WO2018200838A1

WO2018200838A1 - Highly branched non-crosslinked aerogel having macropores, methods of making, and uses thereof

Info

Publication number: WO2018200838A1
Application number: PCT/US2018/029603
Authority: WO
Inventors: Garrett Poe; Alan SAKAGUCHI; Nicole LAMBDIN; Kenneth KOLDAN; David J. Irvin
Original assignee: Blueshift Materials Inc
Current assignee: Blueshift Materials Inc
Priority date: 2017-04-28
Filing date: 2018-04-26
Publication date: 2018-11-01
Anticipated expiration: 2019-10-28

Abstract

An aerogel, and methods for making and using the same, are disclosed. The aerogel can include an open-cell structure and a branched polyimide matrix comprising macropores, wherein the matrix contains less than 5% by weight of crosslinked polymers.

Description

HIGHLY BRANCHED NON-CROSSLINKED AEROGEL HAVING MACROPORES,

METHODS OF MAKING, AND USES THEREOF

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims benefit to U.S. Provisional Application No. 62/491833 filed April 28, 2017 and U. S. Provisional Application No. 62/508,506 filed May 19, 2017, both of which are incorporated herein by reference in their entirety without disclaimer.

BACKGROUND OF THE INVENTION

A. Field of the Invention

[0002] The present disclosure relates to the field of polymeric aerogels. In particular, the invention concerns aerogels made from a branched polyimide matrix having low, or substantially no crosslinked polymers. The aerogels of the present invention are porous and can be structured such that the majority of the pore volume in the aerogels are made up of macropores (pores having a size of greater than 50 nm in diameter).

B. Description of Related Art

[0003] A gel by definition is a sponge-like, three-dimensional solid network whose pores are filled with another non-gaseous substance, such as a liquid. The liquid of the gel is not able to diffuse freely from the gel structure and remains in the pores of the gel. Drying of the gel that exhibits unhindered shrinkage and internal pore collapse during drying provides materials commonly referred to as xerogels.

[0004] By comparison, a gel that dries and exhibits little or no shrinkage and internal pore collapse during drying can yield an aerogel. Aerogels are generally characterized as having high porosity where the majority of the pore volume being made up of micropores (pores having a size of less than 2 nm in diameter) and/or mesopores (pores having a size of 2 nm to 50 nm in diameter), high specific surface area, and relatively low densities. High porosities can confer a number of useful properties to aerogels, including high surface area, low refractive index, low dielectric constant, low thermal-loss coefficient, and low sound velocity.

[0005] Aerogels made from organic polymers (e.g., polyimides or silica/polyimide blends) provide lightweight, low-density structures; however, they tend to exhibit low glass transition temperatures and degrade at temperatures less than 150 °C. Attempts to improve the thermal properties of the aerogels have included cross-linking tri, tetra, or poly-functional units in the structure. NASA Technical Brief LEW 18486-1 describes polyimide aerogels having three- dimensional cross-linked tri -functional aromatic or aliphatic amine groups or, in the alternative, capping long-chain oligomers with latent reactive end caps that can be cross-linked after a post cure of the dried gels. U.S. Patent No. 8,974,903 to Meader et al. discloses a porous cross-linked polyimide-urea network that includes a subunit having two anhydride end-capped polyamic acid oligomers in direct connection via a urea linkage. U.S. Patent No. 9, 109,088 to Meader et al. discloses cross-linked polyimide aerogels that include cross-linked anhydride end-capped polyamic acid oligomers. While these cross-linked polyimide aerogels have demonstrated good mechanical properties, they are difficult to manufacture commercially, and cross-linked polymers are difficult to reprocess or recycle. The lack of manufacturability and recyclability can have a negative impact on production scale-up, large-scale manufacturing, conformation to irregular surfaces, or maintaining integrity in dynamic conditions.

SUMMARY OF THE INVENTION

[0006] A discovery has been made that provides a polyimide aerogel with improved manufacturability and recyclability over conventional polyimide aerogels. The discovery is premised on an aerogel made from a polyimide polymer having a high degree of branching and low or no cross-linking in combination with the presence of macropores in the polymeric aerogel matrix. It was surprisingly found that a large amount of multifunctional monomer could be incorporated into the polyimide structure with a minimal amount to no crosslinking. Further, the presence of macropores can help facilitate the manufacture of aerogels, because macropores are larger and less likely to collapse during the drying stage of manufacturing. This can result in a more economically efficient and less complicated drying process, thereby allowing for a more commercially scalable process when compared with known mesoporous and/or microporous structured aerogels. Additionally, the presence of macropores can improve any one of or all of the flexibility, strength, gas permeation, and/or the strength to density ratio of the formed aerogels. In some preferred embodiments, the majority {e.g., more than 50%) of the pore volume in the aerogels of the present invention can be made up from macropores. In even further instances, over 55 %, 60 %, 70 %, 80 %, 90 %, 95 %, 99%, or 100%> of the pore volume of the aerogels can be made up of macropores. In instances where less than 100%> of the pore volume is made up of macropores, such aerogels can also include mesopores and/or micropores. For example, aerogels of the present invention can include macropores, a combination of macropores and mesopores, a combination of macropores and micropores, or a combination of macropores, mesopores, and micropores. This porous architecture along with the incorporation of the multifunctional monomer in the polyimide structure is believed to contribute to the improved manufacturability and recyclability properties of the aerogels of the present invention.

[0007] Even further, the methods presented herein provide a novel method for the production of polyimides having little to no crosslinking. Previous polyimide matrix production methods rely upon adding a trifunctional monomer/crosslinking agent and imidizing the chemicals simultaneously or near simultaneously. This concerted process has proven to be difficult to control. The polymers presented herein are more highly branched than previously available polymers.

[0008] In one aspect of the invention, macroporous-structured highly branched polyimide aerogels are described. A macroporous-structured branched polyimide aerogel can include a polymeric matrix that includes macropores. At least 10% of the aerogel's pore volume is made up of macropores. In some aspects, the present disclosure provides an aerogel that includes an open- cell structure, a branched polyimide matrix, and macropores present within the matrix. In some particular embodiments, the aerogel can be a macroporous aerogel such that a majority of its pore volume is made up of macropores. In some instances, the macroporous aerogel can also include micropores and/or mesopores. The pore size of the aerogel can be designed to meet the application. In some embodiments, the aerogel average pore size (diameter) can be greater than 50 nm, greater than 50 nm to 5000 nm, preferably 250 nm to 2000 nm, more preferably 500 nm to 2000 nm, even more preferably 500 nm to 1400 nm, and most preferably about 1200 nm. In certain embodiments, the average pore size can be greater than 50 nm in diameter, greater than 50 nm to 1000 nm, preferably 100 nm to 800 nm, more preferably 250 nm to 750 nm. In some embodiments, the matrix contains less than 5% by weight of crosslinked polymers. The branched polyimide matrix of the aerogel composition may include less than 1% by weight of crosslinked polymers. In some embodiments, the branched polyimide matrix of the aerogel composition is not crosslinked. In some embodiments, the aerogel composition includes a hyperbranched polyimide. A hyperbranched polymer is a highly branched macromolecule with three-dimensional dendritic architecture. In some embodiments, the branched polyimides can include a degree of branching (DB) of at least 0.2, 0.3, 0.4, 0.5, or more branches per polyimide polymer chain. In further embodiments, DB may range from 0.2 to 10. In some instances, the DB can be 0.2 to 1 or any value or range therein (e.g., 0.2. 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, or 1). In one preferred instance, the DB can be 0.2 to 0.7, 0.2 to 0.4, 0.3 to 0.4, or preferably about 0.32. In another instance, the DB can be 0.4 to 0.7, 0.4 to 0.6, 0.45 to 0.55, or preferably about 0.51. In another aspect, the DB can range from 1.2 to 8, or from 3 to 7. In a non-limiting aspect, the degree of branching can

6.3.

[0009] In some embodiments, the branched polyimide can have a general structure of:

where R¹ is a multifunctional amine residue, Z is a di-anhydride residue; R² is a diamine residue, m is a number average per chain ranging from 0.2 to 10, and n is 1 to 25. In further embodiments, the branched polyimide can have a general structure of:

where R³ and R⁴ are each individually a capping group, R³ is preferably a hydrogen, or alkyl group and R⁴ is preferably an anhydride residue. Other non-limiting capping groups include amines, maleimides, nadimides, acetylene, biphenylenes, norbornenes, cycloalkyls, and N-propargyl. In some embodiments, R¹ is a multifunctional amine residue, and R² is at least one substituted or unsubstituted diamine residue. The multifunctional amine residue can be a substituted or unsubstituted aliphatic multifunctional amine, a substituted or unsubstituted aromatic multifunctional amine, or a multifunctional amine can include a combination of an aliphatic and at least two aromatic groups, or a combination of an aromatic and at least two aliphatic groups. In particular embodiments, the aromatic multifunctional amine may be l,3,5,-tris(4- aminophenoxy)benzene, 4,4',4"-methanetriyltrianiline, Ν,Ν,Ν' ,Ν' -tetrakis(4-aminophenyl)- 1 ,4- phenylenediamine, or a polyoxypropylenetriamine. In some embodiments, the multifunctional amine can include three primary amine groups and one or more secondary and/or tertiary amine groups, for example, N',N'-bis(4-aminophenyl)benzene-l,4-diamine. In some embodiments, the di- anhydride residue can be biphenyl-3,3',4,4'-tetracarboxylic dianhydride; hydroquinone dianhydride; 3,3',4,4'-biphenyltetracarboxylic dianhydride; pyromellitic dianhydride; 3,3',4,4'-benzophenone- tetracarboxylic dianhydride; 4,4'-oxydiphthalic anhydride; 3,3',4,4'-diphenylsulfone-tetracarboxylic dianhydride; 4,4' (4,4' isopropylidenediphenoxy)bis(phthalic anhydride); 2,2-bis(3,4- dicarboxyphenyl)propane dianhydride; 4,4'-(hexafluoroisopropylidene)diphthalic anhydride; bis(3,4-dicarboxyphenyl)sulfoxide dianhydride; polysiloxane-containing dianhydride; 2,2', 3, 3'- biphenyltetracarboxylic dianhydride; 2,3, 2', 3' benzophenonetetraearboxylic dianhydride; naphthalene-2,3,6,7-tetracarboxylic dianhydride; naphthalene-1,4,5,8 tetracarboxylie dianhydride; 4,4'-oxydiphthalic dianhydride; 3, 3', 4,4' biphenylsulfone tetracarboxylie dianhydride; 3,4,9,10- perylene tetracarboxylie dianhydride; bis(3,4 dicarboxyphenyl)sulfide dianhydride; bis(3,4 dicarboxyphenyl)methane dianhydride; 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride; 2,2- bis(3,4-dicarboxyphenyl)hexafluoropropene; 2,6-dichloronaphthalene 1,4,5, 8-tetracarboxylic dianhydride; 2,7-dichloronapthalene 1,4,5,8 tetracarboxylie dianhydride; 2,3,6,7 tetrachloronaphthalene-1,4,5,8 tetracarboxylie dianhydride; phenanthrene 1,8,9, 10 tetracarboxylie dianhydride; pyrazine-2,3,5,6-tetracarboxylic dianhydride; benzene- 1, 2,3, 4-tetracarboxylic dianhydride; thiophene 2,3,4,5 tetracarboxylie dianhydride; or combinations thereof. In a particular instance the dianhydride can include biphenyl-3,3',4,4'-tetracarboxylic dianhydride, pyromellitic dianhydride, or both. In some embodiments, the diamine is a substituted or unsubstituted aromatic diamine, a substituted or unsubstituted alkyldiamine, or a diamine that includes both aromatic and alkyl functional groups. In some embodiments, the diamine can be 4,4'-oxydianiline; 3,4'- oxydianiline; 3,3'-oxydianiline; ?ara(¾⁾-phenylenediamine; weto w -phenylenediamine; ort z phenylenediamine; diaminobenzanilide; 3,5-diaminobenzoic acid; 3,3' diaminodiphenylsulfone; 4,4'-diaminodiphenyl sulfones; l,3-bis-(4-aminophenoxy)benzene; 1,3- bis-(3-aminophenoxy)benzene; 1,4 bis (4 aminophenoxy)benzene; l,4-bis-(3- aminophenoxy)benzene; 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane; 2,2-bis(3 aminophenyl)hexafluoropropane; 4,4'-isopropylidenedianiline; l-(4-aminophenoxy)-3-(3- aminophenoxy)benzene; l-(4-aminophenoxy)-4-(3-aminophenoxy)benzene; bis[4-(4 aminophenoxy)phenyl]sulfone; bis[4-(3-aminophenoxy)phenyl]sulfone; bis(4-[4- aminophenoxy]phenyl)ether; 2,2'-bis(4-aminophenyl)hexafluoropropene; 2,2'-bis(4- phenoxyaniline)isopropylidene; meta-phenylenediamine; 1,2-diaminobenzene; 4,4'- diaminodiphenylmethane; 2,2-bis(4-aminophenyl)propane; 4,4'diaminodiphenyl propane; 4,4'- diaminodiphenyl sulfide; 4,4-diaminodiphenylsulfone; 3,4'diaminodiphenyl ether; 4,4'- diaminodiphenylether; 2,6-diaminopyridine; bis(3-aminophenyl)diethylsilane; 4,4'- diaminodiphenyldiethylsilane; benzidine-3'-dichlorobenzidine; 3,3'-dimethoxybenzidine; 4,4'- diaminobenzophenone; N,N-bis(4-aminophenyl)butylamine; N,N-bis(4-aminophenyl)methylamine; 1,5-diaminonaphthalene; 3,3'-dimethyl-4,4'-diaminobiphenyl; 4-aminophenyl-3-aminobenzoate; N,N-bis(4-aminophenyl)aniline; bis(p-betaaminotertbutylphenyl)ether; p-bis-2-(2-methyl-4- aminopentyl)benzene; p-bis(l, l-dimethyl-5-aminopentyl)benzene; l,3-bis(4- aminophenoxy)benzene; m-xylenediamine; p-xylenediamine; 4,4'-diaminodiphenylethe hosphine oxide; 4,4'-diaminodiphenyl N-methylamine; 4,4'-diaminodiphenyl N-phenylamine; amino-terminal polydimethylsiloxanes; amino-terminal polypropyleneoxides; amino-terminal polybutyleneoxides; 4,4'-methylenebis(2-methylcyclohexylamine); 1,2-diaminoethane; 1,3-diaminopropane; 1,4- diaminobutane; 1,5-diaminopentane; 1,6-diaminohexane; 1,7-diaminoheptane; 1,8-diaminooctane; 1,9-diaminononane; 1, 10-diaminodecane; 4,4'-methylenebisbenzeneamine; 2,2'-dimethylbenzidine; bisaniline-p-xylidene; 4,4'-bis(4-aminophenoxy)biphenyl; 3,3'-bis(4 aminophenoxy)biphenyl; 4,4'- (l,4-phenylenediisopropylidene)bisaniline; and 4,4'-(l,3-phenylenediisopropylidene)bisaniline, or any combination thereof, preferably, 4,4' -oxydianiline; 2,2'-dimethylbenzidine, or both. In some embodiments, the diamine can include two primary amine groups and one or more secondary and/or tertiary amine groups, for example, 2,2'-(l,2-dimethylhydrazine-l,2-diyl)diethanamine. In some embodi

R² is selected from:

, or any combination thereof.

In some aspects, the molar ratio of anhydride to total diamine is from 0.80: 1 to 1.2: 1. In further aspects, the molar ratio of anhydride to triamine is 8: 1 to 125: 1. The polyimide can further include a mono-anhydride group, preferably phthalic anhydride.

