QENS and NSE for the Investigation of Dynamics in Soft Condensed
Matter
NIST Center for Neutron research
Antonio Faraone
Oxford School on Neutron Scattering, 9/2-12/2019
Outline
• General trends
• Polymer Nanocomposites
– Introduction
– QENS role in the study of nanocomposites
– The role of Nanoparticle size on chain dynamics
– Chain Dynamics in attractive polymer nanocomposites subjected to
large deformations
• Conclusion
Polymers
Gels
Polyectrolytehttps://en.wikipedia.org/wiki/Contact_lens
Nanocomposites
ACS Macro Lett., 3, 1262 (2014)
Ionomers
Membranes, 7, 25 (2017)
Adv. in polym. Sci., 174, 1 (2005)
Membranes
Proteins
JPCL, 10, 1709 (2019)
PNAS, 102, 17646 (2005)
Atomic Motions
BBA, 1861, 3638 (2017)
More Complex/Realistic Samples
Insights on the nanoscopic origin of rheological properties in polymer
nanocomposites
Acknowledgement
• Erkan SensesChemical and Biological Engineering, Koç University
• Madhusudan Tyagi, Yimin MaoNIST Center for Neutron Research
• Bharath NatarajanMaterials Measurement Laboratory, NIST
• Suresh NarayananAdvanced Photon Source, ANL
• Chris Kitchens, Mohamed AnsarChemical and Biomolecular Engineering,
Clemson University
50 wt% composite materials
Reinforced, lightweight, flexible,..
Boeing 787-Dreamliner http://www.boeing.com/commercial/787/
Multifunctionality!
Polyimide + 0.03 wt % CNTshttp://www.nasa.gov/exploration/systems/orion/#.VF16wfnF_dg
Electrostatic charge dissipation for spacecraft• Heat & chemical resistance
• Electrically Conductive
• Light weight
• Flexible
• Insulating
Mechanically adaptive composites for
improved lifetime and performance
Polymer Nanocomposites (PNC)
Properties of PNCs
• Polymer matrix• Nanoparticles: size, shape, amount• Particle dispersion
• Controlled dispersion • Orientation• Stability • Spatial distribution …• History
• Interface and interphase
Polystyrene-Silica
Jouault, Nicolas, et al. Macromolecules 42.6 (2009): 2031-2040
10-2
10-1
100
101
102
100
101
102
103
104
105
106
107
0%8 %
17 %
30 %
G '
[Pa
]
[rad/s]
45 %
Polyethylene oxide-Silica by wt
Mechanical Reinforcement in PNCs
Loop TailTrain
Particle surface
PMMA- SiO2
NP surface/polymer interaction: Attractive
No direct particle contact. Polymer driven Reinforcement
J. M. H. M. Scheutjens and G. J. Fleer. JPC, 84, 178 (1980).M. Krutyeva, et al., PRL, 110, 108303 (2013).
Well Dispersed NP
Courtesy of Michihiro Nagao
Scattering techniques, and neutrons in particular, are well suited to investigate the
microscopic origin of the rheological behavior.
Experimental Techniques
Mixture of d/h polymers
Isotopic Substitution, contrast matching techniques
Structure
Complementarity with Small Angle X-Ray and microscopy
Length scale Time scale
bulkd
2
tube ed lN
2
1 1o
N
e
GN d
Microscopic chain parameters that determine the macroscopicdynamics:
Microscopic Dynamics
Neutron scattering can simultaneously access the length and time scales relevant to Rouse and Reptation motion
D. Richter, M. Monkenbusch, A. Arbe and J. Colmenero, Neutron Spin Echo in Polymer Systems, 2005, 1–221.Dynamics of Soft Matter, Neutron Applications, Eds: GARCIA SAKAI, V., Alba-Simionesco, C., Chen, S.-H.
