Size-dependent ultrafast electronic energy relaxation and enhanced fluorescence of copper nanoparticles

Article abstract of DOI:10.1021/jp0545445

The energy relaxation of the electrons in the conduction band of 12 and 30 nm diameter copper nanoparticles in colloidal solution was investigated using femtosecond time-resolved transient spectroscopy. Experimental results show that the hot electron ener

Full text of DOI:10.1021/jp0545445

J. Phys. Chem. B 2006, 110, 143-149
143
Size-Dependent Ultrafast Electronic Energy Relaxation and Enhanced Fluorescence of
Copper Nanoparticles
Qusai Darugar, Wei Qian, and Mostafa A. El-Sayed*
Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology,
770 State Street, Atlanta, Georgia 30332-0400
Marie-Paule Pileni
Laboratoire des Mate´riaux Me´soscopiques et Nanome´triques, UMR CNRS 7070, UniVersite´ Pierre et Marie
Curie, BP 52, 4 place Jussieu, 75252 Paris Cedex 05, France, and School of Chemistry and Biochemistry,
Georgia Institute of Technology, 770 State Street, Atlanta, Georgia 30332-0400
ReceiVed: August 12, 2005; In Final Form: October 25, 2005
The energy relaxation of the electrons in the conduction band of 12 and 30 nm diameter copper nanoparticles
in colloidal solution was investigated using femtosecond time-resolved transient spectroscopy. Experimental
results show that the hot electron energy relaxation is faster in 12 nm copper nanoparticles (0.37 ps) than that
in 30 nm copper nanoparticles (0.51 ps), which is explained by the size-dependent electron-surface phonon
coupling. Additional mechanisms involving trapping or energy transfer processes to the denser surface states
(imperfection) in the smaller nanoparticles are needed to explain the relaxation rate in the 12 nm nanoparticles.
The observed fluorescence quantum yield from these nanoparticles is found to be enhanced by roughly 5
orders of magnitude for the 30 nm nanoparticles and 4 orders of magnitude for the 12 nm nanoparticles
(relative to bulk copper metal). The increase in the fluorescence quantum yield is attributed to the
electromagnetic enhancement of the radiative recombination of the electrons in the s-p conduction band
below the Fermi level with the holes in the d bands due to the strong surface plasmon oscillation in these
nanoparticles.
I. Introduction
Physical properties of nanoparticles could be tailored by
simply controlling their size and/or shape.10,25,26 This fact led
The study of electronic and optical properties of metallic
nanoparticles is presently one of the most active areas of
nanoscience and technology. The results have attracted more
and more attention from experimentalists, theorists, and tech-
nologists during the past decade.1-12 There are several motiva-
tions from both scientific and technological points of view that
drive the intensive investigations of both static and dynamic
electronic/optical properties of metallic nanoparticles. First, it
is possible to discover new physical phenomena in metallic
nanoparticles. Metallic nanoparticles have electronic structures
that are in transition between atomiclike and bulklike structures.
Many phenomena related to the properties of the electronic wave
function, such as electronic and thermal transport,13-15 the inter-
action processes of the elementary excitations,16,17 and the cou-
pling between elementary excitations with the environment,18,19
will be different in metallic nanoparticles with respect to those
present in the corresponding isolated atoms and bulk metal.
Second, the metallic nanoparticles have numerous potential
applications ranging from optical waveguides to biosensors.20-22
The basis for most of the potential applications of metallic
nanoparticles is their unique localized surface plasmon resonance
(LSPR) and scattering due to the excitation of collective
oscillations of the electrons in the conduction band. For example,
the LSPR oscillations can tremendously enhance the local
electromagnetic field, making it possible to use surface-enhanced
spectroscopy for single-molecule detection.23,24
to intense research to understand the dependence of the physical
properties on the size and shape.10,25,27-33 For steady-state ab-
sorption spectra, it is well-known that both the LSPR frequency
and the line width depend on the nanoparticle size and shape
and this dependence could be explained using classical elec-
trodynamics theory.25 According to this theory, if the metallic
particle size is comparable to or smaller than the mean free path
of the conduction electrons in the bulk, then the electrons will
be scattered by the surface,25 and then both the dielectric func-
tion of particle that determines the LSPR frequency and the
phase-coherence time of the collective excitation that determines
the LSPR line width become size- and shape-dependent.
