Size dependence investigations of hot electron cooling dynamics in metal/adsorbates nanoparticles

Article abstract of DOI:10.1016/j.chemphys.2005.06.040

The size dependence of electron-phonon coupling rate has been investigated by femtosecond transient absorption spectroscopy for gold nanoparticles (NPs) wrapped in a shell of sulfate with diameter varying from 1.7 to 9.2 nm. Broad-band spectroscopy gives

Full text of DOI:10.1016/j.chemphys.2005.06.040

Chemical Physics 319 (2005) 409–421
www.elsevier.com/locate/chemphys
Size dependence investigations of hot electron cooling dynamics
in metal/adsorbates nanoparticles
*
Christophe Bauer , Jean-Pierre Abid, Hubert H. Girault
Laboratoire dÕElectrochimie Physique et Analytique, Facult e´ des Sciences de Base, Ecole Polytechnique F e´ d e´ rale de Lausanne,
CH-1015, Lausanne, Switzerland
Received 13 December 2004; accepted 15 June 2005
Available online 28 July 2005
Abstract
The size dependence of electron–phonon coupling rate has been investigated by femtosecond transient absorption spectroscopy
for gold nanoparticles (NPs) wrapped in a shell of sulfate with diameter varying from 1.7 to 9.2 nm. Broad-band spectroscopy gives
an overview of the complex dynamics of nonequilibrium electrons and permits the choice of an appropriate probe wavelength for
studying the electron–phonon coupling dynamics. Ultrafast experiments were performed in the weak perturbation regime (less than
one photon in average per nanoparticle), which allows the direct extraction of the hot electron cooling rates in order to compare
different NPs sizes under the same conditions. Spectroscopic data reveals a decrease of hot electron energy loss rates with metal/
adsorbates nanosystem sizes. Electron–phonon coupling time constants obtained for 9.2 nm NPs are similar to gold bulk materials
(
ꢀ1 ps) whereas an increase of hot electron cooling time up to 1.9 ps is observed for sizes of 1.7 nm. This is rationalized by the
domination of surface effects over size (bulk) effects. The slow hot electron cooling is attributed to the adsorbates-induced long-lived
nonthermal regime, which significantly reduces the electron–phonon coupling strength (average rate of phonon emission).
ꢀ
2005 Elsevier B.V. All rights reserved.
Keywords: Electron–phonon coupling; Metal; Adsorbates; Surface femtochemistry; Size behavior; Nanoparticles; Ultrafast spectroscopy; Nonth-
ermal regime
1
. Introduction
a metal electrode and a molecule in solution represents
the heart of electrochemistry [2]. The lack of a clear pic-
ture for heterogeneous ET comes from the technical dif-
ficulties to investigate interfacial or surface phenomena
[3]. Furthermore, the interfacial dynamical phenomena
may be more complex than in homogeneous media
due to the appearance of novel energy dissipation
channels.
The purpose of the present study is to obtain infor-
mation on the dynamical behavior of nonequilibrium
electrons at the metal/molecule interface with a particu-
lar interest here for the electron–phonon coupling. In
other words, we would like to know how a bidirectional
ET process between adsorbates and metal can affect the
global dynamics of the nanosystem. Indeed, metal/
adsorbates NPs under investigations here exhibit
Electron transfer (ET) reactions are the most basic
processes in chemistry and are ubiquitous in physics
and biology [1]. ET processes can be divided in two clas-
ses: (i) homogeneous ET and (ii) heterogeneous ET.
Homogeneous ET mainly deals with ET in solution
and is very well understood with the Marcus theory.
On the opposite, the understanding of heterogeneous
ET lies far behind the analogous homogeneous problem
despite the observation that most of efficient natural and
technological chemical transformation occurs at inter-
faces. ET processes underlying redox reactions between
*
Corresponding author.
E-mail address: christophe.bauer@epfl.ch (C. Bauer).
0
301-0104/$ - see front matter ꢀ 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2005.06.040