[0010] In some aspects, an article of manufacture is disclosed. The article of manufacture can include an open-cell aerogel with a branched polyimide matrix with less than 5% by weight of crosslinked polymers, wherein macropores are present in the branched polyimide matrix. As explained above and throughout this specification, the branched polyimide matrix can also include mesopores and/or micropores. In some preferred instances, the aerogels can be a macroporous aerogel such that a majority of its pore volume is made up of macropores. In some embodiments, the article of manufacture is a thin film, monolith, wafer, blanket, core composite material, substrate for radiofrequency antenna, a sunscreen, a sunshield, a radome, insulating material for oil and/or gas pipeline, insulating material for liquefied natural gas pipeline, insulating material for cryogenic fluid transfer pipeline, insulating material for apparel, insulating material for aerospace applications, insulating material for buildings, cars, and other human habitats, insulating material for automotive applications, insulation for radiators, insulation for ducting and ventilation, insulation for air conditioning, insulation for heating and refrigeration and mobile air conditioning units, insulation for coolers, insulation for packaging, insulation for consumer goods, vibration dampening, wire and cable insulation, insulation for medical devices, support for catalysts, support for drugs, pharmaceuticals, and/or drug delivery systems, aqueous filtration apparatus, oil-based filtration apparatus, and solvent-based filtration apparatus. In some embodiments, the highly branched polyimide aerogels described herein are included in an antenna, a sunshield, sunscreen, a radome, or a filter.

[0011] In some aspects, a method of making an aerogel of the present invention can include, the steps of: (a) providing at least one dianhydride compound to a solvent to form a solution or mixture; (b) providing a multifunctional amine compound and at least one diamine compound to the solution of step (a) under conditions sufficient to form a branched polymer matrix solution, where the branched polymer matrix is solubilized in the solution; and (c) subjecting the branched polymer matrix solution to conditions sufficient to form an aerogel having an open-cell structure. The macropores present in the resulting aerogel matrix can be formed by selecting processing conditions that favor the formation of macropores vs mesopores and/or micropores. The amount of macropores can be adjusted by implementing any one of, any combination of, or all of the following variables: (1) the polymerization solvent; (2) the polymerization temperature; (3) the polymer molecular weight; (4) the molecular weight distribution; (5) the copolymer composition; (6) the amount of branching; (7) the amount of crosslinking; (8) the method of branching; (9) the method of crosslinking; (10) the method used in formation of the gel; (11) the type of catalyst used to form the gel; (12) the chemical composition of the catalyst used to form the gel; (13) the amount of the catalyst used to form the gel; (14) the temperature of gel formation; (15) the type of gas flowing over the material during gel formation; (16) the rate of gas flowing over the material during gel formation; (17) the pressure of the atmosphere during gel formation; (18) the removal of dissolved gasses during gel formation; (19) the presence of solid additives in the resin during gel formation; (20) the amount of time of the gel formation process; (21) the substrate used for gel formation; (22) the type of solvent or solvents used in each step of the solvent exchange process; (23) the composition of solvent or solvents used in each step of the solvent exchange process; (24) the amount of time used in each step of the solvent exchange process; (25) the dwell time of the part in each step of the solvent exchange process; (26) the rate of flow of the solvent exchange solvent; (27) the type of flow of the solvent exchange solvent; (28) the agitation rate of the solvent exchange solvent; (29) the temperature used in each step of the solvent exchange process; (30) the ratio of the volume of solvent exchange solvent to the volume of the part; (31) the method of drying; (32) the temperature of each step in the drying process; (33) the pressure in each step of the drying process; (34) the composition of the gas used in each step of the drying process; (35) the rate of gas flow during each step of the drying process; (36) the temperature of the gas during each step of the drying process; (37) the temperature of the part during each step of the drying process; (38) the presence of an enclosure around the part during each step of the drying process; (39) the type of enclosure surrounding the part during drying; and/or (40) the solvents used in each step of the drying process. The multifunctional amine and diamine compounds may be added separately or together in one or more portions as solids, neat, or dissolved in an appropriate solvent. In other aspects, a method of making an aerogel can include the steps of: (a) providing a multifunctional amine compound and at least one diamine compound to a solvent to form a solution; (b) providing at least one dianhydride compound to the solution of step (a) under conditions sufficient to form a branched polymer matrix solution, where the branched polymer matrix is solubilized in the solution; and (c) subjecting the branched polymer matrix solution to conditions sufficient to form an aerogel having an open-cell structure. The macropores present in the resulting aerogel matrix can be formed in the manner noted above. In one preferred and non-limiting aspect, the formation of macropores vs smaller mesopores and micropores can be primarily controlled by controlling the polymer/solvent dynamics during gel formation. By doing so, the pore structure can be controlled, and the quantity and volume of macroporous, mesoporous, microporous cells can be controlled. In one instance, this can be done by adding a curing agent to the solution to reduce the solubility of polymers formed in the solution and to form macropores in the gel matrix, the formed macropores containing liquid from the solution. For example, a curing additive that reduces the resultant polyimide solubility, such as l,4-diazabicyclo[2.2.2]octane, can produce a polyimide containing a higher number of macropores compared to another curing additive that improves the resultant polyimide solubility, such as triethylamine. In another example, using the same dianhydride such as biphenyl-tetracarboxylic acid dianhydride (BPDA) but increasing the ratio of rigid amines incorporated into the polymer backbone such as /?-Phenylenediamine (p-PDA) as compared to more flexible diamines such as 4,4'-Oxydianiline (ODA), the formation of macropores as compared to smaller mesopores and micropores can be controlled. All or a first portion of the multifunctional amine can be added to the solution in step (a). A portion or all of the remainder of the multifunctional amine may be added at any time. In some embodiments, the conditions in step (b) sufficient to form the branched polymer matrix solution can include the steps of (i) adding the dianhydride incrementally to the step (a) solution at a temperature of 20 °C to 30 °C, preferably 25 °C, until a target viscosity is obtained to form the branched polymer, where the branched polymer is soluble in the solution; (ii) agitating the mixture overnight, or about 8 to 16 hours, at a temperature of 20 °C to 30 °C, preferably 25 °C to form the branched polymer matrix solution (iii) adding a sufficient amount of mono-anhydride compound to the solution of step (i) under conditions sufficient to react with any monoamine groups of the branched polymer matrix. In some embodiments, the step of adding the dianhydride incrementally can include (iv) adding a first portion of the dianhydride to the step (a) solution to form a mixture; (v) monitoring the viscosity of the mixture; (vi) adding a second portion of the dianhydride to the solution, where the amount of the second portion is based on the viscosity of the mixture in step (v), or adding a second portion of a multifunctional amine and then a second portion of the dianhydride to the solution, where the amounts of the multifunctional amine and dianhydride are based on the viscosity of the mixture in step (v); and (vi) repeating steps (v) and (vi) until the target viscosity is obtained. In some embodiments, target viscosity of the solution is from 500 to 2000 cP, preferably 1000 to 1500 centipoise (cP). In some embodiments, a method for making an aerogel can include the steps of (I) adding diamine to a solvent; (II) adding 1/X of a pre-determined amount of multifunctional amine to the reaction mixture and stirring for 15 minutes, where X is an integer ranging from 1 to 20; and (III) adding 1/X of a pre-determined amount of a dianhydride to the reaction mixture, and stirring for 20 minutes. Steps (II) and (III) can be repeated X-1 times. In some embodiments, a method for making an aerogel can include the steps of: (I) adding 1/X of a pre-determined amount of the diamine and 1/X of a pre-determined amount of multifunctional amine to the reaction mixture and stirring for 15 minutes, where X is an integer ranging from 1 to 20; and (II) adding 1/X of a predetermine amount of dianhydride to the reaction mixture, and stirring for 20 minutes. Steps (I) and (II) are then repeated X-1 times. In other embodiments, the branched polyimide matrix contains less than 1% by weight of crosslinked polymers or is not crosslinked. In some aspects, the branched polyimide has a degree of branching of at least 0.2, 0.3, 0.4, 0.5, or more branches per polymer chain. In some embodiments, the degree of branching is from 0.2 to 10, or 1.2 to 8, 3 to 7. Alternatively, the degree of branching may range from 0.2 to 5, preferably 0.2 to 1, more preferably 0.2 to 0.6, or even more preferably about 0.2 to 0.4, or about 0.32. In another aspect, the degree of branching may range from 0.3 to 0.7, 0.4 to 0.6, or about 0.51. The solvent may be dimethylsulfoxide (DMSO), diethylsulfoxide, Ν,Ν-dimethylformamide (DMF), N,N- diethylformamide, Ν,Ν-dimethylacetamide (DMAc), Ν,Ν-diethylacetamide, N-methyl-2- pyrrolidone ( MP), l-methyl-2-pyrrolidinone, N-cyclohexyl-2-pyrrolidone, l, 13-dimethyl-2- imidazolidinone, diethyleneglycoldimethoxyether, o-dichlorobenzene, phenols, cresols, xylenol, catechol, butyrolactones, hexamethylphosphoramide, or a mixture thereof. In a preferred embodiment, dimethyl sulfoxide is the solvent. In some embodiments, the step of subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure can include subjecting the branched polymer matrix gel to conditions sufficient to freeze the solvent in to form a frozen material, and subjecting the frozen material from step (i) to a drying step sufficient to form an open-cell structure. In some embodiments, the step of subjecting the branched polyimide solution to conditions sufficient to form an open-cell structure can include removing the solvent under a stream of air. In some embodiments, the step of subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure can include the addition of chemical curing agents in appropriate amounts to form a gel. In some embodiments, a method of making an aerogel includes subjecting the branched polyimide solution to at least one solvent exchange with a different solvent. In further embodiments, the different solvent may be exchanged with a second different solvent. In a preferred embodiment, the second different solvent is acetone. In some aspects, a method of making an aerogel includes not subjecting the branched polyimide to crosslinking conditions.

[0012] In some aspects, filtration methods using nay one of the macroporously structured branched polyimides of the present invention are disclosed. A method can include filtering a fluid using the branched polyimide aerogel of the present invention. The fluid can contain impurities and/or desired substances. The method can include contacting a feed fluid with the branched polyimide aerogel under conditions sufficient to remove at least a portion of the impurities and/or desired substances from the feed fluid and produce a filtrate. In some instances, the aerogel can be in the form of a film, powder, blanket, or a monolith. In some instances, the feed fluid used in the methods disclosed herein can be a liquid, a gas, a supercritical fluid, or a mixture thereof. The feed fluid can contain water (H2O) and/or be a non-aqueous liquid. The non-aqueous fluid can be an oil, a solvent, or any combination thereof. In some instances, the feed fluid can be a solvent (e.g., an organic solvent). The feed fluid can be an emulsion (e.g., a water-oil emulsion, an oil-water emulsion, a water-solvent emulsion, a solvent-water emulsion, an oil-solvent emulsion, or a solvent- oil emulsion). The feed fluid can be a biological fluid (e.g., blood, plasma, or both). The feed fluid can be a gas (e.g., air, nitrogen, oxygen, an inert gas, or mixtures thereof). In some instances, the filtrate can be substantially free of impurities and/or a desired substance.

[0013] In some aspects, the present disclosure provides a system for filtering a fluid that includes impurities and/or desired substances. The system can include the branched polyimide aerogel described herein and a separation zone in fluid communication with the aerogel, a feed fluid and a filtrate.

[0014] In the context of the present invention 65 embodiments are described. Embodiment 1 is an aerogel comprising: (a) an open-cell structure; and (b) a branched polyimide matrix comprising macropores, wherein the matrix contains less than 5% by weight of crosslinked polymers. Embodiment 2 is the aerogel of embodiment 1, wherein at least 10 % of the aerogel's pore volume is made up of macropores. Embodiment 3 is the aerogel of embodiment 2, wherein at least 50 % of the aerogel's pore volume is made up of macropores. Embodiment 4 is the aerogel of embodiment 3, wherein at least 75 % of the aerogel' s pore volume is made up of macropores. Embodiment 5 is the aerogel of embodiment 4, wherein at least 95 % of the aerogel' s pore volume is made up of macropores. Embodiment 6 is the aerogel of embodiment 5, wherein 100 % of the aerogel' s pore volume is made up of macropores. Embodiment 7 is the aerogel of any one of embodiments 1 to 5, wherein the aerogel further comprises micropores or mesopores or both micropores and mesopores. Embodiment 8 is the aerogel of embodiment 7, wherein less than 90, %, 80 %, 70 %, 60 %, 50 %, 40 %, 30 % 20 %, 10% or less than 5 % of the aerogel's pore volume is made up of micropores and/or mesopores. Embodiment 9 is the aerogel of any one of embodiments 1 to 8, wherein the branched polyimide matrix contains less than 1% by weight of crosslinked polymers or is not crosslinked. Embodiment 10 is the aerogel of any one of embodiments 1 to 9, wherein the branched polyimide matrix has an average pore size of greater than 50 nanometers (nm) to 5000 nm in diameter. Embodiment 1 1 is the aerogel of embodiment 10, wherein the branched polyimide matrix has an average pore size of 1000 nm to 1400 nm in diameter. Embodiment 12 is the aerogel of embodiment 1 1, wherein the branched polyimide matrix has an average pore size of 100 nm to 350 nm, preferably about 250 nm in diameter. Embodiment 13 is the aerogel of any one of embodiments 1 to 12, wherein the branched polyimide has a degree of branching of at least 0.2 branches per polyimide polymer chain. Embodiment 14 is the aerogel of embodiment 13, wherein the degree of branching is from 0.2 to 10, preferably from 0.2 to 1, or more preferably 0.2 to 0.7. Embodiment 15 is the aerogel of embodiment 14, wherein the degree of branching is 0.2 to 0.4, preferably about 0.3, or 0.4 to 0.6, preferably about 0.5. Embodiment 16 is the aerogel of any one of embodiments 1 to 15, wherein the branched polyimide has a general structure of:

where: R¹ is multifunctional amine residue; Z is a dianhydride residue; R² is a diamine residue; m is a number average per chain ranging from 0.2 to 10; and n is 1 to 25. Embodiment 17 is the aerogel of embodiment 16, wherein the branched polyimide has a general structure of:

where R³ and R⁴ are each individually a capping group, and are independently selected from a hydrogen, an anhydride residue, an isocyanate residue, an acid residue, or an alkyl group. Embodiment 18 is the aerogel of any one of embodiments 16 to 17, wherein the dianhydride residue is hydroquinone dianhydride; 3,3',4,4'-biphenyltetracarboxylic dianhydride; pyromellitic dianhydride; 3,3',4,4'-benzophenone-tetracarboxylic dianhydride; 4,4'-oxydiphthalic anhydride; 3,3',4,4'-diphenylsulfone-tetracarboxylic dianhydride; 4,4'-(4,4'-isopropylidenediphenoxy)bis(phthalic anhydride); 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride; 4,4'-(hexafluoroisopropylidene)diphthalic anhydride; bis(3,4- dicarboxyphenyl)sulfoxide dianhydride; polysiloxane-containing dianhydride; 2,2', 3,3'- biphenyltetracarboxylic dianhydride; 2,3,2', 3'-benzophenonetetraearboxylic dianhydride; 3, 3', 4,4'- benzophenonetetraearboxylic dianhydride; naphthalene-2,3,6,7-tetracarboxylic dianhydride; naphthalene-l,4,5,8-tetracarboxylie dianhydride; 4,4'-oxydiphthalic dianhydride;

