Block Copolymers under Cylindrical Confinement

Shell with Striped, Helical, and Bipolar Lamellae Structures from Soft Confinement-Induced Self-Assembly of AB Diblock Copolymers on a Nanocylinder

The soft confinement-induced self-assembly of AB diblock copolymers on a nanocylinder is studied via a simulated annealing method. The formation of multiple copolymer shells was predicted by varying the interfacial interaction, the size of confinement, and the height and diameter of the nanocylinder. The competition between solvent repulsion and nanocylinder attraction determined the degree of encapsulation of the copolymer shell. The formation of a helical copolymer shell was induced by the maximization of conformational entropy. The preferential distribution position of copolymers on anisotropic nanocylinder surfaces was induced by interfacial energy minimization. Our study contributes to the understanding of the formation mechanism of the helical structure in block copolymer aggregates and the fabrication of copolymer shells with predesigned morphologies.

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.

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.

Revealing the 3D Structure of Block Copolymers with Electron Microscopy: Current Status and Future Directions

Block copolymers (BCPs) are considered model systems for understanding and utilizing self-assembly in soft matter. Their tunable nanometric structure and composition enable comprehensive studies of self-assembly processes as well as make them relevant materials in diverse applications. A key step in developing and controlling BCP nanostructures is a full understanding of their three-dimensional (3D) structure and how this structure is affected by the BCP chemistry, confinement, boundary conditions, and the self-assembly evolution and dynamics. Electron microscopy (EM) is a leading method in BCP 3D characterization owing to its high resolution in imaging nanosized structures. Here we discuss the two main 3D EM methods: namely, transmission EM tomography and slice and view scanning EM tomography. We present each method's principles, examine their strengths and weaknesses, and discuss ways researchers have devised to overcome some of the challenges in BCP 3D characterization with EM- from specimen preparation to imaging radiation-sensitive materials. Importantly, we review current and new cutting-edge EM methods such as direct electron detectors, energy dispersive X-ray spectroscopy of soft matter, high temporal rate imaging, and single-particle analysis that have great potential for expanding the BCP understanding through EM in the future.

Confined Self-Assemblies of Chiral Block Copolymers in Thin Films

Self-assembly of chiral block copolymers (BCPs*) can give rise to ordered chiral nanostructures, that is, a helical phase (H* phase), via chirality transfer from the molecular level to mesoscale. In the present work, we reported the self-assembly of BCPs* under one-dimensional spatial confinement. The morphological dependence of self-assembled BCPs* on the molecular weights and the film thickness was investigated. As chiral nanostructures, the H* phase can be formed in bulk, nonchiral nanostructures that were observed in the thin films. Also, the topology effect of self-assembly of BCPs* was examined. The self-assembly of BCPs* with a star-shaped topology exhibited a distinct morphology compared with that of linear BCPs*. The present work provides new insight into the chirality transfer of macromolecules under spatial confinement.

Orbital Angular Momentum from Self-Assembled Concentric Nanoparticle Rings

Ring-shaped nanostructures can focus, filter, and manipulate electromagnetic waves, but are challenging to incorporate into devices using standard nanofabrication techniques. Directed self-assembly (DSA) of block copolymers (BCPs) on lithographically patterned templates has successfully been used to fabricate concentric rings and spirals as etching masks. However, this method is limited by BCP phase behavior and material selection. Here, a straightforward approach to generate ring-shaped nanoparticle assemblies in thin films of supramolecular nanocomposites is demonstrated. DSA is used to guide the formation of concentric rings with radii spanning 150-1150 nm and ring widths spanning 30-60 nm. When plasmonic nanoparticles are used, ring nanodevice arrays can be fabricated in one step, and the completed devices produce high-quality orbital angular momentum (OAM). Nanocomposite DSA simplifies and streamlines nanofabrication by producing metal structures without etching or deposition steps; it also introduces interparticle coupling as a new design axis. Detailed analysis of the nanoparticle ring assemblies confirms that the supramolecular system self-regulates the spatial distribution of its components, and thus exhibits a degree of flexibility absent in DSA of BCPs alone, where structures are determined by polymer-pattern incommensurability. The present studies also provide guidelines for developing self-regulating DSA as an alternative to incommensurability-driven methods.

