Optical Properties of Nanoscale Optical Properties of Nanoscale MaterialsMaterials

David G. StroudDavid G. Stroud, ,

Department of PhysicsDepartment of Physics,,

Ohio State University Columbus OH 43210Ohio State University Columbus OH 43210

Work supported by NSF Grant DMR01-04987 and NSF DMR04-12295 Work supported by NSF Grant DMR01-04987 and NSF DMR04-12295 and by the Ohio Supercomputer Centerand by the Ohio Supercomputer Center OUTLINEOUTLINE

Introduction: Linear Optical Properties and Surface PlasmonsIntroduction: Linear Optical Properties and Surface Plasmons

Liquid-Crystal Coated NanoparticlesLiquid-Crystal Coated Nanoparticles Surface Plasmons in Nanoparticle ChainsSurface Plasmons in Nanoparticle Chains

Composites of Gold Nanoparticles and DNAComposites of Gold Nanoparticles and DNA ConclusionsConclusions

““Labors of the Months” (Norwich, England, ca. Labors of the Months” (Norwich, England, ca. 1480).1480).

(The ruby color is probably due to embedded(The ruby color is probably due to embeddedgold nanoparticles.)gold nanoparticles.)

The Lycurgus Cup (glass; The Lycurgus Cup (glass; British Museum; 4British Museum; 4thth century A. century A.

D.) D.)

When illuminated from outside, it appears green. However, whenIlluminated from within the cup, it glows red. Red color is due to very small amounts of gold powder (about 40 parts per million)

Lycurgus Cup illuminated from Lycurgus Cup illuminated from withinwithin

When illuminated from within, the Lycurgus cup glows red. The red color is due to tiny gold particles embedded in the glass, which have an absorption peak at around 520 nm

What is the origin of the color? What is the origin of the color? Answer: ``surface plasmons’’ Answer: ``surface plasmons’’

An SP is a natural oscillation of the electron gas An SP is a natural oscillation of the electron gas inside a inside a goldgold nanospherenanosphere..

SP frequency depends on the SP frequency depends on the dielectricdielectric functionfunction of the gold, and the of the gold, and the shapeshape of the nanoparticle. of the nanoparticle.

electron sphere

Ionic background

Electron cloud oscillates with frequency of SP; ions provide restoring force.

(not to scale)

Sphere in an applied electric Sphere in an applied electric field field

Surface plasmon is excited when a long-Surface plasmon is excited when a long-wavelength electromagnetic wave is wavelength electromagnetic wave is

incident on a metallic sphere.incident on a metallic sphere.

Metallic sphere

EM wave

Incident electric field is E_0exp(-i w t)

Calculation of SP FrequencyCalculation of SP Frequency

00

0

2

3EE

inin

0E

2

2

1

pin

0

0

21

applied electric field;

= Drude dielectric function

Surface plasmon frequency is therefore:

0host dielectric function

(This assumes particle is small compared to wavelength.)

Extinction coefficient, dilute suspension of Extinction coefficient, dilute suspension of Au particles in acqueous solutionAu particles in acqueous solution

Crosses: experiment [Elghanian et al, Science 277, 1078 (1997); Storhoff et al, JACS 120, 1959 (1998). Dashed and full curves: calculated with and without quantum size corrections [Park and Stroud, PRB 68, 224201 (2003)].

Control of Surface Plasmons Control of Surface Plasmons Using Nematic Liquid CrystalsUsing Nematic Liquid Crystals

A nematic liquid crystal (NLC) is a liquid A nematic liquid crystal (NLC) is a liquid made up of rod-like molecules, which can made up of rod-like molecules, which can be oriented by an applied dc electric be oriented by an applied dc electric field.field.

The axis of the NLC is known as the The axis of the NLC is known as the director.director.

The dielectric tensor of the NLC is The dielectric tensor of the NLC is anisotropic, with different components anisotropic, with different components parallel and perpendicular to the parallel and perpendicular to the director.director.

Schematic of experimental configuration

Experiment to show electric field control of surface plasmon frequency of gold nanoparticles, using nematic liquid crystals [J. Muller et al, Appl. Phys. Lett. 81, 171 (2002).]

