Self-assembled morphologies of diblock copolymers confined in nanochannels: Effects of confinement geometry

Controlling the Formation of Polyhedral Block Copolymer Nanoparticles: Insights from Process Variables and Dynamic Modeling

This study delves into the formation of nanoscale polyhedral block copolymer particles (PBCPs) exhibiting cubic, octahedral, and variant geometries. These structures represent a pioneering class that has never been fabricated previously. PBCP features distinct variations in curvature on the outer surface, aligning with the edges and corners of polyhedral shapes. This characteristic sharply contrasts with previous block copolymers (BCPs), which displayed a smooth spherical surface. The emergence of these cornered morphologies presents an intriguing and counterintuitive phenomenon and is linked to process parameters, such as evaporation rates and initial concentration, while keeping other variables constant. Using a system of coupled Cahn-Hillard (CCH) equations, we uncover the mechanisms driving polyhedral particle formation, emphasizing the importance of controlling relaxation parameters for shape variable u and microphase separation v. This unconventional approach, differing from traditional steepest descent method, allows for precise control and diverse polyhedral particle generation. Accelerating the shape variable u proves crucial for expediting precipitation and aligns with experimental observations. Employing the above theoretical model, we achieve shape predictions for particles and the microphase separation within them, which overcomes the limitations of ab initio computations. Additionally, a numerical stability analysis discerns the transient nature versus local minimizer characteristics. Overall, our findings contribute to understanding the complex interplay between process variables and the morphology of polyhedral BCP nanoparticles.

Self-assembly of colloids with competing interactions confined in spheres

At low temperatures, colloidal particles with short-range attractive and long-range repulsive interactions can form various periodic microphases in bulk. In this paper, we investigate the self-assembly behaviour of colloids with competing interactions under spherical confinement by conducting molecular dynamics simulations. We find that the cluster, mixture, cylindrical, perforated lamellar and lamellar structures can be obtained, but the details of the ordered structures are different from those in bulk systems. Interestingly, the system tends to form more perforated structures when confined in smaller spheres. The mechanism behind this phenomenon is driven by the relationship between the energy of the ordered structures and the bending of the confinement wall, which is different from the mechanism in copolymer systems.

Hierarchical colloidosomes self-assembled from block copolymer micelles via emulsion interfacial confinement

Hierarchical self-assembly of polymeric building blocks into high-level colloidosomes is desirable to not only design novel nanostructures but also fabricate the complex artificial materials across many length scales with multifunctionality. Although great progress has been made in the designing the hierarchical colloidosomes, the fabrication of polymeric colloidosomes self-assembled from block copolymer (BCP) colloidal nanoparticles still remains challenge. Here, we report the fabrication of the hierarchical polymeric colloidosomes with typical hollow internal structures self-assembled from the polystyrene-block-poly (2-vinyl pyridine) (PS-b-P2VP) BCP spherical micelles through the emulsion interfacial confinement, which is constructed through the water-in-1-butanol emulsion system. Moreover, the hierarchical colloidosomes can disassemble into the original uniform spherical micelles under the acid aqueous solution, indicating that the colloidosomes possess good pH stimuli-responsibility. Finally, the stability of the colloidosomes can be greatly improved by cross-linking the P2VP corona of original spherical micelles, offering the effective templates for construction of the multifunctional materials. This finding provides a simple yet effective method for the fabrication of the hierarchical colloidosomes from the BCP building blocks.

Ionic Transport and Robust Switching Properties of the Confined Self-Assembled Block Copolymer/Homopolymer in Asymmetric Nanochannels

