Super-elasticity at 4K of Covalently Crosslinked Polyimide Aerogels with Ultrahigh Negative Poisson’s Ratio

The deep cryogenic temperatures encountered in aerospace present significant challenges for the performance of elastic materials in spacecrafts and related apparatus. Reported elastic carbon or ceramic aerogels overcome the low-temperature brittleness in conventional elastic polymers. However, complicated fabrication process and high costs greatly limited their applications. In this work, super-elasticity at deep cryogenic temperature of covalently crosslinked polyimide (PI) aerogels is achieved based on scalable and low-cost directional dimethyl sulfoxide crystals assisted freeze-gelling and freeze-drying strategy. The covalently crosslinked chemical structure, cellular architecture, negative Poisson’s ratio (-0.2), extremely low volume shrinkage (3.1%) and ultralow density (6.1 mg/cm) endow the PI aerogels with an elastic compressive strain up to 99% even in liquid helium (4K), almost zero loss of resilience after dramatic thermal shocks (∆T=569 K), and fatigue resistance over 5000 times compressive cycles. This work provides a new pathway for constructing polymer-based materials


Introduction
In the field of aerospace exploration, spacecrafts and supporting apparatus often suffer from the impact of deep cryogenic environments. For instance, the lowest temperature on the surface of Mars is 130~140 K 1 , while the temperature is as low as 50 K on the moon's poles 2 . The Space Shuttle Challenger event shocked the whole world as exploding within 73 seconds after its takeoff due to the elastic failure of rubber O-ring at low temperature, indicating the vitally essential role of elastic materials resistant to cryogenic environment for aerospace exploration.
Unfortunately, most of the conventional intrinsic elastic materials, such as thermo plastic elastomers, natural and synthetic rubbers, generally tend to lose their intrinsic elasticity in deep cryogenic environments. 3,4 To address this problem, structurally elastic aerogels, mainly based on carbon 5 and ceramics 6 , have captured researchers' attention due to their satisfactory elasticity from three-dimensional (3D) network architectures and excellent resistance to deep cryogenic conditions. For instance, graphene coated carbon nanotubes (CNTs) aerogels 7-10 and CNFs aerogels 11 can bear compressive strain of 50% to 90% at 173 K. Notably, Chen et al created graphene aerogels with satisfying recoverability under 98% compressive strain at 77 K 12 or resilience under 90% strain at the deep cryogenic temperature of 4 K 13 . Moreover, ceramic aerogels of BN nanoribbon and nanofibrous SiO2-based composites are also in possession of compressive super-elasticity at 77 K [14][15][16][17] . These newly emerged carbon and ceramic aerogels make significant promotion for the development of elastic materials in deep cryogenic environments, while their complex fabrication process and high cost still raise misgivings.
In this regard, with easy processability and low-cost fabrication, it will be much more intriguing if special polymers can be synthesized and achieve super-elasticity at deep cryogenic environments. Wang et al recently demonstrated a polymeric aerogel composed of low-cost chitosan and melamine-formaldehyde resin, with super-elasticity 3 at liquid nitrogen temperature (77 K), which opens up a new avenue for further development of elastic polymeric materials resistance to deep cryogenic temperature. 18 Among polymeric materials, polyimide (PI) with remarkable resistance to extreme conditions (fire, radiation, chemical corrosion, low and high temperature, etc.) is considered to be potentially ideal candidates for elastic materials applied at deep cryogenic temperatures. [19][20][21][22] Generally, freeze-casting techniques based on watersoluble PI precursors of poly (amic acid) ammonium salt (PAAS) are widely applied in the fabrication of elastic PI aerogels. 23,24 Based on this strategy, various elastic PI aerogels composited with carbon nanotubes 25,26 , graphene 27,28 , silica 29 , MXene 30, 31 and nanofibers 32,33 have been produced, endowing PI aerogels with such promising applications as electromagnetic shielding, oil-water separation, pressure sensors, etc.
Unfortunately, the thermal imidization after freeze-drying in the above strategy inevitably causes large shrinkage up to 40%, greatly impairing the compressibility of elastic PI aerogels. 34 Furthermore, the decomposition of PAAS in water cannot be completely avoided as a result of imperfect salinization of poly (amic acid) (PAA), leading to weak resilience of elastic PI aerogels because of low molecular weight. The recently emerged electro-spun nanofibrous PI aerogels provide an effective pathway to avoid the large shrinkage and decomposition of PAAS in water [35][36][37] , but the incorporation of electro-spun process complicates the whole fabrication process and increases the costs.
In this study, we proposed a novel directional dimethyl sulfoxide crystal assisted freezegelling and freeze-drying (DMSO-FGFD) strategy to construct covalently crosslinked PI aerogels with super-elasticity at deep cryogenic temperatures even down to 4 K.
Chemical imidization without water can be realized to transform PAA into PI oligomers at room temperature in this strategy, thus resulting in extremely low volume shrinkage of 3.1% and density of 6.1 mg/cm 3 , which are far superior to elastic PI aerogels from conventional thermal imidization. Meanwhile, innovative mold design and temperature adjustment endow the obtained PI aerogels with radially distributed cellular structure to realize negative Poisson's ratio (NPR) behavior. Thanks to the covalently crosslinked chemical structure, favorable NPR behavior, extremely low shrinkage and density, the 4 prepared PI aerogels are endowed with fully reversible super-elastic behavior of up to 90% strain, satisfying stability of compressive cycles over 5000 times. Furthermore, the fantastic super-elasticity and fatigue resistance is proved to be temperature invariant over wide temperature range from 4 K to 573 K, and almost zero loss of resilience is observed even after dramatic thermal shocks (∆T=569 K).

