{'fraction_non_alphanumeric': 0.025669395884045144, 'fraction_numerical': 0.016185628931811715, 'mean_word_length': 5.101060752169721, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Carbon ablators with porosity designed for enhanced aerospace thermal protection

Porous carbon ablators offer cost-effective thermal protection for aerospace vehicles during re-entry into planetary atmospheres. However, the exploration of more distant planets requires the development of ablators that are able to withstand stronger thermal radiation conditions. Here, we report the development of bio-inspired porous carbon insulators with pore sizes that are deliberately tuned to enhance heat-shielding performance by increasing scattering of high-temperature thermal radiation. Pore size intervals that promote scattering are first estimated using an established model for the radiative contribution to the thermal conductivity of porous insulators. On the basis of this theoretical analysis, we identify a polymer additive that enables the formation of pores in the desired size range through the polymerization-induced phase separation of a mixture of phenolic resin and ethylene glycol. Optical and electron microscopy, porosimetry and mechanical tests are used to characterize the structure and properties of porous insulators prepared with different resin formulations. Insulators with pore sizes in the optimal scattering range reduce laser-induced damage of the porous structures by up to 42%, thus offering a promising and simple route for the fabrication of carbon ablators for enhanced thermal protection at high temperatures.

entry into planetary atmospheres. However, the exploration of more distant planets requires the development of ablators that are able to withstand stronger thermal radiation conditions. Here, we report the development of bio-inspired porous carbon insulators with pore sizes that are deliberately tuned to enhance heat-shielding performance by increasing scattering of hightemperature thermal radiation. Pore size intervals that promote scattering are first estimated using an established model for the radiative contribution to the thermal conductivity of porous insulators. On the basis of this theoretical analysis, we identify a polymer additive that enables the formation of pores in the desired size range through the polymerization-induced phase separation of a mixture of phenolic resin and ethylene glycol. Optical and electron microscopy, porosimetry and mechanical tests are used to characterize the structure and properties of porous insulators prepared with different resin formulations. Insulators with pore sizes in the optimal 2 scattering range reduce laser-induced damage of the porous structures by up to 42%, thus offering a promising and simple route for the fabrication of carbon ablators for enhanced thermal protection at high temperatures.

