Neutrons and Soft Matter
Aurel RADULESCU
Jülich Centre for Neutron Science JCNS, Outstation at MLZ, 85747 Garching, Germany
7 July 2014
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
2
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
crystalline state
Soft Matter
liquid state
structure: short range to long range order
dynamic 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
mechanical response rubbers
elongated several hundred % of initial lenght
no linear relation between stress and strain
- slow, non-equilibrium response
response time
liquid ~ 10-9 s
polymer or colloidal solution ~ 1 … 10-4 s
Soft Matter –
qualitative and quantitative
“Soft” – qualitative property
shear modulus G – quantitative parameter
restoring force of a deformed material which
shear modulus
tends to recover its own shape (elastic materials)
“softness” – smallness of G
bulk modulus K of soft mater same order as for metals
Shear modulus G
metals: some 10 GPa
soft matter: < 0.1 GPa
liquids: 0 Gpa
bulk modulus
Bulk modulus K
metals and soft matter: >1 GPa
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
L
G
2
L
L
S. Kaufmann et al.
J Mater Sci (2012) 47:4530–4539
F – shearing force
L – crystal deformation
G ~ energy/(length)3
typical interaction energy ~ kBT
Gcolloidal crystal is 12 orders of magn.
smaller than Gusual crystal
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
Soft-Matter Triangle
Applications – everyday life
Soft Matter – high-tech applications
polymeric and soft
composite materials as
additives for oil industry
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
Static properties – statistical parameters
statistical „random walk“ effect
segment length: a
number of segments: N
contour length: Na
End-to-end length
Ree  a N
Full length contour:
length of the stretched polymer
L=((bond length)*(cos(109.47°-90°)/2))*(#C-1)
Radius of gyration
(average extension from R 2 
g
the center of mass)
 R  R 
2
i
CM
i
N
Rg  Ree
1
6
Polymer architecture
homopolymer
heteropolymer (diblock)
Polymer aggregates – shape
distance distribution function for different shapes
Polymer conformation
long-range
repulsion
R  L  aN
good solvent
R  aN3/5
Monomer size a~0.1nm
Number of monomers N~102 – 1010
Contour length L~10nm – 1m
q-solvent
R  aN1/2
poor solvent
R  aN1/3
homopolymer
star-like block copolymer: n and m – number of repetitive units for
the blue-solvophilic and the red solvophobic blocks
Polymer morphology
Morphologycal behavior
of PEP-PEO in solution
Dynamical properties
A. Wischnewski & D. Richter,
Soft Matter vol. 1, 2006
Ed. G. Gompper & M. Schick
polymer chains in the melt
3D Fickian
diffusion
local
reptation
Rouse
dynamics
center-of-mass
diffusion
each chain can be considered to
be constrained within a tube –
topological constraints
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
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
Scattering Theory
Small-angle neutron scattering
1
A 
VA
b
i
i
Small-angle neutron scattering
The form factor
intraparticle correlations
Contrast Variation
hPS-dPB micelles
(Fpol=0.25%) in different
solvents for different contrasts
R. Lund et al., 2013
Experimental aspects –
resolution and polydispersity
SANS - Examples
PEP-PEO
J. Stellbrink et al., 2005
structure factor effect
effect of asymmetry in MW
L. Willner et al., 2010
Neutron Spin-Echo
l/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
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 meansquare displacement <r2(t)>
fit – Rouse model
Q=1nm-1
Neutron Spin-Echo
A. Wischnewski et al., 2003
plateau –
topological constraints
PEP melt, 492K
the only free parameter –
the tube diameter: d=6nm
Tube concept – pair correlation function of a single chain in the melt
SANS and NSE at JCNS@MLZ
KWS-2 SANS diffractometer
l=4.5 .. 20Å; l/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; l/l=10%
Fourier time range t=2ps.. 350ns
Phase behavior of C28H57-PEO
M. Amann et al., 2014
f=15%
fcc
f=30%
using chopper at
KWS-2: solid-solid
phase transition
fcc → bcc
observed
expected change in
aggregation number Nagg →
exploring the phase diagram
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