Methoden moderner Röntgenphysik II: Struktur und Dynamik kondensierter Materie

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1 Methoden moderner Röntgenphysik II: Struktur und Dynamik kondensierter Materie Vorlesung zum aupt/masterstudiengang Physik SS 2011 G. Grübel, M. Martins, E. Weckert et al. SemRm3, Physik, Jungiusstrasse Di: 14:00-15:30 Do: 11:20-12:50 S. V. Roth (SR) , & finden statt fällt aus 1 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

2 im Overview over use of soft matter and x-ray scattering of soft matter Soft matter Structure function relationship Definition Occurence ow to produce Polymers, nanocomposites Chemistry, biology, physics Characterization methods GPC, centrifuging X-ray scattering Micro- & nanofocused x-ray beams 2 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

3 Literature [Strobl] G. Strobl, "The Physics of Polymers", Springerverlag, eidelberg (1997), ISN [Springer] T. Springer et al., "Streumethoden zur Untersuchung kondensierter Materie", Forschungszentrum Jülich Gmb, Jülich (1996), ISN [Lechner] M.D. Lechner et al., "Makromolekulare Chemie", irkhäuser Verlag, erlin (1993), ISN [Lindner] P. Lindner et al., Neutron, X-rays and light: Scattering Methods pplied to Soft Condensed Matter", North olland, msterdam (2002), ISN [Stribeck] N. Stribeck, "X-ray Scattering of Soft matter", Springerverlag, eidelberg (2007), ISN [iggins] J.S. iggins and.c. enoit, "Polymers and Neutron Scattering", Clarendon Press, Oxford (1996), ISN Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

4 asics, theory, preparation a primer What is soft matter? asic Definition a try! Notion for description, constituents, architecture Characterization of polymers, molar masses, polydispersity Chain conformation, constitution, configuration, chain models Flory-uggins-theory, mixture of polymers, Interaction, phase separation Colloids Polymer-Metal nanocomposites Take care here, metals (hard matter, actually) comes into play. ut it s still soft matter this is no contradiction, as you will see! 4 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

5 Soft Matter Soft matter is not hard matter! Metallic alloys, ceramics Polymers (bottles) Colloids (wall paintings) Nanocomposites (Metal-Polymer-Composites, airplanes, credit cards) Fibres (Textiles) Wood (natural nanocomposite) Cells (iology) Glue (quite complex!) Characteristics: Polydispersity, heterogeneity Stribeck: Scattering, not diffraction 5 We will first start with polymers! Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

6 Example: Cracks in industrial Polystyrene bulk material µsxs Optical micrograph Strong overlap to materials science Roth et al., J. ppl. Cryst. 36, 684 (2003) 6 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

7 asic definition Polymers: Macromolecules uild up of a large number of molecular units Covalent bonds Molecules: N 2, O 2, 2, C 3, Standard example: Polyethylene (PE) Note: Names are often abbreviated by capital letters, e.g. Polypropylene - PP, Poly(mehtylmethacrylate) PMM, Polystryrole (PS), Poly(ethyelene terephtalate) PET, Poly(p-phenyleneterephtahalamide) PPT: Kevlar and often have commonly used trade names: Kevlar, nylon Difference in chemical constituents, architecture and hence in physical properties! morphous, crystalline, glassy, viscous, Deformation, cracks, SXS, GISXS 7 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

8 asic definition Standard example: Polyethylene (PE) Ethylene: C C Structure unit Monomeric unit Covalent bond: Interaction between nearest neighbours dominates inding and anti-binding orbitals: Spatial overlap of electron wave functions, binding energy Increased electron density between nuclei Strongly directed bonding (diamond, sp3-hybridisation) Polyethylene C C C C backbone Number of monomers: Degree of polymerization: N Polymerization process: starts from low molar mass compounds 8 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

9 Distribution functions Polymerization reactions: mixture of macromolecules of different molecular weight Monomer: molecular weight M Distribution function: p(m) -> number density (number per ) p(m)dm : fraction of polymers M M+dM Normalization: Number average molecular weight: p ( M ) dm =1 M n = p( M ) MdM Strictly speaking: M -> discrete (monomer units), but degree of polymerization high Weight average: p'( M ) = p( M ) M p( M ) MdM Weight fractions p( M ) M MdM M W = p'( M ) MdM = p( M ) MdM 9 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

10 Distribution functions Source: Stribeck Source: Stribeck 10 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

11 Polydispersity MW Note: M W > M n Characterize distribution of molecular weight U = 1 M 2 Variance of p(m) ΔM = p( M )( M M n ) dm 2 p( M ) M dm p( M )2M nmdm + = p( M ) M dm 2 2 n n U M = M W n = M M M W 1 = n ΔM M 2 2 n 2 n using M n = p( M ) MdM 11 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

12 The polymer chain C C C C C C C C C C C C C C C C Linear chains exist, but more realistically: Rotational degree of freedom R Mean segment length l= Contour length path length L =12 v l r v i N=12 l l v Chain end distance R Center of gravity 12 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

