Supporting Information Carbonized Electrospun Nanofiber Sheets for Thermophones Ali E. Aliev 1 *, Sahila Perananthan 2, John P. Ferraris 1,2 1 A. G. MacDiarmid NanoTech Institute, University of Texas at Dallas, Richardson, TX, 75083 2 Department of Chemistry and Biochemistry, University of Texas at Dallas, Richardson, TX, 75083 Corresponding Author * E-mail address for corresponding author: Ali.Aliev@utdallas.edu Contents S1. Electro-spinning setup S2. Processing of 120 µm thick carbonized PAN mat S3. Resistive annealing in vacuum S4. Resistivity of C-PAN nanofibers and sheets S5. Electrical Resistance of C-PBI sheets S6. Self-heating 3-omega method using bridge compensation technique S7. Thermal conductivity of thin PBI sheet S8. Heat Capacity of C-PAN sheets measured using scanning differential calorimeter S9. A single layer of freestanding MWNT sheet as a reference nanostructure for thermoacoustic heaters S10. Temperature measurements on the surface of the TA heater
S-2 S1. Electro-spinning setup Figure S1. The custom build electrospinning setup. The high-voltage power supply (Gamma High Voltage Research Inc.) with the solution flow control system (syringe) is shown on the left top corner. As deposited 25x20 cm 2 large electrospun PAN sheet on aluminum foil. S2. Processing of 120 µm thick carbonized PAN mat (c) Figure S2. Thick electrospun PAN mat carbonized in nitrogen furnace (N 2 /5%H 2 ) for 1 hour at temperature 950 o C. Layered structure of electrospun PAN can be easily split to many layers. (c) The freestanding C-PAN sheet is attached to two copper electrodes by silver paste. S3. Resistive annealing in vacuum 25 o C 700 o C 900 o C 1200 o C 1500 o C Figure S3. The resistive annealing in vacuum (shown for sample C-PAN #4) improves the crystallization within the individual fibers, but increases the inhomogeneity between adjacent current pathway.
S-3 S4. Resistivity of C-PAN nanofibers and sheets. Figure S4. Temperature dependences of resistance of PAN sheets post-annealed at 800 o C and heat treated at 1300 o C with temperature scanned down (open circles) and up (solid circles). Insets show the slope of R(T) and calculated resistance gradients, R' and temperature coefficients of resistivity, α at room temperature. Figure S5. The single freestanding C-PAN fiber attached to two gold-coated copper electrodes using silver paste. The fiber length is 134 µm, the diameter of fiber is 250 nm.
S-4 S5. Electrical Resistance of C-PBI sheets. Figure S6. The temperature dependence of resistance of thin C-PBI sheet post-annealed at 900 o (thin #2), 950 o C (thin #1) and thick C-PBI mat (h ~ 250 µm) post-annealed at 900 o C (thick) was measured using AC bridge option of PPMS (Physical Property Measurement System, Quantum Design Inc.) at f = 1 khz in high vacuum (0.1 mtorr). Figure S7. The slope of R(T) for 250 µm thick and and 2 µm thin (#1) C-PBI sheets. The calculated resistance gradients R' and temperature coefficients of resistivity, α at temperatures close to the room temperature are shown on left bottom corner. S6. Self-heating 3-omega method using bridge compensation technique. The conventional schematic diagram of 3ω measurement setup is shown in Figure S8A. The Agilent 33220A Functional Generator which has spurious 3ω signal below 0.1 µv was used in high impedance mode as a current source. The Stanford Research System SR830 DSP Lock-In Amplifier can digitally pick up the third harmonic signal across the specimen, which contains valuable thermal transport data.
S-5 The sample was suspended in vacuum (Janis Research VPF-475 Cryostat, 0.1 mbar, with liquid nitrogen cooling) on four gold deposited cupper bars. Silver-epoxy glue (H-20) deposited on outward electrodes was cured at 100 o C for 30 min. A schematic diagram of 3-omega method with four-probe connection of freestanding sample, shown in Figure S8A, is perfectly works for thin metallic wires and large diameter carbon fibers. It was emphasized, that four-probe connection has an advantage over other methods because it has no contact resistance problem and much reduced spurious signal. However for suspended carbonized sheet with low thermal coefficient of resistivity (α ~ 2 10-3 K -1 ) the high U 1ω /U 3ω ratio and phase uncertainty of suspended shoulders, suggest another circuitry with advanced pick up the 3ω signal from heat modulated sample: we have changed the circuit diagram from simple four probe reading to compensation method shown in Figure S8B. To avoid the shorting of the 3ω signal by generator output the top resistors in the bridge should be much higher (x10) than the resistance of the sample (constant current mode). Figure S8. Schematic diagram of measurement setup for 3ω method. A. Four-probe signal acquisition. Input signal contains five order higher first harmonic signal, than the measured 3ω signal. B. Compensation method. The four-probe connection is used for electrical resistance measurement and two-probe for the third- harmonic acquisition. The first harmonic signal is balanced with R2 and totally diminished.
