Size distribution and shape of nano-nucleus of polyethylene simultaneously determined by SAXS

Nucleation mechanism of polymers was studied by means of small angle X-ray scattering (SAXS) by improving our two previous studies. The first one showed first direct SAXS observation of nucleation of polyethylene (PE). The second one reported how “size distribution f(N,t)” of nuclei of nano-meter size (nano-nuclei) evolves with time (t), where N is number of “repeating unit” in a nucleus. Unfortunately the f(N,t) was obtained by incorrect analysis of SAXS intensity (IX), i.e., too simple one-dimensional (1D) nucleus was assumed to analyze the IX. In this paper, we determined simultaneously correct f(N,t) and “two-dimensional (2D) shape” of nano-nucleus. From this it is clarified that nano-nucleus shows significant fluctuation in size and shape and repeats frequent generation and disappearance, which corresponds to the conclusion that the end surface free energy of the nano-nucleus (σe(nano)) is 1/5 times as large as that of macroscopic crystal (σe(macro)). f(N,t) decreased with increase of N. f(N,t) increased and saturated with increase of t.