Thermal management of thermoacoustic sound projectors using a free-standing carbon nanotube aerogel sheet as a heat source

The thermoacoustically created variation in gas pressure p is proportional to the temperature variation ΔT_a on the surface of a free-standing MWNT sheet: p ∼ ΔT_a/T₀, where T₀ is the ambient temperature. Therefore, reliable measurement of the temperature on the surface of resistively heated CNTs is a crucial step for thermal management of a TA device. Direct contact measurement of the temperature on the surface of a free-standing CNT sheet is impossible due to nanoscale structure and fragility of the sheet. Temperatures on the surface of single-walled carbon nanotubes (SWNTs) [5] and graphene [6] have been remotely measured using the temperature-sensitive position of the G peak in Raman spectra. However, the temperature dependence of Raman shift ω is small, even for SWNTs (ω⁻¹dω/dT  ∼ 10⁻⁵ K⁻¹), and the much wider G peak width for MWNTs grown by catalytic chemical vapour deposition (CVD) method leads to a relatively low resolution of the peak position. This suggests that an alternative and simpler means to extract the temperature of free-standing MWNT sheets should be developed.

Remote temperature measurement using integrated black-body radiation power requires knowledge of the surface emissivity of the CNT sheet ε, which depends upon the polarization of emitted light with respect to the CNT alignment direction and sheets' areal density [7]. Here, we combine temperature measurements for free-standing MWNT sheets using the temperature coefficient of resistance (TCR = (ΔR/R₀)/ΔT) [8] with optical transmission measurements to extract the needed ε and thereby compute the correct temperature from optical measurements. Despite the near-perfect black-body behavior of the CNT forest (ε = 0.98–0.99) and the relatively high emissivity of roll-pressed SWNT forest (ε = 0.75 [9]) and bucky-paper, the emissivity of single layer MWNT aerogel sheets is very low because of low sheet density and thickness. The emissivity of an MWNT sheet can be directly estimated from the optical absorption coefficient α using Kirchhoff's law of thermal radiation (ε = α). Here, the dimensionless coefficient of absorption (or the absorptivity) α is the fraction of incident light (power) that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium. The visible optical transmittance spectra of single, double, and triple layers of superimposed MWNT sheets, shown in figure 1 for parallel and perpendicular light polarization, respectively, show the increase in absorption with increase in the number of stacked sheet layers. The pronounced absorption peaks at 495 nm (S₁₁) and 446 nm (S₂₂) suggest the existence of semiconducting few-wall or SWNTs in predominantly MWNT sheets.

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Because the majority of remote temperature detectors work in the 3–5 μm and 8–14 μm IR-transparent windows, we recorded the transmittance spectra of one to six layered MWNT sheets using a PerkinElmer Fourier Transform-Infrared (FT-IR) spectrometer (AutoIMAGE microscope combined with Raman spectrometer Spectrum GX). The IR transmittance spectra taken for non-polarized incident light exhibits smooth absorption in the entire 1–20 μm wavelength range [figure 2(a)], enabling reliable evaluation of the evolution of emissivity of MWNT sheets with increasing number of layers. The dimensionless coefficient of absorption (the absorptivity), α = (I₀-I)/I₀ = 1−τ, extracted from these spectra are further compared with the emissivity obtained by comparison of optical temperature measurements for the resistively heated MWNT sheets with temperatures obtained using the resistance change method. Here, αI₀ is the absorbed part and I₀ and I are incident and transmitted intensities of light, respectively. The remote optical temperature measurements were conducted using an IR thermocamera MobIR (Wuhan Guide Infrared Technology Co., Ltd) with different reference emissivities.

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The calibration curve shown in figure 2(b) was used in this study for comparative measurements of the temperature of free-standing MWNT sheets. The normalized R/R₀ plot was averaged for three consecutive measurements of an MWNT sheet attached to the surface of a ceramic heater in high vacuum (<0.1 mTorr) [8]. This curve has been tested for over 100 forest-derived samples made by CVD with acetylene gas [1] during the past eight years, including individual MWNTs and bundles of MWNTs, extracted directly from the side of a forest, and single and multilayered MWNT sheets and yarns. The measured temperature coefficients of resistance at different temperature regions (the room temperature TCR = (ΔR/R₀)/ΔT = −7.6 × 10⁻⁴ K⁻¹, where R₀ is the resistance at 295 K) for all of these measured samples were surprisingly similar and invariant of forest height, sheet dimension, and number of superimposed layers. The reason for this consistency in the TCR for nanotubes from different preparations is that the TCR is determined by the concentration of defects in the conduction channels of individual nanotubes [10], and only a very narrow range of CNT growth conditions enables forest spinnability [1].

