1 Introduction

Aerogels are highly porous, predominantly mesoporous solids, typically obtained via sol–gel processes by replacing the liquid component of a wet gel with a gas. Kistler created the first aerogels nearly a century ago, including silica and biopolymer aerogels [1]. Due to their extremely low thermal conductivity, large surface area, and (very) low density, aerogels find application in many fields, such as thermal insulation [2,3,4,5], oil–water separation [6], Cherenkov detectors [7], optical and energy storage devices [8], catalysis [9, 10], electronic [11, 12], aerospace [13, 14], and acoustic applications [15, 16]. In the market, silica aerogels, and their composites are the dominant products, often used for oil-and-gas pipeline and building insulation, and more recently, as thermal runaway protection barriers in Li-ion battery packs for electric vehicles [17].

A key obstacle to the further development of silica aerogels is their poor mechanical behavior, namely, brittleness and dustiness [18], polymeric aerogels have attracted increased research and industry interest mainly due to their better mechanical performance [19]. The research possibilities of organic aerogels are extensive due to the variety of possible precursors and polymer systems [20,21,22,23]. Among polymer aerogels, polyimide aerogels offer the highest thermal stability (>550 °C) due to the imide ring and aromatic backbone structure, along with excellent mechanical properties [24]. These properties, combined with low thermal conductivity, low dielectric permittivity, and low density, encourage the use of polyimide aerogels in aerospace [13], thermally agnostic drones [25], thermal insulation [26], fire-retardancy [27], dielectric insulation [28,29,30], filtration [31], adsorption [32, 33], and absorption [34].

Although polyimide aerogels can also be produced from polyisocyanate and dianhydride [35], their synthesis with the classical DuPont process from diamines and dianhydride is more common [36, 37]. Generally, there are four major stages in the fabrication procedure. First, poly(amic acid) (PAA) oligomers are formed via the addition reaction of diamines and dianhydrides, where the stoichiometry of diamines and dianhydrides adjusts the repeating unit number (an average oligomer length). Then, subsequent cross-linking of oligomers using multifunctional cross-linkers takes place. During the third stage, chemical imidization, a polyimide structure is obtained from cross-linked PAA oligomers through thermal or chemical imidization (condensation, evolved water reacts with water scavengers). The final step is the gel-to-aerogel transformation using supercritical CO2 drying.

Various polyimide aerogels with different properties have been obtained by changing the synthesis parameters over the last decade [38,39,40,41,42]. Many parameters affect the final microstructure and properties of polyimide aerogels, including the selection of monomers and their molar ratios for addition and polycondensation [43], the number of repeating units, cross-linking agents [44], gelation and exchange solvents, and imidization as well as drying conditions. Two of the essential parameters in aerogel fabrication are the total polymer concentration in the sol (mdiamine + mdianhydride + mcross-linker)/(msolvent + mdiamine + mdianhydride + mcross-linker) and the number of repeat units (n = the average oligomer length in the PAA solution = the average number of repeat units between the cross-links in the gel). Repeat unit (n) is inversely related to the cross-linking density, and typically, the cross-linker concentration is adjusted to achieve nominal full cross-linking, the same in this study.

Many studies were carried out to understand the effect of monomers [45,46,47], diverse oligomer’s lengths [36], polymer concentration [39, 48, 49], choice of cross-linkers [39, 44, 45], and different solvents [38, 50] (single or mixed) on final properties of polyimide aerogels. The eternal dilemma is that, in most cases, as one property improves, the other deteriorates. Therefore, it is necessary to prioritize the essential properties of the final material based on its further application. Some comparison studies showed that by choosing different monomers and tuning their ratio for various aerogel formulations, thermal stability increased, but some density and porosity were reduced [36]. Systems with a more flexible polymer backbone with fluorine in the structure possess good dielectric properties, lower water uptake, and better mechanical performance [46]. Aerogels from monomers (4,4′-oxydianiline (ODA) and biphenyl-3,3′,4,4′-tetracarboxylic dianhydride (BPDA)) taken in a ratio of 50:50 mol% result in enhanced mechanical strength, increased hydrophobicity and lower dielectric constant [40]. Specific cross-linkers reduced shrinkage and density [39, 44]. Solvent systems are also critical: simply by tuning the solvents ratio or surfactant concentration, tailored polymer strand diameter, mesopore and macropore fractions, SSA, and improved compressive modulus could be achieved using N,N-dimethylformamide (DMF), N-methyl-2-pyrrolidon (NMP) and N,N-dimethylacetamide (DMAc) as a single solvent or their mixture [38].