With the advancement of ultrafast laser spectroscopy, it is
possible to study the nonequilibrium relaxation dynamics of
excited conduction electrons in metallic films and nano-
particles.13,34-40 The large difference in the heat capacity of the
electrons and the lattice makes it possible to create a significant
temperature rise in the electrons with respect to the ionic lattice
in metallic nanoparticles by irradiating them with a sufficiently
short laser pulse. Before irradiation, the electrons are located
in energy states below the Fermi level. Immediately upon irra-
diation, the energy is transferred to the electrons by absorption
of photons via interband and intraband transitions. This quasi-
instantaneous excitation of multiple electrons is a coherent
collective excitation process, where the phase memory is
conserved between the electromagnetic field and the newly
occupied electronic states. According to Fermi-Dirac statistics,
the excited electrons are in a nonthermal distribution. The
* Author to whom correspondence should be addressed. Phone:
(404) 894-0292. Fax: (404) 385-0294. E-mail: mostafa.el-sayed@
chemistry.gatech.edu.
10.1021/jp0545445 CCC: $33.50 © 2006 American Chemical Society
Published on Web 12/10/2005

144 J. Phys. Chem. B, Vol. 110, No. 1, 2006
Darugar et al.
relaxation process of the nonthermally distributed electrons starts
with the rapid thermalization of electrons via electron-electron
(e-e) scattering on a time scale of tens of femtoseconds. At
this point the electrons tend to have a Fermi-Dirac distribution
with a well-defined temperature that depends on the incident
laser intensity. After the thermalization of electrons, electrons
relax by transferring energy to the lattice via electron-phonon
(e-ph) coupling on a sub-picosecond to several picosecond time
scale. This forms a new thermal equilibrium of the electron-
lattice system. The energy is finally dissipated throughout the
surrounding matrix by phonon-phonon coupling. This process
corresponds to the heat transfer from the metal nanopaticles to
the environment, and therefore it is expected to be dependent
on the thermal conductivity of the surrounding medium.
electron-surface phonon coupling should be much stronger in
copper nanoparticles than in gold and silver nanoparticles.
Therefore, copper nanoparticles may offer a better test system
to detect the effects of coupling to the surface phonons on the
electron energy relaxation by studying the effect of the size on
the e-ph relaxation time.
In this paper, we present time-resolved transient absorption
data for copper nanoparticles with diameters of 12 and 30 nm.
Analysis of the data shows that conduction electron energy
relaxation is faster in 12 nm copper nanoparticles than in 30
nm copper nanoparticles. Our result could be interpreted by
including the contribution of size-dependent electron-surface
phonon mode coupling. Furthermore, additional coupling of the
excited electron to surface imperfections is necessary to account
for the observed relaxation rate of the excited (hot) electrons in
12 nm nanoparticles. We have also observed strong fluorescence
from the 30 nm particles and weak fluorescence from the 12
nm copper particles. Fluorescence quantum yield in the particles
we studied is found to be enhanced by about 4-5 orders of
magnitude compared to that of bulk copper metal.
From the above, it is obvious that there has been considerable
interest in obtaining a comprehensive understanding of the
electron energy relaxation dynamics in metallic nanoparticles.
This research enables us to gain insight into several elementary
processes, such as e-e scattering and e-ph coupling in systems
with sizes between those of isolated atoms and the bulk metal.
These processes are the source of a wide range of phenomena
in solid-state physics. For example, e-e scattering plays an
essential role in optical, electronic, and magnetic properties of
disordered metallic systems. Electron-phonon coupling is of
major importance to the laser-induced transformation of materi-
als,41 selective heating in condensed-phase and biological
systems,42 and the formation of the superconducting state in
both conventional and high-transition-temperature superconduc-
tors.43,44 It has been predicted that due to the reduced dimen-
sionality the surface phonon modes (both acoustic and capillary)