Introduction
The increasing interest in space exploration in the public and private sectors has motivated the development of new material systems that can withstand the extreme conditions of hypersonic flights. [1,2] Ceramic matrix composites, [3] ultra-high temperature ceramics [4] and carbonbased ablators [5] are some of the materials used for thermal protection in aerospace applications. Thermal protection systems are crucial to ensure safe entry of space vehicles and probes in the atmosphere of planets and to shield vehicles from the heat generated by propulsion systems. [2,6] During entry into the atmosphere, friction between the outer gas and the surface of the hypersonic vehicle causes extreme local heating and the formation of a boundary layer of ionized gas at the leading edge. [1] To cope with these extreme conditions, polymer-based ablative materials that consume part of the heat upon pyrolysis are often used as thermal protection system. [5] Phenolic impregnated carbon ablators (PICA) are an example of a thermal protection system that has been successfully employed for lunar and Martian missions. [7,8] In addition to a weight reduction of 50% compared to previous heat shields, PICA also relies on a precursor infiltration approach that is simple, cost-effective and scalable.
However, future planetary missions will impose even more challenging requirements for thermal protection systems, since heat transfer will likely be dominated by radiation instead of convection. [9] The thin and CO2-rich atmosphere of Mars and the ever larger spacecrafts, for example, should lead to a much stronger radiation during re-entry, which cannot be effectively addressed by state-of-the-art heat shield materials.
Several approaches have been proposed for the design of thermal protection systems showing low thermal conductivity and reduced radiative heat transfer in the near infrared wavelength range. These include reflective woven fibres with photonic bandgaps, [10,11] reflective flakes, [12] porous materials, [13,14] periodic woodpile structures and reflective porous glasses. [15] High-temperature photonic structures have also been developed to tune the optical properties of thermal barrier coatings for turbine applications [16,17] or emitters for thermophotovoltaic technologies. [18,19] Such materials can potentially also be used for thermal radiation protection if incorporated in the form of photonic filler particles into conventional ablators. 3 Following this rationale, multilayered metal-dielectric structures have been designed and fabricated as a possible route to create photonic additives for enhanced radiative thermal protection. [12] Recent work has also shown the possibility to manufacture polymer fibers with a highly reflective titania coating, [20] which could in principle also be applied for the fabrication of fiber-based composites with improved near infrared reflectance. Although these reflective and photonic bandgap structures may offer prospective solutions for the next generation of heat shields, their implementation in thermal protection systems remains challenging due to the high cost, cumbersome fabrication process, insufficient high temperature resistance or limited scalability of the technologies developed so far.
Heat shields for more demanding planetary missions may also be developed by enhancing the reflective and scattering properties of state-of-the-art carbon-based ablators, thus taking advantage of the high temperature resistance of carbon and of the scalability, low cost and readiness of current manufacturing technologies. State-of-the-art PICA is manufactured by impregnating a phenolic resin into a porous network of carbon fibers, [21] followed by thermal polymerization and removal of the processing solvents. [7] Because most research and development on carbon ablators have been driven by space agencies and companies, very limited information is available in the literature on the processing-structure-property relationships of these materials. [22] Microstructural analysis of as-fabricated PICA and related formulations indicates that the phenolic resin forms an aerogel-like porous structure between the carbon fibers upon thermal curing (Figure 1a). [23,24] Carbon ablators with an aerogelfilled fibrous structure have recently been shown to effectively withstand the harsh thermal conditions in arc jet tests that simulate atmospheric re-entry conditions. [22,25] Porosity in these materials is generated via a self-assembly process that relies on the polymerizationinduced phase separation of the resin during curing. While the aerogel structure is clearly important for the thermal insulation properties of such fibrous materials, [24] a systematic evaluation of the role of porosity and how it can be possibly tuned to reduce radiative heat transfer in carbon ablators has not yet been reported. In this context, living organisms provide inspiring examples of how reflective photonic structures can be created using up-scalable selfassembly processes. [26][27][28][29][30] For example, Cyphochilus beetles produce scales with a photonic chitinous network that has been evolutionary optimized for the multiple scattering of white light. The development of processing routes that enable the incorporation of such structures in synthetic materials may lead to thermal protection systems with enhanced scattering efficiency and radiative heat transfer resistance. 4 Here, we develop and study an up-scalable self-assembly route to control the porous architecture and enhance the radiative thermal resistance of a phenolic impregnated carbon ablator. Porosity is introduced in conventional PICA using a polymer that directly influences the phase separation process that takes place during thermal treatment of the phenolic resin. To identify the pore sizes required to promote radiation scattering in the near infrared range, we first perform a theoretical analysis of the thermal properties expected for the porous structures at high temperatures. Phase separation of the resin in the presence of different fractions of polymer and solvent is then thoroughly investigated to enable the manufacturing of carbon ablators with the desired average pore size. Finally, we measure the mechanical properties and thermal radiation resistance of the fibrous structures to quantify the effect of the controlled porosity on the performance of the carbon ablator.

