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Time-Resolved Photodynamics ofTriangular-Shaped Silver
Nanoplates
Luigi Bonacina, Andrea Callegari, Camilla Bonati, Frank van
Mourik, and
Majed Chergui*
Laboratoire de Spectroscopie Ultrarapide, Ecole Polytechnique
Federale de Lausanne
(EPFL), CH-1015 Lausanne, Switzerland
Received October 28, 2005; Revised Manuscript Received November
16, 2005
ABSTRACT
We measured the ultrafast response of triangular silver
nanoparticles upon femtosecond excitation of their plasmon
resonance. After a fast
electron relaxation, the signature of a bimodal mechanical
vibration of the particle is apparent as a spectral modulation. We
identify the two
lowest frequency, totally symmetric vibrations of the particle
as responsible for this modulation, through their influence on the
plasmon peakposition and width, in full agreement with the results
of a variational elastodynamic model that is also presented. From
the analysis of the
phase we conclude that thermal expansion and electron pressure,
respectively, are responsible for the excitation of the two
vibrations.
The short-time optical response of metals involves the
excitation-relaxation dynamics of electrons, plasmons,
andphonons. In nanoparticles (NPs), these dynamics are further
modified by confinement and by the interplay between bulk
and surface effects. Characterizing the optical response of
metal nanoparticles, therefore, provides fundamental insight
into the physics of these systems and essential information
for nanoparticle-based technological applications. Ultrafast
pump-probe spectroscopy has been applied to probe theresponse of
spherical metal nanoparticles as a function of
particle size (from a few to a few hundred nanometers),
composition (mainly noble metals), and environment (liquid
solvents, glassy matrixes).1-9 The influence of shape has
received much less attention, mostly because of the
difficul-
ties associated with preparing uniform samples of nonspheri-
cal nanoparticles and with interpreting the results.
Measure-
ments of the dynamics of such particles remain, at present,
limited to a handful of cases: Ag nanoellipsoids,10 Au
nanorods11,24 and, very recently, Ag nanoprisms,12,13 and
arrays of Au nanoprisms.14
The chain of processes triggered by impulsive laser
excitation with photon energies below the intraband
transition
(4 eV, for silver) has been characterized for spherical
metal
NPs.6,8,15 Conduction band electrons driven out of
equilibrium
rapidly evolve into a hot thermal gas which cools in a few
picoseconds, warming up the lattice and causing it to
expand.
Both the pressure from the hot electrons and the sudden
thermal expansion can excite mechanical vibrations of the
particle. Eventually, all of this mechanical and thermal
energy
is lost to the surrounding environment and the particle
returns
to its initial state. Each of these processes is accompanied
by a change of the optical spectrum as the surface plasmon
resonance (SPR) shifts and/or broadens.
The lower symmetry of nonspherical particles results in a
richer optical response but, at the same time, complicates
its interpretation with practical and conceptual issues.
Specif-
ically, the triangular nanoparticles investigated here
differ
from spherical ones in two important ways. First, the
dominant mechanism of vibrational excitation for spherical
particles is thermal expansion when the particle is large (r>
6 nm) and electron pressure when it is small.16 Nonspheri-cal
particles have at least two characteristic length scales,
and it is not a priori obvious which is the relevant one in
determining the dominant mechanism. Second, the SPR
frequency of spherical NPs is rather insensitive to their
size
(because of scale invariance of the underlying equations17),
up to sizes of several tens of nanometers where retardation
effects become nonnegligible. Therefore, the finite
dispersion
of the sample size does not affect its optical spectrum.
Conversely, nonspherical particles do not have properties of
scale invariance, and at least one of their dimensions is
usually large enough to make retardation effects nonnegli-
gible; hence, the sample size dispersion does affect the
optical
spectrum.
The system under study is a dilute aqueous suspension of
NPs in the shape of equilateral triangles, synthesized in
our
laboratory with a photochemical method that allows control
of their size and shape and,18 hence, tuning of the SPR peak
position. The sample studied here (Figure 1) consists of NPs
of8 nm thickness, 70 nm edge length, and SPR peaking,
in water, at 730 nm. We measure its time- and wavelength-
dependent optical response via transient absorption, in a
NANO
LETTERS
2006Vol. 6, No. 1
7-10
10.1021/nl052131+ CCC: $33.50 2006 American Chemical
SocietyPublished on Web 12/06/2005
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component undergoes a phase change of , as would be
expected if the corresponding particle vibrations modulate
the SPR peak position. The 20 ps component undergoes a
full 2 phase change, suggesting a modulation of the SPR
peak width. However, in both cases, the change of phase is
not sharp, but rather smooth and distributed over a large
fraction of the spectral range.
To discuss the implications of this finding, it is important
to determine whether this smooth change results from the
sample inhomogeneity or it is a signature that these
particlesbehave somewhat differently than spherical ones.11
Therefore,
we explicitly included in the analysis of the transient
spectra
the contribution of the finite particle size distribution.
The
model, which will be described in detail in a forthcoming
publication,22 incorporates the size-dependent
single-particle
spectrum, taken as a quasi-Lorentzian,15 the width (0) of
the SPR, which is determined by the decay time of the
plasmon resonance15 (0), and is taken to be the same for all
particles. At a given time after excitation, the position of
the plasmon resonance peak is determined by the instanta-
neous particle size x (reflecting the lack of particle scale
invariance), electron temperature Te, and lattice
temperature
Tl. This dependence is taken to be linear about the particle
equilibrium size and temperature. The width of the SPR also
depends on electron temperature and lattice temperature. In
turn, the hot electron temperature decays exponentially,
while
the lattice temperature initially increases and subsequently
decreases, as heat is first transferred from the electrons
to
the lattice and then further to the environment. Finally,
the
change of particle lateral size follows a damped cosine with
a period v proportional to the particle lateral size. Within
this model, the particles have uniform thickness and a
Gaussian distribution of lateral sizes, with average xj and
variance x (in the simulations, a population with
30-100different sizes is sufficient to give a good description of
the
sample). The parameters reported in the caption of Figure 2
are obtained by fitting this model to the experimental data.
The agreement between the fitted function and the experi-
mental data is very satisfactory and confirms the ability of
the model to capture the relevant details of the dynamics of
this complex system. In particular, it becomes unambiguous
that the smooth phase change displayed in Figure 4 reflects
the sample inhomogeneity. Even if the pump pulse excitesonly a
narrow subset of the particles in the sample (x
