Fig. 1. Liquid crystal structure of （a） rod-line shape （line-rod-line shape）， （b） multi-chain form and （c） dendritic.

Fig. 2. Schematic diagram of four common polyphilic liquid crystal molecules. （a） Bola T-shaped； （b） Bola π-shaped； （c） Bola K-shaped； （d） Bola X-shaped.

Fig. 3. Sequence of LC phases formed by self-assembly of Bola T-shaped polyphiles as observed on increasing the size of the lateral chain

Fig. 4. Intermediate phases at the transitions from triangular to square honeycombs：Transition from （a） triangular to （f） square honeycomb phases occurring via （b） rhombic honeycomb， （c） superlattice or （d， e） inclined columnar phase.

Fig. 5. （a） Structures of molecular 1_n； （b） Rhombic honeycomb as the intermediate phase between triangular and square honeycomb.

Fig. 6. （a） Structure of molecular 2； （b~d） SAXS integral diagram of three liquid crystal phases formed by the cooling of molecule 2 from the cubic phase.

Fig. 7. Electron density maps of （a） quadrilateral column phase Col_squ^T/p4 mm， （b） hexagonal superlattice Col_hex^G/p6mm， （c） hexagonal column phase Col_hex/p6mm （red line represents a cell）， and （d~f） corresponding molecular arrangement model. The three colors of red， green and blue represent three different orientations， and the dashed line represents the triangulation formed by the average of the diamond shapes in different directions. （g） Ratio of the area to the circumference of the molecules arranged in different shapes.

Fig. 8. （a） Structures of molecular 3_n and molecular arrangement model of liquid crystal phase；Comparison of phase sequence of molecular （b） molecule 3_Hn and （c） molecule 3_Fn during cooling.

Fig. 9. Structures of （a） classical bicontinuous cubic network phases （Cub_bi）， （b） unicontinuous network phases （Cub_net） and （c） unicontinuous sphere packings， known as micellar cubic phases.

Fig. 10. Structures of molecular 4_n and summary diagram of phase sequence during cooling

Fig. 11. Topological duality in Pm3¯n cell. （a） 12-weight and 14-weight nodes in the cell； （b） VT of the cell corresponds to dodecahedron and decahedron； （c） DT of the cell corresponds to three different tetrahedrons， and DT and VT are topological duals of each other； （d） and （e） show the topological duality between a single dodecahedron and a tetrahedron， respectively.

Fig. 12. （a） SAXS integration diagram and calibration results； （b） Reconstructed electron density map； （c） Comparison chart of simulated strength and experimental strength； （d） Schematic diagram of the structural model used in the simulation.

Fig. 13. （a） Comparison of volume dV/dr curves of different structures， DP is dual network structure based on P-TPMS， SP is single network structure based on P-TPMS， Im3¯m-8 is open octahedral structure based on I-WP TPMS（the illustration shows the relationship between dV/dr and molecular structure）； （b） Transformation of the triangular honeycomb structure Col_hex/p6mm hex‍a‍⁃gonal columnar phase to（c） the tetrahedral network structure Cub/Pm3¯n cubic phase （magenta represents the polar end group， green represents the OPE core， for visual comparison of the side chain omitted to fill the remaining volume）.

Fig. 14. Structure of molecular 5

Fig. 15. （a） Synchrotron radiation SAXS diffraction pattern and （c） corresponding electron density map； （d） Geometric model diagram used to simulate the cubic Cub/Im3¯m phase SAXS results and （b） the simulation results； （e） GISAXS results of thin-film oriented samples and （f） corresponding structural models.

Fig. 16. I-WP TPMS schematic， in which transparent cyan represents a minimal surface， red and blue networks represent a central network of two spaces separated by TPMS.

Fig. 17. Comparison of dV/dr curves of the volume radial distribution of the relevant structures， DP is double network structure based on P-TPMS， SP is single network structure based on P-TPMS， Oct is 8-node network， that is， the structure formed by molecular 5_F， Squ is quadrilateral column phase （the illustration shows the relationship between dV/dr and molecular structure）.

Fig. 18. Schematic diagram of common in the cubic phase （a） P-， （b） D- and （c） G-TPMS， in which transparent cyan represents a minimal surface， red and blue networks represent the central network of a two-part space separated by TPMS， and symmetries in parentheses represent symmetries when one/two networks are included.