For free-standing CNT sheets containing differing numbers of sheet layers, figures 3(a)–(e) compare plots of temperature versus applied power from resistance measurements (solid circles), using the figure 2(b) calibration curve, with those obtained optically using the IR camera MobIR (open circles with dashed lines for differing assumed sample emissivities from 0.1 to 0.8). By selecting the sample emissivity that provides a match between the optically determined power dependence of sample temperature and that determined by resistance measurements, good agreement is obtained between the layer number dependence of this emissivity and that derived from the measured IR absorption coefficient at room temperature in air (table 1 and figure 3(f)). Hence, the temperature of a free-standing CNT sheet can be reliably obtained by remote measurement of IR emission using the emissivity derived from optical absorption measurements. At least for the present MWNT aerogel sheet, the visible transmittance at 550 nm (averaged for vertically and horizontally polarized light or measured using non-polarized light), is nearly the same as that for the 1–20 μm wavelength range for sheets containing various number of sheet layers. Hence, one can use visible transmittance to evaluate the needed IR emissivity of MWNT aerogel sheets. The IR thermometry method is preferable for visualization of the temperature profile along the sheet, or to measure possibly different rates of temperature evolution for different areas of the aerogel sheet. However, for MWNT sheets encapsulated between two plates with unknown IR absorption, temperature measurement by the resistance change method provides more reliable data. Though the resistance change method captures the averaged resistance along the sheet, it can be used to measure and control in situ fast dynamic changes of temperature.

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Figure 4 presents an example of thermal imaging of an encapsulated TA projector without any emissivity adjustment (ε = 0.8). The 3D temperature profile in figure 4(a) and a 2D cross section of the temperature profile in figure 4(b) captured through the central line for different power levels are taken over the TA device shown in the inset to figure 1(a). The thermal imaging was conducted using a ThermaCAM SC640 (FLIR Systems Inc.). The temperature profile along the central line refers each region to the actual device shown in the top inset. There is a clear distinction between the temperature profiles across each of the three different layering segments, despite the impact of temperature smoothening by absorption of the glass plate and its thermal conductivity. For example, for 10 W input power, distributed as 1.67, 3.33, and 5 W between the strips (see dark yellow triangles in figure 4(b)), the thermocamera yields ∼40, ∼60, and ∼80 °C, respectively. In fact, the temperatures for all three strips (as measured by R/R₀ and adjusted emissivities: 0.16, 0.3, and 0.4) are very close: ∼127 °C for 1.67 W of input power for the one layer strip (figure 3(a)), 123 °C for 3.33 W of input power for the two layer strip (figure 3(b)), and 125 °C for 5 W of input power for the three layer strip (figure 3(c)). Thus, emissivity adjustment for each MWNT assembly is crucial for remote temperature measurement.

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To estimate the maximum power density and the range of current levels that the suspended MWNT sheet stack can withstand when it contains various numbers of superimposed layers, we gradually increased the applied ac voltage across the sheet until the sample was destroyed. We recorded the temperature, ac power (f = 1 kHz), root mean square (rms) values of voltage and current, and recorded pictures for more than 50 samples placed in a high vacuum or an argon gas environment. As an example, figure 5 shows the response of a 1 × 3.2 cm² MWNT sheet attached to 2 mm thick copper electrodes to the increasing applied ac power and resulting black-body radiation in a vacuum. The attachment was performed by densification of the MWNT sheet on the outer sides of the copper rods using a volatile liquid (methanol) for wetting, followed by quick drying. This densification method provides robust electrical connections through van der Waals forces and is especially important for high-temperature applications where many metallic interconnects do not work. Voltages were applied along the sheet width direction, which is the direction of nanotube alignment.

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The maximum input power density obtained in a vacuum (<0.1 mTorr) for a given interelectrode separation distance of 1 cm was 22 W cm⁻². Further increasing the applied power dramatically increases the resistance of the sample (controlled by a voltage bias on a series-connected 2.5 Ω reference resistor) and a break progressively appears in the sheet along a line perpendicular to the direction of sheet alignment. Apparently, in the obtained vacuum of <0.1 mTorr, there are still a sufficient number of oxygen molecules to eventually lead to burning the CNTs. Damage starts at the location of some defect or where the local temperature is highest (in a vacuum, the hottest areas usually are at the center of the sheet). As soon as a break (burned hole) appears, the current redistributes to neighboring channels, forcing them to overload and break when constant input power is maintained. A small flash spot can be seen that immediately propagates perpendicular to the sheet alignment in both directions and eventually disconnects the entire circuit, as shown in the last panel of figure 5.

