lock -in amplifier of the AC -chip
calorimeter was set to be between two and three times the value of U R of the sample at 160
Hz and the corresponding T g,160 Hz , to assure an optimal signal and a re du ced noise. Second,
pairs of empt y sensors were first mea sured in the identica l frequenc y and temperature ran ge
as for the samples to obtain the ex cess contributi on of the sensors. Third, aft er the
measurement o f the films spin coated on one o f the a nal y zed empty s ensors, the re al part of
the complex voltage o btained for the two empt y sensors was subtracted from the
co rresponding U R recorded for the f il ms. This procedure leads to a corrected U R .
Instead of analysing the tempera tur e dependence of the phase an gle, the derivative of the
corrected real part of the complex voltage versus temperature was emplo y ed. Since U R
ch anges step -like at th e dy namic glass transition, its first derivative will result in a peak.
The temperature of the peak maximum can be take n a s the dyna mic glass transition
temperature at 160 Hz. The derivative method will also allow estimating dU R /dT whi ch is
related to dc p /dT for both the glassy and the li quid state. To calculate the derivative of the
corrected real part of the complex voltage was adj acent-point averaged (ov er 300 points; for
the two thinnest films over 500 points) in the who le measured t emperature range. This will
result in a smoothed si gnal. To have equidistant points, U R (T) was inte rpolated (1000
points). After th at the derivative was calculated. I t is worth to mention that the difference in
the smoothing methods and parameters was pre viousl y reported to result in about  2 K
differe nce in the T g values, which is within the uncertaint y of the measurement . 40 The
advantage of this method is strong when anal y z ing measurements of ultrathin films , where
the signal is weak and changes of the phase angle are hardl y to detect. Fo r films thinner than
15 nm, one can usuall y still see a small step in U R , y et it is not unambiguously to determine
where the step st arts and ends. Moreover, in a first crude approximation the derivative ca n
be considered as a representation of the relax ation time spec tra.

72

Four n ew samples w ere prepared (10 nm, 20 nm, 8 5 nm and 220 nm) and the measurements
were analy z ed as described above.

81
Fig ure 7.8 sho ws the d erivative calculated as described versus temper ature for three
differe nt sample thi cknesses at a frequency of 160 Hz. For each value of th e thicknesses a
well-define d p eak is visible indicating the dynamic glass transition. With decre asing
thickness, a sy stematic shift of the dy n amic g lass tra nsition to lower temperatures is
observed. This shift up to 7 K is e ssentially l arger t han the error of the AC -c hip calorimetric
measurement.
The derivative method was also applied to the other samples prepared previously and a
dyna mic g lass transition temperature at 160 Hz was estimated from the max imum position
of the d erivative. The se data were plotted in f i gure 7.9 versus the thi ckness of the f ilm. The
dyna mic glass transition temperature of the bulk sample is take n a s the averag e value of the
dyna mic glass transition temperature for the five samples with the highest thicknesses.

320 340 360 380 400 420 440
f=160 Hz
10 nm
20 nm

(dU R / dT) / d [ a.u.]
T [K]
7 K
220 nm

Figure 7.8. Derivative of the co rrected real part of the complex differential voltage with regard to
temperature versus temperatu re for th e indicated film thicknesses at th e frequency of 160 Hz. F or sake of
clearness the cu rves were shift ed a long the y -scale.

For small film thicknesses, the value of the d ynamic glass tr ansition is below this averag e
value and further decreases with decreasing film thickness. Because a decrease o f the
dyna mic glass temperatu re is considere d as the influence of a free surface , 19 this result can
be considered as an evi dence for a free surface with a hi gh er molecular mobi lit y f rom
calorimetric measure ments.

82

0 100 200 300 400
388
392
396
400
404

T g, 160 Hz [K]
d [nm]

Figure 7 .9. Dynamic glass tran sition tempera ture measured at 160 Hz versus film thickn ess d . The dashed
line is the a verage va lue of the five da ta points with largest th ickne sses.

It should be shortly sum marized why the traditional and the derivative ba sed data anal ysis
give diff erent results. Firstly , in the phase angle two different quantities with well -de fined
physica l me anings are mix ed up, the rea l and the loss part of t he complex differential
voltage . Th e correction of the phase angle for the rea l part of the complex v oltage cannot be
done una mbiguousl y especiall y for low film thickness as discussed above. Secondl y , the
derivative of the real pa rt of the complex differenti al voltage can be considered as an
estimation of the underlying relax ation time spec tra. 72 This means both quantities we ight
the underl y in g d y namics in a different wa y. This fact in unimportant for thick film s but
might become relevant for low film thi cknesses. A closer inspection of figure 7.5 that also
the phase angle measur ed for hi gher thickn ess seem to be lo cated at s omewhat hi gher
temperatures which is consistent with the derivative a nal y sis .
Some further evidence for a mobile surface la y e r comes from the shape of dU R /dT versus
temperature. A more d etailed inspection of figure 7 .8 reveals that the width o f the derivative
for a thin film (for instance se e 10 nm) is broader than that measured for a larger thickn ess.
This fact is illust rated in more detail in figure 7.10, where the derivative f or a 10 nm and a
40 nm thi ck film are compared. There fore, the derivative is norma li zed with re spect to both
its intensit y and pe ak temperature. Figure 7.10 rev eals that the peak for the 10 nm thick film
is much broader than that for the 40 nm on e. Firstly , compared to the 40 nm thick la y er, the
film with a thickness of 10 nm shows a considerable broadenin g at the lo wer temperatur e

83
side. In the sense of di stribution of r elaxation ti mes, this corresponds to an increased
contribution of relaxation modes havin g shorter relaxation ti mes. W ith decreasing film
thickness, the influence of a surface la y er with a higher mobi lit y will increase. Th erefore,
in addition to the decreas e of the d ynamic glass transition with decreasing film thi ckness,
the broadening of the relaxation spectra on the low temperature side gives further evidence
for the existence of a surface layer with a highe r mol ecular mobilit y at the pol y mer ai r
interface.

-75 -50 -25 0 25 50
0.0
0.4
0.8
1.2
Slow Process
Nanocomposites
Adsorbed Lay er

(dU R /dT) / (dU R /dT) Max
T-T Max [K]
Mobile Surface
Layer

Figure 7. 10 . Normalized d erivative (dU R / dT) / (dU R / dT) Max versus temperatu re at a frequency of 160 Hz
for a 10 nm (open squares) and a 40 nm (open stars) thick film.

Besides the broadenin g of the spectra at the low te mperature side fo r the thin film for the 10
nm thin film there is also a broadening of the derivative at te mperatures above the dy namic
glass transition temperature. This broadenin g at t he hi gh temper ature side of the spectra is
due to relaxation modes having a reduced mo bilit y . As shown b y th e contact angle
measurements, discussed above, the P2VP segments should strongly inte ract with the S iO 2
surface of the sensor, w hich shoul d result in slowing down of the mol ecular d y namics of
the pol y me r se gments close to the surface. Theref ore, the bro adening of the spectra at hi gh
temperatures is assig ned t o pol y m er segments, whi ch are in interaction with the SiO 2 surface
of the sensor. A co rresponding broadening was observe d by dielectric spectroscop y
employing nanostructured electrodes. 28 A closer inspection of the data for the 10 nm thick
film reve als that there is a small shoulder at T-T Max =28 K (T=424 K). This shoulder is found
at the same temperature frequenc y position, w here for the nanocomposites of P 2VP with
silica nanoparticles, disc ussed in reference [48 ], the relaxation process is observed, which

84
was related to th e fluct uations of P2VP segments adsorbed at the surf ace of the silica
particles. This coincidence provides further evidence that a reduc ed mobilit y layer is formed
at surfac e of the ca lorim eter. Probably, due to t he high molec ular weight of the used P2VP,
the for mation of this reduced mobili ty la yer wil l take long er time. Under the emplo y ed
experimental conditions, it is likel y th at the thi ckness of this la yer is sm all and will not
influence the d ynamic glass transition behavior of the whole film. For future work,
additional investigations are planned where the ann ealing time and temperature, during film
preparation, are varied in broader ranges. This includes further a variation o f the molecular
weig ht because it was shown for inst ance that for pol y st yrene 71 the chang e of the g lass
transition temperature depends on molecular weight due to a changed adsorption kinetics.
It is w ell known that the specific h eat capacit y in the g lass y state h as a stronger temperature
dependence than in the li quid,

73

which means (dc p /dT) Glass > (dc p /dT) Liquid . Close to the g lass
transition c p (T) can be approx imated b y linear d ependencies in both the glass y and liquid
state. In the derivative representation, this is reflected b y constant values o f the derivative
dU R /dT which corresponds to dc p /d T independent of temperature below and above the
dyna mic glass transition. The inset of figure 7.11 depicts the derivative versus temperature
for a relativel y thick film of 347 nm. For this film, which can be considered as bulk -like,
the expected relationshi p (dc p /dT) Gl ass > (dc p /dT) L i quid is fulfilled. However, figure 7.11
shows fur ther that with decreasing film thickness, this relationship chang es. For a film with
a 220 nm thickness, (dU R /dT) Gl a ss  (dU R /dT) Liquid holds; whe reas for a thinner film with a
thickness of 70 nm the r elationship is reversed (dU R /dT) Gl a ss < (dU R /dT) Liquid . This is not
only observed for the considered thicknesses, but also for the other thic knesses as we ll (see
figures 7.8 and 7.10). Obviousl y , confinement effe cts influence the temperature
dependencies of the spe cific hea t capacity in the liquid and glassy state. Such change in the
temperature depe ndence of specific heat ca p acit y before and after the d y namic glass
transition reg ion was able to be observed at relativel y hi gh thicknesses, above 220 nm in the
present stud y . The c ritical thi ckness is possibly mol ecular weight dependent, which needs
further quantitative me asurements. It was already r eported that for PS with Mw=1400
kg/mol, a change in the temperature dependence of specific heat capacit y at the glass
transition occurred from seve ral hundred nm . 43 In the glassy state, c p (T) originates from
vibrations. The same vibrations are also responsible for the temperature de pendence of the
thermal ex pansion. The specific heat capacit y and the thermal expansion coefficient are

85
linked to each other.

74

It h as been reported previously that the thermal expansion coefficient
in the glassy state for thin films decreases with the film thickness.

75

,

76

325 350 375 400 425 450
360 380 400 420 440
(dU R /dT) Glass > (dU R /dT) Liquid
~
(dc p /dT) Glass (dc p /dT) Liquid
347 nm
70 nm
(dU R / dT) / d [a.u.]
T [K]
220 nm
(dU R /dT) Glass < (dU R /dT) Liquid
~
T [K]

Figure 7 . 11 . Derivative (dU R / dT ) /d versus te mperatu re a t a frequen cy of 1 60 Hz for a 220 n m (open
diamon ds) an d a 70 nm (open triangles) th ick film. The inse t shows th e same for a film with a th ickness of
347 nm.

These findings are quite similar to the results fou nd here for P2VP. Moreover, quasielastic
neutron scattering experiments for thin films o f polystyre n e and polycarbonate

77

,

78

showed
that the mea n square displacement <r 2 > decreases with decreasing film thickness. Also a
direct investi gation of the vibrational densit y of states in the fre quenc y range of ex cess
vibrations chara cteristic for the glassy state ( Boson Peak) show a decre as e of the intensity
of the Boson Peak with de creasin g film thickness for poly st y rene for relativel y hig h
thicknesses of 100 nm.

