Self-assembly of diblock copolymers confined in cylindrical nanopores

The mechanism underlying the transitions between stripes, helices, and stacked toroids in the cylindrical shell formed by AB diblock copolymers on a long nanocylinder

The self-assembly of block copolymers on nanocylinders has attracted a lot of interest due to its potential application in biomedicine and other fields. In this study, the self-assembly phase behavior of AB diblock copolymers on long nanocylinders in soft confinement has been studied by using a simulated annealing method. A square phase diagram of the morphology was constructed by increasing the number of chains of copolymers (cn) and the cylindrical diameter (D). As a result, morphological transitions from striped to helical and axially stacked toroids, as well as reversible transitions, started to appear. By analyzing the chain packing in a fan-shaped region and calculating the mean-square end-to-end distance (DEE2) of the copolymers and number of AB contacts, both types of transitions were found to be driven by the competition between conformational entropy and AB interfacial energy. The number of stripes increased and the helical angle decreased with the increase in cylinder diameter. The chirality of the helix was found to be random.

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.

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 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.

Surface-induced phase transitions in thin films of dendrimer block copolymers

The phase morphologies and phase transitions of dendrimer block copolymer thin films confined between two homogeneous, planar hard substrates had been investigated by a three-dimensional real space self-consistent field theory (SCFT). From the perspectives of property and strength of the preferential substrate, when the film system confined within neutral substrates, the thinner film was easier to take the undulated and perpendicular cylinder phases. For the attractive preference of the substrate on block segment A, the polymer films tended to take the surface-wetting structures that was composed by block segment A. On the contrary, for the repulsive preference of the substrate on block segment A, a phase transition of cylinder-lamellae could be observed increasing with the relative surface strength of the preferential substrate.

Nanoporous thin films in optical waveguide spectroscopy for chemical analytics

Spectroscopy with planar optical waveguides is still an active field of research for the quantitative analysis of various supramolecular surface architectures and processes, and for applications in integrated optical chip communication, direct chemical sensing, etc. In this contribution, we summarize some recent development in optical waveguide spectroscopy using nanoporous thin films as the planar substrates that can guide the light just as well as bulk thin films. This is because the nanoporosity is at a spacial length-scale that is far below the wavelength of the guided light; hence, it does not lead to an enhanced scattering or additional losses of the optical guided modes. The pores have mainly two effects: they generate an enormous inner surface (up to a factor of 100 higher than the mere geometric dimensions of the planar substrate) and they allow for the exchange of material and charges between the two sides of the solid thin film. We demonstrate this for several different scenarios including anodized aluminum oxide layers for the ultrasensitive determination of the refractive index of fluids, or the label-free detection of small analytes binding from the pore inner volume to receptors immobilized on the pore surface. Using a thin film of Ti metal for the anodization results in a nanotube array offering an even further enhanced inner surface and the possibility to apply electrical potentials via the resulting TiO₂ semiconducting waveguide structure. Nanoporous substrates fabricated from SiN_x thin films by colloid lithography, or made from SiO₂ by e-beam lithography, will be presented as examples where the porosity is used to allow for the passage of ions in the case of tethered lipid bilayer membranes fused on top of the light-guiding layer, or the transport of protons through membranes used in fuel cell applications. The final example that we present concerns the replication of the nanopore structure by polymers in a process that leads to a nanorod array that is equally well suited to guide the light as the mold; however, it opens a totally new field for integrated optics formats for direct chemical and biomedical sensing with an extension to even molecularly imprinted structures. Graphical abstract.

