future prediction of wireless technology using nano devices

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

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

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’’

 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

electron sphere

Ionic background

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

(not to scale)

Sphere in an applied electric field

Surface plasmon is excited when a wavelength electromagnetic wave is incident on a

Calculation of SP Frequency

0 0

+

=

applied electric field;

= Drude dielectric function

(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

 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.

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 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)

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 Approximation

 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

 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

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

 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)]

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

Effects of Higher Multipoles

 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

1) /

Linker DNA

Melting and Optical Properties of

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.

Description of Previous Slide

 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

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

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)]

any two bonds on different Au particles form a link, using

an equilibrium condition from simple chemical reaction theory

percolation model; (ii) More elaborate model involving

reaction-limited cluster-cluster aggregation (RLCA)

the ``Discrete Dipole Approximation’’ (multiple scattering approach)

212202 (2003); B68, 224201 (2003); Physica B338, 353 (2003)

Simple Percolation Model [Park and

Stroud, 2003a]

 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)]

 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

 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)]

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

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

Tm higher for larger particles

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)

 Diffuse and coherent SHG and THG generation

 Control of SP resonances using liquid crystals.

 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 Al-Saidi, 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.