Substrate-Dependent Temperature Response of Single Gold

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Substrate-Dependent Temperature Response of Single Gold
Supporting Information
Observation of Nanoscale Cooling Effects by Substrates and the Surrounding
Media for Single Gold Nanoparticles under CW-laser Illumination
Kenji Setoura, Yudai Okada, Daniel Werner, Shuichi Hashimoto*
Department of Optical Science and Technology, The University of Tokushima, Tokushima 770-8506,
Japan.
*E-mail: [email protected]
1
S1. TEM micrographs of reshaped Au NPs
100 nm
Figure S1 TEM images and corresponding size distribution Au NPs (BBI EMGC 100) after
reshaping by irradiating 532 nm ns laser pulses (10 Hz, 3 h, ~10 mJ cm-2).
2
S2. Thermophysical and optical properties of media and substrates.
Table S1. Thermophysical and optical constants
material
refractive
temperature coefficient thermal conductivity:
softening
index: n
of n: dn/dT /K-1
k / W m-1 K-1
point / K
air[*1]
1.0
-0.09×10-5
0.024
N/A
glycerol[*2]
1.47
Fig S2-a
0.28
N/A
water[*3]
1.33
Fig S2-a
0.6
N/A
borosilicate glass[*4]
1.52
-1.45×10-5
1.0
1009
CaF2[*5, *6]
1.43
-1.13×10-5
9.72
1073
sapphire[*7]
1.77
-1.3×10-5
42.0
2073
References:
[*1] Owens, J. C. Appl. Opt. 1967, 6, 51-59.
[*2] Setoura K.; Werner D.; Hashimoto S. J. Phys. Chem. C, 2012, 116, 15458−15466.
[*3] Setoura K.; Werner D.; Hashimoto S. J. Phys. Chem. C, 2012, 116, 15458−15466.
[*4] D 263 t glass catalogue, Schott: www.jnsglass.com/pdf/D263_Glass.pdf.
[*5] CaF2 catalogue, Corning Inc.:
www.lightmachinery.com/Materials/H0607_CaF2_Product_Sheet.pdf.
[*6] Rouffignac, E.; Vinegar, H. J. Electric heater. U. S. Patent. 6, 023, 554. 02-08-200.
(for temperature-dependent thermal conductivity at high temperature)
[*7] Sapphire Properties catalogue, roditi: www.roditi.com/SingleCrystal/Sapphire/Properties.html.
3
Figure S2.
(a)
(b)
0.8
kmedium / W m-1 K-1
nmedium
water
glycerol
glycerol
water
1.5
1.4
1.3
1.2
0.7
0.6
0.3
300
400
T/K
0.2
500
300
400
500
T/K
(b) Temperature-dependent thermal conductivity
curves for superheated water and glycerol.
(a) Temperature-dependent refractive index curves
for superheated water and glycerol at 589nm.
(c)
(d)
20
1.2
kCaF2 / W m-1 K-1
kglass / W m-1 K-1
16
1.1
1
12
8
4
0.9
300
400
T/K
0
500
300
400
T/K
500
600
(c) Temperature-dependent thermal conductivity (d) Temperature-dependent thermal conductivity
for borosilicate glass.
curve for CaF2.
(e)
ksapphire / W m-1 K-1
60
40
20
0
300
400
T/K
500
600
(e) Temperature-dependent thermal conductivity curve for sapphire.
4
S3. Fitting functions for the temperature-dependent refractive indices of water and
experimental  vs. laser peak power density curves in water/glass, water/CaF2, and
water/sapphire.
Table S2. Parabolic fitting functions
function form: y ( x)  a  x b
Item
n(T )  1.33  8.87  10 13  T 4.009
Temperature-dependent nwater
water / glass (Mie calculation)
 (T p )  7.53  10 14  T p
water / glass (experimental)
 ( I )  0.1694  I
water / CaF2 (experimental)
1.772
 ( I )  0.0544  I
water / sapphire (experimental)
 ( I )  0.002  I
2
Tp: Au NP temperature / K; I: peak power density / mW m
5
5.105
1.417
2.316
S4. Calculated spectral peak shift as a function of particle temperature of a 100nm diameter
Au NP in various media.
