Theoretical Framework of SERS George C. Schatz Northwestern - - PowerPoint PPT Presentation

Theoretical Framework of SERS

2014 Castl Summer School July 9-11, 2014

George C. Schatz Northwestern University

Metal nanoparticle optical properties

Electronic Structure Studies: Lasse Jensen (Penn St) Christine Aikens (Kansas St) David Masiello (U. Wash.) Jonathan Mullin (Wright-Patt) Hanning Chen (GWU) Nick Valley (Oregon-PD) Lindsey Madison Fredy Aquino (PD-ARL) Dan Hannah Adam Ashwell Emily Weiss, Teri Odom, Rick Van Duyne Chad Mirkin, Joe Hupp Monica Olvera, M. Ratner Stephen Gray (Argonne) Electrodynamics: Kevin Shuford (Drexel) LinLin Zhao (Penn St) Shengli Zou (UCF) Leif Sherry (PD-Tex) Anatoly Pinchuk(Col. Spr) Jon Camden(Tenn) Jing Zhao (PD-MIT) Jeff McMahon(PD-UIUC) Logan Ausman (IDA) 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

1.7 nm

350 400 450 500 550 600 650 700

Wavelength (nm)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Extinction (Optical Density) 3.5 nm 5.2 nm 20 nm 60 nm 100 nm 160 nm Spectra of dispersed colloidal gold for selected diameters (data from Turkevich (1954), Doremus (1964))

Colloidal Gold

Extinction = absorption + scattering (color of solution=color of light not absorbed or scattered) Michael Faraday, 1856

E-field e

• cloud

Metal sphere

Plasmon excitation: collective excitation

• f the conduction electrons
• sp

2 e

1 shape/surroundings 2 c chemical properties 4 ne m + χε λ = = π π

Plasmon wavelength: n=electron density χ = shape factor (2 for sphere, >2 for spheroid) εo = dielectric constant of surroundings

Charge cloud of conduction electrons Nuclear framework

• f particle

Colloidal Silver

5000 nm 5000 nm

200 nm

A

200 nm

C

200 nm

B

1 m µ

D

Ag/Au Nanoparticle Optical Properties

Size-Tunable Surface Plasmon Resonances

width

95 120 145 145 145 150 150

Wavelength (nm) 400 500 600 700 800 900 Normalized Extinction lmax

565 638 720 747 782 497 446

height

48 46 59 55 50 62 70 120 42 426

shape

Ag/mica Extinction spectra of size/shape-selected Ag particles

Mie Extinction for 13 nm Au spheres 0.0 0.2 0.4 0.6 0.8 1.0 Extinction Efficiency 200 300 400 500 600 700 800 wavelength(nm) 20 nm

Extinction for 20 nm spheres

Extinction Cross Section = (long wavelength limit) ε = dielectric function of metal = ε1 + iε2

2 3 2 2 2 1 2

3 8 2 ( radius ) ( ) ε π λ ε λ ε ε + + + +

Mie Theory (1908)

real imaginary Dielectric constants of Au 200 300 400 500 600 700 800 wavelength (nm)

• 15.0
• 10.0
• 5.0

0.0 5.0 Real or Imaginary part of dielectric constant

ε1 ε2 (Lorenz-Mie-Debye) Theory

Computational Electrodynamics Methods for Nanoparticles

Grid or Finite element methods:

• Discrete Dipole Approximation
• Finite Difference Time Domain Method
• Whitney-form Finite Element Method

Beyond Conventional Maxwell:

• Coupled QM + EM

1 H E t µ ∂ = − ∇× ∂ v v

1 E H J t ε ∂ = ∇× − ∂ v v v

( ) ( ) ( )

2 p p p p

d J t J t E t dt γ ω ε + = r r r

Modeling the Spectra of Silver Bipyramids using EM

400 600 800

Wavelength (nm)

Zhang, Li, Wu, Schatz, and Mirkin Angew. Chem. Int. Ed., 48, 7787, (2009)

Simulations Extinction

400 600 800

Experiments and simulations are in good agreement with each other. Wavelength (nm) Extinction Experiments

Ag right bipyramid Au rod-sheath

a = 106, 131, 165, 191 nm

b a

a = 2b

Right-handed Left-handed Right-handed Right-handed

E E

Right-handed

Positive Cotton effect

Chengyi Song, Martin G. Blaber, Gongpu Zhao, Peijun Zhang, H. Christopher Fray, George C. Schatz, Nathaniel L. Rosi, Nano Lett. 13, 3256-61 (2013).

