Flame-retardant polymethacrylimide foams modified by grafting with amino-terminated phosphorous polyborosiloxane

To improve the flame retardancy of Polymethacrylimide (PMI) foam, in this study, a series of flame-retardant PMI foams were prepared by grafting with flame retardant amino-terminated phosphorous polyborosiloxane (N-PBSi), using tert-butanol (TBA) as the foaming agent. The structure, mechanical properties, thermal behavior, and flame retardancy of the resultant PMI foams were characterized. These as-prepared foams tended to be more compact in structure as N-PBSi content increased. The tensile, compressive, and bending strength of these PMI foams therefore was greatly enhanced, which were about 2 times, 9 times, and 3 times that of pure PMI foam, respectively. Besides, the introduction of N-PBSi also attributed to PMI foams better performance in char forming, especially in the air, which is beneficial for obtaining better retardancy against flame. Their advantages in flame retardancy and smoke inhabitation were confirmed by limiting oxygen index (LOI) and cone calorimeter tests (CCT). The total heat release (THR) and the peak of smoke generation rate (pSPR) of PMI/N-PBSi-20 were reduced by 23.1% and 69.9%, respectively. The N-PBSi incorporated were thought to not only generate phosphorus-containing fragments to capture free radicals in gas phase, but also rearrange in the solid phase to form a denser carbon layer to provide a better barrier between external heat and internal flammable pyrolysis gases. Given these, it can be envisaged that the flame-retardant PMI foams modified by N-PBSi may be more attractive in a wider range of applications.


Introduction
Polymethacrylimide (PMI) foams are usually isotropic rigid with a closed cell rate of up to 100% and possess superior mechanical and thermodynamic properties thanks to their ubiquitous six-membered imide rings [1][2][3][4][5]. They have found a wide range of applications in many fields including civil aviation and can be used as spherical sealing frames for Airbus A380 and A340 super jumbos [6][7][8][9]. However, PMI foams are naturally highly flammable and may bring severe fire risks to the places where they are used. This poses a great threat to their widespread applications [10,11].
Many studies have been carried out to alleviate this, by improving the flame retardancy of PMI foams. For example, Baumgartner et al [12] added nonpolar phosphorus containing XCH 2 -PO(OR) 2 (where R could be methyl, ethyl or chloromethyl, X represented hydrogen, halogen, hydroxyl or RO-CO-) as flame retardant into PMI foams, the PMI foams with XCH 2 -PO(OR) 2 introduced still maintaining excellent thermodynamic performance. Manfred et al [13] obtained flame-retardant PMI foams, by mixing 3,4-dimethyl pyrazole phosphate with epoxy resin as flame retardant, and then copolymerizing it with acrylonitrile (AN) and methacrylonitrile (MAN) (i.e., the monomers of PMI foams). The LOI value of the modified PMI foams increased from 20.6% to over 25%, with outstanding mechanical properties. Fan et al [5] introduced ammonium polyphosphate (APP) as flame retardant into the reaction system. The dispersion of APP in PMI, however, was heterogeneous, even with a certain amount of thickener added. Further incorporation of an antiwear agent was observed to be favorable to overcome this issue, but greatly increased the cost and degraded the structure and properties of the polymer matrix [14,15]. These are the common byproducts of physical addition to improve the flame retardancy of PMI foams [16][17][18]. Flame-retardant modifications by chemical grafting therefore have aroused more and more attention. Chen et al [19] for instance, synthesized a structural flame retardant of (3-chloro-2-hydroxyl) propyl phosphate dimethyl ester (DMCPP), then esterified it with the monomer of PMI foam. The LOI value of the PMI foams with 10 wt% DMCPP is much higher, up to 29.2%. But the foam cells showed a tendency to be larger, which resulted in a visible reduction in mechanical properties. Yang et al [1] applied N-(2,4,6-tribromophenyl) maleimide (TBPMI) to modify PMI foams by adding it to the double bonds of monomers. The modified PMI foams showed a higher LOI value of 25.5% at a TBPMI content of 17 wt%. Nevertheless, the PMI foams with TBPMI grafted tended to release large amounts of black smoke when burning occurred, which was far from the requirements of eco-friendly and emergency rescue. This is also what needs to be addressed. It thus is of great significance for preparing superior PMI foams whose flame retardancy is greatly improved and well balanced with the foam's other properties [20].
In the present study, a series of flame-retardant PMI foams were prepared by grafting with N-PBSi, an eyecatching flame retardant synthesized in our previous study [21]. The structure of N-PBSi is shown in figure S1, which contains flame retardant elements of P, Si, B, and active amino groups. To begin with, the structure and morphology of the resultant PMI foams were characterized. The experimental results revealed that the foam cells tended to be smaller and more compact after adding N-PBSi, which was conducive to improving the foam's mechanical performance. Besides, the thermal decomposition and flame-retardant behavior of the PMI foams were discussed, based on thermogravimetric (TG) analysis, limiting oxygen index (LOI), and cone calorimeter tests (CCT). The PMI foams also performed better in char foaming and flame retardancy. These advantages enable the flame-retardant PMI foams to be promising for a wider range of applications.

