Phase Behavior The Sequence-Assembly Problem

Heteropolymers can self-assemble into highly ordered patterns of microstructures, both in solution and in bulk. This subject has been reviewed extensively [1,123-127]. The driving force for structure formation in such systems is competing interactions, i.e., the attraction between one of the monomer species and the repulsion between the others, on the one hand, and covalent bonding of units within the same macromolecule, on the other hand. The latter factor prevents the separation of the system into homogeneous macroscopic phases, which can, under specific conditions, stabilize some types of microdomain structures. Usually, such a phenomenon is treated as microphase separation transition, MIST, or order-disorder transition, ODT. 

For diblock copolymers, periodically arranged spheres (micelles), hexago-nally packed cylinders, and a lamellar phase have been observed [1]. A more complex bicontinuous cubic phase with QIasymmetry (gyroid structure) has also been identified. These supramolecular structures, with length scales on the order of 1 to 102 nm, may be controlled by changing the amount of solvent, the length of blocks, or the proportions of A and B monomeric units [128-131]. 

The theoretical approaches mentioned above mostly deal with diblock or regular multiblock AB copolymers [1,123-125]. It has been shown theoretically [146-149] that for random copolymers the existence of ordered microphases is also not excluded. In particular, it has been shown that in addition to the classical microdomain superstructures, chemical irregularities in multiblock copolymers may result in formation of very exotic positionally ordered structures with many levels (length-scales) of organization 

In this section, we discuss the phase behavior of protein-like copolymers that can be considered as a specific type of correlated copolymers. One can expect that the presence of long-range correlations in protein-like chains will influence the phase behavior of such copolymers. 

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