18 February 2000

Chemical Physics Letters 318 Ž2000. 1–6
www.elsevier.nlrlocatercplett

Ultrafast energy transfer of silver ultrafine particles in aqueous
solutions as investigated by the ultrafast lensing effect technique
Kazuki Ito a , Isao Tsuyumoto b, Akira Harata c , Tsuguo Sawada a,)a

Department of Applied Chemistry, School of Engineering, The UniÕersity of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-8656, Japan
Department of EnÕironmental Systems Engineering, Faculty of Engineering, Kanazawa Institute of Technology, 7-1 Ohgigaoka,
Nonoichi, Ishikawa 921-8501, Japanc
Department of Molecular and Material Sciences, Graduate School of Engineering Sciences, Kyushu UniÕersity, 6-1 Kasugakoen,
Kasuga-shi, Fukuoka, 816-8580, Japanb

Received 1 August 1999; in final form 24 September 1999

Abstract
Ultrafast relaxation dynamics of silver ultrafine particles in aqueous solutions was measured by an ultrafast lensing effectŽULE. method using two types of samples with SDS Žsodium dodecyl sulfate. and without SDS. The fit to the ULE time
evolution required three exponential components: one for the increase and two others for the decrease. The time constants
were estimated as 1, 3, 7 ps for the sample without SDS and as 1, 2, and 23 ps for the sample with SDS. The ultrafast
relaxation dynamics was discussed in connection with the behavior of photoexcited electrons. q 2000 Elsevier Science B.V.
All rights reserved.

1. Introduction
Metallic ultrafine particles Ž1–100 nm in diameter. have received a growing attention because they
exhibit anomalous physical properties which are notobserved in bulk solid phases w1,2x. Among them,silver ultrafine particles have been exclusively investigated in connection with surface-enhanced Raman
spectroscopy ŽSERS., nonlinear optical effect, quantum size effect, etc. The relaxation process in silver
ultrafine particles after photo-excitation can be regarded as the fundamental process of these effects.
Therefore, the observation of the ultrafast relaxation
via energy transfer across the silver-solution inter)
Corresponding author. Fax: q81-3-5841-6037; e-mail:tsuyu@neptune.kanazawa-it.ac.jp

face will provide great insight into the anomalous
physical properties of the ultrafine particles. Moreover, the ultrafast energy transfer across theliquidrsolid interface represents the most interestingand important processes in various fields of physicalchemistry, biophysics and engineering because it isfundamental for understanding photocatalysis, electrode reaction, etc. In the present study we focus on
the ultrafast energy transfer at the interface between
the silver ultrafine particles and the aqueous solutions.
Based on the recent development of femtosecond
pulsed-laser technologies, a number of ultrafast spectroscopic techniques have been developed and haveprovided information on ultrafast processes such asenergy transfer and molecular dynamics w3–7x.
Among them, transient absorption spectroscopy has

0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 4 3 9 - 6

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K. Ito et al.r Chemical Physics Letters 318 (2000) 1–6

been widely used to monitor the transient processes
in solutions after excitation w3x, but it cannot detect
transient species with low concentration because of
its low sensitivity. Fluorescence measurements using
up-conversion techniques have been reported for various luminescence samples w5x, but this techniquecannot be applied to non-luminescent samples. An
optical technique with high sensitivity and high applicability is highly desirable.
We have developed and reported on a number ofphotothermal spectroscopic techniques, which haveadvantages of sensitivity and applicability over theother spectroscopic methods w8–10x. After a preliminary trial to combine the same optical configuration
as that adapted in a thermal lens method with anultrafast pump–probe technique, we have developed
a femtosecond ultrafast lensing effect ŽULE. technique and have successfully investigated ultrafast
nonradiative dynamics of all-trans-b-carotene and
Auramine O in dilute n-hexane solutions w11,12x.
In this work, we performed ULE measurements ofsilver ultrafine particles in aqueous solutions. The
aim of this work is to reveal the process of ultrafast
energy transfer across the interface between silver
ultrafine particles and aqueous solutions. We present
the first measurements of the ultrafast relaxation of
the excited silver ultrafine particles in aqueous solutions.

