A process for producing an aerogel which comprises reacting the following components: (a1) at least one polyfunctional isocyanate, (a2) from 5 to 20% by weight of at least one polyfunctional aromatic amine having the general formula I where R 1 and R 2 can be identical or different and are each selected independently from among hydrogen and linear or branched alkyl groups having from 1 to 6 carbon atoms and where all substituents Q 1 to Q 5 and Q 1' to Q 5' are identical or different and are each selected independently from among hydrogen, a primary amino group and a linear or branched alkyl group having from 1 to 12 carbon atoms, where the alkyl group can bear further functional groups, with the proviso that - the compound having the general formula I comprises at least two primary amino groups, where at least one of Q 1 , Q 3 and Q 5 is a primary amino group and at least one of Q 1' , Q 3' and Q 5' is a primary amino group, and - Q 2 , Q 4 , Q 2' and Q 4' are selected so that the aromatic amine having the general formula I has at least one linear or branched alkyl group having from 1 to 12 carbon atoms, which may optionally bear further functional groups, in the alpha position relative to at least one primary amino group bound to the aromatic ring, (a3) from 0 to 15% by weight of water, and (a4) from 1 to 4.9% by weight of at least one carboxylate as catalyst, in each case based on the total weight of the components (a1) to (a4), where the % by weight of the components (a1) to (a4) add up to 100% by weight, and where the reaction is carried out in the presence of a solvent (C) which is removed under supercritical conditions after the reaction, where a gel is obtained in the reaction, which gel is subsequently dried. (a1) at least one polyfunctional isocyanate, (a2) from 5 to 20% by weight of at least one polyfunctional aromatic amine having the general formula I where R 1 and R 2 can be identical or different and are each selected independently from among hydrogen and linear or branched alkyl groups having from 1 to 6 carbon atoms and where all substituents Q 1 to Q 5 and Q 1' to Q 5' are identical or different and are each selected independently from among hydrogen, a primary amino group and a linear or branched alkyl group having from 1 to 12 carbon atoms, where the alkyl group can bear further functional groups, with the proviso that - the compound having the general formula I comprises at least two primary amino groups, where at least one of Q 1 , Q 3 and Q 5 is a primary amino group and at least one of Q 1' , Q 3' and Q 5' is a primary amino group, and - Q 2 , Q 4 , Q 2' and Q 4' are selected so that the aromatic amine having the general formula I has at least one linear or branched alkyl group having from 1 to 12 carbon atoms, which may optionally bear further functional groups, in the alpha position relative to at least one primary amino group bound to the aromatic ring, - the compound having the general formula I comprises at least two primary amino groups, where at least one of Q 1 , Q 3 and Q 5 is a primary amino group and at least one of Q 1' , Q 3' and Q 5' is a primary amino group, and - Q 2 , Q 4 , Q 2' and Q 4' are selected so that the aromatic amine having the general formula I has at least one linear or branched alkyl group having from 1 to 12 carbon atoms, which may optionally bear further functional groups, in the alpha position relative to at least one primary amino group bound to the aromatic ring, (a3) from 0 to 15% by weight of water, and (a4) from 1 to 4.9% by weight of at least one carboxylate as catalyst, <EOS>