The production cross sections for primary and residual fragments with charge number from $Z$=70 to 120 produced in the collision of $^{238}$U+$^{238}$U at 7.0 MeV/nucleon are calculated by the improved quantum molecular dynamics (ImQMD) model incorporated with the statistical evaporation model (HIVAP code). The calculation results predict that about sixty unknown neutron-rich isotopes from element Ra ($Z$=88) to Db ($Z$=105) can be produced with the production cross sections above the lower bound of $10^{-8}$ mb in this reaction. And almost all of unknown neutron-rich isotopes are emitted at the laboratory angles $theta_{lab}leq$ 60$^circ$. Two cases, i.e. the production of the unknown uranium isotopes with $Ageq$ 244 and that of rutherfordium with $Ageq$ 269 are investigated for understanding the production mechanism of unknown neutron-rich isotopes. It is found that for the former case the collision time between two uranium nuclei is shorter and the primary fragments producing the residues have smaller excitation energies of $leq$ 30 MeV and the outgoing angles of those residues cover a range of 30$^circ$-60$^circ$. For the later case, the longer collision time is needed for a large number of nucleons being transferred and thus it results in the higher excitation energies and smaller outgoing angles of primary fragments, and eventually results in a very small production cross section for the residues of Rf with $Ageq$ 269 which have a small interval of outgoing angles of $theta_{lab}$=40$^circ$-50$^circ$.
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