Recent advances in the fundamental understanding of the ordered phases of multi-block copolymers (MBCPs) at the molecular level have attracted considerable scientific interest in recent years. Herein, by employing molecular dynamics simulation, we focus on the four typical systems: linear alternating, branch-like, star-like AB-type MBCPs and linear copolymers filled with nanoparticles (NPs). First, we establish the phase diagram for the linear tetrablock copolymers (ABAB) as a function of the composition ratio between A- and B-block, exhibiting six typical phase states. Furthermore, increasing the mutual repulsive interaction strength, the temperature and the periodic dynamic shearing cycle result in the merging of spheres, presenting a clear beginning of the order-to-order transition (OOT) behavior. Second, we examine the branch-like and star-like copolymers and find that increasing branch density significantly leads to the occurrence of phase transition. Particularly, we illustrate that the sphere configurations of the MBCPs can be described in terms of tail, loop and bridge conformations. Increasing the number of distinct blocks in linear alternating copolymers results in an enhancement of the bridge conformation, in which case some spheres are separated to smaller ones. Furthermore, for the tail conformation, we present a unified theoretical framework to rationalize the topological state of the chain arrangements of spheres and infer that the entanglements within the internal reaction layer between different A-blocks result in the inhomogeneous distribution of the spheres sizes even with controlled molecular weight and composition ratio between each block. Finally, we find that the ABAB tetrablock copolymers filled with moderate spherical NPs exhibit a clear OOT from spheres to double gyroid or cylinders. We infer that the maximum amount of the B-block within the second and/or third layers for the filled spherical NPs connects different NPs effectively, leading to the complicated OOT behavior. Generally, this fundamental study could provide some guidelines for designing and fabricating high performance BCPs by manipulating the formation of the ordered phases.
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