Fabrication of PI aerogels
Fabrication of covalently crosslinked PI aerogels with super-elasticity was demonstrated in Scheme 1. Firstly, PI oligomers end-capped by anhydride were obtained through chemical imidization at room temperature by adding acetic anhydride and triethylamine into PAA precursors which were synthesized from 4,4'-oxydianiline (ODA) and 4,4'-oxydiphthalic anhydrides (ODPA) in DMSO solvent ( Figure S1, supporting information). Subsequently, a directional freeze-gel process was carried out by adding the DMSO solution containing PI oligomers and 1,3,5triaminophenoxybenzene (TAB) crosslinkers into a predesigned model subjected to a programmable temperature gradient. At the initial freeze-gelling stage, the DMSO crystals grew horizontally from the periphery to the center, resulting in radially distributed crystals due to a predesigned model and temperature adjustment. After that, the covalently crosslinked PI was formed between vertically grown DMSO crystals.
Finally, 3D honeycombed PI aerogels with radially distributed cellular structure were obtained after freeze-drying to remove DMSO and a thermal treatment to transform residual PAA units into PI. The crosslinking degree of the obtained PI aerogels could be controlled by adjusting the molar ratio of ODPA, ODA and TAB, which is described detailly in the section of materials and methods. The obtained crosslinked PI aerogel is marked as PI-10, PI-20, PI-30, PI-40 when the initial PI oligomers maintain the polymerization degrees of 10, 20, 30 and 40, while PI-L is corresponding to PI aerogels prepared without crosslinker. Theoretically, shorter polymer chains are easier to orient under shear stress due to fewer entanglements between them, resulting in a faster shearthinning effect and lower shearing viscosity. As shown in Figure S2 (supporting 5 information), the shearing viscosity curves of the PI oligomers solution demonstrated an increasingly rapid decrease of viscosity in the shearing thinning region from PI-L to PI-10 as well as progressively lower constant shearing viscosity in the constant viscosity region, illustrating progressively shorter polymer chains from PI-L to PI-10.
More TAB crosslinkers are added into the solution containing shorter PI oligomers to ensure complete reaction of the anhydride groups terminated PI oligomers, resulting in higher crosslinking degrees in the final PI aerogels in accordance with the initial design.
Benefiting from the facile process and low cost of raw materials, bulk PI aerogels with a volume of 300 cm 3 and diverse shapes have been prepared, demonstrating the feasibility of large-scale fabrication based on this creative DMSO-FGFD strategy.

