Block copolymers are a class of soft matter that self-assemble to form ordered morphologies on the scale of nanome- ters, making them ideal materials for various applications. These applications directly depend on the shape and size of the self-assembled morphologies, and hence, a high degree of control over the self-assembly is desired. Grafting block copolymer chains onto a substrate to form copolymer brushes is a versatile method to fabricate functional surfaces. Such surfaces demonstrate a response to their environment, i.e., they change their surface topography in response to different external conditions. Furthermore, such surfaces may possess nanoscale patterns, which are important for some applica- tions; however, such patterns may not form with spun-cast films under the same condition. In this review, we summarize the recent progress of the self-assembly of block copolymers grafted onto a flat substrate. We mainly concentrate on the self-assembled morphologies of end-grafted AB dibloek eopolymers, junction p0int-grafted AB diblock copolymers （i.e., Y-shaped brushes）, and end-grafted ABA triblock copolymers. Special emphasis is placed on theoretical and simulation progress.
Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent （S1） and a selective solvent （S2） for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent Cs2, the concentration of the polymer Cp, and the polymers-solvent interactions εij （i = A, B; j = S1, S2）. Morphology diagrams are constructed as functions of Cp, Cs2, and/or εAs2. The copolymer morpho- logical sequence from dissolved → sphere → rod → ring/cage → vesicle is obtained upon increasing Cs2 at a fixed Cv. This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure signifi- cantly. In particular, when tile interaction εBS2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar ag- gregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing Cp or with decreasing Cs2, but remains almost unchanged with variations in εAS2.
The self-assembly of symmetric diblock copolymers confined in the channels of variously shaped cross sections （regu- lar triangles, squares, and ellipses） is investigated using a simulated annealing technique. In the bulk, the studied symmetric diblock copolymers form a lamellar structure with period LL. The geometry and surface property of the confining channels have a large effect on the self-assembled structures and the orientation of the lamellar structures. Stacked perpendicular lamellae with period LL are observed for neutral surfaces regardless of the channel shape and size, but each lamella is in the shape of the corresponding channel＇s cross section. In the case of triangle-shaped cross sections, stacked parallel lamel- lae are the majority morphologies for weakly selective surfaces, while morphologies including a triangular-prism-shaped B-cylinder and multiple tridentate lamellae are obtained for strongly selective surfaces. In the cases of square-shaped and ellipse-shaped cross sections, concentric lamellae are the signature morphology for strongly selective surfaces, whereas for weakly selective surfaces, stacked parallel lamellae, and several types of folding lamellae are obtained in the case of square-shaped cross sections, and stacked parallel lamellae are the majority morphologies in the case of ellipse-shaped cross sections when the length of the minor axis is commensurate with the bulk lamellar period. The mean-square end- to-end distance, the average contact number between different species and the surface concentration of the A-monomers are computed to elucidate the mechanisms of the formation of the different morphologies. It is found that the resulting morphology is a consequence of competition among the chain stretching, interfacial energy, and surface energy. Our results suggest that the self-assembled morphology and the orientation of lamellae can be manipulated by the shape, the size, and the surface property of the confining channels.
