Picosecond self-induced thermal lensing from colloidal silver nanodisks

Article abstract of DOI:10.1021/jp049943z

The optical and nonradiative relaxation dynamics of 5 nm thick silver nanodisks with a 25 nm diameter have been investigated in an organic solvent by continuous wave (cw) and femtosecond pump - probe time-resolved spectroscopies. Several surface plasmon absorption bands are observed due to the disk shape of these particles. In the time-resolved experiments, the time dependence of the bleach resulting from femtosecond pulsed excitation is studied. On the 1-3 ps time scale, a decay resulting from electron - phonon relaxation is observed. On a longer time scale (>20 ps), a rise rather than a further decay of the bleach intensity is observed. This is shown to result from the formation of a thermal lens due to the induced thermal gradients produced from heating the organic solvent by the phonon - phonon relaxation processes of the photoexcited nanodisks.

Full text of DOI:10.1021/jp049943z

5230
J. Phys. Chem. B 2004, 108, 5230-5234
Picosecond Self-Induced Thermal Lensing from Colloidal Silver Nanodisks
†
Mathieu Maillard and Marie-Paule Pileni*
Laboratoire des Materiaux Mesoscopiques et Nanom e´ triques, BP 52, UniVersit e´ Pierre et Marie Curie, 4 Place
Jussieu, 75005 Paris, France
‡
Stephan Link and Mostafa A. El-Sayed*
Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, 770 State
Street, Atlanta, Georgia 30332-0400
ReceiVed: January 6, 2004; In Final Form: February 20, 2004
The optical and nonradiative relaxation dynamics of 5 nm thick silver nanodisks with a 25 nm diameter have
been investigated in an organic solvent by continuous wave (cw) and femtosecond pump-probe time-resolved
spectroscopies. Several surface plasmon absorption bands are observed due to the disk shape of these particles.
In the time-resolved experiments, the time dependence of the bleach resulting from femtosecond pulsed
excitation is studied. On the 1-3 ps time scale, a decay resulting from electron-phonon relaxation is observed.
On a longer time scale (>20 ps), a rise rather than a further decay of the bleach intensity is observed. This
is shown to result from the formation of a thermal lens due to the induced thermal gradients produced from
heating the organic solvent by the phonon-phonon relaxation processes of the photoexcited nanodisks.
Introduction
the rate of phonon-phonon relaxation processes that cool off
the nanoparticles could be limited by the heat diffusion away
from the surrounding medium (through the capping material
and immediate surrounding solvent). In this case, the long decay
time would be a measure of the surrounding solvent cooling,
which then controls the overall rate of the nanoparticle cooling.
Research concerning nanomaterials is at the interface of a
variety of scientific domains as different as materials chemistry,
quantum physics or optical physics. Shape controlled nanopar-
ticle synthesis is of great interest for numerous groups because
it is important in understanding and controlling their particular
physical properties. This has been carried out for a wide variety
In the present work, we present a time-resolved study of the
thermal relaxation dynamics of disk-shaped silver nanoparticles
encapsulated in micelles using femtosecond pulse excitation.
Silver disk-shaped particles have been synthesized by a new
chemical method that enables one to synthesize particles
of particle shapes such as spheres, nanorods,2 cubes, or
1
3
triangles.4 A wide variety of physical methods have been
developed to characterize them and determine their properties
as a function of shape. In the field of time-resolved spectroscopy,
the nanoparticle electronic confinement as well as electron-
14,15
differing in their size at constant aspect ratio.
The disk shape
induces a large modification of the optical properties by splitting
the plasmon resonance. By probing the bleach recovery of the
surface plasmon resonance after laser excitation, we can follow
the electron-phonon relaxation of an excited metal nanoparticle,
which is on the order of a few picoseconds. After the initial
bleach recovery we observe, however, an increase in the bleach
intensity on a much longer time scale (>20 ps). We attribute
this effect to the creation of a thermal lens induced by the heat
transfer from the hot nanoparticles to the surrounding medium.
This gives additional information on the energy transfer
processes involved between the particles and the medium.
phonon coupling or thermal and acoustic relaxation have been
studied.5-8 Most of the time-resolved studies have focused on
the size and shape dependence of the electron-phonon relax-
ation trying to understand how the electron-phonon coupling
changes when the size of the particles is reduced. Recently, the
question of thermal energy transfer between the excited nano-
particles and the surrounding medium was addressed in several
studies.9-12
Thermal equilibration between the lattice and the
surrounding medium becomes especially important for higher
1
3
laser excitation powers. In the case of gold nanorods, using
higher excitation densities, a shape transformation of the gold
nanorods in aqueous solution into spherical particles was
observed. The time scales involved and the efficiencies of the
laser-induced shape transformation should be highly influenced
by the thermal heat loss of the particles following excitation.
