Liquid Plasmonics: Manipulating Surface Plasmon Polaritons via ...
SUPPORTING INFORMATION
Liquid Plasmonics: Manipulating Surface Plasmon Polaritons via Phase Transitions S. R. C. Vivekchand†,‡, Clifford J. Engel†,‡, Steven M. Lubin†, Martin G. Blaber†, Wei Zhou §, Jae Yong Suh†, George C. Schatz† and Teri W. Odom*,†,§ †
Department of Chemistry, §Department of Material Science and Engineering, Northwestern University, Evanston, IL, 60208, United States
‡
These authors contributed equally to the work.
*Corresponding Author; Email: [email protected]
Figure S1. Solid-to-liquid phase transition..…………………………………………….…….S2 Figure S2. Supercooling characteristics of Ga in the grating structure ….…….…….…….S3 Figure S3. Dielectric constants of the liquid and solid Ga …...……………………...………S4 Figure S4. Density of States (DOS) during the DFT-MD simulations ...……………………S5 Effect of thermal expansion of PU on the SPP modes ...……………………….…………….S6 Supporting Information Reference …………………………………………………………..S6
S1
Figure S1. Solid-to-liquid phase transition. Real-time reflectance spectral map recorded at θ = 10° to study the evolution of the (-1) SPP mode during the solid-to-liquid phase transition. Although bulk Ga melts at 29.8 °C, the melting was observed at 28.0 °C. Note that the transition between the solid and liquid phases was gradual.
S2
Figure S2. Supercooling characteristics of Ga in the grating structure. The Ga liquid-to-solid phase transition in the grating structure was affected by supercooling where the Ga freezing point (Tf) depended on the initial holding temperature (TH) of the liquid phase. The behavior we observed was slightly different from what has been observed.S1 Our data is presently limited by the Peltier heating-cooling system, which allows the sample to be cooled to 15 °C.
S3
80
ε’’
60
Liquid Ga (measured) Liquid Ga (theory) Solid Ga (measured) Solid Ga (theory)
40
20
0 -20
ε’
-40 -60 -80 -100 400
500
600
700
800
900
1000
Wavelength (nm)
Figure S3. Dielectric constants of the liquid and solid Ga. The imaginary and the real part of the dielectric constant for liquid and solid Ga obtained from ellipsometry (measured) and by DFT-MD (theory). There was excellent agreement between the experimentally measured and theoretically calculated dielectric constants for liquid Ga.
S4
Solid
4
Liquid
States per eV
Energy (eV)
70
2
EF
0
35
-2 -4 0
0
1
2
3
4
5
Time (ps)
Figure S4. Density of States (DOS) during the DFT-MD simulations. Around 3 ps, melting of the solid Ga is observed which is accompanied by the spreading of the interband transitions over the energy spectrum because of a loss in crystallinity.
S5
Effect of thermal expansion of PU on the SPP modes Thermal expansion of PU can lead to small changes in the lattice spacing, which would also produce small shifts in the wavelength of the SPP resonance. The thermal expansion coefficient of cured PU (Norland 61 optical adhesive) is 250 µm/m per °C. The total expansion in PU for the Ga grating is 6.25 µm (sample size = 1 inch). For grating periodicity of 400 nm, a change of 0.1 nm/°C is expected from thermal expansion of PU. Using the Bragg coupling equation with the dielectric constant of Ga (liquid), we observe a 0.17 nm/°C shift in the (-1) SPP mode at 10°. For example, without considering the different dielectric constants of the solid and liquid Ga, a 10 °C increase in temperature would result in a 1.7 nm red shift. (Note that this estimate does not consider the thermal expansion of Ga (1.2 µm/m per °C) and glass (8.5 µm/m per °C)).
Supporting Information Reference 1. Kofman, R.; Cheyssac, P.; Garrigos, R., “Optical investigation of the solid-liquid transition in gallium”, J. Phys. F: Met. Phys., 1979, 9, 2345-2351.
