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Polymers and Neutron Scattering

Using neutrons to “see” and track polymer molecules

Julia S.HigginsImperial College, London

ANSTOFebruary 6 2012

Effect of Mw on flow

Common polymers

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Effect of Mw on flow

Advanced polymers

CH2 CH

Cl

n

PVC poly(vinylchloride)

PMMA poly(methylmethacrylate)

CH2 CH CH CH2 n

PB poly(butadiene)

CH2 CHn

PS poly(styrene)

CH2 CH2 n

PE poly(ethylene)

BPA-PC bisphenol-A polycarbonate

O C O C

CH3

CH3

n

O

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Physics of polymer molecules and polymeric materials

1920 Hermann Staudinger first proposed plastics were composed of very long molecules with co-valent bonds

1953 Paul J Flory described the shape and size of individual polymer molecules in solutions and melts. In the melt dimensions vary as √N, but they are larger in solution

Single polymer molecule in a melt

1000 repeat units long

Described by the maths of a random walk – dimensions vary as √N

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Entangled polymers – many random walks

Big questions for polymer scientists still open in 1970

• Is the individual polymer molecule a “random walk” in a melt sample (Flory)?

• How does the individual polymer molecule relax after it has been stretched in a melt?

• How to relate models of polymer dynamics to rheology of melt polymers?

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Neutron scattering

neutron beam

Molecules In sample

Scattering can be coherent – remembering spatial arrangementof molecules

Or

Incoherent – sensitive only to energy changes induced by molecular motion in the samplel

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The Neutron

mn

λ

v Wave-particle duality

λ = hmnv

de Broglie(1924)

mn = 1.674 x 10-27 kg Thus: λ ~ 10-10 mE ~ kBT

Neutrons scattered by nucleusisotopic substitution - labelling

bH = -3.74 x 10-15 mbD = +6.67 x 10-15 m

Neutrons highly penetrating & non-destructivecomplex sample environmentrepetitive measurements

Very Expensivenuclear reactors or spallation sources

Coherent and incoherent scattering

Coherent scattering – the neutron “remembers” spatial arrangements

Scattering lengthsH -3.7x10-15mD +6.6x10-15m

Incoherent scattering – no spatial “memory” only energy changes are detected.

Cross sectionsH 80x10-28m2

D 1.8x10-28m2

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Time of flight spectrum from a molten polymer at two values of q (incoherent scattering) Experiments at Harwell 1971

inelastic

elastic

quasielastic

Inelastic incoherent scattering from poly(propylene oxide)

CH3

CD3

O

CH3

H

H

H

n

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How far does a molecule move in a unit of time?

Incoherent quasi-elastic scattering

For very short times around 10 -12s the polymer is as mobile as the water molecule

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The resolution problem – three different models of polymer motion are extremely difficult to distinguish

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The reactor with the French Alps behind

Large apparatus to investigate shape, size, organisation and motion of molecules

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Small Angle Neutron Scatteringa coherent scattering technique

• Used to investigate size and shape of labelled molecules in dense polymeric systems such as glasses and rubbers

• Used to follow deformation as a function of time in stress relaxation

• Used in reflection mode to follow development of interfacial structure – as a function of time

• Was delayed until 1975 onwards until area detectors and high flux reactors became available

Entangled polymers – many random walks

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Neutron scattering

C

H

H

C

H

H

C

H

H

C

D

D

C

D

D

C

D

D

chemically identical

enormous neutron contrast

neutron beamH

D

melt (θ)

good solvent

Rg

Rg

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Short vs long macromolecules (Mw)

Effect of deformation on polymer conformation

polystyrene-D8 (3%) in polystyrene-H8 (97%) stretched by 200% and then allowed to relax before quenching

Polymer 22 1157 (1981)

Affine deformation?

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Big questions for polymer scientists still open in 1970

• Is the individual polymer molecule a “random walk” in a melt sample? SANS confirms Flory.

• How does the individual polymer molecule relax after it has been stretched in a melt? SANS shows affine deformation and relaxation

• How to relate models of polymer dynamics to rheology of melt polymers? Need high resolution quasi-elastic scattering

Physics of polymer molecules and polymeric materials

1967 Sam Edwards – polymer molecules in rubbers and glasses are trapped by their neighbours in a “tube

1971 Pierre Gilles de Gennes – in rubbers the trapped molecules move like snakes in their tube and eventually escape - reptation

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The Tube Model

Polymer chains inthe melt

Each chain can be considered to beconstrained withina tube

Polymer Motion

t

t = τe

Entanglement time

t = τR

t = τd

Rouse relaxationtime

Reptation time

t = 0

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Back scattering

(1976) Higher resolution but still problems at small q – long distances

Resolution problem

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Quasielastic scattering

• Time of flight 1968- incoherent• Back scattering 1974- incoherent• Neutronspin echo 1978- coherent

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What are the advantages of neutron spin echo?