Measured deviation of surface plasmon resonance Measured deviation of surface plasmon resonance energy from mean value, vs. angular position of energy from mean value, vs. angular position of

polarization analyzer. From Muller et al, Appl. Phys. polarization analyzer. From Muller et al, Appl. Phys. Lett. 81, 171 (2002).Lett. 81, 171 (2002).

Maximum splitting: 30 mev (expt).

Plausible configurations of liquid crystal coating: (a) “uniform” (director always in same direction); (b) “melon” (two singularities); (c) “baseball” (four singularities; tetrahedral)

Pictures (b) and © from D.R.Nelson,Nano Lett.(2002).

Discrete Dipole Discrete Dipole ApproximationApproximation

Purcell & Pennypacker, Ap. J. 186, 175 (1973); Purcell & Pennypacker, Ap. J. 186, 175 (1973); Goodman, Draine & Flatau, Opt. Lett. 16, 1198 (1991).Goodman, Draine & Flatau, Opt. Lett. 16, 1198 (1991).

Idea: break up small particle into small volumes, each Idea: break up small particle into small volumes, each of which carry dipole moment.of which carry dipole moment.

Dipole moment due to local electric field from all the Dipole moment due to local electric field from all the other dipoles.other dipoles.

Calculate total cross-section, using multipole-Calculate total cross-section, using multipole-scattering approach.scattering approach.

Can be used for anisotropic, and absorbing, scatterers.Can be used for anisotropic, and absorbing, scatterers. Connect polarizability of small volume to dielectric Connect polarizability of small volume to dielectric

function, using Clausius-Mossotti approximation function, using Clausius-Mossotti approximation

Calculated surface plasmon frequency as a Calculated surface plasmon frequency as a function of metal particle fraction p’ in the coated function of metal particle fraction p’ in the coated

nanoparticle, for light oriented parallel and nanoparticle, for light oriented parallel and perpendicular to nematic director (uniform perpendicular to nematic director (uniform

configuration) [S. Y. Park and D. Stroud, Appl. configuration) [S. Y. Park and D. Stroud, Appl. Phys. Lett 85, 2920 (2004)]Phys. Lett 85, 2920 (2004)]

Computed peak in extinction coefficient Computed peak in extinction coefficient versus angle of polarization of incident light versus angle of polarization of incident light rel. to coating symmetry axis: three coating rel. to coating symmetry axis: three coating

morphologies [S. Y. Park and D. Stroud, morphologies [S. Y. Park and D. Stroud, unpublished(2004)]unpublished(2004)]

(Experimental splitting at zero applied field closest to “melon” morphology. Maximum splitting in expt: 30 meV; in melon config, 22 mev)

Propagating Waves of Surface Propagating Waves of Surface Plasmons in Chains of Plasmons in Chains of

NanoparticlesNanoparticles A chain of closely spaced metallic A chain of closely spaced metallic

nanoparticles allows WAVES of surface nanoparticles allows WAVES of surface plasmons to propagate down the chain.plasmons to propagate down the chain.

The waves can be either transverse (T) or The waves can be either transverse (T) or longitudinal (L) modes, and can have group longitudinal (L) modes, and can have group velocities up to 0.1c or higher.velocities up to 0.1c or higher.

Studied extensively by Atwater group at Studied extensively by Atwater group at Caltech, and by other groups at Stanford and Caltech, and by other groups at Stanford and elsewhere.elsewhere.

Potentially useful for propagating energy Potentially useful for propagating energy along effectively very narrow waveguides, along effectively very narrow waveguides, controlling energy flow around corners, etc.controlling energy flow around corners, etc.

Nanoparticle chainNanoparticle chain

Surface plasmons can propagate along a periodic Surface plasmons can propagate along a periodic chain of metallic nanoparticles (above)chain of metallic nanoparticles (above)

a

d

Photon STM Image of a Chain Photon STM Image of a Chain of Au nanoparticles [from of Au nanoparticles [from Krenn et al, PRL 82, 2590 Krenn et al, PRL 82, 2590

(1999)](1999)]

Individual particles: 100x100x40 nm, separated Individual particles: 100x100x40 nm, separated by 100 nm and deposited on an ITO substrate. by 100 nm and deposited on an ITO substrate. Sphere at end of waveguide is excited using the Sphere at end of waveguide is excited using the

tip of near-field scanning optical microscope tip of near-field scanning optical microscope (NSOM), and wave is detected using fluorescent (NSOM), and wave is detected using fluorescent

nanospheres.nanospheres.