As shown above, the choice of precursors, cross-linkers, and reaction solvents has a tremendous effect on the final properties of aerogels, which have been studied in detail. However, there are few systematic studies on the influence of repeating unit number (oligomer length and cross-linking density) and polymer concentration on the properties of polyimide aerogels, particularly where thermal conductivity is concerned.

Here, we use the most common reagents for polyimide aerogels as a reference system to investigate the effect of polymer concentration and repeating unit numbers on the aerogel microstructure and properties. Specifically, BPDA and ODA were utilized as monomers, NMP as a general solvent, 1,3,5-Tris(4-aminophenoxy)benzene (TAB) as a cross-linker, and acetic anhydride and pyridine as chemical imidizers (Scheme 1). Systematically, 16 formulations of polyimide aerogels with different repeating units, polymer concentrations, and identical backbone structures were fabricated (Table S1) and characterized by nitrogen sorption analysis, SEM, mechanical testing (compression and three-point bending), and thermal conductivity measurements.

Scheme 1
scheme 1

The synthesis of ODA–BPDA polyimide aerogels

Full size image

2 Experimental section

2.1 Materials

3,3′,4,4′-Biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-oxydianiline (ODA) were purchased from Sigma Aldrich. The cross-linking agent 1,3,5-Tris(4-aminophenoxy)benzene (TAB) was produced from Haorui Chemicals Co., Ltd. Pyridine (99 + % extra pure) was obtained from Acros Organics, and acetic anhydride (AA, 99.5%) was obtained from Lonza. N-methyl-2-pyrrolidon (NMP) was purchased from Gute Chemie abcr. Ethanol (95 v% ethanol/5 v% isopropanol, Alcosuisse AG) was used as a solvent for solvent exchange and supercritical CO2 drying. All reagents were used as received without further purification.

2.2 Preparation of polyimide aerogels

Diamine (ODA) and dianhydride (BPDA) were taken in the ratio of n:(n + 1) to form anhydrate-terminated PAA oligomers, and the TAB content matches the excess dianhydride was kept at 3:2 to guarantee the full cross-linking, i.e., a 2:3 ratio of (tri-functional) TAB to (di-functional) excess dianhydride. The repeating unit was set at 5, 15, 30, and 45; the polymer concentration was set at 4, 7, 10, and 13 wt%.

ODA (1.8339 g, 9.16 mmol) was mixed with 40 mL of NMP in a three-neck round-bottom flask with a mechanical overhead stirrer. Once ODA was wholly dissolved (10 min), BPDA (2.7545 g, 9.36 mmol) was added to the flask and stirred for 40 min to ensure anhydride-terminated PAA oligomers formed. Afterward, the solution of TAB dissolved in an additional 20 mL of NMP was added to cross-link the PAA oligomers. Once a homogenous solution was obtained (2–3 min after adding TAB), the premix containing acetic anhydrate (6.9 mL, 73.28 mmol) as a water scavenger and pyridine (5.9 mL, 73.28 mmol) as an imidization catalyst was added and stirred for 2–3 min. Afterward, the polyimide solution was poured into various molds (Fig. 1b): stripes for flexural testing, cylinders for uniaxial compression, and square-shaped plates for thermal conductivity measurement. After casting, the gelation process was monitored using by video. The gelation time was defined as the duration until the transparent yellow PAA/polyimide solution became opaque polyimide gels. The gels were aged for 24 h at room temperature before solvent exchange. Within 72 h, solvent was exchanged four times: 30 v% ethanol–70 v% NMP, 50 v% ethanol–50 v% NMP, 70 v% ethanol–30 v% NMP, and 100 v% ethanol to make sure the gels were filled with over 99.5 v% of ethanol (determined by solvent density) before drying.