3,3',4,4'-biphenylsulfone tetracarboxylic dianhydride; 3,4,9,10-perylene tetracarboxylic dianhydride; bis(3,4-dicarboxyphenyl)sulfide dianhydride; bis(3,4-dicarboxyphenyl)methane dianhydride; 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride; 2,2-bis(3,4- dicarboxyphenyl)hexafluoropropene; 2,6-dichloronaphthalene-l,4,5,8-tetracarboxylic dianhydride; 2,7-dichloronapthalene-l,4,5,8-tetracarboxylic dianhydride; 2,3,6,7-tetrachloronaphthalene- 1,4,5,8-tetracarboxylic dianhydride; phenanthrene-8,9, 10-tetracarboxylic dianhydride; pyrazine- 2,3,5,6-tetracarboxylic dianhydride; benzene-l,2,3,4-tetracarboxylic dianhydride; thiophene-2,3,4,5-tetracarboxylic dianhydride; or combinations thereof. Embodiment 19 is the aerogel of embodiment 18, wherein the dianhydride is 3,3',4,4'-biphenyltetracarboxylic dianhydride, pyromellitic dianhydride, or both. Embodiment 20 is the aerogel of any one of embodiments 16 to 19, wherein R¹ is a substituted or unsubstituted multifunctional amine comprising at least three primary amine functionalities and R² is at least one substituted or unsubstituted diamine. Embodiment 21 is the aerogel of embodiment 20, wherein the multifunctional amine is a substituted or an unsubstituted aliphatic multifunctional amine or a substituted or an unsubstituted aromatic multifunctional amine. Embodiment 22 is the aerogel of embodiment 21, wherein the aromatic multifunctional amine is l,3,5,-tris(4-aminophenoxy)benzene, 4,4',4"-methanetriyltrianiline, N,N,N',N'-tetrakis(4-aminophenyl)-l,4-phenylenediamine, or a polyoxypropylenetriamine. Embodiment 23 is the aerogel of embodiment 21, wherein the diamine is a substituted or unsubstituted aromatic diamine, a substituted or an unsubstituted alkyldiamine, or combinations thereof. Embodiment 24 is the aerogel of embodiment 23, wherein the diamine is 4,4'-oxydianiline; 3,4'-oxydianiline; 3,3'-oxydianiline; p-phenylenediamine; weto-phenylenediamine; or t/zo-phenylenedi amine; /?ara-phenylenedi amine; diaminobenzanilide; 3,5-diaminobenzoic acid; 3,3'-diaminodiphenylsulfone; 4,4'-diaminodiphenyl sulfones; l,3-bis-(4-aminophenoxy)benzene; 1 , 3 -bi s-(3 -aminophenoxy)benzene; 1 ,4-bi s-(4-aminophenoxy)benzene; 1 ,4-bi s-(3 - aminophenoxy)benzene; 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane; 2,2-bis(3-aminophenyl)hexafluoropropane; 4,4'-isopropylidenedianiline; l-(4-aminophenoxy)-3-(3- aminophenoxy)benzene; l-(4-aminophenoxy)-4-(3-aminophenoxy)benzene; bis[4-(4-aminophenoxy)phenyl]sulfone; bis[4-(3-aminophenoxy)phenyl]sulfone; bis(4-[4- aminophenoxy]phenyl)ether; 2,2'-bis(4-aminophenyl)hexafluoropropene; 2,2'-bis(4- phenoxyaniline)isopropylidene; meta-phenylenediamine; 1,2-diaminobenzene; 4,4'- diaminodiphenylmethane; 2,2-bis(4-aminophenyl)propane; 4,4'-diaminodiphenyl propane; 4,4'- diaminodiphenyl sulfide; 4,4-diaminodiphenylsulfone; 3,4-'diaminodiphenyl ether; 4,4'- diaminodiphenyl ether; 2,6-diaminopyridine; bis(3-aminophenyl)diethyl silane; 4,4'- diaminodiphenyl diethyl silane; benzidine-3'-dichlorobenzidine; 3,3'-dimethoxybenzidine; 4,4'- diaminobenzophenone; N,N-bis(4-aminophenyl)butylamine; N,N-bis(4-aminophenyl)methylamine; 1,5-diaminonaphthalene; 3,3'-dimethyl-4,4'-diaminobiphenyl; 4-aminophenyl-3-aminobenzoate; N,N-bis(4-aminophenyl)aniline; bis(p-beta-amino-tert-butyl phenyl)ether; p-bis-2-(2-methyl-4- aminopentyl)benzene; p-bis(l, l-dimethyl-5-aminopentyl)benzene; l,3-bis(4- aminophenoxy)benzene; m-xylenediamine; p-xylenediamine; 4,4'-diaminodiphenyl ether phosphine oxide; 4,4'-diaminodiphenyl N-methyl amine; 4,4'-diaminodiphenyl N-phenyl amine; amino-terminal polydimethylsiloxanes; amino-terminal polypropyleneoxides; amino-terminal polybutyleneoxides; 4,4'-methylenebis(2-methylcyclohexylamine); 1,2-diaminoethane; 1,3- diaminopropane; 1,4-diaminobutane; 1,5-diaminopentane; 1,6-diaminohexane; 1,7-diaminoheptane; 1,8-diaminooctane; 1,9-diaminononane; 1, 10-diaminodecane; and 4,4'-methylenebisbenzeneamine; 2,2'-dimethylbenzidine; bisaniline-p-xylidene; 4,4'-bis(4-aminophenoxy)biphenyl;

3,3'-bis(4-aminophenoxy)biphenyl; 4,4'-(l,4-phenylenediisopropylidene)bisaniline; and 4,4'-(l,3- phenylenediisopropylidene)bisaniline, or any combination thereof, preferably, 4,4'-oxydianiline; 2,2'-dimethylbenzidine, or both. Embodiment 25 is the aerogel of any one of embodiments 16 to 24, where: R¹ is selected from:

or any combination thereof; and R² is selected from:

, or any combination thereof. Embodiment 26 is the aerogel of any one of embodiments 16 to 25, wherein the molar ratio of anhydride to total diamine is from 0.80: 1 to 1.2: 1. Embodiment 27 is the aerogel of any one of embodiments 16 to 26, wherein the molar ratio of anhydride to multifunctional amine is 8: 1 to 125 : 1. Embodiment 28 is the aerogel of any one of embodiments 1 to 27, wherein the polyimide further comprises a mono- anhydride group, preferably phthalic anhydride.

[0015] Embodiment 29 is a method of making the aerogel of any one of embodiments 1 to 28, the method comprising: (a) providing at least one dianhydride compound to a solvent to form a solution or mixture; (b) providing a multifunctional amine compound and at least one diamine compound to the solution or mixture of step (a) under conditions sufficient to form a branched polymer matrix solution, wherein the branched polymer matrix is solubilized in the solution; and (c) subjecting the branched polymer matrix solution to conditions sufficient to form an aerogel having an open-cell structure with macropores present in the branched polyimide matrix of the aerogel.

[0016] Embodiment 30 is a method of making the aerogel of any one of embodiments 1 to 28, the method comprising: (a) providing a multifunctional amine compound and at least one diamine compound to a solvent to form a solution; (b)providing at least one dianhydride compound to the solution of step (a) under conditions sufficient to form a branched polymer matrix solution, wherein the branched polymer matrix is solubilized in the solution; and (c) subjecting the branched polymer matrix solution to conditions sufficient to form an aerogel having an open-cell structure with macropores present in the branched polyimide matrix of the aerogel. Embodiment 31 is the method of any one of embodiments 29 to 30, wherein the branched polyimide matrix contains less than 1% by weight of crosslinked polymers or is not crosslinked. Embodiment 32 is the method of any one of embodiments 29 to 31, wherein the branched polyimide has a degree of branching of at least 5 branches per polymer chain. Embodiment 33 is the method of embodiment 32, wherein the degree of branching is from 0.2 to 10, preferably 0.2 to 1, more preferably 0.2 to 0.7, or even more preferably 0.2 to 0.4 or 0.4 to 0.6. Embodiment 34 is the method of any one of embodiments 29 to 33, wherein all or a first portion of the multifunctional amine is added to the solution. Embodiment 35 is the method of any one of embodiments 30 to 34, wherein the step (b) conditions sufficient to form the branched polymer matrix solution comprises: (i) adding the dianhydride incrementally to the step (a) solution at a temperature of 20 °C to 40 °C, preferably 25 °C, until a target viscosity is obtained to form a branched polymer, wherein the branched polymer is soluble in the solution; (ii) agitating the mixture overnight, or about 8 to 16 hours, at a temperature of 20 °C to 30 °C, preferably 25 °C to form the branched polymer matrix solution; and (iii) adding a sufficient amount of mono-anhydride compound to the solution of step (i) under conditions sufficient to react with any monoamine groups of the branched polymer. Embodiment 36 is the method of embodiment 35, wherein adding the dianhydride incrementally comprises: (iv) adding a first portion of the dianhydride to the step (a) solution to form a mixture; (v) monitoring the viscosity of the mixture; (vi) adding a second portion of the dianhydride to the solution, wherein the amount of the second portion is based on the viscosity of the mixture in step (v), or adding a second portion of a multifunctional amine and then a second portion of the dianhydride to the solution, wherein the amounts of the multifunctional amine and dianhydride are based on the viscosity of the mixture in step (v); and (vii) repeating steps (v) and (vi) until the target viscosity is obtained. Embodiment 37 is the method of any one of embodiments 29 to 36, wherein the target viscosity of the solution is from 50 to 2000 centipoise (cP), preferably 1000 to 1500 cP. Embodiment 38 is the method of any one of embodiments 29 to 37, wherein the solvent is dimethylsulfoxide, diethylsulfoxide, N,N- dimethylformamide, Ν,Ν-diethylformamide, N,N-dimethylacetamide, Ν,Ν-diethylacetamide, N- methyl-2-pyrrolidone, l-methyl-2-pyrrolidinone, N-cyclohexyl-2-pyrrolidone, l, 13-dimethyl-2- imidazolidinone, diethyleneglycoldimethoxyether, o-dichlorobenzene, phenols, cresols, xylenol, catechol, butyrolactones, hexamethylphosphoramide, and mixtures thereof, preferably, dimethyl sulfoxide. Embodiment 39 is the method of any one of embodiments 29 to 38, wherein subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure comprises the addition of chemical curing agents in appropriate amounts to form a gel. Embodiment 40 is the method of any one of embodiments 29 to 39, wherein subjecting the branched polyimide solution to conditions sufficient to form an open-cell structure comprises: subjecting the branched polyimide gel to conditions sufficient to freeze the solvent in to form a frozen material; and subjecting the frozen material to a drying step sufficient to form an open-cell structure. Embodiment 41 is the method of any one of embodiments 29 to 40, wherein subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure comprises removing the solvent under a stream of air. Embodiment 42 is the method of embodiment 41, further comprising subjecting the branched polyimide solution to at least one solvent exchange with a different solvent. Embodiment 43 is the method of embodiment 42, wherein the different solvent is exchanged with acetone. Embodiment 44 is the method of any one of embodiments 29 to 43, wherein the branched polyimide has not been subjected to crosslinking conditions.

[0017] Embodiment 45 is an article of manufacture comprising the aerogel of any one of embodiments 1 to 28. Embodiment 46 is the article of manufacture of embodiment 45, wherein the article of manufacture is a thin film, monolith, wafer, blanket, core composite material, a substrate for radiofrequency antenna, substrate for a sunshield, a substrate for a sunshade, a substrate for radome, insulating material for oil and/or gas pipeline, insulating material for liquefied natural gas pipeline, insulating material for cryogenic fluid transfer pipeline, insulating material for apparel, insulating material for aerospace applications, insulating material for buildings, cars, and other human habitats, insulating material for automotive applications, insulation for radiators, insulation for ducting and ventilation, insulation for air conditioning, insulation for heating and refrigeration and mobile air conditioning units, insulation for coolers, insulation for packaging, insulation for consumer goods, vibration dampening, wire and cable insulation, insulation for medical devices, support for catalysts, support for drugs, pharmaceuticals, and/or drug delivery systems, aqueous filtration apparatus, oil-based filtration apparatus, and solvent-based filtration apparatus, or any combination thereof. Embodiment 47 is the article of manufacture of embodiment 45, wherein the article of manufacture is an antenna. Embodiment 48 is the article of manufacture of embodiment 45, wherein the article of manufacture is a sunshield or sunscreen. Embodiment 49 is the article of manufacture of embodiment 45, wherein the article of manufacture is a radome. Embodiment 50 is the article of manufacture of embodiment 42, wherein the article of manufacture is a filter.

[0018] Embodiment 51 is a method of filtering a fluid comprising impurities and/or desired substances, the method comprising contacting a feed fluid with the aerogel of any one of embodiments 1 to 28 under conditions sufficient to remove at least a portion of the impurities and/or desired substances from the feed fluid and produce a filtrate. Embodiment 51 is the method of embodiment 51, wherein the feed fluid is a liquid, a gas, a supercritical fluid, or a mixture thereof. Embodiment 53 is the method of embodiment 52, wherein the feed fluid comprises water. Embodiment 54 is the method of embodiment 52, wherein the feed fluid is a non-aqueous liquid. Embodiment 55 is the method of embodiment 54, wherein the non-aqueous fluid is an oil, a solvent, or combinations thereof. Embodiment 56 is the method of embodiment 55, wherein the feed fluid is a solvent. Embodiment 57 is the method of embodiment 55, wherein the feed fluid is an organic solvent. Embodiment 58 is the method of any one of embodiments 51 to 57, wherein the feed fluid is an emulsion. Embodiment 59 is the method of embodiment 58, wherein the emulsion is a water- oil emulsion, an oil-water emulsion, a water-solvent emulsion, a solvent-water emulsion, an oil- solvent emulsion, or a solvent-oil emulsion. Embodiment 60 is the method of embodiment 51, wherein the feed fluid is a biological fluid. Embodiment 61 is the method of embodiment 60, wherein the biological fluid is blood, plasma, or both. Embodiment 62 is the method of embodiment 51, wherein the feed fluid is a gas. Embodiment 63 is the method of embodiment 62, wherein the gas comprises air, nitrogen, oxygen, an inert gas, or mixtures thereof. Embodiment 64 is the method of any one of embodiments 51 to 63, wherein the filtrate is substantially free of impurities and/or a desired substance. Embodiment 65 is a filtration system comprising: (a) an aerogel of any one of embodiments 1 to 28; and (b) a separation zone in fluid communication with the aerogel, a feed fluid and a filtrate.

[0019] The following includes definitions of various terms and phrases used throughout this specification. [0020] The term "aerogel" refers to a class of materials that are generally produced by forming a gel, removing a mobile interstitial solvent phase from the pores, and then replacing it with a gas or gas-like material. By controlling the gel and evaporation system, density, shrinkage, and pore collapse can be minimized. In the context of the present invention, aerogels have macropores. Aerogels of the present invention can also include mesopores and/or micropores. In preferred aspects, the majority (e.g., more than 50%) of the aerogel's pore volume can be made up of macropores. Macroporously structured polyimide aerogels of the present invention can also include mesopores and/or micropores or can consist only of macropores. In other alternative aspects, the majority of the aerogel's pore volume can be made up of mesopores and/or micropores such that less than 50% of the aerogel's pore volume can be made up of macropores. In some embodiments, the aerogels of the present invention can have low bulk densities (about 0.75 g/cm³ or less, preferably about 0.01 to 0.5 g/cm³), high surface areas (generally from about 10 to 1,000 m²/g and higher, preferably about 50 to 1000 m²/g), high porosity (about 20% and greater, preferably greater than about 85%), and/or relatively large pore volume (more than about 0.3 mL/g, preferably about 1.2 mL/g and higher).

[0021] The presence of macropores, mesopores, and/or micropores in the aerogels of the present invention can be determined by mercury intrusion porosimetry (MIP) and/or gas physisorption experiments. The MIP test can be used to measure mesopores and macropores (i.e., American Standard Testing Method (ASTM) D4404-10, Standard Test Method for Determination of Pore Volume and Pore Volume Distribution of Soil and Rock by Mercury Intrusion Porosimetry) Gas physisorption experiments can be used to measure micropores (ASTM D 1993 -03 (2008) Standard Test Method for Precipitated Silica - Surface Area by Multipoint BET Nitrogen).

[0022] The terms "impurity" or "impurities" refers to unwanted substances in a feed fluid that are different than a desired filtrate and/or are undesirable in a filtrate. In some instances, impurities can be solid, liquid, gas, or supercritical fluid. In some embodiments, an aerogel can remove some or all of an impurity.

[0023] The term "desired substance" or "desired substances" refers to wanted substances in a feed fluid that are different than the desired filtrate. In some instances, the desired substance can be solid, liquid, gas, or supercritical fluid. In some embodiments, an aerogel can remove some or all of a desired substance.