Calculation of SP modes in Calculation of SP modes in nanoparticle chainnanoparticle chain

In the dipole approximation, there are In the dipole approximation, there are threethree SP SP modes on each sphere, two polarized modes on each sphere, two polarized perpendicularperpendicular to chain, and one polarized to chain, and one polarized parallelparallel. . The propagating waves are linear combinations The propagating waves are linear combinations of these modes on different spheres. of these modes on different spheres.

In our calculation, In our calculation, wewe includeinclude allall multipolesmultipoles, not , not just dipoles. Then there are a infinite number of just dipoles. Then there are a infinite number of branches, but only lowest three travel with branches, but only lowest three travel with substantial group velocity.substantial group velocity.

Can be compared to Can be compared to nanoplasmonicnanoplasmonic experimentsexperiments, , as discussed by Brongersma et al [Phys. Rev. as discussed by Brongersma et al [Phys. Rev. B62, 16356 (2000) and S. A. Maier et al [Nature B62, 16356 (2000) and S. A. Maier et al [Nature Materials 2, 229 (2003)]Materials 2, 229 (2003)]

Calculated dispersions relations for gold Calculated dispersions relations for gold nanoparticle chain, including only dipole-dipole nanoparticle chain, including only dipole-dipole

coupling in quasistatic approximation [S. A. Maier et coupling in quasistatic approximation [S. A. Maier et al, Adv. Mat. 13, 1501 (2001)]al, Adv. Mat. 13, 1501 (2001)]

(L and T denote longitudinal and transverse modes)

Surface plasmon dispersion relations, Surface plasmon dispersion relations, nanoparticle chain, including ALL multipole nanoparticle chain, including ALL multipole moments [Park and Stroud, Phys. Rev. B69, moments [Park and Stroud, Phys. Rev. B69,

125418 (2004)]125418 (2004)]

Calculated surface plasmon dispersion relations (left) Calculated surface plasmon dispersion relations (left) and group velocity for energy propagation in the and group velocity for energy propagation in the lowest two bands. lowest two bands. SolidSolid curves: Lcurves: L modesmodes; ; dotteddotted

curves: Tcurves: T modesmodes. Light curves; . Light curves; dipoledipole approximation; dark curves, including approximation; dark curves, including allall multipolesmultipoles. . a/d=0.45, a= a/d=0.45, a= particleparticle radiusradius; d= ; d= particleparticle separationseparation

TL

L

TL

L

T T

Effects of Higher MultipolesEffects of Higher Multipoles

Strong distortion of dispersion relation, Strong distortion of dispersion relation, compared to dipole-dipole interactioncompared to dipole-dipole interaction

Percolation effect when gold particles Percolation effect when gold particles approach contact: frequency of L branch approach contact: frequency of L branch approaches 0 at k=0approaches 0 at k=0

Single-particle damping can be included. Single-particle damping can be included. Still to include: radiation corrections. Also Still to include: radiation corrections. Also omitted: disorder (in shape, size, omitted: disorder (in shape, size, interparticle distance).interparticle distance).

Calculated dispersion relations s(k) for L and T modes in a chain of nanoparticles, plotted vs. k for (a-f) a/d=0.25,0.33,0.4,0.45,0.49,0.5 (spheres touching). a=sphere radius, d=distance between sphere centers. Open symbols: point dipole approx. The symbol 1)/1( sms

[Park and Stroud, PRB69, 125418 (2004)]

Linker DNA

Melting and Optical Properties Melting and Optical Properties of Gold/DNA Nanocompositesof Gold/DNA Nanocomposites

[Schematic from R. Elghanian et al, Science 277, 1078 (1997)]

At high T, single Au particles float in aqueous solution, with DNA strands attached (via thiol groups). At lower T, particles freeze into a clump. Freezing is detectable optically.