Investigation of DMSO-FGFD process
The DMSO-FGFD process was further investigated in depth. To explore the process of gelling interaction between PI oligomers and TAB crosslinkers, the rheological behavior of PI/TAB/DMSO mixtures was observed on a rotational rheometer as shown in Figure 1a. Under a constant shearing rate, PI-L/DMSO without TAB crosslinkers shows a relatively high zero shear viscosity, but stays constant. In contrast, the viscosity of the PI/TAB/DMSO mixtures possesses a sharp increase at the initial stage demonstrating a high reactivity between PI oligomers and TAB to form covalently crosslinked PI. Besides, from PI-40 to PI-10, the viscosity rising rate and final viscosity tend to increase, which should be mainly attributed to a higher content of reactive groups in the solution with shorter oligomers. Figure 1b illustrates the mechanism of the freeze-gelling process. PI oligomers and TAB show a very low reaction rate and almost stayed uniform in a dilute solution. Upon freezing, phase separation took place, and PI oligomers with TAB were expelled to the boundaries of the DMSO crystals because of the volume exclusion effect, resulting in an increase in the localized concentration of PI/TAB around vertical DMSO crystals. 38 With the continuing growth of DMSO crystals, PI oligomers and TAB diffused to diluted area driven by the concentration gradient, thus forming a high concentration area between DMSO crystals, which significantly promoted the reactivity between PI oligomers and TAB to form the crosslinked PI networks. As a result, an anisotropic frozen gel composed of covalently 6 crosslinked PI and DMSO crystals was obtained. After thawing at 35 ℃, the frozen gel with TAB transformed into an agglomerate wet gel (Figure 1c), verifying the formation of PI with covalent crosslinking in the freeze-gelling process, while the frozen gel without TAB returned to a flowing state in contrast ( Figure S3, supporting information).
Different from the process using water as the solvent, the freeze-drying process with DMSO has rarely been investigated previously. It is generally accepted that stabilization of frozen monoliths is crucial to obtain a satisfactory 3D architecture in a freeze-drying process. The Differential Scanning Calorimetry (DSC) curves demonstrated the melting temperature range of DMSO crystals containing different amounts of PI oligomers (Figure 1d). As the contents of PI oligomers in DMSO reduced from 12 wt% to 0.5 wt%, the melting points (peak value) tend to increase from 9.4 to 16.9 ℃ closing to the melting point of pure DMSO (18.3 ℃). The onset melting points of DMSO solution with different concentrations ranging from -10 to 0 ℃, which determines the upper limit of the freeze-drying temperature at the initial stage.
Furthermore, PI/DMSO solution with a content of 2.0 wt% was chosen to in-situ observe the formation of DMSO crystals in the pre-freeze and analyze temperature range of vacuum drying by the vacuum freeze-drying microscopy system. As shown in Figure 1e, when cooled down from 25 ℃ to -60 ℃ at ambient pressure, parallel DMSO crystals come into being as templates to push PI chains to aggregate between them, demonstrating that the DMSO solvent was beneficial to prepare PI aerogels with wellorganized directional frameworks. The dried area began to enlarge as the temperature rising from -60 to -35 ℃ at vacuum (5 Pa), and then crystal fusion was observed as the temperature reaching -2.0 ℃, which was in accord with the DSC results. It illustrated that temperature range of the vacuum freeze-drying process is -35 to -2 ℃. As a high boiling solvent (189 ℃) with low saturated vapor pressure, DMSO is not easy to be dried. According to simulated results from COMSOL Multiphysics, 4 days are necessary to completely finish the vacuum drying process, which is in line with the experimental results (Figure 1f). 7 The chemical structure of PI aerogels has been characterized by Fourier Transform Infrared Spectroscopy-Attenuated Total Reflection (FTIR-ATR). As seen in Figure S4 (supporting information), the spectra exhibit typical characteristic peaks of imide structure at 1776 cm -1 (imide C=O asymmetric stretching), 1714 cm -1 (imide C=O symmetric stretching), 1371 cm -1 (C-N stretching vibration), 1014 cm -1 and 742 cm -1 (C-N-C stretching vibration). DSC was further taken to analyze the crosslinking structure in PI aerogels. According to the research of Loshaek 39 , Tg of a polymer shows a positive correlation with its crosslinking degree as shown in the following equation. PI aerogels produced by freeze-casting based on PAAS precursor usually suffer from severe volume shrinkage due to thermal stress shock and free volume reduction during the thermal imidization process at 200 ~ 300 ℃, which greatly hinder its practical applications. In this work, benefiting from the good solubility of DMSO, the chemical imidization process and a covalently crosslinked structure were achieved simultaneously to fabricate PI aerogels, which synergistically mitigate the volume shrinkage of the obtained aerogels. As shown in Figure 2b, PI aerogels made by chemical imidization with DMSO display volume shrinkage less than 7.3%, which is much superior to those of 19.5~25.3% from thermal imidization. Additionally, with the increasing of crosslinking degrees, shrinkage tends to be inhibited gradually whether by chemical imidization or thermal imidization. Notably, the volume shrinkage of PI-10 aerogels by chemical imidization can be as low as 3.1%, which is far superior to any reported PI aerogels. 23,32,40 It can be attributed that chemical imidization can transform PAA into PI before thermal annealing in ahead, thus avoiding the decrease of free volume in thermal imidization (proved by molecular dynamic simulation in Figure S5, 8 supporting information). Apart from that, the covalently crosslinked structure usually endows PI aerogels with much better thermal resistance and mechanical properties, which could inhibit the structural damage by thermal stress shock in thermal annealing at high temperatures. Shrinkage of elastic PI aerogels can vary with different chemical structures and constitutions in thermal imidization, while the chemical imidization based on DMSO-FGFD method should be universal for most of elastic PI aerogels to restraint shrinkage effectively.