increase the energy transfer between the electrons and the lattice
in metallic nanoparticles, and the electron energy relaxation rate
should increase with the decreasing size of the particles.45,46
II. Experimental Section
A. Photochemical Synthesis of Copper Nanoparticles.
Copper nanoparticles are more easily oxidized than gold and
silver nanoparticles, which makes the synthesis of stable copper
nanoparitlces more difficult. Currently, very few methods have
been reported on the preparation of copper nanoparticles in
solution.50,51 The copper nanoparticles in ethanol solution used
in this paper are made by photochemically reducing a com-
mercially available precursor bis(2,4-pentanedionato)copper(II)
(Cu(acac)2) with UV light as proposed by Giuffrida et al.51 In
a typical copper nanoparticle synthesis, 5 × 10-4 M Cu(acac)2
in deoxygenated ethanol is irradiated at 254 nm at an intensity
of 5 mW/cm-2 under anaerobic conditions. Growth of copper
nanoparticles is monitored by the appearance of an absorption
peak around 570 nm, which is characteristic of the plasmon
band of copper nanoparticles.27,50 The irradiation is stopped
when a maximum value of plasmon absorption is observed.
Copper nanopaticles prepared this way are very unstable. To
increase their stability, poly(N-vinylpyrrolidone) (PVP) was
added to the solution before irradiating with UV light. This
allowed the formation of isolated copper nanoparticles that were
stable for days when left in an inert atmosphere. Particle size
variation was very critical for our research and was difficult to
obtain by only controlling the parameters of one-step photo-
chemical reduction (such as concentration of solution, irradiation
light intensity, and irradiation time). Through the use of
previously synthesized nanoparticles (about 10 nm) as seeds
(seed-mediated growth method), copper nanoparicles in ethanol
with an average diameter of 30 nm were successfully grown.
The size and morphology were examined by using a JEOL
100CX II transmission electron microscope (TEM), and the
linear absorption spectrum of our samples was measured by
using a Shimadzu UV-3101-PC spectrophotometer. The TEM
images of two samples, Cu1 and Cu2, are shown in Figures 1a
and 1b, respectively. The average diameters of Cu1 and Cu2,
determined by measuring the sizes of roughly 200 particles, were
12 and 30 nm, respectively. The linear optical absorption spectra
of Cu1 and Cu2 are shown in Figure 2. A plasmon absorption
band is clearly seen in both samples with a slight blue shift
from 568.5 nm for Cu1 to 565.0 nm for Cu2. The blue shift of
the surface plasmon absorption of copper nanoparticles as their
sizes are increased is consistent with the theoretical prediction
made by Pileni’s group.52 By taking into account the size effect
Extensive work has been carried out on several different noble
metal nanoparticle systems by examining particle size effects
on electron energy relaxation. Logunov47,48 from our group
studied thiol-modified gold nanoparticles with diameters of 1.9,
2.6, and 3.2 nm in toluene. Link et al.49 in our group reported
on 9 and 50 nm diameter gold nanoparticles in aqueous
solutions. Hartland’s group5,30,39 obtained data on both 10 and
50 nm silver and 4.6-120 nm gold particles in aqueous solution.
None of these papers reported any effect of particle size on the
electron energy relaxation rates, and all of the e-ph coupling
constants were found to be similar to the corresponding bulk
values. However, for very small silver nanoparticles in dielectric
matrices with 3-10 nm diameters, Bigot and Del Fatti have
observed an increase in the relaxation rate when the particle
size is decreased.31,32 The results are interpreted as size-
dependent coupling between the electrons and surface phonon
modes and energy transfer to the dielectric matrix. As far as
we know, there has not been a report of size-dependent electron
energy relaxation in large noble metal nanoparticles with
diameters larger than 10 nm. The reason for the few observations
of size-dependent electron energy relaxation is due to the
relatively small contributions of surface phonon modes to the
total e-ph coupling. For gold nanoparticles with a diameter as
small as 2 nm, calculations33 show that the contribution of the
electron scattering from the surface phonon modes is less than
10% of the total e-ph processes. The contribution of the surface
phonon modes to the total e-ph coupling is determined by the
ratio of the free electron density to the metal density (n/F), which
is proportional to the valence of the metal divided by its atomic
