Glass transition effects in ultra-thin polymer films · 4. Glass transitions effects in ultra -thin...
Transcript of Glass transition effects in ultra-thin polymer films · 4. Glass transitions effects in ultra -thin...
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Glass transition effects in ultra-thin polymer films
Wierzba, 12 May 2004
Michael Wübbenhorst
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Outline
1. Introduction
2. Phenomenology of the glass transition
3. Polymer chains in nano-scale geometry – general issues
4. Glass transitions effects in ultra-thin polymer films – main
findings and models
5. Dielectric relaxations in ultra-thin polymer films – basic
issues
6. DRS results on ultra-thin PMMA films
7. Liquid-like surface mobility in supported PS-films
8. Summary and Future work
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1. Introduction
Introduction
Motivation of this lecture:
1. new materials:
• clay-based "nano"composites, other materials containing "nanofillers",
• nano-structured materials, e.g. alignment layers, nano-porous materials
2. ongoing miniaturization of devices and structures, lithographic structurizing below 100 nm !
3. new insights in physics of macromolecules and the glass transition
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2. Phenomenology of the glass transitionThe glass transition:
2nd route from liquid to solid state by avoiding crystallization
Example:Crystallization of a supercooled liquid (sodiumacetate/water)
V
TTgTK Tm
glass
crystal
liquidsupercooled liquid
Tg < T < Tm:
Viscosity and structural relaxation time τ obey Vogel-Fulcher-Tammann (VFT) law:
( ) exp( )
V
V
ET
k T Tτ τ∞
= − −
Phenomenology of the glass transition
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Rationalization of VFT law:Temperature dependent length scale ξ=ξ(T) of cooperatively rearranging regions (CRR) (Adam and Gibbs, 1965)
ξ
CRR's in confined geometry:deviations of ξ(T) from bulk behaviour likely
àà finite size effects3.0 4.0 5.0 6.0 7.0
1000/T
-10
-8
-6
-4
-2
0
τ [s
]
1,2-propanediol ξ
ξ
Phenomenology of the glass transition
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In polymers:
Additional contribution of chain connectivity expected
cooperative motions of a few monomer units (polymer segments) at T>Tg
t=t0 t=t0+τ
Dynamic glass transition
Phenomenology of the glass transition
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more or less pronounced curvature of η(1/T) dependence
classification into fragile and strong glass formers
Dynamic glass transition
Phenomenology of the glass transition
fragility: nothing to do with mechanical "fragile" behaviour
strong
fragile
fragility or steepness index:
linked to VFT parameters
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( )vv fexp1 ∝τ1. Free volume approach
• assumption of an activation volume (∝ free volume) which links dynamics to specific volume/density
• Lowering the temperature results in progressive slow-down in relaxation rate due to faster decrease in the free volume vf à effective barrier changes with T
Free volume concept:- rationalises the VFT behaviour, works reasonably well for many
polymers - fails to predict the pressure dependence τ(p) and Tg(p)
Dynamic glass transition – theoretical concepts
Phenomenology of the glass transition
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TTSC
AsC
AG ⋅+=
)()/log(τ
2. Adams-Gibbs theory
• assumption of cooperatively rearranging regions (CRR)
• links transition probability W ∝ τ-1 to temperature dependent configurational entropy Sc(T):
Sc(T) = Smelt – Scrystal
• AG theory introduces cooperativity
• Unfortunately no predictions about length scale of CRRs
Phenomenology of the glass transition
Dynamic glass transition – theoretical concepts
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- allows determination of length scale of cooperativity ξ(T) from Cp(T) steps at Tg
nmTTT
T g 32)(,)(
1)(
320
−≈−
∝ ξξ
3. Fluctuation approach (Donth)
How does CRR look like ?
n(z,L)
α(z,L)
L
classical picture string-like CRR from simulations
Phenomenology of the glass transition
Dynamic glass transition – theoretical concepts
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Homologue series of alcoholes
Dynamic glass transition – simple liquids
3.0 4.0 5.0 6.0
1000/T
-10
-8
-6
-4
-2
0
2
4
log(
τ [s
])
GlycerolThreitolXylitolSorbitol
α
HO OOCH
H
H CH
H
CH
H
OOOOCH
H
H CH
H
CH
H
HCH
H
OOOOOCH
H
H CH
H
CH
H
HCH
H
CH
H
OH
OOOOOCH
H
H CH
H
CH
H
HCH
CH
H
CH
H
Phenomenology of the glass transition
glycerol
threitol
xylitol
sorbitol
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-10
-8
-6
-4
-2
0
2
4
0.6 0.7 0.8 0.9 1.0
1000/T
log
τGlycerol
Threitol
Xylitol
Sorbitol
Fragility classification
Phenomenology of the glass transition
-6.0
-24.5
-46.0
-83.3
Tg [C] m
112.1sorbitol
97.2xylitol
79.9threitol
55.5glycerol
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Fragility classification
Phenomenology of the glass transition
m
112.1sorbitol
97.2xylitol79.9threitol
55.5glycerol
Interpretation of fragility/steepness index:
intermolecular
intramolecula
r
cooperativitycooperati
mvity
∝
alcoholes: H-bonding glass formersnumber of OH-groups/molecule varies from 3 à 6
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First: simple glass formers (low molecular mass)
Phenomenology of the glass transition
Dynamic glass transition – effect of confinement
1st example:Confining ethylene glycol (EG) in zeolites
[Huwe et al., PRL 1999]
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15Phenomenology of the glass transition
Dynamic glass transition – effect of confinement
Study of glass transition of ethylene glycol (EG) in different confinement
Confined geometry provided by various zeolites having channels or cages of different shape and size
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Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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Interpretation of results from ethylene glycol/zeolite systems:
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
àà Minimum number of nearest neighbors of 6 required to establish VFT-type dynamics
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formation of nm-sized droplets of EG due to physical network formation between EG/starch
à 3-dim. ConfinementJ. Phys. Chem B, Smits et al., 2001
freshly mixed annealed sample
α-relaxation of ethylene glycol (EG) in Amylopectine/ethyleneglycol (AP/EG) mixtures:
2nd example:
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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2 separate glass transitions of EG and AP/EG phase
α (AP+EG)
α (EG)
"derivε
[Hz][°C]
α (AP+EG)
α (EG)
"derivε
[Hz][°C]
freshly mixed
annealed sample
2.0 3.0 4.0 5.0 6.0 7.01000/T [1/K]
-10
-8
-6
-4
-2
0-lo
g(τ
[s])
25øC40øC60øC80øC100øC120øCEG bulk
αAP+EG
αEG-bulk
Tanneal.
