A trace carbon aerogel sample was adhered to a conductive substrate and coated with gold for 45 s. The microscopic morphology of the carbon aerogel sample was then captured using a scanning electron microscope (TESCAN MIRA LMS, Czech Republic). The acceleration voltage for the morphology analysis was set to 3 kV, utilizing a secondary electron detector (SE) with a magnification range of 2,000 to 150,000. The particle size distribution of the carbon aerogel samples was measured using a laser particle size analyzer (Malvern Mastersizer 2000, United Kingdom). Due to the small particles of carbon aerogel, the agglomeration of particles is easy to occur when the dry method is used, which leads to a large tail peak and a large error in the test results. Therefore, the wet method is used to measure carbon aerogel, and water is used as dispersant. After ultrasonic dispersion, the manual test program was run to test, and the analysis mode was free distribution; According to the results of electron microscope observation and shooting, it is found that the carbon aerogel particles are different in shape, not perfect spherical, and their size cannot be directly expressed by particle size. Therefore, the equivalent particle size is used to describe the particle size of carbon aerogel particles. The automatic surface and porosity analyzer (Micromeritics ASAP2460, Mack, United States) was used to measure the pore parameters of carbon aerogel samples with nitrogen as adsorb. Sample weight 0.12g; The analysis temperature is 77.3 K. The measurement equilibrium interval is 20 s; Analysis free space: 85 cm³; Low pressure dose 15 cm³ g^-1; No automatic degassing and thermal correction.

The interference performance parameters of carbon aerogel samples in the infrared bands of 1–3 μm, 3–5 μm, and 8–14 μm were tested by a smoke box test system, and the effects of porosity and pore size distribution of carbon aerogel on the infrared interference performance of carbon aerogel were studied. The schematic diagram and test diagram of smoke box test system are shown in Figures 1, 2 respectively. Oval smoke box: volume 33.8 m³, optical path 4.8m, self-built; Fan: Oxx FS1608RC, China; 3∼5μm, 8–14 μm infrared radiation source: 800W electric furnace wire, homemade; 1∼3 μm infrared radiation source: halogen lamp TEQI LIGHT 21V/150W; 1∼3 μm infrared radiometer: EOS, PbSe-020-H, United States; 3∼ 5 μm infrared radiometer: EOS, FYM-PBS-020-H, United States; 8–14 μm infrared radiometer: EOS, FYM-LT020-H, United States.

Before releasing the carbon aerogel interference material, the light path was obscured and the background signal U₀ was measured, unit: V; Smooth light path, measure calibration signal U_d, unit: V. After the smoke screen is released, the infrared signal voltage received by the infrared radiometer becomes weak due to the scattering and absorption of the smoke screen to the infrared radiation. After the smoke concentration in the smoke box is uniform, the output voltage of the infrared radiometer is tested and recorded, and the sampling is continued for more than 300 s to obtain the sampling signal U_t, unit: V. The sampling signal U_t is less than the calibration signal U_d. The infrared transmittance τ is calculated according to the following formula, unit: %. The transmittance - time curve of carbon aerogel sample smoke screen to infrared attenuation is obtained. τ = U t − U 0 U d − U 0 (1)

The specific operation steps of smoke box test are as follows: ① The product value of smoke screen concentration and smoke box volume of the sample to be tested is 16.9g, so that the sample concentration in the smoke box is 0.5 g/cm³, the temperature in the smoke box is 22°C–25 °C, and the ambient humidity is 61%RH ∼ 69%RH. Infrared radiometers and heat sources of 1 ∼ 3μm, 3 ∼ 5μm and 8–14 μm were arranged in the Windows on both sides of the smoke box. ② Instrument calibration, masking light path, determination of background signal U₀; Unblock the light path and determine the calibration signal U_d. ③ After the calibration signal U_d of the radiometer remains stable, the air pump is turned on to feed into the smoke box, and the fan is stirred to make the carbon aerogel sample dispersed evenly to form a smoke screen. The sampling signal is recorded at the sampling frequency of once per second and the real-time transmittance curve is drawn. After the smoke concentration is uniform, the sampling is continued for more than 200 s to obtain the sampling signal U_t. ④ Record the sampling signal U_t, measure the shielding performance of the sample to each band, open the smoke box and exhaust the carbon aerogel samples in the smoke box, record the detailed data of infrared transmitrate with time, the total time is 721 s ⑤ Repeat the experimental steps until all the carbon aerogel samples are tested.