Au NP in glass
Au NP in air
 / nm
0
-0.4
-0.8
-1.2
400
600
T/K
800
1000
Figure S4-1. Calculated spectral peak shifts as a function of the particle temperature of a 100nm
diameter Au NP exposed to air and immobilized in glass. In this calculation, both media are
assumed to have uniform temperature distributions and only the spectral shifts caused by the
refractive index reduction in the media were considered (Tp was set to 283 K).
air / glass
glycerol / glass
water / glass
 / nm
5
0
-5
-10
-15
300
400
500
600
Tp / K
Figure S4-2. Calculated spectral peak shifts as a function of the particle temperature of a 100nm
diameter Au NP supported on a glass substrate in air, glycerol and water (effective medium
refractive index at room temperature: air/glass: 1.12, glycerol/glass: 1.47, water/glass: 1.41).
Ref.: Setoura K.; Werner D.; Hashimoto S. J. Phys. Chem. C, 2012, 116, 15458−15466.
6
S5. Temperature profile: T(r) when the finite interface resistivity was included or excluded
from the CW laser heating of a Au NP in a homogeneous medium.
500
inside NP with g
inside NP without g
medium
temperature / K
450
400
350
300
0
40
80
120
160
distance from NP center / nm
200
Figure S5. Calculated temperature profiles for a 100nm diameter Au NP in water. The temperature
gap between inside and outside the particle arises when the finite interface resistivity, g was
considered. This gap does not result when g is ignored. The profiles inside the NP without g and
medium are calculated using equation 3. The equation for inside the NP taking g into consideration
was taken from the literature.1 Parameters for all profiles were determined at the peak power density
of 3.1 mW m-2 (excitation wavelength: 488nm), kmed = 0.60 W m-1 K-1, Cabs = 1.79  10-14 m-2. For
steady-state heating, g introduced a slight temperature gap between inside and outside the NP. Note
that the medium temperature profile is always independent of g.
Reference:
1. Baffou, G.; Rigneault, H. Phys. Rev. B, 2011, 84, 035415.
7
S6. Experimental and computational laser peak power density-dependent Tp on three
substrates in glycerol and air.
(a)
(b)
700
700
600
glycerol / sapphire
600
glycerol / sapphire
Tp / K
Tp / K
glycerol / glass
glycerol / CaF2
glycerol / glass
glycerol / CaF2
500
400
500
400
300
300
0
5
10
15
20
25
0
peak power density / mW m-2
5
10
15
20
25
peak power density / mWm-2
(c)
(d)
air / glass
air / CaF2
air / sapphire
700
air / glass
air / CaF2
air / sapphire
700
Tp / K
Tp / K
600
500
500
400
300
300
0
2
4
6
8
10
0
peak power density / mW m-2
5
10
15
20
25
peak power density / mWm-2
Figure S6. The peak power density vs. Tp estimated from experimental laser power-dependent 
(a) and (c), in comparison with the same relationship obtained by calculation in terms of equation 3.
(a) and (b) for three substrates in glycerol; (c) and (d) in air.
8
S7. Absorption cross section obtained by Mie theory and numerical simulation, and
experimental and calculated scattering spectra of a d=100nm Au NP.
The calculation of absorption and scattering cross section spectra of a single Au NP supported on a
substrate and exposed to a media theory was carried out by applying Mie using the effective
medium refractive index, neff:
neff  0.42  n sub  0.58  nmed
where nsub is the substrate refractive index and nmed is the medium refractive index.1 The spectra
calculated in this way well-reproduced the experimental single particle spectra. Because of a large
disparity in the refractive indices, neff: values obtained from this relationship cannot describe
properly a system containing air as a medium. Thus we determined experimentally neff: by
neff  0.33  n sub  0.77  nair
For the determination of neff values, we measured the scattering spectra and SEM images of 100 Au
NPs (average diameter: 100 nm) and compared the histograms of spectral peak positions and
particle diameters.
Table S3 gives the values of neff determined for various medium/substrate pairs used in this
study.
Table S3. Empirical neff for various medium/substrate pairs.
air
glycerol
water
glass
1.12
1.49
1.41
CaF2
sapphire
1.08
1.45
1.37
1.20
1.57
1.49
neff
2
Table S4 lists the values of absorption cross section (Cabs) [m ] at the laser excitation
wavelength of 488 nm. The values were calculated using Mie theory with neff given in Table S3.
Table S4. The values of Cabs for various medium/substrate pairs.
Cabs [m2]
air
glycerol
14
1.49  10
water
14
1.59  10 14
glass
1.87  10
CaF2
sapphire
1.85  10 14
1.54  10 14
1.59  10 14
1.75  10 14
1.46  10 14
1.54  10 14
The scattering spectra of a 100-nm Au NP supported on three substrates in three media calculated
using Mie theory with neff were compared with the experimental scattering spectra in Figure S7. A
9
good agreement was obtained between the calculated and experimental spectral peak positions and
envelopes.