2. Experimental
2.1. Principle and apparatus
The principle and apparatus have been describedin our previous Letter w11x. A brief outline follows
here based on Fig. 1. The ULE method detects theultrafast change in refractive index induced by apump beam. In some cases, the change in the refractive index can occur before the light energy is transformed into heat. We term this an ‘ultrafast lensing
effect ŽULE.’. There are many possible physicalorigins of ULEs w13,14x. It should be noted that thepresent ULE signal change includes both the real andthe imaginary components of the refractive index.
Distinguishing between the real and the imaginary
components will be possible by getting the ULE
signals with various wavelengths and analyzing themFig. 1. Experimental setup for the ultrafast lensing effect method.
AOM, acousto-optic modulator; DM, dichroic mirror; F, coloredglass filter; SHG, second harmonic generator; HM, half mirror;
BPF, band-pass filter; ADC, analog-to-digital converter; PC, personal computer. The other optical elements are mirrors.

with the Kramers–Kronig relation. This will be anext topic of our research.
The laser system consisted of a mode-locked
Ti:sapphire laser ŽCoherent, Mira 900F. pumped by
an Ar-ion laser ŽCoherent, Innova 310., which produced femtosecond optical pulses with a repetition
rate of 76 MHz, centered at 780 nm. Each pulse had
an energy of 1 nJrpulse and 150 fs duration ŽFWHM.
for the autocorrelation. The output beam was divided
into two by a half mirror. One was used as a probe
beam after passing it through a computer-controlled
optical delay line. The other beam was frequencydoubled to generate a 390 nm pump beam after
being intensity-modulated by an acousto-optic modulator at 1.4 MHz. The pump and probe beams were
coupled with a dichroic mirror, focused by a convex
lens Ž f s 50 mm. and collinearly incident into thesample solution with a 0.5 mm optical path length.
Polarization planes of the pump and probe beams
were set both parallel and vertical to each other inorder to examine the directionality of the energy
transfer. The change in the divergence of the probe
beam was detected as an intensity change at thecenter of the probe beam, which was measured witha small-area avalanche photodiode Ž0.1 mm B.. The
photodiode output was passed through a pre-amplifier and a home-made passive band-pass filter before
being fed into a lock-in amplifier ŽEG & G Princeton

K. Ito et al.r Chemical Physics Letters 318 (2000) 1–6

3

Applied Research, Model 5202. used for sensitive
phase detection.
The fluence of the pump beam was 0.3 mJrcm2 ,and the magnitude of the temperature change wasestimated to be 70 K. These were chosen to avoid
boiling of the solvent. The relative change in intensity at the detector was 10y5 –10y4 .
2.2. Sample preparation
A colloidal silver solution was prepared by reducing silver nitrate ŽAgNO 3 . by sodium borohydrideŽNaBH 4 . in water at 08C w15x. The formation ofultrafine particles Ž; 10 nm. was confirmed by absorption spectra with a UV-visible spectrometerŽJASCO, V-570.. The concentration of the prepared
solution was estimated to be ca. 8 = 10y9 M. In
order to investigate the effect of adsorbate to theenergy transfer across solidrliquid interfaces, wemeasured two kinds of samples: colloidal silver solutions Ž1. without SDS Žsodium dodecyl sulfate. andŽ2. with SDS. In case of preparation of the colloidal
silver solution with SDS Ž2., SDS was added to
NaBH 4 aq Ž2 mM. in advance before reduction of
AgNO 3 . The concentration of SDS in this case was 1
mM. The SDS molecules are adsorbed at the surfaceof the ultrafine silver particles forming a monolayer
with a thickness of ca. 20 nm and stabilize thecolloidal silver solution.

3. Results and discussion
ULE signals of aqueous colloidal silver solutions
with SDS and without SDS are shown in Fig. 2. For
comparison, the signal for pure solvent Žwater. isalso shown. The increase in the signal corresponds tothe photo-induced increase in the refractive index ofsamples and vice versa. Around delay time zero, thesignals show an abrupt rise over the baseline followed by an abrupt fall. After the initial sharp riseand fall, the signals increase again gradually beyond
the baseline and subsequently decrease gradually
toward the baseline.
The initial sharp rise and fall show a symmetricpeak shape, which was fitted to a Gaussian shapewith less than 400 fs of full-width at half maximum

Fig. 2. The raw data of ULE signals for silver colloidal aqueous
solutions. Baselines are shifted for good visibility.

ŽFWHM.. Such a signal was also observed for theblank sample. As we reported previously, the initial
sharp peak is attributable to the optical Kerr effectŽOKE., a third nonlinear effect, of the solvent w11,12x.
The OKE for the solvent increases the refractive
index and the OKE temporal evolution follows across correlation between the pump and probe pulses
because the electronic response time dominating the
sharp signal is on the order of 1 or 10 fs faster thanthe pulse width Ž; 200 fs.. Thus we regard thecenter of the initial sharp peak as delay time zero.
The component around the OKE before the signal
reached its minimum was neglected in the analysisof the ultrafast relaxation of ultrafine particles. Since
the signals of the OKE diminished within several
hundred femtoseconds, they had no influence on thetime constants we determined for ultrafine silver
particles.
The observed ULE signals were analyzed using aleast-square fitting method. The curve was fittedwith a summation of some exponential functions. A
tri-exponential model was found to provide the best
fitting with ULE signals. The curve I Ž t . is formalized as
R Ž t . s C1 exp Ž ytrt 1 . q C2 exp Ž ytrt 2 .
q C3 exp Ž ytrt 3 . .
The first exponential function is for the primary
gradual increase and the other two for the subsequent
decrease. The time constants were estimated as 1, 3,
and 7 ps for the colloidal silver solution without SDS

K. Ito et al.r Chemical Physics Letters 318 (2000) 1–6

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Table 1Results of multi-exponential fitting
Ag colloid

Polarization

Time constants Žps.