79

,

80

This behavior is equival ent to a decrease of the mean square
displacement. Using a h armonic a pprox imation < r 2 > can be re lated to a forc e constant f K b y
f K ~1/<r 2 > . A decrease of the mean square displ acement can ther efore be ex plained by an
increase of the force constant. This m eans a cha n ge from a soft to hard potential. Taking as
well as anharmonic contributions into account, the chan ge of the temperature dependence
of the specific h eat capacit y in the glass y state mi ght be explained by a harde nin g of the
potential of the vibrations. However, it is worth to note that the change of t he specific heat
capacity in the glass y a nd liquid state mi ght also be e xplained by a three la yer model whic h
also applies here.

81

To differentiate betw een both possibilit ies, additional investigations on
a broad er r ange o f samples and different pol y mers are re quired. Such stu dies are under
preparation, which will also include a more quantitative discussion.

86
7.4. Conclusion
Specific hea t spectroscop y emplo y in g diffe rential AC -c hip calorimetry i n the frequenc y
range from 1 Hz to 10 4 Hz with a sensitivit y of pJ /K was used to stud y t he d ynamic glass
transition behavior of ultra thi n poly(2-vin y l p y rid ine) films with thicknesses from 405 nm
down to 10 nm. To character ize the interaction of the P2VP segments with the surface of
the subst rate, contact angle me asurements was uti lized along with AFM investigation to
study the topol og y of the films. Broadba nd di electric spectroscopy was us ed to obtain t he
molecular dyna mics for the bulk sample.
AC -chip calorimetr y deli vers the real part and the phase angle of the comp lex differential
voltage as a measure of the c ompl ex heat capacity as function of temperature and frequenc y
simultaneously. The data were anal y z ed by two different m ethods. In a ra ther traditional
data anal y sis, the dynamic glass transition tempe ratur e is estimated from the maximum
position of the measure d phase an gle. Thes e data showed no thickness dependence of the
dyna mic glass transition temperature down to ca. 22 nm, within in the error of the
measurement o f  3 K. This result is in agreement with dielectric d ata obtained for samples
having one free surface, yet sti ll in disagreement to other literature data. Therefore , a second
method was established which is bas ed on the first derivative of th e real part of the complex
differe ntial volta ge with regard to temperature. T hese data show a decreas e of the d y n amic
glass transition temperature with decreasing thickness of about 7 K. This decrease c an be
explained as a result of the influence of surface la y er with a higher molecular mobilit y.
Moreover, for thin films the data showed a broadening at the low er temper ature side of th e
dyna mic glass transition, which can be considered as a further prove for a surface la y er.
Moreover, contact a n gle measure ments showed th at the P2VP/SiO 2 intera ction wa s rather a
strong one, 4.1 mJ m -2 , which suggests that an a bsorbed layer of reduced mobilit y shoul d
exist at the pol y m er/substrate interface. An absorbed layer was evid enced for films below
50 nm, through another broade ning of the peak with the appearance of a shoulder at the
higher temperature side of the spectra that superimposes with the fluctuations of P2VP
segments adsorbed at the surface of the silica particles, as reported in literature.
Finally , evidence was provided the temperature dependence of the specific heat capacit y in
the glass y and th e liquid state cha n ges depends on the film thickness. These changes w ere
observed fo r relativel y high film th ickness of s ome 100 nm and can b e considered as
confinement effects. For t he glass y state these changes are in a greement with severa l n eutron
scattering studi es and can be explained b y a h ardening of the potential of the vibrations, and

87
thus the exist ence of a reduced mobile la yer, in agreement of the thr ee-layer model.
Neverthe less, additional investigations are required.

88
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Füllbrandt, M.; P urohit, P. ; Schönhals, A. Macromolecu le s, 2013 , 46, 4626 -4632.

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Efremov, M.; Olson, E. ; Zhan g, M.; Zhang, Z.; Allen, L. P h ys. Rev. Lett . 2003 , 91, 085703 -085707.

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Paeng, K.; Ric hert, R.; Ed iger , M.D. Soft Ma tter , 2012 , 8, 819- 826.

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van Herwaaden, S. A pplicatio n no te for Xsensor ’ s calorimter e chips o f XEN - 39390 series
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Schick, C. Calorime try in Polymer scien ce: A co mprehen sive reference , Mat yjaszewwski, K. Möller
(Eds) Elsevier B . V., Amsterda m, 2012 , pp 793- 823 .

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Huth, H.; Schic k, C. Per sonal Co mmunica tion .

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Reiter, G.; Ha mieh, M.; Da mman, P. ; Sclavo ns, S.; Gabriel e, S.; Vilmin, T .; Raphael, E .; Nat. Mater.
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Huth, H.; Schic k, C. Perso nal Commu nicatio n .

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Huth, H.; Mina kov , A.; Ser ghei, A.; Kremer , F .; Schick, C. E ur Phys J -Spec T op, 2 007 ,141,153 -60.

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90

CH A P TER 8 - Un veiling the D ynamics of Self -Assem bled
La y ers of Thin Films of PVME b y Na nosized Relaxati on
Spectroscop y
This chapter is reproduc ed with permission from ( Madkour, S.; Szymoniak, P.; Heidari, M.;
von Klitzing, R.; Schönhals , A. Unveiling the Dynamics of Self-Asse mbled L ayers of Thin
Films of Poly(v inyl methyl ether) (PVM E) by Nanosized Relaxation Spectroscopy . AC S
Appl. Mater. Interfaces. 2017, 9, 7535-7546. DOI: 10.1021/acsami.6b144 04). Cop y ri ght
(2017) American Chemical Society .
*Supporting information is given in Appendix I
DOI: http://dx.doi.org/10.1021/acsami.6b14404
A bstract
A combination of nanosized diel ectric relaxation (B DS) and therm al spectroscop y (SHS)
was utilized to c haracterize the d y n amics of thin films of Pol y(vinyl meth yl ether ) (PVME)
(thicknesses: 7 nm – 16 0 nm). For the BDS m easurements, a recentl y designed nano -
structured electrode s ystem is employed. A thin film is spin -coated on an ultra-flat hi ghly
conductive silicon wafer serving as the bottom electrode. As top electrode, a hi ghly
conductive wafer with non-conductin g nanostructured SiO 2 nano-space rs with heights of 35
nm or 70 nm is assemble d on the bottom electrode. This procedure results in thin supported
films with a fr ee pol y mer/air interf ace. The BDS measurements show two relaxation
processes, which are anal y zed unambiguously for thicknesses smaller than 50 nm. The
relaxation rates of both proce sses have different temperature dependenci es. One process
coincidences in its position and temperature dependence with the glassy d y namics of bulk
PVME and is ascribe d to the d y n amic glass transiti on of a bulk -like la y er i n the middle of
the film. The relaxation ra tes we re found to be thic kness independent as c onfirmed b y SHS.
Unexpectedly , the relaxation rates of the second process obe y an Arrhenius -like temperature
dependence. This process was not observed b y SHS and was related to the constra ined
fluctuations in a la yer, which is irreversibl y adsorbed at the subst rate with a heterogeneous
structure. I ts molecular fluctuations undergo a confinement effect r esulting in the
localization of the segmental d y namics. To ou r knowledge, this is the fir st report on the
molecular dyna mics of an adsorbed la y e r in thin fil ms.

91

8.1. Introdu cti on
Advance s in functional coatings, batteries, innovative organic ele ctronics, and h y brid
materials depend stron gly on organic and/or pol ymeric materials confined in t hin films or
adsorbed at surfaces.

1

-

2

F or innovative applications of thin poly mer films, a n unde rstanding
of the molecular r easons for the possible deviations of the prop erties of confined material
from that of the bulk is essential.

3

-

5

In the nanometer vicinit y , solid interfa c es and free
surfaces could alter for instance entanglements, glassy d ynamic s (  -r elaxation), and the
thermal g lass transition temperature (T g ), compared to the bulk behavior. Subseque ntly, thi s
could change macroscopic quantities of thin films like a dhesion, wett ability, fr iction,
reac tivit y, and biocompatibil it y , which a re topical problems fo r h y brid m aterials.

6

For thin
films (<100 nm), local heterogeneities can be induced, which mi ght result in local glass
transition temperature s th at are different from the bulk value.

7

Scientifically , pol ymers i n the fo rm of thi n films c an be conside red as s ample g eometr y to
study 1-dimentional con finement effects. For films with thicknesses of few na nometres, the
question is whether or not the glass transition phen omenon deviates from th e bulk behaviour
and what the mol ecular reasons for thes e possible c hanges are. Th e foundin g work of Keddie
and Jones,

8

,

9

was followed by a variet y of studies, which investigated the dependence of T g
on the film thickn ess, where the results hav e been controversiall y discuss ed. Especiall y, thi n
films prepared from simple homopoly m ers have been ex tensively studied throug h the so-
called static experiments, e.g. ellipsometry ,

10

,

11

fluorescence sp ectroscopy, 7 a nd dielectric
expansion dilatometry 11 ,

12

,

13

as well as by techniques that explore the segmental mobility at
temperatures above the thermal T g , e.g. dielec tric

14

-

16

and specific heat spectroscopy
( dynamic experiments, see for instance references

17

-

19

). To be precise, he re a thermal T g
is defined as a glass transition tempera ture me asured b y a static method where the
thermody namic state of the film changes from an equilibrium liqui d (melt) to a non -
equilibrium glass. 10 ,5 Subse quently, th e contradicting r esults existing in the li terature are due
to the usage of different methods ( static or dyna mic ) and/or different preparation methods
(cappe d versus free pol ymer/air inter face). 10
For thin polymeric films, the thermal T g 13 ,

20

,

21

and the melti ng temperature (T m )

22

,

23

c ou ld
deviate substantial ly from its bulk value. I t is commonly accepted that the thickness
dependence of the thermal T g of supported thin films results as a combined effect of a self -
assembled spatial dynamic heterogeneous structure across the who le film; composed of a
so -called mobi le surface lay er (polymer/air interface), a la yer having bulk -like properties

92

(in the middle of the film), and a la y er adsorbed at the substrate. 10 , 30 The measure d thermal
glass transition temperature results a complicated average including all of these effects in
dependence on the pol ymer and the interaction energ y of the s egments with the subst rate,
as well as the preparation co nditions. Due to missing segment-se gment interactions,
compared to th e bulk, a mobile surface la y er is formed at the interface of the polymer with
air. For non-attractive pol y mer/substrate interactions, this fre e surface layer becomes more
dominant, y ielding a lower th ermal T g . Fo r attractive pol ymer/substrate int eractions,
segments can a dsorb at the poly mer/substrate interface. I n this adsorbed lay er th e segments
have a reduced mobility and may result in a higher thermal T g compared to the bulk. One
has to bear in mind that the formation of this adsorbed la y er requires a given time. The
diffusive mobilit y o f a pol ymer chain dep ends on molecular weight (M w ). 14 The higher the
M w , the longer the time is needed to f orm an adso rbed la y er. This means that the decrease
or increase of the thermal T g of a thin film can be also be due to the annea ling condition
during film preparation. This was concluded from investiga tions b y e llipsometry on
polystyre ne

24

,

25

as well as broadband dielectric spe ctroscopy (BDS) of isolated, semi-
isolated,

26

and brushes of high M w poly(2- vin yl pyridine) (P2VP) films.