• D. L. Jeanmaire and R. P. Van Duyne, J. Electroanal. Chem. 84, 1-20 (1977)

Nanoparticles Nanoparticles ωex ωex - ωvib

Normal Raman Spectrum (NRS) 2.5 M Pyridine Surface - Enhanced Raman Spectrum (SERS): enhancement factor = 106 Surface Pyridine

Surface Enhanced Raman Spectroscopy (SERS)

SERS enhancement =~|E(ω)|2|E(ω’)|2~ (|E|4)

Plasmon enhancement factors:

Absorption Enhancement=~|E(ω)|2 SERS enhancement =~|E(ω)|2|E(ω’)|2~ (|E|4)ave~106-12 Fluorescence enhancement =~|E(ω)|2|G(ωstokes)|2Q G = scattering from particle by emitted dipole Q = nonradiative quenching

SERS enhancement ~|E(ω)|2|E(ω’)|2~ (|E|4)ave~106 This implies: (|E|2)ave~ 103

Electromagnetic Enhancement factors In Surface Enhanced Raman Spectroscopy

(|E|2)ave for prolate silver spheroids 1:1 2:1 3:1 4:1 5:1

15

Excitation Spectrum of Benzenethiol

benzenethiol on Ag triangles WS-SERS profile peak is blue-shifted from LSPR by ½ of the vibrational frequency.

McFarland, Young, Dieringer and Van Duyne. J.

• Phys. Chem. B 2005, 109, 11279-11285

Theory:

Extinction ~ |E(ω)|2 SERS~|E(ω)|2|E(ω’)|2

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)

edge length = 106 nm

Average |E|4: 6.3x103 Maximum |E|4: 8.2x106

diameter = 19 nm, height = 52 nm

Average |E|4: 1.8x106 Maximum |E|4: 4.5x107

length = 60 nm, height = 12 nm

Average |E|4: 1.0x106 Maximum |E|4: 1.8x108

inner diameter = 100 nm, thickness = 10 nm

Average |E|4: 1.0x103 Maximum |E|4: 3.8x104 Average |E|4: 4.2x101 Maximum |E|4: 1.0x103 λinc = 686 nm

prism diameter = 180 nm

λinc = 716 nm

sphere

k E λinc = 650 nm

cube

k E λinc = 720 nm

shell

k E λinc = 688 nm

rod

E k

Results show that rods and triangles give the best average enhancements for isolated particles.

Avg |E|4 is 7.0x107 Max |E|4 is 1.6x109

λinc = 876 nm

2 nm gap

Larger Enhancements for Dimers of Nanoparticles

a (nm)

parallel rods

|E|4

ln(|E|4) ln(a)

slope ¡= ¡−1.8 ¡ for ¡a ¡≤ ¡10nm ¡ ¡ |E|4~1/a2 ¡

diameter = 19 nm, height = 52 nm

Average |E|4: 1.8x106 Maximum |E|4: 4.5x107

λinc = 688 nm

Optimized enhancement factors for sphere dimers, 1 nm gap

Metal |E|4 (max) wavelength diameter background index Ag 1.3x1012 794 nm 20 nm 2.25 Au 2.8x1011 723 50 1.5 Al 2.0x109 204 22 1.0 In 1.2x109 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 LSPR spectrum

• J. Dieringer, J. Camden, Y. Yang, L. Marks, G. C. Schatz and R. Van Duyne, JACS 130, 12616 (2008)

HRTEM of simplest active SMSERS nanoparticle cluster to date.

EF = 1015 (cross section is 10-15 cm2 while normal SERS 10-30 cm2) RR contributes 107 and EM contributes 108.

Gold Trimers

LSPR (solid) and SERS (red)

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 (E4) has no interference.

Calculated enhancements at 630 nm for trimer, showing hot spots.

Calculated Measured

K.L. Wustholz et al, JACS 132, 10903 (2010).

Dark plasmon modes can still have large local field enhancements

bright dark

• S. L. Kleinman, B. Sharma, M. Blaber, A-I. Henry, R. G. Freeman, M. J. Natan, GCS, RPVD, JACS 135, 301 (2012)

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

Raman intensity ~

α = polarizability Q= normal coordinate of molecule ω= frequency (needs to be on-resonance for metal excitation)

2

d ( ) dQ α ω

Determine from TDDFT using ADF

α ω α ω d ( ) ( ) and 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).

• Extinction ~ Im(α(ω))

TD-DFT Linear Response

Time-dependent Kohn-Sham equations First-order change in the density (linear response): ρ=ρstatic+ρ’(r,ω) Polarizability (H : dipole matrix in α-direction) Real Imaginary

Width (~0.1 eV) due to coupling of QM system with environment (electron dephasing/relaxation) Formal theory: Masiello and Schatz, PRA 2008.

3.6 eV (344 nm)

Extinction spectrum of Ag20

• Buttet, et al, Phys. Rev. B, 1993,

47, 10706

• L. Jensen, GCS, JACS 128, 2911 (2006)
• C. Aikens, GCS, JPC C112, 11272 (2008)

20 nm Ag tetrahedron 105 atoms

2.5 eV 2.5 eV 0.84 nm

Connection of Electronic Structure Results with Continuum Electrodynamics

Ag120 2.0 nm

1/edge length (atoms) 0.0 0.1 0.2 0.3 0.4 0.5 photon energy (eV) 2.50 3.00 3.50 4.00 4.50 5.00 20 120

Ag20 3.6 eV 3.0 eV

• C. Aikens, S. Li, GCS, JPC C 112, 11272 (2008)

Results for Ag84: plasmon band represented by a clump of lines, with the clump corresponding to a broad range of intraband excitations.

