MPIP-Mainz T.Still,W.Cheng,N.Gomopoulos G.F FORTH Heraklion G.F Sculpture by E.Sempere (Madrid) Cubic arrays of hollow stainless-steel cylinders [diameter: 2.9 cm and lattice constant:a=0 cm] Minimum sound transmision at f=.67 KHz (stop band)* ( ~a) *R.Martinez et al Nature 378,23,995
Sonic Crystal Pb silicone Spectral gab :lattice a<<λ sound wavelength (usually a/λ ~) silicone :soft spring, Pb:heavy mass P.Sheng et al Science 2000 Strong and Deaf Periodic Structures Phononic Materials Experimental techniques (ω(k ) Examples of fabricated structures /phenomena Colloid-based sub-μm structures (music & concert) D Hybrid multilayer SiO2/PMMA films (unidirectional gap) Biological structures (spider dragline silk) Thessaloniki /09 2
Material vibration? in bulk: longitudinal and transverse waves q q longitudinal c l transverse c t structured materials: c l, c t & density vary in space elastic wave equation displacement u(r,t) at surfaces or in thin films: + boundary conditions Phononic Materials control the flow elastic energy (993,995) periodic modulation (ρ, c l,two c t, anisotropy) standard manufacturing: sonic,ultasonic range Bragg gap at λ ~a commensurate lattice constant a Strong local resonances : λ >>a (P.Sheng 2000) Hypersonic phononics : fabrication,characterization Dual gaps(phoxonics) : hypersonic phononics & visible wavelentgh photonics optomechanical crystals (Nature 462,78,2009) 3
Brillouin Light Scatterin (BLS) =cq, q=(4 / )sin( /2) Fabricated sub- m structures.polymer based Phononic Crystals (optical lithography) PRL 94,550(2005) 2a.Colloid- based Phononic Crystals (vertical lifting) PRL00, 9430 (2008) 2b.Colloid- based Phononic Crystals (melt compression,shear induced) (Adv.Mater.20,484(2008) 4
Fabricated sub- m structures 3.Anodic Aluminium Oxide- based Phononic Crystals (electrochemistry) J.Chem.Phys.23,204(2005) 4..D hybrid Phononic Crystals (spincoating) Nano lett.submitted SiO 2 &PMMA Phononic Materials Experimental techniques (ω(k ) Colloid-based sub-μm structures (music & concert) a) Particles: Local resonances (music) PRL(2000),J.C.P(2005),Langmuir(2005),Nano lett.(2008),jcis(2009) D Hybrid multilayer SiO2/PMMA films (unidirectional gap) Biological structures (spider dragline silk) 5
Dry colloidal crystals Top view Vertical lifting deposition Lifting (several m/s) Side view colloidal suspension (0.5%-2.5%W/W) fcc J.Wang,M.Retsch U.Jonas BLS spectra d=856nm 0, Intensity (a.u.) 0,0 0, d=856nm big size 0,0 0, 0, d=636nm d=636nm 0,0 0,0 0, 0, d=383nm d=383nm 0,0 0,0 0, d=256nm d=256nm 0, 0,0 0,0 0, 0, d=70nm d=70nm 0,0 0,0-5 -0-5 0 f (GHz) 5 0 5 No q dependence! small size -8000-4000 0 4000 fd (GHz nm) 8000 Scaling f~d-! W. Cheng et al. J. Chem. Phys. 23, 204 (2005). 6
Theoretical Calculations The elastic wave equation: 2 ( λ + 2μ) ( u) μ u + ρω u = 0 u: the displacement vector, λ = ρ = : the elastic coefficients 2 2 2 ( cl ct ), μ ρct I. Isolated particle Scattering cross section vs. frequency of a sound wave Energy density distribution II. Periodic lattice: u( r, t) = w( r) exp[ i( kr ωt) ] Plane wave single scattering (G reciprocal lattice vector) Multiple phonon scattering formalism Elastic field S(q,ω) (neglecting relaxation effects) w = w exp( ikg) k G G (q=k+g) particle vibrations Frequency (GHz) 8 6 4 2 0 8 6 4 2 0 0 2 3 4 5 6 /d (μm - ) Single-phonon scattering-cross-section calculations σ/πr 2 Air PS fd (GHz nm) 7
particle vibrations (eigenmodes) 8 6 Frequency (GHz) 4 2 0 8 6 4 2 0 0 2 3 4 5 6 /d (μm - ) moduli (E,G),Poisson ratio confinment effects σ/πr 2 (a.u.) Single-phonon scattering-cross-section calculations Air PS fd(ghzm) Phononic Materials Experimental techniques (ω(k ) Colloid-based sub-μm structures (music & concert) a) Particles:Local resonances (music) b) Crystal:Band gaps (particles concert) Nature Mater.(2006), PRL(2008) D Hybrid multilayer SiO2/PMMA films (unidirectional gap) Biological structures (spider dragline silk) 8