The cooling dynamics of the lattice is therefore an important
but also much less understood part of the electron dynamics in
The thermal lens effect has widely been used to probe the
nonradiative relaxation of excited states in molecules.1
6,17
In
analogy, the cooling of the excited metal nanoparticles also
involves nonradiative heat loss, which can be followed by
thermal lens spectroscopy. Recently, imaging using the thermal
lens effect has been demonstrated as an important new method
because it allows the imaging of subwavelength objects with a
1
0-12
small nanoparticles. In fact, it has been pointed out that
1
8,19
far field technique.
*
Corresponding authors. E-mail: M.P.P., pileni@sri.jussieu.fr; M.A.E.,
mostafa.el-sayed@chemistry.gatech.edu..
Experimental Section
†
Current address: Department of Chemistry, Columbia University, 3000
Broadway, New York, NY 10027.
Current address: School of Chemistry and Biochemistry, University
of Texas at Austin, Austin, TX 78712.
‡
Silver Nanodisks Synthesis. Silver bis(2-ethylhexyl)sulfo-
succinate, Ag(AOT), is made as described previously.20 Col-
1
0.1021/jp049943z CCC: $27.50 © 2004 American Chemical Society
Published on Web 03/27/2004

Thermal Lensing from Colloidal Silver Nanodisks
J. Phys. Chem. B, Vol. 108, No. 17, 2004 5231
from the spheres and nanodisks.14 The absorption band centered
at 420 nm is mainly due to the spheres. Similar to gold nanorods
for which the surface plasmon resonance splits into two modes,8
the surface plasmon resonance for silver nanodisks also strongly
depends on the particle shape and size. The high-energy plasmon
resonance of the silver disks, located at 350 nm, corresponds
to the nanodisk transverse plasmon mode. The low-energy one,
located at 500 nm, is attributed to the nanodisk longitudinal
surface plasmon resonance.
Isooctane solutions of nanodisks are studied by femtosecond
time-resolved pump-probe spectroscopy. The wavelength of
the pump is 400 nm whereas the probe can be tuned between
4
50 and 700 nm using a white light continuum to probe the
entire spectrum of the nanodisks. For the dynamics studies, the
wavelength of the probe was set to coincide with the longitudinal
nanodisk surface plasmon absorption. After femtosecond laser
excitation (∼100 fs), the particle electronic temperature is
increased above that of the lattice of the particles. It has been
Figure 1. Continuous wave (cw) absorption spectrum of a solution of
silver nanodisks. The strong band at 420 nm is due to spheres whereas
the shoulder at 350 nm and the strong band at 500 nm are due to the
transverse and longitudinal surface plasmon resonance of the nanodisks
having a diameter of 25 nm with a thickness of 5 nm.
5
shown for spherical silver particles that the surface plasmon
resonance is red shifted and broadened at higher electronic
temperatures. For this reason, if the probe wavelength is below
the plasmon resonance, it can be observed as a transient bleach.
Conversely, above the plasmon resonance, it can be observed
as an increase in absorption. The transient absorption spectrum
of silver nanodisks after 400 nm excitation is shown in the inset
of Figure 2A. The spectrum was recorded 850 fs after excitation
just before a complete temperature equilibrium between the
electrons and lattice is reached. The spectrum exhibits the
expected bleach and absorption for the longitudinal surface
plasmon resonance at 500 nm. The main part of Figure 2A
shows the absorption before and 850 fs after excitation whereas
the inset is the difference spectrum.
loidal silver particles are obtained by mixing two solutions.14
The first one is a reverse micelle solution made of 60% 0.1 M
Ag(AOT) and 40% 0.1 M Na(AOT) solubilized in isooctane.
The water molar ratio, w ) [H2O]/[AOT], is kept at 2. The
second one is 0.1 M Na(AOT) in isooctane, with water replaced
by hydrazine (N2H4). The overall hydrazine concentration varies
from 0.5 to 1.66 M and the molar ratio y ) [N2H4]/[AOT], is
changed from 5 to 16.6. After the hydrazine is added, the
solution is stirred for 20 min and becomes opalescent because
of a phase transition as the reverse micelles are no longer
formed. The two solutions are then mixed together and a dark
color quickly appears. The solution is then diluted 100 times in
A thermal equilibrium between the initially excited electrons
and the lattice is reached as a result of electron-phonon
relaxation processes in a few picoseconds for most metal
0
.1 M Na(AOT) solution and ultrasonicated for 10 min.