Experimental details 2.1. Materials
To prepare flame-retardant PMI foams, acrylonitrile (AN, 99%) methacrylic acid (MAA, 98%), 2, 2'-azobis (2methylpropionitrile) (AIBN, 99%), tert-Butanol (TBA, 99%) and N-PBSi were used. Among them, the monomers of PMI, i.e., AN and MAA, were purchased from Aladdin Reagent Co, Ltd (Shanghai, China), and were used as received without further purification. The AIBN and TBA were also supplied by the same company, and acted as initiator and foaming agent, respectively. The N-PBSi was obtained according to our previous study and was used as the reactive flame retardant for PMI [21].

Preparation of flame-retardant PMI foams
The precursor solution for preparing PMI foams were prepared firstly by directly mixing AN, MAA, AIBN, and TBA in a given proportion shown in table S1 in the Supplementary Material. The flame retardant, i.e., N-PBSi, was then added into the above solution until completely dissolved. Subsequently, the formed copolymer solution was treated at 50°C for 20 min before being poured into the mold in figure 1, according to the report procedure by Zhang et al [22]. The mold is composed of two pieces of glass plates with a sealed rectangular rubber ring between them. Before casting, polyethylene terephthalate (PET) film was pasted on the inside surface of each glass plate, to make the removal of the intermediate copolymer sheet easier.
The copolymer sheet obtained was then placed between two steel plates clamped at a distance greater thickness than the copolymer sheet, to provide enough height for foaming. The steel plates with copolymer sheet embedded were treated for 10 min at 140°C, followed by another heat treatment process at 200°C for 20 min. This is to enable the copolymer sheet to foam sufficiently. After these, the resultant PMI foams were treated at 160°C for 6 h further, to improve their mechanical properties. The corresponding schematic diagram for preparing flame-retardant PMI foams is also given in figure 1.

FTIR spectroscopy
Fourier transform infrared (FTIR) spectra with a wavenumber range of 400-4000 cm −1 were obtained by a NEXUS 870 Fourier transform infrared spectrometer (Nicolet, USA) at a resolution of 4 cm −1 . Before the test, each sample was well blended with KBr powder and laminated into a thin slice for characterization.

Scanning electron microscopy
The morphology of PMI foams and residual chars were observed by Sigma 500 scanning electron microscopy (SEM, Zeiss, Germany) with an acceleration voltage of 10 kV. Meanwhile, the energy dispersive x-ray (EDX) spectroscopy was conducted using the QUANTAX system (Bruker, USA).

Thermogravimetric analysis
Thermogravimetric (TG) analysis was performed by a TGA2 thermogravimetric analyzer (Mettler-Toledo, Swiss) from room temperature to 700°C under N 2 or air atmosphere, with a heating rate of 20°C·min −1 .

TG-IR spectrometry
Thermogravimetric-Fourier transforms infrared spectrometry (TG-IR) was performed to recognize the gaseous pyrolysis fragments of the foams using TA Q50 thermal analyzer interfaced with an FTIR spectrophotometer (Nexus870, Nicolet).

Raman spectra
The Raman spectra of the carbon residues after cone calorimetry tests were obtained by Tensor II from BRUKER, Germany.

Flame retardant tests
Besides, the limiting oxygen index (LOI) tests was carried out by a JF-9 oxygen index instrument (SFMIT, China) according to the ASTM D 2863-2008 standard. The size of the specimens for LOI tests was 80 mm × 10 mm × 4 mm. Cone calorimeter tests (CCT) were conducted based on the standard of ISO 5660-2016. The heat flux of the cone was set to 35 kW m −2 , and the foams were cut into squares of 10 cm 2 for testing.