27

In contrast to static ex periments, results obtained b y dyna mic methods often show that the
glassy d ynamics (  -relaxation, dynamic T g ) is independent of film thickness. (Please note,
a dynamic T g is me asured in equilibrium, above the thermal T g at a given measurement
freque nc y). These results are discussed as a combination of multiple measurement and
sample preparation eff ect s. For in stance, at tempera tures above the thermal T g , the thickness
of the mobile surface la yer becomes smaller with increasing t emperature.

28

Therefore , its
influence on a measured dynamic T g diminishes with increasing temper ature. This effect
might be the reason that dynamic methods do not show a change o f the dynamic T g , while
the thermal T g estimated in static experiments dec reases or increa s es with decreasing film
thickness.

29

-

30

A mobile surface la y e r was evidenced b y s everal experiments like by photobleaching
experiments, the sinki ng of gold nanospheres into a surface

31

, measure men ts on poly mer
blends

32

and a recent study on P2VP thin films .

33

On the contrary, little is known about the
molecular fluctuations in the adsorbed la yer of th in films. Although, related s yst ems li ke
nanocomposites of P2VP,

34

poly (vin y l acetate) (PVAc),

35

a nd poly ( dimeth yl siloxane )
(PDMS)

36

-

37

filled with silica nanoparticles show so me dynamics of an adsor bed interface
layer, there is no dire ct mea surement that probes the d yna mics o f this r educ ed mobi lit y

93

layer, independentl y from the bulk-like d y namics, in thin films ti ll now. This is due to the
hard accessibilit y of th e dy n amics of the pol y m er/substrate interface and its weak
intensity . 14
Of particular interest here is the d y namics in the irreversible adsorb ed layer, which is formed
at the polymer/substrate, where the chains ge t trapped into non -equilibrium confor mations
that reduces their effecti ve viscosit y. To achieve equilibrated conformations, the reptation
model

38

predicted that the annealing times should be longer than the te rminal relaxation
time. This was found for P S

39

, PMMA, and P VAc.

40

Rotella et al .

41

showed that only the
molecules in dire ct c ontact with an a dsorbing surface are influe nced resulting in changes of
the local T g . I t was further suggested 14 that, at the molecular level, these alterations have a
finite lifetime. Furthermore, these changes corres pond to metastable conf ormations of the
polymer cha in corresponding local minim a in the free energ y l andscape rat her than a global
one.
In this stud y, well-annealed thin films of low molecular weight (M w ) P VME (film
thicknesses from the bulk down to 7 nm) we re investigated b y combining su rface an aly ti cal
techniques with two volume sensitive methods. As surface s ensitive tools, contact angle
measurements (CAM), atomic force micros cop y (AFM), as well as ellipsometry were used.
As volume sensitive ex periments, BDS and S HS, utilizing a recently d evelo ped capacitor
with a nanostructured space r arra ngement 26 ,

42

a nd a pJ/K sensitive AC -nanochip
calorimeter , respectivel y . Nano-size relaxation spectroscop y that probed the dyna mics of
the adsorbed la y e r of PVME thin films showed for the first time, that the segments adsorbe d
at the poly mer/subtract interface ha ve constraint segmental fluctuations. These fluctuations
are independent of the film thickness.
8.2. Expe rimental Sectio n
Materials
PVME was obtained from Al drich Inc. as an aque ous solut ion (50 wt %) with a M w of 10,455
g/mol (~ lower th an the PVME entanglement M w

43

). The pol y dispe rsit y index is 3. To
remove the water before the preparation of the films, the obtained PVME solution was kept
in an oil free vacuum at 303 K for 72 h, then at 323 K for anothe r 96 h. Differential scannin g
calorimetry (DSC ) was used to estimate the therm al glass transition temperature T g for the
bulk sample to be 246 K (10 K/min, second heati ng run). A conc entrated solution of the
dried PVME in tol uene was prepared as a m aster solution. This solu ti on wa s fur ther diluted

94

by toluen e to p repare dif ferent polymer solution with different concentrations, which were
used to control the films thicknesses.
Spin coating and annealing procedure
T hin films were prepared by spin coating in a fl ow box to insure a dust - free atmosphere.
The filtered (Minipore, 0.2 µm) dil uted solutions were spin coated with rotational speed
3000 rpm for 60 s. The concentration of the solution was varied to adjust the f ilm
thicknesses. Aft er spin c oating p rocess, the samples were d ried in v acuum (10 -4 mbar, oil -
free) and a nnealed at 313 K (T ann =T g ,Bu lk + 67 K) f or 72 h. This annealing p rocedure insures
firstly the removal of th e solvent. Secondly , the induced stress durin g spin coating was also
released. 44 I t is important to note that AFM topography ima ges revealed that films have low
roughness down to 7 nm, a s shown in Figure S1. F urther, no inhomogeneities nor dewetting
was observed.
An important point is that the spin coating and ann ealing procedures and conditions we kept
identical for all thin film s amples; AC chip sensors, nanostructured capacitors, and crossed
electrode capacitors (see below).
Volume sensitive methods and Sample preparation
Broadband dielectric spectroscopy (BD S ): The dielectric properties of samples were
character ized b y a hi gh - resolution AL PHA analy z er ( Novocontrol) including a sample
holder with an active head. The complex dielectric permittivity ε*(f) = ε ′(f) − iε″(f) were
measured at frequencies b etw een 10 − 1 and 10 7 H z. Here f denotes the frequenc y where ε′
and ε″ are the real and i maginar y (loss) part of t he complex dielectric function. 𝑖 = √ −1
symbolizes the imaginary unit. A Quatro cr yosystem (Novocontrol) was interfaced to the
cryostat to control the sample temperature (tem perature stabilit y better than 0.1 K.). For
more experimental details the reader is referred to ref [ 45 ]. It is important to note the sample
was purged with dry nitrogen during the course of the measurement.
BDS sample preparation:

95

Figure 8. 1 . (A ) Sch ematic of a b ulk sample in p arallel plate arrangeme nt w ith sp acers. 3D (B) - view of the
crossed electrod e sample and, (C) n anostructured capacito r samp le. (D) AFM picture of the n anostructured
top electrod e with 70 nm spacers . (E) Side view schematic o f the n anostructured ca pacito r .
Bulk samples ( f igure 8. 1 A): The bulk sample was prepared b y melti ng th e PVME between
the contacting elec trod es (two round gold plated br ass electrode s with a diameter of 20 mm)
in parallel pl ate geometry. Fus ed silica spacers were emplo yed to control the sample
thickness to be 50 μm.
Crossed electrodes cap acitors (CEC, f igure 8. 1B and 8. 1 C ): For these dielectric
experiments, thin films were p repared b etween two thin eva porated alu minum strip s as
described in deta il in reference [ 12]. I n short, the used glass substrates were first cleaned in
an ultrasound bath using alkaline solution at 333 K for 15 min. This treatment was followed
by a further ultrasound bath trea tment employing Millipore wa ter (re sistivit y >18 MΩ/cm).
After that, the substr ates were flushed in acetone (Uvasol quality) and furt her dried und er
nitroge n. As bottom el ectrode on th e substrate, served a 2 mm wide a luminum strip with
thickness ca. 60 nm, whi ch was pr epared b y thermal depositi on. 12 This step was followed
by a fu rther cleanin g step, where the subst rate w as is rinsed again with acetone. After that,
thin films were pre pared by spin - coati ng and further a nnealed, as described above . As final
step of the preparation of this sample capacitor a t op electrode (width 2 mm, thickness ca.

96

60 nm) on the poly mer film as described above oriented perpendicular to the bottom
electrode ( fi gure 8.1 B and 8.1C). I n general, the eva poration of metals could damage the
polymer surface, 21 althoug h this is not alway s the case .

46

,

47

. Nevertheless, to minimize th is
risk and to avoid a diffusion of metal atoms into the fi lm , a so-called flash evaporation
(deposition rate >30 nm/s) was applied. Such m ethod, as well as the Alumin um used, allows
for a smooth and defined metal/polymer interface.

48

,

49

Nanostructured capac itors (NEC, figure 8.1D and 8.1E): Here th e sample capacitor was
prepared b y t wo doped silicon wafers, which are highl y conductive with a specific resistance
 < 0.003 Ωcm. The R MS roughness is 0.23 nm. An ultra -flat wafer with a size of 3 x 8
mm 2 is used as the bottom elec trode and the substrate for spin coating the thin films. (The
thickness of the native oxide la y e r is about 1 – 2 nm.) This electrode is first dipped in acetone
for 2 minutes to remove the photore sis t layer. It was then plac ed in a plasma oven in a pur e
ox y ge n a tmosphere (20 W, 300 sec) to clean th e substrate and further to activate the natural
silica. As final step, before spin coating, a CO 2 snow jet gun w as applied to further clean
the surface , down to the microsc ale. Fu rther cle aning and assembly details can be found in
reference [26] . Spin coa ting und er the exact same conditions was employ e d to prepare the
thin films , which we r e fu rther annealed a s d escribed above. A silicon w afer dice with a size
of 1 x 1 mm 2 was used as the top electrode. I t has an arr a y of highly insulatin g silica spa cers.
These sil ica spacers have quadratic cross sections of 5 x 5 µm 2 and heights of 35 nm or 70
nm (Figure 1D ). The nanostructured electrodes we re p repared b y a m icrolithographic
process. For det ails see ref [ 26,42] . I dentic al cleaning p rocedures, as described for the
bottom electrodes, w ere also applied for the nanostructures. This means acetone flushin g
and plasma treatment finalized b y C O 2 snow jet c leaning . As a final step for the capacitor
assembly, the top elec tro de was carefull y plac ed on the wafer with the spin coated film. To
avoid dust-contamination all describe d procedures were done in a flow box.
Differential AC chip calorimetry: For specific heat spectroscopy the nano calorimeter chip
XEN 39390 (Xenso r inte grations, Nl) was employed. At thi s chip, two 4-wi re h eaters he ater
are located in the middle of a free standing thin silicon nitride membrane (thickness 1 µm)
supported b y a Si frame. The theor etical heated area is about 30 µm ×3 0 µ m, where an
integrated 6 -couple thermopile senses the tempe rature

50

. Note that the heater-connecting
lines can contribute sli ghtl y to the he ated area, in addition to the hot spot. A 0.5 to 1 µm
thick SiO 2 la y er protects the described microstructure. Althou gh the thin film was spin

97

coated a cross the whole sensor, onl y the small hea ted area is an alyzed. Theoretically, it
could be modelled and treated a s point he at source.
Further, one has to consider that the empt y se nsor itself contributes to measured heat
capacity . The differential approach to AC chip c alorimetry minimiz es this effect under the
assumption of identical chips. 17 I n the thin film limit (submicron film thicknesses), the h eat
capacity of the sample C S is then calculated to
where  - radial fre qu ency, S - sensitivit y of the th ermopile, P 0 P 0 - applied heating powe r. 17
The effective heat capacit y of the empt y sensor i s given b y


i
G
C C eff   0

, where G/i 
models the heat loss b y t he surroundin g atmosphere. Additionall y ,  U denotes the complex
differe ntial voltage measured for a sample and a n empt y reference sensor. Analogousl y,
 U 0 is the the rmopile si gnal obtained for two empty s ensors. Absolute valu es of C S can b e
deduced usin g calibration techniques.

