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  • OPTICAL PROPERTIES OF OPTICAL PROPERTIES OF METALLIC NANOPARTICLES, METALLIC NANOPARTICLES,

    MOLECULES AND POLYMERSMOLECULES AND POLYMERS

    Dr. Mica GrujicicDr. Mica Grujicic

    April, 2004April, 2004Department of Mechanical EngineeringDepartment of Mechanical Engineering

  • Mie Theory Mie Theory --Dilute Colloidal Dilute Colloidal Solution LimitSolution Limit

  • Spherical ParticlesSpherical Particles

    Ref: Ref: C. F.C. F.Bohren Bohren and D. R. Huffman, Absorption and D. R. Huffman, Absorption and Scattering of Light by Small Particles, and Scattering of Light by Small Particles,

    Wiley: New York, 1983Wiley: New York, 1983..

  • Extinction CrossExtinction Cross--section of section of Spherical ParticlesSpherical Particles

    ( ) 222/332

    224

    pmp

    pmpext

    RC

    ++

    =

    mm Dielectric Function of the MediumDielectric Function of the Medium

    RRpp -- Particle Radius Particle Radius -- Incident WavelengthIncident Wavelength

    pp Real Part of Dielectric Function of ParticlesReal Part of Dielectric Function of Particles

    pp Imaginary Part of Dielectric Function of ParticlesImaginary Part of Dielectric Function of Particles

    ppp i +=

    Dielectric Function of the NanoparticlesDielectric Function of the Nanoparticles

  • Complex Dielectric Function Complex Dielectric Function For Bulk MaterialFor Bulk Material

    ( ) ( ) ( ) ( )

    bulkbulke

    Pbulk iim

    +=+

    = 22

    1

    Excitation Angular FrequencyExcitation Angular Frequency

    mmee Mass of ElectronMass of Electron

  • 1

    ==e

    F

    lv

    vvFF FermiFermi VelocityVelocity

    02 eP mne=

    nn Density of Free ElectronsDensity of Free Electrons

    ee Electron ChargeElectron Charge

    00 Permittivity of Free SpacePermittivity of Free Space

    llee Mean Free PathMean Free Path

    Relaxation TimeRelaxation Time

    Damping Damping FrequencyFrequency

    Bulk Bulk PlasmonPlasmon FrequencyFrequency

  • ( ) 222

    1+

    =

    Pbulk

    Real Part of Dielectric Function of Bulk MaterialReal Part of Dielectric Function of Bulk Material

    ( ) ( )222

    +

    =

    Pbulk

    Imaginary Part of Dielectric Function of Bulk MaterialImaginary Part of Dielectric Function of Bulk Material

    ( ) 222

    +=

    Pbulk

    Corrected Real Part of Dielectric Function of Bulk MaterialCorrected Real Part of Dielectric Function of Bulk Material

    High Frequency Dielectric ConstantHigh Frequency Dielectric Constant

  • peeff Rll111

    +=

    Particle Size Effective MeanParticle Size Effective Mean--Free PathFree Path

    eff

    Feff l

    v=

    Effective Damping FrequencyEffective Damping Frequency

    Effect of the Small Particle SizeEffect of the Small Particle Size

  • ( ) 222

    eff

    Pp +

    =

    ( ) ( )222

    eff

    effPp +

    =

    FreeFree--electron Real Part of the electron Real Part of the Dielectric Function of Spherical ParticlesDielectric Function of Spherical Particles

    FreeFree--electron Imaginary Part of the electron Imaginary Part of the Dielectric Function of Spherical ParticlesDielectric Function of Spherical Particles

    Effect of Effect of Intrabound Intrabound TransitionsTransitions

  • ( ) ( ) ( ) ( )pbulkierbandifreeii ,int =+= Total Complex Dielectric FunctionTotal Complex Dielectric Function

    ( ) ( ) ( ) ( ) freebulkbulkfreepp +=Dielectric Constant in Metallic NanoparticlesDielectric Constant in Metallic Nanoparticles

    Nextddl C =

    DiluteDilute--dispersion Limit dispersion Limit Adsorption CoefficientAdsorption Coefficient

    NN Number Density of ParticlesNumber Density of Particles

  • NonNon--spherical Particlesspherical Particles

    Ref: R. Ref: R. GansGans, Ann. Phys., 47 (1915) 270, Ann. Phys., 47 (1915) 270

  • Extinction Cross Section of Extinction Cross Section of NonNon--Spherical ParticlesSpherical Particles

    ( )cbaj

    PP

    PRCj

    pmj

    jp

    pjmext ,,

    1

    13

    8

    2

    2

    22332

    =

    +

    +

    =

    21

    ;111ln

    211

    2

    2a

    cbaP

    PPrr

    rrrP

    ==

    +

    =

    ( )21 abr =

    Depolarization Vector for Nanorod (a>b=c)Depolarization Vector for Nanorod (a>b=c)

    wherewhere

  • Gold

    SilverGold

    Silver

    Input: Real and Imaginary Parts of the Dielectric Constants For Input: Real and Imaginary Parts of the Dielectric Constants For Gold and Silver as a Function of the Photon WavelengthGold and Silver as a Function of the Photon Wavelength 43704370

