How Unstructured are Amorphous Polymer Melts?

Solid-State NMR Studies of Local Dynamic Order

in Amorphous Polymer Melts

Robert Graf

Max-Planck-Institut für PolymerforschungMainz

Technische Universiteit EindhovenFebruary 17th, 2004

How Unstructured are Amorphous Polymer Melts? Solid-State NMR Studies of Local Dynamic Order in

Amorphous Polymer Melts

Introduction •

Solid State NMR •

Polymer dynamics •

Conclusions •

interactions in solid state NMR

resolution enhancement in solid state NMR, magic angle spinning, recoupling methods, double quantum NMR spectroscopy.

I. Schnell, K. Saalwächter, M. Feike, R. Graf

Reptation model, polybutadiene, PEMA

How unstructured are amorphous polymers ?

Molecular Structures and Dynamics via NMR

i

i0iZ BH I∑γ−=

Important NMR interactions:

Zeemann Interaction :

i

i0iCS BH Iσ∑γ−=Electronic Shielding :

i

i

i)1I2(I2

eQQH IVI∑ −−= hQuadrupol Interaction :

[ ]∑≠

γγπ

μ ⋅−⋅⋅−=ji

jijir3

r4D )r)(r(H 23ji0 IIIIh

Dipol-Dipol Interaction :

∑≠

⋅−=ji

jijiJH IJIIndirect Spin-Spin Interaction :

H = HZ + HQ + HCS + HD + HJ

Interactions in Solid State NMR Spectroscopy

ij0,2ij

2

ji21

r4D )1cos3(H 3ij

ji0 T−θ= ∑≠

γγπ

μ h

PerturbationTheory Orientation dependence of local spin interaction on B0

HQ, HD, HCS, HJ

Isotropic ContributionsHCS: chemical shift

HJ: J-couplings

Liquid state NMR

Anisotropic Contributions

SymmetricHQ: quadrupol

HD: dipol-dipol

HCS: chemical shift

AsymmetricHQ: quadrupol

HCS: chemical shift

Zeemann interaction dominates all other NMR interactions

Distance Orientation

θ

B0B0 θ

1H NMR Spectra in Liquid and in Solid State

60 40 20 0 -20 -40 k-60 Hz

5 0 kHz

20 10 0 kHz

static

30 kHz MAS

Solution

isotropic moleculardynamics

3 kHz4HRMAS soft

matter

rigid solid

dipolarbroadening

Spectral Resolution Enhancement in Solid State NMR

dipol-dipol coupling:

i

j

θij

B0

RF irradiation:

$ ( cos ) ( $ $ $ $ ), ,Hr

I I I Iij

ij i j Z i Z j i j∝ − − ⋅1

3 1 3312

2 θ γ γ

$ $ $, ,H R T= ⋅2 0 2 0

$,T2 0

0

space spin

0 tC

-x y -y x

tτ ττ τ2τ τ ττ τ2τ τ ττ 2τ

-x y -y x -x y -y

tC

magic angle spinning:

$,R2 0 0 ωR

θ

θm

ωR

θm

ωR

B0 B0 B0 B0

0 tR

t

tR

(CRAMPS)

(Recoupling)HD,eff.

x y -y-x

τ τ

x y -y-x

τ τ

x y-x

τ

Double Quantum NMR Spectroscopy under MAS

ω ωDQ SQ ii

= ∑ ,

I f D tDQ ij ij, ( )= ⋅

d Mdt ≈ 0

preparation reconversionevolution t1 detection t2

6.0 5.0 4.0 3.0 2.0 ppm12

10

8

6

4ppm

CH CH2

-CH2

CH2-CH

CH=CH

doub

le q

uant

umdi

men

sion

(f 1)

single quantum dimension (f2)

properties of double quantum coherences :

Order Parameter in Liquid Crystalline Phases

2.54 Å

1.83 Å

2.49 Å

2.48 Å

1.83 Å

2.56 Å

A

B

C

CD

F

G

FE

D

chemical structur of nematic model

compound

order parameter Sij :

)1cos3(S 221

ij −θ=

stat,ij

eff,ijij D

DS =

c

A BC

D

E

F

G

G-GF-FE-E

D-E

D-D

C-D

B-CA-C

ppm

8 7 6 5 4 3 2 ppm16

14

12

10

8

6

4

2

doub

le q

uant

um d

imen

sion

single quantum dimension

Order Parameters in Liquid Crystalline Systems

0,0 0,1 0,2 0,3 0,4 0,5 0,60,0

0,1

0,2

0,3

0,4

0,5

BC DQ coherences

DQ

Inte

nsity

[a.

u.]