self-assembling and infiltration procedures Dry opals Wet colloidal crystals vertical lifting deposition dry colloidal crystal liquid infiltration blow off excess liquid infiltrated colloidal crystal W.Cheng et.al Nature Mat.5,830,2006 Scattering Geometry q=(4π/λ)sinα 9
2.Wet Opals (in silicon oil) fcc colloidal crystal in silicon oil q in () plane q (nm - ) 0,060 Intensity (a.u.) 0,056 0,052 0,048 0,044-8 -6-4 4 6 8 f (GHz) Dispersion (ω(q)) relation 0 8 d (PS) =256 nm PS f (GHz) 6 4 2 silicon oil Bragg gap 0 -M 0,000 0,005 0,00 0,05 0,020 0,025 q (nm - ) W. Cheng et al. Nature Mater. 5, 830 (2006). 0
elastic contrast : Z=( p c p / f c f )- Glycerol : Z~0 Silicon oil: Z~0.7 PDMS : Z~.2,6,2 in PDMS in silicon oil in glycerol Tuning the gap (different fluids) ωa/2πc eff 0,8 0,4 Γ Μ 0,0 0,0 0,4 0,8,2,6 (2/3) (3/2) qa/π Frequency (GHz) 8 7 6 5 4 3 ωa/2πc.2 0.8 0.4 0.0 L Bragg-stop band Γ 2 256 nm 307nm 0 0.000 0.005 0.00 0.05 0.020 0.025 L q (nm - ) Tuning the gap (particle size) W.Cheng et.al Nature Mat.5,830,2006 Views&News p.773
current situation structure signature Bragg-gap particle properties multipole resonances hybridization- gap SEM images of a colloidal crystal (PS-307nm) and a hybrid(ps-307nm/360nm (FT-images over an area of 4μm x 4μm) 2
Phononic band diagrams of soft opals BZ BZ T.Still et al. PRL 00,9430,2008 So far, 2D and 3D systems and longitudinal polarization D periodic structures are model systems: separate treatment of the longitudinal and transverse polarizations prove the robustness of (q) to disorder, structural imperfections deal with the vector nature of the elastic wave propagation corroborate the theoretical predictions with experiment (impedance, moduli,poisson ratio, mass density) Create a facile platform for D-phononics 3
Phononic Materials Experimental techniques (ω(k ) Sub-μm structures:colloid-based a) Particles:Local resonances (music) b) Crystal:Band gaps (particles concert) D Hybrid multilayer SiO2/PMMA films Biological structures (spider dragline silk) D Hybrid multilayer SiO2/PMMA films N.Gomopoulos et. al Nano lett. 4
Phononic Materials Experimental techniques (ω(k ) Sub-μm structures:colloid-based a) Particles:Local resonances (music) b) Crystal:Band gaps (particles concert) D Hybrid multilayer SiO2/PMMA films Biological structures (spider dragline silk) spider dragline silk a. View of the spider spinnerets under the microscope. b. Major ampullate fiber is probed along two symmetry directions 5
spider dragline silk Erase the stop band in regenerated amorphous and semicrystalline silk Mechanical anisotropy. A unidirectional phononic gap. spider dragline silk The effect of strain on the : dispersion diagram and mechanical anisotropy. N.Gomopoulos et al Nature Materials? 6
spider dragline silk Scheme of the structure of dragline spider silk N.Gomopoulos et al Nature Materials? Summary Wave Propagation in Microstructured Materials (Tailor the band structure :unexplored fundamental research) Particle vibration modes (flat ω~q 0 ) Acoustic phonons (ω~q) (average medium Hypersonic Band Gaps (Bragg, hybridization) in fabricated structures Band gap in natural structures origin? Geometrical/Morhological characteristics Micro-nanomechanical properties 7
Acknowledgments M.Retsch,U.Jonas, M. D Acunzi,D. Vollmer (MPIP) (colloidal systems) N.Stefanou (Athens) R.Sainidou(Lille) (theory) H.Koh,E.L.Thomas (MIT) D Hybrid structures P.Papadopoulos,F.Kremer (Leipzig) Spider dragline silk DFG for funding Thank you very much!!! Thank you very much!!! Thank you very much!!! Thank you very much!!! Thank you very much!!! 8