b2815 Tissue Engineering and Nanotheranostics “9.61x6.69”
156 Tissue Engineering and Nanotheranostics
a > b = c. The depolarization factors isotropically alter the values of
ε 1 and ε2 and the resulting LSPR peak frequencies. Explicitly, they are
as follows:
2
2
1 11
P ln 1
A 21
ee
ee e
−+
=−
−
1
P,
2
A
BC
P
P
−
==
(10)
where e is the following factor, which includes the particle aspect
ratio R:
(^11)
(^222)
2
1
11.
B
e
AR
=−=−
(11)
The resulting extinction spectrum display nonsphere nanoparti
cles have two peaks: one result from the transverse plasmon mode
from the x and y contributions to the sum, and the other come form
the longitudinal plasmon mode from the z contribution. Equation (9)
could be used to analyze the effect of the aspect ratio on the LSPR
peak wavelength. Increase in the aspect ratio of nonsphere nanopar
ticles could result in an increase in weighting εm [(1–Pj) /Pj ], which
is 2 for spherical particles. This leads to a redshift of the plasmon
peak with increasing aspect ratio, as well as increased sensitivity to the
dielectric constant of the surrounding medium.
2.3. Large Particles Theory
In order to obtain quantitative results for larger particles, the logarith
mic derivative was introduced in the context of computing scattering
coefficient for a sphere.^5
nn() ln ().
d
D
d
ρψρ
ρ
=
(12)
