Fast mixing and fast heat transfer of a flow microreactor enable living cationic polymerization of vinyl ethers without any additives to stabilize an active propagating polymer end. Such polymerization involves no equilibrium between the active species and the dormant species, and thus proceeds fast and is complete in a short time. Setting a short residence time enables the propagating polymer end to be usable in a subsequent reaction such as polymerization of a different monomer to make a block copolymer and end functionalization. The flow microreactor enables anionic polymerization of styrene or methacrylate monomers at higher temperatures than in a conventional batch reactor. The propagating polymer end in anionic polymerization can be used in a subsequent reaction, allowing synthesis of a polymer containing a functional group at its end or allowing synthesis of a block copolymer.