410
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
ultrafast back and forth charge resonance tunneling
between metal and empty electronic states of adsorbates.
Dynamical events occurring at the metal/adsorbates
junction play a crucial role for a wide range of applica-
tions [4], like for example, surface femtochemistry [5],
catalysis [6], manipulations with scanning tunneling
microscope tips [7], organic light emitting devices [8,9],
surface enhanced Raman scattering [10], and molecular
electronic devices [11,12].
Nascent nonthermal electrons (NNEs)
electron-electron scattering
PI
electron-Molecular Vibration scattering
Hot electron gas
PII
electron-phonon interaction
Hot lattice
phonon-phonon interaction
PIII
A
Surrounding medium
1
.1. Nonequilibrium electron relaxation processes in metal
Metal
Adso rr bates
Let us first describe the behavior of nonequilibrium
Nonth ee rmal
electrons
electrons in bulk metal. The classical picture of the
different events of nonequilibrium electron relaxation
occurring in metal involves three main processes which
are illustrated in Fig. 1A: (i) electron–electron scattering
LUMO
Ε
i
h
ν
Εf
EF
∆
i
E = E - Ef
(
P ), (ii) electron–phonon interaction (P ) and (iii) pho-
I
II
non-medium interaction (P ). The perturbation of the
III
electron distribution upon absorption of a femtosecond
laser pulse by a metal leads to the creation of a popula-
tion of nascent nonthermal electrons (NNEs). In bulk
metal, NNEs redistribute the photonic energy by e–e
scattering with free ‘‘cold’’ conduction electrons giving
rise to a well-defined temperature of the hot electron
B
Fig. 1. (A) Schematic diagram of the different steps of photonic energy
redistribution in metal NPs. Nascent nonthermal electrons created
upon the absorption of a femtosecond laser pulse dissipate the excess
energy among free electrons via e–e scattering and leads the formation
of a hot electron gas with a well defined electronic temperature, the
process PI is called internal thermalization and corresponds to the
gas (internal thermalization process P ). The electronic
I
temperature rise varies from hundreds to thousands of
Kelvin depending on the laser pump fluence. The hot
electron gas transfers the energy toward the lattice by
electron–phonon interaction leading to a thermal equi-
librium between the hot electron gas and the lattice. This
process is referred to the external thermalization process
PII, which is also called hot electron cooling and is the
main topic of this work. In the last step, the phonons
transfer their energy to the surrounding medium (heat
build-up of
a Fermi–Dirac distribution. The electron–molecular
vibration scattering is a process specific to the adsorbates/metal
systems and occurs via a bidirectional inelastic electron tunneling into
adsorbates (see B). During the external thermalization (PII), the hot
electron gas transfers the energy to the lattice through electron–
phonon coupling. Finally, the last process corresponds to the heat
dissipation toward the surrounding medium via phonon-medium
coupling (PIII). (B) Schematic picture showing the inelastic resonant
scattering of nonequilibrium electrons into empty electronic states of
adsorbates. Immediately after the absorption of the femtosecond pulse,
a nonequilibrium distribution of nascent nonthermal electrons (as
photoexcited) is created with energies Ei in the range EF 6 E <
F
E + hm for intraband transitions. The nonequilibrium electron is
temporary transferred into an empty electronic level with an energy E
with the subsequent creation of an intermediate negative ion state, the
lifetime of this state is very short on the order of tens of femtoseconds.
dissipation process P ) within hundreds of picoseconds.
III
All these processes of electron and energy redistribution
are not necessary sequential but may overlap in time.
Due to the diversity of the terms to describe these phe-
nomena, a note is given to present the equivalences [13].
i
i
1
.2. The two-temperature model
The electron then scatters back with an energy E
conduction band. The nascent nonthermal electrons have deposited
energy DE = E in the affinity electronic levels of adsorbates and
is converted in molecular vibrational energy. The amount of energy
loss into adsorbates is directly related to the hot electron resident
lifetime.
F
into the gold metal
The two-temperature model (TTM), which is the
i
ꢁ E
F
most commonly employed model to describe hot elec-
tron cooling process divides the problem into two sub-
systems [14,15]. The first subsystem is represented by
the population of hot electrons defined by an electronic
temperature T whereas the second one is linked the
population of phonons defined by the lattice tempera-
e
oTe
ot
C ðT Þ
e
e
¼ ꢁgðT ꢁ T Þ;
e
l
ð1aÞ
ð1bÞ
ture T . Within the TTM, the rate of energy exchange
l
oT
l
between the hot electron gas and the lattice is given by
two dependent differential equations (Eqs. (1a) and
C
l
¼ gðT
e
ꢁ T
l
Þ.
ot
(
1b)) with g, the electron–phonon coupling constant,
The TTM implies that the metal nanoparticle system
C and C , the electronic and the lattice heat capacity,
with the two subsystems T and T can be seen as a closed
e
l
e
l
respectively
system. In other words, energy can only be exchanged

C. Bauer et al. / Chemical Physics 319 (2005) 409–421
411
between two subsystems represented by the populations
of hot electron and phonons since the energy transfer
toward the surrounding medium is not taken into
account within these assumptions. On the other hand,
from a temporal point of view, the TTM assumes that
the electronic temperature can be defined at any time
of the process of nonequilibrium electrons relaxation.
This assumption implies that the internal thermalization
time (e–e scattering time) can be neglected with respect
to the cooling time of hot electrons (se–e ꢂ se–ph).
However, recent experiments [16,17] and theoretical
models [18] have highlighted the fact that under certain
conditions, the dynamics of nonequilibrium electrons
can quit the frame of the TTM [19]. Indeed, it appears
that e–e scattering time cannot be neglected with respect
to e–ph coupling time when adsorbates affect the
nonequilibrium electron dynamics.
1.4. Technical approaches to investigate interfacial charge
transfer processes
In the past, studies on interfacial ET between metal
and molecules were mainly performed by electrochemi-
cal methods. This steady-state approach only allows
the determination of the rate-limiting step and the fast-
est processes remain elusive. Time-resolved optical spec-
troscopic techniques permit obtaining real-time
information on heterogeneous ET reactions. While most
of the ultrafast investigations on adsorbates/metal sys-
tems (surface femtochemistry) have been performed
with time-resolved two-photon photoemission (a nonop-
tical technique) studies with optical spectroscopic meth-
ods are poorly known. Indeed, ultrafast optical
spectroscopy is difficult to perform on metal/molecule
interfaces due to the very weak signal arising from a
monolayer of adsorbates. However, the use of nanopar-
ticles covered by a monolayer of adsorbates allows the
study of electronic surface phenomena by overcoming
this technical problem since the huge surface-to-volume
ratio of NPs permits the enhancement of the signal hun-
dreds of times compared to a metal film covered by a
monolayer of adsorbates.
1
.3. Surface femtochemistry
When molecules are chemisorbed on metal surfaces,
additional energy loss channels for nonequilibrium elec-
trons may appear. A part of the photonic energy can be
transferred to the adsorbates instead of heating up the
bulk lattice by electron–phonon coupling. The so-called
field of surface femtochemistry deals with chemical
reactions induced on metal surfaces by photoexcited
electrons created in the substrate [5,20,21]. Fig. 1B illus-
trates the primary steps of energy transfer from the
metal toward the adsorbates. The photoexcited non-
equilibrium electrons experience an inelastic resonant
scattering process into empty electronic states of adsor-
bate to form a transient negative ion, which accumu-
lates kinetic energy while the evolution of the wave
packet on potential energy surface. After a certain res-
ident time, nonequilibrium electrons scatter back into
metal leaving behind ‘‘hot’’ adsorbates (highly vibra-
tionally excited adsorbates). If the kinetic energy depos-
ited into adsorbates by nonequilibrium electrons is high
enough, chemisorbed species can either desorb or disso-
ciate through the MGR [22,23] or Antonivietz model
1.5. Size dependence investigations on electron–phonon
coupling rate in metal NPs
Although the electron–phonon interaction process
has been extensively studied in metal nanoparticles [27–
31], there are still controversies for size dependence
behavior on hot electron cooling dynamics in metal
NPs. These discrepancies likely come from the difficulties
to extract electron–phonon coupling constants and/or
from different experimental conditions. Size independent
e–ph coupling constants have been reported for Au NPs
sizes from 2 to 8 nm [32]. These results are understood by
the domination of bulk electron–phonon coupling con-
stant due to weak interaction between hot electron gas
and surface phonon modes [32]. Ahmadi et al. [33,34]
also observed independent hot electron cooling times
for 1.9–50 nm gold NPs within the high perturbation re-
gime. As it will be discussed below, the dependence of hot
electron cooling rate on pump fluence makes difficult a
direct comparison between NPs sizes. Very recently,
Arbouet et al. [35] reported size dependent electron–
phonon scattering times in Ag and Au NPs for sizes be-
low 10 nm, which has been rationalized by a reduction of
the screening electron–ion interaction due to a spill-out
effect. The acceleration of the hot electron cooling pro-
cess as the NPs size decrease is caused by a confinement
(size) effect linked to metal bulk properties. These reports
dealt with the so-called ‘‘naked metal NPs’’, that means
either metal NPs without adsorbates or a situation where
the surrounding medium (matrix) does not affect non-
equilibrium electron dynamics. Several studies have
[
24]. Usually, the hot electron gas is thought to be the
only nature of photoexcited electrons, which induce
desorption or dissociation via inelastic resonant scatter-
ing. Indeed, the description of the interaction of
nonequilibrium electrons with LUMO of adsorbates
with the TTM draws outside the possible implication
of nonthermal electrons in the process of inelastic
electron tunnelling since the population of nonthermal
electrons has disappeared when an electronic tempera-
ture is established. However, nonthermal electrons
may also drive surface chemistry as proposed from
the desorption yield dependence on excitation wave-
length [25,26], from long-lived nonthermal electrons
[
17] or from the direct observation by transient absorp-
tion spectroscopy [19].