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.

Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta-Kawasaki model. The projection saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward and upward search algorithms. A variety of stationary solutions are identified and classified in the solution landscape, including Flower class, Mosaic class, Core-shell class, and Tai-chi class. The relationships between different stable states are shown by either transition pathways connected by index-1 saddle points or dynamical pathways connected by a high-index saddle point. The solution landscapes also demonstrate the symmetry-breaking phenomena, in which more solutions with high symmetry are found when the domain size increases.

Regular ordering of spherical microdomains in dewetted monolayer islands induced by thermal annealing of spin-coated ultrathin films of a triblock copolymer

We report here spontaneous dewetting of a spin-coated, ultra-thin film of a sphere-forming block copolymer (BCP) upon thermal annealing, and that the dewetting resulted in the formation of plateau-shaped islands with a constant thickness consistent with the thickness of a monolayer, in which the spherical microdomains are regularly ordered two-dimensionally in a deformed hexagonal lattice. Thus, the spontaneous dewetting was ascribed to a mismatch between the initial spin-coated film thickness with respect to the monolayer thickness. Such dewetting of sphere-forming BCPs is considered to be deterministic compared to the cases of lamella- and cylinder-forming BCPs, as incommensuration in thickness is avoided by attaining perpendicular orientation without dewetting. We further quantitatively examined the ordering regularity of spherical microdomains in the dewetted monolayer islands to clarify the effect of confinement on sphere ordering. The degree of deformation of the hexagonal lattice was found to have an increasing tendency as a function of the degree of the deformation of the dewetted islands (the island shape), irrespective of the size of the island. Namely, islands with almost round shapes exhibit a well-ordered arrangement of the spherical microdomains in a perfect hexagonal lattice. Another notable finding is that the regular ordering of the spherical microdomains was found to be spoiled in the vicinity of the edge of the island. In other words, the spherical microdomains were well-ordered in a hexagonal lattice far from the edge of the island, while they were not regularly ordered in the vicinity of the edge, which may be due to mismatch between the curvature of the island's perimeter and the polygonal shape of ordered sphere grains.

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.

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.

Hierarchical self-assembly of a PS-b-P4VP/PS-b-PNIPAM mixture into multicompartment micelles and their response to two-dimensional confinement

Finely tuned synergistic effects among different blocks could realize intriguing hierarchical self-assembly of block copolymers and such hierarchical self-assembly could be manipulated by cylindrical confinement to tune the structures of assemblies.

Influence of Branches on the Phase Behavior of (AB)f Starlike Block Copolymer under Cylindrical Confinement

Experimentally, self-assembled morphologies of the (AB)_f starlike block copolymer are strongly dependent on the number of arms, f. For example, the 2- and 4-arm starlike block copolymers exhibited the morphologies of hexagonally arrayed polystyrene cylinder in the polyisoprene matrix while order-bicontinuous nanostructures were observed in 8-, 12-, and 18-arm stars. Theoretically, we found that the transition sequence for (AB)₃ is C₁^B → Dk^B → P₂^B → L₂^B, which becomes C₁^B → L₁^B when f > 6. To explore the influence of f on the phase behavior of (AB)_f under cylindrical confinement, we calculated the two-dimensional phase diagram with respect to the volume fraction and the pore diameter. Our conclusions show that the topologies of the phase diagram are independent of the number of arms; however, the number of arms does affect the phase boundary, which inevitably leads to the different phase transition sequences at fixed volume fraction. Therefore, from the calculated phase diagram, the influence of f on the phase behavior of the starlike copolymer is fully understood.

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.