The corresponding mass extinction coefficient (αe) was calculated according to the average infrared transmittance. α_e is the core index of infrared interference performance, which can be calculated from infrared transmittance. The calculation formula of α_e is as follows: α e = − ln ⁡ τ c l (2)

Where: c is the smoke concentration in the smoke box test system, g/cm³; l is the optical path, m.

The microscopic morphology results of samples one to nine observed by electron microscope are shown in Figure 3, where Figures 3a–i correspond to samples one to nine respectively. In Figure 3, the black area is the pore structure, and the gray area is the skeleton structure.

Figure 3 reveals that the nine carbon aerogel samples consist of powdered particulates composed of three-dimensional carbon skeletons. These particulates exhibit distinct boundaries and good dispersion. The size of a single particle is about 1–20 μm, and the internal particle has a continuous network structure in the three-dimensional space, with uniform skeleton and developed pore structure. Given the absence of significant differences in particle morphology, the influence of carbon aerogel morphology on infrared interference performance is not considered a significant factor following smoke dispersal and smoke screen formation.

The particle size distribution of the samples was tested by laser particle size analyzer, and the volume percentage of the nine carbon aerogel samples in the range of 0.01–2000 micron and the particle size values of D ₁₀, D ₅₀ and D ₉₀ of the nine samples were obtained. Table 1 lists the particle size measurement results of nine kinds of carbon aerogel samples. According to the particle size measurement results, the particle size distribution curve is made with the logarithm value as the abscisordinate, as shown in Figure 4.

It can be seen from Table 1 that the D ₉₀ of sample three is 31.435 μm, and the D ₉₀ of the other eight samples is less than 20 μm. The particle size measured by laser particle size meter is consistent with the observation results of microscopic morphology.

The particle size distribution of sample 2 has the weakest consistency and the most dispersed distribution. In Figure 4, the particle size distribution curve of sample 2 has an obvious raised shape at 10–30 μm, indicating that the particle size distribution of sample two is wide, and the two results are consistent. Sample 6 has the best consistency in particle size distribution and the most concentrated distribution, which is consistent with the curve of sample six in Figure 4.

Figure 5 shows the adsorption and desorption isotherms of carbon aerogel samples 1-9. It can be seen from Figure 5 that samples one to nine show obvious rapid adsorption when P/P0 < 0.01, indicating that there is a strong interaction force between carbon aerogel and nitrogen (Yu J. et al., 2024), and the adsorption becomes saturated after reaching a certain relative pressure. This phenomenon is the result of microporous volume filling, indicating that the material contains a large number of micropores. When P/P0 is close to 1, the adsorption and desorption isotherms do not tend to be flat, but have upward adsorption, indicating that there are a small number of macropores in the material. On the other hand, it may also be that the isotherm rises rapidly near the saturated vapor pressure, due to the presence of gaps between the particles and the occurrence of adsorption similar to macropores. By observing Figure 5a, it can be seen that the shapes of absorption and desorption isotherm of samples 1, two and three are similar, indicating that the pore structure is similar, which is consistent with the selected carbon aerogel model, and they are all carbon aerogel G25-1 materials; The adsorption and desorption isotherms of sample eight and nine have similar shapes and pore structures, so they are carbon aerogel A materials. According to the IUPAC classification standard (Xu, 2023), the adsorption and desorption isotherms of sample five belong to Langmuir isotherms, corresponding to the reversible adsorption process of Langmuir monolayer, which is adsorbed by micropores. When P/P0 of samples 1, 2, 4, five and seven is close to 1, the adsorption curve has an upward adsorption amount, indicating that there are a small amount of stacked macropores, indicating that the samples have mesopores or macropores (Yu W. et al., 2024; Xu, 2023), which may be due to the occurrence of capillary condensation, resulting in adsorption lag. The starting point of the hysteresis loop indicates the condensation of the minimum capillary. The end point of the hysteresis loop indicates that the largest hole is filled with condensate. The overall shape of the adsorption-desorption isotherm is retained, and the pore volume increases. Samples 1, 2, 3, four and seven have relatively insignificant hysteresis loops between P/P0 = 0.5 and 0.8, but it can still be indicated that these five carbon aerogel samples are micro-mesoporous composites. There is almost no hysteresis loop in the adsorption and desorption isothermal curve of sample 5. When approaching the saturated vapor pressure, due to the gap between particles, adsorption similar to macropores will occur, and the isotherm will rise rapidly, belonging to type I isotherm, indicating that the pores in sample five are mainly micropores (Yu Z. et al., 2024; Yu J. et al., 2024; Wu et al., 2023).