Mechanical properties
The tensile, compressive and bending properties of the obtained PMI foams were analyzed by using a WDW-1M electronic universal testing machine. Of the three, the bending tests was carried out according to ISO 1209-1-2004, while the tensile and compressive tests were carried out according to ISO 1926-1976and ISO 844: 2004 respectively. The specimens for the tensile tests were dumbbells in shape and 125 mm × 12.7 mm × 3.2 mm in size. Those for the compressive and bending tests were 20 mm × 20 mm × T and 60 mm × 20 mm × T in size, respectively, where T represented the thickness of the foam.

Foam density and structure
The densities of the resultant PMI foams were measured according to the mass-to-volume method. Figure 2 represents the variation of foam density with different contents of N-PBSi. It is apparent that the density of PMI foams increases with increasing N-PBSi content. The density of PMI/N-PBSi-20 with 20 wt% of N-PBSi incorporated is up to 544 kg·m −3 , about 10 times of pure PMI foam. This is mainly because the addition of N-PBSi with high density has changed the nature of PMI skeleton and made PMI more difficult to foam, resulting in PMI foams with more compact structure (see figures 3(c)-(e)). Figure 3 illustrates the SEM images of PMI foams with different contents of N-PBSi incorporated. As shown in figure 3(a), pure PMI foam has a typical closed-cell structure with smooth and thin walls [23]. These cells are tens to hundreds of microns in size, about 80-200 μm, just like what figure (a 4 ) shows. When adding 5 wt% of N-PBSi, most of the closed cells in PMI/N-PBSi-5 remain the initial structure. The cell walls, however, tend to be thicker. And more walls show a sandwich structure, with many very small cells that fail to foam stuck in the middle. The diameter of these cells is concentrated in the range of 110-200 μm, as shown in figure 3 illustrate the distribution of C, P, B and Si elements in PMI/N-PBSi-5 observed by Energy Dispersive x-ray Spectroscopy. It is observed that there appear abundant and evenly dispersed N-PBSi in the imperfectly foamed areas, which to some extent indicates that the N-PBSi degrades the foaming of PMI. With the N-PBSi content increases gradually, the resultant PMI foams become more and more compact (see figures 3 (c 1 ) and (d 1 )). The foam cells, as a result, are reduced to just a few microns in size. The statistical data in figures 3 (c 4 ) and (d 4 ) reveals that the diameters of the formed cells in PMI/N-PBSi-10 and PMI/N-PBSi-15 are much smaller, about 3-8 μm and 2-5 μm, respectively. Besides, the walls and edges of the cells also continue to thicken. Nevertheless, due to their relatively uniform and robust porous structure, PMI/N-PBSi-10 and PMI/ N-PBSi-15 foams still attractive. When the content of N-PBSi added reaches 20 wt%. However, the foaming of PMI is greatly suppressed, the cell size becomes different, the cell wall thickness is uneven, and there is no existing cell structure at some positions (see figures 3 (e 1 ) and (e 2 )). This is due to the introduction of excessive N-PBSi, the porous cell walls with many small cells sandwiched that can be seen everywhere above are almost gone, replaced by crater-like dense matrix (see figure 3(e 2 ) and (e 3 )). The diameter distribution of these cells can be seen in figure 3(c 4 ). This change seems to be unacceptable in the present study, as it goes too far against the porous nature of the foam.