mass.29,33 The values of n/F for gold, silver, and copper are 3.06
× 1021, 5.57 × 1021, and 9.46 × 1021 g-1, respectively. So

Relaxation and Fluorescence of Cu Nanoparticles
J. Phys. Chem. B, Vol. 110, No. 1, 2006 145
C. Femtosecond Transient Time-Resolved Absorption
Apparatus. Time-resolved transient absorption experiments
performed with a femtosecond laser system have been described
elsewhere.53 Briefly, an amplified Ti:sapphire laser system
(Clark MXR CPA 1000) is pumped by a frequency-doubled
Nd:vanadate laser (Coherent Verdi). This generates laser pulses
of 100 fs in duration (full width at half-maximum (fwhm)) with
energies of 1 mJ at 800 nm and a repetition rate of 1 kHz. The
femtosecond laser pulses of 800 nm are frequency-doubled in
a 1 mm â-barium borate (BBO) crystal to generate 400 nm
pump pulses. A small portion of the fundamental pulse (about
40 µJ) was used to generate a femtosecond white light
continuum in a 1 mm sapphire plate, which was used as the
probe. The range of the femtosecond continuum was from 400
to 1100 nm. The pump beam traveled through a computer-
controlled variable optical delay line with a resolution of 3 µm
(20 fs) and was mechanically chopped at a frequency of 500
Hz by a synchronous light beam chopper (HMS 221). A master
clock generated by Clark-MXR DT 505 was used to set the
chopper frequency and phase. The pump and probe beams were
focused and overlapped at the sample with a diameter of about
250 µm. To minimize noise due to fluctuations in the intensity
of the white light continuum, a reference beam was split off
from the probe beam before the sample. Both the reference beam
and the transmitted signal beam were focused into an optical
fiber cable coupled to a monochromator (Acton Research). After
passing the monochromator, the signal and reference beams were
detected by two matched photodiode (Thorlabs)-boxcar inte-
grator (Stanford Research System, SR 250) systems. The output
from the signal boxcar was divided by the output from the
reference boxcar with an analog divider. A lock-in amplifier
(Stanford Research System SR 530), referenced to the synchro-
nous chopper, monitored the output of the divider. The induced
changes of the sample absorption were probed at the peak of
the LSPR absorption by measuring the differential transmis-
sion ∆T(t)/T ) (Ton(t) - Toff)/Toff ) -∆R(t)L as a function of
the temporal delay between the pump and the probe. Here,
Ton(Toff) refers to the transmission with (without) the pump
beam, and L is the interaction length between the pump (probe)
pulse and the sample. The high stability of our femtosecond
laser system and phase lock technique permit high-sensitivity
measurements with a noise level for ∆T/T in the 10-4 range.
The cross correlation between the pump beam and the probe
beam at the peak of the LSPR absorption of our samples had a
fwhm of 180 fs at the sample position. All of the experiments
reported below were completed at room temperature with pump
pulse energy used within 0.01-0.1 µJ/pulse.
Figure 1. Transmission electron microscope images of (a) copper 12
nm and (b) copper 30 nm particles. The measured average diameter of
these nanoparticles was determined by measuring sizes of roughly 200
particles. In part b, we also observed nonspherically shaped copper
nanoparticles synthesized by the photochemical method.
Figure 2. Absorption spectra of copper nanoparticles in ethanol
solution synthesized by photochemical reduction of the precursor bis-
(2,4-pentanedionato)copper(II) (Cu(acac)2) in ethanol in the presence
of PVP with 254 nm UV radiation. The absorption around 570 nm is
characteristic of the plasmon band of copper nanoparticles.
III. Results and Discussion
of dielectric constant ꢀ2(R), using the Mies’ theory, they have
demonstrated that there is a progressive blue shift of surface
plasmon absorption upon increasing the size of copper nano-
particles. Besides the TEM images, the absorption spectra also
confirm that the size of Cu2 is larger than that of Cu1.
B. Steady-State Fluorescence. The steady-state fluorescence
spectra were obtained using a PTI model C60 steady-state spec-
trofluorometer with an arc lamp source and a photomultiplier
detection system. Copper nanoparticles were excited with a 337
nm emission from a xenon arc lamp, and fluorescence spectra
were taken from 540 to 660 nm with 1 nm spectral resolution
and a 500 ms integration time. The fluorescence quantum yield
of copper nanoparticles was determined by comparing their
fluorescence intensities with the fluorescence of rhodhamine
6G, assuming 100% quantum yield for rhodhamine 6G.
