Mesophase Separation of Diblock Copolymer Confined in a Cylindrical Tube Studied by Dissipative Particle Dynamics

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.

The Effect of Colloidal Nanoparticles on Phase Separation of Block and Heteroarm Star Copolymers Confined between Polymer Brushes

The effect of colloidal nanoparticles on the phase changes of the amphiphilic AB linear diblock, A1A2B, and A2B heteroarm star copolymers confined between two polymer brush substrates was investigated by using a real-space self-consistent field theory. By changing the concentrations of nanoparticles and polymer brushes, the phase structure of the amphiphilic AB copolymer transforms from lamellar to core-shell hexagonal phase to cylinder phase. The pattern of A2B heteroarm star copolymer changes from core-shell hexagonal phases to lamellar phases and the layer decreases when increasing the density of the polymer brushes. The results showed that the phase behavior of the system is strongly influenced by the polymer brush architecture and the colloidal nanoparticle numbers. The colloidal nanoparticles and the soft confined surface of polymer brushes make amphiphilic AB copolymers easier to form ordered structures. The dispersion of the nanoparticles was also investigated in detail. The soft surfaces of polymer brushes and the conformation of the block copolymers work together to force the nanoparticles to disperse evenly. It will give helpful guidance for making some new functional materials by nano etching technology, nano photoresist, and nanoprinting.

A decade of innovation and progress in understanding the morphology and structure of heterogeneous polymers in rigid confinement

When confined in nanoscale domains, polymers generally encounter changes in their structural, thermodynamics and dynamics properties compared to those in the bulk, due to the high amount of polymer/wall interfaces and limited amount of matter. The present review specifically deals with the confinement of heterogeneous polymers (i.e. polymer blends and block copolymers) in rigid nanoscale domains (i.e. bearing non-deformable solid walls) where the processes of phase separation and self-assembly can be deeply affected. This review focuses on the innovative contributions of the last decade (2010-2020), giving a summary of the new insights and understanding gained in this period. We conclude this review by giving our view on the most thriving directions for this topic.

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.

Semicrystalline Block Copolymers in Rigid Confining Nanopores

We have investigated PLLA crystallization in lamellae-forming PS-b-PLLA confined to straight cylindrical nanopores under weak confinement (nanopore diameter D/equilibrium PS-b-PLLA period L0 ≥ 4.8). Molten PS-b-PLLA predominantly forms concentric lamellae along the nanopores, but intertwined helices occur even for D/L0 ≈ 7.3. Quenching PS-b-PLLA melts below TG(PS) results in PLLA cold crystallization strictly confined by the vitrified PS domains. Above TG(PS), PLLA crystallization is templated by the PS-b-PLLA melt domain structure in the nanopore centers, while adsorption on the nanopore walls stabilizes the outermost cylindrical PS-b-PLLA shell. In between, the nanoscopic PS-b-PLLA melt domain structure apparently ripens to reduce frustrations transmitted from the outermost immobilized PS-b-PLLA layer. The onset of PLLA crystallization catalyzes the ripening while transient ripening states are arrested by advancing PLLA crystallization. Certain helical structure motifs persist PLLA crystallization even if PS is soft. The direction of fastest PLLA crystal growth is preferentially aligned with the nanopore axes to the same degree as for PLLA homopolymer, independent of whether PS is vitreous or soft.

Order-order transitions of diblock copolymer melts under cylindrical confinement

The self-assembly behavior of AB diblock copolymers under cylindrical confinement is investigated using the self-consistent field theory. We focus on the impact of the confinement on the order-order transitions of three-dimensional morphologies by constructing two types of phase diagrams with continuously varying block compositions. One type is with respect to the block composition and the immiscibility parameter for various pore sizes, in which the order-order transitions are shown to be strongly impacted by the pore curvature and thus largely different from the bulk ones. Note that the morphologies are categorized by the intrinsical geometry of their domains, i.e., that helical morphologies are regarded as one type of cylindrical phase. Another type of phase diagram is with respect to the block composition and the pore diameter, which exhibits a number of interesting order-order transitions, especially the transition sequence from a straight line of spheres, to one straight cylinder and stacked disks as the pore diameter increases. A critical point is observed at which the stability region of the straight cylinder vanishes and thereby the spheres transform into the stacked disks continuously. The mechanism of these phase transitions is rationalized in the context of the bulk factors as well as an additional factor, i.e., the competition between the spontaneous curvature of the copolymer and the imposed curvature by the nanopore.

