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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
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