Dynamic Neutron Scattering
2
[ ( , ) ( , )]f
coh coh incoh incoh
i
kN S Q S Q
E k
𝑆𝑐𝑜ℎ 𝑄, 𝜔 =1
2𝜋න−∞
∞
𝐼𝑐𝑜𝑙𝑙 𝑄, 𝑡 𝑒−𝑖𝜔𝑡𝑑𝑡
𝐼𝑐𝑜𝑙𝑙 𝑄, 𝑡 =1
𝑁
𝑖
𝑗
𝑒−𝑖𝑸 𝒓𝑖 𝑡 −𝒓𝑗 0
𝑆𝑖𝑛𝑐𝑜ℎ 𝑄,𝜔 =1
2𝜋න−∞
∞
𝐼𝑠𝑒𝑙𝑓 𝑄, 𝑡 𝑒−𝑖𝜔𝑡𝑑𝑡
𝐼𝑠𝑒𝑙𝑓 𝑄, 𝑡 =1
𝑁
𝑖
𝑒−𝑖𝑸 𝒓𝑖 𝑡 −𝒓𝑖 0
Single Chain Dynamics – Neutron Spin Echo
2
[ ( , ) ( , )]f
coh coh incoh incoh
i
kN S Q S Q
E k
2
[ ( , ) ( , )]f
coh coh incoh incoh
i
kN S Q S Q
E k
dtent.<t<tRouse
Reptation
motion
tRouse<t<tTerminal
Partially escape
from the tube
t<tentanglement
Unrestricted
Rouse motion
within tube
t>tTerminal
Center of Mass
Diffusion
time scale (t) length scale (1/Q) Intermediate scattering function
Single Chain Dynamics – Neutron Spin Echo
In the appropriate Q-t range:Rouse Dynamics
Segmental Dynamics - Backscattering
H containing samples 𝜎𝑖𝑛𝑐𝑜ℎ𝐻 ≫ 𝜎𝑐𝑜ℎ
𝐻,𝐷,𝐶,𝑂,𝑆𝑖,𝐴𝑢, 𝜎𝑖𝑛𝑐𝑜ℎ𝐷,𝐶,𝑂,𝑆𝑖,𝐴𝑢
2
[ ( , ) ( , )]f
coh coh incoh incoh
i
kN S Q S Q
E k
H/D Polymers, contrast match:Single chain dynamicsNeutron Spin Echo
Complementarity
Hydrogenated Polymers:Single particle segmental dynamicsBackscattering
Nanoparticles dynamicsX-ray Photon Correlation Spectroscopy (XPCS)
The role of Nanoparticle size on chain dynamics
Mackay, Michael E., et al. Science 311.5768 (2006): 1740-1743.
Mackay, Michael E., et al. Nature materials 2.11 (2003): 762-766.
Particle size >> Chain size
Particle size < Chain size & tube size
Polystyrene NPs in polystyrene matrix: athermal
Viscosity Reduction in PNCs
Size and Interaction DependenceKalathi, Jagannathan T., Gary S. Grest, and Sanat K. Kumar. Phys. Rev. Lett., 109, 198301. (2012).
• Viscosity reduction
independent of polymer size.
• Similar to a plasticizer.
• Valid for sizes up to
entanglement mesh size.
Attractive interactions reverse
the size effect.
Need for Experiments
Samples
Particles are PEG coated (< 1nm) to provide entropic stabilization
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
14020.2 4.3 nm
Fre
quency
Diameter (nm)
0 1 2 3 4 5 6 7 8 9 100
100
200
300
400
500
3.5 0.7 nm
Diameter (nm)
Fre
quency
Large NPs Small NPs
dtube≈ 5 nm
D=20 nm
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
14020.2 4.3 nm
Fre
quency
Diameter (nm)
0 1 2 3 4 5 6 7 8 9 100
100
200
300
400
500
3.5 0.7 nm
Diameter (nm)
Fre
quency
Large NPs Small NPs
We made nanocomposites with these particles (20 % by volume)and long chain poly (ethylene glycol) (PEG) matrix (35 kg/mol).
D=3.5 nm
dtube≈ 5 nm
Particles are PEG coated (< 1nm) to provide entropic stabilization
Samples
Dispersion
EDX mapAu yellow
• In the NSE range, we observe the single chain form factor of Gaussian PEO chains.
NSE
Rg≈7 nm
76/24 d/h PEO
Contrast Matched PEO/NP (hPEO/dPEO 76 % / 24 %)
• The PEO in nanocomposites remains Gaussian.
Fetters, L. J., D. J. Lohse, and R. H. Colby. Physical Properties of Polymers Handbook. Springer New York, 2007. 447-454.
Single Chain Conformation
Rouse dynamics is not modified in
nanocomposites!
