Supporting Information. Observation of Nanoscale Cooling Effects by Substrates and the Surrounding

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1 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 , Japan. * 1

2 S1. TEM micrographs of reshaped Au NPs 1 nm Figure S1 TEM images and corresponding size distribution Au NPs (BBI EMGC 1) after reshaping by irradiating 532 nm ns laser pulses (1 Hz, 3 h, ~1 mj cm -2 ). 2

3 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] N/A glycerol [*2] 1.47 Fig S2-a.28 N/A water [*3] 1.33 Fig S2-a.6 N/A borosilicate glass [*4] CaF 2 [*5, *6] sapphire [*7] References: [*1] Owens, J. C. Appl. Opt. 1967, 6, [*2] Setoura K.; Werner D.; Hashimoto S. J. Phys. Chem. C, 212, 116, [*3] Setoura K.; Werner D.; Hashimoto S. J. Phys. Chem. C, 212, 116, [*4] D 263 t glass catalogue, Schott: [*5] CaF 2 catalogue, Corning Inc.: [*6] Rouffignac, E.; Vinegar, H. J. Electric heater. U. S. Patent. 6, 23, (for temperature-dependent thermal conductivity at high temperature) [*7] Sapphire Properties catalogue, roditi: 3

4 Figure S2. (a) (b) glycerol water water glycerol n medium k medium /Wm -1 K T/K T/K (a) Temperature-dependent refractive index curves for superheated water and glycerol at 589nm. (c) 1.2 (b) Temperature-dependent thermal conductivity curves for superheated water and glycerol. 2 (d) 16 k glass /Wm -1 K k CaF2 /Wm -1 K T/K T/K (c) Temperature-dependent thermal conductivity (d) Temperature-dependent thermal conductivity for borosilicate glass. curve for CaF 2. (e) 6 k sapphire /Wm -1 K T/K (e) Temperature-dependent thermal conductivity curve for sapphire. 4

5 S3. Fitting functions for the temperature-dependent refractive indices of water and experimental vs. laser peak power density curves in water/glass, water/caf 2, and water/sapphire. Table S2. Parabolic fitting functions Item Temperature-dependent n water function form: y( x) a 13 n( T ) T b x 4.9 water / glass (Mie calculation) T ) T ( p p water / glass (experimental) ( I).1694 I water / CaF 2 (experimental) ( I ).544 I water / sapphire (experimental) ( I).2 I T p : Au NP temperature / K; I: peak power density / mw m 2 5

6 S4. Calculated spectral peak shift as a function of particle temperature of a 1nm diameter Au NP in various media. Au NP in glass Au NP in air /nm T/K Figure S4-1. Calculated spectral peak shifts as a function of the particle temperature of a 1nm 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 (T p was set to 283 K). 5 air / glass glycerol / glass water / glass /nm Figure S4-2. Calculated spectral peak shifts as a function of the particle temperature of a 1nm 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, 212, 116,

7 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 inside NP with g inside NP without g medium temperature / K distance from NP center / nm Figure S5. Calculated temperature profiles for a 1nm 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), k med =.6 W m -1 K -1, C abs = 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, 211, 84,

8 S6. Experimental and computational laser peak power density-dependent T p on three substrates in glycerol and air. 7 6 (a) glycerol / glass glycerol / CaF 2 glycerol / sapphire 7 6 (b) glycerol / glass glycerol / CaF 2 glycerol / sapphire peak power density / mw m peak power density / mw m -2 (c) (d) 7 air / glass air / CaF 2 air / sapphire 7 air / glass air / CaF 2 air / sapphire peak power density / mw m peak power density / mw m -2 Figure S6. The peak power density vs. T p 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

9 S7. Absorption cross section obtained by Mie theory and numerical simulation, and experimental and calculated scattering spectra of a d=1nm 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, n eff : n eff.42 n. 58 n sub med where n sub is the substrate refractive index and n med 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, n eff : values obtained from this relationship cannot describe properly a system containing air as a medium. Thus we determined experimentally n eff : by n eff.33 n. 77 n sub air For the determination of n eff values, we measured the scattering spectra and SEM images of 1 Au NPs (average diameter: 1 nm) and compared the histograms of spectral peak positions and particle diameters. Table S3 gives the values of n eff determined for various medium/substrate pairs used in this study. Table S3. Empirical n eff for various medium/substrate pairs. n eff air glycerol water glass CaF sapphire Table S4 lists the values of absorption cross section (C abs ) [m 2 ] at the laser excitation wavelength of 488 nm. The values were calculated using Mie theory with n eff given in Table S3. Table S4. The values of C abs for various medium/substrate pairs. C abs [m 2 ] air glycerol water glass CaF sapphire The scattering spectra of a 1-nm Au NP supported on three substrates in three media calculated using Mie theory with n eff were compared with the experimental scattering spectra in Figure S7. A 9

