1. Neutrons and Soft Matter
Aurel RADULESCU
Jülich Centre for Neutron Science JCNS, Outstation at MLZ, Garching, Germany
7 July 2014
Topic-2 1

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

3. 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 Matter
crystalline state
liquid state
structure: short range to long range order
dynamic response: elastic and viscous properties

4. 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
mechanical response rubbers
elongated several hundred % of initial lenght
no linear relation between stress and strain
response time
liquid ~ 10-9 s
polymer or colloidal solution ~ 1 … 10-4 s

5. Soft Matter – qualitative and quantitative
“Soft” – qualitative property
shear modulus G – quantitative parameter
restoring force of a deformed material which
tends to recover its own shape (elastic materials)
“softness” – smallness of G
bulk modulus K of soft mater same order as for metals
bulk modulus
shear modulus
Shear modulus G
metals: some 10 GPa
soft matter: < 0.1 GPa
liquids: 0 Gpa
Bulk modulus K
metals and soft matter: >1 GPa

6. Example: molecular vs macromolecular crystals
macromolecular (colloidal) crystals: molecule size ~1mm
molecular crystals (NaCl): unit size ~ 1Å
unit size molecular crystal << unit size colloidal crystal
F – shearing force
DL – crystal deformation
G ~ energy/(length)3
typical interaction energy ~ kBT
Gcolloidal crystal is 12 orders of magn. smaller than Gusual crystal
S. Kaufmann et al.
J Mater Sci (2012) 47:4530–4539

7. Examples of soft matter systems
Complex fluids including colloids, polymers, surfactants, foams, gels, liquid crystals, granular and biological materials.
Y. Roiter and S. Minko
AFM
biological membrane

8. Soft-Matter Triangle

9. Applications – everyday life

10. Soft Matter – high-tech applications
polymeric and soft composite materials as additives for oil industry
tyres containing nanostructured aggregates: less energy to roll → save fuel
understanding formation of nanoparticles: key for new products from detergents to cosmetics
environmentally friendly cleaners

11. Static properties – statistical parameters
statistical „random walk“ effect
segment length: a
number of segments: N
contour length: Na
End-to-end length
Full length contour:
length of the stretched polymer
L=((bond length)*(cos(109.47°-90°)/2))*(#C-1)
Radius of gyration (average extension from the center of mass)

12. Polymer architecture
homopolymer
heteropolymer (diblock)

13. Polymer aggregates – shape
distance distribution function for different shapes

14. Polymer conformation long-range repulsion R  L  aN good solvent
q-solvent
R  aN1/2
poor solvent
R  aN1/3
Monomer size a~0.1nm
Number of monomers N~102 – 1010
Contour length L~10nm – 1m
homopolymer
star-like block copolymer: n and m – number of repetitive units for the blue-solvophilic and the red solvophobic blocks

15. Polymer morphology
Morphologycal behavior of PEP-PEO in solution

16. Dynamical properties polymer chains in the melt 3D Fickian diffusion
A. Wischnewski & D. Richter, Soft Matter vol. 1, Ed. G. Gompper & M. Schick
polymer chains in the melt
3D Fickian diffusion
local reptation
each chain can be considered to be constrained within a tube – topological constraints
Rouse dynamics
center-of-mass diffusion

17. Dynamical properties – tube concept
Lateral confinement
Rouse model – dynamics of Gaussian chain at intermediate scale
Local reptation – random walk
Diffusion along the tube - reptation

18. Neutron Scattering – key in Soft-Matter

19. Length scale – Time scale

20. Neutrons exhibit very special properties
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

21. Scattering Theory

22. Small-angle neutron scattering

23. Small-angle neutron scattering

24. The form factor
intraparticle correlations

25. Contrast Variation
hPS-dPB micelles (Fpol=0.25%) in different solvents for different contrasts
R. Lund et al., 2013

26. Experimental aspects – resolution and polydispersity

27. SANS - Examples structure factor effect effect of asymmetry in MW
PEP-PEO
J. Stellbrink et al., 2005
structure factor effect
effect of asymmetry in MW
L. Willner et al., 2010

28. Neutron Spin-Echo Dl/l=10-20%
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

29. Neutron Spin-Echo relaxation-type scattering, function of time
J – integral of the magnetic induction
– gyromagnetic ratio
D. Richter et al., 1994
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)>
fit – Rouse model
Q=1nm-1

30. Neutron Spin-Echo plateau – topological constraints
A. Wischnewski et al., 2003
plateau –
topological constraints
the only free parameter – the tube diameter: d=6nm
PEP melt, 492K
Tube concept – pair correlation function of a single chain in the melt

31. SANS and NSE at JCNS@MLZ
KWS-2 SANS diffractometer l= Å; Dl/l=2%..20%
max. flux 2x108 ncm-2 s-1
Q-range: 1x Å-1 (with lenses)
J-NSE spectrometer
l= Å; Dl/l=10%
Fourier time range t=2ps.. 350ns

32. Phase behavior of C28H57-PEO
M. Amann et al., 2014
f=15%
fcc
expected change in aggregation number Nagg →
exploring the phase diagram
using chopper at KWS-2: solid-solid phase transition
fcc → bcc observed
f=30%

33. 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