Observe the absorption and desorption curves of samples 6, eight and nine in Figure 5: The amount of nitrogen absorption increased significantly when P/P0 = 0.5, and there was an obvious hysteresis loop between P/P0 = 0.5 and 0.9. The isotherm obtained during desorption did not coincide with the isotherm obtained during adsorption. The desorption isotherm was above the adsorption isotherm, and the hysteresis loop of isotherm did not have an obvious saturated adsorption platform, indicating that the pore structure of the sample was very irregular. According to IUPAC standards, they all show similar IV isotherms with H4 hysteresis loops, indicating that the particles have irregular voids and wide pore size distribution (PSD) curves. The pores of samples 6, eight and nine include micropores and mesopores (Wu et al., 2023; Chao et al., 2022). The pores are mainly composed of arrow slit holes, typical “ink bottle” holes, tubular holes with uneven pore size distribution and densely packed spherical particle gap holes (Yu W. et al., 2024). From a structural point of view, the reason for these different pores is the structural shrinkage due to surface tension during the decomposition of volatile substances in the dense organogels during the pyrolysis of organic aerogels at high temperatures (Gloria et al., 2015). Because the specific surface area of macropores is very small, the contribution of macropores to the total adsorption amount is usually negligible compared to the adsorption amount of mesopores and micropores. Samples 6, 8, and nine had the highest relative positions of the adsorption and desorption isotherms, indicating the maximum porosity of the sample, while samples 1, 2, 4, 5, and seven had the lowest relative positions of the adsorption and desorption isotherms, indicating the lowest porosity of the sample.

The porous structure of materials is usually characterized by analyzing the adsorption isotherms of different gases (N₂, CO₂, Ar and H₂) at different temperatures (Ashwini et al., 2023). Classical (Dubinin-Radushkevich, BJH or t plot) and molecular simulation methods are widely used to determine the apparent surface area, pore volume and pore size distribution. The analysis of pore size distribution is usually done separately, that is, different models are used to analyze pores of different sizes respectively. HK (Horvath-Kawazoe) method, SF (Saito-Foley) method and T-plot method are usually used for micropores. The BJH (Barret-Joyner-Halenda) method is usually used for mesopores, and the mercury injection method is generally used for macropores. In addition, the Density Function Theory (DFT) model method can be used to analyze the pore size distribution of all pores.

The HK method (Horvath and Kawazoe, 1983) is a semi-empirical analysis method to calculate the effective pore size distribution from the nitrogen adsorption isotherms of samples on micropores. This method assumes that the material is a slit hole. The experimental materials and characterization methods meet the three conditions for the HK method to analyze the pore size distribution of microporous materials: 1) the materials are microporous materials, based on the adsorption isotherm of N₂ at the temperature of liquid nitrogen; 2) Microporous materials are carbon molecular sieve and activated carbon samples; 3) Assume that the hole type is slit hole. HK method was used to analyze the micropore sizes of samples, and the number density distribution of micropore sizes of samples one to nine was obtained as shown in Figure 6. It can be seen from Figure 6 that the nine kinds of carbon aerogel samples have rich microporous structures, and the pore sizes of the micropores are concentrated around 0.4 nm. The median pore sizes of the nine kinds of samples are obtained by HK method.

DFT method is a kind of molecular dynamics method that can truly reflect the thermodynamic properties of fluid in pores of porous materials. It not only provides a microscopic model of adsorption, but also reflects the pore size distribution more accurately than the traditional thermodynamic method. It can relate the molecular properties of adsorb gases to their adsorption properties in pores of different sizes. The Non-Local Density Function Theory (NLDFT) method describes the characteristics of fluids confined to pores at the molecular level and can be used in a variety of adsorbents/adsorbents systems. The NLDFT method for characterizing pore size distribution is applicable to the full range of micropores and mesopores (Terazona, 1985; Terazona et al., 1987). In this test, nitrogen adsorbate and analysis temperature meet the analysis conditions of NLDFT method, and NLDFT method is used to analyze the pore structure of carbon aerogel from micropores to mesopores.

