Numerical Simulation Of Two Dimensional Quasicrystal In Block Copolymers

In recent years,quasicrystalline phases have been observed in various con-densed matter systems including soft materials and hard condensed materials.Since comparing to crystals,quasicrystalline phases possess a more unique na-ture,in particular the aperiodic,attracting tremendous attention from material science,solid-state physics,condensed matter physics and soft matters.In the past few decades,although the aperiodic order theory of quasicrystals has devel-oped rapidly in the fields of mathematics and physics.But theoretical research is still scarce and there are still many problems required to be solved,such as the study on the thermodynamic stability of quasicrystals.This paper is mainly inspired by[Macromolecules,2018,51:7713-7721],we combine the self-consistent field theory to study the thermodynamic stability of two dimensional dodecagonal quasicrystalline phase in AB₁CB₂tetrablock terpolymers with equal symmetric interaction observing the stable periodic tilling structures.In this process,self-consistent field theory model is used to calculate the free energy of different phase structures accurately by using BDF4 discrete format and Anderson mixing itera-tion,and then energy diagram is drawn.The similarities are:we both choose the AB₁CB₂tetrablock terpolymers as research object to analysis the stability of each phase structure with self-consistent field theory;The differences are:the numerical method,the parameters in the calculation and the method of optimizing the calcu-lation area.In addition,we try to add a more precise method,projection method,to the self-consistent field iteration to calculate dodecagonal quasicrystalline phase,but the present result is not ideal.