Fig. 19. Structures of molecular 6， 7 and the molecular arrangement model of the SP structure formed by their self-assembly.

Fig. 20. Radial distribution of volume functions dV/dr for DG， SG， DD， SD， DP and SP phases.

Fig. 21. （a） Structures of molecular 8_n； （b） Phase structure models of DG and SD formed by 8_n， according to different chain lengths.

Fig. 22. Molecular arrangement models of a single continuous double network DD structure consisting of （a） two and （b） one molecular bundle to form a network segment

Fig. 23. Molecular structures of the 9_n series and the structural model and node change process of each phase during the phase transition. （a~d） Structural diagrams of DD， Fmmm， P6₃/m and DG phases， respectively； （e） Change process of node shape and angle； （f） Change process of molecular arrangement at the node.

Fig. 24. Network structures of different liquid crystal phases. （a） Cub/Pn3¯m； （b） Cub/Ia3¯d； （c） Ortho/Fmmm； （d） Hex/P6₃/m. The blue-purple semi-transparent plane in （a~d） is a close-packed plane containing polar node balls， the dotted line represents the layer plane， and the red， blue and green balls and columns represent double or triple networks. （e， f） Node ball distribution of Ortho/Fmmm and Hex/P6₃/m phases perpendicular to the close-packed plane， and the yellow dotted line represents the （near） hexagonal close-packed node balls in the plane.

Fig. 25. DG structure molecular arrangement models. （a） Rod-shaped core is arranged parallel to the network， and the polar groups at both ends gather to form network nodes； （b） Rod-shaped core is arranged parallel to the network， and two coaxial rod bundles form a network segment； （c） Rod-shaped aromatic core is arranged vertically along the minimal surface， and the polar groups at both ends form a network structure.

Fig. 26. （a） Structure of molecular 10； Symmetry of the structure is broken from （b） achiral DG（Cub/Ia3¯d） to （c） chiral AG（Cub/I4₁32）.

Fig. 27. Molecular arrangement model of molecule 10 assembled into an AG structure， in which the molecular rod-shaped core is arranged in parallel along the minimal surface， and the side chains form a network structure.

Fig. 28. Structure of molecular 11

Fig. 29. Energy scan results of molecule 11 from 270 eV to 290 eV. Both （110） and （200） signals are resonance signals. The thick red solid line indicates the absorption edge energy of carbon element is 284 eV.

Fig. 30. （a， c） RSoXS experimental results of molecule 11 and theoretical calculation results based on a simplified model； （b， d） Self-assembly structure of molecule 11 and its simplified structural model.

Fig. 31. Molecular arrangement model of molecule 11 assembled into a DG structure， in which the molecular rod-shaped core is arranged perpendicular to the network helix and the side chains fill the remaining volume.

Fig. 32. （a~c） SAXS and WAXS results and calibration of the self-assembled structure of molecule 11 at different temperatures； （d~f）Electron density distribution diagram obtained by inverse Fourier transform based on the SAXS intensity，where purple is the high electron density area， red is the low electron density area， and green is the medium electron density area.

Fig. 33. （a） 2D RSoXS scattering spectrum of molecule 11 at 283.5 eV at 120 °C， red is the extinction signal， black is the resonance enhancement signal； （b， c） Two different molecular arrangement models： （b） randomization and （c） helical in the same direction along the network. The （200） resonance enhancement signal can only be seen if and only if there is a molecular helix in the structure； （d， e） Comparison of RSoXS and SAXS results.

Fig. 34. Simplified molecular arrangement models of （a） Ia3¯d， （b） P4₁2₁2 and （c） I23 structures.

Fig. 35. Structure of molecular 12

Fig. 36. （a） SAXS diffraction results of variable temperature （cooling at 2 K/min）， from Iso to Gyr to I23 phase； （b） SAXS diffraction results at 122 ℃ isothermal after cooling from Iso； （c） SAXS zoomed in image after cooling from Iso to 122 ℃ isothermal for 1 min， at this time it is the new intermediate phase Gyr.

Fig. 37. （a） CD spectra of 12_R and 12_S films at different temperatures； （b） Temperature-dependent ellipticity of CD at 355 nm when heating and cooling12_R and 12_S at 2 K/min.

Fig. 38. Molecular helical arrangement models of （a， c） Ia3¯d Gyroid and （b，d） Chiral Gyroid.