Figure 2.10: Surface plasmons are collective oscillations of nearly-free electrons at a metal-dielectric interface.
Metal colloids with nano-scale dimensions demonstrate plasmon resonance effects. The ori- gin of the surface plasmon resonance effect is believed to be a result of the oscillation of free electrons in noble metals induced by an electromagnetic radiation field [57]. In metals, the almost-free conduction electrons behave similarly to those in a plasma. Density fluctuations in the distribution of free electrons are known as a plasma-oscillation, or a ‘plasmon’. When parallel-polarised light strikes the metal-dielectric interface, it generates an evanescent elec- tric field which can interact with the free electrons in the metal layer exciting electron density waves, or plasmons. The resonant coupling of an incident electromagnetic perturbation with a surface plasmon mode induces a propagating wave among the electron plasma known as a surface plasmon polariton (SPP), bound to the metal-dielectric interface (see Figure 2.10). The plasmon tends to occur along the surface region of the metal, due to higher absorption as light travels through a larger distance in the metal material, attenuating the electromagnetic (EM) field.
The wavelength of electromagnetic radiation at which coupling with the surface plasmon occurs is metal and size dependent. In contrast to bulk metals, where electrons are more likely to lose energy by non-radiative processes as a result of collisions and scattering, in nanoscale structures such as a nanoscale thickness film or nano-sized particles, the electrons
2.5 Surface Plasmon Resonance and Nanoparticles 22 are trapped. Consequently, in nanostructures, the interaction between the free conduction electrons leads to collective oscillations between the upper and lower energy states, forming a more intense absorption band typically in the visible region of the spectrum. When illu- minated with light of wavelengths in this absorption band, energy is transferred exciting a surface plasmon. This effect is known as surface plasmon resonance (SPR).
Figure 2.11: When light couples with a surface plasmon mode, a propagating surface plasmon polariton is generated with an evanescent field.
The excited surface plasmon polariton features an electromagnetic wave propagating parallel to the surface with an evanescent field decaying exponentially perpendicular to the interface (see Figure 2.11). The evanescent field penetrates into the adjacent media to a depth of approximately that of the incident radiation wavelength. Consequently, the SPP is very sensitive to the surrounding materials. This affects the wavelengths at which SPR can be excited. At resonance, light is absorbed and the intensity of reflected light is reduced [58].
The reason for the intense colours in the visible region of the electromagnetic spectrum exhibited by metal nanoparticles in solutions, is from their small size. The typical diameter of an atom is a few angstroms (˚A= 10−10 m). Nanoparticle diameters used are typically
in the range from 1− 150 nm, corresponding to the aggregation of atoms in groups of a few hundred atoms to a few million. When in solution, the particles are isolated from each other resulting in the confinement of free conduction electrons to the surface of the nanoparticle (free electrons accumulate on the surface of an object due to electrostatics) [59]. The collective oscillations between upper and lower energy states accessible to surface plasmons confined on the particle form an intense and sharp absorption band at visible wavelengths. Note that the size of the nanoparticles is much smaller than the wavelength of visible light, which is in the region of 400−750 nm.
Figure 2.12: The wavelength of the plasmon band absorption maximum is red-shifted with increas- ing particle diameter, as indicated on the appropriate line (Figure from [57]).
understand the intense colours and optical spectra associated with nanoparticles compared to macroscopic bulk material. The plasmon bandwidth increases with decreasing particle size for ‘intrinsic’ size particles (less than 25 nm diameter), and increases with increasing particle size for ‘extrinsic’ size particles (diameter greater than 25 nm)[57]. The plasmon band maximum is red-shifted for increasing particle diameter (see Figure 2.12), creating more absorption at red-wavelengths, and greater transmission at shorter wavelengths of light. For small particles in the region of 10− 20 nm diameter, the peak absorption of light is at 520 nm. For larger diameter particles the absorption peak red-shifts to 535 nm for 50 nm
particles, and 575nm for 100 nm particles. A smaller effect of temperature dependence of plasmon absorption is also observed. Increased temperature slightly reduces the maximum absorption of the plasmon band due to greater damping of the collective electron oscillation through increased scattering.
By solving Maxwell’s equations with boundary conditions for spherical particles Mie theory was developed, quantifying the extinction cross-section for small particles [57]. The total extinction cross-section is a summation over all electric and magnetic multipole oscillations, incorporating scattering and absorption. When the wavelength of lightλ >>2Rp (whereRp
is the particle radius), only the dipole absorption contributes to the extinction cross-section. This occurs for gold when 2Rp <2.6 nm [60]. In this region, the dielectric function of the
nanoparticles is assumed to become size dependent; an intrinsic feature.
Surface Plasmon Resonance (SPR) effects can also be tuned by coating nanoparticles with thin shells of different materials. Composite particles with nanometre thick metal shells
2.5 Surface Plasmon Resonance and Nanoparticles 24
Figure 2.13: (a) Absorption spectra for varying gold shell thickness on silica core. (b) Maximum optical resonance wavelength as a function of the core:shell thickness ratio (Figures from [61]).
and dielectric cores have been created [61]. The optical resonance is selected from visible to infrared wavelengths, by varying the relative dimensions of the core-shell ratio. The composite particles are made from molecular self-assembly and colloid reduction chemistry. For larger core to thin shell ratios, the optical resonance peaks at longer wavelengths, as shown in Figure 2.13. Each nanoparticle type could then be used as a label for a molecular biosensor.
An alternative to metal coating of dielectric cores uses the reverse geometry of coating metal cores with a dielectric shell. By covering the surface of gold nanoparticles with a thin layer of silica, the plasmon band maximum is slightly red shifted in frequency and the intensity strengthened [62].
The exact electromagnetic absorption spectrum observed for sufficiently isolated nanoparti- cles of a given size depends on the volume and shape of the particle, the chemical composition of the particle and the dielectric constant of the surrounding medium. When the nanoparti- cles are very close together they exhibit quantum mechanical coupling effects resulting from overlap of the adjacent particles’ wavefunctions. Hence, the interparticle distance can have a very significant impact upon the frequency of the plasmon band maximum absorption of incident light. Both particle-particle interactions between close nanoparticles and the aggre- gation of nanoparticles cause the location of the plasmon band maximum to shift towards longer wavelengths i.e. it is red-shifted [63, 64]. These effects are noted in DNA-nanoparticle aggregate studies by Mirkinet al (see Section 2.7.2).