2014 Castl Summer School July 9-11, 2014 Theoretical Framework of SERS George C. Schatz Northwestern University
Metal nanoparticle optical properties Electronic Structure Studies: Electrodynamics: Lasse Jensen (Penn St) Kevin Shuford (Drexel) Christine Aikens (Kansas St) LinLin Zhao (Penn St) David Masiello (U. Wash.) Shengli Zou (UCF) Jonathan Mullin (Wright-Patt) Leif Sherry (PD-Tex) Hanning Chen (GWU) Anatoly Pinchuk(Col. Spr) Emily Weiss, Teri Odom, Nick Valley (Oregon-PD) Jon Camden(Tenn) Rick Van Duyne Lindsey Madison Jing Zhao (PD-MIT) Chad Mirkin, Joe Hupp Fredy Aquino (PD-ARL) Jeff McMahon(PD-UIUC) Monica Olvera, M. Ratner Dan Hannah Logan Ausman (IDA) Stephen Gray (Argonne) Adam Ashwell Ana Gonzalez (Mex) Shuzhou Li (Singapore) Nadine Harris(Nokia) Marty Blaber (Seagate) Montacer Dridi Yong Zhou Mike Ross Nicolas Large Mike McAnally Natalie Gruenke
Outline 1. Extinction spectra of silver and gold nanostructures; electrodynamics of plasmonic materials 2. Electromagnetic enhancement factors, SERS, optimizing nanostructures, small gaps, dark modes, Raman emission 3. Quantum description of plasmons in small particles; SERS chemical effect 4. Ultrafast theory and experiment
Colloidal Gold Michael Faraday, 1856 Spectra of dispersed colloidal gold for selected diameters (data from Turkevich (1954), Doremus (1964)) 0.8 60 nm 100 nm 0.7 20 nm Extinction (Optical Density) 0.6 5.2 nm 160 nm 0.5 0.4 0.3 3.5 nm 0.2 0.1 1.7 nm 0.0 350 400 450 500 550 600 650 700 Wavelength (nm) Extinction = absorption + scattering (color of solution=color of light not absorbed or scattered)
Plasmon excitation: collective excitation of the conduction electrons E-field Metal sphere Nuclear framework of particle Charge cloud of conduction electrons - cloud e Plasmon wavelength: 1 shape/surroundings + χε o 2 c λ = = π sp chemical properties 2 4 ne π m e n=electron density χ = shape factor (2 for sphere, >2 for spheroid) ε o = dielectric constant of surroundings
Colloidal Silver
Ag/Au Nanoparticle Optical Properties 5000 nm A B 5000 nm 200 nm 200 nm C D 200 nm 1 m µ Size-Tunable Surface Plasmon Resonances Extinction spectra of size/shape-selected Ag particles width 120 150 150 95 120 145 145 145 height 42 62 48 46 59 55 50 70 shape Normalized Extinction l max 426 446 497 565 638 720 747 782 Ag/mica 400 500 600 700 800 900 Wavelength (nm)
Mie Theory (1908) (Lorenz-Mie-Debye) Theory 2 3 8 ( radius ) 3 π ε Extinction Cross Section = 2 2 2 ( 2 ) λ λ ε ε + + + + ε (long wavelength limit) 1 2 ε = dielectric function of metal = ε 1 + i ε 2 Extinction for 20 nm spheres Mie Extinction for 13 nm Au spheres 1.0 Dielectric constants of Au 5.0 20 nm ε 2 imaginary 0.8 Real or Imaginary part of dielectric constant 0.0 Extinction Efficiency ε 1 0.6 real -5.0 0.4 0.2 -10.0 0.0 200 300 400 500 600 700 800 -15.0 200 300 400 500 600 700 800 wavelength(nm) wavelength (nm)
Computational Electrodynamics Methods for Nanoparticles r r r v v v v v 1 1 d J ∂ ∂ 2 E H J H E t J t E t ( ) ( ) ( ) = ∇× − = − ∇× + γ = ω ε p p p p 0 t t dt ∂ µ ∂ ε Grid or Finite element methods : • Discrete Dipole Approximation • Finite Difference Time Domain Method • Whitney-form Finite Element Method Beyond Conventional Maxwell : • Coupled QM + EM
Modeling the Spectra of Silver Bipyramids using EM Simulations Ag right bipyramid Experiments b a = 106, 131, 165, 191 nm Extinction Extinction a a = 2 b 400 600 800 400 600 800 Wavelength (nm) Wavelength (nm) Au rod-sheath Experiments and simulations are in good agreement with each other. Zhang, Li , Wu, Schatz, and Mirkin Angew. Chem. Int. Ed. , 48, 7787, (2009)
Right-handed Right-handed Left-handed Positive Cotton Right-handed effect Right-handed E E Chengyi Song, Martin G. Blaber, Gongpu Zhao, Peijun Zhang, H. Christopher Fray, George C. Schatz, Nathaniel L. Rosi, Nano Lett. 13, 3256-61 (2013).
