Scattering of electromagnetic radiation by a multilayered sphere

Peña, O.; Pal, U.

doi:10.1016/j.cpc.2009.07.010

Cited by 164 publications

(132 citation statements)

References 21 publications

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“…Optical properties of Ag nanoparticles were calculated using analytical, multilayer Mie theory (21,35) and the model structure depicted in Fig. 3B.…”

Section: Methodsmentioning

confidence: 99%

Reversing the size-dependence of surface plasmon resonances

Peng

McMahon

Schatz

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

436

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The size-dependence of surface plasmon resonances (SPRs) is poorly understood in the small particle limit due to complex physical/chemical effects and uncertainties in experimental samples. In this article, we report an approach for synthesizing an ideal class of colloidal Ag nanoparticles with highly uniform morphologies and narrow size distributions. Optical measurements and theoretical analyses for particle diameters in the d ≈ 2-20 nm range are presented. The SPR absorption band exhibits an exceptional behavior: As size decreases from d ≈ 20 nm it blue-shifts but then turns over near d ≈ 12 nm and strongly red-shifts. A multilayer Mie theory model agrees well with the observations, indicating that lowered electron conductivity in the outermost atomic layer, due to chemical interactions, is the cause of the red-shift. We corroborate this picture by experimentally demonstrating precise chemical control of the SPR peak positions via ligand exchange.T he ability to control surface plasmon resonances (SPRs) in metal nanostructures is critical for achieving advances in many areas, including chemical and biological sensing, imaging, optoelectronics, energy harvesting and conversion, and medicine (1-12). Metal nanoparticles (NPs), particularly those of the noble metals (e.g., Au and Ag) that exhibit strong SPRs, have been the focus of much work (13-17). SPRs have intense and broad optical absorption bands that arise from coherent oscillations of conduction electrons near the NP surfaces. In general, SPRs are influenced by their size, morphology, composition, surface chemistry, and surrounding environment (18,19). However, the size-dependence of SPRs that is important for the aforementioned applications (1-12) is poorly understood in the small particle limit due to complex physical and chemical effects as well as uncertainties in experimental samples. Here, we report an approach for synthesizing an ideal class of colloidal Ag NPs with highly uniform morphologies and narrow size distributions. The SPR absorption band for particles with diameters, d, in the range of 2-20 nm is found to exhibit an exceptional behavior: As size decreases from d ≈ 20 nm it blue-shifts but then turns over near d ≈ 12 nm and strongly red-shifts. We have developed a multilayer Mie theory model and the corresponding calculation results agree well with the observations, indicating that the lowered electron conductivity in the outermost atomic layer, due to chemical interactions, is the cause of the red-shift. We corroborate this picture by experimentally demonstrating precise chemical control of the SPR peak positions via ligand exchange. Such chemical control of the NP surface layer may provide a promising strategy for sensitively probing species strongly adsorbed (or bonded) to the NPs.For metal NPs with d or structural features larger than 20 nm, often a purely continuum-level, classical electrodynamics picture suffices for interpretation or prediction of their optical properties. In this approach the bulk dielectric constants for the vario...

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“…Optical properties of Ag nanoparticles were calculated using analytical, multilayer Mie theory (21,35) and the model structure depicted in Fig. 3B.…”

Section: Methodsmentioning

confidence: 99%

Reversing the size-dependence of surface plasmon resonances

Peng

McMahon

Schatz

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

436

View full text Add to dashboard Cite

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“…The particle can be modeled as a series of concentric shells, each with a distinct refractive index. We use the algorithm provided by Peña and Pal to compute the scattering coefficient for a layered particle (29), considering the specific case of a sucrose particle subjected to an abrupt increase in RH, from 20% to 40%. For the majority of calculations, 97 evenly spaced layers are used.…”

