Morphologies of ABC triblock copolymer thin films

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.

DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

Hierarchical colloidosomes self-assembled from block copolymer micelles via emulsion interfacial confinement

Hierarchical self-assembly of polymeric building blocks into high-level colloidosomes is desirable to not only design novel nanostructures but also fabricate the complex artificial materials across many length scales with multifunctionality. Although great progress has been made in the designing the hierarchical colloidosomes, the fabrication of polymeric colloidosomes self-assembled from block copolymer (BCP) colloidal nanoparticles still remains challenge. Here, we report the fabrication of the hierarchical polymeric colloidosomes with typical hollow internal structures self-assembled from the polystyrene-block-poly (2-vinyl pyridine) (PS-b-P2VP) BCP spherical micelles through the emulsion interfacial confinement, which is constructed through the water-in-1-butanol emulsion system. Moreover, the hierarchical colloidosomes can disassemble into the original uniform spherical micelles under the acid aqueous solution, indicating that the colloidosomes possess good pH stimuli-responsibility. Finally, the stability of the colloidosomes can be greatly improved by cross-linking the P2VP corona of original spherical micelles, offering the effective templates for construction of the multifunctional materials. This finding provides a simple yet effective method for the fabrication of the hierarchical colloidosomes from the BCP building blocks.

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.

Numerical implementation of pseudo-spectral method in self-consistent mean field theory for discrete polymer chains

In the standard self-consistent field theory (SCFT), a polymer chain is modeled as an infinitely flexible Gaussian chain, and the partition function is calculated by solving a differential equation in the form of a modified diffusion equation. The Gaussian chain assumption makes the standard SCFT inappropriate for modeling of short polymers, and the discrete chain SCFT in which the partition function is obtained through recursive integrals has recently been suggested as an alternative method. However, the shape of the partition function integral makes this method much slower than the standard SCFT when calculated in the real space. In this paper, we implement the pseudospectral method for the discrete chain SCFT adopting the bead-spring or freely jointed chain (FJC) model, and a few issues such as the accurate discretization of the FJC bond function are settled in this process. With the adoption of the pseudospectral method, our calculation becomes as fast as that of the standard SCFT. The integral equation introduces a new boundary condition, the neutral boundary, which is not available in the standard SCFT solving the differential equation. This interesting physical situation is combined with the finite-range interaction model for the study of symmetric block copolymers within thin films. We find that the surface-perpendicular block copolymer lamellar phase becomes preferable to the surface-parallel one when both the top and bottom surfaces are neutral.

Dissipative particle dynamics simulation on the self-assembly of linear ABC triblock copolymers under rigid spherical confinements

Although a great deal of unique nanostructures were already obtained from polymer self-assemblies in terms of conventional parameters, the self-assembly under the confinement is still not well understood. Here, dissipative particle dynamics simulations were used to explore the self-assemble behaviors of linear ABC triblock copolymers under rigid spherical confinements. First several unusual morphologies, such as multilayer onion, coupled helix, and stacked lamella, were distinguished from the total 210 simulations. Second, the influences of three important parameters (block sequence, wall selectivity, and spherical radius) on the morphologies were discussed in detail. Finally, the dynamics evolution of several typical aggregates was examined. This simulation enriches micelle morphologies for the self-assembly of linear ABC triblock copolymers under rigid spherical confinements and is helpful to understand the formation of valuable nanostructures from linear ABC terpolymers.

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM3 (ll) -HFs), perpendicular lamellar phase with cylinders at the interface (LAM(⊥)-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C2 (⊥)-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.

Diblock and triblock copolymer thin films on a substrate with controlled selectivity

Using self-consistent field theory (SCFT), morphology development in symmetric linear ABC triblock copolymer films on neutral and selective substrates has been studied, and it is compared with the triblock copolymer morphologies in bulk. In particular, the effects of the substrate preferable to B (interior) block on nanopattern formation of the copolymer films are of our central interest. Here, we report various nanopatterns with tunable square morphologies. The domain patterns are much more diverse than those parallel to the substrate with substrate selectivity for end-block or those vertical to the substrate without substrate selectivity. Furthermore, in order to figure out an economical and efficient way to fabricate useful passive pattern transfer layers, which have potential applications in microelectronic processes and ultrahigh density storage media, we propose a two-step strategy and scrutinize the conditions for generating square symmetries using cylinder-forming or lamella-forming AB diblock copolymers deposited on substrates created from ABC triblock copolymer films. It is found that a thinner film with weak incompatibility can produce square patterns.