Mechanical properties
The tensile, compressive, and bending stress-strain curves of PMI foams with different contents of N-PBSi are plotted in figure 4. As shown in figure 4(a), with the increase of N-PBSi content, the fracture tensile stress of PMI foam gradually increased, while the tensile strain at break decreased with the increase of N-PBSi content. The tensile stress and the strain of PMI/N-PBSi-15 at break was tested to be about 2.4 MPa and 5.8%, respectively. When the addition of N-PBSi was 20 wt%, the tensile stress and strain at break was tested to be about 3.6 MPa and 5%, respectively. The tensile stress at break is much higher than the 1 MPa of pure PMI foam, but the tensile strain at break is much lower than the 11% of pure PMI foam. This means that the addition of N-PBSi makes PMI foams more rigid but brittle. This change of foam structure and cell wall are mainly attributed [24][25][26], which become denser and thicker, respectively, as the content of N-PBSi increases. The result brings the PMI/ N-PBSi foams significantly improved tensile strength. Meanwhile, the semi-inorganic nature of N-PBSi also makes the foams less flexible, shown as lower strain values at broken. Figure 4(b) shows the compressive stress-strain curves of these PMI foams. It is clear that pure PMI foam undergoes a yield stage in the process of compression. The PMI/N-PBSi foam with only 5 wt% or 10 wt% of N-PBSi added also shows a similar compressive stress-strain curve, with the nature of pure PMI foam well preserved. The foam's compressive strength, however, is greatly enhanced. The stress of PMI/N-PBSi-5 and PMI/N-PBSi-10 foams at 10% strain were tested to be 1.2 MPa and 4.5 MPa, about twice and nine times that of pure PMI foam, respectively. Further increase N-PBSi content will continue to improve the foam's ability to  against compression. The curve in figure 4(b) shows that the stress of PMI/N-PBSi-15 corresponding to 10% compression rises to 10.42 MPa, while the PMI/N-PBSi-20 foam rises beyond the upper limit of the sensor used. The reason for this can also be given by the SEM images in figures 3(d) and (e). That is, the thicker cell walls together with sturdier edges resulting from the introduction of N-PBSi enable the resultant PMI/N-PBSi foams to bear a much heavier load. As to the bending curves in figure 4(c), pure PMI foam, which breaks at a loading distance of about 31% of its thickness, shows the largest breaking strain value. The bending strain of PMI/ N-PBSi foams at the break, however, is greatly reduced, varying from 11% to 21%. The heterogeneity between N-PBSi and PMI should be responsible. For the foam of PMI/N-PBSi-5, its structure does not change much. However, the added N-PBSi has already destroyed the cyclization of polymer molecules by grafting onto the PMI skeletons and led to incomplete crystallization of polymer. That is, the incorporation of semi-inorganic N-PBSi endows PMI foam with many fragile sites. The significant reduction in bending strain for PMI/N-PBSi-5 foam therefore makes sense. Similar results are also observed for the tensile tests. As the content of N-PBSi increases, the PMI foams resulted become denser and denser, making the change of porous structure of foam play a more dominant role in bending strain than the change of chemical structure [27]. In other words, the negative effect of adding N-PBSi to PMI foam on bending strain is compensated by the densification of foam cells and the thickening of cell walls and edges. For the same reason, the breaking stress of PMI/N-PBSi foams at high N-PBSi contents (>5 wt%) under bending is also enhance. The bending stress of PMI/N-PBSi-15 at break is about 1.6 MPa, about three times that of pure PMI foam.
From an overall viewpoint, N-PBSi does have a great influence on the mechanical properties of PMI foam, inducing the foams to be more rigid that can support much heavier loads but suffer obvious degradation in flexibility. Table 1 summarizes the characteristic TG temperatures and the carbon residue at 700°C of PMI foams with and without N-PBSi incorporated. T −5 wt% in the table refers to the temperature at which PMI and PMI/N-PBSi foams lose 5% of their weight. Similarly, T −10 wt% is the temperature at which the specimen suffers a weight loss of 10%. T max represents the temperature of the highest point of each DTG peak, i.e., the temperature corresponding to the maximum weight loss rate (R max ) in the given weight-loss stage.

