Cylinder-Forming Triblock Terpolymer in Nanopores: A Monte Carlo Simulation Study

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 Lipid Molecules under Shear Flows: A Dissipative Particle Dynamics Simulation Study

The self-assembly of lipid molecules in aqueous solution under shear flows was investigated using the dissipative particle dynamics simulation method. Three cases were considered: zero shear flow, weak shear flow and strong shear flow. Various self-assembled structures, such as double layers, perforated double layers, hierarchical discs, micelles, and vesicles, were observed. The self-assembly behavior was investigated in equilibrium by constructing phase diagrams based on chain lengths. Results showed the remarkable influence of chain length, shear flow and solution concentration on the self-assembly process. Furthermore, the self-assembly behavior of lipid molecules was analyzed using the system energy, particle number and shape factor during the dynamic processes, where the self-assembly pathways were observed and analyzed for the typical structures. The results enhance our understanding of biomacromolecule self-assembly in a solution and hold the potential for applications in biomedicine.

Surface-Induced Nanostructures and Phase Diagrams of ABC Linear Triblock Copolymers under Spherical Confinement: A Self-Consistent Field Theory Simulation

We investigate the nanostructures and phase diagrams of ABC linear triblock copolymers confined in spherical cavities by using real-space self-consistent field theory. Various 3D morphologies, such as spherical concentric lamellae, dumbbell-like cylinder, and rotational structures, are identified in the phase diagrams, which are constructed on the basis of the diameters of spherical cavities and the interaction between the polymers and preferential surfaces. We designate specific monomer-monomer interactions and block compositions, with which the polymers spontaneously form a cylindrical morphology in bulk, and firstly study morphology transformation with a neutral surface when a confining radius progressively increases. We then focus on phase morphologies under the preferential surfaces and consolidate them into phase diagrams. The spherical radius and the degree of preferential interactions can obviously induce the formation of a cylindrical morphology. Theoretical results correspond to an amount of recent experimental observations to a high degree and contribute to synthesising functional materials.

Monte Carlo Study of Degenerate Behavior of AB Diblock Copolymer/Nanoparticle under Cylindrical Confinement

Degenerate behavior (i.e., forming different self-assembled structures for a given block copolymer (BCP) under the same confinement) commonly exists in various confined systems. Understanding degenerate behavior is crucial for precise control over the structures formed by self-assembly systems under confinement. In this study, the degenerate behavior of a self-assembled AB diblock copolymer/nanoparticle (NP) mixture in a cylindrical pore is studied using Monte Carlo simulation. We find that the degenerate behavior of such a mixture depends on the introduction of the NP. Under different pore sizes, four typical degenerate structures [i.e., single helices (S-helices), double helices (D-helices), parallel cylinders, and stacked toroids] can be obtained if the NP content is zero. However, when the NP content in the mixture is increased, it is found that the number of degenerate structures decreases, that is, only blocky structures can be obtained in the case of high NP content. Moreover, the probability of forming S-helices decreases, whereas the probability of forming D-helices increases with increase in the NP content. Analysis of the interactive enthalpy densities and the chain conformation of the systems indicates that entropy plays an important role in the degenerate structure formation. This study provides some new insights into the degenerate behavior of a BCP/NP mixture under confinement, which can offer a theoretical reference for further experiments.

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.

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.

Monte Carlo simulations of the phase separation of a copolymer blend in a thin film

Monte Carlo simulations were carried out to study the phase separation of a copolymer blend comprising an alternating copolymer and/or block copolymer in a thin film, and a phase diagram was constructed with a series of composed recipes. The effects of composition and segregation strength on phase separation were discussed in detail. The chain conformation of the block copolymer and alternating copolymer were investigated with changes of the segregation strength. Our simulations revealed that the segment distribution along the copolymer chain and the segregation strength between coarse-grained beads are two important parameters controlling phase separation and chain conformation in thin films of a copolymer blend. A well-controlled phase separation in the copolymer blend can be used to fabricate novel nanostructures.

Segmented helical structures formed by ABC star copolymers in nanopores

Self-assembly of ABC star triblock copolymers confined in cylindrical nanopores is studied using self-consistent mean-field theory. With an ABC terpolymer forming hexagonally-arranged cylinders, segmented into alternative B and C domains, in the bulk, we observe the formation in the nanopore of a segmented single circular and non-circular cylinder, a segmented single-helix, and a segmented double-helix as stable phases, and a metastable stacked-disk phase with fourfold symmetry. The phase sequence from single-cylinder, to single-helix, and then to double-helix, is similar as that in the cylindrically-confined diblock copolymers except for the absence of an equilibrium stacked-disk phase. It is revealed that the arrangement of the three-arm junctions plays a critical role for the structure formation. One of the most interesting features in the helical structures is that there are two periods: the period of the B/C domains in the helix and the helical period. We demonstrate that the period numbers of the B/C domains contained in each helical period can be tuned by varying the pore diameter. In addition, it is predicted that the period number of B/C domains can be any rational in real helical structures whose helical period can be tuned freely.