412
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
shown that the surrounding medium strongly influences
the dynamics of hot electron cooling within the strong
perturbation regime [36–38]. Furthermore, the chemical
nature of adsorbates can also affect the electron–phonon
coupling rates in gold core-shell NPs as reported by
Westcott et al. [39]. Up to now, investigations on size
dependence of nonequilibrium electron dynamics in
adsorbates/metal NPs cannot be found in the literature.
succinic acid (MSA) to a TiO mesoporous thin film.
2
The elementary TiO2 particle size is 15 nm and the
thickness of the mesopourous films measured by profil-
ometry is 5 lm. Before the insertion of gold NPs, the
TiO nanocrystalline films exhibit a porosity of 60%
2
with an average pore size of 20 nm. Aqueous solution
of primary 1.7 nm gold NPs were synthesized by
ꢁ
NaBH4 reduction of AuCl4 in a mixture of water
and methanol. The synthesis includes five consecutive
washing and centrifugation steps with pure methanol.
This sequence ensures the removal of inorganic ions.
The solvent excess was evaporated at temperatures
1.6. Nonequilibrium electron dynamics in metal/
adsorbates nanosystems
ꢁ
3
below 40 ꢁC and a pressure lower than 5 · 10 Torr
for 12 h. The core size of the resulting particles exhi-
bited an average diameter of (1.7 ± 0.4) nm. The final
gold NPs used to perform laser spectroscopic measure-
ments was obtained by heat treatment at 723 K gener-
ating gold NPs wrapped in a shell of sulfate with sizes
of 2.5–9.2 nm in diameter depending on wet-grafting
time. The shell of sulfate results from the complete oxi-
dation of the molecular bridge (mercapto succinic acid)
as revealed by FT-IR spectroscopy and X-ray photo-
emission spectroscopy. The sizes of the gold NPs have
been revealed by transmission electronic microscopy
using a Philips CM20. For each NPs system, hundreds
of NPs are counted resulting in a size distribution of
For the present size dependence investigation, we
have prepared metal/adsorbates systems from 1.7 to
9
.2 nm where the ratios of surface metal atoms to total
metal atoms vary from 73% to 13%, respectively. The
study is focused on electron–phonon coupling dynamics,
the energy loss relaxation processes of hot electron gas.
However since the different dynamical processes are
interdependent and may overlap in time, let us present
the knowledge available at the moment for these systems
Previous ultrafast transient absorption measurements
have shown that nonthermal electrons (NNEs) experi-
ence an inelastic resonant scattering process into empty
electronic states of adsorbates in small metal NPs
wrapped in a shell of adsorbates [19]. More strictly
speaking, when chemical interface damping provides
the main mechanism for the surface plasmon damping,
ultrafast chemical interface scattering (UCIS) has been
recognized as an important channel of energy and
momentum loss for NNEs [19]. As a result of UCIS
process, internal thermalization (build-up of a Fermi–
Dirac, i.e., establishment of electronic temperature) is
slowed down and this effect is even more pronounced
as NPs sizes decrease below 5 nm [40]. The mechanism
behind the retardation of internal thermalization is be-
yond the scope of this paper. However, it could be useful
to state here that this mechanism is directly related to
surface effects, i.e., properties of adsorbates. In this
paper, results obtained by ultrafast transient absorption
spectroscopy on size behavior of hot electron cooling
dynamics are presented for metal/adsorbates nanosys-
tems in the critical size range below 10 nm. Further-
more, these systems provide information as to how
internal thermalization influences hot electron cooling
process (electron–phonon interaction).
1
5–20%. Full details concerning the preparation and
the characterization will be published elsewhere. Final-
ly, adsorbates/metal nanosystems under investigation
consist of gold NPs wrapped in a shell of sulfate and
embedded in a matrix of TiO2.
2
.2. Steady-state spectroscopy
UV/Visible spectra were recorded on an HP-8353
(Hewlett–Packard) spectrophotometer.
2
.3. Femtosecond laser set-up
The femtosecond transient absorption set-up features
a compact CPA-2001 Ti:Sa-amplified femtosecond laser
Clark-MXR) with a repetition rate of 1 kHz, a funda-
(
mental wavelength at 775 nm, a pulse width of 120 fs
and an energy of 1 mJ per pulse [41]. The output beam
was split into three parts for pumping two double-stage
noncollinear optical parametric amplifiers (NOPA) and
to produce a white light continuum in a 2 mm thick
sapphire plate. The output pulses of the NOPAs were
compressed in SF10-glass prism pair compressors to
obtain pulses of 50 fs. Pump and probe beams were direc-
ted parallel to each other toward a 60ꢁ off-axis parabolic
mirror that focused them into the sample. The resulting
2
. Experimental
2
.1. Samples preparation
ꢁ
4
2
spot area of the pump pulse is 1.25 · 10 cm . The
pump–probe cross-correlation measured by Kerr gating
in a 0.3 mm thick PBH21 glass window (Ohara, Japan)
at the sample position was typically 80 fs.
The three dimensional Au/TiO2 nanoarchitectures
were prepared by wet-grafting of initial Au NPs of
.7 ± 0.4 nm in diameter derivatized with mercapto
1