Fig. 1
figure 1

a Picture of synthesized polyimide aerogels. b Synthesis scheme

Full size image

The polyimide alcogels were converted to aerogels using supercritical CO2 drying at 120 bar (12 MPa), 50 °C for 7 h, followed by 1-h ambient pressure oven drying at 65 °C to remove any possible residual solvent from the samples. The size and mass of square-shaped and cylindrical samples were recorded to calculate the shrinkage during and after processing and the bulk density. The duration of all steps during the fabrication process was kept constant, as described in the protocol above. However, depending on the composition of formulated aerogels (larger total polymer concentration), for the more viscous formulations, the stirring time after the addition of BPDA was extended up to 1.5 h to obtain a transparent homogeneous PAA solution (e.g., 13 wt%, n = 30 and n = 45).

From the 16 formulations, three of the aerogels at the extremes in parameters show visible defects (Fig. 1a): the 4 wt%/n = 5 aerogel was very fragile, and intact monoliths could not be prepared, whereas the 13 wt%, n = 30/45 aerogels were not very homogenous in color and microstructure, presumably due to insufficient mixing/degassing due to the high sol viscosity. Some characterizations were not possible for these parameter combinations.

2.3 Density and pore volume

Bulk density (ρbulk) of polyimide aerogels was calculated after SCD as mass/volume ratio for cylindrical and square-shaped samples. The uncertainty on the bulk density arises almost entirely from the volume determination and is on the order of 1–3% relative. Skeletal density (ρskeletal) was measured using Accupyc II 1340 Helium Pycnometer from Micromeritics, with an uncertainty below 1% relative, and the values were utilized for the porosity calculations: Vpore,cal = 1/ρbulk − 1/ρskeletal. The average pore size was calculated from the pore volume and SSA (SBET) assuming cylindrical pores Dpore,cal = 4Vpore,cal/SBET.

2.4 Microstructural analysis

The nitrogen adsorption–desorption was obtained by analyzer Micromeritics, 3Flex at 77 K. Quantitative information such as SSA and pore size distribution was calculated based on Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Hacienda (BJH) methods accordingly. Before analysis, aerogels were degassed for 15 h at 80 °C at 0.02 mbar (2 Pa). Although the statistical uncertainty for the SSA is typically very low (<1% relative), the accuracy on the surface area is lower when the limitations of the BET model and its assumptions are taken into account. The pore volume and pore size distribution, as determined by BJH analysis, do provide a measure of the mesopore structure, but values should not be over-interpreted due to the known limitations for aerogel, e.g., the inability to probe macropores (>100 nm) and the possible sample deformations during nitrogen sorption analysis. SEM images were acquired on a ZEISS GeminiSEM 460 at an accelerating voltage of 5 kV, and a working distance of ~6.5 mm. Fifteen nanometers of Pt (measured with a flat piezo detector) were coated to avoid charging before the measurement. An accelerating voltage of 2 kV was used only for the TAB 1 (4 wt%, 5n) sample to achieve better focus under high resolution.

2.5 Mechanical properties

Mechanical performance (compression and three-point bending) was recorded on an AllroundLine universal testing machine Z005 by Zwick Roell (Germany) equipped with a 5 kN load cell. For compression testing, cylindrical samples were prepared with a length/diameter ratio of 1.5–2. Samples were polished to get smooth and parallel upper and bottom surfaces to ensure uniaxial compression. The specified test speed was 5 mm/min, and the compression test was completed as soon as 80% deformation of the sample was achieved. The compressive Young’s modulus (E) was obtained from the slope of the initial linear region of the stress–strain curve up to ~4–5% strain (average of three specimens of each batch). The standard deviation on the compressive Young’s modulus was below 5% relative for all samples, except those prepared from the highest polymer concentration (13 wt%, standard deviations from 5 to 20%). Stripe samples nominally in dimensions of 80.5 × 10.0 × 4.8 mm3 were prepared for a three-point bending test, but it should be noted that variable shrinkage of aerogels among formulations led to different sample sizes. The specified test speed was 5 mm/min, and the support span length is 50 mm. The flexural Young’s modulus was derived from the initial slope of the bending curve (linear elastic region, average of five specimens of each formulation). On average, the standard deviation on the flexural modulus was 18% relative (between 3 and 45%).