S6
Liquid Plasmonics: Manipulating Surface Plasmon Polaritons via Phase Transitions S. R. C. Vivekchand†,‡, Clifford J. Engel†,‡, Steven M. Lubin†, Martin G. Blaber†, Wei Zhou §, Jae Yong Suh†, George C. Schatz† and Teri W. Odom*,†,§ †
Department of Chemistry, §Department of Material Science and Engineering, Northwestern University, Evanston, IL, 60208, United States
‡
These authors contributed equally to the work.
*Corresponding Author; Email: [email protected]
Figure S1. Solid-to-liquid phase transition..…………………………………………….…….S2 Figure S2. Supercooling characteristics of Ga in the grating structure ….…….…….…….S3 Figure S3. Dielectric constants of the liquid and solid Ga …...……………………...………S4 Figure S4. Density of States (DOS) during the DFT-MD simulations ...……………………S5 Effect of thermal expansion of PU on the SPP modes ...……………………….…………….S6 Supporting Information Reference …………………………………………………………..S6
S1
Figure S1. Solid-to-liquid phase transition. Real-time reflectance spectral map recorded at θ = 10° to study the evolution of the (-1) SPP mode during the solid-to-liquid phase transition. Although bulk Ga melts at 29.8 °C, the melting was observed at 28.0 °C. Note that the transition between the solid and liquid phases was gradual.
S2
Figure S2. Supercooling characteristics of Ga in the grating structure. The Ga liquid-to-solid phase transition in the grating structure was affected by supercooling where the Ga freezing point (Tf) depended on the initial holding temperature (TH) of the liquid phase. The behavior we observed was slightly different from what has been observed.S1 Our data is presently limited by the Peltier heating-cooling system, which allows the sample to be cooled to 15 °C.
S3
80
ε’’
60
Liquid Ga (measured) Liquid Ga (theory) Solid Ga (measured) Solid Ga (theory)
40
20
0 -20
ε’
-40 -60 -80 -100 400
500
600
700
800
900
1000
Wavelength (nm)
Figure S3. Dielectric constants of the liquid and solid Ga. The imaginary and the real part of the dielectric constant for liquid and solid Ga obtained from ellipsometry (measured) and by DFT-MD (theory). There was excellent agreement between the experimentally measured and theoretically calculated dielectric constants for liquid Ga.
S4
Solid
4
Liquid
States per eV
Energy (eV)
70
2
EF
0
35
-2 -4 0
0
1
2
3
4
5
Time (ps)
Figure S4. Density of States (DOS) during the DFT-MD simulations. Around 3 ps, melting of the solid Ga is observed which is accompanied by the spreading of the interband transitions over the energy spectrum because of a loss in crystallinity.
S5
Effect of thermal expansion of PU on the SPP modes Thermal expansion of PU can lead to small changes in the lattice spacing, which would also produce small shifts in the wavelength of the SPP resonance. The thermal expansion coefficient of cured PU (Norland 61 optical adhesive) is 250 µm/m per °C. The total expansion in PU for the Ga grating is 6.25 µm (sample size = 1 inch). For grating periodicity of 400 nm, a change of 0.1 nm/°C is expected from thermal expansion of PU. Using the Bragg coupling equation with the dielectric constant of Ga (liquid), we observe a 0.17 nm/°C shift in the (-1) SPP mode at 10°. For example, without considering the different dielectric constants of the solid and liquid Ga, a 10 °C increase in temperature would result in a 1.7 nm red shift. (Note that this estimate does not consider the thermal expansion of Ga (1.2 µm/m per °C) and glass (8.5 µm/m per °C)).
Supporting Information Reference 1. Kofman, R.; Cheyssac, P.; Garrigos, R., “Optical investigation of the solid-liquid transition in gallium”, J. Phys. F: Met. Phys., 1979, 9, 2345-2351.
S6