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.

Simulation study on the assembly of rod-coil diblock copolymers within coil-selective nanoslits

Dissipative particle dynamics simulations are performed to study the self-assembly of rod-coil (RC) diblock copolymers confined in a slit with two coil-selective surfaces. The effect of rod length and slit thickness on the assembly structure is investigated. A morphological phase diagram as a function of slit thickness and rod length is presented. We observe several ordered structures, such as perpendicular cylinders, parallel cylinders, and puck-shaped structure. In the assembly structures, long-range rod-rod orientational order is observed when the rod length exceeds a critical rod length. Our results show that the coil-selective slit influences the assembly structure as well as the rod orientation of RC diblock copolymers.

Self-assembly of symmetric rod-coil diblock copolymers in cylindrical nanopore

Self-assembly of rod-coil (RC) symmetric diblock copolymers (DBCs) in a cylindrical nanopore is investigated by performing dissipative particle dynamics simulation.

Structure and Dynamics of Asymmetric Poly(styrene-b-1,4-isoprene) Diblock Copolymer under 1D and 2D Nanoconfinement

The impact of 1- and 2-dimensional (2D) confinement on the structure and dynamics of poly(styrene-b-1,4-isoprene) P(S-b-I) diblock copolymer is investigated by a combination of Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM), Grazing-Incidence Small-Angle X-ray Scattering (GISAXS), and Broadband Dielectric Spectroscopy (BDS). 1D confinement is achieved by spin coating the P(S-b-I) to form nanometric thin films on silicon substrates, while in the 2D confinement, the copolymer is infiltrated into cylindrical anodized aluminum oxide (AAO) nanopores. After dissolving the AAO matrix having mean pore diameter of 150 nm, the SEM images of the exposed P(S-b-I) show straight nanorods. For the thin films, GISAXS and AFM reveal hexagonally packed cylinders of PS in a PI matrix. Three dielectrically active relaxation modes assigned to the two segmental modes of the styrene and isoprene blocks and the normal mode of the latter are studied selectively by BDS. The dynamic glass transition, related to the segmental modes of the styrene and isoprene blocks, is independent of the dimensionality and the finite sizes (down to 18 nm) of confinement, but the normal mode is influenced by both factors with 2D geometrical constraints exerting greater impact. This reflects the considerable difference in the length scales on which the two kinds of fluctuations take place.

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.

Controllable hierarchical microstructures self-assembled from multiblock copolymers confined in thin films

Hierarchical microstructures self-assembled from A(BC)n multiblock copolymers confined between two solid surfaces were explored by dissipative particle dynamics simulations. The strategy using confinement allows us to generate hierarchical microstructures with various numbers and different orientations of small-length-scale lamellae. Except for the hierarchical lamellar microstructures with parallel or perpendicular arrangements of small-length-scale lamellae, the coexistence of two different hierarchical lamellae was also discovered by varying the film thickness. The dynamics of hierarchical microstructure formation was further examined. It was found that the formation of the hierarchical microstructures exhibits a stepwise manner where the formation of small-length-scale structures lags behind that of large-length-scale structures. The present work could provide guidance for controllable manufacture of hierarchical microstructures.

Three-dimensional nanofabrication by block copolymer self-assembly

Thin films of block copolymers are widely seen as enablers for nanoscale fabrication of semiconductor devices, membranes, and other structures, taking advantage of microphase separation to produce well-organized nanostructures with periods of a few nm and above. However, the inherently three-dimensional structure of block copolymer microdomains could enable them to make 3D devices and structures directly, which could lead to efficient fabrication of complex heterogeneous structures. This article reviews recent progress in developing 3D nanofabrication processes based on block copolymers.