2.6 Thermal conductivity

Thermal conductivity measurements were conducted using a custom-built guarded hot-plate device (50 × 50 mm2 of guarded zone and 25 × 25 mm2 of measuring zone) [35]. Square-shaped monolithic polyimide aerogels with nominal dimensions of around 55 × 55 mm2 and thickness of 7–12 mm were prepared for the measurement. The reproducibility of the measurements is high, <0.5 mW/(m·K), but the accuracy is estimated to be on the order of ±1 mW/(m·K) when calibration uncertainties and deviations from ideal sample geometries are taken into account.

2.7 Thermal stability

Thermogravimetric analysis was conducted on a Netzsch TG 209F1 Thermogravimetric Analyzer operating at 10 K/min in a reconstituted air atmosphere.

2.8 Chemical structure

Attenuated total reflectance–Fourier transform infrared (ATR–FTIR) measurements were performed on a spectrometer from Bruker Switzerland AG with the ATR name Tensor 27 over the wavenumber range from 500 to 4000 cm−1.

3 Results and discussion

3.1 Gelation time and chemical characterization

The gelation time is defined here as when the transparent PAA/polyimide solutions become opaque polyimide gels, i.e., where the phase separation of polyimide from the solvent (NMP) occurs. After the addition of chemical imidizers (the mixture of acetic anhydride and pyridine), soluble PAA is converted into insoluble polyimide gradually, confirmed by FTIR (Fig. S1), and the accumulation of insoluble polyimide induces the phase separation, which is reflected optically from the transition to an opaque state. Apparent gelation times for polyimide aerogels were recorded using a camera (Table S1, Fig. 2). Because the gelation time is based on visual inspection of the camera footage, there is some subjectivity in defining the time. However, because the transition was prominent, we estimate that this visual determination of gelation time is based on phase separation and microstructure formation (in response to imidization). This deviates from the classical view on gelation based on the rapid increase in viscosity as a spanning cluster forms across the sample. During the preparation, the imidization agents were added quickly after the addition of the TAB cross-linker to the PAA solution (after 2–3 min of stirring). During this short time, a rapid increase in viscosity or gelation of the PAA solution was not observed.

Fig. 2
figure 2

The function of apparent gelation time vs. polymer concentration for different n

Full size image

With the increase of total polymer concentration, the apparent gelation time strongly reduces, from as long as 2.5 h at the lowest polymer concentration to as short as 2 min at the highest polymer concentration. For all polymer concentrations, the gelation time decreases as the number of repeat units n increases (Table S1, Fig. 2). As seen from the variation of the gelation times, the number of repeat units (oligomer length) and polymer concentration play a role in the phase separation process. Higher polymer concentration induces fast phase separation from solvents. High repeating units, i.e., longer oligomer chain lengths and less cross-linking, cause faster phase separation, attributed to the higher degree of rotational and conformational freedom that enables the polymers to bundle up and align into nanofibers more rapidly.

The chemical structure of synthesized polyimide aerogels (Scheme 1) was confirmed by FTIR for a selected formulation (Fig. S1, 7 wt%, 30n). The spectrum is nearly identical to that of ODA–BPDA based polyimide aerogel in a previous study, where the peak assignment and structure are discussed in detail [26]. For example, the peaks at 1780, 1720, and 1380 cm−1 confirm the presence of the imide ring. Solid-state NMR studies on polyimide aerogels prepared with near-identical formulations confirmed the chemical structure as well [36, 51]. Polyimide in general and polyimide aerogels are well-known for their outstanding thermal stability. Thermogravimetry analysis (TGA) was performed on the selected synthesized polyimide aerogels (4 wt%, 45n) in an air atmosphere, showing the temperature for 5% weight loss at 330 °C and the major decomposition peak at 655 °C (Fig. S2).