In argon gas atmosphere, the useable input power density is higher, P_max = 28 W cm⁻², due to the additional heat dissipation channels through direct thermal conduction to the gas. The free convection of heated gas (vertical flow of hot gas) significantly alters heat distribution across the sheet area. The top part of a vertically fixed MWNT sheet in large chambers was always much hotter than the bottom part, inducing much earlier thermal breakage, which usually started at the central uppermost point and continued downward. A horizontally fixed MWNT sheet in a large argon chamber experienced strong vertical gas flow perpendicular to the sheet orientation and induced sheet flapping, which increased the bundling of nanotubes into larger diameter fibers. The effect of convection can be mitigated by reducing the volume of the enclosure and partitioning the heater into small sections.

The obtained power density per square sheet divided by the averaged number of aligned individual MWNTs (∼384 600 tubes per one cm width) suggests a much lower breakdown current (I_vac ∼ 0.52 μA) than found for a single MWNT tube (9.5 nm in diameter) directly attached to the metallic electrodes, I ∼ 175 μA or 19 μA per shell (L < 200 nm) [11]. The idealized picture of single-tube channels obtained from atomic force microscopy areal analyses of a densified highly aligned MWNT sheet shows that the average separation distance between 10 nm tubes is 26 nm, which is consistent with the observed transparency of the sheet. Despite a low breakdown current, the average resistance of an individual tube of 46.5 kΩ μm⁻¹ is independent of the sheet length in the nanotube orientation direction (the current flow direction), and consistent with results for other CVD-grown MWNTs [12]. The high thermal conductance of short individual tubes used in [11] (taking aside the resistively created heat) assists in realizing the high breakdown current level. The macroscopic distance between electrodes and high aspect ratio of individual tubes (∼35 000) in studied sheets make the contribution of thermal conductivity along the sheet negligible. Apparently, the strong tube–tube interconnects having only slightly higher resistance in highly aligned MWNT sheets [13] and the correspondingly higher temperature might have little contribution to this lowering of the current limit.

The shorter the distance between electrodes (along the nanotube alignment direction), the higher the power density that the MWNT sheet can withstand. For example, a single 2 × 18 cm² MWNT sheet in argon gas could withstand only ∼10 W cm⁻², whereas a small 2 × 2 mm² multilayered (five layers) sheet could withstand ∼300 W cm⁻². However, the temperature modulation (important for TA sound generation) on the sheet surface of short length samples (L < 2 mm, [14]) is much lower due to the direct heat dissipation along the CNTs to the copper electrodes.

The residual oxygen (4–10 ppm) in the argon glove box or in the vacuum chamber filled with ultra-high-purity gas is the main limiting factor for achieving a high power density. Due to the large surface area of the aerogel MWNT sheet, there is a strong interaction with residual oxygen (based on six samples tested in the argon glove box). Oxidation in the argon glove box increases the sheet resistance at T = 650 °C at a rate of 20% per hour, which eventually destroys the sample. An increase in the number of superimposed layers increases the allowable power density. However, heat accumulation inside of a stacked sheet assembly makes the dependence of maximum allowable power density on number of stacked sheets nonlinear. Stable operation of the sound projector in air and argon gas was achieved at MWNT sheet temperatures below 600 °C, with the highest realized stable power density of 5 W cm⁻² (f = 1 kHz). The use of getter coating on the inner surface of encapsulated TA devices, which captures residual oxygen, might increase the stable operation temperatures. Note that the low exposed surface area of twisted MWNT yarns (ρ = 0.8–1 g cm⁻³) makes their operation in 0.1 mTorr vacuum, or high-purity argon, much longer (several days at T = 2000 °C).

The visual inhomogeneity of spectral temperatures (see the picture in figure 5 with T = 1200 °C) results in deviation of the power-temperature dependence P(T) from the Stefan–Boltzmann law: P = AεσT⁴. Assuming that, in a vacuum, the applied ac power (rms value) is totally transferred to black-body radiation, the upper limits of observed temperatures are higher than estimated from the power increase. Due to the negative temperature dependence of resistivity in CVD-grown MWNTs, current redistribution toward larger bundles with higher temperature (hence, lower resistance) is reinforced at higher power and increases the inhomogeneity. Apparently, due to the higher radiation power of high-temperature spots (bundles⁴ and interconnects), the spectrometer picks up the temperature of those spots, whereas the average temperature is much lower (by ∼10% relative to ambient temperature).