C. Bauer et al. / Chemical Physics 319 (2005) 409–421
1.5
413
For the monochromatic probing, a DET-110 silicon
diode (Thorlabs) was placed directly after the samples
to measure the transmitted light intensity. The signal
from the detector was connected to a SR-830 lock-in
amplifier (Stanford Research Instruments) tuned at
9
8
.2 nm
.0 nm
1
.0
.5
2
20 Hz by a chopper modulating the pump beam. Time
delays between pump and probe pulses were controlled
with a linear translation stage (Physic Instrument
M511).
Transient absorption spectra were obtained using a
white light continuum produced in a 2 mm thick
sapphire plate. The white beam was collimated using a
4.2 nm
2.5 nm
0
1
.7 nm
0.0
9
0ꢁ off-axis parabolic mirror and steered to the sample
400
500
600
700
800
900
using only reflective optics. A smooth monotonic spec-
tral distribution between 470 and 680 nm was obtained
by controlling the pump energy with an iris and a
variable density filter. A broad-band membrane beam
splitter was placed before the sample to split the white
light beam into signal and reference arms. Both were
collected by fiber bundles and sent into a Triax 320 spec-
trograph (Jobin-Yvon). Reference and signal beams
were separated vertically during their travel in the
spectrograph and detected individually by diode array
detector (A ST116 double Princeton Instrument). Both
Wavelength (nm)
Fig. 2. Steady-state UV–Vis spectra of metal/adsorbates nanosystem
with core diameter of 1.7, 2.5, 4.2, 8 and 9.2 nm. Interference patterns
arise from the homogeneous thickness of the TiO nanocrystalline film.
2
the NPs sizes decrease, the surface plasmon band be-
comes broader due to the scattering of collective elec-
trons with NPs surface [44]. Indeed when the NP size
is below the mean free path of bulk gold, surface scatter-
ing acts as an efficient damping mechanism for the sur-
face plasmon. The electron scattering frequency C
1
024 elements detector arrays allowed for recording
more than 200 nm wide spectra averaging at a time.
Chirped pulse duration was 210 fs as measured by Kerr
gating in PBH21 glass between 490 (2.53 eV) and
(
surface plasmon lifetime) is defined with Eq. (2) with
A the damping constant, C , the bulk damping constant,
0
vF is the Fermi velocity of electrons and R is the nano-
7
00 nm (1.77 eV). The group velocity dispersion of the
particles radius [42,44]
white light continuum was compensated in the transient
absorption spectra. The absorbance change was calcu-
lated using the ratio between data obtained with and
without the pump pulses reaching the samples and cor-
rected for fluctuations in the white light continuum
intensity using the reference beam spectra. The low rep-
etition rate of 1 kHz of the present femtosecond set-up
ensures that there is no continuous heating up during
measurements due to a possible incomplete heat dissipa-
tion before the arrival of the second pump laser pulse.
Av
R
F
C ¼ C þ
.
ð2Þ
0
3.2. Chemical interface damping
However with the presence of adsorbates on the NPs
surfaces, an additional process for the damping of the
surface plasmon, which is called the chemical interface
damping may arise [42,45–47]. When adsorbates inter-
act strongly with metal nanoparticles surface, electrons
from metal NPs may tunnel back and forth into empty
electronic states of the adsorbates [45]. The resident
time of electrons in the adsorbates is long enough to
break the plasmon phase coherence, leading therefore
to a decrease of surface plasmon lifetime [45]. Thus,
the term A should be divided into two terms (A =
Asize + Aadsorbates) when the chemical interface damping
strongly contributes to the surface plasmon damping.
The parameter A contains contribution from both pure
size (bulk) effects Asize as well as the chemical interface
damping Aadsorbates. The term Asize depends on metal
bulk properties whereas Aadsorbates is related to the
chemical environment directly in contact with the metal
nanoparticles surface, i.e., the adsorbates. Strictly
speaking, Aadsorbates is thought to be dependent on the
barrier width for electron tunnelling, the position and
3
. Results and discussion
3
.1. Steady-state UV/Vis spectra
Fig. 2 shows the UV/Vis spectra of gold NPs
wrapped in a shell of adsorbates with core metal sizes
varying from 1.7 to 9.2 nm. The increase of absorption
below 450 nm is due to interband transitions from the
d-band to sp-band of gold as well as band gap transition
from TiO matrix. The manifestation of confinement in
2
metal nanoparticles is characterized by the presence of
surface plasmon, which corresponds to the collective
oscillations of conduction electrons [42,43]. The surface
plasmon bands are observed between 525 and 545 nm
depending on metal/adsorbates nanosystem sizes. As