[0024] The term "radio frequency (RF)" refers to the region of the electromagnetic spectrum having wavelengths ranging from 10^"4 to 10⁷ m. [0025] The use of the words "a" or "an" when used in conjunction with any of the terms "comprising," "including," "containing," or "having" in the claims or the specification may mean "one," but it is also consistent with the meaning of "one or more," "at least one," and "one or more than one."

[0026] The terms "wt.%", "vol.%", or "mol.%" refers to a weight, volume, or molar percentage of a component, respectively, based on the total weight, the total volume of material, or total moles, that includes the component. In a non-limiting example, 10 grams of component in 100 grams of the material is 10 wt.% of component.

[0027] The terms "about" or "approximately" are defined as being close to as understood by one of ordinary skill in the art. In one non-limiting embodiment, the terms are defined to be within 10%, preferably within 5%, more preferably within 1%, and most preferably within 0.5%.

[0028] The term "substantially" and its variations are defined to include ranges within 10%, within 5%, within 1%, or within 0.5%.

[0029] The use of the term "or" in the claims is used to mean "and/or" unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and "and/or."

[0030] The words "comprising" (and any form of comprising, such as "comprise" and "comprises"), "having" (and any form of having, such as "have" and "has"), "including" (and any form of including, such as "includes" and "include") or "containing" (and any form of containing, such as "contains" and "contain") are inclusive or open-ended and do not exclude additional, unrecited elements or method steps.

[0031] The highly branched polyimide aerogel of the present invention can "comprise," "consist essentially of," or "consist of particular ingredients, components, compositions, etc. disclosed throughout the specification. With respect to the transitional phase "consisting essentially of," in one non-limiting aspect, a basic and novel characteristic of the macroporously structured highly branched polyimide aerogel of the present invention is that it has good mechanical properties and also includes macropores.

[0032] Other objects, features and advantages of the present invention will become apparent from the following figures, detailed description, and examples. It should be understood, however, that the figures, detailed description, and examples, while indicating specific embodiments of the invention, are given by way of illustration only and are not meant to be limiting. Additionally, it is contemplated that changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. In further embodiments, features from specific embodiments may be combined with features from other embodiments. For example, features from one embodiment may be combined with features from any of the other embodiments. In further embodiments, additional features may be added to the specific embodiments described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Advantages of the present invention may become apparent to those skilled in the art with the benefit of the following detailed description and upon reference to the accompanying drawings.

[0034] FIG. 1 is a schematic of system of an embodiment for filtering a fluid using a branched polyimide aerogel, the system having a separation zone, an inlet, and an outlet.

[0035] FIG. 2 is a schematic of system of an embodiment for filtering a fluid using a branched polyimide aerogel, the system having a separation zone and an inlet.

[0036] FIG. 3 is a schematic of system of an embodiment for filtering a fluid using a branched polyimide aerogel, the system having a separation zone and an outlet.

[0037] FIG. 4 is a distribution of pore size diameter for a first non-limiting aerogel of the present invention.

[0038] FIG. 5 is a distribution of pore size diameter for a second non-limiting aerogel of the present invention.

[0039] FIG. 6 is a distribution of pore size diameter for a third non-limiting aerogel of the present invention.

[0040] While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and may herein be described in detail. The drawings may not be to scale.

DETAILED DESCRIPTION OF THE INVENTION

[0041] A discovery has been made that provides a polyimide aerogel with improved manufacturability and processability over conventional polyimide aerogels. The aerogels of the present invention can include an open cell structure and a branched polyimide matrix that includes macropores. Notably, the amount of macropores present in the aerogels can be tuned or controlled to a desired amount. For example, aerogels can be produced where 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 99, or 100 % of the aerogel's pore volume can be made up of macropores. In instances wherein less than 100 % of the aerogel's pore volume is derived from macropores, such aerogels can include mesopores and/or micropores. In some embodiments, the aerogel is a film or a molded shaped. In one non-limiting example, macroporously structured highly branched polyimide aerogel can have an average pore diameter of 100 nm to 2000 nm, more preferably 250 nm to 2000 nm, even more preferably 500 nm to 1400 nm, and most preferably about 1200 nm. In another example, a macroporously structured aerogel film can have an average pore diameter greater than 50 nm in diameter, greater than 50 nm to 1000 nm, preferably 100 nm to 800 nm, more preferably 250 nm to 750 nm. The macroporously structured aerogel can be any thickness or have any shape. In another non-limiting example, the macroporous-structured aerogel can be 0.01 to 1000 mm thick or at least, equal to, or between any two of 0.01, 0.1, 1, 10, 25, 50, 75, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, and 1000 mm. These and other non-limiting aspects of the present invention are discussed in further detail in the following sections.

A. Highly Branched Non-Crosslinked Aerogels

[0042] In some aspects, the present disclosure provides an aerogel that includes an open-cell structure and a branched polyimide matrix having macropores. As explained above and throughout this specification, the matrix can also include mesopores and/or micropores. In some embodiments, the matrix contains less than 5%, less than 4%, less than 3%, or less than 2% by weight of crosslinked polymers. The branched polyimide matrix of the aerogel composition can include less than 1% by weight of crosslinked polymers. In some embodiments, the branched polyimide matrix of the aerogel composition is not crosslinked.

[0043] The characteristics or properties of the final aerogel are significantly impacted by the choice of monomers, which are used to produce the aerogel. Factors to be considered when selecting monomers include the properties of the final aerogel, such as the flexibility, thermal stability, coefficient of thermal expansion (CTE), coefficient of hydroscopic expansion (CHE) and any other properties specifically desired, as well as cost. Often, certain important properties of a polymer for a particular use can be identified. Other properties of the polymer may be less significant, or may have a wide range of acceptable values; so many different monomer combinations could be used. The aerogel composition of the current invention can include a high degree of branching and low degree of crosslinking, which has a positive effect the polymers' mechanical properties. A highly crosslinked polymer can be considered a thermoset polymer, which is a polymer that has been irreversibly cured. The polymers presented herein display a low degree of crosslinking, thereby more closely resembling a thermoplastic. As such, the polymer may be re-shaped and re-cycled. In some aspects, the current aerogel composition includes polyimides having a large amount of trifunctional, tetrafunctional, or multifunctional monomer, specifically triamine monomer, yet displays little to no crosslinking.

[0044] Other factors to be considered in the selection of monomers include the expense and availability of the monomers chosen. Commercially available monomers that are produced in large quantities generally decrease the cost of producing the polyimide polymer since such monomers are in general less expensive than monomers produced on a lab scale and pilot scale. Additionally, the use of commercially available monomers improves the overall reaction efficiency because additional reactions are not required to produce a monomer, which is incorporated into the polymer.

[0045] The highly branched aerogels on the current invention may contain polyimides that include relatively rigid molecular structures such as aromatic/cyclic moieties. These typical structures may often be relatively linear and stiff. The linearity and stiffness of the cyclic/aromatic backbone reduces segmental rotation and allows for molecular ordering which results in lower CTE than many thermoplastic polymers having more flexible chains. In addition, the intermolecular associations of polyimide chains provide resistance to most solvents, which tends to reduce the solubility of many typical polyimide polymers in many solvents. In some aspects, the use of more aliphatic monomers can reduce the stiffness of the aerogel, if desired.

[0046] In some embodiments, the aerogel composition can include a hyperbranched polyimide polymer. A hyperbranched polymer is a highly branched macromolecule with three-dimensional dendritic architecture. Hence, the molecular weight of a hyperbranched polymer is not a sufficient parameter that characterizes these polymers. Since the number of possible structures becomes very large as the polymerization degree of macromolecules increases, there is a need to characterize also this aspect of hyperbranched polymers. Thus, the term degree of branching (DB) can be used as a quantitative measure of the branching perfectness for hyperbranched polymers. In some embodiments, the branched polyimides of the current aerogels can include a degree of branching (DB) of at least 0.2, 0.3, 0.4, 0.5, or more branches per polyimide polymer chain. In further embodiments, DB may range from 0.2 to 10, preferably from 1.2 to 8, or more preferably from 3 to 7. In one non-limiting instance, the degree of branching is 6.3. Alternatively, the DB may range from 0.2 to 5, preferably 0.2 to 1, more preferably 0.2 to 0.6, or even more preferably about 0.2 to 0.4, or about 0.32. In another aspect, the DB may range from 0.3 to 0.7, 0.4 to 0.6, or about 0.51. In some aspects, DB may be represented by the following equation:

2Q_T

where p is the extent of reaction, and Qr and Q are parameters representing the fractions of monofunctional and trifunctional monomers at the beginning of the reaction according to the following equations:

where Nr, NM, and NB are the initial number of trifunctional, monofunctional, and bifunctional monomers, respectively.

[0047] In one embodiment, the aerogel of the current invention is a branched polyimide having a general structure of:

where R¹ is a hydrocarbon residue, a branched hydrocarbon residue, a heteroatom substituted hydrocarbon residue, a heteroatom substituted branched hydrocarbon residue, or a multifunctional amine residue, Z is a dianhydride residue; R² is a diamine residue, m is a number average per chain ranging from 0.5 to 1000, 0.5 to 500, 0.5 to 100, or specifically 0.5 to 10, and n is 1 to 1000, 1 to 500, 1 to 100, or specifically 1 to 25. In further embodiments, the aerogel composition branched polyimide can have a general structure of:

where R³ and R⁴ are each individually a capping group, R³ is preferably a hydrogen, or alkyl group and R⁴ is preferably an anhydride residue. Other non-limiting capping groups include amines, maleimides, nadimides, acetylene, biphenylenes, norbornenes, cycloalkyls, and N-propargyl and specifically those derived from reagents including 5-norbornene-2,3-dicarboxylic anhydride (nadic anhydride, NA), methyl-nadic anhydride, hexachloro-nadic anhydride, cis-4-cyclohexene-l,2- dicarboxylic anhydride, 4-amino-N-propargylphthalimide, 4-ethynylphthalic anhydride, and maleic anhydride.

[0048] In some aspects, the molar ratio of anhydride to total diamine is from 0.4: 1 to 1.6: 1, 0.5 : 1 to 1.5 : 1, 0.6: 1 to 1.4: 1, 0.7: 1 to 1.3 : 1, or specifically from 0.8: 1 to 1.2: 1. In further aspects, the molar ratio of dianhydride to multifunctional amine (e.g., triamine) is 2: 1 to 140: 1, 3 : 1 to 130: 1, 4: 1 to 120: 1, 5 : 1 to 1 10: 1, 6: 1 to 100: 1, 7: 1 to 90: 1, or specifically from 8: 1 to 125 : 1. The polyimide can also include a mono-anhydride group, including for example 4-amino-l,8-naphthalic anhydride, endo-bicyclo[2.2.2]oct-5-ene-2,3-dicarboxylic anhydride, citraconic anhydride, trans- 1,2- cyclohexanedicarboxylic anhydride, 3,6-dichlorophthalic anhydride, 4,5-dichlorophthalic anhydride, tetrachlorophthalic anhydride 3,6-difluorophthalic anhydride, 4,5-difluorophthalic anhydride, tetrafluorophthalic anhydride, maleic anhydride, l-cyclopentene-l,2-dicarboxylic anhydride, 2,2-dimethylglutaric anhydride 3,3-dimethylglutaric anhydride, 2,3-dimethylmaleic anhydride, 2,2-dimethylsuccinic anhydride, 2,3-diphenylmaleic anhydride, phthalic anhydride, 3- methylglutaric anhydride, methylsuccinic anhydride, 3-nitrophthalic anhydride, 4-nitrophthalic anhydride, 2,3-pyrazinedicarboxylic anhydride, or 3,4-pyridinedicarboxylic anhydride. In some embodiments, the di-anhydride group is phthalic anhydride.

[0049] In some embodiments, the branched polyimide matrix contains less than 1% by weight of crosslinked polymers or is not crosslinked. In some aspects, the branched polyimide has a degree of branching of at least 0.1, 0.2, 0.3, 0.4, 0.5, or more branches per polymer chain. In some embodiments, the degree of branching is from 0.2 to 10, 1.2 to 8, or 3 to 7. In some embodiments, the degree of branching can be approximately 6.3 branches. Alternatively, the degree of branching may range from 0.2 to 5, preferably 0.2 to 1, more preferably 0.2 to 0.6, or even more preferably about 0.2 to 0.4, or about 0.32. In another aspect, the degree of branching may range from 0.3 to 0.7, 0.4 to 0.6, or about 0.51.

B. Polyimides

[0050] An embodiment of the present invention provides highly branched non-crosslinked aerogels prepared from step-growth polymers. Step-growth polymers are an important group of polymeric chemicals that have many uses and beneficial properties. Step-growth polymers can be formed via step-growth polymerization in which bifunctional or multifunctional monomers react to form first dimers, then trimers, then longer oligomers, and eventually long chain polymers. Generally, step-growth polymers have robust mechanical properties including toughness and high temperature resistance that make them desirable over other polymer types. There are numerous varieties of step-growth polymers, including polyimides, polyurethanes, polyureas, polyamides, phenolic resins, polycarbonates, and polyesters. The aerogels of the current invention are prepared from polyimides.

[0051] The characteristics or properties of the final polymer are significantly impacted by the choice of monomers, which are used to produce the polymer. Factors to be considered when selecting monomers include the properties of the final polymer, such as the flexibility, thermal stability, coefficient of thermal expansion (CTE), coefficient of hydroscopic expansion (CHE) and any other properties specifically desired, as well as cost. Often, certain important properties of a polymer for a particular use can be identified. Other properties of the polymer may be less significant, or may have a wide range of acceptable values; so many different monomer combinations could be used.

[0052] Polyimides are a type of polymer with many desirable properties. In general, polyimide polymers include a nitrogen atom in the polymer backbone, where the nitrogen atom is connected to two carbonyl carbons, such that the nitrogen atom can be stabilized by the adjacent carbonyl groups. A carbonyl group includes a carbon, referred to as a carbonyl carbon, which is double bonded to an oxygen atom. Polyimides are usually considered an AA-BB type polymer because usually two different classes of monomers are used to produce the polyimide polymer. Polyimides can also be prepared from AB type monomers. For example, an aminodicarboxylic acid monomer can be polymerized to form an AB type polyimide. Monoamines and/or mono anhydrides can be used as end capping agents if desired.

[0053] One class of polyimide monomer is usually a diamine, or a diamine monomer. The diamine monomer can also be a diisocyanate, and it is to be understood that an isocyanate could be substituted for an amine in this description, as appropriate. There are other types of monomers that can be used in place of the diamine monomer, as known to those skilled in the art. The other type of monomer is called an acid monomer, and is usually in the form of a dianhydride. In this description, the term "di-acid monomer" is defined to include a dianhydride, a tetraester, a diester acid, a tetracarboxylic acid, or a trimethylsilyl ester, all of which can react with a diamine to produce a polyimide polymer. Dianhydrides are sometimes referred to in this description, but it is to be understood that tetraesters, diester acids, tetracarboxylic acids, or trimethylsilyl esters could be substituted, as appropriate. There are also other types of monomers that can be used in place of the di-acid monomer, as known to those skilled in the art.

[0054] Because one di-acid monomer has two anhydride groups, different diamino monomers can react with each anhydride group so the di-acid monomer may become located between two different diamino monomers. The diamine monomer contains two amine functional groups; therefore, after the first amine functional group attaches to one di-acid monomer, the second amine functional group is still available to attach to another di-acid monomer, which then attaches to another diamine monomer, and so on. In this manner, the polymer backbone is formed. The resulting polycondensation reaction forms a poly(amic acid).