Oriented crystallization of PEG induced by confinement in cylindrical nanopores: structural and thermal properties

Nanoporous ion track-etched polycarbonate is ideally suited for the study of confined polymers via small angle X-ray scattering (SAXS) due to the strictly parallel orientation of the pores as well as their uncorrelated lateral distribution. Nanopores with radii ranging from 17 to 213 nm are prepared and coated with SiO2via atomic layer deposition in order to obtain a well-defined and homogeneous surface. A low molecular weight polyethylene glycol (PEG) homopolymer with a semicrystalline lamellar bulk structure is introduced into the nanopores via melt infiltration. At high temperatures SAXS measurements confirm a uniform filling of the pores with amorphous polymer. Upon cooling below the melting point of PEG, a concentrical structure of semicrystalline lamellae is revealed for large pore radii. We introduce models which successfully describe the combined scattering from nanopores and semicrystalline or amorphous PEG inside. DSC measurements of the confined polymer show a decrease of melting temperature and heat of fusion per gram polymer upon reduction of the pore radius and hint at a change in the lamellar configuration.

Critical Contact Angle to Induce Capillary Rise of Polymers in Nanopores Does Not Depend on Chain Length

We study the effect of physical confinement on the capillary infiltration of polymers into cylindrical nanopores using molecular dynamics simulations. In particular, we probe whether the critical contact angle (θ_c) above which capillary rise infiltration ceases to occur changes for long-chain polymers, possibly due to loss of conformation entropy induced by chain confinement. Surprisingly, θ_c does not strongly depend on the length of polymer chains and stays constant for large N. A free energy model is developed to show that θ_c depends strongly on the size of statistical segments rather than N, which we confirm by performing MD simulations of infiltration with semiflexible polymers. These results could provide guidelines in manufacturing polymer nanostructures and nanocomposites using capillary rise infiltration.

Directed Self-Assembly of Star-Block Copolymers by Topographic Nanopatterns through Nucleation and Growth Mechanism

Exploring the ordering mechanism and dynamics of self-assembled block copolymer (BCP) thin films under confined conditions are highly essential in the application of BCP lithography. In this study, it is aimed to examine the self-assembling mechanism and kinetics of silicon-containing 3-arm star-block copolymer composed of polystyrene (PS) and poly(dimethylsiloxane) blocks as nanostructured thin films with perpendicular cylinders and controlled lateral ordering by directed self-assembly using topographically patterned substrates. The ordering process of the star-block copolymer within fabricated topographic patterns with PS-functionalized sidewall can be carried out through the type of secondary (i.e., heterogeneous) nucleation for microphase separation initiated from the edge and/or corner of the topographic patterns, and directed to grow as well-ordered hexagonally packed perpendicular cylinders. The growth rate for the confined microphase separation is highly dependent upon the dimension and also the geometric texture of the preformed pattern. Fast self-assembly for ordering of BCP thin film can be achieved by lowering the confinement dimension and also increasing the concern number of the preformed pattern, providing a new strategy for the design of BCP lithography from the integration of top-down and bottom-up approaches.

Simultaneous uniaxial extensional deformation and cylindrical confinement of block copolymers using non-equilibrium molecular dynamics

Using coarse-grained nonequilibrium molecular dynamics, symmetric block copolymers are simulated under the combined effects of cylindrical confinement and uniaxial extensional deformation. For a given confinement diameter, a block copolymer (BCP) will self-assemble into a fixed number of concentric cylinder lamellae at equilibrium. The changing diameter during uniaxial extensional deformation therefore is expected to affect the morphology of the BCPs. The aim of this study is to investigate the interplay of deformation and confinement on BCP morphology by varying the simulation strain rate and diameter. Two different simulation approaches are conducted: constant time simulations with varying initial diameter and constant strain simulations with varying simulation time. A comparison of self-assembly at different strain rates shows that for low strain rates, near-equilibrium morphology can form despite the deformation, while for progressively higher strain rates, extra lamellae and disordered morphologies appear. By defining a Weissenberg number based on the deformation and polymer self-assembly time-scales, the morphologies at different strain rates and diameters are explained. Using the time scale analysis, ordered morphologies appear for Wi < 1, while extra lamellae and disordered morphologies occur at Wi > 1. For the latter case, the cylinder diameter shrinks too quickly for polymers to form the equilibrium morphology, which results in a mixture of lamellar structures along the cylinder length.

