Position transitions of polymer-grafted nanoparticles in diblock-copolymer nanocomposites

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.

Unveiling the Mechanism of the Location of the Grafted Nanoparticles in a Lamellar-Forming Block Copolymer

Through coarse-grained molecular dynamics simulation of polymer-grafted nanoparticles (NPs) in a lamellar-forming diblock copolymer (BCP), we systematically study the effects of the grafting density (N_g), the compatibility between the grafted chains and the A-block of BCPs (ε_gA), and the NP number (N) on the distance (D) of the NPs from the interface by proposing novel characterization parameters of the orientation and distribution of the grafted chains. The NP gradually migrates away from the interface and into the A-block region with the increase of ε_gA for all studied N_g, while slightly returning toward the interface at high ε_gA and great N_g, which is the first observation of nonmonotonic migration at the molecular level. We ascribe the reason of this to the behavior of the grafted chains that are near the interface. Furthermore, we classify the grafted chains into three types along the normal direction of the interface and the migration process is illustrated by the distribution and orientation of the different types of grafted chains, together with the radial distribution function between the NP and the A-block chains. We observe the formation of the NP layers parallel to the interface for N < 20, and a similar nonmonotonic migration of the layers is as well observed. The D is the largest for a small N because of the excluded volume effects between the NPs. Increasing N_g and N pushes the neighboring NP layers toward the interface due to the mutual repulsion. Generally, this study may shed some light on how to better understand and design high-performance polymer nanocomposites with a tunable location of NPs.

Self-assembly of grafted nanoparticles in the lamellar mesophase of a symmetric triblock copolymer

The self-assembly behavior of brush-grafted nanoparticles in the ordered mesophase of a symmetric triblock copolymer is studied using the self-consistent field theory. The emphasis is on the templated localization of nanoparticles in a two-dimensional lamellar microstructure formed by an ABA triblock copolymer. While particles grafted with either A-type or B-type polymeric chains preferentially localize in the respective micro-domain, the spatial distribution of particles within the selective domain is of great interest in controlling the properties of the nano-ordered morphologies. As the mid-block of an ABA triblock copolymer is entropically constrained, the localization behavior of B-grafted nanoparticles is found to be qualitatively different from that of A-grafted particles. The absence of free ends and the bridge conformation of the mid-block tend to reduce the spatial segregation of B-grafted particles at the center of the B-domain, a behavior in contrast to an AB diblock copolymer. Under similar conditions, while A-grafted particles self-assemble at the center of the A-domain, the B-grafted particles with a non-selective core segregate predominantly at the interface of A and B domains, especially when the particle size is large or grafting is weak. Upon increasing the grafting density, the morphology transitions from interface to center localization. The spatial localization of particles, governed by the interplay of enthalpic and entropic contributions to the free energy, is found to be strongly influenced by particle size, selectivity, volume fraction, and number and size of grafted chains. Controlling the self-assembly behavior of particles by tuning these parameters will be immensely helpful in designing advanced nanostructured materials with desired physical properties.

The effect of particle size on the morphology and thermodynamics of diblock copolymer/tethered-particle membranes

A combination of self-consistent field theory and density functional theory was used to examine the effect of particle size on the stable, 3-dimensional equilibrium morphologies formed by diblock copolymers with a tethered nanoparticle attached either between the two blocks or at the end of one of the blocks. Particle size was varied between one and four tenths of the radius of gyration of the diblock polymer chain for neutral particles as well as those either favoring or disfavoring segments of the copolymer blocks. Phase diagrams were constructed and analyzed in terms of thermodynamic diagrams to understand the physics associated with the molecular-level self-assembly processes. Typical morphologies were observed, such as lamellar, spheroidal, cylindrical, gyroidal, and perforated lamellar, with the primary concentration region of the tethered particles being influenced heavily by particle size and tethering location, strength of the particle-segment energetic interactions, chain length, and copolymer radius of gyration. The effect of the simulation box size on the observed morphology and system thermodynamics was also investigated, indicating possible effects of confinement upon the system self-assembly processes.