The pressure variation p_rms of an open-to-air TA projector increases linearly with increased applied power P_h [4]:

$$\begin{eqnarray}&&{{p}_{rms}}=\frac{f}{2\sqrt{2}{{C}_{p}}{{T}_{0}}}\cdot \frac{1}{r}\cdot {{P}_{h}}.\end{eqnarray} \tag{ 1 }$$

Unlike other sound generation techniques (coil loudspeakers, piezoelectric, magnetostrictive, and electromechanical transducers), the efficiency of TA transducers η is also proportional to the applied power:

$$\begin{eqnarray}&&\eta =\frac{\pi \cdot {{f}^{2}}}{{{\rho }_{g}}{{\upsilon }_{g}}C_{p}^{2}T_{0}^{2}}{{P}_{h}}.\end{eqnarray} \tag{ 2 }$$

Indeed, because the TA loudspeaker acts as a heat engine, the maximum energy conversion efficiency, according to Carnot's theorem, cannot exceed η = 1 − T_c/T_h, where T_c is the absolute temperature of the cold reservoir and T_h is the temperature of the hot reservoir. Therefore, high applied power, which implies a high temperature gradient, is a preferable working regime for TA transducers. For T_c = 295 K and T_h = 373 K, the Carnot's efficiency limit is 20%. CNTs oxidize above ∼820 K in air (for pristine 10 nm MWNTs [15]), thereby limiting the maximum Carnot's efficiency in air to ∼60%.

In inert gases, like ultra-high-purity argon, we have shown that a single MWNT sheet can withstand a temperature of 2300 K with a power density of 28 W cm⁻², which can provide a substantially increased Carnot's efficiency of η = 85%. However, the heat dissipation from the interior of encapsulated devices becomes a substantial obstacle for high-power TA projectors, which we address here via structural modification of the CNT sheet assemblies and thermal management of the TA sound projectors.

2.3.1. High-voltage input

2.3.2. Stacking of MWNT sheets

The resistance of a TA heater, and consequently, the applied voltage, can be reduced by parallel stacking multiple layers directly on top of each other or through spacers (figure 6(a)). The direct stacking of aerogel density MWNT sheets one over another increases the conductivity of the assembly, which is proportional to the number of layers nL. Assuming the heat transfer coefficient β is constant for low nL, the temperature gradient ΔT = (T–T₀) created by a double-layered (2L) assembly at a fixed applied power should be two-fold lower. Indeed, at low power, a 2L assembly in figure 6(b) shows almost half the temperature gradient of a single layer when the same total power is applied in ambient air. However, this tendency for the measured sheet temperature is quickly saturated with further increase of nL. The non-linear increase of temperature versus applied ac power in figure 6(b) results from the non-linear thermal conductivity behavior of air (κ ∼ (T/M)^1/2 for monatomic gases with molar weight M), which is enhanced at high power by black-body radiation.

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For the case of a specific heat capacity of air, C_p = 1006 J kg⁻¹ · K, f = 3 kHz, and a distance from the microphone of 3 cm, the pressure variation slope, p_rms = 0.117 Pa W⁻¹, obtained using equation (1) (shown by a dashed line in figures 6(c), (e), (g)) is consistent with the p_rms(P_h) slope measured for the single MWNT layer. The stacking of contacting sheets decreases gas access to the inner layers (reduces the heat transfer coefficient β) and at increased power, creates an accumulation of heat interior to the stack, which produces an undesired increase in static background temperature T₀ (the right side upward swing of temperature at high input power in figure 6(d)) and a corresponding decrease of the p_rms(P_h) slope in figure 6(c).

2.3.3. Spacing between stacked MWNT sheets

2.3.4. Interdigitated electrodes

Another solution for the issue of high resistance and reduced heat dissipation from the interior of the encapsulated TA projector is the use of narrow parallel strips of single (or few) layer MWNT sheets using interdigitated electrodes, as shown in figure 7(a). The proper choice of electrode–electrode distances reduces the input impedance to the desired value and can improve the heat dissipation conditions by increasing the direct heat conductance through the MWNT sheet to the electrodes. The pure ohmic input electrical impedance of a flexible TA projector, shown in figure 7(a), is 30 Ω, and for the TA projector shown in figure 7(b) is 33 Ω.

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2.3.5. Enhanced heat dissipation