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.

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.

Diversifying Nanoparticle Assemblies in Supramolecule Nanocomposites Via Cylindrical Confinement

Many macroscopic properties such as collective chiral responses enhanced by coupled plasmonic nanoparticles require complex nanostructures. However, a key challenge is to directly assemble nanosized building blocks into functional entities with designed morphologies. For example, the DNA templated nanoparticle assembly has low scalability and requires aqueous conditions, while other approaches such as controlled drying and polymer templating access only simple 1-D, 2-D, and 3-D structures with limited assembly patterns. Here, we demonstrate a new self-assembly strategy that expands the diversity of 3-D nanoparticle assemblies. By subjecting supramolecular nanocomposites to cylindrical confinement, a range of new nanoparticle assemblies such as stacked rings and single and double helices can be readily obtained with a precisely defined morphology. Circular dichroism dark field scattering measurements on the single nanowire with Au helical ribbon-like assembly show chiral plasmonic response several orders of magnitude higher than that of natural chiral materials. The phase behavior of supramolecular nanocomposite under geometric constraints is quite different from that of block copolymer. It depends on the complex interplay among nanoparticle packing and phase behavior of parent block copolymers under confinement and can be governed by nanoparticle diffusion.

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.

Nanochannel Arrays for Molecular Sieving and Electrochemical Analysis by Nanosphere Lithography Templated Graphoepitaxy of Block Copolymers

The ability to design, fabricate, and manipulate materials at the nanoscale is fundamental to the quest to develop technologies to assemble nanometer-scale pieces into larger-scale components and materials, thereby transferring unique nanometer-scale properties to macroscopic objects. In this work, we describe a new approach to the fabrication of highly ordered, ultrahigh density nanochannel arrays that employs nanosphere lithography to template the graphoepitaxy of polystyrene-polydimethylsiloxane, diblock copolymers. By optimizing the well-controlled solvent vapor annealing, overcoating conditions, and the subsequent reactive ion etching processes, silica nanochannel (SNC) arrays with areal densities, ρ_A, approaching 1000 elements μm^-2, are obtained over macroscopic scales. The integrity and functionality of the SNC arrays was tested by using them as permselective ion barriers to nanopore-confined disk electrodes. The nanochannels allow cations to pass to the disk electrode but reject anions, as demonstrated by cyclic voltammetry. This ion gating behavior can be reversed from cation-permselective to anion-permselective by chemically inverting the surface charge from negative to positive. Furthermore, the conformal SNC array structures obtained could easily be lifted, detached, and transferred to another substrate, preserving the hierarchical organization while transferring the nanostructure-derived properties to a different substrate. These results demonstrate how nanoscale behavior can be replicated over macroscale distances, using electrochemical analysis as a model.

Blending Homopolymers for Controlling the Morphology Transitions of Block Copolymer Nanorods Confined in Cylindrical Nanopores

The microphase separation of block copolymers in confined geometries has been widely investigated over the last few decades. The controllability and versatility of the confinement-induced morphologies, however, are still difficult to be achieved because of the limited experimental parameters in the process of fabricating the confined nanostructures. In this work, we study the morphology transitions of lamellae-forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS) nanorods confined in the nanopores of anodic aluminum oxide (AAO) templates. The nanorods are formed by solvent-assisted template wetting, and the morphologies are compared to those in the bulk state. By blending PS-b-PDMS with homopolystyrene (hPS), the morphologies of the nanorods can be controlled because of the changes of the effective volume fractions. Special morphology transitions from concentric lamellar morphology, to multihelical morphology, and finally to spherical-like morphology are observed by increasing the weight ratios of hPS. hPS with different molecular weights is also applied to investigate the effect of hPS on the morphologies of the PS-b-PDMS/hPS blend nanostructures. The unusual morphologies are further confirmed by a selective removal process, which also generates nanochannels for possible refilling with functional materials.

