Neutrons and Soft Matter

Aurel RADULESCUJülich Centre for Neutron Science JCNS, Outstation at MLZ, 85747 Garching, Germany

7 July 2014

2

Outline

• Soft Matter – definition, examples, applications

• Soft Materials – structural and dynamical properties

• Relevance of Neutron Scattering

• Small-Angle Neutron Scattering (SANS)

• Neutron Spin-Echo (NSE)

• SANS and NSE at JCNS and FZJ

• Conclusions

Soft Matter – Definition

Soft Materials

“molecular systems giving a strong response to very weak command signal” PG deGennes (1991)

- easily deformed by small external fields, including thermal stresses and thermal fluctuations- relevant energy scale comparable with RT thermal energy - subtle balance between energy and entropy rich phase behavior and spontaneous complexity

Soft Mattercrystalline state liquid state

structure: short range to long range orderdynamic response: elastic and viscous properties

Soft Materials

Soft Matter materials: common features

- structural units: much larger than atoms- large molecules, assemblies of molecules that move together

- large, nonlinear response to weak forces

- slow, non-equilibrium response

response time liquid ~ 10-9 spolymer or colloidal solution ~ 1 … 10-4 s

mechanical response rubbers elongated several hundred % of initial lenghtno linear relation between stress and strain

bulk modulus

shear modulus

Soft Matter – qualitative and quantitative

“Soft” – qualitative propertyshear modulus G – quantitative parameter

restoring force of a deformed material which

tends to recover its own shape (elastic materials)

“softness” – smallness of Gbulk modulus K of soft mater same order as for metals

Shear modulus Gmetals: some 10 GPasoft matter: < 0.1 GPaliquids: 0 Gpa

Bulk modulus Kmetals and soft matter: >1 GPa

Example: molecular vs macromolecular crystals

macromolecular (colloidal) crystals: molecule size ~1mmmolecular crystals (NaCl): unit size ~ 1Å unit size molecular crystal << unit size colloidal crystal

L

LG

L

F

2F – shearing forceDL – crystal deformationG ~ energy/(length)3

typical interaction energy ~ kBTGcolloidal crystal is 12 orders of magn. smaller than Gusual crystal

S. Kaufmann et al.J Mater Sci (2012) 47:4530–4539

Examples of soft matter systemsComplex fluids including colloids, polymers, surfactants, foams, gels, liquid crystals, granular and biological materials.

Y. Roiter and S. MinkoAFM

biological membrane

Soft-Matter Triangle

Applications – everyday life

Soft Matter – high-tech applications

understanding formation of nanoparticles: key for new products from detergents to cosmetics

tyres containing nanostructured aggregates: less energy to roll → save fuel

environmentally friendly cleaners

polymeric and soft composite materials as additives for oil industry

statistical „random walk“ effectsegment length: anumber of segments: Ncontour length: Na

Radius of gyration (average extension from the center of mass)

Full length contour:length of the stretched polymerL=((bond length)*(cos(109.47°-90°)/2))*(#C-1)

End-to-end length

N

RRR i

CMi

g

2

2

NaRee

6

1eeg RR

Static properties – statistical parameters

Polymer architecture

homopolymer

heteropolymer (diblock)

distance distribution function for different shapes

Polymer aggregates – shape

long-range repulsionR L aN

good solventR aN3/5

q-solventR aN1/2

poor solventR aN1/3

Polymer conformation

Monomer size a~0.1nmNumber of monomers N~102 – 1010 Contour length L~10nm – 1m

star-like block copolymer: n and m – number of repetitive units for the blue-solvophilic and the red solvophobic blocks

homopolymer

Polymer morphology

Morphologycal behavior of PEP-PEO in solution

polymer chains in the melt

each chain can be considered to be constrained within a tube –

topological constraintsRouse dynamics

local reptation

center-of-mass diffusion

3D Fickian diffusion

Dynamical properties

A. Wischnewski & D. Richter, Soft Matter vol. 1, 2006 Ed. G. Gompper & M. Schick

Dynamical properties – tube concept

Lateral confinement

Rouse model – dynamics of Gaussian chain at intermediate scale

Local reptation – random walk

Diffusion along the tube - reptation

Neutron Scattering – key in Soft-Matter

Length scale – Time scale

• Organic and biological compounds consist of primarily C, H, N, O

• Hydrogen (H) and Deuterium (D) scatter very differently

• Simple H/D substitution allows highlighting / masking structures

Ideal for Soft Matter

Neutrons exhibit very special properties

Scattering Theory

i

iA

A bV

1

Small-angle neutron scattering

Small-angle neutron scattering

intraparticle correlations

The form factor

hPS-dPB micelles (Fpol=0.25%) in different solvents for different contrasts

Contrast Variation

R. Lund et al., 2013

Experimental aspects – resolution and polydispersity

effect of asymmetry in MW

structure factor effect

PEP-PEO

J. Stellbrink et al., 2005

L. Willner et al., 2010

SANS - Examples

decoupling detectability of tiny velocity changes caused by the scattering process from the width of the incoming velocity distribution

the key is the neutron spin

/Dl l=10-20%

Neutron Spin-Echo

relaxation-type scattering, function of time

J – integral of the magnetic inductiong – gyromagnetic ratio

Neutron Spin-Echo

meaning of the scattering function

- deuterated polymer matrix containing a few % protonated chains → coherent single chain dynamics in the SANS regime

- sample containing only protonated chains → incoherent scattering function – self-correlation of protons of chain segments → segmental mean-square displacement <r2(t)>

Q=1nm-1

D. Richter et al., 1994

fit – Rouse model

Neutron Spin-Echo

Tube concept – pair correlation function of a single chain in the melt

A. Wischnewski et al., 2003

PEP melt, 492K

plateau – topological constraints

the only free parameter – the tube diameter: d=6nm

SANS and NSE at JCNS@MLZ

KWS-2 SANS diffractometer l=4.5 .. 20Å; /Dl l=2%..20%max. flux 2x108 ncm-2 s-1

Q-range: 1x10-4 .. 0.5Å-1 (with lenses)

J-NSE spectrometer l=4.5 .. 16Å; /Dl l=10%Fourier time range t=2ps.. 350ns

Phase behavior of C28H57-PEO

f=15%

fcc

f=30%

expected change in aggregation number Nagg → exploring the phase diagram

using chopper at KWS-2: solid-solid

phase transition

fcc → bcc observed

M. Amann et al., 2014

Conclusions

• Soft Matter Systems – great richness of properties, complex systems

• SANS – unique method for structural investigation

• NSE – unique method for dynamical investigation

• KWS-2 & J-NSE – dedicated neutron scattering instruments to soft-matter systems