1. Introduction

The photoacoustic effect has found application in a variety of areas such as biological imaging [1–4], gas detection [5], ultrasound transmitters [6], and photoacoustic communication [7]. Graphene is a promising material for photoacoustic conversion of light because of its ultra-broadband optical absorption [8,9], low heat capacity per unit area [10], and excellent thermal conductivity [11]. Lalwani et al. showed that by adding single- and multi-layer graphene oxide nanoribbons to blood, photoacoustic tomography signals exhibit approximately 5–10-fold enhancement as compared to that of pure blood [12]. Moon et al. reported that by reducing graphene oxide-coated gold nanorods, the amplitude of the photoacoustic signal was amplified by a factor of 2 [1]. Toumia et al. obtained a photoacoustic signal that is approximately 17 times higher than that of water when graphene microbubbles were increased to 5% in an aqueous suspension [13]. Compared with few- or multi-layer graphene-based materials, GFs are interconnected by randomly oriented [14] and wrinkled [15] graphene sheets, leading to widely distributed microscale pores [16,17] and a large specific surface area of 356 m²/g [16]. Its numerous pores not only enable efficient heat transfer between GF and the surrounding air but also reduce thermal effusivity [18] that enhances the photoacoustic effect [19]. Giorgianni et al. reported that GF exhibited an unprecedented efficiency in photoacoustic conversion spanning a frequency range of 0.1–20 kHz [20]. However, if a compressive strain of 50% to 99% is applied to GF, its void space shrinks, leading to a reduction in the photoacoustic conversion efficiency [20]. De Nicola et al. experimentally achieved superhigh photoacoustic efficiency from GF, where the sound pressure level increased from 19 to 36 dB by reducing mass density from 15 to 0.25 kg/m³ under 1 W light modulated at 1 kHz [18]. Studies of Giorgianni and De Nicola have shown the important influence of microporous structure of GFs on photoacoustic effect. However, theoretical analysis for the dependency of the acoustic pressure field on GF pores is lacking.

It is necessary to simulate the relationship between the acoustic pressure field and micro pores, or the heat flow absorbed by the boundary layer of air [21], which helps to find ways for the enhancement of photoacoustic effect. In this study, periodically heated air models were used to simulate the distribution of the thermo-acoustic pressure field of the thermo-acoustic process, which is the second stage of photoacoustic effect. In addition, a system-level GF speaker was developed (Fig. 1(a)). Together with a cell phone, the speaker can create resonant photoacoustic waves in the frequency range of 0.2 − 16 kHz (Fig. 1(b) and Fig. S1 in the Supplement 1) or reproduce music (Visualization 1, Visualization 2, Visualization 3). This helps to experimentally verify and intuitively understand the photoacoustic effect of GF.

 

Fig. 1. (a) System-level GF speaker, which includes a square horn, GF, an LED, and a specially designed LED driving circuit. (b) Photoacoustic pressure, $p_{\textrm{air}}^\textrm{F}$, created by GF at LED modulation frequency, ${f_\textrm{l}}$, between 0.2–16 kHz. (c) SEM image of highly porous GF. (d) Specially designed LED driving circuit (left), the size and thickness of GF (right). (e) Primary experiment of smoke detection.

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2. Method

2.1 Materials

GF (Fig. 1(c)) was prepared by Huang et al. from Nankai University [17]. The carbon nanotube (CNT) sponge was purchased from Jiangsu XFNANO Materials Tech. Co., Ltd. The CNT sponge had an outer diameter of 30–50 nm and an inner diameter of 10–20 nm. Scanning electron microscope (SEM) images of GF and CNT sponges are shown in Figs. S2 and S3 (Supplement 1), respectively. Table S1 in the Supplement 1 lists the manufacturers and models of the equipment used in this work.