5-8
nanoparticles.
This can be measured by probing the bleach
Dodecanethiol is then added (20 µL/mL). After 2 h the solution
is centrifuged, the supernatant solution is removed and the
particles are dispersed in a 0.1 M Na(AOT) solution in isooctane.
recovery dynamics at 480 nm as a function of delay time
between the pump and probe pulses and is shown in Figure
3
A. The bleach recovery is dominated by a fast decay
11
Time-Resolved Experiments. Transient absorption studies
were performed using an amplified Ti:Sapphire laser system
Clark CPA 1000). The second harmonic of the 800 nm
component ascribed to the electron-phonon coupling. This fast
-t/τ
component can be fitted to an exponential decay e ph where
(
τph ) 1.8 ps corresponding to the electron-phonon relaxation
fundamental was used as excitation and a white light continuum
probe beam was generated by focusing a small part of the
fundamental beam into a sapphire window. The beam was split
into two parts and used for signal and reference. The signal
beam is overlapped with the pump beam after focusing and is
then collected behind the sample and focused onto the entrance
of a fiber optic cable connected to the monochromator/
spectrograph. The pump beam was mechanically chopped and
the differential transmission signal was recorded using a pair
of Si photodiodes (Thorlab) and a lock-in amplifier (Stanford
Research Systems). For spectral measurements a liquid nitrogen
cooled CCD camera (Princeton Instruments) in combination with
a spectrograph were used.
time (see Figure 3A). This is comparable to the values observed
5,8
for the silver and gold spheres as well as rods. This confirms
8
the previous conclusion that the electron-phonon relaxation
in gold and silver is shape independent for particles larger than
about 10 nm.
Thermal relaxation of the particle lattice, which transfers the
excitation energy to the surrounding medium, is the final
relaxation of the hot metal nanoparticles. Often a second longer
decay component of the plasmon band bleach is observed on
6
-8
the few hundred picosecond time scale,
which has been
attributed to the time it takes the heat to exchange between the
particle and the surrounding medium and the solvent to reach
1
1,12
thermal equilibrium. However, some studies
suggest that
the local energy exchange between the nanoparticles and the
solvent molecules surrounding the particles can occur on a
similar time scale as the electron-phonon relaxation. The long
decay component is thus mainly due to the heat transfer away
from the medium immediately surrounding the particle surface.
In general, the amplitude of the second component increases
Results and Discussion
The synthesis of silver nanodisks described above produces
a mixture of disk-shaped particles as well as spheres as
impurities. As observed by a transmission electron microscope
(TEM), spherical particles have been estimated as 30% in
6
-8
volume. The absorption spectrum of a solution containing disks
and spheres is shown in Figure 1 and exhibits mainly three
absorption bands attributed to the surface plasmon resonance
with increasing excitation power.
In the case of the silver
nanodisks in isooctane solution, however, a very different
behavior is observed at longer delay times. Figure 3B shows

5232 J. Phys. Chem. B, Vol. 108, No. 17, 2004
Maillard et al.
Figure 2. Examining the shape of the transient absorption of the
nanodisk at different time delays after laser excitation. (A) cw (dashed
line) and transient (solid line) absorption spectra of silver nanodisks at
a delay time of ∆t ) 0.85 ps and pump energy of 0.17 µJ per pulse at
4
00 nm. The inset shows the difference spectrum. The spectral shape
Figure 3. (A) Transient absorption dynamics recorded as a function
of time delay between 400 nm pump and 480 nm probe pulses. The
pump energy is 0.17 µJ. The fast decay dynamics can be fitted to a
monoexponential decay with a decay time τph ) 1.8 ps. This bleach
relaxation corresponds to the thermal equilibration between the electrons
and the lattice (electron-phonon relaxation). (B) Transient absorption
dynamics recorded for different excitation energies (λpump ) 400 nm;
of the transient absorption spectrum is caused by a shift and a
broadening of the plasmon resonance due to a higher electron
temperature. (B) cw (dashed line) and transient (solid line) absorption
spectra of silver nanodisks at a time delay of ∆t ) 100 ps. The pump
energy is 0.17 µJ per pulse. The inset shows the difference spectrum.