3.1.Theoretical analysis of radiative transfer
State-of-the-art carbon ablators rely on the aerogel formed between the carbon fiber network to reduce radiative transfer through the structure at high temperatures ( Figure 1a). [7] While the formation of the aerogel has been shown to enhance the ablation resistance of the structure, the reported sizes of the pores in the aerogel are below 100 nm [22,24,25] and thus much smaller than the micrometer wavelengths ( ) of the incoming and re-emitted radiation at hightemperature entries. For temperatures ranging from 1000 to 3500C, the incoming and reemission radiation is expected to peak at wavelengths between 0.77 and 2.28 m, as predicted by Wien's law for black-body radiation. [31,32] This suggests that the pore size of state-ofthe-art ablators reported in the literature might not be in a suitable range to promote strong scattering of the thermal radiation. Indeed, strongest radiation scattering is expected to take place when the pore size is comparable to the wavelength corresponding to maximum blackbody radiation. [13] To test this hypothesis, we theoretically estimate the effect of the pore size on the thermal conductivity of carbon ablators at temperatures in the range 1000-3500C, following analytical models outlined in a previous study. [32] It is important to note that the model is used to predict the thermal conductivity of the material and not its behavior in the specific conditions of planetary entry or of the laser experiment performed later in our study.
Therefore, the theoretical analysis considers scattering in all directions of the radiation generated by the material at high temperatures. Our basic assumption is that the ablation 5 resistance should be enhanced if the material shows low thermal conductivity at the high temperatures expected during the laser test and planetary entry conditions. This keeps heat at the surface of the ablator, effectively shielding the vehicle from thermal damage.
The thermal conductivity of porous materials at these high temperatures is dominated by thermal radiation and therefore depends strongly on the size and density of light scattering pores present in the structure. [32] The radiative contribution to the thermal conductivity can be expressed by the following relation: where is the Stefan-Boltzmann constant, is the effective refractive index of the material, is the absolute temperature and is the Rosseland extinction coefficient.
Assuming the material to behave as a black body emitter, one can estimate the Rosseland coefficient from Planck's thermal radiation spectrum and the spectral extinction coefficient of the porous structure, ( ). [32] To simplify our analysis, we calculate the coefficient for the wavelength that corresponds to the maximum thermal radiation emitted by a black body at the considered temperatures. Under this assumption, is equal to and can be directly estimated from the relation (supporting information): where and correspond to the absorption and scattering coefficients, respectively.
Previous experiments indicate that the absorption coefficient ( ) of carbon aerogels is four times higher than the scattering coefficient ( ) for wavelengths in the range 2-16 m and at room temperature. [33] The reduced level of scattering in such aerogels can be explained by the presence of pores much smaller than the typical wavelengths considered in the experiments.
However, we expect the scattering contribution to the Rosseland coefficient ( ) to play a major role in carbon ablators featuring pore sizes comparable to the wavelength relevant at temperatures above 1000C ( 1 m). Therefore, we focus our theoretical analysis on the 6 scattering coefficient ( ) and later compare our predictions to the absorption coefficient experimentally measured for porous carbon.
The influence of the porosity and pore size of the carbon ablator on the scattering coefficient, , can be described using the following relation: where ( ) is the scattering efficiency for a pore of radius , is the number of pores per unit volume of material and is the cross-sectional area of the pore. One can show that the product is equal to 3 (4 ) ⁄ , with P being the porosity. In another series of simulations (not shown), we observed that our analysis leads to similar conclusions if we use a solid phase with = 1.47, [35] which is the refractive index of the phenolic resin. The rationale behind the choice of these refractive indices is that the heat shielding effect of the ablator arises in a first moment from the virgin porous phenolic structure, and later from the pyrolyzed porous carbon structure as the ablation process proceeds.
The opposing effects of the pore size on ( ) and eventually lead to a maximum in the Rosseland extinction coefficient at values comparable to the wavelength taken in the analysis.
Pores smaller than 100 nm result in a favorable high volumetric density ( ) but are not strong scatterers (low ) for the selected wavelength of 1.4 m. This indicates that the pore sizes of 7 reported aerogels ( < 100 nm) are indeed too small to reduce radiative transfer in the ablator at high temperatures. With average pores typically around 70 m, the non-impregnated carbon fiber network contains highly scattering elements but at an insufficient volumetric number density. Our analysis shows that spherical pore sizes in the range 0.1-10 m should thus be most effective in reducing the high-temperature thermal conductivity of the ablator. For this pore size range, the scattering coefficient ( ) at an arbitrary high temperature of 1800C varies between 0.25 and 3.7 m -1 , which is on the same order of magnitude or up to 10-fold higher than the absorption coefficient previously measured for carbon aerogels for the same temperature (see supporting information). [33] This confirms the relevance of scattering for porous carbon ablators with pore sizes in the range 0.1-10 m.
To assess the importance of radiative transfer in ablators with pore sizes between 100 nm and 10 m, we also evaluated the contribution of heat conduction ( ) to the total thermal conductivity ( ) of such optimized porous structures. Assuming convection to play a minor role for these pore sizes, the total thermal conductivity is then given by = + .
The conductive term was estimated taking into account the relative contributions of the gas and solid phases to the propagation of phonons through the porous structure (see supporting information). [32] Heat conduction in the ablator is expected to depend mainly on the porosity of the structure but not on the pore size ( Figure 1c). By comparing the and terms of the total thermal conductivity at 1800C, we find that pore diameters close to 10 m generate sufficient scattering to reduce the radiative transfer term to values comparable to those of the conductive contribution. Estimations of the total thermal conductivity of the ablator at other temperatures reveal that the upper limit of the optimum pore size window shifts from approximately 10 m to 1 m as the temperature is raised from 1800C to 3500C ( Figure 1d).
According to this analysis, processing routes that enable the formation of pores in the size range 0.1-10 m have the potential to significantly improve the thermal insulation properties of carbon ablators at temperatures up to 1800C.

