The optical properties of metal nanoparticles have long been of interest in physical chemistry, starting with Faraday's investigations of colloidal gold in the middle 1800s. More recently, new lithographic techniques as well as improvements to classical wet chemistry methods have made it possible to synthesize noble metal nanoparticles with a wide range of sizes, shapes, and dielectric environments. In this feature article, we describe recent progress in the theory of nanoparticle optical properties, particularly methods for solving Maxwell's equations for light scattering from particles of arbitrary shape in a complex environment. Included is a description of the qualitative features of dipole and quadrupole plasmon resonances for spherical particles; a discussion of analytical and numerical methods for calculating extinction and scattering cross-sections, local fields, and other optical properties for nonspherical particles; and a survey of applications to problems of recent interest involving triangular silver particles and related shapes.

A photoinduced method for converting large quantities of silver nanospheres into triangular nanoprisms is reported. The photo-process has been characterized by time-dependent ultraviolet-visible spectroscopy and transmission electron microscopy, allowing for the observation of several key intermediates in and characteristics of the conversion process. This light-driven process results in a colloid with distinctive optical properties that directly relate to the nanoprism shape of the particles. Theoretical calculations coupled with experimental observations allow for the assignment of the nanoprism plasmon bands and for the first identification of two distinct quadrupole plasmon resonances for a nanoparticle. Unlike the spherical particles they are derived from that Rayleigh light-scatter in the blue, these nanoprisms exhibit scattering in the red, which could be useful in developing multicolor diagnostic labels on the basis not only of nanoparticle composition and size but also of shape.

In this paper, we explore the optical properties of Ag nanoparticles chemically modified with alkanethiol self-assembled monolayers (SAMs) by measuring the localized surface plasmon resonance (LSPR) spectrum using UV−vis extinction spectroscopy. For all the experiments presented here, the Ag nanoparticles were fabricated using the technique of nanosphere lithography (NSL) and had in-plane widths of 100 nm and out-of-plane heights of 50 nm. We first demonstrate that unmodified nanoparticles are extremely susceptible to slight changes in 3-dimensional structure when exposed to various solvents. These structural effects can have dramatic effects on the extinction maximum, λmax, of the LSPR shifting it to the blue by over 100 nm. The significant discovery reported here is that λmax for NSL fabricated Ag nanoparticles is extremely sensitive to the SAM properties. We will demonstrate the following new features:  (1) λmax of the LSPR linearly shifts to the red 3 nm for every carbon atom in the alkane chain; (2) spectral shifts as large as 40 nm are caused by only 60 000 alkanethiol molecules per nanoparticle, which corresponds to only 100 zmol of adsorbate; and (3) the nanoparticles' sensitivity to bulk external environment is only attenuated by 20% when the nanoparticles are modified with the longest chain alkanethiol (1-hexadecanethiol, ∼2 nm). Experimental extinction spectra were modeled by using Mie theory for Ag nanospheres with dielectric shells intended to mimic the self-assembled monolayer (SAM) in thickness and refractive index. We find that the Mie theory qualitatively predicts the experimentally observed trend that λmax linearly shifts to the red with respect to shell thickness, or alkanethiol chain length; however, the theory underestimates the sensitivity by approximately a factor of 4. Excellent correlation between theory and experiment was observed when Mie theory was used to predict the degree of attenuation in LSPR sensitivity to bulk external environment when the nanoparticle is encapsulated in a dielectric shell similar to an alkanethiol SAM. Finally, we demonstrate that Ag nanoparticles modified with functionalized SAMs can be used in sensing applications. Here, we show that the LSPR shifts to the red 5 nm with the adsorption of the polypeptide poly-l-lysine (PL) to Ag nanoparticles modified with deprotonated carboxylate groups from 11-mercaptoundecanoic acid (11-MUA). Furthermore, we will show that this system behaves reversibly and exhibits no detectable nonspecific binding.

We use high-quality electrodynamics methods to study the extinction spectra of one-dimensional linear chains and two-dimensional planar arrays of spherical silver nanoparticles, placing emphasis on the variation of the plasmon resonance wavelength and width with array structure (spacing, symmetry), particle size, and polarization direction. Two levels of theory have been considered, coupled dipoles with fully retarded interactions and T-matrix theory that includes a converged multipole expansion on each particle. We find that the most important array effects for particles having a radius of 30 nm or smaller are captured by the couple dipole approach. Our calculations demonstrate several surprising effects that run counter to conventional wisdom in which the particle interactions are assumed to be governed by electrostatic dipolar interactions. In particular, we find that for planar arrays of particles with polarization parallel to the plane the plasmon resonance blue shifts as array spacing D decreases for D larger than about 75 nm and then it red shifts for smaller spacings. In addition, we find that the plasmon narrows for D > 180 nm but broadens for smaller spacings. The results can be rationalized using a simple analytical model, which demonstrates that the plasmon wavelength shift is determined by the real part of the retarded dipole sum while the width is determined by the imaginary part of this sum. The optimal blue shifts and narrowing are found when the particle spacing is slightly smaller than the plasmon wavelength, while red shifts and broadening can be found for spacings much smaller than the plasmon wavelength at which electrostatic interactions are dominant. We also find that the array spectrum does not change significantly with array symmetry (square or hexagonal) or irradiated spot size (i.e., constant array size or constant particle number).

In this paper we examine the effect of solvent on the optical extinction spectrum of periodic arrays of surfaceconfined silver nanoparticles fabricated by nanosphere lithography (NSL). By use of NSL, it is possible to systematically vary the out-of-plane height of the nanoparticles, and by thermal annealing, we can control the nanoparticle shape. We have studied four separate samples of nanoparticle arrays; three samples have nanoparticles that are truncated tetrahedral in shape but that differ in out-of-plane height and one sample has nanoparticles that are oblate ellipsoidal in shape. By performing UV-vis extinction spectroscopy measurements at 12 µm spatial resolution, we show that the defect sites that occur as a byproduct of the NSL fabrication process play a negligible role in the macroscale extinction spectrum. We find that the extinction spectrum of the nanoparticles that are oblate ellipsoidal in shape is least sensitive to the surrounding dielectric medium, and the extinction spectrum of the nanoparticles that are truncated tetrahedral in shape with the smallest out-of-plane height is most sensitive. A 1 nm shift in the extinction maximum corresponds to a 0.005 change in the refractive index of the external medium. Theoretical calculations based on the discrete dipole approximation (DDA) are presented. The DDA is a coupled finite element method capable of calculating the extinction of light for particles of arbitrary shape and size. The discrepancy between the experimental and theoretical results is small for the oblate ellipsoidal-shaped particle but progressively increases for the truncated tetrahedral-shaped particles as they become more oblate. This discrepancy is lessened by including the effect of substrate-particle interactions in the calculation. The DDA theory predicts a significantly larger red shift in the extinction maximum with increasing solvent refractive index than is observed experimentally.