51

Nevertheless, the real part of the comple x
differe ntial volt age and the correspondin g phase ang le can be c onsidered as measure for the
complex heat capa cit y 17 .
The experiments we re carried out in the tempe rature scan mode. This means that during the
measurement, the f requency was fixed while the temperature was r amped. To ensure
stationary conditions during the m easurement, the scanning rate was v aried in the ran ge
from 1 K/min to 2.0 K/min depending on the programmed frequenc y . The theoretical basis
for AC chip calorime try i s founded on having the re sponse taking place in the linear reg ime.
Therefore, the power for temperature modulation was kept constant at about 25 µW. This
value ensures that the maximum amplitude of the tempera ture oscillation is smaller than
0.25 K and so a li near regime. A fr equenc y ra nge from 10 to 10 4 H z is considered here for
AC chip calorimetry. Further details ca n b e found in reference [17 ].
AC -chip Film preparation: The se nsors were pla ced in a n oxyge n plasma, for 300 sec at 20
W to clean the surface an d activate the sil ica. Thin films were obt ained b y s pin coating the
filtered solution of P VME on the senso r. Finall y, the samples were annealed according to
the procedure de scribed above (see section spin coating and annealing procedure).
Surface analytical methods

S P
U U C i
C e ff
s
0
0 ) (   



(8.1)

98

Contact angle measurements : The automated contact angle s ystem OCA20 (Dataphysics,
Germany) was applied to conducted the contact ang le measurements. This s ystem is
equipped with a si x-fold power zoom lens and a CCD camera. Ha lo gen lamps were used to
ensure a homo geneous b ack li ghting . The contact angle (CA) was det ermined using the
tangent fitti ng method. The used test liquids were Glycerol, n -hexadecane, n-tetradecane,
and a pol y eth ylene gl ycol (M w =200g/mol). The measurements were ca rried out in an
atmosphere saturat ed by the vapor of the test liquid. To insure the complete s aturation of the
atmosphere, samples were place in a cuvette with the test liquid for 15 mins prior to the
measurements. 3 drops were dropped at the surface of a PVME film with a thickness of 200
nm. The film was treated identically to what is disc ussed above. The drops had volume of 4
μl. Mean values of the c ontact angles values we re estimated b y averaging th e angles of both
sides of the drop ov er 10 minutes. The data for SiO 2 and AlO x were taken from reference
[33] and [12], respectively .
Film thickness estimation:
CEC: Ellipsometric measurements could not be carr i ed out for the CEC samples, due to
transpare nc y of glass. Therefore, after the de position of the bottom Al -elec trod e, its
thickness was me asured by atomic for ces microscopy (N anopics 2100) b y esti mating the
height of a step r esulting from a scr atch a cross the Al -electrode. After s pin coating and
annealing the film, similarly, the step h eight o f a g ap, obtained b y cutting through the film
on top of the Al-electrode, was measured. The film thi ckness was estimated as the difference
between these two measurements.
NSC: Film thicknesses were estimated b y ellipsometry usin g the p rocedure described b elow.
Film thickness determination for AC chip sensors: The films thicknesses could not be
measured on the s ensor d irectly. This is due to the small dimensions of the chip and the light
reflected b y connecting bond wire s. The refore, a f urther s eries of films were re-prepared on
a sil icon wafer to estimate the thi ckness b y ellipsometry. The same solutions and identical
conditions were used as for the preparation o f AC chips. Assuming that the sil icon wafer
has similar surface properties as the sensor, the film on silicon wafer shoul d have the same
thickness as that supported on the se nsor. 17 - 19 , 32 - 33
Ellipsometry: The films thicknesses were meas ured using an ellipsometer based on a
polarizer-compensator sample a nal y ser (PCSA) (Optre l GbR, Sinzing, Germa n y ). The
wavelength of the laser light was 632.8 nm and the measurements were done at an angle of

99

incidence of 70 d egrees. The anal ysis of the measurements emplo y ed a m ultilayer model;
consisting of air/PVME/SiO 2 /Si-substrate. I n ord er to reduce th e number of fit parameters,
firstly the thickness of th e SiO 2 layer was estimated before spin coating the pol y m er film.
This value (ca. 1.7 nm) was kept constant durin g the data anal ysis for the p olymer film. A
linear increase of the film thickness with the concentra tion was obtaine d (Figure S2), which
is expected. Furthermore, the ellipsometric mea surements agree with the AFM data.
8.3. Results an d Discu ssion
Contact angle measurements (CAM) were conducted to estimate the interaction of the
polymer with the substrates. During the course of t his investigation, two different substrate
materials SiO 2 (na nostructured capacitors, AC nanochip calorimetr y ) and AlO x (crossed
electrode s ca pacitors) w ere use d. To insure that PVME segments interact with both SiO 2
and AlO x , the int erfacial energies between P VME and both substrate systems were
estimated. To estimate the interfacial tension of PVME, Owens/W endt a pproa ch w as
utilized. It combines the Young relation with the Good equation (for detail s see [

52

]). Using
this approac h, the polar (  P ) and dispersive (  LW ) components of the surface energy of the
solid (S=PVME) and the test liquid ( L ) can be ex tracted by

LW
S
LW
i L
p
i L
P
S
LW
i L
i L i





 
 

,
,
,
,
2
) c os 1 (

(8.2)

(  i – contact angle, i co unts the different test liquids). Lite rature values are used for the
surface tensions of the test liquids.

53

Appl y ing at least four test liquids, from the
Owens/Wendt plot (see Fig u re S7) according to Equ. (1),  P and  LW of t he surface energy
of the sample we re obtained. Using the Fowkes e quation ( see the supporting information,
Table S1 and S2 ), the interfacial energ y

T o tal


of PVME/SiO 2 was found to be 2.73 mJ/m 2
while for PVME/AlO x

T o tal


= 0.66 mJ/m 2 was obtained.
These values of the interfacial energ y confirm that PVME interacts wit h both surf aces,
which provide one basis f or the formation of an ads orbed surface la yer. Further, as discussed
above, the formation of an adsorbed la yer r equires time, which is determ ined by b oth the
molecular wei ght and a nnealing temperature. Both quantities are related to the longest
reptation time, which is found to be relevant for the adsorption of chain segments at solid
interfaces building an a dsorbed la yer [ 24,25] . To allow fo r an adsorptio n process here,

100

firstly, a PVME with a relative low molecular weig ht was chosen, which has shorter
reptation time than a sample with a higher molecular w eight. S econdl y, the films were
annealed at a high temperature (T g +67 K, see preparation conditions) providing a high
enoug h molecular mobili ty. C omparing these conditions to a recent study, 24 where a full y
developed adsorbed la yer was found for pol y st yrene on silica, which has a ca. 100 times
higher molecular weight and was annea led onl y at T g +40 K, the 72 h employ ed as annealing
time is much longer tha n what would be expected for the formation of an adsorbed laye r of
PVME on sil ica. Further, preliminary ellipsometric investigations have star ted for samples;
where the bulk-like layer of the films is removed b y a solvent -leaching approa ch. These
measurements give first d irect evidence for an adsorbed layer in the s y stem considered he re.
These studies are ongoing and will be published elsewhere.
Dielectric spe ctroscopy senses the fluctuations of dipoles within a sample. For the bulk
material, which had to be me asured for com parison, the pol y mer w as measured in
conventional parallel plate arran gement betw een two gold-plat ed e lectrodes. This
measurement displa y s one relaxation process observed as a peak in the die lectric loss. As
expected, this peak is ob served for higher temperatures at hi gher f requencies (se e Figure
S3). I t is due to the  -relaxation connected to se gmenta l fluctuations (dy n amic glass
transition) and agrees with li terature da ta [

54

]. Conduc tivit y contributions due to mobile
charge carriers cause the increase of ε ″ at low f requencies.
The empirical formula o f Havriliak/Negami (HN-function) 45 is employ ed t o quantitatively
character ize the  -relaxati on process. It reads

 



  
) )) ( 1 (
) (
0
*
i
HN


  

(8.3)

where  0 is a r ate connected to the frequenc y of maximal loss f p of the peak ( relaxation
rate).  and  are shap e parameters (0 <   1 and 0<   1) characterizing t he width and the
asy mmetr y of the proce ss, where   ex presses t he dielectric str ength.  ∞ models  ´ for
 >>  0 (  =2  f) . The con ductivity contribution is desc ribed b y adding ε ´´ = σ/(ω s ε 0 ) to the
loss part of the di electric sp e ctra. Here σ is connected to the DC conductivit y, s is a
parameter to model non-Ohmic effects s is one f or Ohmic contac ts, s<1 holds for a non -
Ohmic behavior. ε 0 is the permittivit y of va cuum. The reader is referred to reference [ 45 ]
for further details.

101

For thin pol y mer films, the crossed electrode capacitors (CEC, see experimental section )
were used to characterize films, with thicknesses of 160, 110, 80 and 50 nm . By thi s
preparation technique, the pol y mer film is capped betwe en two the rmall y deposited
Aluminum electrode strips (se e Figures 8.1B and 8.1C). Howeve r, this approa ch has two
disadvantages. Firstly , the prep aration o f the upp er electrode b y thermal evaporation can
attack the structure of the polymer chemically and /or the metal atoms can diffuse int o
polymer film, thereby leadin g to il l -defined interfaces and also electrical short cuts.
Secondly , this sample geometry do es not allow for a free surface at the pol y mer/air int erface.
Therefore, compa risons with other techniques are questionable, due to the different
ge ometrical constrains and the different interfacial energ y of th e samples.
To overcome these limi tations, a recently developed nanostructured c apacitor (NSC)
arra ngement (Figures 8.1 D and 8.1E), was emplo yed. 26 , 42 I n this geometry, t he pol y m er film
has a free su rface at the poly mer/ai r int erface. For more details, see ex perimental section
and references [26,27,42] . S amples with thi cknesses between 50 nm and 7 n m were prepared
in this arra n gement. For film thickness of 50 nm, 36 nm, an d 26 nm, nanostructured
electrode s with 70 nm high SiO 2 nanospacers wer e employ ed, while the films with 15 nm
and 7 nm thickness were prepared with 35 nm high nanostructured SiO 2 spacers. It is
important to note that the height of the emplo yed nanostructured spa cers should be at lea st
around twice as the thic kness of the films, to insure a free surf ace e ven in the case whe n the
silica spacers sinking into the film. However, due to the limited available spacer heights,
CECs were used for films, which are thicker than 50 nm, as described above. To e nsure that
both methods will lead to consistent results, to samples with a thickness of 50 nm were
prepared b y both crosse d electrodes and nanostructured capacitors. The results of the
differe nt measurements overlap ( se e Figure S4 ). This means that the two different surface
conditions (ca pped - free) does not influence the dynamics of the PVME segments
significa ntl y.

