The size of critical secondary nuclei of polymer crystals does not depend on supersaturation

It is still a great challenge to determine the size of critical nuclei, which is crucial for a comprehensive understanding of crystallization and for testing the controversial crystallization theories. Here, we propose a method to determine the size of critical secondary nuclei on growth faces of poly(butylene succinate) single crystals in solution, basing on the probability of statistically selecting crystallizable units in random copolymers. In a dilute solution and for a given crystallization temperature, we reveal that the size of critical secondary nuclei was independent of supersaturation, contrary to the well-accepted prediction of existing theories which expect that the size of the critical nucleus increases with decreasing supersaturation. Accounting correctly for the dilution-caused change in the steady-state concentration of clusters of various sizes, we remedy inconsistencies of existing theoretical approaches in deriving the correct size of critical secondary nuclei in solution being independent of supersaturation.