In order to better show the pore distribution in the range of micro-mesopores, the horizontal coordinate is plotted by logarithmic scale, and the pore distribution of micropores and mesopores of nine kinds of samples is shown in Figure 7. Figure 7a is the pore volume distribution, and Figure 7b is the pore density distribution, which are basically the same. The pore size distribution of samples 6, 8, and 9 has a peak at 9–20 nm, indicating that there are mesopores in samples 6, 8, and 9, and the mesopore pore size is concentrated at 9–20 nm, and the micropore pore size of all samples is concentrated between less than 0.8 nm and 1–2 nm. The results of NLDFT analysis are consistent with those of HK analysis.

Brunau Emmet-Teller (BET) model was used to calculate the specific surface area and average pore size of carbon aerogel samples. The pore parameters of carbon aerogel samples are summarized in Table 2. It is generally considered that pores less than 2 nm are micropores, pores between 2 and 50 nm are mesopores, and pores larger than 50 nm are macropores. The specific surface area of the nine samples is greater than 700 m² g^-1, the average pore size is less than 10 μm, the total pore volume is about 0.5–1.5 cm³ g^-1, and the median pore size is about 0.5 nm. The pore test results show that the carbon aerogel samples have micropores, mesopores and macropores, with rich pore structure. The average pore size value is about one order of magnitude larger than the median pore size value, because the pores of the sample are mainly composed of micropores and mesopores, and the number of macropores is small, which is consistent with the analysis results of NLDFT method. The different methods used to evaluate the pore structure of nine carbon aerogel samples with ultra-high porosity showed good agreement in terms of pore volume, specific surface area and average pore size (Gloria et al., 2015).

The micropore volume ν_vz is obtained by t-plot analysis, and the total micromesopore volume ν_vjz and total mesopore volume ν_zz are obtained by single-point analysis. The total mesopore volume ν_jz = ν_vjz-ν_vz, ν_dz = ν_zz-ν_vjz, and the pore volume per unit mass is called the pore volume or porosity of the material. Make the radar plot ν_vzp, ν_jzp, and ν_dzp, as shown in Figure 8.

Calculate the infrared transmittance according to Equation 1. The infrared interference performance test results are plotted into infrared transmittance curves, as shown in Figures 9–11.

From the curves in the 100–400 s sections of Figures 9–11, it can be observed that under the same smoke concentration, the infrared transmittance curves at shorter wavelengths exhibit smaller fluctuations and lower transmittance. This is because the smaller-sized carbon aerogels can produce stronger interference effects through Rayleigh scattering for short-wave infrared. Additionally, the smaller-sized carbon aerogels have more stable floating performance in the confined space of the smoke chamber, resulting in smaller fluctuations in the infrared transmittance curves. The small-sized carbon aerogels primarily interfere with long-wave infrared through absorption, while their scattering effect on long-wave infrared is weak. Therefore, the interference effect of small-sized carbon aerogels on long-wave infrared is significantly reduced. The extinction effect on long-wave infrared mainly comes from the Mie scattering of larger-sized carbon aerogels, which have weaker stability in floating within the smoke chamber. As a result, the transmittance curves for long-wave infrared exhibit larger fluctuations.

Upon opening the smoke box door at approximately 450 s, smoke was released, leading to a steady increase in the infrared transmittance curve. This observation indicates that the smoke curtain formed by the carbon aerogel sample exhibited a uniform concentration, allowing it to move easily with the airflow and demonstrating good suspension stability. After injecting the sample into the smoke chamber for 30 s, continuously test the infrared transmittance for 180 s and use Equation 2 to calculate the infrared mass extinction coefficient. From the 180 recorded infrared mass extinction coefficients, an average value was derived. This average value was subsequently adopted as the representative infrared mass extinction coefficient of the sample across various wavelengths.

The three infrared mass extinction coefficients of nine kinds of samples are shown in Figure 12 as the radar diagram.

It can be seen from Figure 12 that the α_e8 of all samples is between 0.6 and 0.9, α_e3 is between 0.89 and 1.3, and α_e1 is between 0.9 and 1.7. The reason is that with the increase of infrared wavelength, the infrared transmittance is reduced by the influence of particle size, and the influence of sample particle size on the infrared mass extinction coefficient decreases. Therefore, the difference of the interference effect of the nine kinds of carbon aerogel samples on the infrared band of 8–14 μm is the smallest, and the difference of the interference effect on the infrared band of 1–3 μm is the largest.

Based on the parameters of the carbon aerogel samples listed in Table 1, Table 2, and Table 3, calculate the Pearson correlation coefficients r_αe1, r_αe3, and r_αe8 between the particle size and porosity parameters and the mass extinction coefficients in three infrared bands.