13 The polymer chain End-to-end distance: R = N v l 2 = N l R G = 1 N v M mass of macromolecule 2 mir 1 i m i mass of segment M Mean over all configurations Radius of gyration (for a gaussian, uncorrelated chain) Measure for extension of macromolecule Relation between R G and R Using v r i = v r R G = R / 6 r v ' v + l = r r i i CM R r v 0 l v i r v i ' r v i r v CM We will need this for small angle x-ray scattering! l 13 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

14 rchitectures Short chain and Long chain branches Star polymers Network of crosslinked chains 14 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

15 Polymerization methods Industrial PS p Schulz-Zimm Source: Strobl Schulz-Zimm Step polymerization Poisson chain polymerization Equal degree of polymerization Same p M [g/mol] p = M M n 0 =10 4 Mass of an individual molecule M M n W = = g / mol 15 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

16 Polymerization methods Establishing of covalent bonds Chain polymerization Step polymerization G+G -> G G +G -> G G M+M 0 -> MM 0 =M M -> M M 0 Monomeric unit (M 0 ) groups of monomers (G) 16 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

17 Polymerization via radicals Well-known Large industrial scale Many polymers accessible 1) Start: Initiator I I -> 2R t T, which are suitable for polymerisation e.g. peroxides In-situ formation light Many radicals start polymerization in presence of monomers (M) R + M -> RM 2) Growth reaction: RM + nm -> P 3) Stop: End of polymer chain growth Reaction of radicals at end of polymer chain Combination: -C2-CX + XC-C2- -C2-CX-CX-C2- Doubling of polymerization degree Disproportionality: -C2-CX + XC-C2- C=CX + XC2-C2- Double bond via transfer of 17 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

18 Copolymers Ethylene Propylene C C C C C 3 Statistical: lock structure.. n -block- m n,m>10 lock-copolymers we will see a variety of structure, especially in thin films Di-, tri-, multiblock copolymers e.g.: hard, viscous (depending on Tg) 18 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

19 Glass transition temperature more during part II, summer semester lectures (ermann Franz) rief introduction important to understand structure of thin films! Crystalline (lectures by M) Melt (liquid state) Solid morphous : frozen in liquid state, glassy -> isotropic -> physical parameters not direction dependent 19 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

20 Glass transition temperature owto characterize glassy state: Characteristic temperature: T g Not a phase transition of 1st or 2nd degree Dynamic interpretation: α,β-relaxation Source: Lechner Latent heat Melting, crystallization, Viscoelastic: Elastic response at small interaction times Creep at long interaction times Source: Lechner Not in equilibrium, might even recrystallize 20 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

21 Flory-uggins-Theory Polymer mixtures Polymer blends -> mixing = route to combine different materials properties igh fracture resistance and stiff Problem: increase in elastic moduli -> brittle high fracture resistance tough material Still stiff enough PS: stiff, but brittle Polybutadiene ~rubber Fracture starts here and is initially localized here! Example: (Y. Men) 21 We will look with SXS into deformation and crack propagation! Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

22 Flory-uggins-Theory Q: when do we obtain a homogenous or heterogenous morphology during blending? : Flory-uggins theory phase diagrams as function of T and M: When can we expect single, binary phases n n n n V V V +V Consider liquid state G G G Reminder: dg = SdT + Vdp + { μ dn + γd Change in composition S entropy µ chemical potential (keyword: diffusion), change in phase: equilibrium µ1=µ2 γ surface tension (2D) For mixing: ΔG = G ( G + G ) mix 22 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

23 Flory-uggins-Theory It states: ΔG mix = TΔS t + ΔG loc Change in entropy: Mixing -> increase ssociated with motions of center of mass of all polymer molecules + : favours mixing Change of local interactions and motion of monomers General rule: Van-der-Waals interactions -> attractive energies between equal monomers are stronger than between different ones - : unfavorable for mixing Change in V: Shrinking, expansion Formulas? 23 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

24 Flory-uggins-Theory 1) ΔS t = Rn V ln + V ΔS t ΔG Rn mix ln = Rn = TΔS V V lnφ ssumption: Polymer chains ~ ideal gas t + ΔG φ loc, = Rn V. V lnφ 24 2) ΔG loc = RT V v C χφ φ The higher the concentration, the more likely the interaction χ Flory-uggins-Parameter Empirical parameter Nearest neighbour interactions contact energies This makes sense: v C Δ G loc φ, φ Molar volume of a reference unit common to and 0 0 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

25 Flory-uggins-Theory ΔG loc = RT V v C χφ φ ΔG mix = TΔS t + ΔG loc Derivation general for solid state physics! Now one -chain in mixture ence: Increase in potential energy: Number of nearest neighbours: z z φktχ' 2 void double counting Increase in G only when -pair is formed > probability: Energy increase by dimensionless parameter: ΔG ence: ( φ φ φ φ ) loc kt z χ + 2 ~ χ' φ with respect to kt 25 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

26 Phase diagrams ΔG mix = φ RTV v φ χ lnφ + + lnφ φφ v Molar volume v vc Low molar mass -> entropy leads to mixing Polymers: large molecular weights v, S 0 Δ t Mixing takes place, when ΔG mix <0 χ < 0 Mixing! χ > 0 incompatibility Symmetric mixture: Equal degree of polymerization N v,, = N N = N vc ΔG mix = RT ( n + n = φ φ = 1 ) + ( φ lnφ + φ lnφ + χnφ φ ) 26 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