414
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
The metal mediated-electron delocalization into the
adsorbates shell can be seen as a strong mixing of molec-
ular wave functions with electronic bands of the metal
substrate. Concerning the geometry of the chemisorp-
tion of sulfate molecule onto gold surface, calculations
revealed that an oxygen atom of a sulfate molecule is
surrounded by three surface gold atoms on face (1 1 1)
5
00
550
600
Wavelength (nm)
650
Fig. 3. Differential transient absorption spectra recorded after a delay
time of 200 fs and 5 ps after pumping at 480 nm for metal/adsorbates
nanosystems of 4.2 nm core size.
[
54]. The LUMOs are mainly formed by sulfur orbitals
and the first LUMOs are r* and p* molecular orbitals
54]. An electron flow occurs from the oxygen atom of
evolution of the transient absorption spectra [19].
Concerning the distribution of nonequilibrium electron,
an important feature is the observation of different spec-
tral signatures for the nonthermal and the thermal
distributions, as revealed by broad-band spectroscopy
in Fig. 3. Nonthermal distribution is associated to the
population of NNEs whereas the internally thermalized
is linked to the hot electron gas. The spectral signature
of NNEs (nonthermal distribution) consists of a broad
featureless bleach (transmission) with a minimum close
to surface plasmon resonance in the differential transient
absorption spectrum. An important point here is that
NNEs do not exhibit any absorption at any wavelength
over the whole visible spectrum [62]. Concerning the
internally thermalized hot electron gas, the bleach is nar-
rower compared to NNEs and the differential transient
spectrum exhibits absorption on both sides of the
bleach. In contrast to the spectral signature of NNEs,
the shape of hot electron gas has been widely observed
for gold NPs [33,34,63–65]. The absorption cross-section
of NNEs is much lower compared to the hot electron
gas because nonthermal electrons cover a wide energy
range with a small electron distribution change whereas
hot electron gas covers a narrow energy range with a
high electron distribution change. Spectral signatures
of NNEs (nonthermal regime) and hot electron gas
(thermal regime) obtained here by broad-band spectros-
copy are in excellent accordance with calculations based
on bulk metal electron kinetics and band-structure mod-
eling in gold NPs [66]. As observed by broad-band
spectroscopy, the nonthermal contribution (out of
Fermi–Dirac distribution) gives a negative response over
the whole probe spectral region while the thermal distri-
bution either exhibits a negative (bleach) or a positive
response (wings) responses. It should be noted that the
[
sulfates HOMOs (r and p molecular orbitals) toward
empty electronic sp states of the metal. Only the sp
bands of the metal is thought to contribute to the inter-
action since the d-bands for gold are fully occupied and
lie far below the Fermi level. On the other hand, the re-
sponse of the metal is a charge transfer toward the sul-
fate LUMO leading to an increase of charge density
around the sulfur atom. The gold-sulfate bonding has
both r* and p* character [54]. Finally, the decrease of
electron density around oxygen atoms and the increase
around the sulfur atom can be rationalized by r dona-
tion from oxygen atoms toward metal and r* and p*
back donation from the metal toward the sulfur atom.
3.4. Femtosecond spectroscopy: optical response of metal:
broad-band spectroscopy
Let us describe the main features of the optical
response of metal NPs upon absorption of a laser pulse.
The change of absorption measured by ultrafast pump–
probe transient absorption spectroscopy is linked to the
transient change of metal optical properties [55]. Indeed,
the perturbation in electron distribution affects the
dielectric constant of the metal [56,57]. Thus, with this
optical technique, it is possible to obtain information
in real-time on the thermalization and cooling dynamics
of nonequilibrium electrons [58–61]. Fig. 3 shows differ-
ential transient absorption spectra recorded with a delay
time of 200 fs and 4 ps upon pumping at 480 nm for
4
.2 nm adsorbates/metal NPs. The dynamics extracted
from femtosecond transient absorption spectroscopy
may be complicated due to the continuous shape

C. Bauer et al. / Chemical Physics 319 (2005) 409–421
415
shape of the spectral response may change as a function
of NPs sizes and that the chemical interface damping
can influence the transient spectra.
1.2
1.0
0.8
0.6
3
.5. Different spectral regions for the metal response
The spectral map of nonequilibrium electrons can be
divided in three regions as illustrated in Fig. 3. Within
region I at the surface plasmon resonance, the overlap
of NNEs and hot electron gas responses can make the
response complex within this probe region, where a
negative signal is observed at any time of process (see
Figs. 5 and 6). The absorption cross-section of NNEs
is much lower compared to the hot electron gas [55].
These absorption cross-section differences at the early
stage can lead to a mutual compensation of the absor-
bance changes by the simultaneous recovery of the
bleach due to the decay of nascent electrons and
the increase of the bleach linked to the formation of
the hot electron gas. As a result, a fast bleach is formed
0
0
0
.4
.2
.0
0
2
4
6
8
10
12
14
Delay Time (ps)
Fig. 4. Transient absorption data after pumping at 535 nm and
probing at 625 nm (spectral region III, off resonance) for 2.5 nm
adsorbates/metal nanosystems.
(
not necessary within the instrument response) followed
by an exponential recovery until the baseline. Within
region II at the red side of surface plasmon resonance,
the signal exhibits a change of sign, which is expected
in view of the transient absorption spectra. The signal
exhibits within this region a bleach (negative signal),
which is formed within the instrument response (this
bleach reflects the instantaneous creation of NNEs)
followed by an exponential recovery to give a positive
signal, which further decay to baseline. The change of
sign in region II is directly linked to the slow internal
thermalization observed with the metal/adsorbates
NPs. Within the last region III, only a positive signal
is observed with a rise slower than the instrumental re-
sponse. This transient absorption (wing at the red side
of resonance) is linked to the response of hot electron
gas. Since the absorption on the red side of the bleach
is directly linked to the thermal distribution [55], it is
possible to follow the formation of the hot electron
gas with the rise of the signal [19].
[55]. Arbouet et al. have monitor electron–phonon
coupling interaction far off the surface plasmon reso-
nance, at the red side of the bleach [35]. Transient
thermomodulation transmitivity studies have shown
that the response far off resonance (out of region I)
directly reflects the nonthermal electron distribution at
early stages [55]. This behavior is confirmed in Fig. 4,
which shows transient absorption data recorded at
625 nm (in region III). The signal exhibits a slow rise
with a short plateau around 2.5 ps followed by a fast
and a slow decay until the baseline. Other NPs sizes
exhibit a similar behavior, however with slower rise as
the NPs size decrease [40]. Therefore, due to the complex
shape of the signal in this region, probe wavelengths out
off resonance (out of region I) could not be selected to
monitor the hot electron cooling process. In summary,
the hot electron energy loss process will be probed in
region I, at the plasmon resonance (also Fermi energy)
because (i) the response of hot electron gas (thermal
distribution) dominates (ii) other regions II and III are
highly sensitive to nonthermal distribution (NNEs) (iii)
consequence of (ii), the signal exhibits complex behavior
3.6. Choice of probe wavelengths to investigate the hot
electron cooling
(slow rise and plateau) making very difficult the extrac-
In previous studies, electron–phonon coupling
dynamics were probed at the minimum of the surface
plasmon bleach of NPs in region I [27,28] or far off
the resonance in region III [35]. The choice of the probe
wavelength for the present work to investigate the hot
electron cooling process was based on the following
observations: From calculations with gold metal, it is
known that the response of the thermal distribution
tion of an accurate value of electron–phonon coupling
times in region III off-resonance.
3.7. Conditions to extract electron–phonon coupling rate
As the purpose of this work is to compare dynamics
of different NPs sizes, it is important to find experimen-
tal conditions where the rates are independent on
external parameters. Prior embarking on ultrafast spec-
troscopic measurements on the hot electron cooling
process, let us first present the parameters that govern
the dynamics e–ph interaction in accordance with the
dominates in region I at the Fermi energy [55] (E =
F
2
.4 eV for gold), which is very close to the surface
plasmon resonance of these NPs. The response of non-
thermal electrons is much weaker in this spectral region