[0055] The polyimide polymer is usually formed from two different types of monomers, and it is possible to mix different varieties of each type of monomer. Therefore, one, two, or more di-acid monomers can be used, as well as one, two or more diamino monomers. The total molar quantity of di-acid monomers is kept about the same as the total molar quantity of diamino monomers if a long polymer chain is desired. Because more than one type of diamine or di-acid can be used, the various monomer constituents of each polymer chain can be varied to produce polyimides with different properties. For example, a single diamine monomer AA can be reacted with two di-acid co monomers, BiBi and B2B2, to form a polymer chain of the general form of (AA-BiBi)x-(AA- B2B2)_y in which x and y are determined by the relative incorporations of B1B1 and B2B2 into the polymer backbone. Alternatively, diamine co-monomers A1A1 and A2A2 can be reacted with a single di-acid monomer BB to form a polymer chain of the general form of (AiAi-BB)_x-(A2A2- BB)y. Additionally, two diamine co-monomers A1A1 and A2A2 can be reacted with two di-acid co- monomers B1B1 and B2B2 to form a polymer chain of the general form (AIAI-BIBI)_w-(AIAI-B2B2)X- (A2A2-BiBi)_y-(A2A2-B2B2)z, where w, x, y, and z are determined by the relative incorporation of A1A1-B1B1, A1A1-B2B2, A2A2-B1B1, and A2A2-B2B2 into the polymer backbone. More than two di- acid co-monomers and/or more than two diamine co-monomers can also be used. Therefore, one or more diamine monomers can be polymerized with one or more di-acids, and the general form of the polymer is determined by varying the amount and types of monomers used.

[0056] There are many examples of monomers that can be used to make polyimide polymers. In some embodiments, the diamine monomer is a substituted or unsubstituted aromatic diamine, a substituted or unsubstituted alkyldiamine, or a diamine that can include both aromatic and alkyl functional groups. A non-limiting list of possible diamine monomers include 4,4'-oxydianiline, 3,4'-oxydianiline, 3,3'-oxydianiline, ^-phenylenediamine, w-phenylenediamine, o- phenylenediamine, diaminobenzanilide, 3,5-diaminobenzoic acid, 3,3'-diaminodiphenylsulfone, 4,4'-diaminodiphenylsulfones, l,3-bis-(4-aminophenoxy)benzene, l,3-bis-(3- aminophenoxy)benzene, l,4-bis-(4-aminophenoxy)benzene, l,4-bis-(3-aminophenoxy)benzene, 2,2-Bis[4-(4-aminophenoxy)phenyl]-hexafluoropropane, 2,2-bis(3-aminophenyl)-l, 1, 1, 3,3,3- hexafluoropropane, 4,4'-isopropylidenedianiline, l-(4-aminophenoxy)-3-(3- aminophenoxy)benzene, l-(4-aminophenoxy)-4-(3-aminophenoxy)benzene, bis-[4-(4- aminophenoxy)phenyl]sulfones, 2,2-bis[4-(3-aminophenoxy)phenyl]sulfones, bis(4-[4- aminophenoxy]phenyl)ether, 2,2'-bis-(4-aminophenyl)-hexafluoropropane, (6F-diamine), 2,2'-bis- (4-phenoxyaniline)isopropylidene, meta-phenylenediamine, para-phenylenediamine, 1,2- diaminobenzene, 4,4'-diaminodiphenylmethane, 2,2-bis(4-aminophenyl)propane,

4,4'diaminodiphenylpropane, 4,4'-diaminodiphenylsulfide, 4,4'-diaminodiphenylsulfone, 3,4'diaminodiphenylether, 4,4'-diaminodiphenylether, 2,6-diaminopyridine, bis(3- aminophenyl)diethyl silane, 4,4'-diaminodiphenyl diethyl silane, benzidine, dichlorobenzidine, 3,3'- dimethoxybenzidine, 4,4'-diaminobenzophenone, N,N-bis(4-aminophenyl)-n-butylamine, N,N- bis(4-aminophenyl)methylamine, 1,5-diaminonaphthalene, 3,3'-dimethyl-4,4'-diaminobiphenyl, 4- aminophenyl-3-aminobenzoate, N,N-bis(4-aminophenyl)aniline, bis(p-beta-amino-t- butylphenyl)ether, p-bis-2-(2-methyl-4-aminopentyl)benzene, p-bis(l, l-dimethyl-5- aminopentyl)benzene, l,3-bis(4-aminophenoxy)benzene, m-xylenediamine, p-xylenediamine, 4,4'- diaminodiphenyletherphosphine oxide, 4,4'-diaminodiphenyl N-methylamine, 4,4'-diaminodiphenyl N-phenylamine, amino-terminal poly dimethyl siloxanes, amino-terminal polypropyleneoxides, amino-terminal polybutyleneoxides, 4,4'-methylenebis(2-methylcyclohexylamine), 1,2- diaminoethane, 1,3-diaminopropane, 1,4-diaminobutane, 1,5-diaminopentane, 1,6-diaminohexane, 1,7-diaminoheptane, 1,8-diaminooctane, 1,9-diaminononane, 1,10-diaminodecane, and 4,4'- methylenebisbenzeneamine, 2,2'-dimethylbenzidine, bisaniline-p-xylidene, 4,4'-bis(4- aminophenoxy)biphenyl, 3,3'-bis(4 aminophenoxy)biphenyl, 4,4'-(l,4- phenylenediisopropylidene)bisaniline, and 4,4'-(l,3-phenylenediisopropylidene)bisaniline, or combinations thereof. In a specified embodiment, the diamine monomer is 4,4'-oxydianiline, 2,2'- dimethylbenzidine, 2,2'-dimethylbenzidine, (also known as 4,4'-diamino-2,2'-dimethylbiphenyl (DMB)), bisaniline-p-xylidene, 4,4'-bis(4-aminophenoxy)biphenyl, 3,3'-bis(4 aminophenoxy)biphenyl, 4,4'-(l,4-phenylenediisopropylidene)bisaniline, and 4,4'-(l,3- phenylenediisopropylidene)bisaniline, or combinations thereof. In a specified embodiment, the diamine monomer is ODA, 2,2'-dimethylbenzidine.or both.

[0057] A non-limiting list of possible dianhydride monomers include hydroquinone dianhydride, 3,3,4,4'-biphenyltetracarboxylic dianhydride (BPDA), pyromellitic dianhydride, 3,3',4,4'- benzophenonetetracarboxylic dianhydride (PMDA), 4,4'-oxydiphthalic anhydride, 3,3',4,4'- diphenylsulfonetetracarboxylic dianhydride, 4,4'-(4,4'-isopropylidenediphenoxy)bis(phthalic anhydride), 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride, 4,4'-

(hexafluoroisopropylidene)diphthalic anhydride, bis(3,4-dicarboxyphenyl) sulfoxide dianhydride, polysiloxane-containing dianhydride, 2,2',3,3 '-biphenyltetracarboxylic dianhydride, 2,3,2', 3'- benzophenonetetraearboxylic dianhydride, naphthalene-2,3,6,7-tetracarboxylic dianhydride, naphthalene-l,4,5,8-tetracarboxylie dianhydride, 4,4'-oxydiphthalic dianhydride, 3,3',4,4'- biphenylsulfonetetracarboxylic dianhydride, 3,4,9, 10-peiylene tetracarboxylic dianhydride, bis(3,4- dicarboxyphenyl)sulfide dianhydride, bis(3,4-dicarboxyphenyl)methane dianhydride, 2,2-bis(3,4- dicarboxyphenyl)propane dianhydride, 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane, 2,6- dichloronaphthalene-l,4,5,8-tetracarboxylic dianhydride, 2,7-dichloronapthalene-l,4,5,8- tetracarboxylic dianhydride, 2,3,6,7-tetrachloronaphthalene-l,4,5,8-tetracarboxylic dianhydride, phenanthrene-, 8,9, 10-tetracarboxylic dianhydride, pyrazine-2,3,5,6-tetracarboxylic dianhydride, benzene-l,2,3,4-tetracarboxylic dianhydride, and thiophene-2,3,4,5-tetracarboxylic dianhydride, or combinations thereof. In a specific embodiment, the dianhydride monomer is BPDA, PMDA, or both.

[0058] In some aspects, the molar ratio of anhydride to total diamine is from 0.4: 1 to 1.6: 1, 0.5 : 1 to 1.5 : 1, 0.6: 1 to 1.4: 1, 0.7: 1 to 1.3 : 1, or specifically from 0.8: 1 to 1.2: 1. In further aspects, the molar ratio of dianhydride to multifunctional amine (e.g., triamine) is 2: 1 to 140: 1, 3 : 1 to 130: 1, 4: 1 to 120: 1, 5 : 1 to 1 10: 1, 6: 1 to 100: 1, 7: 1 to 90: 1, or specifically from 8: 1 to 80: 1. Mono-anhydride groups can also be used. Non-limiting examples of mono-anhydride groups include 4-amino-l,8- naphthalic anhydride, endo-bicyclo[2.2.2]oct-5-ene-2,3-dicarboxylic anhydride, citraconic anhydride, trans- 1,2-cyclohexanedicarboxylic anhydride, 3,6-dichlorophthalic anhydride, 4,5- dichlorophthalic anhydride, tetrachlorophthalic anhydride 3,6-difluorophthalic anhydride, 4,5- difluorophthalic anhydride, tetrafluorophthalic anhydride, maleic anhydride, l-cyclopentene-1,2- dicarboxylic anhydride, 2,2-dimethylglutaric anhydride 3,3-dimethylglutaric anhydride, 2,3- dimethylmaleic anhydride, 2,2-dimethylsuccinic anhydride, 2,3-diphenylmaleic anhydride, phthalic anhydride, 3-methylglutaric anhydride, methyl succinic anhydride, 3-nitrophthalic anhydride, 4- nitrophthalic anhydride, 2,3-pyrazinedicarboxylic anhydride, or 3,4-pyridinedicarboxylic anhydride. Specifically, the mono-anhydride group can be phthalic anhydride.

[0059] In another embodiment, the polyimides used to prepare the aerogels of the present invention include multifunctional amine monomers with at least three primary amine functionalities. The multifunctional amine may be a substituted or unsubstituted aliphatic multifunctional amine, a substituted or unsubstituted aromatic multifunctional amine, or a multifunctional amine that includes a combination of an aliphatic and two aromatic groups, or a combination of an aromatic and two aliphatic groups. A non-limiting list of possible multifunctional amines include propane- 1, 2,3 -triamine, 2-aminomethylpropane- 1,3 -diamine, 3-(2- aminoethyl)pentane-l,5-diamine, bis(hexamethylene)triamine, N',N'-bis(2-aminoethyl)ethane-l,2- diamine, N',N'-bis(3-aminopropyl)propane-l,3-diamine, 4-(3-aminopropyl)heptane-l,7-diamine, N',N'-bis(6-aminohexyl)hexane-l,6-diamine, benzene- 1, 3, 5-triamine, cyclohexane-l,3,5-triamine, melamine, N-2-dimethyl-l,2,3-propanetriamine, diethylenetriamine, 1 -methyl or 1 -ethyl or 1 -propyl or 1 -benzyl- substituted diethylenetriamine, 1,2-dibenzyldiethylenetriamine, lauryldiethylenetriamine, N-(2-hydroxypropyl)diethylenetriamine, N,N-bis(l-methylheptyl)-N-2- dimethyl-l,2,3-propanetriamine, 2,4,6-tris(4-(4-aminophenoxy)phenyl)pyridine, N,N-dibutyl-N-2- dimethyl-l,2,3-propanetriamine, 4,4'-(2-(4-aminobenzyl)propane-l,3-diyl)dianiline, 4-((bis(4- aminobenzyl)amino)methyl)aniline, 4-(2-(bis(4-aminophenethyl)amino)ethyl)aniline, 4,4'-(3-(4- aminophenethyl)pentane-l,5-diyl)dianiline, l,3,5-tris(4-aminophenoxy)benzene, 4,4',4"- methanetriyltrianiline, N,N,N',N'-Tetrakis(4-aminophenyl)- 1 ,4-phenylenediamine, a polyoxypropylenetriamine, octa(aminophenyl)polyhedral oligomeric silsesquioxane, or combinations thereof. A specific example of a polyoxypropylenetriamine is JEFF AMINE® T-403 from Huntsman Corporation, The Woodlands, TX USA. In a specific embodiment, the aromatic multifunctional amine may be l,3,5-tris(4-aminophenoxy)benzene or 4,4',4"-methanetriyltrianiline. In some embodiments, the multifunctional amine includes three primary amine groups and one or more secondary and/or tertiary amine groups, for example, N',N'-bis(4-aminophenyl)benzene-l,4- diamine.

[0060] Non-limiting examples of capping agents or groups include amines, maleimides, nadimides, acetylene, biphenylenes, norbornenes, cycloalkyls, and N-propargyl and specifically those derived from reagents including 5-norbornene-2,3-dicarboxylic anhydride (nadic anhydride, NA), methyl-nadic anhydride, hexachloro-nadic anhydride, cis-4-cyclohexene-l,2-dicarboxylic anhydride, 4-amino-N-propargylphthalimide, 4-ethynylphthalic anhydride, and maleic anhydride.

[0061] In some instances, the backbone of the polymer can include substituents. The substituents (e.g., oligomers, functional groups, etc.) can be directly bonded to the backbone or linked to the backbone through a linking group (e.g., a tether or a flexible tether). In other embodiments, a compound or particles can be incorporated (e.g., blended and/or encapsulated) into the polyimide structure without being covalently bound to the polyimide structure. In some instances, the incorporation of the compound or particles can be performed during the polyamic reaction process. In some instances, particles can aggregate, thereby producing polyimides having domains with different concentrations of the non-covalently bound compounds or particles.

[0062] Specific properties of a polyimide can be influenced by incorporating certain compounds into the polyimide. The selection of monomers is one way to influence specific properties. Another way to influence properties is to add a compound or property modifying moiety to the polyimide. C. Preparation of Highly Branched Polyimide Aerogels with Macropores

[0063] Polyimides may be synthesized by several methods. In a one method of synthesizing aromatic polyimides, a solution of the aromatic diamine in a polar aprotic solvent, such as N- methylpyrrolidone ( MP), can be prepared. A di-acid monomer, usually in the form of a dianhydride, can be added to this solution, but the order of addition of the monomers can be varied. For example, the di-acid monomer can be added first, or the di-acid monomer and the diamine can be simultaneously added. The resulting polycondensation reaction forms a polyamic acid, also referred to as a polyamide acid, which is a polyimide precursor. Other polyimide precursors are known, including polyamic ester, polyamic acid salts, polysilyl esters, and polyisoimides. This process description may be applicable to one or more polyimide precursor solutions. Alternatively the polyimide can be formed from the forward or reverse mixing of amines and anhydrides under appropriate dehydrating conditions and/or catalysts where the lifetime of the polyamic acid intermediate is very short or possibly not even detectable.

[0064] Aerogels of the present disclosure can be made by using a multi-step process that includes 1) preparation of the highly branched polyimide gel, 2) optional solvent exchange, and 3) drying of the polymeric solution to form the aerogel. These process steps are discussed in more detail below.

1. Highly Branched Polyimide Gels

[0065] In the preparation of a highly branched polyimide gel at least one acid monomer can be reacted with at least one diamino monomer in a reaction solvent to form a poly(amic acid), which is then contacted with an imidization catalyst in the presence of a chemical dehydrating agent to form a polymerized polyimide gel via an imidization reaction. As discussed above, numerous acid monomers, diamino monomers, and multifunctional amine monomers can be used to synthesize highly branched polyimides having minimal or no cross-linking. In one aspect of the current invention, one or more diamino monomers and one or more multifunctional amine monomers are premixed in one or more solvents and then treated with one or more dianhydrides that are added in sequentially smaller amounts at pre-defined time increments while monitoring the viscosity. In other aspects, the reverse addition can be performed where one or more diamino monomers and one or more multifunctional amine monomers can be added together or separately as solids, neat, or dissolved in an appropriate solvent to a solution or mixture of dianhydride and solvent. The desired viscosity of the polymerized polyimide gel is 20 to 2,000 cP or specifically 500 to 1,000 cP. By performing the reaction using portion-wise addition of dianhydride or one or more diamino monomers and one or more multifunctional amine monomers while monitoring viscosity, a highly branched non-crosslinked aerogel can be prepared. By way of example, a triamine monomer (about 23 equiv.) can be added to the solvent to give desired molar solution (about a 0.0081). To the solution a first diamine monomer (about 280 equiv.) can be added, followed by second diamine monomer (about 280 equiv.). Next a dianhydride (about 552 total equiv.) can be added in sequentially smaller amounts at pre-defined time increments while monitoring the viscosity. The dianhydride can be added to the solution as neat compound, or mixed with a solvent to form a solution or mixture. The dianhydride can be added (e.g., added neat, as a solution, or as a mixture) until the desired viscosity is reached (e.g., 500 to 1,000 cP). For example, a first portion of dianhydride can be added, the reaction can be stirred (e.g., for 20 minutes), a second portion of dianhydride can be added, and a sample of the reaction mixture was then analyzed for viscosity. After stirring for additional time (e.g., for 20 minutes), a third portion of dianhydride can be added, and a sample can be taken for analysis of viscosity. The reaction mixture can then be stirred for a desired period of time (e.g., 10 hours to 12 hours, or overnight), and then a mono-anhydride (about 96 equiv.) can be added. The resulting reaction mixture can be stirred until no more solid is visible. After a desired amount of time (e.g., about 2 hours), the product can be isolated (e.g., filtered).