27 Phase diagrams Symmetric binary polymer mixture φ = Critical point φ ' 2.4 omogenous -mixture φ '' 2.0 Miscibility gap 1.6 χn φ fter [Strobl] ' φ < φ < φ '' Two phases, demixing 27 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

28 Phase diagrams Consequences χn χ < χ χ > = 2 C χ C = 2 2 N ΔG φ mix 2 φ = = φ φ 2χN Critical value: separates region with miscibility gap Miscibility gap Compatibility through all concentrations, mixing N>>0 χ > 0 = 0 Vanishing curvature No mixing for high molecular weight! Critical concentrations Δ φ G mix = 0 χn Universal! 28 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth φ

29 Phase diagrams In general: upper and lower miscibility gap possible Include T, one can show (thermodynamics!): ΔG loc = Δ mix TΔS loc Endo- or exotherm : >0 or <0 1 2 TC χ ~ χ = > 0 T N T Entropic contributions to ΔG loc ( mobility ) neglected Endothermal polymer mixture miscibility for high temperatures, if molecular weights low enough -> mobile enough! T/T C homogeneous Two-phase 29 Of course, inverse for exothermal Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth φ

30 Partial crystalline polymers PS -> glassy solidification during cooling: no long range order PE, PP, P: long range order -> building-up of lamellar block Lamellae, ~nm Periodic arrangement W<< amorphous Ordered region SXS-pattern qy [Schroer, ppl. Phys. Lett (2006)] Why? Cooling > reduced mobility -> no thermodynamic equilibrium ->multiple folding of polymer chains 30 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

31 lock Copolymers 2 different species couples together by a chemical link [Strobl] We learn from Flory-uggins-Theory: binary polymer mixture -> separation in 2 phases. Linkage ~phase separation microphase separation: mesoscopic domains: nm 100nm >> single block domains: uniform size, arrangement! continous phase possible [Strobl] PS-b-PI this is already a nanocomposite pplications: Solar cells, magnetic data storage, masks, lithography, nanowires 31 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

32 Colloids - Polymers - Metals - Small particles, dispersed in liquid phase - Size: nm.µm - Wall paintings - Polymers: Spheres Production: [Xia, dv. Mat. (2000)] Emulsion polymerization: Example latex particles (styrene/butadiene) 1 Initiator (e.g. Potassium-persulfat) -> dissolved in water: urst of free radicals -> polymerize monomers: nuclei 2 Surfactant: Micelles, swollen by monomer until all monomer consumed: 32 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

33 Colloids and you obtain nice spheres: which you can nicely arrange here in 2D: [Springer] [Frömsdorf, J. Chem. Phys. (2006)] 33 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

34 pplication Optical properties: sharp resonances (visible light) < > plasmon resonances cluster arrangement & shape bsorption [a.u.] λ p λ p Wavelength [nm] J.C. ulteen et al., J Phys. Chem. 101, 7727 (1997) 34 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

35 Colloids Gold, Silica, Fe, CoPt, etc Simple recipies: auer, Nanotechnology (2003) (1) 0.01% (w/v) tetrachloroauric[iii]acid trihydrate (ucl4 32O in 100 ml of water) is heated to boiling. (2) 1 ml of 1% (w/v) trisodium citrate dihydrate is added to the boiling solution under constant stirring. (3) In about 25 s the slightly yellow solution will turn faintly blue (nucleation). (4) fter approximately 70 s the blue colour then suddenly changes to dark red, indicating the formation of monodisperse spherical particles. (5) The solution is boiled for another 5 min to complete reduction of the gold chloride. C65Na3O7 2(2O) u u + byproducts (salts) u u u More structures: Core-Shell: [bul Kashem, Macromolecules (2008)] 35 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

36 Polymer-Metal Nanocomposites iswas et al., Vac. Tech. Coat. 7, 54 (2006). auer et al., Nanotechnology 14,1289 (2003) igh-frequency filters Solar cells ν lim ~ρ/r nti-counterfeiting iosensors 36 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

37 Polymer-Metal Nanocomposites: Production Sputter deposition: r + Substrate - Nice clusters, too - Fast deposition method - Usually broader size distribution - self-assembly: u- u interaction much stronger than u- Polymer interaction Roth et al., ppl. Phys. Lett. 88, (2006) Noble metal (u, g, Cu, ) Polymer film 300nm Substrate (Si, glass, + TiO2) 37 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

38 Polymer-Metal Nanocomposites: Production Sputter deposition: r + Substrate F. Faupel et al., in: Low Dielectric Constant Materials for IC pplications, P. S. o, W. W. Lee, and J. Leu (Eds.), Springer Verlag, 221 (2003) pp Nucleation - Growth - Coalescence Modelling of industrial process: in-situ kinetic of nanoparticle growth 38 Methoden moderner Roentgenphysik II - Vorlesung im aupt/masterstudiengang Physik, Universität amburg, SS2011 S.V. Roth

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