102

Fig ure 8.2 shows the dielec tric loss ε ´´ spectra at three different temperatur es (275, 295 and
305 K) for P VME thi n films with thicknesses of 15, 26, 36, 50, 110, and 160 nm. Two
parasitic features are obs erved in the spectra. Firstl y, similar to the bulk, fo r all temperatures
at lower frequencies a conductivit y contribution is detected. Secondly , fo r thin films, one
has to take into account t he limited resistance R o f the Al - and/or that of the highly doped
silicon electrodes. This resistance causes an additional parasitic loss peak (here called
electrode peak) located at the high-frequenc y side of the spectra havin g a charac t eristic time
constant τ Res = R*C (C  = sample capacitance). The electrode peak obe ys a Deb y e function
in its frequency d ependence. The maximum position of this electrode peak f Res ∼ 1/τ Res ca n
be moved for optimized sample geometries outside the experimental frequenc y w indow. 12
For this reason, the D eb ye function is modeled b y i ts low frequenc y tail. These contributions
have to be added during the data analy sis. Descr ibing the relaxation process by the HN -
function, the following e quation is obtained for the whole f it function


 

  
iA i s
HN F it   
0
* * ) (

(8.4)

A is a para meter mainl y due to τ Res .

0 3 6 0 3 6
0 3 6
295 K
(a)
(b)
log (  ´´ [a. u.])
log (f [Hz])
305 K
(b)
(a)
275 K
(a)
Increasing th ickness

Figure 8 . 2. Dielectric spectra versus frequen cy at the ind icated three d i fferent tempera tures fo r PVME thin
films: squares – 15 nm, circles – 26 nm, triangles – 36 nm, hexagons – 50 nm, stars – 110 nm, a nd
rhombu ses – 160 nm. (a )

-r elaxa tion o f PVME, (b) the relaxation of an adsorbed interfacia l layer. For
sake of clea rness, the data are shifted alon g the y -scale.

103

As a fir st result, a relaxat ion pea k (a) is detec ted at the same freque nc y as the one measured
for the bulk, for the low est temperature. I ts position does not change with lowerin g the film
thicknesses, indicating th at the relaxation rate of the process (a) is thicknesses independe nt.
As a sec ond result, with increasing temperature , a further pe ak (b) becomes visible at lower
freque ncies than process (a). With increasing tem perature, the separation o f both processes
becomes more pronounced. Similarly , to pro cess (a), the relaxation frequency of peak (b ) is
also thickness independent.
By increasing the tempe rature b y 30 K, the max imum fre quenc y of peak (a) shifts by ca. 3
orders o f magnitude to higher frequencies, wh ereas process (b ) onl y shifts by ca. 1.5 orders
of ma gnitude, for the sa me temperature change (see Figure S5). This result indicates, that
the temperature d ependence of the re laxation rate of process (b) is weaker, compared to that
of proce ss (a).
Specific heat spectr osco py detects the thermal response of the films . Figure 8.3A depicts
a result of an AC-nanocalorimetr y m easurement f or a 100 nm thick P VME film. The real
part U R as well as the phase angle  of th e complex differe nti al voltage are depicted at a
freque nc y of 160 Hz as a function of temperature. The d ynamic g lass transition is indicated
by a step-like change in U R together with a peak in  . A dynamic glass transition temperature
can be defined in dependence on the me asuring frequenc y as temperature of the h alf step
height of U R as well as the max imum temperature of the peak of  . Th e as- measured phase
ang le data has to be corr ected for an underl ying step in the signal, which is proportional to
the real part 17 . However, this subtraction proc ess is somewhat ambiguous. Therefor e, a
rece ntl y developed method was applied for esti mating the dynamic T g in dependence on
freque nc y, as described in reference [33]. I n this approa ch, the stepwise function of the re al
part U R (Figure 8.3A) is differentiated with r espect to temperature, which results in a p eak
in the derivative. A Gaussian is fitted to these d ata and the m ax imum temperature of that
peak is taken as dynamic T g (Fi gure 8.3 B). ±2 K can be conside red as the t ypical error in
the estimation of the T g by AC- chip calorimetry. For further details see ref erences [17,33 ].

104

40
50
60
U R [µv]
A
T g
-3
-2
-1
0
 corrected [  ]
200 250 300 350
74
76
78
 [  ]
T [K]
200 225 250 275 300 325 350
0.0
0.3
0.6
0.9 B
dU R /dT [  V/K ]
T [K]

225 250 275 300 325
100 nm
40 nm
(dU R /dT) [a.u.]
T [K]
C
10 nm

Figure 8 . 3. ( A ) Rea l part as well a s the co rrected pha se angle o f the complex differential voltag e versus
temperature at 16 0 Hz for a 100 nm th ick film. The contribution of U R in the raw data o f

(see inset) was
subtracted. ( B ) First deriva tive o f the U R data g iven in A ver sus tempera ture. The red soli d lines in A and
B are fits of Gaussians to the data. ( C ) N ormalized first deriva tive of the real part at a frequency of 160 Hz
for the ind icated different film thickn ess. For clea rness, th e curves we re systematica lly mo ved a long the y -
scale. The so lid lines are n onlinear regressions o f Gaussians to th e data as guid es for the eyes.

Fig ure 8.3c shows the temperature dependence of first derivatives of U R ver sus tempera ture,
for several film thi cknesses normalized to it s max imum heights. Two ma in observations
could be made. 1) Only one relax ation process is detected for all film thicknesses in
differe nce to the dielectric measurements. It is relate d to the dy n amic glass transition of
PVME (  -relaxation, coo perative se gmental motion. 2) Down to the lowest film thi cknesses

105

of 10 nm, all c urves have a maxima at the same te mperature position, which means that the
dynamic T g is thickness independent.
Discussing all results in quantitative wa y , a s o - called relaxation map is used. I n this
repre sentation, the relaxation rate f p is plott ed versus 1/T (see Fi gu re 8 . 4 ).
For an  - process, the temperature dependence of t he relaxation rate f p is expected to be non -
li near in such a plot , w here this depend ence can be approximated b y the well - known
Vogel/Fulcher/Tammann - (VFT - ) equation 45
0
p T T
B
f lo g f lo g 
  

( 8 . 5)
f  and B are fitti ng parameters. T 0 is a parameter known as ideal glass tra nsition or Vogel
temperature. Empirically T 0 is found to be 30 - 70 K below the conventional thermal T g
measured by DSC.

106

Figure 8. 4: ( A) Open symbols: f p versus 1/T for d ifferent film thickn esses mea sured by BDS : down sited
triangles – bulk, stars - 160 nm, squares – 110 nm, hex agonal - 47 n m, asterisks – 36 nm, circles – 26 nm,
crossed star s – 1 5 n m and crossed-righ t sited triangles – 7 nm. So lid symb ols: f p versus 1/T for differen t
estimated by SHS for different film thicknesses: squ ares - 140 n m, sta rs - 1 00 n m, rhombuses – 40 nm,
circles – 30 nm, righ t sited triangles – 20 nm, up- sited triangles – 10nm. The red solid lines correspon d to
fits of the VFT formula to the different da ta. BDS (bulk -like): log (f

[Hz ] )=12, B=646 K, T 0 =202 K; SHS:
log ( f

[ Hz ] )=12, B=560 K, T 0 =208 K. The dotted line is an fit of the Arrhen ius equatio n to the dielectric
data o f p rocess (b) (the part o f th e adsorb ed layer with lo garithmic time dep endence). (B) A schema tic
cartoon of a two- layer structu re (adsorbed laye r and a b ulk - like layer) a s ded uced from the d ata an d
literature.

For the B DS measurements, the proc ess (a), coincidence in its frequency posit ion as we ll as
in it s temperature dependence with the   relaxation of bulk PVME. Therefore, process (a)
is asc ribed to the d y namic glass tra nsit ion of a bulk-like lay e r in the central part of the film.
As discussed above, the tempera tur e dependence of the relaxation rate of process (a) is
thickness independ ent and can be well describ ed b y a c ommon (including all film
thicknesses) VFT-fit. This is further confirmed by the SHS data, which approximatel y
superimpose, within the ex perimental error discussed above, with the BDS r esults,
independent of film thickness. Similar results were found in AC -chip calorimetric studies
for other polymer s. 17 - 19 , 30 , 33
Although process (b) can still be observed for larger film thicknesses as a sh oulder to process
(a), it c an onl y be unambiguousl y analy z ed for thicknesses of 40 nm and below, as it
becomes more pronounced with decre asin g film thickness. This result gives first evidence,
that process (b) is re lated to a lay er, which is relativel y independent from the bulk -like lay e r.
Further, it is worth to note that process (b) is observed onl y b y BDS, but not b y specific heat
spectroscopy, despite of the fact that for both measure m ents the sample s were prepared
under identical conditions (see m ethod section). Compared to process (a), the relaxation
rates of process (b ) ob ey an essentiall y diff erent temperatur e depend ence. It is well
described b y an Arrhenius equation. The estimated activation energ y of 6 2.4 ± 2.6 kJ /mol
is independent of film thickness. Dielectric investigation shows that PVME also has a
conventional  -relaxation, which is found for 1 Hz to be around 120 K, with an ac tivation
energy o f 21.7 kJ /mol.

55

Process (b) is observed at essentially hi gher temperatures, and as
discussed above it s activation energy is ca. three ti mes higher. Therefore, process (b) cannot
be assig ned to the  -relaxation of PVME.
To assig n this process, o ne has to recall that the selected ex perimental co nditions during
sample preparation will allow for the existence of an irreversibl y adsorbed layer on the
attractive sil ica. Since relax ation process (b), compared to the  -p rocess due to the bulk -

107

like la y er, is observed independe ntl y , has slower relaxation rates at highe r temperatures, and
is still observed at temperatures below the T g , it is ascribed for that reas on to molecular
fluctuations in the adsorbed la yer. The existence of such a la y er is shown for most polymers
as reported in references [

56

,

57

], where the segment/surface int eraction energies are in the
order of k B T (k B -B olt zmann constant). The connectivit y of the chains further stabilizes this
layer since the deta chment would require cooperative rearrangement of a l arger set of the
adsorbed seg ments.

58

To understand the ori gin of process (b) in more detail, it is necessary to discuss growth
kinetics of the adsorbed la y er, according to liter ature results. Rec ently, it was shown that
the adsorption process takes place in two different regimes having different time
dependencies. 24 At short times, the kinetics of the adsorption process follows a linear time
dependence and the pol y mer se gments are directl y adsorbed at the substrat e forming a d ense
strongly bounded adsorbed la ye r.

59

,

60

This layer is probabl y completel y immobiliz ed a nd
cannot be detected b y dielectric spe ctroscopy. Th is part of the layer consis ts mainly of the
so - cal led trains.