DQ-Preparation Time [ms]

BC DQ coherence

-100100 0 kHz

orde

r par

amet

erS

0.0

0.1

0.2

0.3

0.4

0.5

0.6

A-C B-C D-D E-E F-F G-G

F

D

C

B

A

CD

E

F

G

orientation of nematic

directorDQ sidebands

DQ intensity

Local Order Parameter in Liquid Crystals and Polymers

ntSS =

Nematic Systems Polymerstim

een

sem

ble

0Sbut

,0S,0S

Nn

Nt

>

=>

⊆

Introduction •

Solid State NMR •

Polymer Dynamics •

Conclusions •

Interaction in solid state NMR

MAS, recoupling, double-quantum NMR

Reptations-model, scaling laws in polymer dynamics, influence of rigid confinements, conformational stability in PEMA melts.

T. Dollase, M. Neidhöfer, M. Wind, A. Heuer, R. Graf

How unstructured are amorphous polymers ?

How Unstructured are Amorphous Polymer Melts? Solid-State NMR Studies of Local Dynamic Order in

Amorphous Polymer Melts

Length- and Time Scales in Polymer Dynamics

t > τeslow, collective

Reptation dynamics

t < τe

fast, local dynamics

separation of time scales!

dynamic regimes of the Reptation model :

τR

log(t)

log

[Rn(

t)-R

n(0)

]2

∝ t1/2

∝ t

∝ t1/4

∝ t1/2

τdτe

I. II. III. IV.

DQ Measurements of Dynamics on Different Time Scales

θ(t1)

θ(t0) θm + α(t)

t = 0 t ≈ τe t > τe

I dt dt D d t d tDQt t

t tt

ij eff m m∝ ′ ′′ ⋅ ′ ′′+

+

−∫∫1

12

0

2

22

22

, ,( )

,( )( ) ( )

return-to-origin probability C (t)

corresponds tod t d tm exc m rec t22

22

,( )

. ,( )

.( ) ( )− ′ ⋅ ′′

S Ne≈ −35

1polymer network theory :

Polybutadien : S MMKuhn

e≈ ≈3

5 003.

static systems : Sij(t)=1isotropic motion : Sij(t)=0

S D Dij ij eff ij= , /local order parameter :

Local Order Parameters in 1,4 Polybutadien Melts

SH-H = 0.13

S = 0.06-H2

S = 0.08H2-HT=Tg+50K

⇒ SC=C = 0.20 ± 0.05 6.0 5.0 4.0 3.0 2.0 ppm

12

10

8

6

4ppm

CH CH2

-CH2

CH2-CH

CH=CHdo

ubel

quan

tum

dim

ensi

on(f 1

)

single quantum dimension (f2)

1H double quantum NMR spectrum Dynamic order parameter

via residual dipolar couplings

S

Time Dependence of Local Order Parameter

10-1

100

101

102

103

t / te(T)

~ t -1/2

~ t -1/4

C (t

)tc( ) tc( )

1,0

0,1PB MW ≈ 76 Me

PB MW ≈ 11 Me

PB MW ≈ 4 Me

double-quantum filtered experiments on 1,4 poly-butadien

Reptation-model predicts two scaling laws:

S~t -1/4 and S~t -1/2

Molecular Weight Dependent Dynamics of PB Melts in PS-PB

Tethering a PB chain end to a rigid PS block stabilizes the t-1/4-regime

10

0.01

0.1

1

10

PS-b-PB 12k-10kPS-b-PB 22k-24kPS-b-PB 90k-120k

101010.01

0.1

1

10

D CH

=CH

/ kH

z

S(t/

t e)

102 103 104 10510010−1

t/ t e

~t −1/4

Influence of Rigid Confinements on Polymer Dynamics

PS-b-PB PS-b-PB-b-PSPB

0.01

0.1

1

~ t −1/4

t / te

PS-b-PB PB

0.01

0.1

1

10

PS-b-PB-b-PS

S (t/ t

e) CH

=CH

DC

H=C

H /

k Hz

102 103 104 10510010−1 101

~ t −1/2

PS-b-PBPB

PB inPS-b-PB

Polymer Dynamics in heterogeneous Polymer Melts

1010.01

0.1

1

10

0.01

0.1

1

10210010−1 103 104 105

t / τe

DC

H=C

H /

kHz

S(t/

τ e) C

H=C

H

PS-b-PB p6 (12k-10k)5 % PB p6 in PS-b-PB d6PB p6 (10k)

~t −1/2

~t −1/4

S(t/

t e)

t / te

Variation of Dynamic Order Along the Polymer Chain

10-2 10-1 100 101 102 10310-3

10-2

chain endchain centerwhole chain

PB(d6)-PB PB(d6)-PB-PB(d6) PB

~ t -1/4

~ t -1/2

t / te

S(t/

t e)