416
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
widely used TTM. Different methods have been employed
to extract the electron–phonon coupling constant. The
hot electron cooling process can be divided in two
regimes: (i) the so-called high and (ii) the low perturba-
tion regime. The frontier between the two regimes is
A
0.0
0.5
-
-1.0
given by the rise of electronic temperature DT , i.e.,
e
the photonic energy deposited in each nanoparticle.
The low-perturbation regime is thought to be reached
4
.2 nm
-1.5
for DT values below 200 K [68].
e
(
i) A direct consequence of the TTM process is the
0
2
4
6
8
10
12
14
dependence of the hot electron cooling rates on elec-
tronic temperature within the high perturbation regime.
This comes from the fact that electronic heat capacity
depends on electron temperature with the relation
C = cT (c = 66 J m
electron cooling rates are dependent on electron temper-
ature rise DT , and therefore on pump fluence. Within
the high perturbation regime, the hot electron cooling
time is given by s = c (T + DT )/g with T the initial
temperature. If the cooling lifetimes vary linearly with
pump fluences until zero pump fluence, the intercept
gives the lifetime for the extrapolation to zero pump
fluence. Within this approach, it could be useful to check
if lowest measurable value is close to the one obtained
with the extrapolation.
Delay Time (ps)
0
.0
-0.2
ꢁ3
ꢁ2
K
for gold). As a result, hot
e
e
-0.4
-0.6
-0.8
-1.0
e
0
0
e
0
8
.0 nm
-1.2
0
2
4
6
8
10
12
Delay Time (ps)
0
.0
-0.2
(
ii) Another approach consists of performing mea-
surements at very low pump fluence in a regime where
the hot electron cooling time becomes independent on
pump fluence. Within the low perturbation regime
DT ꢂ T , the electron–phonon coupling constant can
-0.4
-0.6
-0.8
-1.0
-1.2
e
0
9.2 nm
be directly extracted from the measured hot electron life-
times since then the constant is reduced to s = cT /g.
0
0
This regime is thought to be reached with an average
of one absorbed photon per nanoparticle but the access
is made difficult by the low signal-to-noise ratio. Never-
theless, we have used both methods to extract the
effective hot electron cooling time constants for the com-
parison of NPs sizes. However as pointed out above, the
approach of the problem could be more complicated
compared to ‘‘naked NPs’’ (no influence of the environ-
ment) [35] because the assumptions of TTM are
transgressed due to the long-lived nonthermal regime
observed for the metal/adsorbates nanosystems [19].
The most important point for the present purpose is that
the dynamics depend only on the intrinsic properties of
metal/adsorbates NPs. In other words, the independence
of the dynamics on external parameters allows a direct
comparison between the different sizes.
Fig. 5A shows transient absorption data recorded
with a probe wavelength at 530 nm for different pump
fluences at 480 nm and adsorbates/metal nanosystem
sizes of 4.2, 8 and 9.2 nm. A pump fluence dependence
is observed as expected from the TTM, indicating that
the measurements are performed within the high pertur-
bation regime. Fig. 5B shows the hot electron cooling
lifetimes as a function of pump fluence for different sizes.
0
2
4
6
8
10
12
14
Delay Time (ps)
B
4
3
2
1
0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Pump Fluence Intensity
Fig. 5. (A) Transient absorption change for adsorbates/metal nano-
systems of 9.2, 8.0 and 4.2 nm after pumping at 480 nm and probing at
535 nm with different pump fluences. (B) Hot electron cooling lifetimes
as function of pump fluences for NPs sizes of 9.2, 8 and 4.2 nm extracted
from data obtained after pumping at 480 nm and probing at 535 nm.
The zero pump fluence extrapolation approach with the
intercept of the slope gives values of (1.05 ± 0.15),
(0.92 ± 0.15), (0.69 ± 0.08) ps for NPs sizes of 4.2, 8