61

,

62

At lon ger times, the a dsorption kinetics is changed to a logarithmi c
time dependence. The adsorbed la y er further grows by diffusion of segments through th e
already existing lay e r, on the expense of their entrop y . The structur e of this pa rt of the
adsorbed la ye r is consisting of loops and tails 61 , 62 and is thus less dense than the im mobilized
part. Ther efore, it s structure should a llow for so me molecular fluctuations, which can be
monitored b y dielectric s pectroscopy (se e figure 8. 4B). According to these literature results,
relaxation process (b) is t herefore ascribed to mole cular mobilit y o r fluctu ations within the
part of the adsorb ed la yer, which is formed m ainl y during the logarithmic stage of the
adsorption, leading to constrained PVME segments.
The results reveal that the molecular d yna mics in the adsorbed la yer is not directl y a
coopera tive se gmental motion with a slowed down relaxation time, as i t was observed for
nanoparticles embedded for inst ance in PVAc 35 and P2VP 34 formed b y a solution casting
process. T his means that spin-coating leads to different pol y me r subs trate int erfaces
compared to the solution casting . In the solut ion casting route, a long time is emplo y e d to
remove the solvent from the s y st em, whereas during the spin coating process, most of the
solvent is removed from the s y stem in few seconds . These different time regimes for
solution c asting versus s pin coa ti ng will result in different adsorbed la yers with diffe rent
structures and d ynamics. Whereas in the former case, probabl y an equil ibrated lay e r is

108

formed, while the latter procedure will l ead to a non-equilibrated adsorbed la y er with
constrained dyna mics.
The found ac tivation energy for the constrained f luctuation in the adsorbed layer of 62.4
kJ/mol seems, at the first glance, to be simil ar to th e value of the a ctivation ener gy found b y
Ho usmanns for the adsorption of polysty r ene at a SiO 2 substrate. 24 On the one side, this
agree ment could be a ccidental. Nevertheless, the adsorption/desorption process must also
be related to some molecular mobil ity . To prove this, further experiments, including other
polymer s, are necessar y .
A phenomenolo gical ly analogous behavior is observed fo r two pol y siloxanes -
poly(dimethyl silox ane) (PDMS) and pol y(methyl phenyl silox ane) (PMPS ) – which are
embedded into nanoporous glasses.

63

,

64

With decrea sing confining pore size, a transitio n
from a VFT behavior, i ndicating glassy d y namics, to an Arrhenius law was observed.
Further, the estimated apparent activation energies decrease with decreasing the pore size.
Also a c rossing of the tempe rature dependencies of the relaxation ra tes, which are
character istic for the bulk by that in confinement, is found. For poly m ers embedded into
nanoporous glasses, the transition from the VFT t o the Arrhenius behavior is i nterpreted as
an effect of the spatial confinement due to the pore s on the molecular fluc t uations of the  -
relaxation. Hence, the observed p rocess with an Arrhenius-like temperature dependence is
considered as a degenerated  -relaxation within the pores. This means that due to the
confining effect of the p ores, including int eraction effects with the walls, the cooperative
segmental dynamics degenerates from a coop erative to constrained localized molecular
fluctuation. In the case o f thin PVME films , an a nalogously comp arable interpr etation is
suggested. Here, the con finement originates from the adsorption at the su bstrate together
with the structure of the formed adsorbed la y e r, a s discussed above. A simi lar discussion
has been made for pol ysty r ene films investigated b y neutron scattering.

65

I n a recent stud y , Burroughs and coworkers 25 evidenced that there is a critical annealing
time after which the thi ckness of the adsorbed la y e r becomes constant wi th a value h ∞ . I n
the case of pol ysty r ene, h ∞ was found to be on the order of 0.55 to 0.47 R g . Here, R g is the
radius of gyration of the pol y mer.

66

For PVME, with similar M W to the one used in th is
work, the radius of g y ration was found to be 4.7 n m.

67

The above mentioned scaling factor
might be used to get an es timation for the thickness of the whole adsorbed la y e r, which gives
h ∞ =2.4 ± 0.15 nm for P VME. For this estimation, one h as to k eep in mind that the applied
scaling factor w as obtain ed for a w eakl y interacti ng s y stem. Here, the pol y m er segments

109

and the substrate hav e an attractive interaction. This means that the estimated value of
h ∞ =2 .4 nm has to be considered onl y as a lower bound. This means that the part of the
adsorbed layer formed in the logarithmic regime has even smaller thickness. It is worth to
note that this value c orresponds t o the rang e of pore sizes, where the c han ge from a VFT to
an Arrhenius behavior was found. 63 , 64
Moreover, as discussed above, AC chip calorimetry measures the averaged thermal response
of only the mobile segments throug hout the whole film. How ever, this response is sensitive
to the total mass (thickness) of the film, down to n g. Using Equa ti on (8.1) the change of the
heat ca pacit y a t the glass transition can be expressed by 17 , 51

(8.6)

Here m is the mass of the film. To derive this equation, it was further assumed that the
density of the film is the same as in the bulk. According to Equation ( 8. 6), U R,L iq uid - U R,Gl ass
=  U R should scale li nearly with the thickness of the film. I n Figure 8.5,  U R is given versus
d. The da ta c an be well de scribed b y a line ar re gression line. However, this line does not g o
through the origin, as expected when the whole sample mass contrib utes to the dyna mi c
glass tr ansition. I t intercepts the x -axis at ca. 3.5 ± 0.8 nm. From this result, one might
conclude that there is ca. 3.5 nm thi ck laye r of the film immobilized at the substrate with
regard to molecular fluctuations, which cannot be sensed by specific heat spectroscopy .
Therefore, it does not contribute to the dy namic glass transition. This value includes both
parts of the adsorbed layer; formed during the linear and the logarith mic adsorption
regime. 24 Within the experime ntal error, this value is in good agreement with the 2.4 nm,
evaluated from the adsorption kinetics of poly styrene.

d ~ m ~ SP / ) U U ( C i C C G la s s , R Liq u id , R G la s s , S Liq u id , S 0
2    

110

0 20 40 60 80 100 120
0
1
2
3
4
5
6
 U R, 320 Hz [  V ]
d [nm]
3.5  0.8 nm

Figure 8 .5.

U R versus d for thin PVME films at a frequ ency of 3 20 Hz. Th e solid lin e is a fit to the d ata.

Furthermore, the cooperativit y approach to the glass transition predicts a value for th e
coopera tivit y length scale smaller than 3 nm,

68

which was experimentall y evidenced [see for
instance

69

,

70

]. The calculated thickness of the adsorbed layer is smaller than 3 nm. This
might mean that no glass transition can take place in thi s layer. To be complete, the value
of 2.4 nm means that for a film with a thickness 7 nm, more than one third of the film is the
adsorbed layer.
For P DMS and PMPS c onfined into na nopo rous glasses, at th e change fr om the VFT to the
Arrhenius b ehavior, the s tep-like incr ease of the s pecific heat ca pacit y at t he thermal glass
transition vanishes [63, 64 ] . This indicates that no g lass transition takes place for smaller
pore siz es. This is consistent with the observa ti on that the specific heat spe ctroscop y shows
only one peak related to the glassy d y n amics of the bulk -like layer, y et no process due to
the dynamics of the a dso rbed la y er.
A closer look on Fi gure 8.2 reveals that the dielectric int ensity o f the pro cess due to the
adsorbed la y er increases with decrea sing film thickness compare d to the bulk -like layer.
Therefore, the inset of Figure 8.6 depicts the ratio of the dielectric strength due to the
adsorbed la yer   b to the total dielectric stren gth  a +  b versus film thickness. Although
the data show considerable scattering, this ratio decreases by trend. This indicates t hat the
influence of the adsorbed lay er on the properties of the whole film incre ases with dec reasing
thickness.

111

It is important to note that due to the increa sing complexit y and inhomogen eity of the setup
of the NSC, an a ccurate ex traction of the net diel ectric str ength requires a considera tion of
the ge ometr y of the capacitors. An equivalent circ uit analy sis is n ecessary, to mimic the thin
film, the air gap, the spacers etc. of the nanostructured capacitor, 26 , 27 for the ex traction of
the net dielectric stren gth from the data measured b y NSC. This means that only the trend
of the extracted relaxation strength from the NSC measurements can be considered, when
comparing different film thicknesses measured b y NSC and/or when co mparing NSC to
CEC, and not their estimated values. Fu rthermore, it is worth to mention that these
equivalent circuits are complex and have to be adapted from one system to another.
However, such an analysis will be presented e lsewhere.

280 300 320 340
0.0
0.1
0.2
0.3
0 10 20 30 40
0.0
0.1
0.2
0.3
0.4

T [K]

 b / (  a +  b )
Film Thickness [nm]

Figure 8 . 6. Dielectric strength of the bulk - like laye r (stars) an d interfacia l layer (circles) versus
temperature for the 7 n m P VME film. The inset shows th e dielectric strength of th e a ds orbed layer

b
divided the total dielectric stre ngth

a +

b versus film thick ness.

Fig ure 8. 6 shows Δε a and Δε b as a function of tempera ture for the film which is 7 nm thick.
While Δε a decrea ses with temperature, the dielectric strength of peak (b) increases.
The D ebye theor y of die l ectric relaxation gives for the dielectric strength Δε 45

) (
3
1 2
0 V
N
T k
g
B



 

(8.7)

Here  is the dipole, N the number o f fluctuating d ipoles in the volume V. S tatic correlations
between the dipoles are described b y the so -called Kirkwood correlation factor g. The
Onsager factor is omitted for the sake of simplicity . 35 Gene rall y , the dielectric stren gth

112

decreases with increasin g temperature 45 for glassy d yna mics, as it is also observed fo r bulk
PVME as well as PVME films measured by CEC (see Figure S6). This is also observe d for
the temperature depende nce of  a of the bulk -like relax ation in thin films. In dif ference,
 b of the relaxation process ascribed to the adsorbed la y er increase s with increa sing
temperature. This can be understood by taking into acc ount that the interaction streng th of
the se gments with the substrate decreases with in creasing temper ature. This will increase
the number of mobile dipoles in the adsorbed lay e rs and h ence, according to Eq. 4, th e
dielectric stre ngth.
Finally , as re centl y illustrated in previous work, 33 AC -chip calorimetry was proven to be a
sensitive tool to detect adsorbed and/or surface l ay ers b y ex amini ng the shape and/or the
broadening of the processes . Upon a closer look at Figure 8.3C, one noti ces that the peaks
broaden with decreasing film thickness. To clarify that, Fig ure 8.7 shows the normalized
Gaussian fits to the first deriva ti ve of U R versus normalized temperature (w ith the
corre sponding d y namic T g s). This normalization was done to exclude the error of SHS
which is  3 K and further elucidate the broadening proc ess . F rom the Ga uss ians to the data,
the full width at half max imum (FWHM) can be cal culated, which can be considered as a
parameter to charac t erize the broadening of the curves.

-60 -40 -20 0 20 40 60
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100
14
16
18
Norm. gaussian fit of dU R /dT
T-T g [K]
FWHM Gaussian [K]
Thickness [nm]

Figure 8 . 7. The Gaussian fits to the no rmalized first deriva tive of th e real part at 160 Hz versus
temperature. Purple - 10 0 nm, mag en ta - 20 nm, a nd bla ck - 10nm. The inset shows the full width at half
maximum fo r the Gau ssian fits versus the samp le thickn ess.