In comparison to the early delay time, the spectrum reveals a constant
decrease of the absorption intensity but retains its band shape.
λ
probe ) 480 nm) and monitored for longer delay times. The pulse energy
increases for the traces shown from bottom to top (0.19, 0.26, 0.42,
.68, and 1.05 µJ). The increase in the bleach intensity at longer delay
0
the bleach recovery dynamics probed at 480 nm for different
excitation energies (see figure legend). Instead of observing a
second longer bleach decay component, a rise in the bleach
intensity is observed, which increases with increasing delay time
as well as with excitation energy. This rise can be fitted to an
times is attributed to a thermal lensing effect caused by the rapid heat
transfer from the metal nanodisks to the local environment. The data
were fit to the sum of an exponential decay and a rise according to A
-t/τ
-t/τ
2
+
Be
1
+ C(1 - e
) with τ
1
) 1.5 ps and τ ) 40 ps.
2
exponential growth, 1 - e-t/τ
the observed bleach signal can exceed the initial zero-time signal
as seen in Figure 3B). At longer time (t > 100 ps), the signal
with τ2 ) 40 ps. The intensity of
that measured at short delay times. Figure 2B shows that the
transient absorption spectrum recorded 100 ps after excitation
with 400 nm femtosecond laser pulses compares well with the
ground state spectrum of silver nanodisks. The results show that
the transient absorption on this time scale does not significantly
change its band shape or position. The plasmon resonance
decreases in intensity without a noticeable shift or broadening
of the plasmon band. A change of the dielectric constant alone
due to solvent heating can therefore be ruled out as a possible
explanation of the results.
2
(
is found to keep increasing linearly, up to 500 ps, with a slow
characteristic time τ3 ) 5.9 ns.
A similar increase of the plasmon band bleach was previously
6
8
reported for spherical silver as well as gold nanoparticles. For
the silver nanoparticles it was proposed that a temperature
increase of the solvent (water) changes the dielectric constant
of the surrounding medium, which in turn leads to a blue shift
of the plasmon band according to Mie theory. The blue shift
causes an increase in the bleach intensity at later delay times
as it takes time for the energy exchange with the surrounding
medium. To investigate if the signal in our experiment is also
due to a shift in the plasmon band, a transient absorption
spectrum is recorded at long delay times and compared with
6
8
The increase in the bleach intensity could also be attributed
to the beginning of a coherent breathing mode of the metal
nanoparticles after laser heating, as has been shown for spherical
5
,7
silver and gold nanoparticles. However, on the basis of the
size of the particles, an oscillation period of about 8 ps is
expected. In fact, a steady increase of the bleach intensity up

Thermal Lensing from Colloidal Silver Nanodisks
J. Phys. Chem. B, Vol. 108, No. 17, 2004 5233
to 500 ps is observed, which would correspond to a much slower
oscillation frequency.
isooctane is found22 to be 41 times larger than in water. Hence,
this effect should be further amplified in the presence of the
AOT surfactant.
2
1
Another possible explanation of the observed behavior is that
the concentration of nanoparticles in the excitation volume is
decreased due to a volume expansion of the heated area (after
the absorbed laser energy has been transferred to the medium).
Such an expansion would cause the effective nanoparticle
concentration to decrease, which would also mean that the
absorption intensity decreases. Taking into account that isooc-
In the case of metal particles in the size range of tens of
nanometers and above, the temperature gradient generated
around the particle can be large enough to be measured for
18,19
individual particles.
A large number of photons are absorbed
per particle due to the large absorption cross-section of the
surface plasmon resonance. As the relaxation dynamics after
laser excitation are essentially nonradiative, the absorbed photon
energy is transferred into thermal lattice energy of the particle
on the time scale of the electron-phonon coupling, giving rise
to rapid lattice heating. The thermal equilibrium with the
surrounding medium is then reached by a heat transfer between
the particle lattice and its medium. For the silver nanodisks used
in this study and considering the organic solvent and the
presence of surfactants, the heat conductivity mismatch between
the silver particles and the medium induces a large temperature
gradient at the interface. As the medium refractive index depends
on the temperature as dn/dT < 0, each particle behaves as a
divergent lens with a similar behavior as the one described
2
25
tane has a large thermal relaxation time (τth ) R /R ) 6 ns),
thermalization in the nanoparticles surrounding medium is a
slow process and such a dilatation effect is unexpected at early
time delay in organic solvents. Furthermore, the temperature
and volume variation inside the focal volume can be estimated
as ∆T ) E/mcp ) 0.007 K and ∆V/V ) â∆T/T ) 0.007 ×
-
3
-6
1
0
) 7 × 10 for a maximum pulse energy of 1 µJ. Hence,
volume expansion per pulse is very weak compared to the
measured signal and the sample spinning prevents any further
increase from the pulse repetition rate. For these reasons, if not
negligible, the thermal expansion likely explains the slow rise
component at long time delay (∆t > 100 ps).