    Ref: P. B. Johnson and R. W. Christy, Phys. Rev. B, 6 (1972) 4370

  • Wavelength, nm

    Extin

    ctio

    nC

    oeffi

    cien

    t,M

    -1cm

    -1

    300 400 500 600 7000

    1000

    2000

    3000

    4000

    5000

    Calculated Absorption Spectra of Au Particles in Water

    n = 1.334

    ResultsResults

    Dielectric Constant of

    Water

    Spherical Spherical ParticlesParticles

  • Wavelength, nm

    Nor

    mal

    ized

    Abso

    rban

    ce

    500 525 550 575 6000

    0.5

    1

    1.5

    2

    Calculated Absorption Spectra of Au Particles Media with DifferentDielectric Constant

    n=1.602

    1.3341.376

    1.421

    1.471

    H2O (n=1.334)Cyclohexane (n=1.376)

    Dodecane (n=1.421)Decalin (n=1.471)

    CS2 (n=1.602)

    Medium Dielectric Constant

    Spherical Spherical ParticlesParticles

  • n=1.334n=1.334 n=1.407n=1.407 n=1.481n=1.481 n=1.525n=1.525 n=1.583n=1.583

    Ref: S. Underwood and P. Mulvaney,

    Langmuir, 10 (1994) 3427-3430

    15 nm Au Spherical Particles in Water and in

    Mixtures of Butyl Acetate and

    Carbon Disulfide

    Spherical Gold ParticlesEffect of Dielectric Constant of the Medium

    Mie Mie Theory Theory Transmission Transmission

    ColorsColors

    Spherical Spherical ParticlesParticles

    ExperimentExperiment

    TheoryTheory

  • Elongated Ellipsoidal ParticlesElongated Ellipsoidal Particles

    Wavelength, nm

    Abso

    rban

    ce,a

    .u

    400 500 600 700 800 9000

    50

    100

    150

    200

    250

    300

    350

    400

    450

    Particle Aspect Ratio

    3.63.33.1

    2.9

    2.6Longitudinal Longitudinal

    PlasmonsPlasmons, Red Shift, Red ShiftTransverse Transverse PlasmonsPlasmons, Blue Shift, Blue Shift

    Medium Dielectric Constant = 4.0

  • Wavelength, nm

    Abso

    rban

    ce,a

    .u

    400 500 600 700 800 9000

    50

    100

    150

    200

    250

    300

    350

    400

    450

    Elongated Ellipsoidal ParticlesElongated Ellipsoidal Particles

    Medium Dielectric Constant

    3.0

    2.5 Longitudinal Longitudinal PlasmonsPlasmons, Red Shift, Red ShiftTransverse Transverse

    PlasmonsPlasmons, Red Shift, Red Shift

    3.54.0 4.5

    Aspect Ratio = 3.3

  • Regression Analysis of the Regression Analysis of the Wavelength at the Wavelength at the

    LongitudinalLongitudinal PlasmonPlasmon PeakPeak

    ( ) 31.47231.4634.33max += mR

  • Maxwell Garnett TheoryMaxwell Garnett TheoryNonNon--Dilute Colloidal SolutionsDilute Colloidal Solutions

    Ref: J. C. Maxwell Garnett, Ref: J. C. Maxwell Garnett, PhilosPhilos. Trans. R. Soc. . Trans. R. Soc. London,203 (1904) 385. London,203 (1904) 385.

  • Au Core

    SiO2 Shell

    (a)(a) (b)(b)

    (a) Silica Coated Gold Particle; (b) Ideal Packing of Silica Coated Gold Particles in the Film to Form FCC Lattice with Volume Fraction 0.74.

  • Average Electric Field in Composite MaterialAverage Electric Field in Composite Material

    ( ) pmav EEE += 1

    Particle Volume FractionParticle Volume Fraction

    RRAuAu Radius of the Gold CoreRadius of the Gold Core

    ( )33

    2

    74.0

    SiOAu

    Au

    RRR

    +=

    RRSiO2 SiO2 Thickness of SiOThickness of SiO22 ShellShell

    EEmm Electrical Field in the Matrix MaterialElectrical Field in the Matrix Material

    EEpp Electrical Field in the ParticleElectrical Field in the Particle

  • ( )( ) ( ) ( ) avavppmmav EEEP 000 1111 =+=Average Polarization in Composite MaterialAverage Polarization in Composite Material

    mmp

    mp EE

    2

    3+

    =

    Electric Field Inside the ParticlesElectric Field Inside the Particles(Lorentz Cavity Field)(Lorentz Cavity Field)

    mm Dielectric Function of the Matrix MaterialDielectric Function of the Matrix Material

  • Final Form of the EquationsFinal Form of the Equations

    ( ) mmp

    mmav EEE

    23

    1+

    +=

    Average Electric Field in Composite MaterialAverage Electric Field in Composite Material

    Average Dielectric Function in Composite MaterialAverage Dielectric Function in Composite Material

    ( ) ( )( ) ( )

    ++

    ++=

    211221

    mp

    mpmav

    ( ) av

    av

    avav

    knc

    4Im==

    Average Absorption Coefficient in Composite MaterialAverage Absorption Coefficient in Composite Material

  • Complex Dielectric FunctionComplex Dielectric Function

    ( ) ( )avddliikni iiiii ,2 =+=+=

    ( )avddlin iiii ,2

    21

    22

    =

    ++=

    ( )avddlik iiii .2

    21

    22

    =

    +=

    Complex Refractory IndexComplex Refractory Index

  • Optical ReflectanceOptical Reflectance

    ( )( )

    ( )avddliknkn

    Rii

    ii ,11

    22

    22

    =++

    +=

    ( )( ) ( ) ( )

    ( )avddliRhhR

    RRTii

    ,2cos2expexp