Thermal decomposition behavior
The TG and DTG curves of PMI and PMI/N-PBSi-15 foams in N 2 and air are plotted in figure 5. From figure 5(a), there appears only one DTG peak centered at about 375.8°C for pure PMI foam, which is due to the decomposition of PMI skeletons, and the R max for PMI without flame retardant was 0.82%·°C −1 . The PMI/ N-PBSi-15 foam, however, produces two DTG peaks during the process of heating. The first one centered at 313.3°C should be attributed to the decomposition of phosphorus-containing groups such as P-C and P = O in N-PBSi [28][29][30]. The second one centered at 402.2°C corresponds to the combination of PMI pyrolysis and N-PBSi degradation. It is apparent that the peak for PMI pyrolysis moves to a higher temperature after the introduction of N-PBSi. The R max in these two stages also proves this point, which is 0.25%·°C −1 and 0.67%·°C −1 , respectively. The temperature for PMI/N-PBSi-15 foam to decompose therefore increases from 247.8°C to 266.8°C, together with a slightly enhanced ability in forming char. Figure 5(b) shows the thermal decomposition behavior of PMI and PMI/N-PBSi-15 foams in the air atmosphere. The curves obtained in the air are similar to the corresponding ones in figure 5(a). One of the main differences between them is that there occurs one more DTG peak centered at about 580.1°C and 627.8°C, with the corresponding R max to 0.27%·°C −1 and 0.29%·°C −1 , respectively. This is mainly due to the further oxidation of carbon residue in the presence of oxygen, causing the carbon residue to escape in gaseous form. Before this, the maximum weight loss temperatures of PMI and PMI/N-PBSi foam in the first and second stages do not change much with different atmospheres, while the R max for PMI foam and PMI/N-PBSi-15 changed a lot in the air atmosphere, being 0.75%·°C −1 , 0.27%·°C −1 and 0.48%·°C −1 , respectively. It indicates that the presence or absence of oxygen does not significantly affect the decomposition behavior of N-PBSi and PMI before 500.0°C. But the Si-O-Si and Si-O-B groups in N-PBSi can form a compact interwoven network under the action of oxygen, providing extra protection for the polymer below by blocking outside heat and air from entering while preventing the flammable pyrolytic gases from going out [31][32][33]. This is why the R max per stage in the air is smaller than that in nitrogen. As a result, the carbon residue of PMI/N-PBSi-15 foam remained at 700.0°C in the air is much higher than pure PMI foam, which is beneficial to bring the composite better flame retardancy. Figure 6 displays the LOI values of pure PMI foam and the PMI/N-PBSi foams with different contents of N-PBSi. The results show an expected increasing trend with the increase of N-PBSi. The LOI value of PMI/ N-PBSi-20 foam rises to about 22%, higher than that of pure PMI foam. Nevertheless, the increase in LOI is less than what we expected. The main reason for this is the use of highly flammable TBA as foaming agent, which was Table 1. Characteristic temperatures and the carbon residue at 700°C from relevant TG curves.

Atmosphere
Type sealed inside the foam after foaming. That is to say, the introduction of TBA seriously weakens the flame retardancy of PMI/N-PBSi foams that they deserve. In future studies, non-flammable or even flame-retardant foaming agents should be alternatives. The figure also shows the appearance of PMI/N-PBSi foam after the LOI test. The carbon residues of PMI/N-PBSi have a relatively dense structure and can stay upright. It can also be deduced that the PMI/N-PBSi foam performs better in char forming than pure PMI foam. As shown in figure 7(a), the pHRR of pure PMI foam is as high as 131.13 kW·m −2 , indicating that PMI foam burns violently and releases a large amount of heat. The pHRR of PMI/N-PBSi-5 foam, however, is greatly reduced to 60.18 kW·m −2 , only half of that of pure PMI foam. It means that the burning vitality of PMI is significantly inhibited by introducing N-PBSi. With the further increase of N-PBSi content incorporated, the pHRR continues to decrease. Besides, the THR also continues to decrease with N-PBSi content, and the growth of THR value is indeed gentler than that of PMI foam, from 2.6 MJ·m −2 of pure PMI foam to 2.0 MJ·m −2 of PMI/N-PBSi-20 foam. This can be attributed to the formation of surface barrier from N-PBSi, which can prevent flammable pyrolysis gases from going out and block the entry of oxygen, for reducing the fire risk of PMI foam. Figure 7(b) plots the SPR curves of pure PMI foam and the modified ones with different contents of N-PBSi. It can be seen from the figure that pure PMI foam reaches its SPR peak only after 25 s of thermal radiation exposure. With 5 wt% of N-PBSi added the foam's pSPR value keep almost unchanged, but the arrival time was delayed. For the PMI/N-PBSi foams with more N-PBSi added, their SPR curves change from 'lofty mountains' to 'gentle plateaus', and the corresponding pSPR values were much lower. The results demonstrate that the smoke-generating activity of PMI can be remarkably inhibited by adding N-PBSi, to give better visibility and lower smoke toxicity for escape and rescue in fires [34]. It should be noted from table 2 that the TSP increases with increasing N-PBSi content. This is also due to the presence of N-PBSi, which promotes the  formation of the cross-linked carbon layer structure in PMI foam, resulting in incomplete combustion of PMI foam inside. Figure 7(c) represents the MLR curves of related foams. The MLR curves in the figure show that the PMI foam suffers a violent burning process and it takes only about 100 s to burn out. The residue of pure PMI foam after burning out is only 4.1% of its initial weight, indicative of a poor capability in forming char (see figure 7(d)). With the incorporation of N-PBSi, consequently, the pMLR and mMLR of the resultant composite foams decrease gradually. The burning process of PMI/N-PBSi foams with more than 15 wt% of N-PBSi incorporated can last more than 550 s, resulting in much higher carbon residues above 15%. In other words, the carbon forming ability of PMI foam doped with N-PBSi is greatly enhanced. According to the theory of Van Krevelen [35], higher carbon residue always corresponds to better flame retardancy. Figure 7(d) shows the overall appearance of the carbon residues formed. It is observed that the carbon residues of PMI foams with more N-PBSi contents tend to be denser and thicker. The increase of carbon residue and its denser form improve the flame retardancy of PMI foam [36,37].