Nanoconfined surfactant templated electrodeposition to porous hierarchical nanowires and nanotubes

Porous metal (Pd and Co) and semiconductor (ZnO) nanowires, porous metal (Pt and Ni) nanotubes, and unique multiple Pt nanowires are prepared from a novel nanoconfined surfactant templated electrodeposition approach. More specifically, the overall diameter of nanowires or nanotubes is defined by the pore channels of membranes. Surfactant assembled structure nanoconfined within the pores of membranes is used to generate the porosity and to control the texture of the nanowires or nanotubes. As compared to solid nanowires and nanotubes, the porous nanowires and nanotubes exhibit unique properties. For example, porous cobalt nanowires show higher coercivity.

Templated self-assembly of square symmetry arrays from an ABC triblock terpolymer

Self-assembly provides the ability to create well-controlled nanostructures with electronic or chemical functionality and enables the synthesis of a wide range of useful devices. Diblock copolymers self-assemble into periodic arrays of microdomains with feature sizes of typically 10-50 nm, and have been used to make a wide range of devices such as silicon capacitors and transistors, photonic crystals, and patterned magnetic media(1-3). However, the cylindrical or spherical microdomains in diblock copolymers generally form close-packed structures with hexagonal symmetry, limiting their device applications. Here we demonstrate self-assembly of square-symmetry patterns from a triblock terpolymer in which one organometallic block imparts high etch selectivity and etch resistance. Long-range order is imposed on the microdomain arrays by self-assembly on topographical substrates, and the orientation of both square lattices and in-plane cylinders is controlled by the substrate chemistry. Pattern transfer is demonstrated by making an array of square-packed 30 nm tall, 20 nm diameter silica pillars. Templated self-assembly of triblock terpolymers can generate nanostructures with geometries that are unattainable from diblock copolymers, significantly enhancing the capabilities of block copolymer lithography.

Directed copolymer assembly on chemical substrate patterns: a phenomenological and single-chain-in-mean-field simulations study of the influence of roughness in the substrate pattern

The directed assembly of lamella-forming copolymer systems on substrates chemically patterned with rough stripes has been studied using a Helfrich-type, phenomenological theory and Single-Chain-in-Mean-Field (SCMF) simulations. The stripe period matches that of the lamellar spacing in the bulk. The effect of the line edge roughness (LER) of the substrate pattern on the microphase-separated morphology was investigated considering two generic types of substrate LER with a single characteristic wavelength imposed on the edges of the stripes: undulation and peristaltic LER. In both cases, the domain interfaces are pinned to the rough stripe boundary at the substrate and, thus, are deformed. We study how this deformation decays as a function of the distance from the substrate. The simple theory and the SCMF simulations demonstrate that one of the basic factors determining the decay of the roughness transferred into the self-assembled morphology is the characteristic LER wavelength of the substrate pattern; i.e., the distance over which the roughness propagates away from the substrate increases with wavelength. However, both approaches reveal that, for a quantitative understanding of the consequences of substrate LER, it is important to consider the interplay of the pattern wavelength with the other characteristic length scales of the system, such as the film thickness and the bulk lamellar spacing. For instance, in thin films, the induced deformation of the lamellar interface decays slower with distance from the patterned surface than in thicker films. It is shown that the phenomenological theory can capture many of the same qualitative results as the SCMF simulations for copolymer assembly on substrate patterns with LER, but, at the same time, is limited by an incomplete description of the constraints on the polymer chain conformations imposed by the substrate.

Hard-surface effects in polymer self-consistent field calculations

We have investigated several effects due to the confinement of polymer melts by impenetrable (hard) surfaces in the self-consistent field calculations. To adequately represent such confinement, the total (normalized) polymer segmental density (volume fraction) is usually constrained to an imposed profile that continuously decreases from 1 in the interior of confined melts to 0 at the surfaces over a short distance. The choice of this profile strongly influences the numerical performance of the self-consistent field calculations. In addition, for diblock copolymers A-B the hard-surface confinement has both energetic and entropic effects: On one hand, the decrease of polymer density from 1 reduces A-B repulsion and favors morphologies with more A-B interfaces near the surfaces. On the other hand, the enrichment of chain ends and depletion of middle segments near the surfaces favor parallel morphologies where chains orient mainly perpendicular to the surfaces. These two effects are comparable in magnitude, and for asymmetric diblock copolymers result in an entropic preference of a neutral surface for the shorter block as proposed previously [Q. Wang et al., Macromolecules 34, 3458 (2001)]. The hard-surface effects are weak in practice and thus manifested only when the surfaces are nearly neutral.