2.2 System-level GF speaker

Previous GF speakers were designed using a function generator combined with a power amplifier [22], or a single commercial audio card [18,19]. The resulting sound is generally limited to a single frequency. The GF speaker designed by Giorgianni can play music but does not utilize light driving technology [20]. In this study, we fabricated a system-level GF speaker (Fig. 1(a)) composed of a square horn, GF, LED, and specially designed LED driving circuit (Fig. 1(d)). The GF sample (circled in white in Fig. 1(a)) was attached to a plastic trough and mounted on a horn with an opening area of 16×16 cm² (Fig. 1(a)) to collect photoacoustic waves. The LED was fixed at a relative distance of 1 cm from the GF (For the portion of the emitted light from the LED absorbed by GF, see Fig. S4 in Supplement 1). The pressure of photoacoustic wave (Fig. 1(b)) was measured using a sound level meter (Fig. 1(a)) with a nominal sensitivity of 100 mV/Pa and measurement range of 17–132 dB. Two plano-convex lenses were used to converge the LED light beam into a round spot with a diameter of 10 mm for accurate power measurement (see Paragraph S1 and Fig. S5 in Supplement 1). Furthermore, we quantitatively investigated the dependency of the sound pressure level of photoacoustic waves on the light power, modulation frequency, and light wavelength.

The LED driving circuit developed (Fig. 1(d)) converts and amplifies AC voltage (sinusoidal signals at a frequency of 0.2–16 kHz or music from a cell phone) into a “modulated” voltage with a value that is enough to drive an LED. For example, if the voltage of the original music signal is in the range of -50–50 mV (blue line in Fig. 2(a)), the driving circuit amplifies it 10 times and adds it to a DC bias of 3.5 V. Consequently, 3–4 V driving voltage that is synchronized with that of the music signal is obtained (red line in Fig. 2(a)). This amplified voltage drives the LED, which in turn emits modulated light to illuminate the GF sample. Figure 2(b) shows that the LED light power (red line) maintains a good linear relationship with the LED driving voltage (blue line), ensuring that the LED light carries the audio information. Figure S6 (see Supplement 1) shows the linear relationship between the driving voltage of the LED and its emitted light power at the modulation frequencies of 1, 10, and 15 kHz. Detailed designs of the LED driving circuit are provided in Supplement 1 Paragraph S2 and Fig. S7.

 

Fig. 2. (a) Linear conversion of the original audio signal (blue line) into LED driving voltage (red line) by the driving circuit. (b) Comparison between the LED driving voltage (blue line) and the power of LED light (red line). (c) Variation in sound pressure level with increase in the amplitude of light power. (d) Experimental results of sound pressure level (red asterisks and magenta circles) and theoretical results (blue and green lines). (e) Variation in sound pressure level with increase in the amplitude of light power. (f) Variation in sound pressure level with increase in the modulation frequency of LED.

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2.3 Primary experiment of smoke detection

To test the photoacoustic effect of GFs, we chose a 638 nm laser diode (LD) with good directivity as the light excitation source for smoke detection at distances of 1 m (Fig. 1(e)) and 2 m (see Fig. S8 in Supplement 1). When smoke passes through the path of the modulated light beam, the light is scattered by smoke particles, resulting in the degradation of the photoacoustic wave of the GF (Visualization 4). This may provide a possibility for smoke detection using the photoacoustic effect of GFs.

3. Results and discussion

3.1 Experimental results of GF speaker

As compared to the results obtained by Giorgianni, et al. [20], the photoacoustic pressure generated by our speaker (Fig. 1(b)) possesses better resonant characteristics, especially in the frequency range of 1–5 kHz (see Fig. S9 in Supplement 1). This indicates that the speaker can reproduce high-fidelity audio signals. We further input three types of music into the LED driving circuit to drive a 940 nm LED, and the GF speaker could reproduce music with high fidelity (Visualization 1, Visualization 2, Visualization 3). It should be noted that the videos only present music excerpts because of the limitation of the uploading file size). The three types of music are symphony “From the New World,” Pipa music “Surrounded on All Sides” (played by Chinese ancient musical instrument of Pipa), and pop song “Qinghai Tibet Plateau”. We also used the same speaker setup to compare the photoacoustic effect of GF with that of CNT sponge. Visualization 5 shows the symphony “From the New World,” reproduced by the CNT sponge. We can see that the volume of music played by GF speaker is louder than that of the CNT sponge. A quantitative comparison experiment of photoacoustic effect was conducted between the GF and CNT sponge via a 589 nm LED at the same amplitude of light power of 20 mW (see Fig. S10 for results and Paragraph S3 for theoretical analysis in Supplement 1).