Mechanism in flame retardancy
To probe into the flame-retardant mechanism of N-PBSi on PMI in the gas phase, TG-IR tests on pure PMI and PMI/N-PBSi-20 foams were also performed by heating them from room temperature to 800°C in N 2 . The results are given in figures 8(a) and (b). For pure PMI foam, its spectrum at 400°C is strongest in intensity, with several characteristic peaks corresponding to (CH 4 ; 2950 cm −1 ), (CO 2 ; 2360 cm −1 ), (the carboxylic acid; 1770 cm −1 ), (hydrocarbons; 1172 cm −1 ), (water; 4000-3400 cm −1 ) and a small amount of carbon monoxide (CO) observed [38][39][40]. The PMI/N-PBSi-20 foam also shows a similar strongest TG-IR spectrum at 400°C, but the spectrum is much weaker than pure PMI foam. These, once again, indicate the addition of N-PBSi in PMI foam does not have a great influence on the pyrolysis temperature of PMI itself, but significantly reduces the dose of gaseous products pyrolyzed. Figure 8(c) shows the comparison of several representative pyrolysis products of pure PMI foam and PMI/ N-PBSi-20. The introduction of N-PBSi changes the pyrolysis behavior of PMI foams. The peaks according to H 2 O and CO 2 in the gas phase are weakened in intensity and move towards the high-temperature side, different from that of the peak assigned to CO. It can be deduced that adding N-PBSi can raise the thermal stability of PMI foams and slow down the speed to pyrolyze. More importantly, due to the decomposition of phosphoruscontaining groups in N-PBSi, a certain amount of gaseous (P-C; 1275 cm −1 ) and (P-O-Ph; 944 cm −1 ) fragments are observed as well [29,41]. From figure 8(c 5 ) and (c 6 ), at 200°C-300°C, the PMI/N-PBSi foam curve has one more characteristic absorption peak than the PMI foam curve. N-PBSi in this temperature range decomposes to produce P-C and P-O-Ph groups [21,42]. These phosphorus-containing fragments can act as active flameretardant sites in the gas phase by capturing free radicals. Pyrolysis products containing Si and B, however, are not shown in the spectra, which indicates that these two functional elements for flame retardancy mainly play a role in the solid phase.   Note: The data in the table were all mass-normalized. TTI in the table refers to the time to ignition, which means the time required for the specimen to be able to burn continuously at the given heat radiation. Heat release rate (HRR) means the release rate of heat per unit area after being ignited. The total heat rate (THR) represents the heat released by the specimen during the whole combustion process. The larger the HRR and its peak value (pHRR) is, the more heat is generated during combustion. HRR, pHRR and THR have been regarded as very important parameters to evaluate fire safety. SPR is the smoke generation rate, known as the ratio of specific extinction area to the mass loss rate (MLR). It was also reported that larger SPR and its peak (pSPR) values correspond to more smoke released in the process of combustion. The mMLR and Residue are the mean value of MLR and the rate of carbon residue to the specimen's initial weight, respectively.
To investigate the effect of adding PMI/N-PBSi in the solid phase, Raman spectra of the carbon residues of pure PMI foam and the PMI/N-PBSi ones were obtained. As shown in figure 9(a), the results show that the degree of carbon residue, given by I D /I G , varies with different N-PBSi contents. The I D and I G here are the integral areas of the D and G bands, respectively. Of the two, the D band corresponding to amorphous carbon usually appears at the wavenumber of 1360 cm −1 , while the G band appearing at the wavenumber of 1580 cm −1 corresponds to graphitized carbon. It was reported that the lower the I D /I G , the higher the degree of carbon residue, and thereby the stronger its ability to block heat and mass exchanges [30]. According to the fitted curves shown in figures 9(a 1) -(a 5 ), the ratio value of I D /I G decreases from 3.65 to 2.07 with the content N-PBSi increasing from 0 wt% to 20 wt%. This means that the carbon residue of the PMI/N-PBSi foam with more N-PBSi incorporated performs better in flame retardancy.
As to the SEM image in figure 9(c 1 ), the carbon residue from pure PMI foam has a relatively loose structure with many holes and pits on the surface. The formation of holes and pits should be mainly caused by the escape and migration of pyrolysis gases. Besides, the highly porous structure and thin cell walls of pure PMI foam also contribute to the formation of hole-rich carbon residue. By comparison, the carbon residue of PMI/N-PBSi-20 has a more compact surface, with only a few holes observed (see figure 9(c 2 )). The escape of pyrolysis gases generated by burning therefore will be greatly hindered, which is conducive to forming a highly flame-retardant carbon layer with a compact surface but porous interior. The porous interior of the carbon residue of PMI/ N-PBSi-20 is confirmed by the cross-sectional SEM observation shown in figure 9(c 3 ). It is vital for this unique porous structure to block external heat, and therefore beneficial for flame retardancy. In addition to the degree and structure of carbon residues, through the EDX test, we also analyzed the elements on the surface of the PMI/N-PBSi-20 foam and its carbon residue after burning. It can be seen in table 3 that the percentage of O, P, B, and Si elements on the surface of carbon residue is far higher than that of pristine PMI/N-PBSi-20 foam. There is reason to believe that these functional elements deposit during combustion and accumulate at the surface to form a dense carbon network. Figure 9(b) shows the FTIR spectra of the carbon residues of pure PMI and PMI/N-PBSi-20 foams. The difference between them is that there appear two more characteristic peaks of Si-O-Si at 1100 cm −1 and Si-O-B at 914 cm −1 for the carbon residue derived from PMI/N-PBSi-20 [32]. That is, the introduction of N-PBSi optimized the chemical structure of the carbon residue, resulting in a different network that is full of inorganic elements. This is also why the surface of the carbon residue of PMI/N-PBSi-20 is more compact than pure PMI foam. Beyond that, as can be seen from the results in table 3, the carbon residue of PMI/N-PBSi-20 also contains 3.51 wt% of P element, which means that P element plays a flame-retardant role not only in the gas phase but also in the solid phase.
From the above discussion, it can be concluded that N-PBSi acts as flame retardancy in both gas and solid phases. In the gas phase, the decomposition of N-PBSi can provide free phosphorus-containing groups for trapping free radicals. In the solid phase, the decomposition of N-PBSi is committed to forming a dense carbon layer on the surface, but the interior is porous. The carbon layer performs better in flame retardancy, by alleviating the invasion of external heat and hindering the migration of flammable pyrolysis gases outside.  Effectively isolate the external air and prevent the smoke from escaping. The combination of the above changes contributes N-PBSi an attractive reactive flame retardant for PMI foam.

