Glass transition effects in ultra-thin polymer films · 4. Glass transitions effects in ultra -thin...

1

Glass transition effects in ultra-thin polymer films

Wierzba, 12 May 2004

Michael Wübbenhorst

2

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

3

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

4

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

5

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


6

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


7

more or less pronounced curvature of η(1/T) dependence

classification into fragile and strong glass formers

Dynamic glass transition


fragility: nothing to do with mechanical "fragile" behaviour

strong

fragile

fragility or steepness index:

linked to VFT parameters

8

( )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


9

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



10

- 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



11

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


glycerol

threitol

xylitol

sorbitol

12

-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


-6.0

-24.5

-46.0

-83.3

Tg [C] m

112.1sorbitol

97.2xylitol

79.9threitol

55.5glycerol

13

Fragility classification


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

14

First: simple glass formers (low molecular mass)


Dynamic glass transition – effect of confinement

1st example:Confining ethylene glycol (EG) in zeolites

[Huwe et al., PRL 1999]

15Phenomenology of the glass transition


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

16



17

Interpretation of results from ethylene glycol/zeolite systems:



àà Minimum number of nearest neighbors of 6 required to establish VFT-type dynamics

18

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:



19

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.


Dynamic glass transition – effect of confinement αα-relaxation of amylopectine/ethyleneglycol mixtures:

20

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


Dynamic glass transition – effect of confinement αα-relaxation of amylopectine/ethyleneglycol mixtures:

21

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



3rd example:

22

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“



23

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



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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



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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)



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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



Fit-results: peak relaxation time τταα – details

27

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


Fit-results: peak relaxation time τταα – details


28

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


Lliq(n) ~ ξξ

ξξ(fct) ~ Lliq(n)

ξ(Τ) ξΤ(Τ)ξΝ

Physical meaning of crossover frequency:

Lliq(n) [nm]:

2.5

1.5


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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

30

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

31Polymer chains in nm-scale geometry


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

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


Ideally: Reduction of L only affects the larger processes

REE

ξα

Rentanglement

ξβ

33

Outline

1. Introduction




findings and models


issues




34

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:

35

Ultrathin polymer films: thickness L < 100nm

supported films (polymer on substrate):

capping layer

freely-standing films:

2 basic configurations


36

Ultrathin polymer films – how to prepare them ?


• 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.

37

Ultrathin polymer films – preparation (2)


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

38

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)


39


First results:


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)

40



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

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


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:


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)

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


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)]


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?

46

Supported PMMA films

PMMA supported on Si and Au


• 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

47

Comparison freely-standing PMMA – PS films

nearly equivalent molecular weights


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?


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

49

One possible answer:In thin films, fragility might change differently for of PMMA and PS


1/T

-logτthin PMMA film

thin PS film Is there any evidence for this scenario?

broadband dynamic studies required àà DRS

bulk PS, PMMA

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 ++=

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

52DRS : 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

53


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

54


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

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

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


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


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


59

Outline

1. Introduction




findings and models


issues




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

61

"Bulk" PMMA – large influence of stereoregularity


-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

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


Maximum in Eapp at T where VFT-law breaks down

α

α

α

β

β

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


64

-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


§ Broadening in α-process§ Reduction in relaxation

strength

§ Shift of relaxation spectrum

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


Clear broadening of α-process at low & high temperature (frequency)

general broadening favours existence of mobility profile ττ(L)


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


Tg (ττ=100s)


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):


àSame thickness dependence of T(αα) at very different frequencies:0.01, 10, 104 Hz

68

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


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

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


αα-process of i-PMMA: relaxation strength ∆ε∆εαα(L)

70

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


∆εα (bulk)

finite size effect

Extrapolation of ∆ε∆εαα to zero àà ξξ ~ 5nm


71

More evidence for critical length of αα-process from syndiotactic PMMA

L = 4 nm

L = 9 nmL = 79 nm


L = 4 nm

αα- peak vanishes for L = 4 nm !

72

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


73

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


74

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


75

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


76

Again, isotactic PMMA, ββ-process

§ Below critical thickness Lc ~ 1 – 1.5 REE:

§ Continuous decrease of ∆εβ toward lower L


0 20 40 60 80

L [nm]

0.0

1.0

2.0

3.0

∆ε


∆εα (bulk)

77

ββ-process, relaxation time at 35°°C


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]

78

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


79

ββ-process, activation parameters


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)

80

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


81

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


82

- 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


83

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!


stretching of polymer chains ààincrease of trans conformations

coiling of chains àà increase of gauche conformations

84

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


trans/gauche ratio

85

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


0

100

200

300

400

0 10 20 30 40c [cloisite]

L [

nm

]

1st series

2nd series

3rd series

86


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


87


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


88


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


89


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


90

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


91

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

92

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 !


93

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)


94

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


95


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


96


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)


97

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


no substantial changes in fragility !

98

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:


99

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


100

- 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



101


New series of PS films: thickness as low as 3.7 nm


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

102

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


103

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

105

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

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Glass transition effects in ultra-thin polymer films · 4. Glass transitions effects in ultra -thin...

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