In Fig. 2(c), the sound pressure level increases from 25.0 to 33.8 dB (at 5 kHz), from 23.4 to 32.5 dB (at 10 kHz), and from 20.2 to 31.7 dB (at 15 kHz) with an increase in the amplitude of light power from 10 to 30 mW. This suggests that the sound pressure level increases with an increase in the amplitude of light power. As shown in Fig. 2(d), the sound pressure level of the photoacoustic effect of GF increases rapidly with the increasing of modulation frequency in the range of 0.2–2 kHz. The sound pressure levels in the high frequency range (2–16 kHz) are higher than those in the low frequency range (0.2–1 kHz). For the frequency range of 0.2–5 kHz, the sound pressure levels are in agreement with the theoretical values (obtained by substituting our experimental values of ${f_\textrm{l}}$= 0.2–16 kHz, ${r_0}$= 4 cm, $A$= 0.785 cm², and ${q_0}$= 50 mW into the theoretical model of the GF photoacoustic effect in Ref. [20]. For experimental values of sound pressure level, see Table S2 in the Supplement 1). The increasing trend of our experimental results is generally consistent with that of Ref. [20] in the frequency range of 0.2–5 kHz. Since the frequency response of our sound level meter attenuates in the range of 5–16 kHz (see Fig. S11 in Supplement 1), the measured sound pressure levels are lower than the theoretical values.

To investigate the impact of LED wavelength on the sensitivity of GF speaker, sound pressure levels of GF photoacoustic effect were measured by 520 nm LED (green), 589 nm LED (yellow), and 625 nm LED (red) with the amplitudes of light power set to 10, 20, and 30 mW at a modulation frequency of 5 kHz. In addition, we set the amplitudes of light power of LEDs to 20 mW and measured the sound pressure levels at modulation frequencies from 3 to 15 kHz. In Fig. 2(e), the sound pressure levels of the red LED and yellow LED basically coincide, while those of the green LED are slightly higher. In Fig. 2(f), the sound pressure levels of the red LED and green LED basically coincide, while those of the yellow LED are slightly lower. These slight deviation of the measurement results for LEDs with different wavelength might be mainly caused by the measurement errors such as the measurement accuracy of the light power meter, and the power stability of the LEDs. Therefore, we suggest that the sound pressure level of GF photoacoustic effect is independent of the wavelength of incident light, but related to the amplitude of the incident light power. It is consistent with the conclusion in Ref. [20].

3.2 Simulation of thermo-acoustic process of GF photoacoustic effect

3.2.1 Theoretical model of GF photoacoustic effect

The photoacoustic effect of the GF converts the incident modulated light into acoustic pressure. When GF is illuminated by modulated light with a modulation frequency, ${f_\textrm{l}}$, and light power, ${q_\textrm{l}}(t)$, a photoacoustic pressure field is generated (Fig. 3(a)). The alternating component of ${q_\textrm{l}}(t)$ can be written as:

 

Fig. 3. (a) Theoretical model of the photoacoustic effect of GF. (b) Linear energy dispersion of graphene electrons near Dirac points. Models of (c) cylindrical air layer and (d) micro air unit with a diameter of 42 μm for the simulation of thermo-acoustic process. (e) Heat flow with an amplitude of 2.4×10⁻² mW at 1 kHz. (f) Simulation results of thermo-acoustic pressure at the point of ${\textrm{P}_{\textrm{edge}}}$.