According to the results calculated in Table 4, it was found that among the four parameters related to particle size, D [4,3], D ₁₀, D ₅₀, and D ₉₀, only D ₅₀ has a strong correlation with α_e1, with |r| = 0.62 > 0.6. All four particle size parameters are almost entirely negatively correlated with α_e1, α_e3, and α_e8 (except for the correlation coefficient of D ₅₀ with α_e8, which is 0.03). This indicates that as the particle size decreases, the infrared mass extinction coefficient for 1–3 μm increases, which is consistent with extinction theory. Smaller particle size carbon aerogels exhibit stronger Rayleigh or Mie scattering effects in the infrared wavelength range.

Among the five pore volume parameters (ν_vz, ν_vjz, ν_jz, ν_zz, ν_dz), ν_vz shows a weak positive correlation with α_e1 and α_e3, while it has no correlation with α_e8, indicating that the total micropore volume has no effect on long-wave infrared extinction. ν_dz exhibits a strong positive correlation with α_e1, α_e3, and α_e8, suggesting that as the macropore volume increases, the infrared mass extinction coefficients in all three bands tend to increase. Macropores (typically with a pore diameter >50 nm) may enhance the extinction effect through geometric scattering of light. ν_vjz, ν_jz, and ν_zz have almost no effect on α_e1 and α_e3. The total micropore volume ν_vz has a slight effect on α_e1 and α_e3, but no effect on α_e8. This may be because micropores influence the extinction effect on short-wave infrared through surface scattering, while they have no scattering effect on long-wave infrared.

The correlation coefficients of ν_zz with α_e1, α_e3, and α_e8 are all positive, and the infrared mass extinction coefficient is positively correlated with the total pore volume. This indicates that an increase in porosity is beneficial for enhancing infrared interference performance. The reasons for this can be analyzed as follows: first, the increase in porosity of carbon aerogel reduces the effective dielectric constant of the material, decreasing the reflection of electromagnetic waves at the material’s surface, allowing more electromagnetic waves to enter the material and undergo loss. Second, as the porosity of carbon aerogel increases, the number of sub-wavelength structures that can influence the forced vibrations of electrons in the carbon framework also increases. When electromagnetic waves couple with electron resonance, electrons will vibrate and collide multiple times in narrow spaces, resulting in stronger electromagnetic wave attenuation. Third, as the porosity of carbon aerogel increases, the density of individual carbon aerogel particles decreases. Therefore, when the mass of the samples is the same, the number of particles in the samples increases as the particle density decreases. In the experiments, all samples were injected into the smoke chamber at 16.9 g, which means that during the smoke chamber testing process, the actual number of particles in the samples with higher porosity is slightly higher than that in the samples with lower porosity. Thus, the infrared mass extinction coefficient is positively correlated with porosity.

Comparing the correlation coefficients of ν_vjz, ν_jz, ν_dz with α_e1, α_e3, and α_e8, it is found that the larger the infrared wavelength, the greater the influence of mesopore volume and macropore volume (for example, the total macropore volume ν_dz has correlation coefficients of 0.59, 0.72, and 0.84 with αe1, αe3, and αe8, respectively). The reason for this is that the closer the wavelength is to the pore size, the higher the scattering efficiency. An increase in total macropore volume is beneficial for enhancing the infrared interference performance of carbon aerogel. Long-wave infrared undergoes multiple reflections and scattering within the macropores, extending the propagation path and thereby improving the wave attenuation capability of carbon aerogel (Yu et al., 2024c).

From Table 4, it is found that d_k0.5 has a weaker correlation with α_e1, α_e3, and α_e8 than dave does with α_e1, α_e3, and α_e8. The correlation coefficients of dave with α_e1, α_e3, and α_e8 are all greater than 0.7, and among all the characteristic parameters, dave has the largest correlation coefficients with α_e1, α_e3, and α_e8. This indicates that the average pore diameter is the most significant factor affecting the infrared mass extinction coefficient. An increase in dave can enhance the infrared mass extinction coefficient, which may be due to larger pore diameters enhancing the scattering or absorption of electromagnetic waves within the pores of carbon aerogel, thereby increasing the infrared mass extinction coefficient. Therefore, increasing the average pore diameter of carbon aerogel can improve its infrared mass extinction coefficient. SBET shows almost no correlation with α_e1, α_e3, and α_e8, indicating that in high specific surface area materials, the influence of pore size characteristics on extinction performance is greater than the effect produced by specific surface area.