Local Order Parameters in Star Shaped Polymers

0,1 1,0 10 100 1000

0,01

0,1

~t-1/4

~t-1/2

orde

r par

amet

er S

CH

2

t / t e

cooperation with Prof. Hadjichristidis / Athen.

a-PEMA: Isotropisation of Chain Dynamics

180°

CO

13

ω33<10°

ω22

ω11

180°C

O13

0° - 180°

180°

CO

13 ω

50°ω

400 K

405 K

411 K

433 K

472 K

394 K

250 200 150 100

298 K

ω

ω

ω22

ω33

ω11

1D 13C NMR: experimentsimulation

Melt

Gla

ss

Tg

Melt

a-PEMA: Isotropisation of Chain Dynamics

200

150

100200 150 100250

250

[ppm

]ω

2

[ppm]ω1

T = 300 K

ω11

ω22 ω33

180°

CO

13

ω33<10°

ω22

ω11

200

150

100

200 150 100

T = 416 K

tc = 2,1.10-5 s

[ppm

]ω

2

[ppm]ω1

180°C

O13

0° - 180°

T = 394 K

tc = 3,3.10-4 s

200

150

100

200 150 100

[ppm

]ω

2

[ppm]ω1

ωω

180°

CO

13 ω

50°ω

Dynamic Models: Random Jump vs. Rotational Diffusion

rotational diffusion experimental results random jump

200

150

200 150 [ppm]

[ppm]

200

150

200 150 [ppm]

[ppm]

200

150

200 150

tc=3,3 .10-4s

[ppm]

[ppm]tc =3,3.10-4s T = 394 K

200

150

200 150

tc =8,3.10-5s

[ppm]

[ppm]

200

150

200 150 [ppm]

[ppm]

200

150

200 150

tc=8,3.10-5s

[ppm]

[ppm]T = 405 K

Time Sclaes of Molecular Dynamics PEMA Melts

Arrhenius-diagram of dynamic processes in PEMA

corr

elat

ion

time

[s]

10-8

10-6

10-4

10-2

100

102

2.2 2.4 2.6 2.8 3.0 3.2 3.4

1000 / T [K-1]2.0

Tg = 338K

α-relaxation( tα)

β-relaxation( tβ)

αβ-relaxation( tαβ)

NMR

DielektricPCS

conformationalisotropisation (tR/I)

Length Scale of Isotropisation Process

**

*

*

**

*

*

T - Tg

95 K

55 K

410 K

449 K

395 K

434 K

387 K

426 K

322 K

346 K

379 K

403 K

300 K 300 K 300 K 221 K278 K

δ [ppm]100150200250

δ [ppm]100150200250

δ [ppm]100150200250

δ [ppm]100150200250

δ [ppm]100150200250

Mw = 600 kg mol -1 Mw = 15,9 kg mol -1 Mw = 7,6 kg mol -1 Mw = 1,4 kg mol -1 Mw = 0,46 kg mol -1

Mw/Mn = 1,53 Mw/Mn = 1,61 Mw/Mn = 1,48 Mw/Mn = 1,07 Mw/Mn = 1,14

from radicalic polymerisation from anionic polymerisation

Organisation in Poly(Methacrylats): WAXS(LVDW)

PMMA

PEMA

PBMA

PHMA

Inte

nsity

[a.u

.]

q [nm-1]0 10 20

II/I

WAXS-DataIII

(VDW)

III

?

0

0.4

0.8

1.2

1.6

0 2 4 6 8 10 12number of side chain C atoms

Bra

ggdi

stan

ce d

[nm

]

I

II

III

(VDW)

(LVDW)

Bragg distances

syndiotacticpoly(methacrylate)

main chain

side chains

dI

dIII

d0

dIII

dII

"Nano Layers"

isotacticPEMA

main chains

side chains

extrapolatedlokal structur:

Introduction •

Solid State NMR •

Polymer Dynamics •

Conclusions •

Interaction in solid state NMR

MAS, recoupling, double-quantum NMR

Reptation-model, polybutadiene, PEMA

How unstructured are amorphous polymers ?

How Unstructured are Amorphous Polymer Melts? Solid-State NMR Studies of Local Dynamic Order in

Amorphous Polymer Melts

Längenskalen lokaler Ordnung in Polymerschmelzen

nanodomaindirector

~10 nm~2 nm

< 0.5 nmdynamic interphase

Acknowledgements

Prof. Dr. Hans Wolfgang Spiess ($, €, …)

Prof. Dr. Andreas Heuer (Polymertheory, …)

Dr. Thilo Dollase, Michael Neidhöfer (Polybutadien)

Dr. Michael Wind, Dr. Werner Steffen, Prof. Dr. Do Y. Yoon (PEMA)

Dr. Ingo Schnell, Dr. Kay Saalwächter, Dr. Martin Feike,Dr. Siegfried Hafner, Prof. Dr. Dan Demco. (NMR)