Fig ure 8.7 shows that there is a sy st ematic broade ning of the peaks with dec reasing
thickness. If one assumes that the peak is due to a distribution function of the relaxation

113

times, a broa denin g to lower temperature s would corr espond to increased contribution of
fluctuations with shorter relaxation times, while a broad ening to hi gher temperatures is
related to an increased amount of mol ecular mo bilit y having longer relax ation times. I n
other words, as the thickness of the bulk-like layer decreases with decreasing the thickness,
the influence of the mo bile surface l a ye r and an adsorbed la y er incr eases. This is in
agree ment with ref er ence [28] and further confirms the existence of the adsorbe d la yer
observed by BDS.
8.4. Conclu sion
The molecular d ynamics of low M w PVME thin films (160 nm down to 7 nm) was
investigated via a combination of volume sensitive methods and surfa ce analytic al
techniques. Volume s ensitive techniques like broadband dielectric spectroscop y , utiliz ing
nanostructure d capacitors (NSC) with a nanostructured electrode sample arrangement and
crossed-electrode capacitors (CEC), as well as spe cific heat spectroscop y us ing a nano chip
calorimeter were employed. In addition, contac t angle investigations proved the interaction
of PVME se gments with SiO 2 and AlO X . F or films with thi cknesses up to 50 nm, mea sured
by NSC , BDS measurements showed two relaxation processes, which can be anal y zed for
these film thicknesses in details. One process coin cides in it s frequency pos ition as well as
in its temperature dependence , with the  -relaxation of bulk PVME. For this reasons, it is
assigne d to the d y namic glass tr ansition of a bulk - like layer lo cated in the center of the film.
Furthermore, the temperature dependence of the relaxation rates of this proce ss is
independent of film thickness. This was further confirmed b y the S HS investigations, which
superimpose in its temperature dependence with the BDS results independent of film
thickness.
On the other hand, the relaxation rates of the second process, which became more pounced
with decreasin g film thi ckness, showed an essentiall y different temper ature dependence. Its
dielectric stren gth incr eases with temperature, in c ontrast to that of the bulk-like lay er. This
was ex plained by assu ming that with increasing tempe rature, th e segments s ubstrate
interaction becomes weaker, and hence the numbe r of contributing mobile dipoles increases.
Furthermore, the second process did not show a rather slowed down se gmental d yna mi cs,
as it was the case for a la y e r absorbed at sil ica em bedded in PVAc 35 and P2 VP . 34 However,
the behavior of its r elaxation rates as a function of tempera ture resembles th at of PMPS and
PDMS confined int o nanoporous glass. There fore, thi s p rocess was assigned to a
degenerated constrained  -relax ation of an irreversible adsorbed la y er at th e

114

polymer /substrate interface, which undergoes a confinement effect resulting in the
localization of the segmental d y namics. This was further confirmed b y SHS, where a
systematic s y mm etric b roadening was observed with decreasing thicknes s, as well as an
immobilized 3.5 nm, which does not contributing to the total thermal response of the film.
To our knowledge, this is the first probing of the mol ecular d ynamics of a n adsorbed la y er
in thi n films. Further work will concentra te on evidencing such an adsorbe d la y e r for othe r
systems as well.

115

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117

CH A P TER 9 - U nexpecte d Be ha vior of Ultra -Thin Films of
Blends of Pol y s t y r ene/P ol y ( v i nyl meth yl ether) stu d ied b y
Specific Heat S pectroscop y
The following chapter/ar ticle is reprinted from ( Madkour, S.; Szymoniak, P.; Schick, C.;
Schönhals. A. Unexpe ct ed Be havior of Ultra-thin Films of Blends of Polystyre ne/Poly (vinyl
methyl ether) Studied by Specific Heat Sp ectroscopy. J. Chem. Phys. 2017, 146, 203321 and
may be found at http://dx.doi.org/10.1063/1.4978505 ). With the permission of Ame rican
Institute of Physics (AI P ) Publishing.
DOI: http://dx.doi.org/10.1063/1.4978505

A bstract
Specific hea t spectroscopy (SHS ) employing AC nanoc hip calorimetry was used to
investigate the g lass y dynamics o f ult ra-thin films (thicknesses: 10 nm – 340 nm) of a
polymer blend, which is mi scible in the bulk. I n d etail, a Pol y (vin yl methyl ether)
(PVME)/Polysty rene (PS) b lend with the composition of 25: 75 wt% was st udied. The film
thickness wa s controlled by ellipsometry while the film topo gra ph y was check b y AFM.
The results are discussed in the framework of the balance between an adso rbed and a free
surface la yer on the glassy d y namics. By a self -assembling process, a la yer with a reduced
mobilit y , is irreversibl y adsorbed a t t he pol y mer/substrate interface. This layer is discussed
employing two different scenarios. In the first approach, it is assumed that a PS -rich lay e r
is adsorbe d at th e substrate. Whereas in the second approach, a PV ME -rich layer is
suggested to be formed at the SiO 2 . Further, due to the lower surface tension of PVME, with
respec t to air, a nanometer thick PVME -rich surface la y er, with higher molecular mobilit y ,
is formed at th e pol y mer/air int erface. B y m easuring the glassy d y namics of the thin films
of PVME/P S in dependence on the film thickness, it was shown that down to 30 nm
thicknesses, the dynamic T g of the whole film was strongl y influenced b y th e adsorbed layer
y i eldin g a s ystematic increase in the d y namic T g , with decreasing the film thickness.
However, at a thickness of ca. 30 nm thickness, the influence of the mobile surface la y er
becomes more pronoun ced. This results in a s ystematic decrease in T g with the further
decrease of the film thickness, below 30 nm. These results were discussed with respect to
thin films of PVME/PS b lend with a composition of 50:50 wt% as well a s l iterature re sult s.

118

9.I. Introduct ion
For man y decades, the nature of g lass transit ions of amorphous poly m ers has been
considered as a topic al question of soft matter-ph ysics.

1

-

7

Apart fr om homopol y mers,
miscible blends of amorphous pol y m ers have also attracted much attention in the past
decades,

8

-

20

due to their numerous applications. From the scientific point of view, there ar e
differe nces in their behavior, compared to h omopol y m ers, which are still under
discussion.

21

-

22

For instance, the d y namic heterogeneities observed fo r t he segmenta l
dyna mics or d y namic gla ss transition of bulk blends, as discuss ed below . This stud y deals
with the investigation of the d y namic glass transition (segmental dy namics,  -relaxation) of
ultra-thin films of pol ymer blends, which a re mi scible in the bulk. Therefore, in the first part
of the introduction, some peculiarities of the dynamic glass transition of mi scible blends in
the bulk are discussed, whereas in the sec ond part some im portant fa cts about the g l ass
transition of ultra-thin polymer films are summarized.
Despite the w ealth of kno wledge about th e stru cture of bulk binar y mi scible pol ymer
blends 7- 20 , a number of questions regarding the molecular mobi lit y remain; i.e. how the
segmental dynamics of ea ch component of the blend is affe cted b y blending and by changing
the composition. I t is well accepted that the molecular composition of a miscible pol y mer
blend, is not completely random. It is more likel y that a segment, o f the component A, is
surrounded b y segments of the same kind than by seg ments of the component B. This means
that on a molecular scale, the eff ective composition of a binary miscible b lend is different
from the macroscopic o ne. 7, 13 I n general, th e segmental d y namics of m iscible p ol ymer
blends is affected in two major w a y s. 7 First, a symmetric broadening o f the relaxation
functions in the frequency domain with respect to the corresponding homopol y m ers is
observed. Secondl y , unlike the fact that a sin gle glass transition temper ature (T g ) is obtained
for miscible blends, as measured by differential scanning c alorimetry (D SC), the mol ecular
dyna mics are known to be spatiall y d y namic het erogeneous. These experimental findings
have bee n explained thro ugh the combined e ffect of chain connectivity, w hich results in a
self-concentra tion mechanism, 7 and thermall y d riven concentration fluct uations. 7 These
me cha nisms give rise to spatial regions, which ha ve different local compositions t han the
average one with their own local relaxation behavior, and subsequentl y local T g s.
Asymmetric miscible blends, in which the difference b etween the glass tr ansition
temperatures of the two components is larg e, h ave attracted a high number of studies in the
past few decades. In this case, the pol ymer with the lower mobilit y , at temperatures below

119

its glass transition tempe rature, strongly affects t he dynamics of the component with the
higher mobili ty. This has been elaborated for Pol y (meth y l eth y l et her) (PVME) /
Pol y st yrene (PS) blends, 10 - 11 ,

23

-

25

. A further detailed discussion of the segmental  -
relaxation and the g lob al chain relaxation of the faster component can be found in ref [ 22 ].
While the above discussed behavior appl y for the bulk, confining pol ymer blends into thin
films (1-dimension) introduces additional constrains to the mol ecular d y n amics. In the
nanometer vicinit y, solid int erfaces and free sur faces could a lt er for instan ce intermolecular
entanglements, local a nd e ffective c oncentrations, g lass y d y n amics, and thermal g lass
transition temperatures of miscible pol y mer bl ends, compared to their bulk values.
Subsequently, this could affect macroscopic p roperties such as adhesion, wettabilit y ,
friction, reactivity, and biocompatibilit y of ultra -thin films .

26

Furthermore, for pol y me r
blends, the surf a ce tensio n of e ach component with respect to the air and the substrate pla ys
an important role and co uld further alter the com positional heterogeneities. Consequentl y ,
for films of miscible poly m er blend with thicknesses of few nanometers, the key questions
become: I ) Whether or not glass y d ynamics and glass tr ansition deviates from their bulk
behavior and what are the molecular reasons for these possible chang es? II) Could the
confinement influence the local composition of the blend a nd/or the phase stabilit y ?
The thickness dependence of the thermal T g of supported thin films of ho mopol y m ers has
been probed b y the so-called static measurements,

27

,

28

e.g. DSC, flore sc ence spectrosco p y

29

and ellipsometry.

30

,

31

Here a thermal T g is defined as a glass transition temperature measured
by a static method at the transition from the equilibrium li quid state to the non -equilibrium
glassy state . These measurements have revealed that with decre asing film thickness, the
thermal T g of ultra-thin films can deviate substant iall y from their bulk values, where both
an increase or a decrease of the the rmal g lass transition temperature could b e observ ed with
decreasing film thickness, depending on both the pol y m er and the sub strate.

32

-

34

This
behavior is now generall y explained b y a spatial dyna mi cal heterogeneous structure across
the film thickness as a combined effect of a free surface la y e r, (at the pol ymer/air int erface),
a bulk-like layer (in the middle of the film), and a layer adsorbed at the substrate due to
substrate/polymer interactions. 30 ,

35

At the poly m er/air interface, the s egments have missing
interaction, compared to the bulk, which results in an enhancement of their mobilit y . The
influence of this so-call ed free surface la yer on the measured thermal glass transition
temperature depends on the substrate/polymer interactions. For non -attractive
polymer /substrate interactions the influence of the free surface la y er becomes mor e

120

pronounced with decre asing film thickness, and thus a decrease in the thermal T g is
observed. 30 , 35 Evidence for such a free sur face la y er w as provide d b y photobleaching
experiments

36

,

37

and embedding of gold nanospheres into a polymer surface.

38

,

39

On the
other hand, it was shown that for attractive pol ymer /substrate interactions, an irreversible
adsorbed thin layer is expected to be formed a t the substrate inter face,

40

,

41

where the
segment/surface int erfacial interactions are in the order of k B T (k B – Boltzmann’s constant).
This lay e r is further stabi liz ed b y the chain connectivity, as cooperative d etachment of the
segments would be required for desorption.

42

Recently , it was shown that this adsorbe d layer
has within a self-assembled spatial dynamic heterogeneous structure, which is formed
throughout a two-st ep a dsorption regime with different time dependencies.

43

At shorter
times, the kinetics of th e adsorption p rocess fol lows a linear ti me d ependence and th e
polymer se gments are dir ectly adsorbed at the substrate forming strongl y bounded adsorbed
layer.