We also made a numerical simulation of absorption cross section, Cabs for a single gold
nanoparticle supported on various substrates by using COMSOL Multiphysics v.4.3b to evaluate the
adequacy of Mie calculation.
Simulation parameters are as follows:
Polarization of incident light: Linear polarized light (plane wave)
particle diameter: 100 nm,
surrounding medium: water (n=1.33)
wavelength: 488 nm
relative permittivity of gold : -1.86+3.67i at 488 nm obtained from the literature by Otter2.
The simulation result is given in Table S5.
Table S5. Absorption cross section, Cabs, scattering cross section, Csca, and extinction cross section,
Cext of a Au NP (d=100 nm) at 488 nm in water supported on various substrates.
Substrate
Cabs (m2)
Csca (m2)
Cext (m2)
Glass (n=1.52)
1.83  10-14
6.35  10-15
2.46  10-14
CaF2 (n=1.43)
1.88  10-14
6.12  10-15
2.49  10-14
Sapphire (n=1.77)
1.77  10-14
6.84  10-15
2.45  10-14
Note that the cross sections show no variation with respect to the incident direction of light, forward
or backward. Based on Mie theory, we obtained the absorption cross sections as shown in Table S4.
The values of Cabs by Mie calculation are in good agreement with those obtained by simulation
using COMSOL given in table S5.
References:
1. Curry, A.; Nusz, G.; Chilkoti, A.;, Wax, A. Opt. Express, 2005, 7, 2668.
2. Otter, M. Z. Z. Phys. 1961, 161, 539.
10
Figure S7 shows the calculated scattering and absorption cross section spectra of a d=100nm Au NP
for various medium/substrate pairs.
(b)
2.0x10-14
1.0x10-14
Mie(scattering) in air / CaF2
Mie(absorption) in air / CaF 2
2.0x10-14
1.0x10-14
600
wavelength / nm
650
0.0x10
700
500
550
6.0x10
4.0x10
-14
-14
2.0x10-14
500
550
600
wavelength / nm
650
0.0x100
700
450
-14
2.0x10-14
600
wavelength / nm
650
0.0x100
700
cross section / m2
scattering intensity / arb.unit
scattering intensity / arb.unit
-14
6.0x10
4.0x10
550
0.0x10
700
0
450
500
550
6.0x10
-14
4.0x10
-14
Mie(absorption) in glycerol / CaF2
2.0x10-14
500
550
450
600
wavelength / nm
650
0.0x100
700
6.0x10
-14
4.0x10
-14
Mie(absorption) in water / CaF2
2.0x10-14
550
0.0x10
650
700
450
experimetnal in glycerol / sapphire
Mie(scattering) in glycerol / sapphire
Mie(absorption) in glycerol / sapphire
6.0x10
-14
4.0x10
-14
2.0x10-14
500
550
600
wavelength / nm
650
0.0x100
700
(i)
experimetnal in water / CaF 2
Mie(scattering) in water / CaF2
500
600
wavelength / nm
(h)
experimetnal in water / glass
Mie(scattering) in water / glass
Mie(absorption) in water / glass
500
1.0x10-14
(f)
experimetnal in glycerol / CaF 2
Mie(scattering) in glycerol / CaF2
(g)
450
650
-14
2.0x10-14
(e)
cross section / m2
scattering intensity / arb.unit
scattering intensity / arb.unit
450
600
wavelength / nm
(d)
experimetnal in glycerol / glass
Mie(scattering) in glycerol / glass
Mie(absorption) in glycerol / glass
3.0x10
0
450
cross section / m2
scattering intensity / arb.unit
550
-14
600
wavelength / nm
650
0.0x100
700
cross section / m2
scattering intensity / arb.unit
500
3.0x10
cross section / m2
-14
cross section / m2
scattering intensity / arb.unit
3.0x10
0
450
4.0x10-14
experimetnal in air / sapphire
Mie(scattering) in air / sapphire
Mie(absorption) in air / sapphire
experimetnal in air / CaF2
cross section / m2
scattering intensity / arb.unit
scattering intensity / arb.unit
experimetnal in air / glass
Mie(scattering) in air / glass
Mie(absorption) in air / glass
4.0x10
-14
cross section / m2
4.0x10
(c)
-14
450
experimetnal in water / sapphire
Mie(scattering) in water / sapphire
Mie(absorption) in water / sapphire
6.0x10
-14
4.0x10
-14
2.0x10-14
500
550
600
wavelength / nm
650
cross section / m2
(a)
0.0x100
700
Figure S7. Experimental scattering spectra (relative intensity) and calculated scattering and
absorption cross section spectra of a d=100nm Au NP supported for various medium/substrate
systems: (a) in air/glass; (b) in air/CaF2; (c) in air/sapphire; (d) in glycerol/glass; (e) in
glycerol/CaF2; (f) in glycerol/sapphire; (g) in water/glass; (h) in water/CaF2; (g) in water/sapphire.
