Effect of surface field on the morphology of a symmetric diblock copolymer under cylindrical confinement

Phase behavior of symmetric diblock copolymers under 3D soft confinement

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using self-consistent field theory. Soft confinement is realized in binary blends composed of AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in a homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particles to square SL. When the C homopolymers are strongly selective for the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, and homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement.

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.

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.

Self-assembly of colloids with competing interactions confined in spheres

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

Hierarchical 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.

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.

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.

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.

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.

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.

Defect structures and ordering behaviours of diblock copolymers self-assembling on spherical substrates

One of the main differences of ordered structures constrained on curved surfaces is the nature of topological defects. We here explore the defect structures and ordering behaviours of both lamellar and cylindrical phases of block copolymers confined on spherical substrates by the Landau-Brazovskii theory, which is numerically solved by a highly accurate spectral method with a spherical harmonic basis. For the cylindrical phase, isolated disclinations and scars are generated on the spherical substrates. The number of excess dislocations in a scar depends linearly on the sphere radius. The defect fraction characterizing the ordering dynamics decays exponentially. The scars are formed from the isolated disclinations via mini-scars. For the lamellar phase, three types of defect structures (hedgehog, spiral and quasi-baseball) are identified. The disclination annihilation is the primary ordering mechanism of the lamellar phase.

Assembly of Polymer-Tethered Gold Nanoparticles under Cylindrical Confinement

The assembly of polystyrene (PS)-tethered gold nanoparticles (Au@PS NPs) in anodic aluminum oxide (AAO) cylindrical nanopores was investigated. This cylindrical confined assembly strategy allows us to generate novel assemblies (e.g., linear chain, zigzag, two-NP layer, three-NP layer, and hexagonally packed NP structures) by manipulating the AAO membrane pore size and molecular weight of PS ligands. Moreover, the optical property of the hybrid assemblies can be tuned through varying the interparticle distances and assembly structures. This work provides a guideline for confined assembly of functional NPs and lays groundwork for fabricating well-ordered hybrid nanostructures for optical, electronic, biosensing, and data storage devices.

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 segregation of a symmetric diblock copolymer in constrained space with a square-pillar array

In this study, we apply a self-consistent field theory of polymers to study the structures of a symmetric diblock copolymer in parallel substrates filled with square-pillar arrays in which the substrates and pillars exhibit a weak preference for one block of the copolymer. Three classes of structures, i.e., lamellae, perpendicular cylinders, and bicontinuous structures, are achieved by varying the polymer film thickness, the pillar pitch (the distance between two centers of the nearest neighboring pillars), the gap and rotation of the pillars. Because of the confinement along horizontal directions imposed by the pillar array, eight novel types of perpendicular lamellar structures and eight novel types of cylindrical structures with various shapes and distributions occur. In the hybridization states of the parallel and perpendicular lamellar structures, several novel bicontinuous structures such as the double-cylinder network, pseudo-lamellae, and perforated lamellar structure are also found. By comparing the free energies of the various possible structures, the antisymmetric parallel lamellae are observed to be stable with the larger pillar gap at a certain film thickness. The structural transformations between the alternating cylindrical structures (alternating cross-shaped, square-shaped, and octagonal perpendicular cylinders) and parallel lamellae with increasing film thickness or pillar gap are well explained by the modified strong separation theory. Our results indicate that array confinement can be an effective method to prepare novel polymeric nanopattern structures.

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.

Confined Self-Assembly of Asymmetric Diblock Copolymers within Silica Nanobowl Arrays

The confined self-assembly of asymmetric diblock copolymer polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) within an array of silica nanobowls prepared using a colloidal spheres templating technique is investigated. By manipulation of the nanobowl size, block copolymer (BCP) thickness, and interfacial interaction, a rich variety of ordered BCP nanostructures not accessible in the bulk system or under other confinements are obtained, resulting in hierarchically ordered nanostructures.

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.

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.

Nanostructures self-assembled in polymer solutions confined in cylindrical nanopores

Polymer nanostructures self-assembled from solutions confined in cylindrical nanopores were investigated via Monte-Carlo simulations. The nanostructures, including some novel ones, were self-assembled under a wide range of conditions. It is shown that the interactions of the segments with the wall, reflecting the wetting/dewetting by the polymer segments of the wall, constitute a crucial factor in the nanostructure formation. When there are attractive interactions between the segments of a homopolymer or between one kind of segment of a copolymer and the wall, short nanorods, long nanorods, and long nanorods containing channels are generated, and the diameters of the nanostructures are close to the diameter of the cylindrical nanopores. When the above interactions are repulsive, nanospheres, short nanorods, nanocapsules, long nanorods, and nanocylindroids are formed, and generally, the diameter of the nanostructure is smaller than the diameter of the cylindrical nanopores because of the formation of a depletion layer near the wall of the cylindrical nanopores. Our results also indicate that nanostructures that occupy the entire height of the nanopores are more easily generated in nanopores with larger diameters. It should be noted that the nanostructures formed from solutions are usually irregular and cannot be characterized by a unique diameter.