44

,

45

This layer is de ns e

46

,

47

and probably immobilized. At longer times, the adsorpti on
kinetics is cha racterized by a logarithmic time de p endence. He re, the adsorbed la y er further
grows by diffusion and change s in the conform ation of the seg ments through the alread y
existing la y er, on the expense of their entropy. Accordingl y, for an attractive
polymer /substrate system, this adsorbed la y e r, f ormed at the surface of the substrate with
reduce d segmental mobility, could over compensate the influence of the fr ee surfa ce on the
thermal glass transition tempera tur e. Consequently , an increase in thermal T g compare d to
the bulk value with decreasing film thickne ss would b e expected.
On the other h and, m easurements b y d ynamic methods, e.g. broadband dielectric
spectroscopy ( BDS) and spec ific heat spectroscop y (SHS), on homopol ymer s,

48

-

51

carr ied
out at temperatures wel l above the thermal g lass tra nsit ion ha ve show n no thickness
dependence of the dynamic glass transition, in contrary to the thermal T g .

52

,

53

On the one
side, that was partiall y di scussed b y showin g that the thickness of the mobi le surface la yer
decreases with incr easing temperatures above T g , and thus probing its influence on d y namic
glass transition becomes difficult. 36 On the other side, a second approach to discuss the
differe nt behavior starts f rom the consideration that the d yna mi c measurements are carried
out in a linea r regime, where the static m easurements are related to a tr ansition from an
equilibrium to a non -equilibrium state, which can be considered as a non-l inear response.
For instance, the rate de pendence of the thermal T g over a wide range of cooling rates for
thin pol y st yrene films shows a depression from the bulk T g

54

,

55

in a temperature range ,
where as dynamic measurements are independent of the film thickne ss 48 , 51 , 52 . I t is important

121

to note that the two sets of results ar e obtaine d for films prepare d on the same substrate and
with the same kind of perturbation . The onl y difference b eing is that in th e former case, a
non-linear pe rturbation is applied when measuring the thermal T g , whereas in the latter , the
perturbation is linear.
However, for ultra-thin films of mi scible pol y m er blend, due to the abs ence of entropic
effects, the composition at the free surface is do mi nated b y the component, which has the
lower cohesive en erg y to air

56

-

57

. For PVME/PS bl ends this was de monstrated by X-r ay
photoelectron spectroscop y (XPS)

58

and ellipsometry

59

. This might allow to stud y the
influence of the surface la y e r on the  -relaxation, especiall y in the case of as y mmetri c
polymer blends. It h as b een shown recentl y

60

that for ultra-thin films of PVME/PS with a
composition of 50:50 wt%, throug h a combination of S HS and X-ra y photoelectron
spectroscopy ( XPS), that the pre ferential interfaci al energy o f PS towards SiO 2 results in a
layere d structure; where a PVME -rich la y er is s elf-assembled at the free surface interfa ce.
The influence o f this surfac e lay er is detectable at tempera tures well above the monotonous
T g of the blend, resulting in the decrease of T g with decreasing thickness.
Here, as a continuation of the previous work 16 ,

61

the d y n amic glass transitio n of ultra -thin
films of in the bulk miscible blend P VME/PS with a composition of 25: 75 wt% was
investigated b y e mplo y i ng AC -chip calorimetry. Of a particular interest here is the
understanding, and elaborating the sensitive bal ance between th e adsor bed and the free
surface la y e r. All the findings are discussed with re spect to ult ra -thin films of P VME/PS
wi th an overall composition of 50:50 wt% a s we ll as literature re sult s. A die lectric study on
the same sy stem i s in progress using a recently d eveloped nanostructured electrode s y stem.
This study gives dire ct evidence for the d y namic heteroge neit y for this bl end s ystem and
will be published elsewhere.
9.2. Method s
Pol y mers were pu rchased from Aldrich Inc. PVME was obtained as an aqueous solution (50
wt.%) with a molecular weig ht (M w ) o f 10,455 g/m ol (lower than the enta nglement M w

62

)
and a PI of 3. For sampl e preparation, PVME was dried in an oil fr ee vac uum for 72 h at
303 K, then for another 9 6 h at 323 K. PS has a M w of 524 kg/mol and a polydispersity index
(PI) of 1.04. The therm al T g s o f materials in th e bulk were determined b y diff erential
scanning calorimetr y (DSC) and were found to be 246 K and 376 K (1 0K/min, sec ond
heating run) for PVME and PS, respe ctivel y . A conce ntrated pol y mer solution of PVME

122

and P S with the wei ght ratio of the pol ymers of 25 to 75 wt% was prepared as m aster
solution using toluene. The thin films were then prepared b y spin coating; where the film
thickness is controlled by the concentration of the pol y mer solution. For that the master
solution was diluted by toluene .
Differential AC chip calorimetry: Specific heat spectroscop y is empl o y ed utili zing a
nano calorimeter chip. On the calorimeter chip (XEN 39390, Xensor integrations, Nl), the
heater is located in the center of a free standin g thin silicon ni tride membrane (thickness 1
µm) supported b y a S i frame. The chip has a theoretical heated hot spot area of about 30 µ m
×30 µm, with an integ rated 6-couple thermopile and two 4-wire heaters

63

. I n addition to the
hot spot, the heater strips can contribute to the hea ted area as well. A SiO 2 la y er (thickness
0.5-1 µm) protects the heater a nd the rmopile. The thin film was spin coated over the whole
sensor, but only the sma ll heated area is sensed and can be considered as point heat source.
The differential approach to AC chip calorimetry minimizes the contribution of the heat
capacity of the empt y s ensor to the measured da ta. 48 I n the approx imation of thin films
(submicron film thicknesses) the he at capacity of the sample C S is then given by

C s = iωC eff (∆U − ∆U 0 )
P 0 S

(9.1)

where  - radial frequency, S - sensitivit y of the thermopile, P 0 P 0 - applied heating power. 48
𝐶 𝑒 𝑓𝑓= 𝐶 0 + 𝐺
𝑖𝜔 describes the effective heat capacit y of the empty sensor wer e G/i  is the heat
loss through the sur rounding atmosphere .  U is t he complex differentia l t hermopile signal
for an empt y and a sensor with a sample, and  U 0 is the complex differential voltage
measured for two empt y sensors. Absolute value s of C S can be d educed using calibration
techniques.

64

Here the real part of the complex differential voltage and the p hase angle are
considered as measure for the comple x heat capacit y .
During the measurement the fre quenc y was kept constant while the temperature was
scan ned with a rate of 1… 2.0 K/min depending on the progra mmed frequ ency to guaranty
a stationa ry stat e. It is known that thin PVME/PS films can undergo phase separation.
Therefore, the maximum temperature reached during the me asurement was kept well below
th e cloud temperature of PVME/PS 25:75 wt% , m easured for a 100 nm thi ck film, which is
448 K. 20 The heating po wer for the modulation was kept c onstant at abo ut 25 µ W, which
ensures that the amplitude of the temperature modulation is less than 0.25 K and so a linear

123

regime. Th e frequency i s varied between 10 and 10 4 Hz. Furthe r details can b e found in
reference [48 ].
AC -chip Film preparation: Films were prepare d on the surface of the s ensor. The sensors
were annealed under vacuum at 473 K for 2 h to cure the epox y r esin completel y , which
was used to glue the chip to the housing. Then the sensors were placed in an ox y gen plasma,
for 300 s at 20 W to c lean the surfa ce and activate the OH-groups a t the silica surface. This
procedure might chan ge the surface properties and therefore the inte raction with the
polymer . I t i s worth to note that this step was not done in related studies. 48
Thin films were prepared by spin coating a filtered (Minipore, 0.2 μm) solut ion of PVME/PS
with a composition of 2 5: 75 wt% in toluene (3000 rpm, 60 s ) onto th e c entral part of the
sensor. The film thi ckness was adjusted b y the concentration of the solution. After spin
coating , all samples wer e dried in an oil -free vacuum (10 -4 mbar) and annealed at 313 K
(T ann =T g,Bulk + 50 K) for 72 h in order to remove the solvent and the stress induced durin g
spin coating.

65

The films thicknesses could not be measured on the se nsor directl y, due to the small size of
the sensors surface. Th erefore, a second set of films were prepared under identical
conditions on a silicon wafer to e stimate the thickness b y ellipsometry . Since the silicon
wafer has similar surfa ce propertie s as the sensor, i t is assumed that unde r identica l spin
coating conditions, the film on silicon wafer has th e sa me thickness as that supporte d on the
sensor. 21 ,6, 48 , 50 , 16 - 66 Furthermore, to insure no phase separa tion or dewetting occurs du ring
measurements, all samples we re heated up to the maxim um temperature used in the
measurement and kept th ere for 24 hr. Th e topogr aphy of the films was checked b y atomic
force microscopy (AFM ) before and a fter the tr eatment. The pre pared fi lms have a low
surface rou ghness and no sign of dewetting, or phase separation was obse rved, even after
heating to the max imum tempera ture reached during the measure ment ( see f ig ure 9.1).
Differential scanning calorimetry (DSC): DSC was carried out for the bulk samples
employing a differential scanning calorimeter (Se iko DSC 220C, rates 10 K/min). N 2 was
used as a protection gas.
Ellipsometry: The films thicknesses were measured using a polarizer-com pensator sample
analy s er (PC SA) ellipsometer ( Optrel GbR, Sinz ing, Germany). The wavel ength of the laser
light was 632.8 nm and the measurements were d one at an an gle of incidence o f 70 degrees.
The anal y sis of the measurements emplo yed a mult ila y er mod el consisti ng of air/pol ymer

124

film/SiO 2 /Si-substrate. To reduce th e number of fr ee fit p arameters, th e thickness of the
SiO 2 lay er was d etermined befor e spin coating th e polymer film and then this value (ca. 1.7
nm) was kept constant during the data analy sis for the pol ymer film.

Figure 9.1 . AFM image o f (top panel) top view and (bott om panel) cro ss section view o f scratch acros s
a PVME/PS (25:7 5 w t%) thin film with a thickness of ca. 18 nm after annealing at T = 338 K for 72 hours.
No sign of d ewetting o r phase separa tion is ob served.

9.3. Results an d Discu ssion
Fig ure 9.2 shows the result of an AC chip calorimetry measurement at a frequenc y o f 320
Hz for a PVME/PS 25:75 wt% film with a thickn ess of 100 nm. The measurement gives a
complex diffe rential voltage, which is proportional to the complex heat capacity of the film
(C S ; see Eq. 9.1, method section) as a function of temperature at the selected frequency. The
real pa rt of the complex differential voltag e U R and the phase ang l e  are taken as
measurements of C S . While the real part of the complex voltag e display s a step -like change,
the phase an gle shows a peak indicating the d ynamic glass transition (  -relaxation). A
dyna mic glass transition temperature at the selected measuring frequenc y can be tak en as
the temperature of the half step-hi gh of the U R step (f ig ure 9.2A), or the temperature at
which the phase an gle  displa y s a mi nimum (f ig ure 9.2B). In the r aw data of  (figure 9.2
– top pan el), an underl y ing st ep cont ributes to the measured d ata, which is proportional to
the step in U R . Therefore, the phase angle h as to be corrected b y subtracting this contribution
(fig ure 9. 2B - bottom panel). However, this correction process is someh ow ambiguous.
Therefore, a recentl y d eveloped method was employed to estimate the dy namic T g in

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