Self-assembled one-dimensional nanostructure arrays

A range of proposed devices relies on the electronic, optical or magnetic properties of one-dimensional (1D) chains of nanoparticles. Here, well-controlled 1D arrays have been formed by templating a spherical-morphology block copolymer within a narrow groove. Significantly, the domains are distorted into ellipses with aspect ratio and major axis orientation controlled by the groove width. This technique gives unprecedented control over the period, particle size, aspect ratio, and orientation of nanoparticles in 1D arrays, making it valuable for creating self-assembled masks for the fabrication of novel devices.

Monte Carlo Simulations of Cylinder-Forming ABC Triblock Terpolymer Thin Films

We systematically study the cylinder-forming ABC triblock terpolymer thin films using canonical ensemble Monte Carlo simulations. The simulated annealing procedure is applied to the self-assembling process. By judicious choice of the system dimensions, we elaborately investigate the effect of film thickness on the orientation of the cylinders. This confined triblock terpolymer system exhibits different phase behavior under the weak and strong surface fields. In addition, we also investigate the ensemble-averaged chain orientations and relative density profiles.

Self-assembly of rod-coil block copolymers

We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.

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

We have used lattice Monte Carlo simulations to investigate the molecular assembly of symmetric diblock copolymer melts within cylindrical nanochannels. We studied the effect that the surface field has on the copolymer morphology in three cylinders having different diameters. Upon varying the strength of the surface field, we observed a variety of morphologies, including stacked-disk, single-helix, catenoid-cylinder, gyroidal, stacked-circle, and concentric cylindrical barrel structures. The results of these simulations should be helpful when designing polymeric nanomaterials confined in cylindrical nanochannels.

Density-functional theory for fluid mixtures of charged chain particles and spherical counterions in contact with charged hard wall: Adsorption, double layer capacitance, and the point of zero charge

We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.

Ordered microstructures by assembly of ABC 3-miktoarm star terpolymers and linear homopolymers

Ordered microstructures assembled from the mixture of the ABC 3-miktoarm star terpolymers and the linear homopolymers have been investigated by using dynamic density functional theory. The simulations reveal that completely different ordered microphase pattern is found with addition of a few percent homopolymers that is identical in component to one of the arms on the ABC 3-miktoarm star terpolymer. For example, the original density pattern of ABC 3-miktoarm star terpolymers with parameters of N(A)=N(B)=N(C)=10 and chi(AB)=0.90, chi(BC)=chi(CA)=0.45 is in a perfectly ordered knitting feature. However, with gradual addition of the linear polymer same as block C on ABC 3-miktoarm star terpolymer into the system, the density patterns evolve with the volume fraction of the linear polymer from the ordered knitting patterns into the hexagonal patterns. Furthermore, with addition of linear polymers same as block A, lamellar microstructure has finally resulted. The simulation points out a way for designing and manufacturing nanomaterials with totally different microstructures.

Composite mesostructures by nano-confinement

In a physically confined environment, interfacial interactions, symmetry breaking, structural frustration and confinement-induced entropy loss can play dominant roles in determining molecular organization. Here we present a systematic study of the confined assembly of silica-surfactant composite mesostructures within cylindrical nanochannels of varying diameters. Using exactly the same precursors and reaction conditions that form the two-dimensional hexagonal SBA-15 mesostructured thin film, unprecedented silica mesostructures with chiral mesopores such as single- and double-helical geometries spontaneously form inside individual alumina nanochannels. On tightening the degree of confinement, a transition is observed in the mesopore morphology from a coiled cylindrical to a spherical cage-like geometry. Self-consistent field calculations carried out to account for the observed mesostructures accord well with experiment. The mesostructures produced by confined syntheses are useful as templates for fabricating highly ordered mesostructured nanowires and nanowire arrays.

Ordering mechanisms in triblock copolymers

The ordering mechanisms for an ABC triblock copolymer system are studied using self-consistent field theory. We find a two-phase mechanism, similar to what has been suggested experimentally (two-step mechanism). Analysis of free energy components shows that the two-phase process comes about through a competition between stretching energy and interfacial energy. The mechanism is found to be sufficiently robust so as to make it potentially useful for device applications.