Phenomenology of the glass transition
Dynamic glass transition – effect of confinement αα-relaxation of amylopectine/ethyleneglycol mixtures:
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Clear transition from VFT behaviour àà Arrhenius law
α-process of EG senses size reduction from "bulk" droplets to nm-sized EG clusters
evolution of structure
à time-dependent confinement
3.5 4.5 5.5 6.51000/T [1/K]
-7
-6
-5
-4
-3
-2
-1
0
1
log(
τ [s
])
25°C40°C80°C120°C
EG
3.5 4.5 5.5 6.51000/T [1/K]
-7
-6
-5
-4
-3
-2
-1
0
1
log(
τ [s
])
25°C40°C80°C120°C
EGEG
Phenomenology of the glass transition
Dynamic glass transition – effect of confinement αα-relaxation of amylopectine/ethyleneglycol mixtures:
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Mesogenic nitrostilbene diols of various methylene spacer lengths (LC monomers):
Phase behaviour
n
SB phase
8a (n=2)
8b (n=4)
8c (n=6)
8d (n=11)
isotropic
(nematic)
SA
SE (SX)
T
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
3rd example:
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Dielectric spectrum of C6-compound:Relaxation map
λ2λ1
SAà SX
α
• 2 mesogenic relaxations (in SA state)• 2 phase transitions
2.0 2.5 3.0 3.5 4.0 4.5 5.0
1000/T
-10
-8
-6
-4
-2
0
log(
ç [s
])
I SA
glass + K
λ2
λ1α
unexpected “VFT-process“
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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Coexistence of glass forming (liquid) phase and crystalline mesogenic order
• Analogy to H-bonded liquids ?
OH
smectic layer
smectic layer
spacer/diol phase
HO HO HO OH
OH
HO HO
HO OH OH
OH HO
OH
OH HO OH
HO
OH
HO OH
HO OH
HO
HO
rigid fraction
mobile fraction
Comparison with diols1,3-PD and 1,2-PD
2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2
ç [s
]
8d1,3-PD1,2-PD
n=11
Rigid Fraction
Mobilefraction
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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High frequency relaxation rate: single molecule behaviour
rotational degrees of freedom:
difference in high frequency relaxation rate by < 1 decade plausible
1,3-propanediol
1,3-PD with attached alkoxy-spacer
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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Low frequency relaxation behaviour
Splitting of αα-process for short spacers lengths (n ≤≤ 6)
αSAà SX transition
λ2λ1
αSAà SX transition
8c (C6-spacer) 8d (C11-spacer)
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
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a) C2-spacer b) C4-spacer
2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2
ç [s
]
8a
8a
1,3-PD
n=11
~38 kJ/mol
2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2
ç [s
]
8b
8b
1,3-PD
n=11
Dynamic glass transition – effect of confinement
Phenomenology of the glass transition
Fit-results: peak relaxation time τταα – details
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2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2
ç [s
]
8c
8c
1,3-PD
n=11
c) C6-spacer d) C11-spacer
2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2
ç [s
]
8d1,3-PD1,2-PD
n=11
Crossover-frequency fc : function of spacer length n
Dynamic glass transition – effect of confinement
Fit-results: peak relaxation time τταα – details
Phenomenology of the glass transition
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2.5 3.5 4.5 5.5 6.51000/T
-10
-8
-6
-4
-2
0
2ç
[s]
8d1,3-PD1,2-PD
n=11
Dynamic glass transition – effect of confinement
Lliq(n) ~ ξξ
ξξ(fct) ~ Lliq(n)
ξ(Τ) ξΤ(Τ)ξΝ
Physical meaning of crossover frequency:
Lliq(n) [nm]:
2.5
1.5
Phenomenology of the glass transition
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• ultra-thin polymer films
• clay-based nano-composites
• semicrystalline polymers
• liquid-crystalline polymers
• nano-structured materials
porous silica
MCM-41
Interference between intrinsic length scales of molecular dynamics and geometric dimensions expected
Polymer chains in nm-scale geometry
3. Polymer chains in nm-scale geometry
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chain relaxation(Rouse, Reptation)
segmental motions(dynamic glass transition)
local motions, e.g. simple bond rotations
increasing relaxation time, characteristic length scale
< 1 nm 2 < ξ < 10 nm 10 < ξ < 200 nm
Length scales of motions in polymers
Polymer chains in nm-scale geometry
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31Polymer chains in nm-scale geometry
Length scales of motions in polymers
There are more length scales:
§ reptation model: tube dimensions and there related
relaxation times τd, τe, τr (lecture Prof. Kimmich)
§ mean distance between entanglements (dependent on
Mc and degree of chain coiling
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32Polymer chains in nm-scale geometry
Study of dynamics in confinement:
Successively break-down of molecular motions related to intrinsic length scales > L = imposed length of confined geometry
Length scales of motions in polymers
Ideally: Reduction of L only affects the larger processes
REE
ξα
Rentanglement
ξβ
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Outline
1. Introduction
2. Phenomenology of the glass transition
3. Polymer chains in nano-scale geometry – general issues
4. Glass transitions effects in ultra-thin polymer films – main
findings and models
5. Dielectric relaxations in ultra-thin polymer films – basic
issues
6. DRS results on ultra-thin PMMA films
7. Liquid-like surface mobility in supported PS-films
8. Summary and Future work
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4. Glass transitions effects in ultra-thin polymer films
• Ultrathin polymer films: basic geometries and preparation
• 10 years study of Tg-effects on ultrathin polymer films: typical results
• What remains to be answered?
