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Optical Properties of Nanoscale Materials David G. Stroud, David G. Stroud, Department of Physics, Department of Physics, Ohio State University Columbus OH 43210 Ohio 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 Center and by the Ohio Supercomputer Center OUTLINE OUTLINE Introduction: Linear Optical Properties and Surface Plasmons Introduction: Linear Optical Properties and Surface Plasmons Liquid-Crystal Coated Nanoparticles Liquid-Crystal Coated Nanoparticles Surface Plasmons in Nanoparticle Chains Surface Plasmons in Nanoparticle Chains Composites of Gold Nanoparticles and DNA Composites of Gold Nanoparticles and DNA Conclusions Conclusions

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Labors of the Months (Norwich, England, ca. 1480). (The ruby color is probably due to embedded gold nanoparticles.)

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The Lycurgus Cup (glass; British Museum; 4 th 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)

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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

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What is the origin of the color? Answer: ``surface plasmons An SP is a natural oscillation of the electron gas inside a gold nanosphere. 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. 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)

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Sphere in an applied electric field Surface plasmon is excited when a long- wavelength electromagnetic wave is incident on a metallic sphere. Metallic sphere EM wave Incident electric field is E_0exp(-i w t)

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Calculation of SP Frequency applied electric field; = Drude dielectric function Surface plasmon frequency is therefore: host dielectric function (This assumes particle is small compared to wavelength.)

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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)].

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

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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).]

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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).

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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).

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Discrete Dipole Approximation Purcell & Pennypacker, Ap. J. 186, 175 (1973); Goodman, Draine & Flatau, Opt. Lett. 16, 1198 (1991). 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. 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. Dipole moment due to local electric field from all the other dipoles. Calculate total cross-section, using multipole-scattering approach. Calculate total cross-section, using multipole-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 function, using Clausius-Mossotti approximation Connect polarizability of small volume to dielectric function, using Clausius-Mossotti approximation

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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)]

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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)

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

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

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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.

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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 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. 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)] 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)]

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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)] 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)

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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 separation T L L T L L T T

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Effects of Higher Multipoles Strong distortion of dispersion relation, compared to dipole-dipole interaction 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 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). Single-particle damping can be included. Still to include: radiation corrections. Also omitted: disorder (in shape, size, interparticle distance).

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

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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.

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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)]

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Description of Previous Slide Source: R. Jin et al, J. Am. Chem. Soc. 125, 1643 (2003). 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. 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) Bottom is a schematic of structure of samples before and after agglomeration (which occurs as temperature is lowered)

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Extinction coefficient of Au/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

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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)]

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

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Simple Percolation Model [Park and Stroud, 2003a] Place Au nanoparticles on a simple cubic (SC) lattice 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) 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. 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) 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. p is a much sharper function of T than is p. Melting occurs when p = p_c, the percolation threshold for the lattice. Melting occurs when p = p_c, the percolation threshold for the lattice. Optical properties calculated using Discrete Dipole Approximation Optical properties calculated using Discrete Dipole Approximation Assume N is proportional to surface area: melting temp higher for larger particles Assume N is proportional to surface area: melting temp higher for larger particles

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Reaction-Limited Cluster-Cluster Aggregation Model [Park and Stroud, 2003b)] Start with N gold spheres placed randomly on a lattice Start with N gold spheres placed randomly on a lattice Allow them to aggregate by RLCA (appropriate when repulsive energy barrier between approaching particles) 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 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 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. Once aggregation process is complete, calculate optical properties versus T, using DDA.

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Discrete Dipole Approximation

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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)

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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)]

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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

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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)] 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)]

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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)].

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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.

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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

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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

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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)

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Work in Progress More realistic model for gold/DNA nanocomposites More realistic model for gold/DNA nanocomposites Selective detection of organic molecules, using gold nanoparticles Selective detection of organic molecules, using gold nanoparticles SP dispersion relations in other nanoparticle geometries SP dispersion relations in other nanoparticle geometries Diffuse and coherent SHG and THG generation Diffuse and coherent SHG and THG generation Control of SP resonances using liquid crystals. Control of SP resonances using liquid crystals.

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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. Al-Saidi, I. Tornes, D. Valdez-Balderas, 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. K. Kobayashi. Work supported by NSF, with additional support from the Ohio Supercomputer Center and the U.-S./Israel BSF.

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