C. Bauer et al. / Chemical Physics 319 (2005) 409–421
0.2
.0
0.2
-0.4
417
and 9.2 nm, respectively. The extrapolation indicates a
lower hot electron cooling rate for the smallest nanopar-
ticles. The hot electron cooling time obtained for the
0
9
.2 nm NPs is very close to those for gold NPs in solu-
-
tion [32,67]. However, due to the uncertainties for the
value of electron–phonon coupling constant, the depen-
dence on pump fluence and the narrow range of NPs
sizes studied, it could be useful to perform measure-
ments in the weak perturbation regime in order to
carefully compare the dynamics with different sizes. To
check if the zero pump fluence corresponds to the lowest
measurable lifetimes, we performed additional experi-
ments by pumping and probing at 535 nm with a larger
size range from 1.7 to 9.2 nm.
-
-
-
0.6
0.8
1.0
1.7 nm
-1.2
0
2
4
6
8
Delay Time (ps)
One-colour pump–probe experiments allowed impro-
ving the signal-to-noise ratio of our set-up to explore the
weak perturbation regime. Fig. 6 shows femtosecond
data for 1.7, 2.5 and 4.2 nm NPs sizes with different
pump fluences. The superposition of the normalized
recovery curves below a pump fluence threshold value
indicates that rates of hot electron cooling are indepen-
dent on pump fluence. Fig. 7 shows that the hot electron
cooling lifetimes for NPs of 4.2 nm also become pump
fluence independent below an intensity of 100 nJ per
pulse, indicating that the measurements are performed
within the very low perturbation regime (less than one
absorbed photon per nanoparticles in average). The
same phenomenon is observed for 2.5 nm NPs, the weak
perturbation regime is reached with a higher pump flu-
ence due to the fact that the number of 2.5 nm NPs in
the matrix is about five times higher compared to
0
0
.2
.0
-
-
-
-
-
0.2
0.4
0.6
0.8
1.0
2
.5 nm
-1
0
1
2
3
4
5
6
7
Delay Time (ps)
4
.2 nm NPs. For the 1.7 nm NPs, the weak perturbation
regime is easily attained but the signal to noise ratio is
low due to the weak response (surface plasmon is highly
damped). The minimum electronic temperature rise per
nanoparticule is fixed by the absorption of a photon.
For the smallest NPs (1.7 nm), even with an average
0.2
0.0
-
0.2
0.4
0.6
0.8
1.0
of one absorbed photon per nanoparticle, DT may be
e
-
high due to the confinement of the photonic energy
[
29]. However, this effect does not affect the comparison
-
-
-
between NPs sizes, as checked by Arbouet et al. [35] with
the dependence on pump photon energy. Finally,
energy-loss dynamics for different NPs sizes can be
obtained within the same conditions. For the fitting pro-
cedure, all curves are fitted within the same manner with
an exponential decay plus a baseline. Time constants in
the low perturbation regime depend on intrinsic proper-
ties of the adsorbates/metal nanoparticles and we can
now dress the size behavior for the critical size range.
Fig. 8 showing hot electron cooling lifetimes as a func-
tion metal/adsorbates NPs sizes reveals a decrease of
4
.2 nm
-
1
0
1
2
3
4
5
6
7
Delay Time (ps)
Fig. 6. Transient absorption change for adsorbates/metal nanosystems
sizes of 4.2 and 2.5 nm after pumping and probing at 535 nm. Pump
fluence of 340, 144, 50, 36, 25, 20, 15 nJ/pulse for 4.2 nm, 300, 170, 143,
30, 100, 85 nJ/pulse for 2.5 nm and 210, 180, 150, 100, 80 and 50
nJ/pulse for 1.7 nm. The arrows indicate the decrease of pump fluence.
1
energy loss rate as the NPs sizes decrease. The values
0
s
obtained for the largest gold NP is very close to
e–ph
the lifetime reported for similar gold NPs sizes [35] or
bulk materials [68,69]. To summarize the experimental
results, measurements performed in the weak perturba-
tion regime have shown that hot-electron cooling rates
decrease with metal/adsorbates nanosystem sizes. When
the surface to volume ratio exceeds 30%, surface effects

418
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
4
3
3
2
2
1
.0
.5
.0
.5
.0
.5
become more important and electron–phonon coupling
time as long as 1.9 ps is observed for the smallest
metal/adsorbates nanosystems.
3.8. Effect of incomplete internal thermalization on hot
electron cooling dynamics
In the following section, an explanation for the
delayed hot electron cooling process is proposed based
on electron distribution changes in metal and the pres-
ence of a long-lived nonthermal regime. Experimental
evidence for an incomplete internal thermalization
2
.5 nm
(nonthermal regime) comes from the data obtained by
probing in region III where a slow rise due to the finite
time for the formation of the hot electron gas is clearly
observed [19]. An example of this behavior is shown in
Fig. 4 for the 2.5 nm NPs where the rise of the signal
probed at 625 nm directly reflects the temporal evolu-
tion from a nonthermal to a thermal distribution
50
100
150
200
250
300
Pump Fluence (nJ/pulse)
[
19,55]. The size dependence behavior of internal ther-
2
1
1
.0
.5
.0
malization is beyond the scope of this paper, however,
it is worthwhile noting that this process becomes longer
as the NPs size decrease [40]. In these metal/adsorbates
NPs, the internal thermalization process to form the hot
electron gas consists of e–e scattering and e–MV interac-
tions (electron–molecular vibration coupling). Nonther-
mal electrons spread the excess energy by collision with
4
.2 nm
‘
‘cold’’ electrons and by excitation of adsorbates
vibrational modes. Early works have already shown that
a nonthermal distribution can considerably slow down
the hot electron energy-loss dynamics in bulk gold
0
50
100
150
200
Pump Fluence (nJ/pulse)
[
16,70]. The electron–phonon coupling rate can be
Fig. 7. Examples of hot electron cooling lifetimes as a function of
pump fluences for NPs of 2.5 and 4.2 nm.
defined as the average rate of phonon emission [70].
During the establishment of a Fermi–Dirac distribution,
the average rate of electron–phonon coupling is
expected to increase exponentially with time. Indeed,
during the internal thermalization process, there is a
continuous increase of electron distribution changes
during the evolution from a nonthermal to a thermal
regime. Fig. 9 illustrates the electron distribution
changes as a function of electron energy for a nonther-
mal and a thermal distribution. The main information
from Fig. 9 is the increase of the number of electrons
out of equilibrium during the establishment of a Fer-
mi–Dirac distribution. Since the internal thermalization
does not occur within the laser pulse duration in metal/
adsorbates nanosystems, only a fraction of electrons
2
1
1
.0
.5
.0
(population of NNES) is out of equilibrium. And, as
the population size of NNEs is much lower compared
to the hot electron gas, the probability of electron–pho-
non interaction is significantly decreased within the
nonthermal regime compared to the thermal regime.
As a result, time rates of hot electron cooling are
reduced for the present systems.
0
2
4
6
8
10
12
Nanoparticles Diameter (nm)
Fig. 8. Hot electron cooling lifetimes as a function of adsorbates/metal
NPs sizes. The lifetimes were extracted from data obtained within the
weak-perturbation regime under the same conditions. The solid line is
a guide for the eyes.
It is worthwhile noticing that the TTM does not
account for the existence of a possible nonthermal