• How can Dielectric Relaxation Spectroscopy (DRS) contribute to solve the remaining questions?
Tg-effects on ultra-thin polymer films
In this section:
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Ultrathin polymer films: thickness L < 100nm
supported films (polymer on substrate):
capping layer
freely-standing films:
2 basic configurations
Tg-effects on ultra-thin polymer films
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Ultrathin polymer films – how to prepare them ?
Tg-effects on ultra-thin polymer films
• Spin coating• Physical vapour deposition • Electro spraying • Water transfer technique
Four key stages: 1. fluid dispense 2. spin-up3. stable fluid outflow4. evaporation dominated drying.
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Ultrathin polymer films – preparation (2)
Tg-effects on ultra-thin polymer films
2. spin-up
1. fluid dispense
3. stable fluid outflow
4. evaporation dominated drying. ( )0 20
3
2 1f
eh c
cη
ρω
= −
final thickness
vitrificationthickness reduction
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Electro-spraying:
(semi)dilute polymer solution
substrate+
++
+
charged moleculein droplet
nozzle
polymer molecules
++
+
+
electrical field
drying
à deposition of unentangled single polymer molecules possible
Ultrathin polymer films – preparation (3)
Tg-effects on ultra-thin polymer films
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Tg-effects on ultra-thin polymer films
First results:
Tg-effects on ultra-thin polymer films
0 100 200 300105
110
115
120
125
PMMA on SiPMMA on Au
Tg(
o C)
h (nm)
[Keddie et al., Faraday Discuss. 98, 219 (1994)]
70 80 90 100 1101.462
1.464
1.466
42.8
43.0
43.2
0 down1 up1 down
inde
x of
ref
ract
ion
nT (oC)
0 down1 up1 down
h (
nm)
typical result from ellipsometry:h(T), n(T)
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40
Tg-effects on ultra-thin polymer films
Tg-effects on ultra-thin polymer films
Different techniques:• Ellipsometry (refraction index, thickness)• x-ray reflectivity (volume expansivity)• PALS (free volume expansivity)• Brillouin spectroscopy
In the following: Tg-effects on• different polymers: PS, PMMA• different geometries: supported, freely-standing films• different molecular mass
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41
Supported PS films
PS supported on silicon
From Lecture R. Jones
No Mw dependence between 120k and 2M
Different techniques:• Ellipsometry• Micro-DSC• Dielectric Spectroscopy• PALS
Substrates & conditions:• HF-etched Si, vacuum• HF etched Si, air• SiOx• Hexamethyl disilazane layer on
siliconpretty universal behaviour
Tg-effects on ultra-thin polymer films
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42
20 40 60 80 100 120 140 1600
20
40
60
80
100
Mw < 350 k
Mw= 575 k
Mw= 767 k
Mw= 1.25 M
Mw= 2.24 M
Mw= 6.68 M
Mw= 9.1 M
Tg
(oC
)
h (nm)
Forrest & Mattsson, PRE 61, R53 (2000)]
PS freely-standing, Mw < 347k
strong Mw dependence, but simple scaling:
Tg-effects on ultra-thin polymer films
Supported PS films vs. freely-standing films
freely-standing films behave like supported films with half the thickness à 2 free surfaces
high Mw (> 347k)
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43
Three possible scenarios of changed segmental mobility in freely-standing or supported/capped polymer films:
enhanced segmental mobility due to finite size-effect
bulk dynamics
Surface regions of reduced mobilitye.g. due to specific interactions
bulk dynamics
additional increase of the mobility over the entire thickness due to chain confinement for L < REE
L ~ REEL > REE
REE L
L << REE
or
L ~ REEL > REE
REE L
L << REE
or
L << REE
or
Tg-effects on ultra-thin polymer films
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44Tg-effects on ultra-thin polymer films
Some models that describe the Tg-depression in low-Mw PS films
Tg
bulk
Tg
surf
Tg
surf
ξ( )T
ξ( )T
• near-surface cooperative motion[Forrest & Mattson, PRE 61, R53 (2000)]
segregation of chain ends to free surfaces[Mayes, Macro. 27, 3114 (1994)][Tanaka et al., Macro. 29, 3040 (1996)]
coupling to capillary modes[Herminghaus et al., EPJE 5, 531 (2001)]
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45Tg-effects on ultra-thin polymer films
Implications from 2-layer model
Tg
bulk
Tg
surf
Tg
surf
ξ( )T
ξ( )T
liquid like surface layer
• broadening of glass transition expected - confirmed
• Expansivity experiments average over mobility profile àfilm with 2 free surfaces has larger Tg-reduction - confirmed
bulk-like layer
Question 1: what is actual mobility profile?
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46
Supported PMMA films
PMMA supported on Si and Au
Tg-effects on ultra-thin polymer films
• specific interactions (H-bonding) of PMMA with substrate
• also influence of tacticity on Tg-up/down shift !