1
8
above.
The intermediate exponential behavior (5 < t < 100 ps) is
attributed to a thermal lensing effect. Such an effect is often
observed in solutions containing strongly absorbing molecules
with low fluorescence quantum efficiencies. Thermal lensing
Taking into account that the signal is measured on an
ensemble of particle, the role of the geometric interplay between
the different lenses involved is not clear at this point. Neverthe-
less, the observed effect can be related to the intense heating of
the nanoparticles environment. This thermal relaxation can be
described by the following thermodynamic equation9 for
spherical particles:
1
6,21,22
spectroscopy
has in fact been used to study radiationless
transitions in molecules. After irradiation by light, energy
transfer to the solvent occurs by a nonradiative relaxation of
the molecular excited state. Taking into account that a laser
beam has a Gaussian intensity distribution, molecules are not
equally irradiated in the focal volume. Because of that, solvent
heating is not spatially homogeneous and temperature gradients
are induced in the solvent. As the medium refractive index
depends on temperature, a refractive index gradient causes a
transient divergent lens to be formed in the excitation volume.
,24
T2 )
k1R
k ( τ + τ )
r - R
2
x
1
x
2
T +
(T - T ) τ1 erfc
-
2
i
2i
1i
x
Σr
{
(
t)
Σâ
2
R
x
2
r - R
2 R t
â(r - R)
R t
2
r - R
2 R t
This chromatic aberration has two opposite effects depending
erfc
- exp
+ â t erfc
+ â
x
t
2
3
[
(
)
(
)
]
(
)
}
on the sample position compared to the beam focal point. If
the focal point is in front of the sample, the beam is further
dispersed and the signal decreases. On the other hand, if the
focal point is behind the sample, the beam converges and the
measured signal is increased. In our case, the sample is large
compared to the focal volume and the beam is focused inside
the sample. According to Lambert-Beer’s law, more light is
absorbed by particles in the front part of the sample than in the
back part. The temperature rise is therefore higher in the front
of the sample, and the beam should be converging while it
passes through the solution. Then a smaller volume with fewer
nanoparticles would be sampled for the back part of the sample.
Fewer nanoparticles exposed would lead to less absorption
compared to the original beam, which would explain the increase
of the bleach signal. Basically, due to the creation of the thermal
lens inside the sample caused by strong laser excitation by the
pump beam, more light will be transmitted, which is detected
in the pump-probe experiments. Also, as the light is then
collected behind the sample and focused into the entrance of a
fiber optic cable, the small entrance area of the fiber optic cable
can act as a pinhole. This geometric parameter could therefore
contribute to a further increase in transmission for the sample.
x
2
x
2
x
2
2
where Σ ) k1 τ + k2 τ , â ) (k2 - k1)/Σ, τ ) R /R is the
x
1
x
2
relaxation time, R ) k/Fcp is the thermal diffusivity, k is the
25
thermal conductivity, T is the temperature, R is the particle
radius, and r is the distance from the particle. Subscripts 1 and
2
denote the particle and the medium, respectively. T2i and T1i
are the initial temperatures in each medium.
Calculations have been performed for a 20 nm particle and
an initial electronic temperature variation ∆T between 500 and
9
00 K as a function of the time and the distance from the
nanoparticle surface. The relation between the temperature
variation and the laser energy has been estimated taking into
account the absorption of the silver nanodisk solution and its
concentration. The silver concentration is measured using
Lambert-Beer’s law at 250 nm: OD250 ) ꢀ250lc where ꢀ250 )
-1
-1
1
6 400 L mol cm at λ ) 250 nm is the extinction coefficient,
l ) 0.2 cm is the optical path length and OD250 ) 0.6 is the
optical density in the present experiment. Hence the silver
-9
-1
concentration is found to be CAg ) 1.27 × 10 mol L or C
14
)
7.6 × 10 particles per liter (making use of the average
particle size). Such a calculation is possible in the case of silver
because the absorption in the UV range is due to interband
transitions which do not depend on the particle size and shape.