S-6 At low frequencies (below 10 Hz) the 3ω voltage is strongly proportional to the third power of applied current (useful feature to confirm 1D heat flow). The inhomogeneity of resistance fluctuations is usually very small for bulk specimen like thin metallic wire or carbon fibers at applied currents up-to 10 ma. The negligible heat capacitance of carbonized sheet and extremely high surface area suggests to work with currents as small as possible to be sensitive by lock-in amplifier, but higher than the spurious 3ω signals coming from the current source or other electronic parts of the circuit. Unlike carbon fibers and metallic wires (low surface area), we found that the measured thermal conductivity of carbonized polymer sheet is highly dependent on the vacuum level. All measurements were done under high vacuum (P < 10-4 Torr) to reduce the radial heat loss through the gas convection. Fig. S9 shows the saturation of 3ω signal below 10-3 atm. To minimize the static radial heat current from the specimen we used a simple heat shield consisting of aluminum foil. This measure reduced the apparent thermal conductivity of MWNT sheet at 295 K to 10%. 90 f = 10 Hz, I 1ω =80 µa 80 U 3ω, µv 70 60 50 40 30 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 Pressure, atm. Figure S9. Vacuum pressure dependence of 3ω signal in C-PAN sheet. The inset shows a picture of suspended C-PAN sheet on four electrode assembly and schematic diagram with two aluminum foil mirrors above and below C-PAN sheet homogenizing the temperature distribution along the specimen and reflecting back part of the radiating heat. After reaching high vacuum level each sample was heat treated by an AC current (10 Hz, 10 µa/tube) for 10 min. The AC current was gradually increased until sample color changed from red to orange and then to orange-white. This procedure had dual purposes: First, it anneals the sample up to
S-7 1000 o C and heals the defects; second, it reduces the oxygen doping, which comes from air. Without high temperature treatment the oxygen reduction in high vacuum at room temperature lasted several days. Moreover, the annealing procedure improves the fiber-metal interface conductivity by up to 20%. This treatment significantly stabilized the sample properties and reproducibility of the measurement. S7. Thermal conductivity of thin PBI sheet Figure S10. The frequency dependence of third-harmonic signal and tangent of phase delay for thin C-PBI sheet (h = 2 µm) post-annealed at 950 o C in helium purged furnace for 1 hour (blue open circles, R 0 = 59.4 kω, R'=237.6 Ω/K, U 0 = 2V), resistively heat-treated to 500 o C (open green circles, R 0 = 20.14 kω, R'=81 Ω/K, U 0 = 2V), and then current treated to 1000 o C (open red circles, R 0 = 20.26 kω, R'=44.8 Ω/K, U 0 = 1.5V). L = 2.4 mm, w = 0.78 mm, T = 295 K. S8. Heat Capacity of C-PAN sheets measured using scanning differential calorimeter. Figure S11. The temperature dependence of heat capacity of C-PAN sheets annealed in N 2 / (5% H 2 ) furnace at 1000 o C for 1 hour (blue line) and then resistively heated in high vacuum to 1500 o C for 10 s (red line) measured using differential scanning calorimeter Universal Analysis 2000 (TA Instruments).
S-8 S9. A single layer of freestanding MWNT sheet as a reference nanostructure for thermoacoustic heaters Figure S12. The sound pressure spectra of a single MWNT sheet measured at a distance of 3 cm in open air at T 0 = 25 o C. The sound pressures are normalized to the applied AC power, P h ~ 0.3 W. The open circles show the p rms (f) response of a 1x1 cm 2 MWNT sheet measured by the low frequency (2 Hz - 20 khz) precision microphone model 7046 (ACO Pacific, Inc.) (red circles) and high frequency microphone B&K 4138-A-015 (6 Hz-140 khz) (blue circles), respectively. The brown open squares show the deviation of p rms (f) from linear dependence for the large (5 x 5 cm 2 ) single layer MWNT sheet shown in. This deviation is caused by destructive interference of signals coming from opposite edges of the large sample when the sound wavelength becomes comparable to the sample dimension. The green dashed line shows the ultimate line predicted by Equation 1 for the case C h = 0. S10. Temperature measurements on the surface of the TA heater. The thermoacoustically created variation in gas pressure (p rms ) is proportional to the temperature variation T a on the surface of a free-standing MWNT sheet: p ~ T a /T 0, where T 0 is the ambient temperature. Therefore, reliable measurement of the temperature on the surface of resistively heated carbon nanotubes is a crucial step for thermal management of a TA device. Direct contact measurement of the temperature on the surface of a free-standing nanofiber sheet is impossible due to nanoscale structure and fragility of the used aerogel sheets. We established a very precise and reliable temperature measurement technique combining measurements of the resistance change of freestanding C-PAN (and MWNT) sheets and comparing this change with preliminary measured R/R 0 on supported sheet, where the temperature can be measured by direct contact with thermocouple (assuming the same temperature coefficient of resistivity for supported and freestanding sheets). The temperature measurement using FLIR T650sc thermo-camera is challenging because it needs correct emissivity, ε of porous carbonized sheet.
S-9 The emissivity of studied carbonized electrospun sheets in this work we extracted from optical transmission measurements in infrared region (1-20 µm) and finally the correct temperature was obtained and compared with resistance change technique, [A. E. Aliev et al Nanotechnology 2014, 25, 405704]. (c) (d) Figure S13. The power dependence of sound pressure and temperature were measured simultaneously using high frequency precision B&K microphone model 4138 and FLIR T650sc thermo-camera (FLIR Systems, Inc.) The thermal image and temperature on the surface of transparent PAN sheet shown in the inset to taken by FLIR thermo-camera. (c) The experimental setup showing simultaneous measurement of sound pressure (microphone on the left of PAN sheet), the modulation part of temperature measured by high-speed infra-red detector PDA10PT (ThorLab Inc.), and (d) the average temperature profile taken by T650sc thermocamera on the top-right.