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The photoacoustic effect of GF consists of photothermal and thermo-acoustic processes [18,20,23]. The conduction and valence bands of GF meet at the Dirac point without illumination (For the conical band structure of GF, see Paragraph S4 in Supplement 1). In the photothermal process, electrons are promoted from the valence band to the conduction band via photon absorption [24]. Intensive electron-electron scattering and electron-phonon coupling give rise to inter- and intra-band transitions of the conduction band electrons [25] (Fig. 3(b)). Subsequently, an out-of-equilibrium phonon population is generated within an ultrafast response time of approximately 1 ps, which leads to an increase in temperature [20,25]. A fluctuating temperature, ${T_\textrm{G}}(t)$, [26] arises in the illuminated area (Fig. 3(a)) due to periodic heating of GF. The thermal diffusion length, ${\lambda _\textrm{G}}$, can be calculated by the formula ${\lambda _\textrm{G}} = \sqrt {{{{\alpha _\textrm{G}}} / {\pi {f_\textrm{l}}}}}$, where ${\alpha _\textrm{G}}$ is the thermal diffusivity of the GF.

In the thermo-acoustic process, the area where the temperature of GF rises, periodically heats the boundary layer of the air. This air layer, which expands and contracts like an acoustic piston [21], functions as a thin membrane for traditional mechanical loudspeakers [20] to create acoustic waves. Herein, Rayleigh distance, ${R_0} = {A / {{\lambda _\textrm{s}}}}$ [27], indicates the approximate dividing line between the near- (${r_0}\mathrm{\ < }{R_0}$) and far-field (${r_0} > {R_0}$) photoacoustic waves [28] (Fig. 3(a)). ${\lambda _\textrm{s}}$ and A are the wavelength of the photoacoustic wave and area of the illuminated surface, respectively. ${r_0}$ is the distance between the surface of the GF and the microphone. ${\lambda _\textrm{s}}$ can be expressed as ${\lambda _\textrm{s}} = {{{f_\textrm{s}}} / {{v_{\textrm{air}}}}}$, where ${f_\textrm{s}}$ is the frequency of the photoacoustic waves and ${v_{\textrm{air}}}$ (343 m/s) is the velocity of the acoustic wave in air. In our work, A is calculated using the formula $A = \pi {({d/2} )^2}$, where $d = 1\textrm{ cm}$ is the diameter of the LED light spot. Substituting $A = 0.785\textrm{ c}{\textrm{m}^2}$ into ${R_0} = {{{f_\textrm{s}}A} / {{v_{\textrm{air}}}}}$, the value of ${R_0}$ obtained is in the range of 0.05–3.66 mm at photoacoustic wave frequencies of 0.2–16 kHz.

The photoacoustic wave propagates as a plane wave in the near-field and a spherical wave in the far-field (Fig. 3(a)). The near-field photoacoustic wave satisfies the coupled thermoelastic equations [26]

In our study, ${r_0} =$4 cm, ${r_0}\mathrm{\ > }{R_0}$. The photoacoustic pressure, $p_{\textrm{air}}^\textrm{F}$, has a far-field distribution that can be calculated by multiplying the near-field photoacoustic pressure by ${{{R_0}} / {{r_0}}}$ [22]:

The values of GF parameters are summarized in Table 1.

Table 1. Values of GF parameters^a

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3.2.2 Visualized simulation of thermo-acoustic process

We used transient pressure acoustic interface of COMSOL Multiphysics to simulate thermo-acoustic process. The boundary conditions were set according to the theoretical model of photoacoustic effect presented in Section 3.2.1. Two types of heated air models were built, in which the cylindrical air layer macroscopically represents the boundary layer of air above the illuminated area of the GF (Fig. 3(c)), and the micro-spherical air unit depicts the air cell of the GF pores (Fig. 3(d)).