10 good agreement was obtained between the calculated and experimental spectral peak positions and envelopes. We also made a numerical simulation of absorption cross section, C abs 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: 1 nm, surrounding medium: water (n=1.33) wavelength: 488 nm relative permittivity of gold : i at 488 nm obtained from the literature by Otter 2. The simulation result is given in Table S5. Table S5. Absorption cross section, C abs, scattering cross section, C sca, and extinction cross section, C ext of a Au NP (d=1 nm) at 488 nm in water supported on various substrates. Substrate C abs (m 2 ) C sca (m 2 ) C ext (m 2 ) Glass (n=1.52) CaF 2 (n=1.43) Sapphire (n=1.77) 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 C abs 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, 25, 7, Otter, M. Z. Z. Phys. 1961, 161,

11 Figure S7 shows the calculated scattering and absorption cross section spectra of a d=1nm Au NP for various medium/substrate pairs. (a) (b) (c) scattering intensity / arb.unit experimetnal in air / glass Mie(scattering) in air / glass Mie(absorption) in air / glass 4.x x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in air / CaF 2 Mie(scattering) in air / CaF 2 Mie(absorption) in air / CaF 2 4.x x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in air / sapphire Mie(scattering) in air / sapphire Mie(absorption) in air / sapphire 4.x x x x1-14 cross section / m 2.x wavelength / nm.x wavelength / nm.x wavelength / nm (d) (e) (f) scattering intensity / arb.unit experimetnal in glycerol / glass Mie(scattering) in glycerol / glass Mie(absorption) in glycerol / glass 6.x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in glycerol / CaF 2 Mie(scattering) in glycerol / CaF 2 Mie(absorption) in glycerol / CaF 2 6.x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in glycerol / sapphire Mie(scattering) in glycerol / sapphire Mie(absorption) in glycerol / sapphire 6.x x x1-14 cross section / m 2.x wavelength / nm.x wavelength / nm.x wavelength / nm (g) (h) (i) scattering intensity / arb.unit experimetnal in water / glass Mie(scattering) in water / glass Mie(absorption) in water / glass 6.x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in water / CaF 2 Mie(scattering) in water / CaF 2 Mie(absorption) in water / CaF 2 6.x x x1-14 cross section / m 2 scattering intensity / arb.unit experimetnal in water / sapphire Mie(scattering) in water / sapphire Mie(absorption) in water / sapphire 6.x x x1-14 cross section / m 2.x wavelength / nm.x wavelength / nm.x wavelength / nm Figure S7. Experimental scattering spectra (relative intensity) and calculated scattering and absorption cross section spectra of a d=1nm Au NP supported for various medium/substrate systems: (a) in air/glass; (b) in air/caf 2 ; (c) in air/sapphire; (d) in glycerol/glass; (e) in glycerol/caf 2 ; (f) in glycerol/sapphire; (g) in water/glass; (h) in water/caf 2 ; (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, 25, 7,

12 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=1nm sphere. (b) Physics: heat transfer in solids which has heat source: Q [W]. (c) Physical constant: thermal conductivity of Au: k Au. Subdomain 2: (a) Geometry: W L 8 16 [nm] rectangular. (b) Physics: heat transfer in solids with no heat source. (c) Physical constant: thermal conductivity of medium: k med. Subdomain 3: (a) Geometry: W L 6 16 [nm] rectangular. (b) Physics: heat transfer in solids with no heat source. (c) Physical constant: thermal conductivity of substrate: k sub. Boundary Conditions: Dashed red lines in Figure S1 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

