Extended Data Fig. 2: Structural analysis of amorphous polymer models.

a, PIM-1, cell size: 78.8 × 78.8 × 78.8 Å; b, AO-PIM-1, cell size: 78.8 × 78.8 × 78.8 Å; c, PIM-EA-TB, cell size: 66.8 × 66.8 × 66.8 Å. The surface shown is the Connolly surface with probe radius of 1.55 Å. d-f, Voids coloured with respect to the pore radius. g-l, interconnected (green) and disconnected (red) voids with respect to a probe 1.55 Å in radius (j-l), and a probe 0.85 Å in radius, respectively. The simulations show that PIM-EA-TB, AO-PIM-1 and PIM-1 present sub-nanometre-sized interconnected voids and channels. Apart from the higher surface area of PIM-EA-TB, its pores are also disconnected with respect to a relatively large probe of 1.55 Å, while PIM-1 shows a great portion of connected pores with a probe of the same size. When a smaller probe 0.85 Å in radius was used, the connected pores are observed in PIM-EA-TB and AO-PIM-1, suggesting the presence of ultra-micropores (<7 Å) in both PIM-EA-TB (due to chain rigidity) and AO-PIM-1 (due to hydrogen bonding). m, Normalized pore size distributions of three representative PIMs. The pore size distributions are qualitatively similar, but shift to smaller pores for PIM-EA-TB and AO-PIM-1. Particularly, all pores in the PIM-EA-TB have diameters smaller than 8 Å, whereas PIM-1 has a significant portion that is larger yet still within sub-nanometre range. The most common pore diameter in AO-PIM-1 is 4.5 Å in diameter, and its maximum pore size is intermediate with respect to those of PIM-EA-TB and PIM-1. The narrow distribution of ultramicropores enables the size-selective ion transport.