Memory effect in simulations of asymmetric diblock copolymers under thermal processing

Recent experiments [Kim et al. Science 356,520(2017); PNAS 115,847(2018)] observed that the temperature protocol used to heat and cool an asymmetric diblock copolymer from its disordered micelle liquid state to its ordered micelle crystal phase, and back, can influence which ordered phase is found. This suggests some memory of the initial ordered micelle phase is preserved in the disordered micelle state. To develop an understanding of this memory effect, we perform simulations of a time-dependent Landau-Brazovskii model, which has stability regions for disorder, BCC, FCC, as well as Frank-Kasper phases. Our protocol is to equilibrate a low-temperature ordered micelle phase, rapidly heat to just above the order-disorder transition, anneal for a time t_H, then quench back to the low temperature and observe the time, t_L, it takes for the ordered phase to (re-)form. For small t_H, we find that the ordered phase re-forms quickly (t_L is small), regardless of whether the original ordered phase is stable or metastable. We measure t_L as a function of t_H and find a threshold t_H above which the system remains in the disordered micelle liquid over our (long) simulation time. We examine trends of this memory effect as we move around the low temperature region of the phase diagram.