Two-dimensional polymers (2DPs) and their layer-stacked 2D covalent organic frameworks (2D COFs) are classes of structurally defined crystalline polymeric materials with exotic physical and chemical properties. Yet, synthesizing 2DP and 2D COF single crystals via irreversible reactions remains challenging. Here we report the synthesis of charged 2DP (C2DP) single crystals through an irreversible Katritzky reaction, under pH control, on a water surface. The periodically ordered 2DPs comprise aromatic pyridinium cations and counter BF4− anions. The C2DP crystals, which are composed of linked porphyrin and pyrylium monomers (C2DP-Por), have a tunable thickness of 2–30 nm and a lateral domain size up to 120 μm2. Single crystals with a square lattice (a = b = 30.5 Å) are resolved by imaging and diffraction methods with near-atomic precision. Furthermore, the integration of C2DP-Por crystals in an osmotic power generator device shows an excellent chloride ion selectivity with a coefficient value reaching ~0.9 and an output power density of 4 W m−2, superior to those of graphene and boron nitride. Large single crystals of charged 2D polymers are synthesized on a water surface, under kinetic control, by the irreversible Katritzky reaction. The crystals can act as an anion-selective membrane for osmotic energy generation.