[0066] In other aspects, the reverse addition can be performed where one or more diamino monomers and one or more multifunctional amine monomers can be added together or separately as solids, neat, or dissolved in an appropriate solvent to a solution or mixture of dianhydride and solvent. The desired viscosity of the polymerized polyimide gel is 20 to 2,000 cP or specifically 500 to 1,000 cP. By performing the reaction using portion-wise addition of one or more diamino monomers and one or more multifunctional amine monomers while monitoring viscosity, a highly branched non-crosslinked aerogel can be prepared. By way of example, a dianhydride can be mixed with reaction solvent to form a solution or mixture. One or more diamino monomers can be mixed with a reaction solvent and one or more multifunctional amine monomers can be mixed with a reaction solvent. In some embodiments, a solution of the one or more diamino monomers and the one or more multifunctional amine monomers and reaction solvent can be prepared. A first portion of the one or more diamino monomers and the one or more multifunctional amine monomers can be added to the dianhydride and the resulting reaction mixture can be agitated for a period of time. A second portion of the one or more diamino monomers and the one or more multifunctional amine monomers can then be added to the reaction mixture and the reaction mixture agitated for a period of time. The portion-wise addition of the one or more diamino monomers and the one or more multifunctional amine monomers followed by agitation can be continued until all of the one or more diamino monomers and one or more multifunctional amine monomers is added to the reaction mixture. After addition of all of the one or more diamino monomers and one or more multifunctional amine monomers, a mono-anhydride as a capping agent can be added to the solution, and the resulting reaction mixture can be stirred until no more solid is visible. After a desired amount of time (e.g., about 2 hours), the product can be isolated (e.g., filtered). In some embodiments, the viscosity of the solution is monitored between each addition of the amine compounds.

[0067] The reaction solvent can be DMSO, diethylsulfoxide, DMF, N,N-diethylformamide, DMAc, Ν,Ν-diethylacetamide, MP, l-methyl-2-pyrrolidinone, N-cyclohexyl-2-pyrrolidone, 1, 13- dimethyl-2-imidazolidinone, diethyleneglycoldimethoxyether, o-dichlorobenzene, phenols, cresols, xylenol, catechol, butyrolactones, hexamethylphosphoramide, or mixtures thereof. The reaction solvent and other reactants can be selected based on the compatibility with the materials and methods applied i.e. if the polymerized polyimide gel is to be cast onto a support film, injected into a moldable part, or poured into a shape for further processing into a workpiece. In a specific embodiment, the reaction solvent is DMSO.

[0068] In some aspects, a chemical curing system suitable for driving the conversion of polyimide precursor to the polyimide state can be employed. Chemical imidization catalysts may include pyridine, methylpyri dines, quinoline, isoquinoline, l,8-diazabicyclo[5.4.0]undec-7-ene (DBU), DBU phenol salts, carboxylic acid salts of DBU, triethylenediamine, carboxylic acid slats of triethylenediamine, lutidine, N-methylmorpholine, triethylamine, tripropylamine, tributylamine, other trialkylamines, 2-methyl imidazole, 2-ethyl-4-methylimidazole, imidazole, other imidazoles, or combinations thereof. Any dehydrating agent suitable for use in formation of an imide ring from an amic acid precursor is also suitable for use in the methods of the present invention. Non-limiting examples of dehydrating agents include acetic anhydride, propionic anhydride, n-butyric anhydride, benzoic anhydride, trifluoroacetic anhydride, phosphorus trichloride, dicyclohexylcarbodiimide, or combinations thereof. [0069] The reaction temperature for the gel formation can be determined by routine experimentation depending on the starting materials. In a preferred embodiment, the temperature range can be greater than, equal to, or between any two of 20 °C, 30 °C, 35 °C, 40 °C, and 45 °C. After a desired amount of time (e.g., about 2 hours), the product can be isolated (e.g., filtered), after which a nitrogen containing hydrocarbon (828 equiv.) and dehydration agent (1214 equiv.) can be added. The addition of the nitrogen containing hydrocarbon and/or dehydration agent can occur at any temperature. In some embodiments, the nitrogen containing hydrocarbon and/or dehydration agent is added to the solution at 20 °C to 28 °C (e.g., room temperature) stirred for a desired amount of time at room temperature. In some instances, after addition of nitrogen containing hydrocarbon and/or dehydration agent, the solution temperature is raised up to 150 °C.

[0070] While keeping the above in mind, the introduction of macropores into the aerogel polymeric matrix, as well as the amount of such macropores present, can be performed in the manner described above in the Summary of the Invention Section as well as throughout this specification. In one non-limiting manner, the formation of macropores versus smaller mesopores and micropores can be primarily controlled by controlling the polymer/solvent dynamics during gel formation. By doing so, the pore structure can be controlled, and the quantity and volume of macroporous, mesoporous, microporous cells can be controlled. For example, a curing additive that reduces the resultant polyimide solubility, such as l,4-diazabicyclo[2.2.2]octane, produces a polyimide containing a higher number of macropores compared to another curing additive that improves the resultant polyimide solubility, such as tri ethyl amine. In another example, using the same dianhydride such as BPDA, but increasing the ratio of rigid amines incorporated into the polymer backbone such as p-PDA as compared to more flexible diamines such as 4,4' -OD A, the formation of macropores as compared to smaller mesopores and micropores can be controlled.

[0071] The polyimide solution can be cast onto a casting sheet covered by a support film for a period of time. Casting can include spin casting, gravure coating, three roll coating, knife over roll coating, slot die extrusion, dip coating, Meyer rod coating, or other techniques. In one embodiment, the casting sheet can be a polyethylene terephthalate (PET) casting sheet. After a passage of time, the polymerized gel can be removed from the casting sheet and prepared for the solvent exchange process. In some embodiments, the cast film can be heated in stages to elevated temperatures to remove solvent and convert the amic acid functional groups in the polyamic acid to imides with a cyclodehydration reaction (e.g., imidization). In some instances, polyamic acids may be converted in solution to polyimides with the addition of the chemical dehydrating agent, catalyst, and/or heat. [0072] In some embodiments, the polyimide polymers can be produced by preparing a polyamic acid polymer the reaction vessel. The polyamic acid is then formed into a sheet or a film and subsequently processed with catalysts or heat and catalysts.

2. Optional Solvent Exchange

[0073] After the highly branched non-crosslinked polyimide gel is synthesized, a solvent exchange can be conducted. The solvent exchange can exchange reaction solvent for a second solvent. In one embodiment, the solvent exchange can be conducted where the polymerized gel can be placed inside of a pressure vessel and submerged in a mixture that includes the reaction solvent and the second solvent. Then, a high-pressure atmosphere can be created inside of the pressure vessel thereby forcing the second solvent into the polymerized gel and displacing a portion of the reaction solvent. Alternatively, the solvent exchange step can be conducted without the use of a high-pressure environment. It may be necessary to conduct a plurality of rounds of solvent exchange. In some embodiments, solvent exchange is not necessary.

[0074] The time necessary to conduct the solvent exchange can depending upon the type of polymer undergoing the exchange as well as the reaction solvent and second solvent being used. In one embodiment, each solvent exchange can range from 1 to 168 hours or any period time there between including 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, or 23, 24, 25, 50, 75, 100, 125, 150, 155, 160, 165, 166, 167, or 168 hours. In another embodiment, each solvent exchange can take approximately 1 to 60 minutes, or about 30 minutes. Non-limiting examples of second solvents include methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2- butanol, isobutanol, tert-butanol, 3-methyl-2-butanol, 3,3-dimethyl-2-butanol, 2-pentanol, 3- pentanol, 2,2-dimethylpropan-l-ol, cyclohexanol, di ethylene glycol, cyclohexanone, acetone, acetyl acetone, 1,4-dioxane, diethyl ether, dichlorom ethane, trichloroethylene, chloroform, carbon tetrachloride, water, and mixtures thereof. In a specific embodiment, the second solvent is acetone. In certain non-limiting embodiments, the second solvent can have a suitable freezing point for performing supercritical or subcritical drying steps. For example tert-butyl alcohol has a freezing point of 25.5 °C and water has a freezing point of 0 °C under one atmosphere of pressure. Alternatively, and as discussed below, however, the drying can be performed without the use of supercritical or subcritical drying steps, such as by evaporative drying techniques.

[0075] The temperature and pressure used in the solvent exchange process may be varied. The duration of the solvent exchange process can be adjusted by performing the solvent exchange at a varying temperatures or atmospheric pressures, or both, provided that the pressure and temperature inside the pressure vessel does not cause either the first solvent or the second solvent to leave the liquid phase and become gaseous phase, vapor phase, solid phase, or supercritical fluid. Generally, higher pressures and/or temperatures decrease the amount of time required to perform the solvent exchange, and lower temperatures and/or pressures increase the amount of time required to perform the solvent exchange.

3. Cooling and Drying

[0076] In one embodiment after solvent exchange, the highly branched non-crosslinked polymerized gel can be dried under supercritical conditions. In this instance, the solvent in the gel can be removed by supercritical CO2 extraction.

[0077] In another embodiment after solvent exchange, the highly branched non-crosslinked polymerized gel can be exposed to subcritical drying. In this instance, the gel can be cooled below the freezing point of the second solvent and subjected to a freeze-drying or lyophilization process to produce the aerogel. For example, if the second solvent is water, then the polymerized gel can be cooled to below the freezing point of water (e.g., about 0 °C). After cooling, the cooled polymerized gel can be subjected to a vacuum for a period of time to allow sublimation of the second solvent.

[0078] In still another embodiment after solvent exchange, the highly branched non-crosslinked polymerized gel can be exposed to subcritical drying with optional heating after the majority of the second solvent has been removed through sublimation. In this instance, the partially dried gel material can be heated to a temperature near or above the boiling point of the second solvent for a period of time. The period of time can range from a few hours to several days, although a typical period of time is approximately 4 hours. During the sublimation process, a portion of the second solvent present in the polymerized gel can be removed, leaving a gel that can have macropores, mesopores, or micropores, or any combination thereof or all of such pore sizes. After the sublimation process is complete, or nearly complete, the highly branched non-crosslinked aerogel is formed.

[0079] In yet another embodiment after solvent exchange, the highly crosslinked polymerized gel can be dried under ambient conditions, for example, by removing the solvent under a stream of gas (e.g., air, anhydrous gas, inert gas (e.g., nitrogen (N2) gas), etc.). Still further, passive drying techniques can be used such as simply exposing the gel to ambient conditions without the use of a gaseous stream. D. Articles of Manufacture

[0080] In some aspects, an article of manufacture can include an open-cell aerogel with a branched polyimide matrix with less than 5% by weight of crosslinked polymers. In some embodiments, the article of manufacture can be a thin film, monolith, wafer, blanket, core composite material, substrate for radiofrequency antenna, a sunscreen, a sunshield, a radome, insulating material for oil and/or gas pipeline, insulating material for liquefied natural gas pipeline, insulating material for cryogenic fluid transfer pipeline, insulating material for apparel, insulating material for aerospace applications, insulating material for buildings, cars, and other human habitats, insulating material for automotive applications, insulation for radiators, insulation for ducting and ventilation, insulation for air conditioning, insulation for heating and refrigeration and mobile air conditioning units, insulation for coolers, insulation for packaging, insulation for consumer goods, vibration dampening, wire and cable insulation, insulation for medical devices, support for catalysts, support for drugs, pharmaceuticals, and/or drug delivery systems, aqueous filtration apparatus, oil-based filtration apparatus, and solvent-based filtration apparatus.

1. Fluid Filtration Applications

[0081] In some embodiments, the open-cell aerogel with a highly branched polyimide matrix (branched polyimide aerogel) can be used in fluid filtration systems and apparatus. A feed fluid can be contacted with the branched polyimide aerogel such that some, all or, substantially all, of the impurities and/or desired substances are removed from the feed fluid to produce a filtrate essentially devoid of the impurities and/or desired substances. The filtrate, impurities, and/or desired substances can be collected, stored, transported, recycled, or further processed. The highly branched polyimide aerogel can be further processed to release the impurities and/or desired substances from the aerogel.

[0082] The highly branched polyimide macroporously structured aerogel described herein can be used in or with filtration apparatuses known in the art. Non-limiting examples of filtration apparatuses and applications include gas filters, building air filters, automotive cabin air filters, combustion engine air filters, aircraft air filters, satellite air filters, face mask filters, diesel particulate filters, in-line gas filters, cylinder gas filters, soot filters, pressure swing absorption apparatus, etc. Additional non-limiting examples of filtration apparatuses and applications include solvent filtration systems, column filtration, chromatography filtration, vacuum flask filtration, microfiltration, ultrafiltration, reverse osmosis filtration, nanofiltration, centrifugal filtration, gravity filtration, cross flow filtration, dialysis, hemofiltration, hydraulic oil filtration, automotive oil filtration, or the like. Further, non-limiting examples of the purpose of filtration include sterilization, separation, purification, isolation, and the like.

[0083] A fluid for filtration ("feed") and a filtrate can be any fluid. The fluid can be a liquid, gas, supercritical fluid, or a mixture thereof. In some instances, the fluid can be aqueous, organic, non-organic, biological in origin, or a mixture thereof. In some instances, the fluid can contain solids and/or other fluids. As non-limiting examples, the fluid can be or can be partially water, blood, an oil, a solvent, air, or mixtures thereof. Water can include water, any form of steam and supercritical water.

[0084] In some instances, the fluid can contain impurities. Non-limiting examples of impurities include solids, liquids, gases, supercritical fluids, objects, compounds, and/or chemicals, etc. What is defined as an impurity may be different for the same feed fluid depending on the filtrate desired. In some embodiments, one or more aerogels can be used to remove impurities. Non-limiting examples of impurities in water can include ionic substances such as sodium, potassium, magnesium, calcium, fluoride, chloride, bromide, sulfate, sulfite, nitrate, nitrites, cationic surfactants, and anionic surfactants, metals, heavy metals, suspended, partially dissolved, or dissolved oils, organic solvents, nonionic surfactants, defoamants, chelating agents, microorganisms, particulate matter, and the like. Non-limiting examples of impurities in blood can include red blood cells, white blood cells, antibodies, microorganisms, water, urea, potassium, phosphorus, gases, particulate matter, and the like. Non-limiting examples of impurities in oil can include water, particulate matter, heavy and/or lightweight hydrocarbons, metals, sulfur, defoamants, and the like. Non-limiting examples of impurities in solvents can include water, particulate matter, metals, gases, and the like. Non-limiting impurities in air can include water, particulate matter, microorganisms, liquids, carbon monoxide, sulfur dioxide, and the like.