mentioning

confidence: 99%

Comparing the mechanism of water condensation and evaporation in glassy aerosol

Bones

Reid

Lienhard

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

190

255

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Atmospheric models generally assume that aerosol particles are in equilibrium with the surrounding gas phase. However, recent observations that secondary organic aerosols can exist in a glassy state have highlighted the need to more fully understand the kinetic limitations that may control water partitioning in ambient particles. Here, we explore the influence of slow water diffusion in the condensed aerosol phase on the rates of both condensation and evaporation, demonstrating that significant inhibition in mass transfer occurs for ultraviscous aerosol, not just for glassy aerosol. Using coarse mode (3-4 um radius) ternary sucrose/sodium chloride/aqueous droplets as a proxy for multicomponent ambient aerosol, we demonstrate that the timescale for particle equilibration correlates with bulk viscosity and can be ≫10 3 s. Extrapolation of these timescales to particle sizes in the accumulation mode (e.g., approximately 100 nm) by applying the Stokes-Einstein equation suggests that the kinetic limitations imposed on mass transfer of water by slow bulk phase diffusion must be more fully investigated for atmospheric aerosol. Measurements have been made on particles covering a range in dynamic viscosity from <0.1 to >10 13 Pa s. We also retrieve the radial inhomogeneities apparent in particle composition during condensation and evaporation and contrast the dynamics of slow dissolution of a viscous core into a labile shell during condensation with the slow percolation of water during evaporation through a more homogeneous viscous particle bulk.water uptake | whispering gallery modes | Raman spectroscopy | optical tweezers | viscous aerosol A tmospheric aerosol particles are typically complex mixtures of organic and inorganic species with correspondingly complex equilibria and temporal responses to changes in humidity. Secondary organic aerosols (SOA) continue to receive a great deal of attention due to their impact on radiative forcing, mainly through the indirect effect (1). Ambient aerosol typically contains a significant organic fraction, arising from the oxidation of volatile organic compounds (2). SOA has been largely thought of as existing as a liquid phase, or as a combination of a solid phase within a liquid droplet, but the reality is likely to be far more nuanced. Recently, Virtanen et al. demonstrated that ambient SOA particles can have similar mechanical properties to crystalline ðNH 4 Þ 2 SO 4 particles at 10-20% RH but exist as amorphous glasses to low relative humidity (RH) rather than forming crystalline phases (3). This picture is consistent with the conclusions of Mikhailov et al. (4) and Zobrist et al. (5), who suggested that the existence of glassy states may have profound consequences for the properties of atmospheric aerosol particles, particularly at low temperatures.The term glassy refers to an amorphous, highly viscous state with a dynamic viscosity (η) of greater than 1 × 10 12 Pa s and the mechanical properties of a solid (6). In thermodynamic terms, a glass is in a nonergodic metastable state...

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“…Section 2.1 contains a detailed optical model that provides the means to choose the most suitable material and size of the particle to match the surrounding media and probe laser wavelength, λ probe . (a) schematic representation of the experiment, showing the spherical nanoparticle, the pump and probe laser beams and the vibrations; (b) the absorption cross-section for a 150 nm gold nanoparticle computed [3] with the fixed pump wavelength (λ pump = 415 nm) marked; (c) backscattering cross-section (blue) and the optical sensitivity (orange) of a variable sized gold nanoparticle (0-550 nm) illuminated with a fixed probe laser wavelength (λ probe = 780 nm) in water. The first optimal size for acting as a detector is shown (∼160 nm); here, the backscattering cross-section is very sensitive to the size and, as the particle vibrates, the backscatter is modulated, additional maxima in the sensitivity are shown, but these are for increasingly large particles.…”

Section: Designmentioning

confidence: 99%

“…The optical response of metal nanoparticles can be modelled by the calculation of the scattering, radar backscattering, extinction and absorption cross-sections obtained from a Mie model (Equations (1)- (4)) [3,24]:…”

Section: Optical Design and Modellingmentioning

confidence: 99%

“…This interest stems from their specific behaviour that depends on the particle size and shape and is very different from that of the bulk material. The optical scattering properties of nanoparticles have been well-known since the development of Mie theory [1] and, more recently, the stability of numerical solutions has allowed reliable calculations on spherical structures [2,3]. Additionally, the mechanical properties have been investigated, firstly by Raman scattering [4][5][6] and later by means of pump-probe techniques [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Size Characterisation Method and Detection Enhancement of Plasmonic Nanoparticles in a Pump–Probe System

et al. 2017

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Abstract:The optical resonance of metal nanoparticles can be used to enhance the generation and detection of their main vibrational mode. In this work, we show that this method allows the accurate characterisation of the particle's size because the vibrational frequency of plasmonic nanoparticles only depends on their mechanical properties. Moreover, by a careful selection of the particle size and/or probe laser wavelength, the detected signal can be increased by a large factor (∼9 for the particles used in this work) under the same illumination conditions. Finally, we show experimentally that particles of different sizes inside the point spread function can be observed due to the differences in their vibrational states, which could provide a feasible route to super-resolution.

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Scattering of electromagnetic radiation by a multilayered sphere

Cited by 164 publications

References 21 publications

Reversing the size-dependence of surface plasmon resonances

Reversing the size-dependence of surface plasmon resonances

Comparing the mechanism of water condensation and evaporation in glassy aerosol

Size Characterisation Method and Detection Enhancement of Plasmonic Nanoparticles in a Pump–Probe System

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