Optical Properties of Nanoscale
Materials
David G. Stroud,
Department of Physics,
Ohio State University Columbus OH 43210
Work supported by NSF Grant DMR01-04987 and NSF DMR04-12295
and by the Ohio Supercomputer Center
OUTLINE
Introduction: Linear Optical Properties and Surface Plasmons
Liquid-Crystal Coated Nanoparticles
Surface Plasmons in Nanoparticle Chains
Composites of Gold Nanoparticles and DNA
Conclusions
“Labors of the Months” (Norwich, England, ca. 1480).
(The ruby color is probably due to embedded
gold nanoparticles.)
The Lycurgus Cup (glass; British
Museum; 4th century A. D.)
When illuminated from
outside, it appears
green. However, when
Illuminated 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
within
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?
Answer: ``surface plasmons’’
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An SP is a natural oscillation of the electron gas
inside a gold nanosphere.
SP frequency depends on the dielectric function
of the gold, and the shape of the nanoparticle.
Ionic
background
electron
sphere
(not to
scale)
Electron cloud oscillates with frequency of SP; ions provide restoring
force.
Sphere in an applied electric field
Metallic sphere
Incident electric field
is E_0exp(-i w t)
EM wave
Surface plasmon is excited when a longwavelength electromagnetic wave is incident on a
metallic sphere.
Calculation of SP Frequency
3 0
Ein 
E0
 in  2 0
E0 applied electric field;  0 

 in  1 

2
p
2
host dielectric function
= Drude dielectric function
Surface plasmon
frequency is therefore:

0
1  2 0
(This assumes particle is small compared to wavelength.)
Extinction coefficient, dilute suspension of Au
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 Using
Nematic Liquid Crystals
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A nematic liquid crystal (NLC) is a liquid
made up of rod-like molecules, which can
be oriented by an applied dc electric field.
The axis of the NLC is known as the
director.
The dielectric tensor of the NLC is
anisotropic, with different components
parallel and perpendicular to the director.
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).]
Schematic of experimental configuration
Measured deviation of surface plasmon resonance energy
from mean value, vs. angular position of polarization
analyzer. From Muller et al, Appl. Phys. Lett. 81, 171
(2002).
Maximum
splitting: 30
mev (expt).
Pictures (b)
and © from
D.R.Nelson,
Nano Lett.
(2002).
Plausible configurations of liquid crystal coating: (a) “uniform”
(director always in same direction); (b) “melon” (two
singularities); (c) “baseball” (four singularities; tetrahedral)
Discrete Dipole Approximation
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Purcell & Pennypacker, Ap. J. 186, 175 (1973);
Goodman, Draine & Flatau, Opt. Lett. 16, 1198 (1991).
Idea: break up small particle into small volumes, each of
which carry dipole moment.
Dipole moment due to local electric field from all the
other dipoles.
Calculate total cross-section, using multipole-scattering
approach.
Can be used for anisotropic, and absorbing, scatterers.
Connect polarizability of small volume to dielectric
function, using Clausius-Mossotti approximation
Calculated surface plasmon frequency as a function of
metal particle fraction p’ in the coated nanoparticle, for
light oriented parallel and perpendicular to nematic
director (uniform configuration) [S. Y. Park and D.
Stroud, Appl. Phys. Lett 85, 2920 (2004)]
Computed peak in extinction coefficient versus
angle of polarization of incident light rel. to coating
symmetry axis: three coating morphologies [S. Y.
Park and D. Stroud, 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
Plasmons in Chains of
Nanoparticles
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A chain of closely spaced metallic nanoparticles
allows WAVES of surface plasmons to propagate
down the chain.
The waves can be either transverse (T) or
longitudinal (L) modes, and can have group
velocities up to 0.1c or higher.
Studied extensively by Atwater group at Caltech,
and by other groups at Stanford and elsewhere.
Potentially useful for propagating energy along
effectively very narrow waveguides, controlling
energy flow around corners, etc.