First, we simulated the relationship between the thermo-acoustic pressure and the amplitude of the heat flow, ${A_{\textrm{air}}}$, at a frequency of 1 kHz. Because the impact of the microporous structure of GFs on the photoacoustic pressure at low frequencies (0.1–1 kHz) is almost negligible [20], we regarded the boundary layer of air as a simplified cylindrical air layer. Rosencwaig et al. [21,31] claimed that the boundary layer of air has a thickness of 1–2 mm; thus, the thickness of the cylindrical air layer in thermo-acoustic simulation was set at 1.5 mm. Because the diameter of the illuminated area was approximately 10 mm in the experiment, we constructed a cylindrical air layer with a diameter of 10 mm (Fig. 3(c)). In addition, the heat flow, ${q_{\textrm{air}}}$, was assumed to vary sinusoidally from the GF surface to the air layer [21]. The alternating component of the heat flow is expressed as ${\tilde{q}_{\textrm{air}}} = {A_{\textrm{air}}}{e^{j{\omega _\textrm{h}}t}}$ [26], where ${\omega _\textrm{h}}$ (${\omega _\textrm{h}}\textrm{ = 2}\pi {f_\textrm{h}}$) is the angular frequency. The amplitude of heat flow, ${A_{\textrm{air}}}$, and alternating frequency, ${f_\textrm{h}}$, are set at 0.024 mW, and 1 kHz, respectively (Fig. 3(e)) (The reason for setting ${A_{\textrm{air}}}$ at a magnitude of 0.01 mW is explained in Supplement 1 Paragraph S5). Then, the density of amplitude of the heat flow, ${D_{\textrm{air}}}$, was obtained by ${D_{\textrm{air}}} = {{{A_{\textrm{air}}}} / {{V_{\textrm{air}}}}}$, where ${V_{\textrm{air}}}$ is the volume of the heated air layer. For the cylindrical air layer, ${V_{\textrm{air}}}$ is 0.118 cm³; thus ${D_{\textrm{air}}}$ is 0.2 mW/cm³. According to Rosencwaig et al. [21], ${\omega _\textrm{h}}$ is the same as the angular frequency of the light power, ${\omega _\textrm{l}}$, i.e., ${\omega _\textrm{h}}\textrm{ = }{\omega _\textrm{l}}$, and thus, ${f_\textrm{h}}$ is equal to the modulation frequency of light, ${f_\textrm{l}}$.

The simulated results for the thermo-acoustic pressure at the point of ${\textrm{P}_{\textrm{edge}}}$ (red dot in Fig. 3(c)) are shown in Fig. 3(f). Compared with the variation in the heat flow shown in Fig. 3(e), the thermo-acoustic pressure at ${\textrm{P}_{\textrm{edge}}}$ varies approximately sinusoidally and has the same alternating frequency (1 kHz) as the heat flow. The root mean square of thermo-acoustic pressure, ${p_{\textrm{air - rms}}}$, was calculated as 2.48×10⁻⁵ Pa (Fig. 3(f)), which is slightly higher than the auditory threshold of 2×10⁻⁵ Pa. Considering that the amplitude of the heat flow was set to 0.024 mW (Fig. 3(e)), we conclude that a minimum heat flow amplitude of 0.024 mW enables the air layer to generate an audible sound wave.

To show the variation of the thermo-acoustic pressure distribution in space, we visualized the thermo-acoustic pressure at different time points of 0, 0.2, 0.4, 0.6, 0.8, and 1 ms (Fig. 4(a)–(f)) using colorized isosurfaces that were limited to a 1/4 sphere globe with a diameter of 0.5 m. The isosurfaces are characterized by spherical surfaces and correspond to the propagation of thermo-acoustic waves in the far-field. With the changing of the phase of heat flow, the distribution of thermo-acoustic pressure alters successively as shown in Table 2.