Short time – Rouse Dynamics
0.1 1 100.0
0.2
0.4
0.6
0.8
1.0
0.11 Å-1
PEO-Au (3.5 nm)
PEO-Au (20 nm)
PEO
0.20 Å-1
0.15 Å-1
S (
Q,t)
/ S
(Q,0
)
t [ns]
T=400 K
2 2 22 2 2
2 2, 1
R1 1 2 1( , ) exp( ) cos( )cos( )[1 exp( )]
6 3
N Ne
Rouse R
m n p R
Q p m p n p tS Q t Q D t m n Q l
N p N N
Coherent dynamics structure factor for a Rouse motion
23 :
kTlW monomeric friction coefficient
Parameters Definition Value
used
Unit
N Number of segments 795 -
l Segment length 0.58 nm
End-to-end distance 16.35 nm
Rouse parameter 1.51* nm4/ns
Rouse diffusion coefficient 0.0019 nm2 /ns
Rouse time 4799 ns
2
eR Nl4Wl
4 2(3R )R eD Wl
R
Short time – Rouse Dynamics
0.1 1 100.0
0.2
0.4
0.6
0.8
1.0
0.11 Å-1
PEO-Au (3.5 nm)
PEO-Au (20 nm)
PEO
0.20 Å-1
0.15 Å-1
S (
Q,t)
/ S
(Q,0
)
t [ns]
T=400 K
*K. Niedzwiedz et al., Macromolecules 41, 4866 (2008)
Long time – Confined motionPNC with 20 nm particles
d
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]
Q=0.8 nm-1
Q=1.1 nm-1
Q=1.5 nm-1
Q=2.0 nm-1
PNC with 20 nm particles PNC with 3.5 nm particles
Q=0.8 nm-1
Q=1.1 nm-1
Q=1.5 nm-1
Q=2.0 nm-1
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]
d
Long time – Confined motion
PNC with 20 nm particles PNC with 3.5 nm particles
Q=0.8 nm-1
Q=1.1 nm-1
Q=1.5 nm-1
Q=2.0 nm-1
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]
2 2 2 2
Rept.
( , )[1 exp( )] ( , ) exp( ) ( , )
( ,0) 36 36
coh
local esccoh
S Q t Q d Q dS Q t S Q t
S Q
de Gennes formulation
( , ) exp ( )local o
o
tS Q t erfc t
4 436 ( )o Wl Q 4 4; 1.51 / for PEO @ T=400KWl nm ns
( , ) 1escS Q t
d is the only fitting parameter!
d
Long time – Confined motion
PNC with 20 nm particles PNC with 3.5 nm particles
Q=0.8 nm-1
Q=1.1 nm-1
Q=1.5 nm-1
Q=2.0 nm-1
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
S (
Q,t
) /
S(Q
,0)
t [ns]
5.03 0.1 nmPEOd
20 5.17 0.19 nmPEO nmAud
5.03 0.1 nmPEOd
3 6.11 0.13 nmPEO nmAud
Long time – Confined motion
10-1
100
101
102
103
100
101
102
103
104
105
106
10-1
100
101
102
103
101
102
103
104
[rad/s]
[
Pa-s
]
neat PEO
20 nm Au
3 nm Au
1
2
[rad/s]
G' (f
ille
d)
, G
" (o
pe
n)
[Pa
]
0
2, 33 , ( )
0.67 0.23
Pbulk Au nm b EO PEO nmAuulk PEO d d
One would expect to see ~ 60% decrease rubbery plateau.
32
2
3( )o d
N l
W d
2
.
1 1o
N
ent
GN d
• Viscosity decreased by half with addition of 20 vol. % small particles
• Strong reinforcing effect of large particles
Bulk Rheology
Summary
• Chains disentangle when dparticle<dtube. First direct experimental
evidence.
• Rouse dynamics unaffected (at least in our athermal system).
• An explanation for non-Einstein-like viscosity decrease in polymer
nanocomposites.
homodhomod d
E. Senses, et al., Phys. Rev. Lett, 118, 147801 (2017).
Chain Dynamics in nanocomposites subjected to large deformations
Silica Particles in PolyEthylene Oxide
PEO (35 kg/mol, Rg ≈ 7 nm) / Silica (55 nm diameter)
10-3 10-2
10-1
100
101
102
103
104
0.0110-2
10-1
100
I(Q
)/P
(Q
)Q [Å-1]
28 %
42 %
17 %
8 %2 %
I(Q
) [arb
.unit]
Q [Å-1]
NP %mass (volume)