Structure and morphology
Little volume shrinkage is the premise for ultralow density, high porosity and wellorganized structure in PI aerogels. As shown in supporting information). Such ultralow density, high porosity and well-organized morphology mainly benefit from the minimal shrinkage and ordered DMSO crystals formed in the pre-freezing process. Apart from that, by fine-tuning the solid contents of PI/TAB/DMSO mixtures, the density of final PI aerogels can be tuned from 6.1 mg/cm 3 to 52.5 mg/cm 3 , corresponding to a porosity change from 99.57% to 99.29% ( Figure S7, supporting information). Thus, with this pioneering DMSO-FGFD process, the density, porosity and wall thickness can be adjusted flexibly according to actual practical requirements.
NPR behavior was observed in the obtained PI aerogels due to innovative mold design and temperature adjustment. [41][42][43] With the help of finite element simulation based on COMSOL Multiphysics software, a radial temperature distribution (Figure 2e) was achieved at the initial stage of freeze-gelling through a design with a slightly sunken center on the outer bottom of the mold (Figure S8, supporting information). The contrivable temperature distribution was capable of controlling the growing direction 9 of DMSO crystals from the periphery to the center on the inner bottom (Movie S1, supporting information), resulting in a radially distributed cellular structure of PI aerogels (Figure 2f). According to simulation results, the special structure network reveals a hyperbolic-patterned deformation under compression, depicting obvious NPR behavior (Figure 2g). Figure 2h presents the real longitudinal (εy) and transverse (εx)

Evaluation of Super-elastic performance
Benefitting from the ultra-low density, radially distributed cellular structure with NPR behavior and enhanced crosslinking networks of PI chains, the acquired PI aerogels display anisotropic mechanical performance, such as high stiffness along channel direction and ultra-high flexibility on vertical channel direction. Interestingly, the bulk aerogel is able to bear 2000 times of its own weight ( Figure S9, supporting information) along channel direction, which clearly reveals its strong stiffness. Besides, as shown in The effect of crosslinking degree on compressive stress of PI aerogels was further investigated. As shown in Figure 3b, all prepared PI aerogels can recover under 70% compressive strain, and exhibit a growing tendency of stress with increasing crosslinking degree. Covalently crosslinked structure endows PI-10 aerogels with a compressive stress of 6.5 KPa under 70% strain, which is 2.5 times that of PI-L without crosslinking.
The compressibility and elasticity of PI aerogels have been further evaluated under an ultimate strain of 99%. As shown in Figure 3c, all PI aerogels with different 10 crosslinking degrees can be compressed to 99% due to their extraordinary flexibility and ultra-low density. However, in contrast to complete recovery under 70% compressive strain, PI-L suffers from serious plastic deformation with a residual strain of 37.9% after 99% compression (Figure S10, supporting information). With the incorporation of a covalently crosslinked structure, elastic recovery has been improved, while the residual strain gradually decreases with the increasing of crosslinking degree.
PI-10 aerogels are capable of springing back to their original shape, revealing excellent super-elastic performance. When compared with reported PI aerogels and other polymeric aerogels, PI-10 aerogels display much lower density but far superior elastic properties (Figure 3d). 23, 25-28, 31, 33, 45-51 The highly recoverable compressibility of PI-10 aerogels can be mainly attributed to Interestingly, there was no significant decrease in compressive stress or cracking failure in the cell structure, even after 5000 compression-decompression cycles, indicating excellent long-term stability of PI-10 aerogels (Figure 3g). Additionally, by tailoring the solid content of PI/TAB/DMSO mixtures from 0.5 to 3.0 wt%, the wall thickness of PI-10 aerogels varies from 2 to 10 μm (Figure S13a, supporting information), corresponding to a stress variation of 6.7 to 26.1 KPa at 70% compressive strain ( Figure S13b, supporting information). It reveals that a higher PI concentration in the DMSO solution results in thicker walls and more robust mechanical properties, demonstrating manipulatable structural and mechanical performances.