 

Fig. 4. Visualized results of the distribution of thermo-acoustic pressure field at (a) 0 ms, (b) 0.2 ms, (c) 0.4 ms, (d) 0.6 ms, (e) 0.8 ms, and (f) 1 ms at the heat flow frequency of 1 kHz.

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Table 2. Thermo-acoustic pressure at time points from 0 to 1 ms^b

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Notably, at $t = 1\textrm{ ms}$, the thermo-acoustic pressure is approximately the same as that at $t = 0\textrm{ ms}$. Then, the frequency of thermo-acoustic wave, $f_\textrm{s}^{\prime}$, can be calculated by $f_\textrm{s}^{\prime} = {1 / {\Delta t}}$, where $\Delta t = 1\textrm{ ms}$ is the repetition period of the thermo-acoustic pressure field. Therefore, we conclude that the thermo-acoustic wave propagates at a frequency of 1 kHz in resonance with the heat flow.

Second, we investigated the dependency of the thermo-acoustic pressure field on the frequency of heat flow and microstructure of GF over a wide frequency range of 0.2–16 kHz. Because the widely distributed pores in GF have an obvious impact on photoacoustic pressure at high frequencies of 1–20 kHz [20], the model of a simplified cylindrical air layer is not suitable for the simulation of thermo-acoustics at high frequencies. The GF porosity of 99.9% [17] signifies the existence of a large number of air cells that separate the boundary layer of air over the GF into numerous micro air units. As a result, the air inside the microcells is heated by the cell walls after photon absorption. Then, all the air units together generate photoacoustic emission. It is worth noting that we obtained photoacoustic effect with a CNT sponge having a porosity of 99% [32] (Visualization 5), which indicates the influence of a porous microstructure on the photoacoustic effect. Therefore, we built a model of a micro-spherical air unit to simulate the thermo-acoustic process. Because the mean size of the pores in GF is estimated to be 42 μm [17], the diameter of the spherical air unit, $S\varphi $, was set to 42 μm in the simulation (Fig. 3(d)). To keep the densities of heat flow amplitude for both the spherical air unit and cylindrical air layer at the same value (0.2 mW/cm³), the value of ${A_{\textrm{air}}}$ for spherical air unit was set to 7.8×10⁻⁹ mW in accordance with the relation: ${A_{\textrm{air}}} = {V_{\textrm{air}}} \cdot {D_A}$, where ${V_{\textrm{air}}}$ is 3.88×10⁻⁸ cm³.