Face-to-face distance (h) [nm]SAXS random packing
h/2Rg
5 (2.5) - 93.8 -15 (7.8) 52.3 48.5 3.74
30 (17.1) 21.8 26.4 1.5645 (28.3) 14.8 14.9 1.0660 (41.9) 5.1 7.2 0.51
E. Senses, et al., PRL, 119, 237801 (2017).
Nanoparticle Dynamics and Rheology Decoupling
Nanoparticle Dynamics
E. Senses, et al., PRL, 119, 237801 (2017).
Nanoparticle Dynamics and Rheology Decoupling
Nanoparticle Dynamics
E. Senses, et al., PRL, 119, 237801 (2017).
Payne effect (NanocompositesSubject to Large Deformations)
Narrowing linear regime in nanocomposites and large decrease in modulus with strain: Payne Effect
Large Deformation Do Not Affect Structure
PEO (35 kg/mol, Rg ≈ 7 nm) / Silica (55 nm diameter)
10-3 10-210-910-810-710-610-510-410-310-210-1100
15%
30%
I(Q
) [arb
.unit]
Q [Å-1]
45%
Open Symbols: After Shear
Polymer Chains Conformation
Small Angle Neutron Scatteringcontrast matching
h-PEO/d-PEO 48/52 + Silica
0.1 1
100
101
102
HFBS
PEO matrix
PEO-45% S ilica
PEO-45% S ilica-SHEAR
fit to Debye function
I [a
.u.]
Q [Å-1]
NSE
0.1 1
100
101
102
HFBS
PEO matrix
PEO-30% S ilica
PEO-30% S ilica-SHEAR
fit to Debye function
I [a
.u.]
Q [Å-1]
NSE
a b
Reptation Tube Diameter
0 50 1000.0
0.2
0.4
0.6
0.8
1.0 1.1 nm
-1
1.5 nm-1
2.0 nm-1
S (
Q,t
) /
S(Q
,0)
t [ns]
Entanglements are not modified after shear and recovery
Fitting to de-Gennes equation for t>50 ns, the tube diameter is found (≈ 5 nm)
Single-chain dynamic structure factor: (de Gennes formulation)
2 2 2 2( , )[1 exp( )] ( , ) exp( ) ( , )
( ,0) 36 36
local escS Q t Q d Q dS Q t S Q t
S Q
( , ) exp ( )local
o oS Q t t erfc t
4 436 ( )o Wl Q
Escape of a chain from its original tube
( , ) 1escS Q t (for NSE timescale)
Segmental Dynamics
Sample Wl4 [nm4/ns]
Neat PEO 0.182 ± 0.006
PEO-30 % by weight SiO2 0.140 ± 0.005
PEO-30 % by weight SiO2-SHEAR 0.138 ± 0.004
PEO-45 % by weight SiO2 0.129 ± 0.003
PEO-45 % by weight SiO2-SHEAR 0.106 ± 0.003
Rouse-rate decreases with nanoparticle concentration.
It further decreases after large shear.
h/REE>1 h/REE<1
Segmental Dynamics
Rouse-rate decreases with nanoparticle concentration.
It further decreases after large shear.
Mean-square
displacement of
the segments
22
(Q, t) exp ( )6
self
QS r t
2 4( ) 2 t/r t Wl
Fourier transform of the QENS spectra
Gaussian Approximation
Rouse dynamics with characteristic
rate: Wl4
NanoparticleDynamics - XPCS
10-3 10-210-910-810-710-610-510-410-310-210-1100
15%
30%
I(Q
) [arb
.unit]
Q [Å-1]
45%
Particles speed-up after large shear
https://www.aps.anl.gov/Sector-8/8-ID•https://www.bnl.gov/nsls2/workshops/docs/XPCS/XPCS_Sandy.ppt
Summary
Backscattering shows enhanced pinning
E. Senses, et al., Soft Matter, 13, 7922 (2017).
Conclusion
• QENS data indicate that the viscosity reduction in athermal PNC with nanoparticles smaller that the entanglement size originates from a dilation of the reputation tube.
• In attractive PNC subjected to LAOS, an increased pinning which could originate disentanglement of the interphase region, and therefore fluidization, was observed.
Summary
• QENS and NSE provide information on the nanoscopicdynamics in polymer nanocomposites
• These microscopic insights can be related to macroscopic behavior, providing an explanation for the rheological properties
• An accurate knowledge of the structure, the combined use of several methods, and the exploitation of isotopic substitution techniques are key elements of the research.