Selective solvent-induced reconstruction in confined space: one-dimensional mesoporous block copolymer structures in cylindrical nanopores

The formation of polymer nanostructures confined in cylindrical nanopores via a novel selective solvent-induced reconstruction process is investigated.

Perfectly Ordered Patterns Formed by a Heterogeneous Nucleation Process of Block Copolymer Self-Assembly Under Rectangular Confinement

The heterogeneous nucleation process during the phase separation of binary blends of the AB diblock and the C homopolymer induced by rectangular confinement is studied by cell dynamics simulation based on the time-dependent Ginzburg-Landau theory. The main goal is to yield large-scale ordered hexagonal patterns by tailoring the surface potentials of the sidewalls. Our study reveals a crucial condition to induce the desired heterogeneous nucleation process in which the nucleated domain grains grow and merge into a defect-free pattern. Specifically, nucleations are induced simultaneously by two parallel sidewalls with a strong surface potential, whereas the spontaneous nucleation and the heterogeneous nucleation at the other two walls with a weak surface potential are suppressed. Moreover, the confinement effect of the other two walls can ensure that the two rows of nucleated domains have correlated positions. Importantly, we find that the ordering process under the crucial condition exhibits a high tolerance to the rectangular sizes. Only a few defects in thousands of domains are occasionally caused that are observed to be annihilated in a short-annealing time via various mechanisms. This study may provide a facile route to prepare large-scale ordered patterns via a simple rectangular confinement.

Morphology control of three-dimensional nanostructures in porous templates using lamella-forming block copolymers and solvent vapors

The microphase separation behavior of block copolymers confined in cylindrical nanopores has been extensively investigated. Recently, the solvent-annealing-induced nanowetting in templates (SAINT) method has been demonstrated to be a versatile approach for the infiltration of block copolymers into the nanopores of porous templates. The function of the annealing solvents, however, is still not well understood, especially in the morphology control of the fabricated block copolymer nanostructures. In this work, we elucidate the function of the annealing solvents in the SAINT method using a lamella-forming block copolymer, polystyrene-block-polydimethylsiloxane (PS-b-PDMS), and anodic aluminum oxide (AAO) templates. By changing the composition of the annealing solvents, different morphologies such as the concentric lamellar morphology, the winding cylinder morphology, and the irregular hybrid morphology are observed, mainly caused by the annealing-solvent-induced volume change. The morphology of the block copolymer nanostructures can be further confirmed using an HF solution to remove the PDMS domain selectively.

Tailoring the Static and Dynamic Mechanical Properties of Tri-Block Copolymers through Molecular Dynamics Simulation

Although the research of the self-assembly of tri-block copolymers has been carried out widely, little attention has been paid to study the mechanical properties and to establish its structure-property relation, which is of utmost significance for its practical applications. Here, we adopt molecular dynamics simulation to study the static and dynamic mechanical properties of the ABA tri-block copolymer, by systematically varying the morphology, the interaction strength between A-A blocks, the temperature, the dynamic shear amplitude and frequency. In our simulation, we set the self-assembled structure formed by A-blocks to be in the glassy state, with the B-blocks in the rubbery state. With the increase of the content of A-blocks, the spherical, cylindrical and lamellar domains are formed, respectively, exhibiting a gradual increase of the stress-strain behavior. During the self-assembly process, the stress-strain curve is as well enhanced. The increase of the interaction strength between A-A blocks improves the stress-strain behavior and reduces the dynamic hysteresis loss. Since the cylindrical domains are randomly dispersed, the stress-strain behavior exhibits the isotropic mechanical property; while for the lamellar domains, the mechanical property seems to be better along the direction perpendicular to than parallel to the lamellar direction. In addition, we observe that with the increase of the dynamic shear amplitude and frequency, the self-assembled domains become broken up, resulting in the decrease of the storage modulus and the increase of the hysteresis loss, which holds the same conclusion for the increase of the temperature. Our work provides some valuable guidance to tune the static and dynamic mechanical properties of ABA tri-block copolymer in the field of various applications.

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.