Nanoparticle chain
d
a
Surface plasmons can propagate along a periodic
chain of metallic nanoparticles (above)
Photon STM Image of a Chain of
Au nanoparticles [from Krenn et
al, PRL 82, 2590 (1999)]
Individual particles: 100x100x40 nm, separated by 100
nm and deposited on an ITO substrate. Sphere at end
of waveguide is excited using the tip of near-field
scanning optical microscope (NSOM), and wave is
detected using fluorescent nanospheres.
Calculation of SP modes in
nanoparticle chain
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In the dipole approximation, there are three SP modes
on each sphere, two polarized perpendicular to chain,
and one polarized parallel. The propagating waves are
linear combinations of these modes on different spheres.
In our calculation, we include all multipoles, not just
dipoles. Then there are a infinite number of branches,
but only lowest three travel with substantial group
velocity.
Can be compared to nanoplasmonic experiments, as
discussed by Brongersma et al [Phys. Rev. B62, 16356
(2000) and S. A. Maier et al [Nature Materials 2, 229
(2003)]
Calculated dispersions relations for gold nanoparticle
chain, including only dipole-dipole coupling in quasistatic
approximation [S. A. Maier et al, Adv. Mat. 13, 1501
(2001)]
(L and T denote longitudinal and transverse modes)
Surface plasmon dispersion relations, nanoparticle
chain, including ALL multipole moments [Park and
Stroud, Phys. Rev. B69, 125418 (2004)]
L
T
L
T
L
L
T
T
Calculated surface plasmon dispersion relations (left) and
group velocity for energy propagation in the lowest two
bands. Solid curves: L modes; dotted curves: T modes.
Light curves; dipole approximation; dark curves, including all
multipoles. a/d=0.45, a= particle radius; d= particle
separation
Effects of Higher Multipoles
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Strong distortion of dispersion relation,
compared to dipole-dipole interaction
Percolation effect when gold particles approach
contact: frequency of L branch approaches 0 at
k=0
Single-particle damping can be included. Still to
include: radiation corrections. Also omitted:
disorder (in shape, size, 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
s  (1   m /  s )
1
[Park and Stroud, PRB69,
125418 (2004)]
Melting and Optical Properties of
Gold/DNA Nanocomposites
Linker DNA
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.
[Schematic from R. Elghanian et al, Science
277, 1078 (1997)]
Observed absorptance:
comparison of unlinked and
aggregated Au nanoparticles
Absorptance of unlinked and aggregated Au nanoparticles, as
measured by Storhoff et al
[J. Am. Chem. Soc. 120, 1959 (1998)]
Description of Previous Slide
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Source: R. Jin et al, J. Am. Chem. Soc. 125,
1643 (2003).
Top two pictures show (a) samples under
transmitted light before and after being exposed
to the target (b) UV and visible extinction
coefficients of the two samples.
Bottom is a schematic of structure of samples
before and after agglomeration (which occurs as
temperature is lowered)
Extinction coefficient of Au/DNA
composite at 520 nm
theory
experiment
=melting pt.
=sol-gel
transition
[S. Y. Park and D.
Stroud, Phys. Rev.
B68, 224201 (2003)]
[R. Jin et al, J. Am.
Chem. Soc. 125, 1643
(2003)]
[D. Stroud, Phys. Rev. B19, 1783 (1979)]
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)
Methodology
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To determine structure, we calculate the probability that
any two bonds on different Au particles form a link,
using an equilibrium condition from simple chemical
reaction theory.
Structure determined by two different models: (i)
percolation model; (ii) More elaborate model involving
reaction-limited cluster-cluster aggregation (RLCA)
To treat optical properties (for any given structure) use
the ``Discrete Dipole Approximation’’ (multiple
scattering approach).
References: S. Y. Park and D. Stroud, Phys. Rev. B67,
212202 (2003); B68, 224201 (2003); Physica B338, 353
(2003).
Simple Percolation Model [Park and
Stroud, 2003a]
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Place Au nanoparticles on a simple cubic (SC) lattice
Each Au particle has N single DNA strands, of which N/z point
towards each of z nearest neighbors (z = 6 for SC)
Two-state model for reaction converting two single strands into a
double strand: S+S = D. Probability of double-strand forming is
p(T), determined by chemical equilibrium constant of reaction.