The differential transmission ∆T/T measured for the 12 nm
diameter copper nanoparticles in ethanol solution (Cu1) excited
at 400 nm with the probe wavelength set to the plasmon band
maximum (568 nm) is shown in Figure 3. Each trace corre-
sponds to different incident pump pulse energy. By looking
carefully at the rise of the transient bleach signal, we could find
that the build-up time of the signal is clearly longer than the
fwhm of our instrument response function (180 fs). This
phenomenon has been previously observed and is ascribed to
the internal thermalization of the hot electrons.4,10,38 The
relaxation process of electrons from the nonthermal distribution
to the Fermi-Dirac distribution via electron-electron (e-e)
scattering varies from 5 to about 500 fs, depending on the
intensity and the frequency of the pump laser pulse.39,54 For
the processes of energy relaxation of Fermi-Dirac distributed

146 J. Phys. Chem. B, Vol. 110, No. 1, 2006
Darugar et al.
Figure 3. Differential transmission ∆T/T measured in 12 nm diameter
copper nanoparticles (Cu1) with the probe wavelength set to the
maximum of the plasmon band (568 nm). The different traces
correspond to different pump pulse energies. The inset shows the
dependence of the signal maximum on the pump pulse energy. The
signal amplitude is linearly proportional to the pump pulse energy,
confirming that the transient transmission is dominated by linear free
electron absorption and that nonlinear absorption is negligible.
Figure 4. Normalized traces of the transient transmission signal shown
in Figure 3. It is clear that the e-ph coupling process depends on the
pump pulse energy. A reliable value of electron phonon coupling
constant g can be obtained by extrapolating the lifetimes measured at
different pump powers to zero pump power. The intercept is given by
γT0/g. The inset shows an example of this extrapolation procedure.
where Ce and Cl are the electronic and lattice heat capacities.
Ce(Te) ) γTe (γ ) 96.6 J m-3 K-2 for copper) is proportional
to the electron temperature as long as Te is much smaller than
the Fermi temperature, which is on the order of 104 K. The
first term on the right-hand side of the eq 1 represents thermal-
conductivity losses, and κ is the thermal conductivity. Within
the time scale used in the present work (a few picoseconds after
excitation), the thermal conductivity is thought to have negligible
contribution, and this term could be ignored. The second term
in eq 1 represents electron and lattice temperature coupling
through the e-ph coupling constant g, which is independent of
temperature. Heating due to the incident optical pulse is
accounted for by the source term A(r,t). When the pump
intensity is low, as the situation was in our experiments, the
temperature change in the electron gas is small, and the
relaxation time is given by γ(T0 + ∆T)/g according to eqs 1
and 2, where T0 is the ambient temperature and ∆T is the initial
electronic temperature increase of the electron subsystem
induced by the pump laser pulse after internal thermalizaiton
of nonthermal electrons via electron-electron scattering. A
reliable value of g can be obtained by extrapolating the lifetime
measured at various pump powers to zero, where the intercept
is given by γT0/g.30,39 The inset to Figure 4 shows an example
of this extrapolation procedure.
electrons in metallic nanoparticles, it can be described as two-
exponential decays.3 The fast contribution, on the picosecond
time scale, is due to the relaxation of hot electrons through
coupling with the phonons (lattice). The slow contribution that
decays on a time scale of hundreds of picoseconds is due to
relaxation involving the surroundings (phonon-phonon cou-
pling). The ratio between slow contribution and fast contribution
is increased as the pump pulse energy increases. In our
experiment, due to the low pump power (the maximum pump
pulse energy is 38 nJ), it can be seen in Figure 3 that the
ph-ph coupling contribution to the total transient transmission
is less than 1% and is negligible in the following data analysis.