0 100 200 300105
110
115
120
125
PMMA on SiPMMA on Au
Tg(
o C)
h (nm)
Substrate effects important for PMMA
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47
Comparison freely-standing PMMA – PS films
nearly equivalent molecular weights
Tg-effects on ultra-thin polymer films
20 60 100 140 18040
60
80
100
120
Freely-Standing PMMA M
w= 790 k
PS Mw= 767 k
T g (o
C)
h (nm)
Question 2:
Why do PS and PMMA behave so differently?
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48Tg-effects on ultra-thin polymer films
Why is Tg of PS more sensitive to thickness reduction than in PMMA ?
§ similar Tg
§ similar fragility index
Both PS and PMMA have
what else controls thickness sensitivity of Tg?
bulk PS & PMMA
2.2 2.4 2.6 2.81000/T
-8
-6
-4
-2
0
log(
τ [s
]) a-PMMAPS
α
fragility index ∝ Ea,local(T=Tg)= measure for curvature of VFT curve
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49
One possible answer:In thin films, fragility might change differently for of PMMA and PS
Tg-effects on ultra-thin polymer films
1/T
-logτthin PMMA film
thin PS film Is there any evidence for this scenario?
broadband dynamic studies required àà DRS
bulk PS, PMMA
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50
5. Dielectric relaxations in ultra-thin polymer films – basic issues
DRS : introduction
+
+
+_
+ _
No field
-E
molecular polarisability α
orientational atomic electronic
αaαo αe
LENP α0=N0: concentration of dipoles
EL: local electric field
Loae ENP )(0 ααα ++=
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51
Relaxation phenomena IR VIS/UV
αaαe
αo
polar molecules: orientational polarisability
§ αo depends on T und E§ valid for weak fields
0 1 2 3 4 5 6 7 8
x=æE/kT
0.0
0.2
0.4
0.6
0.8
1.0
L(x
)
kTE
xL L
3)(
µ≈
kTo 3
2µα =
Langevin function
Dielectric relaxation spectroscopy – introduction
DRS : introduction
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52DRS : introduction
Dielectric relaxation spectroscopy – introduction
From microscopic to macroscopic quantities:Clausius-Mosotti relation
++=
+−=
kTNM
P aeAW
M 3321 2
0
µαα
ερεε
MW: molecular weightρ: densityNA: Avogadro’s numberε: dielectric constant
For polymers and other complex dielectrics:Relation by Onsager and Fröhlich
kTgNM
nnn Aw
0
2
22
22
9)2()2)((
εµ
ρεεε =
++−
new: g: dipole-dipole
correlation factor
∞= ε2n
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53
Dielectric relaxation spectroscopy – introduction
DRS : introduction
Dielectric relaxation:Characteristic time to attain thermal equilibrium = τ
0 1 2 3 4 5 6 7 8
time
0.0
0.2
0.4
0.6
0.8
1.0
1.2
P(t)
, E(t
)
E(t)
−=
τt
PtP exp)( 0
τ=1
thermal agitation ac field, frequency ω:
complex dielectric “constant”
)(")()( ' ωεωεωε i−=∗
Real part Imaginary part
storage term loss term
à actually 2 spectra
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54
Dielectric relaxation spectroscopy – introduction
DRS : introduction
Relaxation functions:
Single relaxation time process
-5 -4 -3 -2 -1 0 1 2 3 4 5log(Ô)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Ç'
10|-4
10|-3
10|-2
10|-1
10|0
10|1
10|2
Ç"(loss)
Ôç =1
22'
1)(
τωεεεωε
+−+= ∞
∞s
ωττω
εεωε 22
"
1)(
+−
= ∞s
Distribution in relaxation times à Havriliak-Negami (HN) function:
( )[ ]baiωτ
εεε+
∆+= ∞1
*
à 2 independent shape parameters
• relaxation strength ∆ε• mean relaxation time τ
log(ω)
log(ε)
m= a n= -ab
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55
drawbacks:freely standing geometry hard to
achieveDRS restricted to polar polymers
Fukao, first studiesHartmann, Kremers group Wübbenhorst (coop. with Dutcher)
PS, PVAC,
PMMA, PI...
Sharp, Forrest 2002
?
Al
Al
polymer 2 air gaps
1 air gap
DRS on ultrathin films
advantages:+ sensitivity (C*) increases
with 1/L+ very wide dynamic range + robust sample preparation
DRS on ultra-thin films
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56
à well defined DRS samples with a thickness as low as 4nm without shorts !
optical microscopy & AFM image
4nm àà 10-15 atomic layers !
Top electrode
Polymer film
Lower electrode
Substrate
b
d
a
c
Preparation of ultrathin film "capacitors"
1. spincoating of very dilute solutions on Al-coated glass substrates.
2. evaporation of patterned top electrode
DRS on ultra-thin films
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57
Why does it work?
