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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
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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 ?
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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
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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
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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
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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
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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 :
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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
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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
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Local Order Parameter in Liquid Crystals and Polymers
ntSS =
Nematic Systems Polymerstim
een
sem
ble
0Sbut
,0S,0S
Nn
Nt
>
=>
⊆
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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
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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.
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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 :
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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
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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
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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
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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
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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
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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)
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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.
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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
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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
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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
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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)
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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
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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:
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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
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Längenskalen lokaler Ordnung in Polymerschmelzen
nanodomaindirector
~10 nm~2 nm
< 0.5 nmdynamic interphase
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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)