[0085] In some instances, the feed fluid can contain desired substances. Non-limiting examples of desired substances include solids, liquids, gases, supercritical fluids, objects, compounds, and/or chemicals, and the like. In some embodiments, one or more aerogels can be used to concentrate or capture a desired substance, or remove a fluid from a desired substance. Non-limiting examples of desired substances in water can include ionic substances such as sodium, potassium, magnesium, calcium, fluoride, chloride, bromide, sulfate, sulfite, nitrate, nitrites, cationic surfactants, and anionic surfactants, metals, heavy metals, suspended, partially dissolved, or dissolved oils, organic solvents, nonionic surfactants, chelating agents, microorganisms, particulate matter, etc. Non- limiting examples of desired substances in blood can include red blood cells, white blood cells, antibodies, lipids, proteins, and the like. Non-limiting examples of desired substances in oil can include hydrocarbons of a range of molecular weights, gases, metals, defoamants, and the like. Non- limiting examples of desired substances in solvents can include particulate matter, fluids, gases, proteins, lipids, and the like. Non-limiting examples of desired substances in air can include water, fluids, gases, particulate matter, and the like.

[0086] FIGS. 1, 2, and 3 are non-limiting schematics of system 100 used to carry out a filtration of a fluid using an aerogel. System 100 can include separation zone 102. The materials, size, and shape of separation zone 102 can be determined using standard engineering practice to achieve the desired flow rates and contact time. Separation zone 102 is capable of holding or may be made of one or more aerogels and includes feed fluid inlet 104 (inlet) and/or filtrate outlet 106 (outlet). In some instances, the separation zone is made entirely of one or more branched polyimide aerogels, or one or more branched polyimide aerogels, in, or around, a supporting structure. Feed fluid 108 can be introduced to separation zone 102 through inlet 104 {See, FIGS. 1 and 2) or through direct contact with the separation zone {See, FIG. 3). In some embodiments, feed fluid 108 can be received under greater or reduced pressure than ambient pressure. Introduction of feed fluid 108 into separation zone 102 can be at a rate sufficient to allow optimum contact of the feed fluid with the one or more aerogels. Contact of feed fluid 108 with the aerogel can allow the feed fluid to be filtered by the aerogel, which results in filtrate 110. Filtrate 110 can have less impurity and/or desired substance when compared with feed fluid 108. In certain aspects, filtrate 110 can be essentially free of the impurity and/or the desired substance. Filtrate 110 can exit separation zone 102 via outlet 106 {See, FIGS. 1 and 3) or through directly exiting separation zone 102 {See, FIG. 2). In some instances, filtrate 110 can be recycled back to a separation zone, collected, stored in a storage unit, etc. In some instances, one or more aerogels can be removed and/or replaced from the separation zone. In some instances, filtrate 110 can be collected and/or removed from separation zone 102 without filtrate 110 flowing through outlet 106. In some instances, the impurities and/or desired substance can be removed from separation zone 102. As one non-limiting example, the impurities and/or desired substances can be removed from the separation zone by flowing a fluid through the separation zone in the reverse direction from the flow of the feed fluid through the separation zone.

[0087] The filtration conditions in separation zone 102 can be varied to achieve a desired result {e.g., removal of substantially all of the impurities and/or desired substance from the feed fluid). The filtration conditions include temperature, pressure, fluid feed flow, filtrate flow, or any combination thereof. Filtration conditions are controlled, in some instances, to produce streams with specific properties. Separation zone 102 can also include valves, thermocouples, controllers (automated or manual controllers), computers or any other equipment deemed necessary to control or operate the separation zone. The flow of the feed fluid 104 can be adjusted and controlled to maintain optimum contact of the feed fluid with the one or more aerogel. In some embodiments, computer simulations can be used to determine flow rates for separation zones of various dimensions and various aerogels.

[0088] The compatibility of an aerogel with a fluid and/or filtration application can be determined by methods known in the art. Some properties of an aerogel that may be determined to assess the compatibility of the aerogel may include, but is not limited to: the temperature and/or pressures that the aerogel melts, dissolves, oxidizes, reacts, degrades, or breaks; the solubility of the aerogel in the material that will contact the aerogel; the flow rate of the fluid through the aerogel; the retention rate of the impurity and/or desired product form the feed fluid; etc.

2. Radiofrequency (RF) Applications

[0089] Due to their low density, mechanical robustness, lightweight, and low dielectric properties, the branched polyimide aerogels can be used in radiofrequency (RF) applications. The use of branched polyimide aerogels in RF applications enables the design of thinner substrates, lighter weight substrates and smaller substrates. Non-limiting examples of radiofrequency applications include a substrate for a RF antenna, a sunshield for a RF antenna, a radome, or the like. Antennas can include flexible and/or rigid antennas, broadband planar-circuited antennas (e.g., a patch antennas, an e-shaped wideband patch antenna, an elliptically polarized circular patch antenna, a monopole antenna, a planar antenna with circular slots, a bow-tie antenna, an inverted-F antenna and the like). In the antenna design, the circuitry can be attached to a substrate that includes the branched polyimide aerogel and/or a combination of the branched polyimide aerogel and other components such as other polymeric materials including adhesives or polymer films, organic and inorganic fibers (e.g., polyester, polyamide, polyimide, carbon, glass fibers, or combinations thereof), other organic and inorganic materials including silica aerogels, polymer powder, glass reinforcement, etc. The use of branched polyimide aerogels in antennas enables the design substrates with higher throughput. In addition, the branched polyimide aerogels can have coefficient of linear thermal expansion (CTE) similar to aluminum and copper (e.g., CTE of about 23/K and about 17 ppm/K), and is tunable through choice of monomer to match CTE of other desirable materials. In some embodiments, the aerogel can be used in sunshields and/or sunscreens used to protect RF antennas from thermal cycles due to their temperature insensitivity and RF transparency. In certain embodiments, the aerogel can be used as a material in a radome application. A radome is a structural, weatherproof enclosure that protects a microwave (e.g., radar) antenna. Branched polyimide aerogels can minimize signal loss due to their low dielectric constant, and can provide structural integrity due to their stiffness.

EXAMPLES

[0090] The present invention will be described in greater detail by way of specific examples. The following examples are offered for illustrative purposes only, and are not intended to limit the invention in any manner. Those of skill in the art will readily recognize a variety of noncritical parameters, which can be changed or modified to yield essentially the same results.

[0091] Table 1 lists the acronyms for the compounds used in Examples 1-7.

Table 1

Example 1

(Preparation of a Highly Branched BPDA DMB-ODA Polyimide)

[0092] A reaction vessel with a mechanical stirrer and a water jacket was used. The flow of the water through the reaction vessel jacket was adjusted to maintain temperature in the range of 18-

35 °C. The reaction vessel was charged with DMSO (108.2 lbs. 49.1 kg), and the mechanical stirrer speed was adjusted to 120-135 rpm. TAPOB (65.13 g) was added to the solvent. To the solution was added DMB (1081.6 g), ODA (1020.2 g). A first portion of BPDA (1438.4 g) was then added.

After stirring for 20 minutes, a sample of the reaction mixture was analyzed for viscosity using a

Brookfield DV1 viscometer (Brookfield, AMETEK, U.S.A.). A second portion of BPDA (1407.8 g) was added, and the reaction mixture was stirred for 20 additional minutes. A third portion of

BPDA (138.62 g) was added, and the reaction mixture was stirred for 20 minutes. A sample of the reaction mixture was analyzed for viscosity. After stirring for 8 hours, phthalic anhydride (PA,

86.03 g) was added. The resulting reaction mixture was stirred until no more solids were visible.

After 2 hours, the product was removed from the reaction vessel, filtered, and weighed. Example 2

(Preparation of a Highly Branched Polyimide Aerogel Monolith by Freeze Drying)

[0093] The resin (about 10,000 grams) prepared in Example 1 was mixed with triethylamine

(about 219 grams) and acetic anhydride (about 561 grams) for five minutes. After mixing, the resultant solution was poured into a square 15" x 15" mold and left for 48 hours. The gelled shape was removed from the mold, and placed into an acetone bath. After immersion for 24 hours, the acetone bath was exchanged with fresh acetone. The soak and exchange process was repeated five times. After the final exchange, the bath was replaced with tertiary butyl alcohol. After immersion for 24 hours, the tertiary butyl alcohol bath was exchanged for fresh tertiary butyl alcohol. The soak and exchange process was repeated three times The part was subsequently flash frozen and subjected to subcritical drying for 96 hours in at 5 °C, followed by drying in vacuum at 50 °C for 48 hours. The final recovered aerogel part had open-cell structure as observed by scanning electron microscopy (SEM) performed on a Phenom Pro Scanning Electron Microscope (Phenom-World, the Netherlands), exhibited a density of 0.22 g/cm³ and porosity of 88.5% as measured according to

ASTM D4404-10 with a Micromeritics® AutoPore V 9605 Automatic Mercury Penetrometer

(Micromeritics® Instrument Corporation, U.S.A.), a compression modulus of 2.2 MPa as determined by American Standard Testing Method (ASTM) D395-16, and a compression strength at 25%) strain of 3.5 Mpa as determined by ASTM D395-16. The distribution of pore sizes was measured according to ASTM D4404-10 using a Micromeritics® AutoPore V 9605 Automatic

Mercury Penetrometer (Micromeritics® Instrument Corporation, U.S.A.), and the distribution of pore diameters is provided in FIG. 4. From the data it was determined that 100%> of the pores were macropores and that the average pore diameter was about 1200 nm, thus confirming that a macroporously shaped aerogel was produced.

Example 3

(Preparation of a Highly Branched Polyimide Aerogel Monolith by Thermal Drying)

[0094] The resin (about 10,000 grams) prepared in Example 1 was mixed with triethylamine

(about 219 grams) and acetic anhydride (about 561 grams) for five minutes. After mixing, the resultant solution was poured into a square 15" x 15" mold and left for 48 hours. The gelled shape was removed from the mold and placed into an acetone bath. After immersion for 24 hours, the acetone bath was exchanged with fresh acetone. The soak and exchange process was repeated five times. After the final exchange, the part was dried with an ambient (about 20 to 30 °C) drying process to evaporate a majority of the acetone over 48 hours followed by thermal drying at 50 °C for 4 hours, 100 °C for 2 hours, 150 °C for 1 hour, and then 200 °C for 30 minutes. The final recovered aerogel had similar properties as observed in Example 2. Example 4

(Preparation of a Highly Branched Polyimide)

[0095] TAPOB (about 2.86 g) was added to the reaction vessel charged with about 2,523.54 g

DMSO as described in Example 1. To the solution was added a first portion of DMB (about 46.75 g), followed by a first portion of ODA (about 44.09 g). After stirring for about 20 minutes, a first portion of BPDA (about 119.46 g) was added. After stirring for about 20 minutes, TAPOB (about

2.86 g), DMB (about 46.75 g), and ODA (about 44.09 g) were added. After stirring for about 20 minutes, BPDA (about 119.46 g) was added. After stirring for about 20 minutes, TAPOB (about

2.86 g), DMB (about 46.75 g), and ODA (about 44.09 g) were added. After stirring for about 20 minutes, BPDA (about 119.46 g) was added. After stirring for about 8 hours, PA (about 50.12 g) was added. The resulting reaction mixture was stirred until no more solids were visible. After about

2 hours, the product was removed from the reaction vessel, filtered, and weighed.

Example 5

(Preparation of a Highly Branched Polyimide Aerogel Monolith by Freeze Drying)

[0096] The resin (about 400 grams) prepared in Example 4 was mixed with 2-methylimidazole

(about 53.34 grams) for five minutes and then benzoic anhydride (about 161.67 grams) for five minutes. After mixing, the resultant solution was poured into a square 3" x 3" mold and placed in an oven at 75 °C for 30 minutes and then left overnight at room temperature. The gelled shape was removed from the mold, and placed into an acetone bath. After immersion for 24 hours, the acetone bath was exchanged with fresh acetone. The soak and exchange process was repeated five times.

After the final exchange, the bath was replaced with tertiary butyl alcohol. After immersion for 24 hours, the tertiary butyl alcohol bath was exchanged for fresh tertiary butyl alcohol. The soak and exchange process was repeated three times The part was subsequently frozen on a shelf freezer, and subjected to subcritical drying for 96 hours in at 5 °C, followed by drying in vacuum at 50 °C for 48 hours. The final recovered aerogel part had open-cell structure as observed by scanning electron microscopy (SEM) performed on a Phenom Pro Scanning Electron Microscope (Phenom-World, the Netherlands), exhibited a density of 0.15 g/cm³ and porosity of 92.2% as measured according to

(Micromeritics® Instrument Corporation, U.S.A.). The distribution of pore sizes were measured according to ASTM D4404-10 using a Micromeritics® AutoPore V 9605 Automatic Mercury

Penetrometer (Micromeritics® Instrument Corporation, U.S.A.), and the distribution of pore diameters is shown in FIG. 5. From the data, it was determined that 96.3% of the shaped macroporously structured aerogel's pore volume was made up of pores having an average diameter of 50 nm. Example 6

(Preparation of a Highly Branched Polyimide)

[0097] TAPOB (about 2.05 g) was added to the reaction vessel charged with about 2,776.57 g

DMSO as described in Example 1 at temperature of 18 to 35 °C. To the solution was added a first portion of DMB (about 33.54 g), followed by a first portion of ODA (about 31.63 g). After stirring for about 20 minutes, a first portion of PMDA (about 67.04 g) was added. After stirring for about

20 minutes, TAPOB (about 2.05 g), DMB (about 33.54 g), and ODA (about 31.63 g) were added.

After stirring for about 20 minutes, PMDA (about 67.04 g) was added. After stirring for about 20 minutes, TAPOB (about 2.05 g), DMB (about 33.54 g), and ODA (about 31.63 g) were added.

After stirring for about 20 minutes, PMDA (about 67.04 g) was added. After stirring for about 8 hours, PA (about 18.12 g) was added. The resulting reaction mixture was stirred until no more solids were visible. After about 2 hours, the product was removed from the reaction vessel, filtered, and weighed.

Example 7

(Preparation of a Highly Branched Polyimide Aerogel Monolith by Freeze Drying)

[0098] The resin (about 400 grams) prepared in Example 6 was mixed with 2-methylimidazole

(about 40.38 grams) for five minutes and then benzoic anhydride (about 122.38 grams) for five minutes. After mixing, the resultant solution was poured into a square 3" x 3" mold and placed in an oven at 75 °C for 30 minutes and then left overnight at room temperature. The gelled shape was removed from the mold, and placed into an acetone bath. After immersion for 24 hours, the acetone bath was exchanged with fresh acetone. The soak and exchange process was repeated five times.

After the final exchange, the bath was replaced with tertiary butyl alcohol. After immersion for 24 hours, the tertiary butyl alcohol bath was exchanged for fresh tertiary butyl alcohol. The soak and exchange process was repeated three times The part was subsequently frozen on a shelf freezer, and subjected to subcritical drying for 96 hours in at 5 °C, followed by drying in vacuum at 50 °C for 48 hours. The final recovered aerogel part had open-cell structure as observed by scanning electron microscopy (SEM) performed on a Phenom Pro Scanning Electron Microscope (Phenom-World, the Netherlands), exhibited a density of 0.23 g/cm³ and porosity of 82.7% as measured according to

ASTM D4404-10 with a Microm eritics® AutoPore V 9605 Automatic Mercury Penetrometer

(Micromeritics® Instrument Corporation, U.S.A.). The distribution of pore sizes was measured according to ASTM D4404-10 using a Micromeritics® AutoPore V 9605 Automatic Mercury

Penetrometer (Micromeritics® Instrument Corporation, U.S.A.), and the distribution of pore diameters is shown in FIG. 6. From the data, it was determined that 90.6% of the shaped macroporously structured aerogel's pore volume was made up of pores having pore diameter greater than 50 nm.

Example 8

(Preparation of a Highly Branched Polyamic Film)

[0099] A reaction vessel with a mechanical stirrer and a water jacket was employed. The flow of the water through the reaction vessel jacket was adjusted to maintain temperature in the range of 20-28 °C. The reaction vessel was charged with DMSO (108.2 lbs. 49.1 kg), and the mechanical stirrer speed was adjusted to 120-135 rpm. TAPOB (65.03 g) was added to the solvent. To the solution was added DMB (1,080.96 g), followed by ODA (1,018.73 g). A first portion of BPDA (1,524.71 g) was added. After stirring for 20 minutes, a sample of the reaction mixture was analyzed for viscosity. A second portion of BPDA (1,420.97 g) was added, and the reaction mixture was stirred for 20 additional minutes. A sample of the reaction mixture was analyzed for viscosity. A third portion of BPDA (42.81 g) was added, and the reaction mixture was stirred for 20 additional minutes. A sample of the reaction mixture was analyzed for viscosity. After stirring for 8 hours, PA (77.62 g) was added. The resulting reaction mixture was stirred until no more solid was visible. After 2 hours, the resin was removed from the reaction vessel, filtered, and weighed.