Phase behavior of disk-coil block copolymers under cylindrical confinement: Curvature-induced structural frustrations

In this paper, we explore the self-assembly behavior of disk-coil block copolymers (BCPs) confined within a cylinder using molecular dynamics simulations. As functions of the diameter of the confining cylinder and the number of coil beads, concentric lamellar structures are obtained with a different number of alternating disk-rich and coil-rich bilayers. Our paper focuses on the curvature-induced structural behavior in the disk-rich domain of a self-assembled structure, which is investigated by calculating the local density distribution P(r) and the orientational distribution G(r,θ). In the inner layers of cylinder-confined disk-coil BCPs, both P(r) and G(r,θ) show characteristic asymmetry within a bilayer which is directly contrasted with the bulk and slab-confined disk-coil BCPs. We successfully explain the structural frustration of disks arising from the curved structure due to packing frustration of disks and asymmetric stretching of coils to the regions with different curvatures in a bilayer. Our results are important to understand the self-assembly behavior of BCPs containing a rigid motif in a confined structure, such as a self-assembled structure of bacteriochlorophyll molecules confined by a lipid layer to form a chlorosome, the photosynthetic antennae complex found in nature.

Microwave-annealing-induced nanowetting of block copolymers in cylindrical nanopores

Block copolymers have attracted great attention because of their abilities to self-assemble into well-ordered microphase-separated structures. To generate nanopatterns of block copolymers with long-range ordering and low-defect densities in shorter time scales, microwave annealing has recently been applied. Microwave annealing, however, has so far only been used for block copolymer bulks and thin films. In this work, we discover that microwave annealing can be successfully applied to three-dimensional block copolymer nanostructures by studying the infiltration and microphase separation of block copolymers in cylindrical nanopores upon microwave irradiation. Cylinder-forming and lamella-forming poly(styrene-block-dimethylsiloxane) (PS-b-PDMS) are introduced into the nanopores of anodic aluminum oxide (AAO) templates. In addition, AAO templates with different pore sizes are used to study the effect of the commensurabilities between the pore diameters and the repeating periods of the block copolymers on the morphologies of the block copolymer nanostructures.

Self-assembled morphologies of an amphiphilic Y-shaped weak polyelectrolyte in a thin film

Different from the self-assembly of neutral polymers, polyelectrolytes self-assemble into smaller aggregates with a more loosely assembled structure, which results from the repulsive forces acting between similar electrical compositions with the introduction of ions. The Y-shaped weak polyelectrolytes self-assemble into a core-shell type cylindrical structure with a hexagonal arrangement in a thin film, whose thickness is smaller than the gyration radius of the polymer chain. The corresponding formation mechanism consists of enrichment of the same components, adjustment of the shape of the aggregate, and the subsequent separation into individual aggregates. With the increase in the thickness of the thin film until it exceeds the gyration radius of the polymer chain, combined with the greater freedom of movement along the direction of thin film thickness, the self-assembled structure changes into a micellar structure. Under confinement, the repulsive force to the polymeric components is weakened by the repulsive forces among polyelectrolyte components with like charges, and this helps in generating aggregates with more uniform size and density distribution. In particular, when the repulsive force between the walls and the core forming components is greater than that between the walls and the shell forming components, such asymmetric confinement produces a crossed-cylindrical structure with nearly perpendicular arrangement of two cylinder arrays. Similarly, a novel three-crossed cylinder morphology is self-assembled upon removal of confinement.

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.

One-dimensional Confinement Effect on the Self-assembly of Symmetric H-shaped Copolymers in a Thin Film

The self-assembly of a reformed symmetric H-shaped copolymer with four hydrophilic branches and one hydrophobic stem was systematically investigated. The existence of vacancies is vital to regulate the sizes of self-assembled cylinders to be able to form a hexagonal arrangement. With the introduction of horizontal-orientated confinement, a micellar structure is formed through a coalescence mechanism. The short acting distance and large influencing area of the confinement produces numerous small-sized micelles. Additionally, the cycled “contraction-expansion” change helps achieve hexagonal arrangement. In contrast, the introduction of lateral-oriented confinement with long acting distance and small influencing area cannot change the cylindrical structure. Under the fission mechanism, in which the larger cylinder splits into smaller ones, it is quite efficient to generate hierarchical-sized cylinders from larger-sized cylinders in the middle region and smaller-sized cylinders near both walls. The results indicate the possibility of regulating the characteristics of a nanomaterial by tuning the molecular structure of the copolymer and the parameters of the introduced confinement, which are closely related to the self-assembly structure.