The experimental scattering spectra were normalized with respect to the calculated spectra for
spectral shape comparison.
References:
1. Curry, A.; Nusz, G.; Chilkoti, A.;, Wax, A. Opt. Express, 2005, 7, 2668.
11
S8. Computational procedure using COMSOL Multiphysics.
Figure S8. Geometric configuration used in the calculation by COMSOL
Geometric configuration used in the calculation by COMSOL is shown in Figure S8. The
calculation condition in each subdomain and at the boundary is shown below. For the physical
phenomenon applicable to all subdomains, heat transfer in solids under stationary condition was
chosen.
Subdomain 1:
(a) Geometry: d=100nm sphere. (b) Physics: heat transfer in solids which has heat source: Q [W].
(c) Physical constant: thermal conductivity of Au: kAu.
Subdomain 2:
(a) Geometry: W  L  800  1600 [nm] rectangular.
(b) Physics: heat transfer in solids with no heat source.
(c) Physical constant: thermal conductivity of medium: kmed.
Subdomain 3:
(a) Geometry: W  L  600  1600 [nm] rectangular.
(b) Physics: heat transfer in solids with no heat source.
(c) Physical constant: thermal conductivity of substrate: ksub.
Boundary Conditions:
Dashed red lines in Figure S10 represent a boundary where temperatures and heat fluxes are
continuous (energy conservation). Solid green lines show boundaries of a constant temperature
(ambient temperature, 293[K]).
12
S9. Surface roughness of glass, CaF2, and sapphire substrates.
(b)
(c)
4
4
2
2
2
0
-2
-4
0
height / nm
4
height / nm
height / nm
(a)
0
-2
200
400 600 800 1000
distance / nm
-4
0
0
-2
200
400 600 800 1000
distance / nm
-4
0
200
400 600 800 1000
distance / nm
Figure S9. Surface roughness of substrates: borosilicate glass (a), CaF2 (b) and sapphire (c)
measured by Atomic Force Microscopy (AFM). Nano Wizard II (JPK Instruments) was employed
for the measurement (cantilever: Olympus, OMCL-AC240, radius of curvature: 7 nm, spring
constant: 2 N m-1).
Table S6. Surface roughness indices for the three substrates.
glass
CaF2
sapphire
Average Roughness: Ra / pm
185
148
89
RMS Roughness: Rq / pm
223
189
119
Peak-to-Valley Roughness: Rt / nm
1.1
0.9
0.9
AFM data were processed on a JPK SPM data processing software to obtain the surface roughness
values given above.
13
S10. 2-D temperature distribution and peak power density dependent Tp for a d=100nm Au
NP immersed in water on a CaF2 substrate.
Figure S10-1. 2-D temperature distribution for a d = 100 nm Au NP in water/CaF2 for the
-2
particle-substrate separation of +0.3 nm (laser power density: I = 12.9 mW m , Tp = 395 K).
700
water / CaF2
Tp / K
600
experimental
separated
point contact
embedded
500
400
300
0
5
10
15
20
25
peak power density / mW m-2
Figure S10-2. Computational particle temperature as a function of laser peak power density in
water / CaF2 for three particle-substrate separation: separated (+0.3 nm), point contact (0 nm),
partially embedded (0.3 nm). For comparison, experimental data points were also shown.
14
S11. 2-D temperature distribution and peak power density dependent Tp for a d=100nm Au
NP immersed in glycerol on glass, CaF2, and sapphire substrates.
(a)
(b)
(c)
Figure S11-1. 2-D temperature distributions for systems with 0.3nm separated Au NP (100
2
nm)substrate surfaces: (a) glycerol/glass, I = 2.4 mW m (Tp = 392 K), (b) glycerol/CaF2, I =
2
2
10.2 mW m (Tp = 395 K), (c) glycerol/sapphire, I = 16.6 mW m (Tp = 395 K).