Conclusion
In this study, a series of PMI foams were obtained by using N-PBSi and TBA as flame retardant and foaming agent, respectively. The chemical structure of the resultant foams was characterized at the very beginning, which confirmed that the primary amines in N-PBSi were grafted onto PMI skeleton in the foaming stage. It was observed that the density of the as-prepared foams increased gradually as N-PBSi content increased, and the density of PMI/N-PBSi-20 up to 544 kg·m −3 , about 10 times that of pure PMI foam. Meanwhile, the structure of the foam became more compact with much smaller foam cells. Most of the foam cells for PMI/N-PBSi-15 are a few micron sizes, which is about 2-5 μm, while those for pure PMI foam are mostly more than 100 μm. Benefitting from this, the mechanical strength of the resultant PMI foams was greatly enhanced. The introduction of N-PBSi made PMI foams more rigid but brittle. In addition, N-PBSi also attributed PMI foams to better performance in char forming, especially in air, which is beneficial for flame retardancy. The LOI of PMI/N-PBSi-20 increased to about 22% after testing. The pHRR, pSPR, THR, pMLR, and mMLR were also much lower than pure PMI foam. This is also thanks to the incorporation of N-PBSi, which plays an effective flame-retardant role in both the gas and solid phases. In the gas phase, it can generate phosphorus-containing fragments to capture free radicals in the flame, while in the solid phase it can promote the formation of a more compact carbon layer that acts as a barrier to prevent the entry of external oxygen and heat and at the same time inhibit the escape of internal flammable pyrolysis gases. Given all of these, it can be forecasted that the PMI foams modified by grafting with N-PBSi will be promising for diverse applications.