3.2.Polymerization-induced phase separation
The polymerization-induced phase separation of phenolic resins is a simple and wellestablished approach to create pores with sizes that typically range from 15 nm to 3 m. [36][37][38] To induce spontaneous phase separation upon polymerization, the phenolic resin is first mixed with a good solvent to form a clear homogeneous solution at room temperature ( Figure   2). Ethylene glycol is often used as the solvent in such homogeneous mixture. Phase separation occurs when the mixture is heated up to initiate the polymerization of the phenolic resin ( Figure   2a)

3.3.Fabrication of phenolic impregnated carbon ablators
Phenolic impregnated carbon ablators (PICA) with designed porosity were prepared by infiltrating a carbon fiber network with the solution of phenolic resin, ethylene glycol and poly(vinylpyrrolidone) (Figure 5a). The carbon fiber network is commercially available under the tradename Fiberform. Because of its manufacturing process, it displays carbon fibers oriented within the plane of the monoliths. [47] The carbon fibers are rayon-based and have a diameter of 10-20 m. [48,49] They are bond together by a thin carbonaceous phase generated upon pyrolysis of phenolic resin. [7] The monoliths exhibit a volume fraction of fibers of approximately 10% and an apparent density of 0.18 g/cm 3 . [49,50] For the impregnation process, the pre-assembled carbon fiber monolith is first immersed in the infiltration solution, both of which were pre-heated to 110C. Based on the earlier experiments, the infiltration solutions contained a PVP fraction corresponding to 10 wt% of the resin and a constant PR:EG volume ratio of 1:5. In addition to providing pore sizes in the desired range, 14 this resin:solvent ratio is particularly suitable because it leads to a low-viscosity solution that can easily be infiltrated in the fiber monolith, while also providing a resin fraction that is sufficiently high to build a mechanically robust porous network between the fibers. The  confirms the existence of an optimal PVP content for the creation of pores through phase separation.

3.4.Ablator microstructure and mechanical properties
The microstructure of the porous ablator is strongly affected by the presence of PVP in the infiltration solution. Optical and electron microscopy images of ablators containing 5-10 wt% PVP reveal that the openings within the carbon fiber network are fully occupied by a spacefilling porous phase ( Figure 6). For PVP fractions outside this optimum interval, the carbon fibers can be identified more easily in the microscopy images due to the larger openings inside the network. These results agree well with the microstructural analysis of the polymerized resins ( Figure 4), thus indicating that the phase separation process observed in the solution also occurs when this solution is infiltrated into the carbon fiber monolith. Such an agreement also suggests that the pore-forming process is sufficiently robust to be applied in different processing scenarios. To further characterize the porous structure formed within the carbon fiber network, monoliths with 0 and 10 wt% PVP were also evaluated by BET analysis and mercury intrusion porosimetry (MIP) (Figure 7a,b). BET was used to assess the size distribution and volume of pores smaller than approximately 50 nm, whereas MIP provides information about pores larger than 100 nm. The pore size distribution of the reference PICA sample (0 wt% PVP) displays 16 two main families of pores. Pores with average size of 70 m are found at larger length scales and correspond to the openings within the carbon fiber network of the ablator. At smaller length scales, the aerogel phase within the fiber network gives rise to pores with size ranging from 5 to 50 nm.
Notably, the addition of 10 wt% PVP into the resin mixture shifts the coarser pores of the reference ablator towards the pore size interval required for enhanced scattering of thermal radiation (0.1-10 m). Indeed, the MIP analysis shows that the coarse pores found in the PVPcontaining specimen lie predominantly within the size range 4-12 m. In addition to these coarse pores, samples prepared with 10 wt% PVP also feature aerogel-like pores smaller than