• It is highest energy resolution QENS technique• It is a coherent scattering technique so we can exploit the SANS signal from

labelled molecules• It uses a highly collimated beam so we can measure at low q values – ie

over reasonable spatial distances• It measures the time FT of the normal S(q,E) correlation function. In energy

space this signal is a convolution of the energy spread in the incident beam and the signal from the sample. The FT of a convolution is a product. Hence the resolution function can be divided out from the NSE signal leaving the pure sample S(q,t)

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For how long does a molecule “remember” where it was to start with?

Solid lines are calculated from de Gennes’ predictions

Key parameter is the tube diameter here approx 3nm

Excellent agreement between tunnel width from neutron experiments 2.9nm from rheology 3.0nm (30A)

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Scientists need good luck!

Two parameters are important in deciding whether the effect of entanglementscan be seen in a spin echo experiment, Rouse time AND tunnel width, D

We had all concentrated on the energy resolution question and hence theRouse time. This implied PDMS would be the polymer of choice.

For us however the choice of polymer was driven by necessity!We needed an h/d mixture to give the coherent scattering from single chainsTo reduce the incoherent signal we needed a mix 90% deuterated.Such polymers are expensive or unobtainable! BUT d-tetrahydrofuran is an

NMR solvent and is CHEAP! It is not difficult to polymerise.Our chemists made the d and h polymers for us – in high and low Mw

samples.No-one had measured the rheology or obtained the tunnel width for PTHF

– it was not an important polymer!From the neutron experiments D turned out to be around 30A like PE and

much smaller than D for PDMS (which is around 80A like PS)

Neutron Reflectivity

Neutron reflectivity is a special form of small angle scattering particularly well suited to investigating:-

• structure of sharp interfaces between polymeric species

• obtaining interaction parameters between immiscible polymers

• observing the early stages of inter-diffusion and• Plasticisation• First polymer experiments 1989

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Basics of Neutron Reflectivity

θ < θcrit

θ = θcrit

θ > θcrit

The critical angle for neutrons is about 1 degree! Grazing incidence experiments

θθθθ

I(θθθθ)

θcrit

Reflection

Reflection&

Refraction

The Reflectivity Profile

qz (Å-1)

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Ref

lect

ivity

, R(q

z)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

qc ∆∆∆∆q2

∆∆∆∆q1

(a)

ρ

d

A double thin layer gives rise to interference fringes – cf the pattern of oil on water

Shape of the interface

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• Interdiffusion, e.g., welding

Miscible systems

Immiscible systems

• Copolymers, e.g., di-blocks

• Reduce interfacial tension →

• Entangle with homopolymers →

smaller dispersed phase

increase strength

Interfaces in miscible or immiscible systems

σ

φ

As madet = 0

Annealedt > 0

∆

σσσσ

Polymer Interdiffusion

σ

φ

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Momentum Transfer, Q (Å-1)

0.01 0.1

Reflectivity

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

w = 0 nm

w = 5 nm

w = 10 nm

Effect of Interdiffusion on Reflectivity Profiles

Approaches to Real Time Reflectivity Measurements

Amorphous polymers - Tgwell above RT

1: Measure R(Q) at RT of samples as prepared2: Place on heated plate and measure R(Q) with limited Q window.

Polymers with rapid diffusion - oligomers, plasticisers, etc

1: Measure R(Q) at RT of deuterated layer on silicon2: At t = 0 bring diffusant into contact with polymer layer and measure R(Q) with limited Q window - T > RT

T << Tg

T > Tg

t = 0

t > 0

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Momentum Transfer, Q (A-1)

0.01 0.1

Reflectivity

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

05

32

63

93

124

155

186212

t (mins)

Real Time ReflectivityMeasurements

Si / PS (50k) / dPS (40k) @ 115 C

‘225’Normalised Distance

-3 -2 -1 0 1 2 3

Vol

ume

Fra

ctio

n,

φφ φφ

0.0

0.2

0.4

0.6

0.8

1.0

Polymer 2Polymer 1

w

φ = +

12

12

tanhz

w

Polymer Motion

t

t = τe

Entanglement time

t = τR

t = τd

Rouse relaxationtime

Reptation time

t = 0

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Polymer Interdiffusion

Log ( time (s) )

2.5 3.0 3.5 4.0

Log (w

idth (nm) )

0.6

0.8

1.0

1.2

τr(dPS1) τr(hPS)

t1/4

t1/2

τd(dPS) τd(hPS)

t > ττττd

t < ττττe

ττττe < t < ττττR

ττττR < t < ττττd

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t∞∞∞∞σσσσ

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t∞∞∞∞σσσσ

81

t∞∞∞∞σσσσ

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t∞∞∞∞σσσσ

dPS (40k) / hPS (49k) Interdiffusion @ 115 C

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Polymers and Neutrons

• Hydrogen-deuterium contrast has been the key advantage for polymers

• Neutron scattering is an ideal technique for investigating size and shape of polymer molecules in dense systems. Small angle neutron scattering has been widely used

• It is also possible to “see” the effect on polymer motionof the neighbouring molecules. Spin echo experiments and reflection experiments on multilayer samples have been important but less widely applied.

• Polymers and neutrons are natural partners!

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