Probability that no strand forms between two nearest neighbor
particles is 1 - p’ = 1 – [1 –p(T)]^(N/z)
p’ is a much sharper function of T than is p.
Melting occurs when p’ = p_c, the percolation threshold for the
lattice.
Optical properties calculated using Discrete Dipole Approximation
Assume N is proportional to surface area: melting temp higher for
larger particles
Reaction-Limited Cluster-Cluster
Aggregation Model [Park and
Stroud, 2003b)]
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Start with N gold spheres placed randomly on a lattice
Allow them to aggregate by RLCA (appropriate when
repulsive energy barrier between approaching particles)
Then let cluster “melt” by dehybridization of DNA
duplexes, using T-dependent bond-breaking probability
used for percolation model
Repeat this aggregation/dehybridization process many
times. Result is a fractal cluster with a T-dependent
fractal dimension. Appropriate when aggregation
process is non-equilibrium
Once aggregation process is complete, calculate optical
properties versus T, using DDA.
Discrete Dipole Approximation
Melting of Au/DNA cluster, two
different models
(a), (b) and (c) are a percolation model: all particles on a cubic
lattice. (a): all bonds present; (b) 50% of bonds present; (c)
20% of bonds present. (d) Low temperature cluster formed by
reaction-limited cluster-cluster aggregation (RLCA)
Extinction coefficient, dilute
suspension
Extinction coefficient per unit vol of Au,dilute suspension. Crosses: experiment [Elghanian
et al, Science (1997); Storhoff et al, JACS (1998). Dashed and full curves: calculated
without and with quantum size corrections to gold dielectric function [Park and Stroud,
Phys. Rev. B68, 224201 (2003)]
Calculated extinction coefficient,
RLCA clusters
Calculated extinction coefficient versus wavelength for RLCA clusters
with number of monomers varying from 1 to 343 [Park and Stroud,
PRB68, 224201 (2003)], using DDA
Extinction coefficient for compact
Au/DNA clusters
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Extinction coefficient per unit volume, plotted versus wavelength (in nm) for
LxLxL compact clusters, as calculated using the Discrete Dipole Approximation
(DDA) [from Park and Stroud, Phys. Rev. B67, 212202 (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 coefficients
versus temperature at 520 nm
Normalized extinction coefficient at wavelength 520 nm, calculated for two different models,
plotted vs. temperature in C. Full curves: percolation model (3 different monomer numbers).
Open circles: RLCA model, fully relaxed configuration) (From Park+Stroud, 2003) Note rebound
in RLCA (x), when dynamics are NOT fully relaxed.
Extinction coefficient vs. T at 520
nm for different particle sizes
Tm higher for
larger particles
Calculated extinction coefficient versus T at wavelength 520 nm for particle radius 5,
10, and 20 nm. Inset: comparison of extinction for percolation 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, 212202 (2003)]. Dotted curve in inset is probability
of broken link assuming a much higher concentration of DNA links in solution
Measured extinction at fixed
wavelength vs. temperature
(left) extinction of an aggregate (full curve) and isolated particles
(dashed) at 260nm.
[Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of an
aggregate at 260 nm made from Au particles of three different
diameters [C. H. Kiang, Physica A321, 164 (2003)]
260nm absorption sensitive to single DNA strands
Dependence of structure on time in
RLCA model
Dependence of cluster radius of gyration on “annealing time” (= number of
MC steps). Cluster eventually anneals from fractal to compact with
increasing time – annealing happens faster at higher T. (Park & Stroud,
2003)
Work in Progress
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More realistic model for gold/DNA
nanocomposites
Selective detection of organic molecules, using
gold nanoparticles
SP dispersion relations in other nanoparticle
geometries
Diffuse and coherent SHG and THG generation
Control of SP resonances using liquid crystals.
Collaborators
S. Y. Park, P. M. Hui, D. J. Bergman, Y. M.
Strelniker, X. Zhang, X. C. Zeng, K. Kim, O.
Levy, S. Barabash, E. Almaas, W. A. AlSaidi, I. Tornes, D. Valdez-Balderas,
K. Kobayashi.
Work supported by NSF, with additional
support from the Ohio Supercomputer
Center and the U.-S./Israel BSF.
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