3.2 Shrinkage and density

Gel and aerogel shrinkage occurs after aging (3–12 v%, Fig. S3), solvent exchange (5–16 v%, Fig. S4), and most notably SCD (16–51 v%, Fig. 3b). The shrinkage depends on both the polymer concentration and cross-linking density. Counter-intuitively, the shrinkage increases and volumetric yield decreases (Figs. 1a, 3b) with increasing polymer concentration. This is in line with previous studies on polyimide aerogels using different precursors, which also observed an increased shrinkage at higher polymer concentrations [48, 52]. However, this trend for polyimide aerogels is in stark contrast to most (bio)polymer aerogels, for which an inverse correlation is observed, i.e., sufficiently high polymer concentrations are required to help the gel maintain its volume during the solvent exchange and drying processes [53, 54]. The reason behind the higher shrinkage, i.e., lower volumetric yields, for higher polymer concentrations for the polyimide aerogels investigated here and those investigated previously remains unknown but could be related to the specific structure formation process in polyimide aerogels during the conversion of soluble PAA to insoluble polyimide.

Fig. 3
figure 3

The function of (a) density vs. polymer concentration and n, (b) volumetric shrinkage after drying vs. polymer concentration and n

Full size image

For a given polymer concentration, a lower number of repeat units, hence a higher cross-linking density, helps the gels to resist shrinkage during processing and drying. A similar influence of high cross-linking density on shrinkage has been reported before, but not for all polyimide chemistries. For BPDA, p-phenylenediamine (PDA) formulated polyimide aerogels chemically cross-linked with 2,3,6,7,14,15-hexaaminotriptycene (HMT), the shrinkage was minimal for polyimide aerogel with the highest cross-linking density (around 10 v%), about half of compared to a polyimide aerogel with the same chemical backbone, but without cross-linking [24]. In contrast, polyimide aerogels synthesized using 1,12-dodecyldiamine (DADD), 3,3′-dimethylbenzidine (DMBZ), BPDA as monomers, and TAB as a cross-linker, displayed a shrinkage from 8 to 26 v%, but repeating units (n) and cross-linking density had an insignificant impact [48]. Meador et al. used different combinations of aromatic diamines and dianhydrides cross-linked with TAB and formulated various oligomer chain lengths (n = 15, 20, 25, 30) to examine their effect on final properties and reported that polyimide aerogels shrank between 19 and 48 v% depending on polyimide aerogel’s composition [36].

The final aerogel density increases with the increase of polymer concentration because of the higher fraction of solid skeletons in the final aerogel structures due to the higher polymer concentration in the sol and the higher degree of shrinkage at higher polymer concentration. Because highly cross-linked aerogels, i.e., with a small number of repeating units, shrink less, their density is lower for a given polymer concentration and approaches the density expected theoretically from the polymer concentration in the sol (Fig. 3a).

3.3 Microstructure

The pore structure and SSA were probed by nitrogen sorption analysis and BET & BJH analysis of the isotherms. The polyimide aerogels display typical adsorption/desorption type IV isotherms with H1 or H2 hysteresis of the IUPAC classification (Fig. S5). The hysteresis loop indicates the existence of a substantial mesopore fraction in the aerogels. The SSA varies from 320 to 403 m2/g (Fig. 4a), with a maximum surface area at an intermediate polymer concentration of 7 wt%, except for n = 30 (10 wt%). Additionally, at a fixed polymer concentration, the surface area decreases with the increase in repeating units, i.e., higher cross-linking density leads to higher SSAs.

Fig. 4
figure 4

a BET specific surface area. b BJH pore volume of the fabricated polyimide aerogels vs. polymer concentration and repeat units

Full size image

The BJH pore size distributions are broader for lower-density aerogels (Fig. S6). Moreover, the BJH pore volume increases with increasing polymer concentration (Fig. 4b), despite the overall decrease in porosity (Fig. S7). The increase in BJH pore volume is consistent with the much higher quantities of adsorbed nitrogen at P/P0 approaching 1 in the isotherms (Fig. S5) [55] and with the decrease in pore size with increasing density (Fig. S8). The increase in BJH (and mesopore) volume with increasing polymer concentration is mostly independent of the number of repeating units. Although the SCD process eliminates capillary stress during drying, the higher fraction of mesopores at higher polymer concentrations may be a contributing factor to the increased shrinkage discussed above (Fig. 3b).

