copolymers and pentadecylphenol (PDP) which can be attached to the P4VP blocks via a hydrogen bond. [3,4] In the subsequent work, by using the concepts of supramolecular self-assembly, they observed the formation of lamellar-within-lamellar, lamellar-within-cylindrical, cylindricalwithin-lamellar, spherical-within-lamellar and lamellar-within-spherical morphologies at different volume fraction. [6] In additional to the non-covalent bond in the supramolecules, such as hydrogenbond, [7] ionic interactions, [8] covalent bond was used to synthesize the undecablock copolymer (PISISISISIP), which consists two long poly(2-vinylpyridine) (P) blocks on each end and five short polyisoprene (I) plus four short polystyrene (S) blocks in the middle. [9] They reported the observation of five layers lamellae-in-lamellae hierarchical structure, which results from the large number of molecular configurations in this hierarchical structure. [9] Later, they observed many hierarchical structures and confirmed the phase transition from spheres-in-lamellae into cylinders-in-lamellae, lamellae-in-lamellae, and coaxial cylindrical structures, and finally into onion-like spherical structure as the volume fraction of the tail block increases. [10] However, the number of configurations is only one part of entropy. In addition to the configuration entropy, conformation entropy and enthalpy effect are crucial to the phase behavior. By capturing these effects, researchers study the formation mechanism of hierarchical lamellae by using Self-Consistent Field Theory (SCFT). [11][12][13][14][15][16][17] Besides SCFT, strong-segregation theory (SST) [18,19] and dissipative particle dynamics (DPD) [20,21] were extensively used to study the phase behavior of a number of linear multiblock copolymers. [18,20,22,23] Interestingly, by exhibiting the dynamics process of the formation of hierarchical structures, the small-length-scale nanostructures was found to form behind large-length-scale nanostructures, which shows great guidance for the controllable formation of the hierarchical morphologies. [17,21] Besides the parallel lamellae-in-lamellae structures, perpendicular hierarchical structure was reported by Bates using poly(CECEC-P) (C: cyclohexylethylene, E: ethylene, P: propylene) hexablock terpolymer by sequential anionic polymerization followed by catalytic hydrogenation. [24,25] By using the powerful frame of SCFT, the mechanism of this perpendicular structure was well understood, [12] and a number of hierarchical structures including perpendicular or parallel lamellae, cylinders, and
Hierarchical StructuresDue to more than two length scales properties, hierarchical structures, which can combine several properties and respond to multi external conditions, have attracted the continuing attention over the past decades. The corresponding phase diagram of different hierarchical structures is crucially important for the observation of these morphologies. In this paper, the phase diagram of these hierarchical structures in A(BC) 2 B multiblock copolyme...