Evaluation of Super-elasticity at deep cryogenic temperature
The super-elasticity of PI-10 aerogel was further evaluated in a gradually freezing environment from 573 K to 4 K (Figure 4a). PI aerogels exhibit rising thermal decomposition temperature and glass transition temperature (Figure 2b) with the increase of crosslinking degree, and the Td5 (temperature of 95% residual weight) of PI-10 aerogels is up to 539 ℃ that is 19 ℃ higher than that of PI-L aerogels without crosslinking ( Figure S14, supporting information). Benefiting from the enhanced thermal resistance, PI-10 aerogel is able to completely recover to its original shape after suffering from large compressive deformation at 298 K and 573 K. Furthermore, the 12 PI-10 aerogel was soaked in liquid N2 (77 K). Generally, most polymeric materials become hard and brittle under such circumstance. In contrast, PI-10 aerogel could be circularly compressed with 90% strain several times and still perfectly recover without plastic deformation (Movie S3, supporting information). Moreover, the elastic behavior of PI-10 aerogels was further investigated by a single uniaxial compress-release operation in liquid helium (4 K) using a customized apparatus (Figure S15 Figure S16, supporting information). Through the DMSO-FGFD process, chemical structure with covalent crosslinking and a framework structure with NPR behavior have been incorporated into PI aerogels, generating enhanced strength (Figure 4e) matched with increased modulus and remitted energy impact from compression, endowing PI aerogels with excellent super-elasticity at deep cryogenic temperatures. In terms of the application environment with temperature jumps in aerospace, a rapid thermal shock evaluation between 4 K and 573 K was also carried out on PI-10 aerogels (Figure 4f and Figure S17, supporting information). Before and after thermal shocks with a temperature jump of 569 K, PI-10 aerogel still maintains a similar compressibility up to 99% strain and perfect recoverability, with no obvious structural damage being observed. This excellent resistance to thermal shock is vitally important for practical application in extreme environments in aerospace.

Discussion
In summary, we have reported a novel DMSO-FGFD strategy to design and synthesize covalently crosslinked PI aerogels with super-elasticity. Benefiting from an innovative chemical imidization process, this PI aerogel exhibits remarkably ultralow volume shrinkage of 3.1% and an ultralow density of 6.1 mg/cm 3 , which are superior to reported elastic PI-based aerogels. Innovative mold design and temperature adjustment endowed the obtained PI aerogels with a radially distributed cellular structure to realize NPR of -0.2. Ultralow volume shrinkage and density, covalently crosslinked structure and NPR behavior endow the ultralight PI aerogels with the capacity to bear compressive strain up to 99% and perfectly recover its original shape. Surprisingly, obtained PI aerogels also exhibit marvelous super-elasticity at the deep cryogenic temperature of 4 K, which has never been achieved for any polymeric materials. Even after suffering from a thermal shock between 4 K and 573 K, PI aerogels still retain compressibility up to 14 99% strain and perfect recoverability. To this end, these ultralight PI aerogels possess much promise for application as super-elastic materials resistant to deep cryogenic temperature in aerospace exploration. Dimethyl sulfoxide (DMSO) was purchased from Shanghai Taitan Technology Co.,

Materials
Ltd and dried with molecular sieves prior to use. Acetic anhydride (AR) and triethylamine (AR) were purchased from Sinopharm Chemical Reagent Co., Ltd.

Fabrication of covalently crosslinked PI aerogels
Firstly, PI oligomers end-capped by anhydride were obtained through chemical imidization at room temperature by adding n1 mol acetic anhydride and n1 mol triethylamine into PAA precursors which were synthesized from n1 mol ODA and n2 mol ODPA in DMSO solvent. Subsequently, nTAB mol TAB was added into the DMSO solution containing PI oligomers to obtain a uniform mixture. In this work, to adjust the crosslinking degree, the relationship between n1, n2 and nTAB were designed as follows.

= +
Equation (2) = ( − ) Equation (3) where n (n=10, 20,30,40) is the polymerization degree of PI oligomers, and the corresponding PI aerogels were marked as PI-n. Particularly, n1 is equal to n2 in preparing linear PI (PI-L) without crosslinkers. As an example, the preparation of PI-10 aerogels is described as follows: 133.5 g DMSO was added into a 250 mL three-  curves and SEM images of PI-10 aerogels before and after thermal shock test.