Equilibrium Field Theoretic Study of Nanoparticle Interactions in Diblock Copolymer Melts

Nanoparticles insertion and dimerization in polymer brushes

Molecular dynamics simulations are conducted to systematically investigate the insertion of spherical nanoparticles (NPs) in polymer brushes as a function of their size, strength of their interaction with the polymers, polymer grafting density, and polymer chain length. For attractive interactions between the NPs and the polymers, the depth of NPs' penetration in the brush results from a competition between the enthalpic gain due to the favorable polymer-NP interaction and the effect of osmotic pressure resulting from displaced polymers by the NP's volume. A large number of simulations show that the average depth of the NPs increases by increasing the strength of the interaction strength. However, it decreases by increasing the NPs' diameter or increasing the polymer grafting density. While the NPs' effect on the polymer density is local, their effect on their conformations is long-ranged and extends laterally over length scales larger than the NP's size. This effect is manifested by the emergence of laterally damped oscillations in the normal component of the chains' radius of gyration. Interestingly, we found that for high enough interaction strength, two NPs dimerize in the polymer brush. The dimer is parallel to the substrate if the NPs' depth in the brush is shallow. However, the dimer is perpendicular to the substrate if the NPs' are deep in the brush. These results imply that polymer brushes can be used as a tool to localize and self-assemble NPs in polymer brushes.

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-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.