Observed absorptance: Observed absorptance: comparison of unlinked and comparison of unlinked and aggregated Au nanoparticlesaggregated Au nanoparticles

Absorptance of unlinked and aggregated Au nanoparticles, Absorptance of unlinked and aggregated Au nanoparticles, as measured by Storhoff et alas measured by Storhoff et al

[J. Am. Chem. Soc. 120, 1959 (1998)][J. Am. Chem. Soc. 120, 1959 (1998)]

Description of Previous SlideDescription of Previous Slide

Source: R. Jin et al, J. Am. Chem. Soc. 125, Source: R. Jin et al, J. Am. Chem. Soc. 125, 1643 (2003).1643 (2003).

Top two pictures show (a) samples under Top two pictures show (a) samples under transmitted light before and after being transmitted light before and after being exposed to the target (b) UV and visible exposed to the target (b) UV and visible extinction coefficients of the two samples.extinction coefficients of the two samples.

Bottom is a schematic of structure of Bottom is a schematic of structure of samples before and after agglomeration samples before and after agglomeration (which occurs as temperature is lowered)(which occurs as temperature is lowered)

Extinction coefficient of Extinction coefficient of Au/DNA composite at 520 nmAu/DNA composite at 520 nm

[R. Jin et al, J. Am. Chem. Soc. 125, 1643 (2003)]

[S. Y. Park and D. Stroud, Phys. Rev. B68, 224201 (2003)]

theory experiment

=melting pt.

=sol-gel transition

Thus, SP frequency is red-shifted with increasing p. Therefore, we can red-shift the peak just by having all the particles agglomerate into a large cluster (if metal particles separated)

[D. Stroud, Phys. Rev. B19, 1783 (1979)]

MethodologyMethodology

To determine structure, we calculate the probability To determine structure, we calculate the probability that any two bonds on different Au particles form a that any two bonds on different Au particles form a link, using an equilibrium condition from simple link, using an equilibrium condition from simple chemical reaction theory. chemical reaction theory.

Structure determined by Structure determined by twotwo differentdifferent modelsmodels: (i) : (i) percolationpercolation modelmodel; (ii) More elaborate model ; (ii) More elaborate model involving involving reaction-limitedreaction-limited cluster-clustercluster-cluster aggregationaggregation (RLCA) (RLCA)

To treat optical properties (for any given structure) To treat optical properties (for any given structure) use the ``Discrete Dipole Approximation’’ (multiple use the ``Discrete Dipole Approximation’’ (multiple scattering approach).scattering approach).

References: S. Y. Park and D. Stroud, Phys. Rev. References: S. Y. Park and D. Stroud, Phys. Rev. B67, 212202 (2003); B68, 224201 (2003); Physica B67, 212202 (2003); B68, 224201 (2003); Physica B338, 353 (2003).B338, 353 (2003).

Simple Percolation Model [Park Simple Percolation Model [Park and Stroud, 2003a]and Stroud, 2003a]

Place Au nanoparticles on a simple cubic (SC) latticePlace Au nanoparticles on a simple cubic (SC) lattice Each Au particle has N single DNA strands, of which N/z point Each Au particle has N single DNA strands, of which N/z point

towards each of z nearest neighbors (z = 6 for SC)towards each of z nearest neighbors (z = 6 for SC) Two-state model for reaction converting two single strands Two-state model for reaction converting two single strands

into a double strand: S+S = D. Probability of double-strand into a double strand: S+S = D. Probability of double-strand forming is p(T), determined by chemical equilibrium constant forming is p(T), determined by chemical equilibrium constant of reaction.of reaction.