1. excellent film formingbehaviour of polymers à smooth and close polymer films
2. "self-healing" in case of local shorts
Sometimes: It does not workpermanently shorted samplessamples with high parasitary losses
20 nm
1000 nm
Al coated glass substrate
smooth surface of PMMA on Al, height-range 10nm
V
DRS on ultra-thin films
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58
T [°C]T [°C]f [Hz] f [Hz]
loss ε"loss ε"
Origin of parasitary losses: tunnel junctions
‘proper’ spectrum of i-PMMA i-PMMA spectra with weakly T-dependend low-frequency loss
possible tunnel junctions
unusual loss
DRS on ultra-thin films
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59
Outline
1. Introduction
2. Phenomenology of the glass transition
3. Polymer chains in nano-scale geometry – general issues
4. Glass transitions effects in ultra-thin polymer films – main
findings and models
5. Dielectric relaxations in ultra-thin polymer films – basic
issues
6. DRS results on ultra-thin PMMA films
7. Liquid-like surface mobility in supported PS-films
8. Summary and Future work
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60
6. DRS results on ultra-thin PMMA filmsPoly(methyl methacrylate), PMMA
dielectric ββ-process
2.0 2.5 3.0 3.51000/T
-8
-6
-4
-2
0
2
log(
τ [s
])
α β
a-PMMAEa: 109 kJ/mollog(τ [s]): -19.6
80 kJ/mollog(τ [s]): -15.6
log(τ0)Ea [kJ/mol]
-15.680β
C
O=C
CH3
CH2 – C
CH3n
DRS on ultra-thin PMMA films
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61
"Bulk" PMMA – large influence of stereoregularity
DRS on ultra-thin PMMA films
-25 0 25 50 75 100 125 150
Temperature [°C]
0.01
0.1
tan
δ (2
5 H
z)
i-PMMA, 58 nm
a-PMMA, 158 nm
s-PMMA, 79 nm
β
α (isotactic)
α
β
2.0 2.4 2.8 3.2 3.6 4.0
1000/T [1/K]
-6
-5
-4
-3
-2
-1
0
1
log(
τ [s
])
α (a-PMMA)α (s-PMMA)α (i-PMMA)β (i-PMMA)β (s-PMMA)β (a-PMMA)
αα
:
i-PMMA: Ea ~ 70kJ/mol5670i-PMMA
Tg [°C]Eβ [kJ/mol]
12080s-PMMA
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62
Determination of the glass transition temperature by local activation energy analysis:
( )0 0
20 0
,
,lnapp
T
TE T RT
ω
εωε ω
′∂ ∂= −′∂ ∂
"Bulk" dynamics of stereoregular PMMA
DRS on ultra-thin PMMA films
Maximum in Eapp at T where VFT-law breaks down
α
α
α
β
β
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63
-25 0 25 50 75 100 125 150
Temperature [°C]
0
100
200
300
400
500
Eap
p(T
, 25
Hz)
i-PMMA, 58 nma-PMMA, 158 nms-PMMA, 79 nm
Tg
Ea(β)
Local activation energy analysis for PMMA:
( )0 0
20 0
,
,lnapp
T
TE T RT
ω
εω
ε ω′∂ ∂
= −′∂ ∂
"Bulk" dynamics of stereoregular PMMA
DRS on ultra-thin PMMA films
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-1 0 1 2 3 4 5log(frequency [Hz])
0.1
1.0
2.0
ε"
6.4 nm7.8 nm14.2 nm36.7 nm48.1 nm58.5 nm
i-PMMA, loss spectrumT=70°C
Isotactic PMMA
bulk position
Thickness effects on the αα-relaxation
DRS on ultra-thin PMMA films
§ Broadening in α-process§ Reduction in relaxation
strength
§ Shift of relaxation spectrum
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65
20 40 60 80 100T + ∆ [°C]
0.0
0.4
0.8
1.2
tan
δ/ta
nδ m
ax
6.4 nm
7.8 nm
8.5 nm
14.2 nm
28 nm
36.7 nm
58.5 nm
i-PMMA, f = 6.4 Hz
α
normalized and shifted loss tangent vs. temperature
DRS on ultra-thin PMMA films
Clear broadening of α-process at low & high temperature (frequency)
general broadening favours existence of mobility profile ττ(L)
Thickness effects on the αα-relaxation
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66
àà Shift of αα-peak both at low and high frequencies
-25 0 25 50 75 100 125
Temperature [°C]
10 -2
10 -1
10 0
10 1
ε"
10 -3
10 -2
10 -1
10 0
ε"
6.4 nm7.8 nm14.2 nm28 nm36.7 nm48.1 nm58.5 nm
f = 13 kHz
β
f = 12 Hz
2.5 3.0 3.5 4.01000/T [1/K]
-6
-4
-2
0
2
log(
τ [s
])
58.5 nm48.1 nm36.7 nm28.0 nm14.2 nm8.5 nm8.5 nm6.4 nm
α
β
solid lines correspond to fit of α-peak in T-domain
DRS on ultra-thin PMMA films
Tg (ττ=100s)
Thickness effects on the αα-relaxation
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67
Determination of Tg from VFT-fit of αα-process
0 20 40 60 80
L [nm]
40
60
80
100
T [°C]Tmax(Eapp)Tmax(ε"), 12HzTmax(ε"), 13 kHz
entire speed-up of glass transition dynamics
Tg(L):
DRS on ultra-thin PMMA films
àSame thickness dependence of T(αα) at very different frequencies:0.01, 10, 104 Hz
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Determination of Tg from peak in local activation energy Ea(T):
0 20 40 60 80 100Temperature [°C]
0
100
200
300
400
500
Ea
pp [
kJ/m
ol]
6.4 nm7.8 nm
8.5 nm
14.2 nm
28 nm
48.1 nm
58.5 nm
i-PMMA, f = 6.4 Hz
α
β
Tg-shift
DRS on ultra-thin PMMA films
0 20 40 60 80
L [nm]
40
50
60
70
80
T [°
C] T(τ=100s)
Tmax(ε"), 12Hz
àexcellent agreement between two ways of Tg evaluation
0 20 40 60 80
L [nm]
40
50
60
70
80
T [°
C] T(τ=100s)
Tmax(Eapp)Tmax(ε"), 12Hz
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69
2-stage behaviour in relaxation strength of cooperative dynamics
à 2 characteristic length scales involved
0 20 40 60 80
L [nm]
0.0
1.0
2.0
3.0
∆ε
α-processβ-process
∆εα (bulk)
L = 30 - 40nm close to REE
àà effect of chain confinement
DRS on ultra-thin PMMA films
αα-process of i-PMMA: relaxation strength ∆ε∆εαα(L)
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αα-process of i-PMMA: relaxation strength ∆ε∆εαα(L)
2-stage behaviour in relaxation strength of cooperative dynamics
à 2 characteristic length scales involved
0 20 40 60 80
L [nm]
0.0
1.0
2.0
3.0
∆ε
α-processβ-process
∆εα (bulk)
finite size effect
Extrapolation of ∆ε∆εαα to zero àà ξξ ~ 5nm
DRS on ultra-thin PMMA films
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71
More evidence for critical length of αα-process from syndiotactic PMMA
L = 4 nm
L = 9 nmL = 79 nm
DRS on ultra-thin PMMA films
L = 4 nm
αα- peak vanishes for L = 4 nm !