The self-assembly of block copolymers in a confined space has been proven to be a facile and robust strategy for fabricating assembled structures with various potential applications. Herein, we employed a new pH-responsive polymer self-assembly method to regulate ion transport inside artificial nanochannels. The track-etched asymmetric nanochannels were functionalized with PS_22k-b-P4VP_17k/hPS_4k blend polymers, and the ionic conductance and rectification properties of the proposed system were investigated. The pH-actuated changes in the surface charge and wettability resulted in the selective pH-gated ionic transport behavior. The designed system showed a good switching property to the pH stimulus and could recover during the repetitive experiments. The gating ability of the polymer-nanochannel system increased with increasing the weight of the homopolymer, and the proposed platform demonstrated robust stability and reusability. Numerical and the dissipative particle dynamics simulations were implemented to emulate the pH-dependent self-assembling behavior of diblock copolymers in a confined space, which were consistent with the experimental observations. As an example of the self-assembly of polymers in nanoconfinements, this work provides a facile and robust strategy for the regulation of ion transport in synthetic nanochannels. Meanwhile, this work can be further extended to design artificial smart nanogates for various applications such as mass delivery and energy harvesting.

The influence of confinement on the structure of colloidal systems with competing interactions

Colloidal systems with competing interactions have a complex phase diagram with several periodic microphases, in which particles are arranged in lamellae, cylinders or clusters. Using grand canonical Monte Carlo simulations, we investigate how the structure of the colloidal fluid can be modified by confinement in channels with different cross-section geometries and sizes. We pay particular attention to the hexagonal cylindrical phase since it is the most susceptible to form new structures from. In particular, we considered pores with elliptical, triangular, squared, hexagonal, and wedged-cylindrical cross-sections. Our results show that the structure of the confined fluid depends on the commensurability of the bulk periodic structure with the confining cross-section of the channel. We also find that the structure of the confined fluid can be modified by inserting wedges of appropriate geometry and size. These geometrical modifications of the confining pores can be exploited for the controlled assembly of colloidal structures.

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.

Rich Variety of Three-Dimensional Nanostructures Enabled by Geometrically Constraining Star-like Block Copolymers

The influence of star-like architecture on phase behavior of star-like block copolymer under cylindrical confinement differs largely from the bulk (i.e., nonconfinement). A set of intriguing self-assembled morphologies and the corresponding phase diagrams of star-like (AB)f diblock copolymers with different numbers of arms f (i.e., f = 3, 9, 15, and 21) in four scenarios (ϕA = 0.3 and V0 > 0; ϕA = 0.3 and V0 < 0; ϕA = 0.7 and V0 > 0; and ϕA = 0.7 and V0 < 0 (where ϕA is the volume fraction of A block) and V0 < 0 and V0 > 0 represent that the pore wall of cylindrical confinement prefers the inner A block (i.e., A-preferential) and B block (i.e., B-preferential), respectively) were for the first time scrutinized by employing the pseudospectral method of self-consistent mean-field theory. Surprisingly, a new nanoscopic phase, that is, perforated-lamellae-on-cylinder (denoted PC), was observed in star-like (AB)3 diblock copolymer at ϕA = 0.3 and V0 > 0. With a further increase in f, a single lamellae (denoted L1) was found to possess a larger phase region. Under the confinement of A-preferential wall (i.e., V0 < 0) at ϕA = 0.3, PC phase became metastable and its free energy increased as f increased. Quite intriguingly, when ϕA = 0.7 and V0 > 0, where an inverted cylinder was formed in bulk, the PC phase became stable, and its free energy decreased as f increased, suggesting the propensity to form PC phase under this condition. Moreover, in stark contrast to the phase transition of C1 → L1 → PC (C1, a single cylindrical microdmain) at ϕA = 0.3 and V0 > 0, when subjected to the A-preferential wall (ϕA = 0.7), a different phase transition sequence (i.e., C1 → PC → L1) was identified due to the formation of a double-layer structure. On the basis of our calculations, the influence of star-like architecture on (AB)f diblock copolymer under the imposed cylindrical confinement, particularly the shift of the phase boundaries as a function of f, was thoroughly understood. These self-assembled nanostructures may hold the promise for applications as lithographic templates for nanowires, photonic crystals, and nanotechnology.

Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations

We numerically study a set of coupled Cahn-Hilliard equations as a means to find morphologies of diblock copolymers in three-dimensional spherical confinement. This approach allows us to find a variety of energy minimizers including rings, tennis balls, Janus balls and multipods among several others. Phase diagrams of confined morphologies are presented. We modify the size of the interface between microphases to control the number of holes in multipod morphologies. Comparison to experimental observation by transmission electron microtomography of multipods in polystyrene-polyisoprene diblock copolymers is also presented.

Tuning phase structures of a symmetrical diblock copolymer with a patterned electric field

Electric fields can induce the orientation of the phase interfaces of block copolymers and provide a potential method to tune polymer phase structures for nanomaterial manufacture. In this work, we applied self-consistent field theory to study the self-assembly of a diblock copolymer confined between two parallel neutral substrates on which a set of electrodes was imposed to form a patterned electric field. The results showed that an alternatively distributed electric field can induce the formation of a parallel lamellar phase structure, which exists stably only in the system with selective substrates. The phase structure was proved to be sensitive to the characteristics of the electric field distribution, such as the strength of the electric field, the size and position of the electrodes, and the corresponding phase diagram was calculated in detail. The transition pathway of the phase structure from the perpendicular layered phase to the parallel layered phase was further analysed using the minimum energy path method. It is shown that the path and the active energy barrier of the phase transition depend on the electric field strength. Compound electric field patterns that can be designed to control the formation of novel and complex microphase structures were also examined.

Self-assembly of diblock copolymer confined in an array-structure space

The combination of top-down and bottom-up technologies is an effective method to create the novel nanostructures with long range order in the field of advanced materials manufacture. In this work, we employed a polymeric self-consistent field theory to investigate the pattern formation of diblock copolymer in a 2D confinement system designed by filling pillar arrays with various 2D shapes such as squares, rectangles, and triangles. Our simulation shows that in such confinement system, the microphase structure of diblock copolymer strongly depends on the pitch, shape, size, and rotation of the pillar as well as the surface field of confinement. The array structures can not only induce the formation of new phase patterns but also control the location and orientation of pattern structures. Finally, several methods to tune the commensuration and frustration of array-structure confinement are proposed and examined.

Inverse Design of Topographical Templates for Directed Self-Assembly of Block Copolymers

A computational inverse design algorithm is presented that predicts the necessary topographical template to direct the self-assembly of a diblock copolymer thin film into a desired complex morphology. This topographical template is determined from the spatial configuration of a template that results in an energy minimum for the system. Degenerate solutions are accounted for by performing multiple simulations with random starting configurations of the topographical template and making a statistically weighted template that is tested using self-consistent field theory simulations. The final template is, thus, the inverse design solution of the desired block copolymer morphology. The results also yield nonintuitive post-configuration design principles.

Intraglobular structures in multiblock copolymer chains from a Monte Carlo simulation

Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of 120 A and 120 B monomers, arranged in three distinct microarchitectures: (10-10)12, (6-6)20, and (3-3)40, collapse to globular states upon cooling, as expected. By varying both the reduced temperature T* and the compatibility between monomers ω, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and n clusters with n>3 (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the (T*,ω) space are mapped. The structure factor S(k), for a selected microarchitecture and ω, is calculated. Since S(k) can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.

Self-assembly of diblock copolymers confined in cylindrical nanopores

Self-assembly of AB diblock copolymers confined in cylindrical nanopores is studied using a simulated annealing technique. The pore diameter and surface preference are systematically varied to examine their effects on the self-assembled morphologies and the chain conformations. For bulk lamella-forming and cylinder-forming diblock copolymers, novel structures such as helices and concentric (perforated) lamellae spontaneously form when the copolymers are confined in cylindrical pores. The observed equilibrium morphologies are compared with that obtained from experiments, theory, and other simulations. A simple model is proposed for symmetric diblock copolymers, which gives a reasonable description of the layer thickness for the concentric lamellae. It is found that chains near the pore surfaces are compressed relative to the bulk chains, which can be attributed to the existence of the surfaces. The dependence of the chain conformation on the degree of confinement and strength of the surface preference are reasonably explained. The energetics is discussed qualitatively and used to account for the appearance of the complex phase behavior observed for certain intermediate conditions.