Employment of stereological laws in fast crystal numerical simulation algorithm of polymers and errors analysis of results

Abstract

Both fast solving speed and high accuracy are the goals of polymers’ crystal numerical simulation including the calculation of crystallinity and morphology on the mesoscale (10–3–10–6 m). In our previous work, the stereological Delesse law was applied to improve the solving speed of the crystal simulation algorithm, in which the pixel coloring method and Monte Carlo method were used. However, the new algorithm is imperfect and likely to cause some errors because the idea of statistical average is implicitly included in the Delesse law. This work is to expand the algorithm’s scope with another stereological principle, named Rosiwal law, and quantitatively discuss the errors’ magnitude, influence factors and changing trends when the two stereological principles are employed. The calculation results illustrate that the relative error caused by stereological law is gradually self-reducing, while a big absolute error probably appeared when the very limited cross-section or line is used at some middle time steps. Our results will offer some guidelines on the choice of sections and lines in fast crystal simulation algorithm and its software development.