13 S9. Surface roughness of glass, CaF 2, and sapphire substrates. (a) (b) (c) height / nm 2-2 height / nm 2-2 height / nm distance / nm distance / nm distance / nm Figure S9. Surface roughness of substrates: borosilicate glass (a), CaF 2 (b) and sapphire (c) measured by Atomic Force Microscopy (AFM). Nano Wizard II (JPK Instruments) was employed for the measurement (cantilever: Olympus, OMCL-AC24, radius of curvature: 7 nm, spring constant: 2 N m -1 ). Table S6. Surface roughness indices for the three substrates. glass CaF 2 sapphire Average Roughness: R a / pm RMS Roughness: R q / pm Peak-to-Valley Roughness: R t / nm AFM data were processed on a JPK SPM data processing software to obtain the surface roughness values given above. 13

14 S1. 2-D temperature distribution and peak power density dependent T p for a d=1nm Au NP immersed in water on a CaF 2 substrate. Figure S D temperature distribution for a d = 1 nm Au NP in water/caf 2 for the particle-substrate separation of +.3 nm (laser power density: I = 12.9 mw m -2, T p = 395 K). 7 6 water / CaF 2 experimental separated point contact embedded peak power density / mw m -2 Figure S1-2. Computational particle temperature as a function of laser peak power density in water / CaF 2 for three particle-substrate separation: separated (+.3 nm), point contact ( nm), partially embedded (.3 nm). For comparison, experimental data points were also shown. 14

15 S11. 2-D temperature distribution and peak power density dependent T p for a d=1nm Au NP immersed in glycerol on glass, CaF 2, and sapphire substrates. (a) (b) (c) Figure S D temperature distributions for systems with.3nm separated Au NP (1 nm) substrate surfaces: (a) glycerol/glass, I = 2.4 mw m 2 (T p = 392 K), (b) glycerol/caf 2, I = 1.2 mw m 2 (T p = 395 K), (c) glycerol/sapphire, I = 16.6 mw m 2 (T p = 395 K). (a) (b) (c) (a) glycerol / glass experimental separated point contact embedded (b) glycerol / CaF 2 experimetnal separated point contact embedded (c) glycerol / sapphire experimetnal separated point contact embedded peak power density / mw m peak power density / mw m peak power density / mw m -2 Figure S11-2. Computational particle temperature as a function of laser peak power density in glycerol for.3nm particle-substrate separations on three substrates: (a) glycerol/glass, (b) glycerol/caf 2, (c) glycerol/sapphire. 15

16 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 68 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), 42 K in (b), and 86 Kin (c). 16

17 (a) (b) (c) Figure S D temperature distributions for the separation of 1. nm between the Au NP (d = 1 nm) surface and the substrate surface: (a) air/glass, I = 3.1 mw m 2 (T p = 769 K), (b) air/caf 2, I = 9.4 mw m 2 (T p = 1148 K), (c) air/sapphire, I = 6.3 mw m 2 (T p = 86 K). (a) (b) (c) 7 5 (a)air / glass experimental 1.nm separated.3nm separated point contact embedded 7 5 (b)air / CaF 2 experimental 1.nm separated.3nm separated point contact embedded (c)air / sapphire experimental 1.nm separated.3nm separated point contact embedded peak power density / mw m -2 peak power density / mw m 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. nm between the Au NP surface and the substrate surface: (a) air/glass, (b) air/caf 2, (c) air/sapphire. 17

18 S13. 2-D temperature distribution and k eff as a function of k sub for a d=1nm 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=1nm Au NP half-embedded in sapphire substrate and exposed to air, glycerol and water when the laser intensity of I = 28.2 mw m 2 is applied, in air/sapphire (a), glycerol/sapphire (b), and water/sapphire (c). The particle temperatures reached is 361 K in (a), 35 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) (c) 3 air (COMSOL) air ( k ) 3 glycerol (COMSOL) glycerol ( k ) 3 water (COMSOL) water( k ) (a) in air (b) in glycerol (c) in water k eff /Wm -1 K k eff /Wm -1 K k eff /Wm -1 K k /Wm -1 K -1 sub k /Wm -1 K -1 sub k /Wm -1 K -1 sub Figure S13-2. Calculated k eff as a function of k sub for a d=1nm 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 k sub is also shown for comparison. A fairly good agreement between k eff and k are obtained in all the cases. In the calculation, temperature-dependent thermal conductivities of substrates were not considered. 18

19 S14. Experimental Setup and darkfield images of d=1nm Au NPs. Figure S14-1. Experimental Setup (a) (b) Figure S14-2. Two typical darkfield images of d=1nm Au NPs supported on a glass substrate and immersed in water (6X, NA=.7 objective lens): (a) and (b). 19