SEM images were recorded for selected aerogels to image the microstructure directly (Fig. 5): TAB 1 (4 wt%, 5n), TAB 6 (7 wt%, 15n), TAB 11 (10 wt%, 30n), and TAB 16 (13 wt%, 45n), i.e., the bottom-left to top-right diagonal in Fig. 1a. All polyimide aerogels have an open-porous and 3D interconnected nanofibrillar network structure that is homogenous over supra-micrometer length scales (Fig. 5e). SEM images of aerogels should not be over-interpreted due to possible artifacts related to the conductive coating and different contrast/brightness settings [56]. Nevertheless, Fig. 5a–d shows that with the increase of total polymer concentration from 4 to 13 wt%, the nanofiber networks become denser, and pore sizes get smaller, leading to the more significant mesopore fraction consistent with the BJH pore volumes (Fig. 4b). The SEM images seem to hint that the nanofibers themselves may increase in diameter with increasing polymer concentration, but no efforts were made to quantify this given the afore-mentioned problems with SEM artifacts. If real, the coarsening of the nanofibers would be consistent with the decrease in surface area (Fig. 4a) with increasing polymer concentration, at least in the range from 7 to 13 wt%.

Fig. 5
figure 5

SEM images of polyimide aerogels formulated with (a) n = 5 and 4 wt% polymer concentration, (b) n = 15 and 7 wt% polymer concentration, (c) n = 30 and 10 wt% polymer concentration, (d) n = 45 and 13 wt% polymer concentration, and (e) lower magnification SEM image

Full size image

3.4 Mechanical testing

Uniaxial compression was performed on each formulation, and the stress–strain curves are plotted in Fig. 6a. The repeatability of compression testing for three samples of the same formulation is shown in Fig. S9. Figure 6a represents typical stress–strain curves for each aerogel formulation. All polyimide aerogels could be compressed to at least 80% strain without fracture, confirming the non-brittle nature of polyimide aerogels, in line with most polymer and biopolymer aerogels, but in stark contrast to most silica aerogels. The compression is irreversible, i.e., the aerogels did not recover a significant fraction of their original volume upon decompression, and the compression curves represent mainly plastic deformation. The linear short part of curves at low strain could indicate an elastic region [57], but this was not verified experimentally by compression–decompression cycles between 0 and 3% strain (Fig. 6b). The compressive Young’s modulus (E) was obtained from the slope of the initial linear region of the stress–strain curve up to ~4–5% strain (average of three specimens of each batch). The compressive Young’s modulus varies from 1.7 to 26.8 MPa and increases with increasing polymer concentration (Fig. 6c) and density (Fig. 6d), as is typical for polyimide and other aerogels [36]. Because the shrinkage increases with the number of repeating units n (Fig. 3b), higher E-moduli are expected for n = 45, and this is indeed the case (Fig. 6c), except for TAB 16 (13 wt% and n = 45), which was obtained from a highly viscous sol and thus has many defects and bubbles which reduce mechanical strength (Fig. 1a).

Fig. 6
figure 6

a Typical stress–strain curves for compression of all synthesized polyimide aerogels. b The zoomed-in initial liner part of typical stress–strain curves. c Compressive Young’s modulus vs. polymer concentration for different n. d Compressive Young’s modulus vs. density for different n in log–log scale