3.5.Heat-shielding performance
Porous structures with pore sizes in the desired scattering range were evaluated in terms of thermal radiation resistance by exposing them to laser radiation at intensities comparable to those expected in the harshest atmospheric re-entry conditions. The measurement setup consists of a laser source, an argon-filled chamber, a thermocouple and digital and infrared 18 cameras (Figure 8a,b). For the test, the sample is positioned on top of a ceramic thermal insulator and exposed to the strong laser beam while the surface temperature is recorded. To quantify the layer of char formed within the structure under radiation conditions comparable to that expected during re-entries in the Earth's atmosphere, [51] we use a laser with wavelength of 1.03 m.
The tests were performed on specimens with 0 and 10 wt% PVP prepared at PR:EG volume  Figure S1). The lower char depths observed for PVPcontaining samples likely result from the lower radiative thermal conductivity expected for such porous structures. The assumption underlying this interpretation is that the pore size within the phenolic resin is comparable to that obtained upon pyrolysis of the material at high temperatures. Therefore, our experimental results support the initial hypothesis that the thermal performance of the ablator can be effectively enhanced through the introduction of pores that promote radiation scattering in the insulator at high working temperatures. lower than the ones with 0 wt% PVP (f).

Conclusions
Phenolic-impregnated carbon ablators with pores sizes designed to promote radiation scattering display superior heat-shielding performance at high temperatures compared to stateof-the-art thermal protection systems reported in the literature. Analytical models predict that pores ranging from 100 nm to 10 m should increase the scattering of the radiation expected at 1800 C and thus decrease the radiative contribution to the thermal conductivity of the porous material at such temperature. We experimentally discovered that the addition of poly(vinylpyrrolidone) (PVP) into a conventional impregnation mixture of phenolic resin and ethylene glycol is an effective approach to create 5-20 m pores that enhance scattering of thermal radiation. PVP was found to facilitate the polymerization-induced phase separation of the mixture into polymer-rich and solvent-rich domains. This effect might be driven by specific molecular interactions between the PVP macromolecules with the growing phenolic polymer.
The phase separation observed in PVP-containing phenolic mixtures can be performed inside carbon fiber networks to produce large-scale thermal insulators of enhanced heat-shielding performance without significantly affecting their porosity and mechanical properties. Laser tests point out that the char depth in insulators prepared with PVP is up to 42% lower compared to that measured in the reference carbon ablator. This improved performance shows that tailoring the pore size of thermal insulators is an attractive strategy to produce effective thermal protection systems while keeping the low cost and material availability of porous carbon ablators reported in the literature. Similar to reflective photonic structures created by living organisms in Nature, the porous architectures responsible for the enhanced thermal performance are generated through a self-assembly process that is easily up-scalable to large structures. 21

5.1.Materials
Resole phenolic resin (Cellobond SC1008P™, Hexion), ethylene glycol (>98%, VWR chemicals) and poly(vinylpyrrolidone) ( = 10000 g/mol, Sigma Aldrich) were used without further purification. A carbon fiber porous monolith (Fiberform®) with an apparent density of 0.18 g/cm 3 was supplied by Fiber Materials Incorporated (FMI). Cylindrical specimens with diameter of 50 mm and height of 36 mm were punched directly from carbon fiber monoliths (Fiberform blocks) with the help of a thin-walled steel tube. To polymerize the phenolic resin, the sample was transferred from the vacuum oven to a forced convection oven preheated to 150C, where it was kept for 24h. The sample turned yellow upon polymerization. Subsequently, the sample was allowed to cool down to 50C inside the oven. Next, the sample was extracted from the glass beaker and the excess of polymerized resin 22 around the impregnated ablator was removed to allow the ethylene glycol to evaporate more easily.

5.2.Manufacturing of samples
For the evaporation step, the ablator was placed into a vacuum oven at 150C and a pressure of 50 mbar for 24h. The dried ablator was then placed into a forced convection oven for 12h at 180C for the final curing step. The outermost layer of cured resin around the ablator was removed by grinding the specimen with a 320-grit SiC paper until a final diameter and height of 43 and 31 mm were, respectively, reached (Figure 5a).