EF

Plasmon-like Interband

Ag20 versus Au20

2.9 eV 3.6 eV

• C. Aikens and G. C. Schatz, JPC

B110, 13317-24 (2006).

Need >200 atoms to see plasmonic behavior for spherical gold clusters. Au266 Au314(SH)96

Hakkinen, ACS Nano,asap (2013) silver gold

QM/ED:Combining RT-TDDFT with FDTD

Hanning Chen, Jeff McMahon, M. Ratner and GCS J. Phys. Chem. C, 114, 14384-392 (2010).

2

[ ( , )] 1 ( ', ) ( , ) ' ( , ) ( , ) 2 ' ( , )

α α α

δ ρ ρ ϕ µ ϕ δρ ⎡ ⎤ ∂ = − ∇ − + + + ⎢ ⎥ ∂ − ⎣ ⎦

∑ ∫

u r u r h g

xc

Z E r t r t i r t dr E r t r t t r r r r t ( ) ( , ) ( , ) ( , ) r E r t H r t J r t t ε ∂ = ∇× − ∂ u r u u r r ( ) ( , ) ( , ) r H r t E r t t µ ∂ = −∇× ∂ u u r u r

First solve FDTD for light interacting with the particle. Here the incident field is a pseudo plane wave: Convert E(r,t) to E(r,ω), then convert back, but this time subject to a fs pulse. Insert this into the KS equations to determined perturbed wavefunctions and dipole moment. Derive α(ω) and dα(ω)/dQ from this. Back-coupling to the metal particle is done in the plane wave approximation, in which the dipole interactions are evaluated with the enhanced field E(r,ω) from the FDTD calculation.

QM/ED:Application to SERS

Hanning Chen, Jeff McMahon, M. Ratner and GCS J. Phys. Chem. C, 114, 14384-392 (2010). Pyridine interacting with 20 nm silver sphere leads to enhancement factor of ~104

2 2

( ) ~ ( ) ( ')

k unenhanced

Intensity E E q α ω ω ∂ ∂

Static and Resonance Raman Spectra of Pyridine-Ag20 Cluster

Raman enhancement = 105 Isolated pyridine spectrum SERS spectrum

• L. Jensen, GCS, JACS 128, 2911 (2006)

Zhou, Jensen, Schatz, Nano Letters, 6, 1229-1234 (2006).

Incorporating Chemical Enhancement Effects in SERS using QM/ED

Nonresonant component of chemical enhancement factor can be obtained from the static Raman intensity of a molecule-metal cluster model. Calculated EF (static limit DFT) Four state model

Results for Substituted Benzene Thiols

(N. Valley, N. Greeneltch, RPVD and GCS, J. Phys. Chem. Lett. 4, 2599-2604 (2013)) Ag:benzenethiol, 4-mercaptophenol,4-mercaptobenzoic acid Au: benzenethiol, 4-methoxybenzenethiol, 4-ethoxybezenethiol, 4-nitrobenzenethiol, and 4-mercaptobenzoic acid

Calculated EF (static limit DFT)

Combining Electromagnetic and Chemical Enhancements Using Frequency Domain Calcs for Overlay of Cluster with Nanoparticle

Jonathan Mullin, Nick Valley, Marty Blaber and GCS, JPC A, 116, 9574-81 (2012). Left: fix pyridine as if on surface, but no surface present Right: Static QM calculation of cluster SERS spectrum (which include chemical enhancement) combined with electromagnetic field enhancement.

α ω ω ∂ ∂

2 2

( ) ~ ( ) ( ')

k static

Intensity E E q

What happens during the lifetime of a plasmon?

(joint with Emily Weiss)

Standard model of plasmon photophysics (many groups, but a good paper is Scherer et al, JPC C 111, 116 (2007)):

• 1. Electron dephasing: 10fs timescale
• 2. Electronic relation to a thermal (high

temperature) distribution: 100 fs

• 3. Coupling to phonons in particle: 1 ps
• 4. Phonon relaxation to surroundings: ps to ns

What about the ligands?

Time-resolved absorption studies of ligated Au NPs

Kenneth O. Aruda, Mario Tagliazucchi, Christina M. Sweeney, Daniel C. Hannah, George C. Schatz, Emily A. Weiss, PNAS, 110, 4212-17, (2013)

4.5 ps 3.9 3.3 2.7 2.1 1.5

Two temperature model provides accurate fit to data

Heat Capacity and Electron-Phonon Coupling are related to the density of states

Conclusions and Future Work

• 1. Classical electromagnetic theory works well in the

description of plasmon optical properties, except for small particles or small gaps

• 2. Optimum SERS enhancements are associated with 1 nm

gaps between 50-100 nm particles, with dark modes, SERS emission also important

• 3. Chemical enhancement contributes factor of ~10 to

enhancements, and can be tuned by varying the electron donating ability of the adsorbates.

• 4. Time-resolved photophysics of plasmonic structures is

qualitatively understood but the connection with SERS is missing.