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PS-PMMA-PS Tri-layer samples
• So far, DRS experiments are potentially sensitive to (specific) surface interactions between aluminium (oxide) and polymer chains
• Better: freely standing film geometry
i-PMMA
• Alternatively, replacement of metal-polymer interface by polymer-polymer interface à 3-layer film PS | PMMA | PS
PMMA/PS - interfacespreparation:
PS-layer
spin-coating
i-PMMA
à floating PMMA
PS-layer
à floating PS-2 à Al-deposition
DRS on ultra-thin PMMA films
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Dielectric response dominated by PMMA (PS almost apolar)
PS-PMMA-PS Tri-layer samples (2)
expected mobility profile:
PMMA/PS - interfaces
x
Tg(x)
PMMA/PS - interfaces
56°C
95°C
DRS on ultra-thin PMMA films
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PS-PMMA-PS Tri-layer samples
0 20 40 60 80 100 120
L [nm]
40
60
80
100
T [°C]
i-PMMAi-PMMAi-PMMAPS-PMMA-PSPS-PMMA-PSPS-PMMA-PS
Shifts in the relaxation time τταα – Tg-effects
- slight up-shift in Tg in tri-layer films instead of Tg-depressions
- higher Tg of interdiffusion layerPS/PMMA likely dominates the average glass transition dynamics for ultra-thin films
DRS on ultra-thin PMMA films
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Now discussion of ββ-process in PMMA
-25 0 25 50 75 100 125 150
Temperature [°C]
0.01
0.1
tanδ
(20
4 H
z)
8.8 nm9 nm22 nm48 nm63 nm79 nm4 nm, 880k4.9 nm, 880k6.3 nm, 880k7 nm, 880k
β
α
Tmax(bulk)
ε”max(bulk)
2 diff. molecular weights:• 145×103 g/mol• 880×103 g/mol
§ Below critical thickness Lc ~ 1 – 1.5 REE:
àMaximum of β-peak shifts to lower T
§ Continuous decrease of peak intensity toward lower L
DRS on ultra-thin PMMA films
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Again, isotactic PMMA, ββ-process
§ Below critical thickness Lc ~ 1 – 1.5 REE:
§ Continuous decrease of ∆εβ toward lower L
DRS on ultra-thin PMMA films
0 20 40 60 80
L [nm]
0.0
1.0
2.0
3.0
∆ε
α-processβ-process
∆εα (bulk)
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ββ-process, relaxation time at 35°°C
DRS on ultra-thin PMMA films
àspeed-up of local dynamics in very thin films
àscaling with reduced thickness L/REE
h > REE
REE h
h ~ REE
0.03 0.1 1 10L/R
EE
-3.0
-2.5
-2.0lo
g(τ m
)
s-PMMA (158×103)a-PMMA (130×103)s-PMMA (1.22×106)
MW [g/mol]
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Correlation between relaxation strength and relaxation rate
0.0 0.5 1.0 1.5 2.0 2.5∆ε
β
-4.5
-4.0
-3.5
-3.0
log(
τ m)
s-PMMA 880ka-PMMAs-PMMAi-PMMA
bulk behaviour
simultaneous changes of ∆ε∆εββ
and log(ττββ):
Reduction of amplitude (mean jump angle) of molecular fluctuation à speed-up of dynamics
Reason:
changes in the conformation statistics induced by chain confinement
DRS on ultra-thin PMMA films
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ββ-process, activation parameters
DRS on ultra-thin PMMA films
0.03 0.1 1 10L/REE
-18
-17
-16
-15
-14
log
(τm)
70
80
90
Ea [
kJ/m
ol]
s-PMMA, 158 ×103
s-PMMA, 1.22 ×106
a-PMMA, 130 ×103
Activation parameters of β-process
clear correlation between Ea and log(ττ)
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Starkweather analysis: activation entropy
BA 1 ln ln
2k T
E RT T Sh f
= + + + ∆ π
( ) B
2H RT S Rk T
f T e eh
−∆ ∆=π
1 10 100
L [nm]
0
20
40
60
80
100
Ea(
∆S=
0)
0
20
40
60
80
100
Ea
[kJ/
mol
]
s-PMMA, 146000s-PMMA, 880000a-PMMA, 128k
activation entropy
à dominant role of the activation entropy in thickness effects on the β-process.