[00100] The resin (10,000 grams) was mixed with 2-methylimidazole (250 grams) for five minutes. Benzoic anhydride (945 grams) was added, and the solution mixed an additional five minutes. After mixing, the resultant solution was poured onto a moving polyester substrate that was heated in an oven at 100 °C for 30 seconds. The gelled film was collected and placed into an acetone bath. After immersion for 24 hours, the acetone bath was exchanged for fresh acetone. The soak and exchange process was repeated six times. After the final exchange, the gelled film was removed. The acetone solvent was evaporated under a stream of air at room temperature, and subsequently dried for 2 hrs hours at 200 °C. The final recovered aerogel part had open-cell structure as observed by scanning electron microscopy (SEM) performed on a Phenom Pro Scanning Electron Microscope (Phenom- World, the Netherlands), exhibited a density of 0.20 g/cm³ and porosity of >80% as measured according to ASTM D4404-10 with a Micromeritics® AutoPore V 9605 Automatic Mercury Penetrometer (Micromeritics® Instrument Corporation, U.S.A.). The final recovered film exhibited a tensile strength and elongation of 1200 psi (8.27 MPa) and 14%, respectively, at room temperature as measured according to ASTM D882-02. The film had an average pore size of 400 nm.

Claims

1. An aerogel comprising:

(a) an open-cell structure; and

(b) a branched polyimide matrix comprising macropores, wherein the matrix contains less than 5% by weight of crosslinked polymers.

2. The aerogel of claim 1, wherein at least 10 % of the aerogel's pore volume is made up of macropores.

3. The aerogel of claim 2, wherein at least 50 % of the aerogel's pore volume is made up of macropores.

4. The aerogel of claim 3, wherein at least 75 % of the aerogel's pore volume is made up of macropores.

5. The aerogel of claim 4, wherein at least 95 % of the aerogel's pore volume is made up of macropores.

6. The aerogel of claim 5, wherein 100 % of the aerogel's pore volume is made up of macropores.

7. The aerogel of claim 1, wherein the aerogel further comprises micropores or mesopores or both micropores and mesopores.

8. The aerogel of claim 7, wherein less than 90, %, 80 %, 70 %, 60 %, 50 %, 40 %, 30 % 20 %, 10% or less than 5 % of the aerogel's pore volume is made up of micropores and/or mesopores.

9. The aerogel of claim 1, wherein the branched polyimide matrix contains less than 1% by weight of crosslinked polymers or is not crosslinked.

10. The aerogel of claim 1, wherein the branched polyimide matrix has an average pore size of greater than 50 nanometers (nm) to 5000 nm in diameter

11. The aerogel of claim 10, wherein the branched polyimide matrix has an average pore size of 1000 nm to 1400 nm in diameter.

12. The aerogel of claim 11, wherein the branched polyimide matrix has an average pore size of 250 nm to 750 nm.

13. The aerogel of claim 1, wherein the branched polyimide has a degree of branching of at least 0.2 branches per polyimide polymer chain.

14. The aerogel of claim 13, wherein the degree of branching is from 0.2 to 10 7.

15. The aerogel of claim 14, wherein the degree of branching is 0.2 to 0.45.

16. The aerogel of claim 1, wherein the branched polyimide has a general structure of:

where:

R¹ is multifunctional amine residue; Z is a dianhydride residue; R² is a diamine residue; m is a number average per chain ranging from 0.2 to 10; and n is 1 to 25.

17. The aerogel of claim 16, wherein the branched polyimide has a general structure of:

where R³ and R⁴ are each individually a capping group, and are independently selected from a hydrogen, an anhydride residue, an isocyanate residue, an acid residue, or an alkyl group.

The aerogel of claim 16, wherein the dianhydride residue is hydroquinone dianhydride; 3,3',4,4'-biphenyltetracarboxylic dianhydride; pyromellitic dianhydride; 3,3',4,4'- benzophenone-tetracarboxylic dianhydride; 4,4'-oxydiphthalic anhydride; 3, 3 ',4,4'- diphenylsulfone-tetracarboxylic dianhydride; 4,4'-(4,4'-isopropylidenediphenoxy)bis(phthalic anhydride); 2,2- bis(3,4-dicarboxyphenyl)propane dianhydride; 4,4'-(hexafluoroisopropylidene)diphthalic anhydride; bis(3,4-dicarboxyphenyl)sulfoxide dianhydride; polysiloxane-containing dianhydride; 2,2',3,3'-biphenyltetracarboxylic dianhydride;

2,3,2', 3'-benzophenonetetraearboxylic dianhydride; 3,3',4,4'-benzophenonetetraearboxylic dianhydride; naphthalene-2,3,6,7-tetracarboxylic dianhydride; naphthalene- 1,4,5, 8-tetracarboxylie dianhydride; 4,4'-oxydiphthalic dianhydride;

3,3',4,4'-biphenylsulfone tetracarboxylic dianhydride; 3,4,9, 10-peiylene tetracarboxylic dianhydride; bis(3,4-dicarboxyphenyl)sulfide dianhydride; bis(3,4-dicarboxyphenyl)methane dianhydride; 2,2-bis(3,4-dicarboxyphenyl)propane dianhydride; 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropene;

2.6- dichloronaphthalene-l,4,5,8-tetracarboxylic dianhydride;

2.7- dichloronapthalene-l,4,5,8-tetracarboxylic dianhydride; 2,3,6,7-tetrachloronaphthalene- 1,4,5,8-tetracarboxylic dianhydride; phenanthrene-8,9,10-tetracarboxylic dianhydride; pyrazine-2,3,5,6-tetracarboxylic dianhydride; benzene-l,2,3,4-tetracarboxylic dianhydride; thiophene-2,3,4,5-tetracarboxylic dianhydride; or combinations thereof.

The aerogel of claim 18, wherein the dianhydride is 3,3',4,4'-biphenyltetracarboxylic dianhydride, pyromellitic dianhydride, or both.

The aerogel of claim 16, wherein R¹ is a substituted or unsubstituted multifunctional amine comprising at least three primary amine functionalities and R² is at least one substituted or unsubstituted diamine.

The aerogel of claim 20, wherein the multifunctional amine is a substituted or an unsubstituted aliphatic multifunctional amine or a substituted or an unsubstituted aromatic multifunctional amine.

The aerogel of claim 21, wherein the aromatic multifunctional amine is l,3,5,-tris(4- aminophenoxy)benzene, 4,4',4"-methanetriyltrianiline, N,N,N',N'-tetrakis(4-aminophenyl)- 1,4-phenylenediamine, or a polyoxypropylenetriamine.

The aerogel of claim 21, wherein the diamine is a substituted or unsubstituted aromatic diamine, a substituted or an unsubstituted alkyldiamine, or combinations thereof.

The aerogel of claim 23, wherein the diamine is 4,4'-oxydianiline; 3,4'-oxydianiline; 3,3'- oxydianiline; p-phenylenediamine; weto-phenylenediamine; ort/zo-phenylenediamine; para- phenylenediamine; diaminobenzanilide; 3,5-diaminobenzoic acid;

3,3'-diaminodiphenylsulfone; 4,4'-diaminodiphenyl sulfones;

1.3- bis-(4-aminophenoxy)benzene; l,3-bis-(3-aminophenoxy)benzene;

1.4- bis-(4-aminophenoxy)benzene; l,4-bis-(3-aminophenoxy)benzene; 2,2-bis[4-(4-aminophenoxy)phenyl]hexafluoropropane;

2,2-bis(3-aminophenyl)hexafluoropropane; 4,4'-isopropylidenedianiline; 1 -(4-aminophenoxy)-3 -(3 -aminophenoxy)benzene; 1 -(4- aminophenoxy)-4-(3-aminophenoxy)benzene; bis[4-(4-aminophenoxy)phenyl]sulfone; bis[4-(3-aminophenoxy)phenyl]sulfone; bis(4-[4-aminophenoxy]phenyl)ether; 2,2'-bis(4- aminophenyl)hexafluoropropene; 2,2'-bis(4-phenoxyaniline)isopropylidene; meta- phenylenediamine; 1,2-diaminobenzene; 4,4'-diaminodiphenylmethane; 2,2-bis(4- aminophenyl)propane; 4,4'diaminodiphenyl propane; 4,4'-diaminodiphenyl sulfide; 4,4- diaminodiphenylsulfone; 3,4'diaminodiphenyl ether; 4,4'-diaminodiphenyl ether; 2,6- diaminopyridine; bis(3-aminophenyl)di ethyl silane; 4,4'-diaminodiphenyl diethyl silane; benzidine-3'-dichlorobenzidine; 3,3'-dimethoxybenzidine; 4,4'-diaminobenzophenone; N,N-bis(4-aminophenyl)butylamine; N,N-bis(4-aminophenyl)methylamine;

1.5- diaminonaphthalene; 3,3'-dimethyl-4,4'-diaminobiphenyl; 4-aminophenyl-3-aminobenzoate; N,N-bis(4-aminophenyl)aniline; bis(p-beta-amino-tert-butyl phenyl)ether; p-bis-2-(2-methyl-4-aminopentyl)benzene; p-bis(l,l-dimethyl-5-aminopentyl)benzene; l,3-bis(4-aminophenoxy)benzene; m-xylenediamine; p-xylenediamine; 4,4'-diaminodiphenyl ether phosphine oxide; 4,4'-diaminodiphenyl N-methyl amine; 4,4'-diaminodiphenyl N-phenyl amine; amino-terminal polydimethylsiloxanes; amino-terminal polypropyleneoxides; amino-terminal polybutyleneoxides; 4,4'-methylenebis(2-methylcyclohexylamine); 1,2-diaminoethane; 1,3-diaminopropane; 1,4-diaminobutane; 1,5-diaminopentane; 1,6-diaminohexane; 1,7-diaminoheptane; 1,8-diaminooctane; 1,9-diaminononane; 1, 10-diaminodecane; and 4,4'-methylenebisbenzeneamine; 2,2'-dimethylbenzidine; bisaniline-p-xylidene; 4,4'-bis(4-aminophenoxy)biphenyl; 3,3'-bis(4-aminophenoxy)biphenyl; 4,4'-(l,4-phenylenediisopropylidene)bisaniline; and 4,4'- (l,3-phenylenediisopropylidene)bisaniline, or any combination thereof, preferably, 4,4'- oxydianiline; 2,2'-dimethylbenzidine, or both.

The aerogel of claim 16, where: R¹ is selected from:

combination thereof; and selected from:

or any combination thereof.

The aerogel of claim 1, wherein the polyimide further comprises a mono-anhydride group, preferably phthalic anhydride.

A method of making the aerogel claim 1, the method comprising:

(a) providing a multifunctional amine compound and at least one diamine compound to a solvent to form a solution; (b) providing at least one dianhydride compound to the solution of step (a) under conditions sufficient to form a branched polymer matrix solution, wherein the branched polymer matrix is solubilized in the solution; and

(c) subjecting the branched polymer matrix solution to conditions sufficient to form an aerogel having an open-cell structure with macropores present in the branched polyimide matrix of the aerogel.

28. The method of claim 27, wherein all or a first portion of the multifunctional amine is added to the solution.

29. The method of claim 27, wherein the step (b) conditions sufficient to form the branched polymer matrix solution comprises:

(i) adding the dianhydride incrementally to the step (a) solution at a temperature of 20 °C to 40 °C, preferably 25 °C, until a target viscosity is obtained to form a branched polymer, wherein the branched polymer is soluble in the solution;

(ii) agitating the mixture overnight, or about 8 to 16 hours, at a temperature of 20 °C to 30 °C, preferably 25 °C to form the branched polymer matrix solution; and

(iii) adding a sufficient amount of mono-anhydride compound to the solution of step (i) under conditions sufficient to react with any monoamine groups of the branched polymer.

30. The method of claim 29, wherein adding the dianhydride incrementally comprises:

(iv) adding a first portion of the dianhydride to the step (a) solution to form a mixture;

(v) monitoring the viscosity of the mixture;

(vi) adding a second portion of the dianhydride to the solution, wherein the amount of the second portion is based on the viscosity of the mixture in step (v), or adding a second portion of a multifunctional amine and then a second portion of the dianhydride to the solution, wherein the amounts of the multifunctional amine and dianhydride are based on the viscosity of the mixture in step (v); and

(vii) repeating steps (v) and (vi) until the target viscosity is obtained.

31. The method of claim 27, wherein the target viscosity of the solution is from 50 to 2000 centipoise (cP), preferably 1000 to 1500 cP.

32. The method of claim 27, wherein the solvent is dimethylsulfoxide, diethylsulfoxide, N,N- dimethylformamide, N,N-diethylformamide, Ν,Ν-dimethylacetamide, N,N- di ethyl acetamide, N-methyl-2-pyrrolidone, l-methyl-2-pyrrolidinone, N-cyclohexyl-2- pyrrolidone, l, 13-dimethyl-2-imidazolidinone, diethyleneglycoldimethoxyether, o- dichlorobenzene, phenols, cresols, xylenol, catechol, butyrolactones, hexamethylphosphoramide, and mixtures thereof, preferably, dimethyl sulfoxide.

33. The method of claim 27, wherein subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure comprises the addition of chemical curing agents in appropriate amounts to form a gel.

34. The method of claim 27, wherein subjecting the branched polyimide solution to conditions sufficient to form an open-cell structure comprises: subjecting the branched polyimide gel to conditions sufficient to freeze the solvent in to form a frozen material; and subjecting the frozen material to a drying step sufficient to form an open-cell structure.

35. The method of claim 27, wherein subjecting the branched polymer matrix solution to conditions sufficient to form an open-cell structure comprises removing the solvent under a stream of air.

36. The method of claim 35, further comprising subjecting the branched polyimide solution to at least one solvent exchange with a different solvent.

37. The method of claim 36, wherein the different solvent is exchanged with acetone.

38. The method of claim 37, wherein the branched polyimide has not been subjected to crosslinking conditions.

39. An article of manufacture comprising the aerogel of claim 1.

40. The article of manufacture of claim 39, wherein the article of manufacture is a thin film, monolith, wafer, blanket, core composite material, a substrate for radiofrequency antenna, substrate for a sunshield, a substrate for a sunshade, a substrate for radome, insulating material for oil and/or gas pipeline, insulating material for liquefied natural gas pipeline, insulating material for cryogenic fluid transfer pipeline, insulating material for apparel, insulating material for aerospace applications, insulating material for buildings, cars, and other human habitats, insulating material for automotive applications, insulation for radiators, insulation for ducting and ventilation, insulation for air conditioning, insulation for heating and refrigeration and mobile air conditioning units, insulation for coolers, insulation for packaging, insulation for consumer goods, vibration dampening, wire and cable insulation, insulation for medical devices, support for catalysts, support for drugs, pharmaceuticals, and/or drug delivery systems, aqueous filtration apparatus, oil-based filtration apparatus, and solvent-based filtration apparatus, or any combination thereof.

41. The article of manufacture of claim 39, wherein the article of manufacture is an antenna.

42. The article of manufacture of claim 39, wherein the article of manufacture is a sunshield or sunscreen.

43. The article of manufacture of claim 39, wherein the article of manufacture is a radome.

44. The article of manufacture of claim 43, wherein the article of manufacture is a filter.

45. A method of filtering a fluid comprising impurities and/or desired substances, the method comprising contacting a feed fluid with the aerogel of claim 1 under conditions sufficient to remove at least a portion of the impurities and/or desired substances from the feed fluid and produce a filtrate.