Neutrons and Soft Matter Aurel RADULESCU Jülich Centre for Neutron Science JCNS, Outstation at MLZ, 85747 Garching, Germany 7 July 2014 Topic-2 1

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 Matter crystalline state 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 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

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

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

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 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

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)

Polymer architecture homopolymer heteropolymer (diblock)

Polymer aggregates – shape distance distribution function for different shapes

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

Polymer morphology Morphologycal behavior of PEP-PEO in solution

Dynamical properties polymer chains in the melt 3D Fickian diffusion A. Wischnewski & D. Richter, Soft Matter vol. 1, 2006 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

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

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 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

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

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

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

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 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%

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