5.3.Characterization
The structure of polymerized resin samples and carbon ablators was characterized using optical microscopy (Keyence VHX-6000 digital microscope) and scanning electron microscopy The char depth in the laser-tested specimens was defined as the distance from the test surface at which an alteration of the optical or structural appearance of the sample was visible.
Importantly, no ablation occurs during the laser tests, since the samples are not exposed to a high-velocity gas flux during the measurements. The char depth was obtained by image analysis of stitched optical microscope images (50 X magnification ) (Figure 8d,e,g,h). For a detailed analysis, the images were converted to the HSB (Hue, Saturation, Brightness) color space using the software ImageJ. [54] The vertical gray value profile of the saturation channel, referred to here as the gray saturation profile, was plotted for a square of 30 mm starting at the upper surface of the sample's cross section. This allowed us to average the gray values horizontally. The char depth was taken as the distance at which the derivative of smoothened gray saturation curves approaches zero (Figure 8f,i). 24 To confirm the results obtained by image analysis, we also estimated the char depth from thermogravimetric analysis (TGA). To this end, samples with a density of 0.30 g/cm 3 were cut in 1 mm-thick slices along their depths and a TGA measurement of each slice was performed.
The slices were heated in air from 25C to 850C at heating and cooling rates of 10C/min (NETZSCH STA 449 C and Mettler Toledo TGA/DSC 3+ STARe System). The TGA data was used to estimate the mass fraction of phenolic resin in each slice, given by the mass loss associated with the thermal decomposition of the resin divided by its initial mass. The char depth of the sample was taken as the point at which the mass fraction of the phenolic resin becomes constant and its derivative with respect to depth approaches zero ( Figure S1).

Supporting Information
Carbon ablators with porosity designed for enhanced aerospace thermal protection  where ℎ is Planck's constant, is the light speed in vacuum and is Boltzmann's constant.
The estimation of the Rosseland coefficient ( ) using the equations above can be simplified if one assumes a fixed wavelength corresponding to the maximal thermal radiation emitted by a black body at a certain temperature. This assumption yields:

Absorption and scattering contributions to the thermal conductivity
To compare the contributions of absorption and scattering to the radiative thermal conductivity of the ablator, we compare the absorption coefficient ( ) for carbon reported in the literature [33] with the scattering coefficient ( ) estimated in our work (Figure 1b).
In a previous study, experiments have shown that the mass specific absorption coefficient of carbon aerogels is approximately 150-200 m 2 /kg for wavelengths in the range 2-16 m at room temperature. [33] Taking the specific gravity of 2 g/cm 3 for carbon, these values correspond to ranging from 0.3 to 0.4 −1 .
The theoretical analysis of the scattering coefficient of carbon ablators with pore sizes in the optimum range (0.1-10 m) at an arbitrary temperature of 1800C (Figure 1b) predicts that the value increases from 0.35 −1 at 2 = 0.1 to a maximum of 3.7 −1 at 2 = 0.55 , before it decreases again to 0.25 −1 at 2 = 10 . Although data for carbon absorption was obtained at room temperature, this comparison suggests that the contribution of scattering 33 in carbon ablators with pore sizes within the optimum range is on the same order of magnitude or 10-fold higher than the contribution expected from absorption. Such comparison reveals that our model assumption that scattering dominates the radiative contribution will lead to more accurate thermal conductivity predictions for pore diameters around 0.4 m and less precise estimations at the boundary pore diameters of 0.1 m and 10 m. Despite the poor predictability at the boundary pore diameters, our assumption is still justified by the scarcity of experimental data for the absorption of carbon at the wavelengths and temperatures relevant for this work, and by the lack of simple models that take into account the effect of absorption of the continuous phase on the scattering behavior of porous materials.

Calculation of the conductive contribution ( ) to the thermal conductivity
The contribution of solid and gas conduction to the thermal conductivity of a porous material ( ) is given by: [32] = (1 − ) 3 2 ⁄ + 1 4 ⁄ where is the porosity of the material, is a constant associated with grain boundaries and microcracks, is the thermal conductivity of the solid phase and is the thermal conductivity of the gas phase. The term is calculated by where is the gas thermal conductivity in normal atmospheric conditions, is a constant related to the gas chemical composition, is the absolute temperature, is the gas pressure and is the pore diameter. 34 The values estimated in this study (Figure 1c,d) were calculated assuming = 0.8, = 1.397 , [7] = 0.016 , = 0.000025 and = 101325 .

Confirmation of heat-shielding performance of ablators by TGA analysis
In addition to image analysis, thermogravimetric measurements were also used to estimate the char depth in samples subjected to the laser tests ( Figure 8). The TGA data confirms that the char depth in ablators prepared with 10 wt% PVP is significantly lower than that of the reference specimen without PVP ( Figure S1). In this analysis, slices of 1 mm were cut from samples with a density of 0.30 g/cm 3 and were characterized via TGA. Slices taken deeper into the samples show higher mass losses at 600 C ( Figure S1a,b). This means that the resin fraction in the ablator increases with penetration depth. The char depth was estimated as the depth at which the derivative of the resin fraction curve approaches zero ( Figure S1c).