Full size image

The functional relationship between the compressive modulus (E) and density (ρ) for aerogels is generally described as a power-law behavior, E~ρm, where network material and structure determine the exponent m, which usually varies from 1 to 4 [25]. The polyimide aerogels in this study, formulated with BPDA and ODA, follow a power-law dependence with a strong correlation coefficients of R2 = 0.99 and exponent m of 1.64–2.31, with no significant dependence on the number of repeating unit (Fig. 6d). This exponent is consistent with the theoretically expected value for open-celled foam-like materials [58]. In previously reported polyimide aerogel works, the exponent m is 1.52 for BPDA–ODA, 2.15 for BPDA–ODA/DMBZ, and 2.55 for BPDA–DMBZ, respectively [44]. For carbon and resorcinol-formaldehyde aerogels, m is about 2.7 [59]. For biopolymer-based aerogels, m is ~1.8 for cellulose, ~3.7 for chitosan, ~4.5 for pectin, and ~2.9 for alginate [60]. The exponent m for silica aerogels ranges from 2.5 to 4 [60]. In the case of polyurea-based aerogels, power-law exponent values reported of ~3.5 and ~4.4 differ when using diverse polyols for synthesis [61].

In addition to the compression tests, three-point flexural bending was performed on all obtained polyimide aerogels (Fig. 7). The flexural Young’s modulus was derived from the initial slope of the bending curve (linear elastic region, average of 5 specimens of each formulation, Fig. S10). The flexural modulus increases with increasing total polymer concentration from 4 to 72 MPa. For polymer concentrations up to 10 wt%, there is no significant effect of the number of repeating units on the flexural modulus. For the aerogels prepared from 13 wt% polymer sols, there is a substantial and positive dependence on the flexural modulus on the number of repeat units, but this effect can be accounted for by the difference in shrinkage and density for these samples (Fig. 3). Similar influences of repeat units and polymer concentration on flexural modulus have been noticed while comparing three-point bending data for polyimide aerogels in this work with data reported before [48]: at a fixed n and DADD content, increasing polymer concentration increased the flexural Young’s modulus, with no substantial effects of the number of repeat units, except at the highest polymer concentration. In summary, both the compressive and flexural properties scale first-and-foremost with aerogel density: the observed dependencies on polymer concentration or cross-linking density disappear with all data falling onto a single trend when plotted as a function of density. Hence, the effects of cross-linking density and polymer concentration on the mechanical properties are indirect, i.e., through the effect these parameters exert on shrinkage and final density (Fig. 3). This observation is not unexpected: because aerogel density has such a strong, overriding effect on mechanical properties, and because there are only limited variations in microstructure, e.g., nanofibril diameter or network topology (Fig. 5), possible subtle effects from the polyimide chemistry, e.g., cross-linking density, on the mechanical properties of the polyimide phase itself cannot be discerned.

Fig. 7
figure 7

a Typical stress–strain curves from three-point bending of all synthesized polyimide aerogels. b Flexural Young’s modulus vs. polymer concentration for different n

Full size image

3.5 Thermal conductivity

Thermal conductivity measurements were performed for all formulations (Table S2) except for those that were too fragile (Fig. 1a, TAB 1). The thermal conductivity displays a U-shaped dependence on polymer concentration and density, with a minimum thermal conductivity for polymer concentrations near 7 or 10 wt% (Fig. 8a) and densities around 0.100 g/cm3 (Fig. 8b). The minimum thermal conductivity is shifted to a higher polymer concentration for the n = 5 aerogels, but this appears to be simply due to the reduced shrinkage for these highly cross-linked aerogels (Fig. 3b). Indeed, a single minimum is observed when thermal conductivity is plotted as a density function. In terms of absolute values, the thermal conductivity is around 25 mW/(m·K) for densities around 0.050 g/cm3, decreases to 21–23 mW/(m·K) around 0.100 g/cm3 and then increases to up to 32 mW/(m·K) at densities of 0.200 g/cm3. The thermal conductivity at the minimum is well below that of standing air (26 mW/(m·K) at STP), highlighting the superinsulating, mesoporous nature of the materials.

Fig. 8
figure 8

The function of thermal conductivity vs. (a) polymer concentration for different n, (b) density for different n

Full size image

A U-shaped density dependence is commonly observed for porous materials, in particular for aerogels [62, 63]. At low density, the pores are too large to effectively reduce the gas phase conduction through the Knudsen effect. The solid network becomes too dense and interconnected at high density and solid contributions to the thermal conductivity increase [63].

