Nanoparticles for in-vitro and in-vivo biosensing and imaging

22 Metal nanoparticles
be frequency independent, the latter is complex and is a function of the energy. The
resonance condition is fullfilled when ɛ 1 (ω)=-2ɛ m , if ɛ 2 is small or weakly dependent on
ω [37]. This resonance is independent of particle size.
The dipole approximation is also often described as the quasistatic approximation, which
assumes that the entire surface of the nanoparticle is experiencing a constant electric
field. The above equation has been used extensively to explain the absorption spectra of
small metallic nanoparticles in a qualitative as well as quantitative manner [37].
1.6.2 Size dependence: larger particles
For larger nanoparticles (greater than about 20 nm in the case of gold) where the dipole
approximation is no longer valid, the plasmon resonance depends explicitly on the particle
size as the size parameter x (eq. 1.7-1.10)is a function of the particle radius r. The larger
the particles become, the more important are the higher-order modes in eq. 1.7 as the
light can no longer polarize the nanoparticles homogeneously. These higher-order modes
peak at lower energies and therefore the plasmon band red shifts with increasing particle
size [37],[38]. At the same time, the plasmon bandwidth increases with increasing particle
size [37],[38]. This is illustrated experimentally from the spectra shown in Figure 1.8.
As the optical absorption spectra depend directly on the size of the nanoparticles, this
is regarded as an extrinsic size effects [37].
Figure 1.8: Absorption spectra for increasing radius.
1.7 Intrinsic size effect
The situation concerning the size dependence of the optical absorption spectrum is more
complex for smaller nanoparticles for which only the dipole term is important. As can