Pre-exponential factors

t1

t2

t3

C1

C2

C3

Without SDS

parallelperpendicular

1

3

7

y1
y1

y0.36
q0.45

q0.65
q0.12

With SDS

parallelperpendicular

1

2

23

y1
y1

q0.79
q0.79

q0.06
q0.08

and as 1, 2, 23 ps for the solution with SDS ŽTable
1.. The comparison between the fitted curves and theexperimental ones is shown in Figs. 3 and 4. Interestingly, the second component of the solution without
SDS Ž2 ps. was dependent on the polarization plane,that is, the intensity of the second component changed
by changing the polarization angles between thepump and probe beams from parallel to vertical.
Although the second components Žt 2 . for both samples with SDS and without SDS are in the same time
region Ž2–3 ps., the corresponding phenomena areconsidered to be different from each other. This isbecause the sample without SDS exhibits a depen-

dence on polarization plane whereas that with SDS
shows no dependence.
In the present case, it is considered that therefractive index change mainly reflects energy transfer dynamics from silver ultrafine particles to solvent
molecules. Based on the previous report on thetransient reflectivity measurement of silver thin film
w16x, we assigned t 1 to the relaxation of photoexcited electrons in the particles for both cases withand without SDS. The following relaxations toward
the baseline Žt 2 , t 3 . are considered to reflect theenergy transfer process from silver particles to solvent molecules.

Fig. 3. Comparison between the obtained ULE signals Ždepictedby dots. for silver colloidal aqueous solutions without SDS and
fitted curves Žsolid lines.. The polarization planes of the pump andthe probe beams are Ža. parallel to each other and Žb. perpendicular to each other.

Fig. 4. Comparison between the obtained ULE signals Ždepictedby dots. for silver colloidal aqueous solutions with SDS and fitted
curves Žsolid lines.. The polarization planes of the pump and theprobe beams are Ža. parallel to each other and Žb. perpendicular toeach other.

K. Ito et al.r Chemical Physics Letters 318 (2000) 1–6

Details can be added by analysis based on rateequations describing the energy stream. At first we
assume conventional heat conduction processes inwhich the heat flux is simply proportional to thedifference between the two bodies. In the ultrafast
time region, the temperatures of the electrons and thephonons should be defined separately and each temperature is used instead of the bulk temperature.
Thus, if the thermal conductivity or the time constants estimated from the following equations areinconsistent with the reported conventional values,
the energy transfer process in the present systemcannot be explained by a simple heat conduction. In
such a case, the temperature of photoexcited electrons and novel energy transfer coefficient by themshould be substituted into the equations.
Here we introduce the equations describing theconventional heat conduction. The particles act asheat resources, and heat conduction occurs from theparticles to the solvent. The case with the SDS layer
can be presented as follows. Thermal resistance exists at the interface between the particles and the
SDS layer, and the SDS layer and the solvent. The
rate equations describing this case are formalized as
Q Ž t . s Q0 exp Ž yk 1 t .

rAg CAg VAg

Ž 1.

dTAg Ž t .
dt

s Q Ž t . y h1 SAg TAg Ž t . y TSDS Ž t .

r SDS CSDSVSDS

Ž 2.

dTSDS Ž t .

s h1 SAg TAg Ž t . y TSDS Ž t .
y h 2 SSDS TSDS Ž t .

mined by the heat conduction from the silver particles and that toward the solvent matrix ŽEq. Ž3...
Solving these equations, TAg Ž t . is obtained as thesum of tri-exponential functions.
The case without SDS layer can be presented bymore simple equations.
Q Ž t . s Q0 exp Ž yk 1 t .

rAg CAg VAg

Ž 3.

where Q0 is the energy given to the silver particle bylight, k 1 Žs 1rt 1 . is the rate constant of deactivation of photoexcited electrons, r is the density, C is
the specific heat, V is the volume, T is the temperature, S is the surface area, and h is the thermal
conductivity. QŽ t . corresponds to the heat quantity
generated at the heat sources, i.e., silver particles.
The temperature of the silver particles is determinedby the heat generation by deactivation of photoexcited electrons in the particles and heat conduction
from the silver particles to the SDS layer ŽEq. Ž2...
Similarly, the temperature of the SDS layer is deter-Ž 4.

dTAg Ž t .
dt

s Q Ž t . y h1 SAg TAg Ž t . y Tsol Ž t .