à Separation of activation entropy from Ea as a measure for degree of cooperativity
ββ-process, quantifying cooperativity
DRS on ultra-thin PMMA films
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A refined analysis of the dielectric ββ-process
2.5 3.0 3.5 4.0
1000/T [1/K]
-5
-4
-3
-2
-1
0
log(
τ [s
])
79 nm9.0 nm8.8 nm
s-PMMA, Mn = 145000
Ea = 70.0 kJ/mol
Ea = 82.3 kJ/mol
Kulik et al., (multidim. NMR)Bonagamba et al., (CODEX-NMR)
• curved τβ(T) dependence for ultra-thin films • superposition of two close relaxation modes likely which cross at T ~
30°C• in line with TSD experiments suggesting two distinct β-modes in PMMA
ββ2: cooperative process involving the backbone
ββ1: noncooperative process
Chain confinement (L< REE):
Suppression of (large scale) cooperative component of dielectric ββ-process
DRS on ultra-thin PMMA films
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- DRS study on PMMA reveales two mechanisms that affect the glass transition temperature in supported PMMA-films:
- chain confinement which speeds-up the β-process together with the α-process
- a "true" finite size effect which is related to the cooperativity length of the glass transition
Summary dielectric results on PMMA
- DRS results revealed three characteristic length scales:
L< REE ~ 25 nm: τβ, ∆εβ, Tg
4nm < ξα < 5 nm: α-process vanishes
ξβ < 4 nm: β-process persists
DRS on ultra-thin PMMA films
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ββ-process of PMMA: further considerations
changes in ββ-process ßàßà changes in conformational statistics
What does the ββ-process senses?
Polymer theory:
hardly any change in conformational and orientational statisticsexpected as long L > Lp (persistence length)
However, hold only for thermal equilibrium!
DRS on ultra-thin PMMA films
stretching of polymer chains ààincrease of trans conformations
coiling of chains àà increase of gauche conformations
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ββ-process of PMMA: further considerations
àà additional experiments required to establish relation between dielectric β-relaxation and conformational statistics
chain confinement
variation of solvent quality
macroscopic stretching
?
Very recent experiments on i-PMMA/cloisite nanocomposites
DRS on ultra-thin PMMA films
trans/gauche ratio
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i-PMMA/clay nanocomposites
• Solutions of i-PMMA and cloisite in chloroform
• varying content of clay: 0 – 35wt%
• spin-coating of solutions, envisaged film thickness ~ 250 nm
c(clay) in %
L
viscosity increase
expected behaviour
DRS on ultra-thin PMMA films
0
100
200
300
400
0 10 20 30 40c [cloisite]
L [
nm
]
1st series
2nd series
3rd series
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i-PMMA/clay nanocomposites
DRS results:
• slow down of β-process at thinnest films• transition in activation energy
activation energy Eβ vs. clay content
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0 0.1 0.2 0.3 0.4
c[cloisite]
Ea
[kJ/
mo
l]
conformational transition ?
conformational transitioninduced by shear induced alignment of clay platelets
DRS on ultra-thin PMMA films
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87
i-PMMA/clay nanocomposites
Activation entropy:
β-process makes transition from increasingly cooperativerelaxation to non-cooperative relaxation
zero-entropy activation energy vs. clay content
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 0.1 0.2 0.3 0.4
c[cloisite]
Ea
[ ∆S
=0]
activation entropy vs. clay content
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
0 0.1 0.2 0.3 0.4
c[cloisite]
∆S
Reeks1
DRS on ultra-thin PMMA films
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i-PMMA/clay nanocomposites
Conclusions:• chain stretching causes increase of ∆Sβ (gauche à trans)• thin film confinement decreases ∆Sβ (trans à gauche)
activation entropy vs. clay content
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
0 0.1 0.2 0.3 0.4
c[cloisite]
∆S
Reeks1
1 10 100
L [nm]
0
20
40
60
80
100
Ea(
∆S=
0)
0
20
40
60
80
100
Ea
[kJ/
mol
]
s-PMMA, 146000s-PMMA, 880000a-PMMA, 128k
activation entropy
DRS on ultra-thin PMMA films
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i-PMMA/clay nanocomposites
What do we really see?
stretching of polymer chains increase of trans conf.
coiling of chains increase of gauche conf.
Reason:
drying of spin-coated polymer films in vitrified state causes chain collapse
DRS on ultra-thin PMMA films
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Q1: mobility profile in thin PMMA films
20 40 60 80 100T + ∆ [°C]
0.0
0.4
0.8
1.2
tan
δ/ta
nδ m
ax
6.4 nm
7.8 nm
8.5 nm
14.2 nm
28 nm
36.7 nm
58.5 nm
i-PMMA, f = 6.4 Hz
α
DRS results on ultrathin PMMA films (6.4 < L < 100 nm):
• continuous α-peak broadening implies gradual enhancement of mobility towards film surface
• no hint for sharp 2-layer scenario
Tg
bulk
Tg
surf
Tg
surf
ξ( )T
ξ( )T
Back to initial questions
DRS on ultra-thin PMMA films
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Back to initial questions
Our initial assumption:
1/T
-logτ
PMMA
PS
τ=100s
1/T
-logτ
PMMA
PS
τ=100s
2.5 3.0 3.5 4.01000/T [1/K]
-6
-4
-2
0
2
log(
τ [s
])
58.5 nm48.1 nm36.7 nm28.0 nm14.2 nm8.5 nm8.5 nm6.4 nm
α
β
solid lines correspond to fit of α-peak in T-domain
DRS results on ultrathin PMMA films (>6.4nm)
Q2: "fragility" hypothesis:
For PMMA, no substantial change in fragility found
DRS on ultra-thin PS films
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What happens with PS?
1/T
log(f)
Fukao, 2000
Results from Fukao apparently confirm decrease in fragility for ultra-thin PS films
Problem:relaxation data originate from two different techniques
thermal expansion spectroscopy
dielectric spectroscopy
Equivalence of dielectric relaxation data and volume expansion assumed !