Surface Enhanced Raman Spectroscopy (SERS) SERS enhancement =~|E( ω )| 2 |E( ω ’)| 2 ~ (|E| 4 ) Normal Raman Spectrum (NRS) 2.5 M Pyridine Surface - Enhanced Raman Surface Pyridine Spectrum (SERS): enhancement factor = 10 6 ω ex Nanoparticles ω ex - ω vib Nanoparticles D. L. Jeanmaire and R. P. Van Duyne, J. Electroanal. Chem. 84, 1-20 (1977)
Plasmon enhancement factors: Absorption Enhancement =~|E( ω )| 2 SERS enhancement =~|E( ω )| 2 |E( ω ’)| 2 ~ (|E| 4 ) ave ~10 6-12 Fluorescence enhancement =~|E( ω )| 2 |G( ω stokes )| 2 Q G = scattering from particle by emitted dipole Q = nonradiative quenching
Electromagnetic Enhancement factors In Surface Enhanced Raman Spectroscopy SERS enhancement ~|E( ω )| 2 |E( ω ’)| 2 ~ (|E| 4 ) ave ~10 6 This implies: (|E| 2 ) ave ~ 10 3 3:1 4:1 5:1 (|E| 2 ) ave for prolate silver spheroids 2:1 1:1
Excitation Spectrum of Benzenethiol benzenethiol on Ag triangles Theory: Extinction ~ |E( ω )| 2 SERS~|E( ω )| 2 |E( ω ’)| 2 WS-SERS profile peak is blue-shifted McFarland, Young, Dieringer and Van Duyne. J. from LSPR by ½ of the vibrational 15 Phys. Chem. B 2005, 109, 11279-11285 frequency.
SERS enhancement factor increases with increasing wavelength |E| 4 figure of merit N. Greeneltch, M. Blaber, et al, Anal. Chem. 85(4), 2297-2303 (2013)
Average and Maximum Field Enhancments (particles chosen to have plasmon max near 700 nm) diameter = 180 nm edge length = 106 nm diameter = 19 nm, height = 52 nm λ inc = 716 nm λ inc = 650 nm λ inc = 688 nm k E E rod E sphere k k cube Average |E| 4 : 4.2x10 1 Average |E| 4 : 6.3x10 3 Average |E| 4 : 1.8x10 6 Maximum |E| 4 : 1.0x10 3 Maximum |E| 4 : 8.2x10 6 Maximum |E| 4 : 4.5x10 7 inner diameter = 100 nm, thickness = 10 nm length = 60 nm, height = 12 nm λ inc = 720 nm λ inc = 686 nm Results show that rods and triangles give the best E average enhancements for prism k isolated particles. shell Average |E| 4 : 1.0x10 6 Average |E| 4 : 1.0x10 3 Maximum |E| 4 : 1.8x10 8 Maximum |E| 4 : 3.8x10 4
Larger Enhancements for Dimers of Nanoparticles parallel rods diameter = 19 nm, height = 52 nm λ inc = 876 nm λ inc = 688 nm Average |E| 4 : 1.8x10 6 2 nm gap Maximum |E| 4 : 4.5x10 7 Avg |E| 4 is 7.0x10 7 Max |E| 4 is 1.6x10 9 slope ¡= ¡−1.8 ¡ ln( |E| 4 ) |E| 4 for ¡a ¡≤ ¡10nm ¡ ¡ |E| 4 ~1/a 2 ¡ ln(a) a (nm)
Optimized enhancement factors for sphere dimers, 1 nm gap Metal |E| 4 (max) wavelength diameter background index Ag 1.3x10 12 794 nm 20 nm 2.25 Au 2.8x10 11 723 50 1.5 2.0x10 9 Al 204 22 1.0 1.2x10 9 In 359 54 1.0 M. Ross and GCS, J. Phys. Chem. C 118, 12506-12514 (2014) However gaps below 1 nm is a problem: J. H. Yoon, Y. Zhou, M. G. Blaber, GCS and S. Yoon, JPC Lett 4, 1371-78 (2013).
