Order-order transitions of diblock copolymer melts under cylindrical confinement

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

Self-organization of a 4-miktoarm star block copolymer induced by cylindrical confinement

Self-consistent field calculations have been carried out to reveal the self-assembly behavior of a melt of the ABCD star tetrablock copolymer confined within a cylindrical nanopore. The miktoarm star block copolymer exhibits a rich self-assembly behavior with a myriad of interesting three-dimensional ordered phases with the potential to produce advanced nanomaterials. The broad array of ordered mesophases includes helical microstructures, stack of rings/doughnuts, honeycomb structure, and perforated lamella with beads, depending on the individual block fractions and the size of the cylindrical nanopore. Such chiral motifs generated from achiral polymeric molecules are fascinating due to their superior performance in sophisticated opto-electronic devices. The study also demonstrates an interesting morphology, viz. a honeycomb structure, obtained from the self-organization of ABCD star block copolymer molecules with equal block fractions. The system exhibits order-order phase transition covering a range of ordered morphologies by changing either the block fraction or the nanopore radius. A representative phase diagram in terms of block fractions is constructed. These novel ordered microstructures, arising mainly out of structural frustration and confinement-induced entropy loss, can serve as structural scaffolds to host the spatial distribution of nanoparticles resulting into novel nanocomposites with significantly enhanced as well as controllable properties.

Self-Assembly of Polymer Grafted Nanoparticles within Spherically Confined Diblock Copolymers

Geometric confinement plays an important role in the generation of interesting microstructures on account of structural frustration and confinement-induced entropy loss. In the present study, self-consistent field calculations have been performed to examine the self-assembly behavior of a mixture of diblock copolymers and polymer grafted nanoparticles within a spherical confinement. The analysis is aimed at obtaining the equilibrium distribution of nanoparticles with a high degree of order. The ordered mesophases of diblock copolymers provide useful templates to achieve ordering of nanoparticles in a selective domain. Self-assembly of nanoparticles within frustrated diblock copolymers is found to be very different from the bulk. A rich variety of equilibrium morphologies are observed depending on the degree of confinement and the extent of particle loading. In addition, the role of particle size and selectivity along with the length and the number of polymer chains grafted onto the surface of nanoparticles are analyzed to understand the self-assembly behavior. The specific interest is to obtain the chiral structures out of achiral block copolymers subjected to spherical confinement. The realization of various captivating microstructures, such as chiral ordering of nanoparticles, is highly essential to produce advanced nanomaterials with superior physical properties.

Diblock copolymer templated self-assembly of grafted nanoparticles under circular pore confinement

Geometrical confinement plays an important role in generating novel molecular organization arising out of structural frustration and confinement-induced entropy loss. In the present study, we perform self-consistent mean-field theoretical calculations to examine a mixture of a diblock copolymer and polymer grafted nanoparticles confined in a cylindrical nanopore. The two-dimensional analysis is aimed at constructing the equilibrium nanostructures decorated with particles in an ordered manner. The rich variety of ordered mesophases of the diblock copolymer under confinement provide a template to achieve the self-assembly of nanoparticles in a selective domain. The localization behavior of nanoparticles under confinement is found to be qualitatively different from that in a bulk system. In particular, for the concentric lamellar phase the particles tend to localize predominantly in the region of greater curvature within the curved lamella. The incorporation of grafted nanoparticles also results in a transition in ordered phases. Various equilibrium morphologies are observed depending upon the degree of confinement, particle loading, density of grafted segments and selectivity of the particle core to the polymeric species. The ordering of particles and the ensuing equilibrium nanostructures are analyzed. The comprehensive understanding of the self-assembly behavior of particles enables one to design novel nanomaterials with desirable material properties.

Influence of Branches on the Phase Behavior of (AB)f Starlike Block Copolymer under Cylindrical Confinement

Experimentally, self-assembled morphologies of the (AB)_f starlike block copolymer are strongly dependent on the number of arms, f. For example, the 2- and 4-arm starlike block copolymers exhibited the morphologies of hexagonally arrayed polystyrene cylinder in the polyisoprene matrix while order-bicontinuous nanostructures were observed in 8-, 12-, and 18-arm stars. Theoretically, we found that the transition sequence for (AB)₃ is C₁^B → Dk^B → P₂^B → L₂^B, which becomes C₁^B → L₁^B when f > 6. To explore the influence of f on the phase behavior of (AB)_f under cylindrical confinement, we calculated the two-dimensional phase diagram with respect to the volume fraction and the pore diameter. Our conclusions show that the topologies of the phase diagram are independent of the number of arms; however, the number of arms does affect the phase boundary, which inevitably leads to the different phase transition sequences at fixed volume fraction. Therefore, from the calculated phase diagram, the influence of f on the phase behavior of the starlike copolymer is fully understood.

Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement

Block copolymers confined in nanopores provide unique achiral systems for the formation of helical structures. With AB diblock copolymers, stable single and double helical structures are observed. Aiming to obtain more different helical structures, we replace the AB diblock copolymer with linear ABC triblock copolymers. We speculate that a core-shell superstructure is formed within the nanopore, which is composed of a C-core cylinder wrapped by B-helices within the A-shell. Accordingly, the pore surface is set to be most attractive to the majority A-block and a typical set of interaction parameters is chosen as χACN ≪ χABN = χBCN = 80 to generate the frustrated interfaces. Furthermore, the volume fraction of B-block is fixed as fB = 0.1 to form helical cylinders. A number of helical structures with strands ranging from 1 to 5 are predicted by self-consistent field theory, and in general, the number of strands decreases as the volume fraction of C-block fC increases in a given nanopore. More surprisingly, the variation of helical strand in the confined system has an opposite trend to that in the bulk, which mainly results from the constraint of the cylindrical confinement on the change of the curvature between the outer A-layer and the inner B/C-superdomain. Our work demonstrates a facile way to fabricate different helical superstructures.

Formation of homochiral helical nanostructures in diblock copolymers under the confinement of nanopores

The control of the homochirality of helical structures formed in achiral systems is of great interest as it is helpful for understanding the origin of homochirality in life.