Simulation-aided design and synthesis of hierarchically porous membranes

Free-standing silica membranes with hierarchical porosity (ca. 300 nm macropores surrounded by 6-8 nm mesopores) and controllable mesopore architecture were prepared by a dual-templating method, with the structural design aided by mesoscale simulation. To create a two-dimensional, hexagonal macropore array, polymeric colloidal hemisphere arrays were synthesized by a two-step annealing process starting with non-close-packed polystyrene sphere arrays on silicon coated with a sacrificial alumina layer. A silica precursor containing a poly(ethylene) oxide-poly(propylene oxide)-poly(ethylene) oxide (PEO-PPO-PEO) triblock-copolymer surfactant as template for mesopore creation was spin-coated onto the support and aged and then converted into the free-standing membranes by dissolving both templates and the alumina layer. To test the hypothesis that the mesopore architecture may be influenced by confinement of the surfactant-containing precursor solution in the colloidal array and by its interactions with the polymeric colloids, the system was studied theoretically by dissipative particle dynamics (DPD) simulations and experimentally by examining the pore structures of silica membranes via electron microscopy. The DPD simulations demonstrated that, while only tilted columnar structure can be formed through tuning the interaction with the substrate, perfect alignment of 2D hexagonal micelles perpendicular to the plane of the membrane is achievable by confinement between parallel walls that interact preferentially with the hydrophilic components (PEO blocks, silicate, and solvent). The simulations predicted that this alignment could be maintained across a span of up to 10 columns of micelles, the same length scale defined by the colloidal array. In the actual membranes, we manipulated the mesopore alignment by tuning the solvent polarity relative to the polar surface characteristics of the colloidal hemispheres. With methanol as a solvent, columnar mesopores parallel to the substrate were observed; with a methanol-water mixed solvent, individual spherical mesopores were present; and with water as the only solvent, twisted columnar structures were seen.

Soft confinement-induced morphologies of diblock copolymers

The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.

Aggregation of nanoparticles in a block copolymer bilayer

In this paper, we examine, by dissipative particle dynamics (DPD) simulation, the interactions between nanoparticles and block copolymer bilayer membranes. The bilayer has a hydrophobic core and hydrophilic head groups on both sides of the core. Nanoparticles without or with a grafted homopolymer are considered. For the conditions investigated, the single nanoparticles and small aggregates are located at the interfaces of the membrane, namely the interfaces between the hydrophilic domains of the membrane and the solvent as well as at the interface between the hydrophobic and hydrophilic domains of the membrane. The large aggregates are located in the hydrophilic domains. By increasing the length of the homopolymer grafted on the nanoparticles, the size of the aggregates in the membrane decreases. At relatively short DPD step times, the particles aggregate in the solvent. As the time increases, the single particles and aggregates penetrate into the membrane.

Surfactant two-dimensional self-assembly under confinement

Confinement-induced structural rearrangements in supported self-assembled surfactant layers in aqueous salt solutions are investigated using classical density functional theory. The systematic study of the influence of the nature of electrolyte revealed that 2:1 electrolyte stabilizes the hemicylindrical configuration of ionic surfactant layers, while a confinement-induced transition to a tilted monolayer configuration was found in symmetric 1:1 and 2:2 electrolytes. On the basis of this study, we formulate a general model for the energetics of structural rearrangements in supported surfactant layers. This model provides a basis for directed self-assembly of surfactant templates with desired structure and stability for scalable synthesis of nanocomposite functional materials, templated crystal growth, and biomolecule adsorption.

Block copolymer nanocontainers

Using cell dynamics computer simulation, we perform a systematic study of thin block copolymer films around a nanoparticle. Lamellar-, cylinder-, and sphere-forming block copolymers are investigated with respect to different film thicknesses, particle radii, and boundary conditions at the film interfaces. The obtained structures include standing lamellae and cylinders, "onions", cylinder "knitting balls", "golf ball", layered spherical, "virus"-like and mixed morphologies with T-junctions and U-type defects. The kinetics of the structure formation and difference with planar thin films are discussed. Our simulations suggest that novel porous nanocontainers can be formed by the coating of a sacrificial nanobead by a block copolymer layer with a well-controlled nanostructure. In addition, first scanning force microscopy experiments on a model system reveal surface structures similar to those predicted by our simulations.

Nanoparticle aggregation in the presence of a block copolymer

By employing dissipative particle dynamics simulations, we investigated the cooperative phase behavior of composites containing diblock copolymer molecules and nanoparticles. The nanoparticles and their aggregates are located either in the domains generated by each of the two kinds of segments of the block copolymer and/or at their interface. Various conditions, such as the interactions between nanoparticles, the interactions between them and the segments of the block copolymer, the interactions between the segments of the block copolymer, and the volume ratio of nanoparticles to block copolymer, have been changed to gather information about nanoparticle aggregation and block copolymer/nanoparticles morphology building. The dynamics of nanoparticles aggregation and the evolution of the morphology of the block copolymer have been followed. Our findings have identified two critical repulsive interactions regarding nanoparticle aggregation, one between nanoparticles and the other between the segments of the block copolymer and nanoparticles. Aggregates have been generated for repulsive interactions larger than the former critical value or smaller than the latter one.