(a)
(b)
700
700
700
(b) glycerol / CaF2
(a) glycerol / glass
experimental
separated
point contact
embedded
400
500
400
300
5
10
15
20
peak power density / mW m-2
25
500
400
300
0
experimetnal
separated
point contact
embedded
600
Tp / K
500
(c) glycerol / sapphire
experimetnal
separated
point contact
embedded
600
Tp / K
600
Tp / K
(c)
300
0
5
10
15
20
peak power density / mW m-2
25
0
5
10
15
20
25
peak power density / mW m-2
Figure S11-2. Computational particle temperature as a function of laser peak power density in
glycerol for 0.3nm particle-substrate separations on three substrates: (a) glycerol/glass, (b)
glycerol/CaF2, (c) glycerol/sapphire.
15
S12. 2-D temperature distributions dependent on the particle-substrate separation in air on
glass and CaF2 substrates.
(a)
(b)
(c)
Figure S12-1. Calculated 2-D temperature distributions dependent on the particle-substrate
2
separation in air on glass substrate when the laser intensity of I = 3.1 mW m is applied, for point
contact (a), partially embedded (b), and separated (c) cases. The particle temperatures reached is
625 K in (a), 591 K in (b), and 680 K in (c).
(a)
(b)
(c)
Figure S12-2. Calculated 2-D temperature distributions dependent on the particle-substrate
2
separation in air on CaF2 substrate when the laser intensity of I = 9.4 mW m is applied, for point
contact (a), partially embedded (b), and separated (c) cases. The particle temperatures reached is
433 K in (a), 402 K in (b), and 806 Kin (c).
16
(a)
(b)
(c)
Figure S12-3. 2-D temperature distributions for the separation of 1.0 nm between the Au NP (d =
2
100 nm) surface and the substrate surface: (a) air/glass, I = 3.1 mW m (Tp = 769 K), (b) air/CaF2,
2
2
I = 9.4 mW m (Tp = 1148 K), (c) air/sapphire, I = 6.3 mW m (Tp = 806 K).
(a)
(b)
experimental
1.0nm separated
0.3nm separated
point contact
embedded
700
Tp / K
Tp / K
700
600
(b)air / CaF2
experimental
1.0nm separated
0.3nm separated
point contact
embedded
500
500
0
2
4
6
peak power density / mW m-2
8
experimental
1.0nm separated
0.3nm separated
point contact
embedded
500
400
300
300
300
(c)air / sapphire
Tp / K
(a)air / glass
(c)
0
4
8
12
16
peak power density / mW m-2
0
5
10
15
20
peak power density / mW m-2
Figure S12-4. Computational particle temperature as a function of laser peak power density in
glycerol for the separation of 1.0 nm between the Au NP surface and the substrate surface: (a)
air/glass, (b) air/CaF2, (c) air/sapphire.
17
S13. 2-D temperature distribution and keff as a function of ksub for a d=100nm Au NP
half-embedded in sapphire substrate exposed to air, glycerol and water.
(a)
(b)
(c)
Figure S13-1. Calculated 2-D temperature distributions for a d=100nm Au NP half-embedded in
sapphire substrate and exposed to air, glycerol and water when the laser intensity of I = 28.2 mW
2
m is applied, in air/sapphire (a), glycerol/sapphire (b), and water/sapphire (c). The particle
temperatures reached is 361 K in (a), 350 K in (b), and 353 K in (c). Remarkably, concentric
temperature distributions were obtained in all cases regardless of a large disparity in the thermal
conductivities of the substrate and the medium. In the calculation, temperature-dependent thermal
conductivities of substrates were not considered.
(a)
(b)
air (COMSOL)
air ( k )
30
glycerol (COMSOL)
glycerol ( k )
30
10
10
30
20
30
ksub / W m-1 K-1
40
50
(c) in water
20
keff / W m-1K-1
20
0
water (COMSOL)
water( k )
(b) in glycerol
keff / W m-1K-1
keff / W m-1K-1
(a) in air
0
(c)
10
0
0
10
20
30
ksub / W m-1 K-1
40
50
20
10
0
0
10
20
30
40
50
ksub / W m-1 K-1
Figure S13-2. Calculated keff as a function of ksub for a d=100nm Au NP half-embedded in sapphire
substrate exposed to air (a), glycerol (b) and water (c). Calculated k using equation 1 and 2 as a
function of ksub is also shown for comparison. A fairly good agreement between keff and k are
obtained in all the cases. In the calculation, temperature-dependent thermal conductivities of
substrates were not considered.
18
S14.
Experimental Setup and darkfield images of d=100nm Au NPs.
Figure S14-1. Experimental Setup
(a)
(b)
Figure S14-2. Two typical darkfield images of d=100nm Au NPs supported on a glass substrate and
immersed in water (60X, NA=0.70 objective lens): (a) and (b).
19

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