The inset of Figure 3 shows the signal maximum under different
pump pulse energies. The signal amplitude is found to be
proportional to the pump pulse energy, suggesting that the
transient transmission is dominated by the induced changes of
the linear free electron absorption and that nonlinear absorption
is negligible. The normalized traces of the transient transmission
signals in Figure 3 are shown in Figure 4. It is clear that the
e-ph coupling process depends on the pump pulse energy. This
effect has been studied and is usually interpreted in terms of
the two temperature model (TTM).30,39 Essentially, it is the linear
increase of the electronic heat capacity with the electron
temperature that causes the hot electron energy transfer rate
between the electrons and the phonon baths to be dependent
on the pump pulse energy. In TTM, the electrons and phonon
baths form two subsystems of the metal, each characterized by
a different heat capacity and temperature. The time evolution
of the electron and lattice temperatures Te and Tl can be
described by the following pair of coupled nonlinear differential
equations34,35
The primary aim of this paper is to understand how the
electron energy relaxation depends on the copper nanoparticle
size. Figures 5a-c compare the transient transmission signal
of Cu1 and Cu2 under pump pulse energies of 9.5, 19, and 38
nJ. It is clear that the dynamics of electron energy relaxation
are size-dependent, with the shorter lifetime for smaller nano-
particles. The experimental data of ∆T(t)/T is simulated (red
lines in Figures 5a-c) by convoluting the theoretical response
function I(τ) with the instrumental response function R(t - τ)18,38
∂Te
2
∆T(t)
T
Ce(Te)
) κ∇ Te - g(Te - Tl) + A(r,t)
(1)
) I(τ) X R(t - τ) ) ∞ (1 - exp(- τ/τe-e))
∂t
∫
-∞
exp(-τ/τe-ph) exp(-(t - τ)2/τ0 ) dτ (3)
2
and
∂T
l ) g(Te - Tl)
where τe-e and τe-ph are the thermalization times of the electrons
due to e-e scattering and e-ph interactions, respectively. τ0 is
C
(2)
l ∂t

Relaxation and Fluorescence of Cu Nanoparticles
J. Phys. Chem. B, Vol. 110, No. 1, 2006 147
Figure 5. (a-c) Comparison of the transient transmission signal of Cu1 (black circles) and Cu2 (blue triangles) under pump pulse energies of 9.5,
19, and 38 nJ. It is obvious that electron energy relaxation is size-dependent and the lifetime is shorter for smaller nanoparticles. The experimental
data ∆T(t)/T is simulated (red lines in parts a-c) by convoluting the theoretical response function I(τ) with the instrument response function R(t
- τ).
ν meωl2 V0
2
determined by measuring the cross correlation between the pump
3
gC )
κ
Fn
(6)
and the probe at the sample position (180 fs in our experiments).
For Cu1 (Cu2), the lifetimes of τe-ph obtained from simulation
are 0.48 (0.64), 0.70 (0.86), and 0.93 (1.12) ps under pump
pulse energies of 9.5, 19, and 38 nJ, respectively. Extrapolating
the lifetimes measured at different pump powers, we obtained
lifetimes of τe-ph(0) at zero pump power for both Cu1 and Cu2,
which are 0.37 and 0.51 ps, respectively. Using the equation
16π B R
σ
æ0
( )
where κB is Boltzmann’s constant, νF is the Fermi velocity, R
is the radius of the particle, n is the free electron density, me is
the electron mass, ωl is the maximum frequency of the capillary
modes, σ is the surface tension, V0 is the Fermi energy, and æ0
is the work function of the metal. The limiting frequency ωl is
approximately given by29,33
γT0
τ
e-ph(0) )
(4)
gexp
σ
ωl )
3l(l - 1)(l + 2)
(7)
xFR
we find that the experimental e-ph coupling constants gexp for
Cu1 and Cu2 are 7.8 × 1016 and 5.7 × 1016 W m-3 K-1
,
where F is the density of the metal and l is the angular
momentum number corresponding to the shortest possible
surface wave, which is given by the integer part of πR/d, where
d is the lattice parameter. The electron energy relaxation
associated with electron-surface acoustic mode coupling is
given by33,45,55
respectively. Equation 4 assumes that all of the electron energy
relaxation is due to phonon interactions. However in our case
we believe that surface imperfections in colloidal copper
nanoparticles may also contribute to the overall electron energy
relaxation. Equation 4 is modified to not only account for the
electron energy relaxation due to phonon interactions but also
due to surface imperfections. We replaced τe-ph and gexp with
τeR and ReR, where τeR and ReR are the total electron energy
relaxation time and total electron relaxation coupling constant,
respectively.