Probability that no strand forms between two nearest Probability that no strand forms between two nearest neighbor particles is 1 - p’ = 1 – [1 –p(T)]^(N/z)neighbor particles is 1 - p’ = 1 – [1 –p(T)]^(N/z)

p’ is a much sharper function of T than is p.p’ is a much sharper function of T than is p. Melting occurs when p’ = p_c, the percolation threshold for Melting occurs when p’ = p_c, the percolation threshold for

the lattice.the lattice. Optical properties calculated using Discrete Dipole Optical properties calculated using Discrete Dipole

Approximation Approximation Assume N is proportional to surface area: melting temp higher Assume N is proportional to surface area: melting temp higher

for larger particlesfor larger particles

Reaction-Limited Cluster-Reaction-Limited Cluster-Cluster Aggregation Model Cluster Aggregation Model [Park and Stroud, 2003b)][Park and Stroud, 2003b)]

Start with N gold spheres placed randomly on a Start with N gold spheres placed randomly on a latticelattice

Allow them to aggregate by RLCA (appropriate when Allow them to aggregate by RLCA (appropriate when repulsive energy barrier between approaching repulsive energy barrier between approaching particles)particles)

Then let cluster “melt” by dehybridization of DNA Then let cluster “melt” by dehybridization of DNA duplexes, using T-dependent bond-breaking duplexes, using T-dependent bond-breaking probability used for percolation modelprobability used for percolation model

Repeat this aggregation/dehybridization process Repeat this aggregation/dehybridization process many times. Result is a fractal cluster with a T-many times. Result is a fractal cluster with a T-dependent fractal dimension. Appropriate when dependent fractal dimension. Appropriate when aggregation process is non-equilibriumaggregation process is non-equilibrium

Once aggregation process is complete, calculate Once aggregation process is complete, calculate optical properties versus T, using DDA.optical properties versus T, using DDA.

Discrete Dipole Discrete Dipole ApproximationApproximation

Melting of Au/DNA cluster, Melting of Au/DNA cluster, two different modelstwo different models

(a), (b) and (c) are a percolation model: all particles on a (a), (b) and (c) are a percolation model: all particles on a cubic lattice. (a): all bonds present; (b) 50% of bonds cubic lattice. (a): all bonds present; (b) 50% of bonds

present; (c) 20% of bonds present. (d) Low temperature present; (c) 20% of bonds present. (d) Low temperature cluster formed by reaction-limited cluster-cluster cluster formed by reaction-limited cluster-cluster

aggregation (RLCA)aggregation (RLCA)

Extinction coefficient, dilute Extinction coefficient, dilute suspensionsuspension

Extinction coefficient per unit vol of Au,dilute suspension. Crosses: experiment Extinction coefficient per unit vol of Au,dilute suspension. Crosses: experiment [Elghanian et al, Science (1997); Storhoff et al, JACS (1998). Dashed and full [Elghanian et al, Science (1997); Storhoff et al, JACS (1998). Dashed and full

curves: calculated without and with quantum size corrections to gold dielectric curves: calculated without and with quantum size corrections to gold dielectric function [Park and Stroud, Phys. Rev. B68, 224201 (2003)]function [Park and Stroud, Phys. Rev. B68, 224201 (2003)]

Calculated extinction Calculated extinction coefficient, RLCA clusterscoefficient, RLCA clusters

Calculated extinction coefficient versus wavelength for RLCA Calculated extinction coefficient versus wavelength for RLCA clusters with number of monomers varying from 1 to 343 clusters with number of monomers varying from 1 to 343

[Park and Stroud, PRB68, 224201 (2003)], using DDA [Park and Stroud, PRB68, 224201 (2003)], using DDA

Extinction coefficient for Extinction coefficient for compact Au/DNA clusterscompact Au/DNA clusters

Extinction coefficient per unit volume, plotted versus wavelength (in nm) Extinction coefficient per unit volume, plotted versus wavelength (in nm) for LxLxL compact clusters, as calculated using the Discrete Dipole for LxLxL compact clusters, as calculated using the Discrete Dipole Approximation (DDA) [from Park and Stroud, Phys. Rev. B67, 212202 Approximation (DDA) [from Park and Stroud, Phys. Rev. B67, 212202 (2003)](2003)]

Absorptance of gold/DNA clusters. Top: Experiment [Storhoff et al, JACS 120, 1959 (1998)]. Lower left: calculation; RLCA clusters. Lower right: calculation, compact clusters [both from Park and Stroud PRB68, 224201 (2003)].