Calculations for bridged dimer show CTP
SERS on Gold Dimers, Trimers
Single Molecule SERS: R6G on Ag Colloids SMSER spectrum HRTEM of simplest active SMSERS nanoparticle cluster to date. LSPR spectrum EF = 10 15 (cross section is 10 -15 cm 2 while normal SERS 10 -30 cm 2 ) RR contributes 10 7 and EM contributes 10 8 . J. Dieringer, J. Camden, Y. Yang, L. Marks, G. C. Schatz and R. Van Duyne, JACS 130, 12616 (2008)
Gold Trimers K.L. Wustholz et al, JACS 132, 10903 (2010). Calculations on Au trimers (TEM structure below) show little correlation between SERS and LSPR (spectrum center B) as hot spot interferences lead to LSPR minimum at 730 nm, while field enhancement (E 4 ) has no interference. Calculated Calculated enhancements at 630 nm LSPR (solid) and SERS (red) Measured for trimer, showing hot spots.
Dark plasmon modes can still have large local field enhancements S. L. Kleinman, B. Sharma, M. Blaber, A-I. Henry, R. G. Freeman, M. J. Natan, GCS, RPVD, JACS 135, 301 (2012) bright dark
SERS excitation profiles S. L. Kleinman, B. Sharma, M. Blaber, A-I. Henry, R. G. Freeman, M. J. Natan, GCS, RPVD, JACS 135, 301 (2012)
Raman emitters can light up dark modes S. L. Kleinman, B. Sharma, M. Blaber, A-I. Henry, R. G. Freeman, M. J. Natan, GCS, RPVD, J. Am. Chem. Soc., 135, 301 (2013). SERS enhancement ~|E( ω )| 2 |E( ω ’)| 2 Incident Emitted
� � Describing Plasmons with Quantum Mechanics Extinction ~ Im( α ( ω )) 2 d ( ) Raman intensity ~ α ω dQ α = polarizability Q= normal coordinate of molecule ω = frequency (needs to be on-resonance for metal excitation) d ( ) α ω Determine from TDDFT using ADF ( ) and α ω dQ Jensen, Autschbach, Schatz, JCP 122, 224115 (2005) � Jensen, Zhao, Autschbach, Schatz JCP, 123 (2005) � Much earlier version of this: � P.K.K. Pandey and G.C. Schatz, J. Chem. Phys., 80 , 2959 ‑ 2972 (1984).
TD-DFT Linear Response Time-dependent Kohn-Sham equations First-order change in the density (linear response): ρ = ρ static + ρ ’(r, ω ) Polarizability ( H : dipole matrix in α -direction ) Width (~0.1 eV) due to coupling of QM system Real with environment (electron dephasing/relaxation) Formal theory: Masiello Imaginary and Schatz, PRA 2008.
Extinction spectrum of Ag 20 3.6 eV (344 nm) � Buttet, et al , Phys. Rev. B , 1993, L. Jensen, GCS, JACS 128, 2911 (2006) 47, 10706 � C. Aikens, GCS, JPC C112, 11272 (2008)
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