2
2
ν
κB Fn
R2
me ωD V0
1
gA )
(8)
( ) ( )
16π
F cl æ0
where cl is the longitudinal speed of sound and ωD is the Debye
frequency, with the following parameters:57,58 νF ) 1.57 × 106
m/s, n ) 8.45 × 1028 m-3, F ) 8.93 × 103 K g m-3, d ) 0.256
nm, V0 ) 7.0 eV, and æ0 ) 4.65 eV. Using eqs 6 and 7, we
calculated gC for Cu1 and Cu2, which are summarized in Table
1. From our calculations, the contribution of gA is about two
orders of magnitude smaller than that of gC, so the values of gA
are not reported in Table 1. The total e-ph coupling constant
(Table 1) gtotal ) gbulk + gC for 12 nm and 30 nm diameter
copper nanoparticles were (5.6 ( 0.7) × 1016 and (5.1 ( 0.7)
If the radius of the nanoparticle is comparable or smaller than
the bulk electron mean free path, then surface scattering of the
electrons becomes relevant.29,45,46 In this case, the hot electron
energy relaxation occurs through two different channels: elec-
tron-bulk phonon coupling and electron-surface phonon
coupling. There are two kinds of surface phonon modes,33,45,55
namely, acoustic and capillary surface modes. Since all of these
coupling processes occur simultaneously, the total electron-
phonon coupling, gtotal, is determined by summing of the three
different contributions33
× 1016 W m-3 K-1, respectively, with a reported value of (4.8
36,56
( 0.7) × 1016 W m-3 K-1 for gbulk
.
The size distributions
gtotal ) gbulk + gA + gC
(5)
of the two samples are 15%. Using eqs 5-8, we estimate that
the error bars for e-ph coupling constants because of nonuni-
formity of nanoparticle size are less than 2% and are neglected
in Table 1. By comparing the total e-ph coupling constants
gtotal to the experimental values of the total electron relaxation
coupling constant ReR obtained from the decay of the bleach
spectrum, we see that for both 12 and 30 nm diameter copper
nanoparticles ReR is larger than gtotal. The difference between
ReR and gtotal becomes larger as the diameter of the copper
nanoparticles is decreased from 30 to 12 nm. This suggests that
another size-dependent dissipation channel is needed besides
the electron-surface phonon mode coupling mechanism to
The last two terms, which are size-dependent, stand for the
acoustic and capillary surface mode coupling, respectively.
The value of electron-bulk phonon coupling gbulk in copper
has been reported by Brorson36 and Tien56 to be gbulk ) (4.8 (
0.7) × 1016 W m-3 K-1. The contribution of electron-surface
phonon coupling to the electron energy relaxation in metallic
nanopartilces can be derived with a quantum-kinetic treat-
ment.45,46,55 By considering the Hamiltonian which describes
the interaction of electrons in a spherical potential well of depth
V0, the expression for the coupling constant between the
electrons and the surface capillary modes is33,45,55

148 J. Phys. Chem. B, Vol. 110, No. 1, 2006
Darugar et al.
TABLE 1: Comparison of the Experimentally Determined
Total Electron Relaxation Coupling Constant (reR) for Two
Sizes of the Copper Nanoparticles with the Calculated Total
of bulk copper, suggesting the same electronic origin. This is
due to radiative recombination of the s-p conduction-band
electrons below the Fermi level with the holes in the d bands.
The fluorescence quantum yields of Cu1 and Cu2 are calculated
to be 10-6 and 10-5, respectively, which are greatly enhanced
when compared to the value of 10-10 for the bulk copper metal.
The mechanism for the enhancement of the fluorescence
quantum yield is similar to the mechanism in gold nanorods,61
an LSPR-induced enhancement of the electric fields of the
incoming and the outgoing radiation. The lower fluorescence
quantum yield of Cu1 compared to that of Cu2 suggests more
efficient fluorescence quenching for smaller nanoparticles, which
is probably due to the surface imperfections. This indicates that
the contribution of surface imperfections to the electron energy
relaxation is larger in Cu1 than that in Cu2, which is consistent
with our experimental result. Furthermore, using the numbers
in Table 1, we can estimate the ratios of contribution from bulk
phonons, surface phonons, and surface imperfections to the total
electron energy relaxation, which are 61.6% (84.2%), 10.2%
(5.3%), and 28.2% (10.5%) for 12 nm (30 nm) copper
nanoparticles in ethanol solution.
a
e-ph Coupling Constant gtotal
experimentally
determined
total
calculated
calculated
particle
total electron
electron-surface electron-phonon
diameter relaxation coupling phonon coupling coupling constant
(nm)
constant (ReR)
constant (gC)
gtotal ) gbulk + gC
12
30
bulk
7.8
5.7
4.8 ( 0.7
0.8
0.3
0
5.6 ( 0.7
5.1 ( 0.7
4.8 ( 0.7
a gtotal ) gbulk + gC, assuming that the electron-phonon coupling
within the nanoparticle is the same as that for the bulk.56 The quantities
are given in units of 1016 W m-3 K-1 unless otherwise stated.