The change in the measured signal is usually found to be
2
1,22
proportional to the index gradient in the solution.
The
-
7
thermal lensing effect is therefore enhanced in organic solvents
Assuming a focal volume of Vf ) 10 L, the energy absorbed
per particle, Ep, is estimated by Ep ) Et(1 - e
-
OD
and/or in surfactant solutions because their refractive indices
)/CVf ) 7.56
are very sensitive to temperature changes.2
1,22
As an example,
× 10 Et, where Et is the laser energy. The temperature variation
-9
the thermal lensing signal of excited 9-nitroanthracene in
is then equal to ∆T ) Ep/mcp ) 1262Et with Et in microjoules

5234 J. Phys. Chem. B, Vol. 108, No. 17, 2004
Maillard et al.
particle size and shape and the role of different solvents.
Knowledge of the thermal relaxation in different solvents would
help to understand the laser-induced shape transformations
observed for metal nanoparticles.
Conclusions
Silver nanodisks have been studied by static and ultrafasttime-
resolved pump-probe spectroscopy. The particles exhibit
several surface plasmon resonances related to the particle shape.
By time-resolved spectroscopy a large increase of the bleach
intensity at long delay times (>20 ps) after femtosecond laser
excitation has been observed. This effect is likely to be due to
a thermal lensing phenomenon induced by the fast heat transfer
from the particle to its medium and a strong temperature
dependence of the medium refractive index. This thermal lensing
focuses the monitoring beam resulting in a decrease in the
absorption (i.e., increase in the bleach) intensity.
Figure 4. 4. Variation of the temperature at a distance r ) 100 nm
from a particle of diameter D ) 2R ) 20 nm for different initial electron
temperatures, between ∆T ) 500 and 900 K. An exponential fit to the
calculated temperature dependence shows that the temperature increases
Acknowledgment. We thank the support of the National
Science Foundation (grant No. INT-0129263)sCNRS for an
international cooperative grant.
-
t/τ
2
according to 1 - e
with τ ) 35 ps in qualitative agreement with
2
the experimental results.
-
20
where m ) 2.58 × 10
kg is the particle mass and cp ) 232
References and Notes
-
1
-1
J kg
K
is the specific heat capacity of silver. The distance
(
(
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Figure 4 represents the calculated temperature as a function
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The initial temperatures are related to the experimental pump
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(
)
this time constant is found to be independent of the initial
electronic temperature rise inside the nanoparticle.
(
(
The thermal lens effect (as well as a possible volume
expansion) is most likely enhanced by the presence of spheres.
The spheres absorb only above 450 nm but also contribute to
the temperature increase of the solvent because they have a
strong absorption at the wavelength of the pump pulse. This
might explain why the short time signal, related to the disks
only, is weaker than the long time one related to both shapes.
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depend on the probe wavelength and the plasmon resonance
position. This is clearly observed in Figure 2B where the
transient absorption spectrum exhibits a bleach proportional to
the absorption. The rise time for the bleach at longer delay times
therefore corresponds to the heat transfer between the hot metal
nanoparticles and the surrounding medium, as observed through
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(
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2
(
(
20) Petit, C.; Lixon, P.; Pileni, M. P. J. Phys. Chem. 1993, 97, 12974.
21) Tran, C. D.; Van Fleet, T. A. Anal. Chem. 1988, 60, 182.
(22) Tran, C. D.; Van Fleet, T. A. Anal. Chem. 1988, 60, 2478.
23) Uchiyama, K.; Hibara, A.; Kimura, H.; Sawada, T.; Kitamoro, T.
Jpn. J. Appl. Phys. 2000, 39, 5316.
24) Cooper, F. Int. J. Heat Mass Transfer 1977, 991.
(25) R
(
(
-4
2
-1
-8
2
-1
1
K
) 1.75 × 10 m s , R2 ) 6.71 × 10 m s , k1 ) 428 J
s-
1
m
-1 -1
k2 ) 0.0967 J s
-1 -1 -1
m
K . Tabulated data taken from CRC
Handbook for silver and: Riddick, J. A.; Bunger, W. B.; Sakano, T. K. In
Organic solVents, Physical properties and Methods of Purification.
Techniques of Chemistry; J. Wiley: New York, Chichester, Brisbane, 1986
(for the solvent).