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.