C. Bauer et al. / Chemical Physics 319 (2005) 409–421
419
delay
delay
1
Nonthermal
e-e
scattering
e-ph
interaction
e-e
scattering
e-ph
interaction
AdAdssoorbbaatetses
0
Internal
thermalization
External
thermalization
UCIS
Thermal
Fig. 10. Simplified schematic picture illustrating the dynamical inter-
play between the adsorbates, phonons and electrons in adsorbates/
metal nanosystems. Reduction of internal thermalization by the
adsorbates due to ultrafast chemical interface scattering (UCIS). The
long resulting nonthermal regime affects the electron–phonon coupling
strength. As an effect of the increase of S/V ratio, the role of adsorbates
becomes more important as the NPs sizes decrease.
-
1
-
2
-1
0
1
2
E −Ε
hν F
Electron energy
Fig. 9. Qualitative picture illustrating the change of electron distribu-
tion as a function of electron kinetic energy in a metal for NNEs size
population (nonthermal regime) and for hot electron gas (thermal
regime) assuming intraband electronic transition with equal probabil-
ity and a pump wavelength at 535 nm. The change of electron
distribution reflects the population of electrons out of equilibrium,
which is very low at time zero (NNEs) and increase as NNEs spread
the kinetic energy by e–e collisions with equilibrium (cold) electrons
making kinetic energy range much more narrow for hot electron gas at
the end of internal thermalization (after [55]).
NPs [40]. Let us emphasize the difference between size and
surface effects. Size effects in NPs arise from the confine-
ment whereas surface effects are related to the adsorbed
chemical species interacting with the metal surface. As a
result, for naked NPs only size effects (which are given
by bulk properties) may arise in this case. For adsor-
bates/metal nanosystems bulk properties are not
sufficient to understand the results since surface effects
emerge from the chemical surrounding medium around
the nanoparticle. Therefore, the surface effects governed
by the properties of adsorbates may play a crucial role
on the dynamics of nonequilibrium electrons. The main
difference for sulfate/gold NPs with respect to ‘‘naked’’
gold NPs is the presence of additional channel for non-
thermal electron scattering, the bidirectional electron
tunneling process, i.e., chemical interface damping [19].
Our results confirm that the internal thermalization pro-
cess governs the subsequent dynamical events of nonequi-
librium electron dynamics. According to our findings for
adsorbates/metal NPs, it is possible to drawn the simpli-
fied schematic picture illustrating the interconnection
between the different processes of electron redistribution
and energy dissipation involving the adsorbates, non-
equilibrium electrons and phonons. The proposed
scheme shown in Fig. 10 is the following: Adsorbates
strongly affect the dynamics of internal thermalization
and give rise to a long-lived nonthermal regime. Because
of the crucial role played by the adsorbates, the effect of
the nonthermal regime becomes more important as the
surface to volume ratio of NPs increases. Due to the
reduction of the electron–phonon coupling strength
within the nonthermal regime, the hot electron cooling
process is slowed down compared to the naked gold
NPs or bulk system as the size decreases.
regime for times longer than the laser pulse duration.
Indeed, when the electronic temperature is established,
all nonthermal electrons are supposed to be thermalized
within the hot electron gas. This situation corresponds
to the thermal distribution with a high electron distribu-
tion change over a narrow energy range as shown in
Fig. 9. Therefore, at the end of the internal thermaliza-
tion, the number of electrons out of equilibrium able to
emit a phonon is constant and the electron–phonon cou-
pling constant can be defined since the coupling strength
does not evolve with time [16,70]. In summary, the hot
electron cooling process is delayed because the average
electron–phonon coupling strength increases as long as
the internal thermalization is in progress. For the pres-
ent systems, the internal thermalization can be as long
as 1 ps for the smallest sizes [40].
3.9. Comparison with other size behavior investigations
with metal NPs
It is interesting to notice that for gold and silver NPs
not influenced by the environment, the size dependence
on electron–electron scattering rate [66] follows the same
trend as the electron–phonon coupling rate [35]. Both e–e
[
66,71] and e–ph interaction rates in Ag and Au NPs
increase with the decrease of naked NPs sizes [35]. The
information resulting from the present work concerning
the link between e–e and e–ph scattering processes is com-
parable with the observation of the size behavior of NPs
reported for Ag and Au NPs [35]. The main difference is
that both internal thermalization and electron–phonon
coupling rates for the present adsorbates/metal nanosys-
tems exhibit the opposite trend with respect to Ag and Au
4. Conclusion
The size dependence of hot electron cooling rate in
gold NPs wrapped in a shell of sulfate has been

420
C. Bauer et al. / Chemical Physics 319 (2005) 409–421
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range of 1.7–9.2 nm reveals a decrease of energy loss rate
with NPs sizes. This behavior is attributed to the incom-
plete internal thermalization observed in these systems,
which slows down the hot electron cooling process. A
chain of complex dynamical events takes place in the
adsorbates/metal nanosystem where adsorbates first
slow down the internal thermalization (e–e scattering)
during the early stages of photonic energy dissipation.
Therefore, the rate of phonons emission is initially very
low during the nonthermal regime due to the small pop-
ulation size of electrons out of equilibrium (NNEs) able
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Acknowledgments
C.B. gratefully acknowledges Pascal Comte and
Raphael Charvet for the preparation of the titanium
dioxide matrix, Val e´ rie Devaud for the technical assis-
tance and J.-E. Moser and B. Wenger for the help with
the femtosecond laser set-up. The authors acknowledge
the Centre Interd e´ partemental de Microscopie (EPFL)
for the TEM pictures. The present work is financed by
the ‘‘Fonds National Suisse de la Recherche Scientifi-
que’’ and the ‘‘Office F e´ d e´ rale de lÕEducation et de la
Science (project C02.0010)’’. The Laboratoire dÕElectro-
chimie Physique et Analytique is part of the TMR
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Interfacial Nanostructures).
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