Ž 5.

In this case, TAg Ž t . is obtained as the sum of bi-exponential functions. Thus, if we assume these equations, the ULE relaxation should have two components.
It can be considered that the above Eqs. Ž1. – Ž5.
are consistent with our tri-exponential fitting results,
except for the polarization dependent t 2 of thesample without SDS. Thus, the experimental time
constants from the fitting results can be interpreted
as the time constants of each process in the above
equations, except for t 2 of the sample without SDS.
Based on this interpretation, the observed ultrafast
relaxations were discussed as follows.
First, we discuss the time constants of the colloidal silver particles without SDS. If we assume aconventional heat conduction from silver particles tosolvent, the following equation can be applied to ourexperiment,
h s krR

dt

5

Ž 6.

Here h is the heat conductivity across the sphericalsurface of the silver particle, k is the heat conductivity of water, and R is the radius of the particle.
Based on this equation, the time constant should beover 30 ps. t 2 and t 3 are much faster than this, andthe dependency on the polarization plane of pumpand probe beams cannot be explained by a simple
heat conduction. Thus we assigned t 2 and t 3 toultrafast energy transfer before the energy transforms
into heat. In Eqs. Ž1. – Ž5., we should read the temperature of silver particles ŽTAg . for that of thephotoexcited electrons ŽTele . and the thermal conductivity Ž h1 . for novel energy transfer coefficient. The
polarization plane dependence of the second component Žt 2 : 3 ps. suggests that it accompanies an

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K. Ito et al.r Chemical Physics Letters 318 (2000) 1–6

orientational relaxation of water molecules at thesurface of the particles. In the orientational relaxation process, the relaxation occurs by way of theorientation of water molecules, and the energy of theexcited electrons is transferred to the watermolecules, which are located at the interface. We
consider the orientation of water molecules at thesurface occurs to negate the induced dipole momentof silver particles after excitation. The third component Žt 3 : 7 ps. is considered to correspond to ultrafast energy transfer by photoexcited electrons. In thistransfer process, the electrons which are not in equilibrium with the phonons interact with the interfacialsolvent molecules, and through this interaction theenergy is transferred. The change in the ULE signal
in this case is due to the change in population ofphotoexcited electrons, i.e., the difference in refractive index between the excited state and the groundstate contributes the ULE signal w17x. It is interesting
to note that the photoexcited electrons remain out of
equilibrium for up to 7 ps, because the electrons are
expected to fully relax within 1 ps. Although further
investigation is needed, this long life time of photoexcited electrons may have something to do withthe anomalous phenomena of silver particles such as
SERS. In our previous studies, some experimental
results using transient reflectivity and transient reflecting grating indicated an ultrafast energy relaxation process involving hot electrons at solidrliquidinterfaces w7,18x. These studies also support our present model.
Next, we discuss the time constants of thecolloidal silver particles with SDS. The second component is assigned to ultrafast energy transfer byphotoexcited electrons. The disappearance of the polarization-plane dependency is probably due to theadsorption layer of SDS molecules. The orientationof the water molecules by the induced dipole moment cannot occur because of the layer. The third
component Žt 3 : 23 ps. is consistent with the rate
assuming the conventional heat conduction from silver particles to solvent Ž; 30 ps.. Thus, we concluded that the third component corresponds to heat
conduction from silver particles to the solvent by
way of the adsorption layer of SDS molecules. Suchheat transfer was not observed for the colloidal silver
particles without SDS. This is probably because theadsorption layer of SDS molecules traps the hot

electrons and heat is generated at the adsorption
layer. The direct energy transfer from the hot electrons to the solvent is thus disturbed by the adsorption layer.
In conclusion, ultrafast relaxation dynamics ofsilver ultrafine particles in aqueous solutions wasmeasured using an ultrafast lensing effect ŽULE.
method. The relaxation dynamics was analyzed basedon an energy transfer model from the particles to thesolvent matrix. Our results indicate that ultrafast
energy transfer processes Ž2–7 ps. faster than theconventional heat conduction Ž; 30 ps. exist between the ultrafine silver particles and solvent
molecules. This ultrafast energy transfer is assumed
to be due to hot electrons, which are not in equilibrium with the lattice. We believe that the ULEtechnique will be a powerful tool to investigate thebehavior of hot electrons in solutions.
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