Many studies describe the density dependence of aerogel thermal conductivity for different aerogel systems: for resorcinol-formaldehyde aerogels, a minimum of 12 mW/(m·K) is observed near 0.157 g/cm3 [64]; for silica aerogels, thermal conductivity is <15 mW/(m·K) at 0.11–0.12 g/cm3 [65, 66]; for pectin aerogels the lowest thermal conductivity is 15 mW/(m·K) at 0.100 g/cm3 [62]; for cellulose aerogels, the minimum is about 18 mW/(m·K) at 0.065–0.090 g/cm3 [67, 68]; for polyurea aerogels, the minimum thermal conductivity is about 13 mW/(m·K) at around 0.16 g/cm3 [3]. For polyimide aerogels, the density dependence of thermal conductivity has not been studied in great detail. Our recent papers on polyimide-silica(-fiber) aerogel composites also hint at a U-shaped density dependence, but the interpretation is complicated by the other components in the composites [25, 51]. In addition, a previous parameter study on polymer concentration reported thermal conductivities above 30 mW/(m·K) for all investigated densities (0.080–0.014 g/cm3), with no clear minimum as a function of density [69]. Their precursor, cross-linker, and solvent chemistries were very similar to the current study, so it is not a priori clear where the differences originate from. However, aerogel properties can depend on minor changes in procedure; for example, their surface areas were also lower by about 20%.

The rapid increase in thermal conductivity at densities above 0.150 g/cm3 is somewhat surprising: the increase is more pronounced than for other aerogel chemistries, yet these denser aerogels display a rapid increase in mesopore volume (at least when approximated by nitrogen sorption analysis). Hence, this increase in total thermal conductivity must be related to a strong increase in solid conduction. Given the low thermal conductivity of bulk polyimide, this rapid increase in solid conduction must relate to the microstructure, e.g., a relatively low tortuosity of the nanofibrillar network, strong thermal connections where the fibrils merge, or a combination thereof.

The data clearly indicate that density is the predominant determinant for thermal conductivity. However, the number of repeating units also seems to have a minor impact, with about 2 mW/(m·K) higher values at the minimum for the n = 30 series. Incidentally, the n = 30 series display among the lowest SSAs (Fig. 4a), i.e., the coarser microstructure.

4 Conclusions

In this work, we systematically evaluated the effect of polymer concentration, oligomer length, and cross-linking density on the microstructure and properties of polyimide aerogels, using BPDA and ODA as representative monomers and TAB as the cross-linker. Increasing polymer concentration dramatically reduces gelation time and leads to higher density and improved compressive and flexural mechanical performance. However, increased polymer concentrations also induce higher volumetric shrinkage, with corresponding increases in density. The surface area is highest for intermediate polymer concentrations, whereas the mesopore volume is highest for the highest polymer concentration. The number of repeating units, which determines oligomer length and cross-linking density, strongly influences volumetric yield, with lower shrinkage and higher yield at higher cross-linking density. The number of repeating units also significantly influences the SSA. For a given polymer concentration, lower oligomer length and higher cross-linking density lead to a higher SSA. A typical U-shaped density dependence of the thermal conductivity is observed, with thermal conductivities as low as 21.4 mW/(m·K) at a density near 0.100 g/cm3. For a given density, the thermal conductivity is about 2 mW/(m·K) lower for more highly cross-linked samples, i.e., those with higher surface areas. This study was carried out using two common precursors (BPDA and ODA) and the most common solvent for polyimide aerogel synthesis (NMP). Without experimental confirmation, it is not possible to evaluate in how far the trends observed here can be used to predict the sol–gel behavior and properties of polyimide aerogels prepared from other precursors and/or with other solvent systems. However, at least on a qualitative level, the observed trends on how the microstructure, shrinkage, mechanical properties, and thermal conductivity vary as a function of polymer concentration and cross-linking density may very well translate to other polyimide precursors and gelation solvents. In addition, our study highlights the importance of polymer concentration and cross-linking density. Hence, this systematic study provides inspiration and guidance for future research, materials optimization, application development, and the production of polyimide aerogels.