The sectional distributions of the thermo-acoustic pressure field at heat-flow frequencies of 0.2, 0.6, 1, 8, and 16 kHz are shown in Fig. 5(a)–(e). In response to an increase in ${f_\textrm{h}}$, the half wavelength of thermo-acoustic wave, (the difference between the radii of two adjacent white circles, isopleths of 0 Pa, in Fig. 5(a)–(e)) shortens from 86.73 to 1.07 cm.(For sectional distributions of thermo-acoustic pressure field at frequency of heat flow of 0.2–16 kHz, see Fig. S15 in the Supplement 1). According to the formula, $f_\textrm{s}^{\prime}\textrm{ = }{{{v_{\textrm{air}}}} / {\lambda _\textrm{s}^{\prime}}}$, where $\lambda _\textrm{s}^{\prime}$ is the wavelength of thermo-acoustic wave, the calculated values of $f_\textrm{s}^{\prime}$ are 0.198, 0.594, 1.00, 8.01, and 16.03 kHz corresponding to Fig. 5(a)–(e). Comparing $f_\textrm{s}^{\prime}$ to ${f_\textrm{h}}$, we conclude that the thermo-acoustic wave is in resonance with the heat flow at frequency of 0.2–16 kHz. To analyze the dependency of thermo-acoustic pressure on the frequency of heat flow, thermo-acoustic pressure at point $\textrm{P}_{\textrm{edge}}^{\prime}$ (red dot in Fig. 3(d)) at the frequency of 0.2–16 kHz is extracted. The thermo-acoustic pressure of $\textrm{P}_{\textrm{edge}}^{\prime}$ changes from 0.12×10⁻⁹ to 10×10⁻⁹ Pa with an increase in the frequency of the heat flow and shows a positive linear relationship with the frequency of the heat flow (Fig. 5(f), for thermo-acoustic pressure at each frequency of 0.2–16 kHz, see Table S3 in Supplement 1). Thus, the higher the frequency of heat flow, the higher the frequency of thermo-acoustic waves, and the higher the thermo-acoustic pressure. To further investigate the impact of pore size on the thermo-acoustic pressure, the diameter of the air unit was set as a variable covering a range of 10–80 μm according to the different sizes of pores distributed in the GF (Fig. S2). The thermo-acoustic pressure varies in accordance with the diameter of the air unit as shown in Fig. 5(g). (For thermo-acoustic pressure at each diameter of the air unit, see Table S4 in the Supplement 1). By fitting the thermo-acoustic pressure under different diameters of the air unit at frequencies of 2–16 kHz, the thermo-acoustic pressure is directly proportional to the square of the diameter of the air unit. This positive correlation of acoustic pressure with the pore size is in good agreement with the findings of De Nicola et al. [18]. In particular, the higher the frequency of the heat flow, the greater the impact of increase in pore diameter on the thermo-acoustic pressure (Fig. 5(g)). This also suggests that the thermo-acoustic pressure increases with an increase in the frequency of the heat flow. In addition, simulation results suggest that by increasing the amplitude of heat flow from 7.8×10⁻⁹ to 23.4×10⁻⁹ mW, the thermo-acoustic pressure increases linearly as shown in Fig. 5(h). (For the thermo-acoustic pressure at each amplitude of heat flow, see Table S5 in the Supplement 1). The increase in the thermo-acoustic pressure with increase in amplitude of the heat flow supports the experimental results shown in Fig. 2(c), 2(e). This means that by increasing the amplitude of light power, thermo-acoustic pressure can be enhanced, because the amplitude of heat flow is related to the amplitude of the temperature of the cell walls determined by the amplitude of the light power.

 

Fig. 5. Thermo-acoustic pressure field created by the spherical air unit at heat flow frequencies of (a) 0.2 kHz, (b) 0.6 kHz, (c) 1 kHz, (d) 8 kHz, and (e) 16 kHz. Thermo-acoustic pressure corresponding to the variation in (f) the frequency of heat flow, (g) the diameter of air unit, and (h) the amplitude of heat flow.

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4. Conclusion

We have successfully fabricated a GF speaker prototype to verify the theoretical model of the photoacoustic effect of GF. A cylindrical air layer model with a bottom diameter of 10 mm and height of 1.5 mm was built to prove that a minimum heat flow amplitude of 0.024 mW at a heating frequency of 1 kHz can create audible thermo-acoustic wave (2.48×10⁻⁵ Pa). A micro-spherical air unit with a diameter of 42 μm (the average size of pores in GF) was modeled to demonstrate frequency resonance of thermo-acoustic waves with the heat flow, and the linear relationship between the thermo-acoustic pressure and the frequency of heat flow at a heating frequency of 0.2–16 kHz. It is revealed that the thermo-acoustic pressure is proportional to the square of the diameter of the micro air unit, when the diameter is in the range of 10–80 μm. This suggests that the microporous structure of GF has a significant impact on the enhancement of photoacoustic effect. Furthermore, the photoacoustic wave created by the GF speaker has good resonance with the power of the LED light at a modulation frequency of 2–16 kHz. When a music signal is input into the LED driving circuit, the GF speaker plays audible music with high fidelity. As a sound emitting component, GF, possessing a low density and high flexibility, can eliminate the complex structure of traditional loudspeakers. This work provides a base for developing ultrathin lightweight speakers with simple structure. Simulations of the photothermal process (the first process of photoacoustic effect) of GF will be further studied in the future research.