In their paper on silver nanoparticles embedded in dielectric
matrices,32 Bigot et al. also included the effect of heat transfer
to the dielectric matrix to interpret the size dependence of the
electron energy relaxation. We think this mechanism does not
effectively contribute to observed size dependence of electron
energy relaxation observed in copper nanoparticles in ethanol
solution. This is because the thermal conductivity of ethanol is
about two orders of magnitude smaller than those of the
dielectric matrix used by Bigot et al. This means that heat
transfer in ethanol will occur on a time scale that is much longer
than that in a dielectric matrix, so its effects on the size-
dependent electron energy relaxation are negligible.
Figure 6. Fluorescence emission spectra of from copper nanoparticles
in ethanol solution synthesized using photochemical reduction. The
quantum yield of the 30 nm nanoparticles was found to be as high as
10-5 and ∼10-6 for 12 nm particles. The lower fluorescence quantum
yield of the 12 nm particles could be due to more surface imperfections
in smaller nanoparticles.
account for the observed difference between ReR and gtotal. One
possible mechanism is electron-defect scattering on surface
imperfections.59 For chemically synthesized nanoparticles, there
are always some imperfections on their surfaces. We believe
that, for the copper nanoparticles used here, the surface
imperfections consist of several different kinds of defects, such
as oxidized copper atoms, uncompensated surface charges, the
capping material-surface atom complex, vacancies, dislocations,
and dangling bonds. It is reasonable to believe that this
phenomenon’s contribution to the total electron energy relax-
ation in nanoparticles is size-dependent because smaller metallic
nanoparticles have more surface imperfections due to their
higher surface energy, larger surface curvature, and larger
surface-to-volume ratio. Also, the tendency for copper nano-
particles to be oxidized could produce surface imperfections,
which are formed more easily in smaller nanoparticles. Surface
imperfections could introduce several new mechanisms for the
electronic relaxation process. First, surface imperfections could
trap free electrons and localize them at the defect sites (traps).
Second, surface imperfections could cause stronger inelastic
scattering than from passivated surfaces. Energy transfer
processes to the defect surface states could also lead to an
increase in the rate of the electron relaxation.
IV. Conclusions
We studied the ultrafast relaxation dynamics of hot electrons
in copper nanoparticles in ethanol solution. The results show
that the temporal behavior of the electron energy relaxation has
clear size dependence. Both the size-dependent electron-surface
phonon coupling mechanisms and the additional mechanisms
involving electron trapping or electron energy transfer to surface
imperfections are used to interpret the experimental results. We
also observed an enhancement of the steady-state fluorescence
by 5 orders of magnitude in copper nanoparticles compared with
the bulk metal. The fluorescence is ascribed to radiative
recombination between electrons in the s-p conduction-band
below the Fermi level with the holes in the d bands. The
observed enhancement is attributed to the localized surface-
plasmon-resonance-induced enhancement of the electric field
of the incoming and outgoing radiation.
Acknowledgment. The authors thank Mr. Christopher Tabor
for his careful reading of the manuscript. This work is supported
by the Division of Material Research of the National Science
Foundation (Grant No. 0138391) and the National Science
FoundationsCNRS (Grant No. INT-0129263).
A more effective nonradiative electronic relaxation in smaller
copper nanoparticles is observed from the study of the quantum
yield of fluorescence of these nanocrystals. In 1969, Mooradian
observed fluorescence from bulk copper metal with an emission
maximum at 600 nm.60 The quantum yield of this fluorescence
was found to be about 10-10. We observe much stronger
fluorescence from copper nanoparicles. Figure 6 shows the
fluorescence spectra of Cu1 and Cu2 with excitation at 337 nm.
The fluorescence bands are observed at 610 nm, close to that
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