DRS on ultra-thin PS films
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Dielectric measurements on PS thin films:2 experiments in one:
0 50 100 150T [°C]
2.25
2.30
2.35
2.40ε'(
T)
PS
Tg,dil Kink in εε'(T) marks change from liquid expansivity to expansivity of the glass à Tg, dil
PS, bulk sample
Step in εε'(T) at T>Tg due to dielectric α-relaxation
à frequency dependentLupascu, Wübbenhorst, 2004
• Capacitive dilatometry àà ααv(T)• Dielectric spectroscopy àà τταα(f,T)
DRS on ultra-thin PS films
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Capacitive dilatometry on ultra-thin PS films
0 50 100 150T [°C]
0.95
0.98
1.02
1.05ε'(
T),
norm
aliz
edbulk PS285nm20nm15nm8.7nm
• Systematic reduction of Tg,dil with lower film thickness
• Broadening of volumetric glass transition at lowest film thicknesses
Lupascu, Wübbenhorst, 2004
DRS on ultra-thin PS films
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Capacitive dilatometry on ultra-thin PS films
Tg reductions from capacitive dilatometry in good agreement with typical literature data (blue line)
àAl/polymer/Al sandwich samples behaves like filmshaving 1 free surface.
0 20 40 60 80
L [nm]
40
60
80
100
T [°C]
Fukao, Mw = 1.8×106
Fukao, Mw = 2.8×105
Limit supported films
Limit freely standing films
Fukao's results (PRE 2000)
Asymmetric electrode system – interface between top electrode and polymer film mimics free surface
DRS on ultra-thin PS films
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Capacitive dilatometry on ultra-thin PS films
Larger Tg- reductions found for same film thickness than Fukao
à Tg-reductions partially close to values known for freely standing PS films
Possible reason:
0 20 40 60 80
L [nm]
40
60
80
100
T [°C]
Wübbenhorst, M w = 1.6×105
Fukao, Mw = 1.8×106
Fukao, Mw = 2.8×105
Limit supported filmsLimit freely standing films
Comparison of recent own data with Fukao's results
Our Al-polymer-Al sandwich films mimics freely standing geometry to some extent (reduced surface roughness of lower Al-layer)
DRS on ultra-thin PS films
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Glass transition temperature from αα-process
Tg determination from relaxation time of structural relaxation:
2.0 2.5 3.0
1000/T
-8
-6
-4
-2
0
log(
τ [s
])
15 nm (0.35%)20 nm (0.70%)286 nm (5%)8.7 nm (0.22%)
αPSTg(ττ=100s)
§ dielectric α-process found in PS films as thin as 8.7 nm
§ systematic speed-up of α-process towards lower L
DRS on ultra-thin PS films
no substantial changes in fragility !
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Glass transition temperature from αα-process
5 10 100 500
L [nm]
40
50
60
70
80
90
100
T [°C]
Tg (dil)
Tg (α)
Increasing discrepancy between Tg(dil) and Tg(α) for thin PS filmsàà decoupling of volume expansivity from structural relaxation as seen by DRS?
Comparison of volumetric Tg with Tg(αα)
dilatom. Tg = 61°C
Tg from α-process:
77.3°C
PS-film 8.7 nm:
DRS on ultra-thin PS films
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PS film L=8nm:
2nd dielectric process
0 50 100 150
T [°C]
2.45
2.50
2.55
2.60
ε'(T
)
260 Hz
16 Hz
2.8 Hz
0.7Hz
0 50 100 150
T [°C]
0.00
0.01
0.02
0.03
ε"K
K(T
)
α
αs
αs
α
An additional relaxation process in PS-films with L<15 nm
Recent DRS results from ultra-thin PS films
DRS on ultra-thin PS films
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- thermally activated process, Ea = 71 kJ/mol
- non-cooperative (τ∞ ~ 10-12s
2.0 2.5 3.0 3.5 4.01000/T
-8
-6
-4
-2
0
log(
τ [s
]) P S 5 % ( 2 5 0 n m )
P S 5 - 0 . 2 2 % ( 8 n m )
P S 5 - 0 . 2 2 % ( 8 n m )
αPS
VFT-fit, log(τ∞) = -12
direct evidence for 2-layer model (?)ααs process most likely related to dynamics in surface layer
αs
α
2nd dielectric process: αs
Recent DRS results from ultra-thin PS films
DRS on ultra-thin PS films
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Recent DRS results from ultra-thin PS films
New series of PS films: thickness as low as 3.7 nm
DRS on ultra-thin PS films
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
-50 0 50 100 150 200T [°C]
eps'
3.8
5.1
6.0
7.2
9.1
15.1
22.8
23.7
30.9
33.0
44.7
52.5
0
5
10
15
20
25
30
35
0 0.2 0.4 0.6 0.8 1
c [%]
L [n
m]
PS series 6
Lineair (PS series 6)
kink in εε '(T) vanishes for L < 5nm
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Dielectric spectroscopy on ultra-thin films of PMMA and PS revealed
- Tg reductions due to finite size effect
- disapperance of the α-relaxation at films below 5nm
- Tg effects and changes in local β-relaxation due to chain confinement
- PMMA films: changes in the β-relaxation proof existence of "undersized" polymer coils in ultra-thin films
Conclusions
DRS on ultra-thin PS films
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Conclusions (2)
There are clear differences in thin film dynamics between PS and PMMA:
- Apparent Tg-reductions are much larger for PS than for PMMA
- Finite size effect manifests in different way:
- PMMA: deviation from bulk-VFT behaviour
- PS: separate relaxations related to core and surface dynamics à layer-like mobility profile confirmed
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AcknowledgmentsUniversity of Guelph, Canada
John Dutcher
Chris Murray
University of Berne, Switzerland
Jürg Hulliger
Norwid-Rasmus Behrnd
Delft University of Technology, group PMEDaniele Cangialosi
Veronica Lupascu