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.

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.

Probing the Effect of Molecular Nonuniformity in Directed Self-Assembly of Diblock Copolymers in Nanoconfined Space

Various complex self-assembled morphologies of lamellar- and cylinder-forming block copolymers comprising poly(dimethylsiloxane)-b-polylactide (PDMS-b-PLA) confined in cylindrical channels were generated. Combining top-down lithography with bottom-up block copolymer self-assembly grants access to morphologies that are otherwise inaccessible with the bulk materials. Channel diameter (D) was systematically varied with four diblock copolymers having different compositions and bulk domain spacing (L0), corresponding to a range of frustration ratios (D/L0 from 2 to 4). Excessive packing frustration imposed by the channels leads to contorted domains. The resulting morphologies depend strongly on both D/L0 and copolymer composition. Under several circumstances, mixtures of complex morphologies were observed, which hypothetically arise from the severe sensitivity to D/L0 combined with the inherent compositional/molar mass dispersities associated with the nonuniform synthetic materials and silicon templates. Stochastic calculations offer compelling support for the hypothesis, and tractable pathways toward solving this apparent conundrum are proposed. The materials hold great promise for next-generation nanofabrication to address several emerging technologies, offering significantly enhanced versatility to basic diblock copolymers as templates for fabricating complex nanoscale objects.

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.

Patchy nanoparticles self-assembled from linear triblock copolymers under spherical confinement: a simulated annealing study

The self-assembly of linear ABC triblock copolymers confined in spherical nanopores is studied using a simulated annealing technique. Morphological phase diagrams as a function of the pore diameter, the selectivity of the pore-wall to the terminal blocks, and the copolymer composition are constructed. A variety of patchy nanoparticles and multiple morphological transitions are identified. Janus nanoparticles, which can be regarded as particles with one patch, are observed inside small nanopores. With increasing the pore diameter, the number of patches on a nanoparticle surface increases from one to two, four, five, six, and seven. The size of each patch increases periodically. The number of patches also increases with increasing the wall selectivity. The distribution of the patches on the surface of a given particle is highly symmetric. The interior structures of the patchy nanoparticles and the morphological transition are investigated by calculating the bridging fraction, the mean square end-to-end distance and the average contact number between different components. A series of entropy-driven morphological transitions is predicted. Furthermore, it is found that the overall patchy morphology is largely controlled by the volume fraction of the middle B-block, while the internal structure is largely controlled by the volume fraction ratio of the two terminal blocks. Our study demonstrates that the size of nanopores, the pore-wall selectivity, and the copolymer composition could be utilized as effective means to tune the structure and properties of the anisotropic nanoparticles.

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.

Phase behavior of binary blends of diblock copolymer/homopolymer confined in spherical nanopores

Binary blends of a diblock copolymer (AB) and an incompatible homopolymer (C) confined in spherical cavities are studied using a simulated annealing technique. The phase behavior of the blends is examined for four typical cases, representing the different selectivity of the pore surface to the A, B, and C species. The internal morphology of the spherical polymeric particles is controlled by the homopolymer volume fraction, the degree of confinement, and the composition of the copolymer. Inside a particle, the homopolymers segregate to form one or, under some conditions, two domains; thus, the homopolymers may act as an additional controlling parameter of the shape and symmetry of the copolymer domain. A rich array of confinement-induced novel diblock copolymer morphologies is predicted. In particular, core-shell particles with the copolymers as the shell wrapping around a homopolymer core or a copolymer-homopolymer combined core and Janus-like particles with the copolymers and the homopolymers on different sides are obtained.

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.

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.