Calculated extinction Calculated extinction coefficients versus coefficients versus

temperature at 520 nmtemperature at 520 nm

Normalized extinction coefficient at wavelength 520 nm, calculated for two different Normalized extinction coefficient at wavelength 520 nm, calculated for two different models, plotted vs. temperature in C. Full curves: percolation model (3 different models, plotted vs. temperature in C. Full curves: percolation model (3 different

monomer numbers). Open circles: RLCA model, fully relaxed configuration) (From monomer numbers). Open circles: RLCA model, fully relaxed configuration) (From Park+Stroud, 2003) Park+Stroud, 2003) Note rebound in RLCA (x), when dynamics are NOT fully relaxed.Note rebound in RLCA (x), when dynamics are NOT fully relaxed.

Extinction coefficient vs. T at Extinction coefficient vs. T at 520 nm for different particle 520 nm for different particle

sizessizes

Calculated extinction coefficient versus T at wavelength 520 nm for particle Calculated extinction coefficient versus T at wavelength 520 nm for particle radius 5, 10, and 20 nm. Inset: comparison of extinction for percolation radius 5, 10, and 20 nm. Inset: comparison of extinction for percolation

model (open circles) and RLCA model (squares). Full line in inset is model (open circles) and RLCA model (squares). Full line in inset is probability that a given link is broken at T [from Park and Stroud, PRB 67, probability that a given link is broken at T [from Park and Stroud, PRB 67,

212202 (2003)]. Dotted curve in inset is probability of broken link assuming 212202 (2003)]. Dotted curve in inset is probability of broken link assuming a much higher concentration of DNA links in solution a much higher concentration of DNA links in solution

Tm higher for larger particles

Measured extinction at fixed Measured extinction at fixed wavelength vs. temperaturewavelength vs. temperature

(left) extinction of an aggregate (full curve) and isolated (left) extinction of an aggregate (full curve) and isolated particles (dashed) at 260nm.particles (dashed) at 260nm.

[Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of [Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of an aggregate at 260 nm made from Au particles of three an aggregate at 260 nm made from Au particles of three

different diameters [C. H. Kiang, Physica A321, 164 (2003)] different diameters [C. H. Kiang, Physica A321, 164 (2003)]

260nm absorption sensitive to single DNA strands

Dependence of structure on Dependence of structure on time in RLCA modeltime in RLCA model

Dependence of cluster radius of gyration on “annealing time” (= Dependence of cluster radius of gyration on “annealing time” (= number of MC steps). Cluster eventually anneals from fractal to number of MC steps). Cluster eventually anneals from fractal to

compact with increasing time – annealing happens faster at higher compact with increasing time – annealing happens faster at higher T. (Park & Stroud, 2003)T. (Park & Stroud, 2003)

Work in ProgressWork in Progress

More realistic model for gold/DNA More realistic model for gold/DNA nanocompositesnanocomposites

Selective detection of organic molecules, Selective detection of organic molecules, using gold nanoparticlesusing gold nanoparticles

SP dispersion relations in other nanoparticle SP dispersion relations in other nanoparticle geometriesgeometries

Diffuse and coherent SHG and THG Diffuse and coherent SHG and THG generationgeneration

Control of SP resonances using liquid crystals.Control of SP resonances using liquid crystals.

CollaboratorsCollaborators

S. Y. Park, P. M. Hui, D. J. Bergman, Y. S. Y. Park, P. M. Hui, D. J. Bergman, Y. M. Strelniker, X. Zhang, X. C. Zeng, K. M. Strelniker, X. Zhang, X. C. Zeng, K. Kim, O. Levy, S. Barabash, E. Almaas, Kim, O. Levy, S. Barabash, E. Almaas, W. A. Al-Saidi, I. Tornes, D. Valdez-W. A. Al-Saidi, I. Tornes, D. Valdez-Balderas,Balderas,

K. Kobayashi.K. Kobayashi.Work supported by NSF, with additional Work supported by NSF, with additional

support from the Ohio Supercomputer support from the Ohio Supercomputer Center and the U.-S./Israel BSF.Center and the U.-S./Israel BSF.