Self-Consistent Field Theory of Multiply-Branched Block Copolymer Melts

We present a numerical algorithm to evaluate the self-consistent field theory for melts composed of block copolymers with multiply-branched architecture. We present results for the case of branched copolymers with doubly-functional groups for multiple branching generations. We discuss the stability of the cubic phase of spherical micelles, the A15 phase, as a consequence of tendency of the AB interfaces to conform to the polyhedral environment of the Voronoi cell of the micelle lattice.Comment: 12 pages, 10 includes figure

Structure variation and evolution in microphase-separated grafted diblock copolymer films

The phase behavior of grafted d-polystyrene-block-poly(methyl methacrylate) diblock copolymer films is examined, with particular focus on the effect of solvent and annealing time. It was observed that the films undergo a two-step transformation from an initially disordered state, through an ordered metastable state, to the final equilibrium configuration. It was also found that altering the solvent used to wash the films, or complete removal of the solvent prior to thermal annealing using supercritical CO2, could influence the structure of the films in the metastable state, though the final equilibrium state was unaffected. To aid in the understanding to these experimental results, a series of self-consistent field theory calculations were done on a model diblock copolymer brush containing solvent. Of the different models examined, those which contained a solvent selective for the grafted polymer block most accurately matched the observed experimental behavior. We hypothesize that the structure of the films in the metastable state results from solvent enrichment of the film near the film/substrate interface in the case of films washed with solvent or faster relaxation of the nongrafted block for supercritical CO2 treated (solvent free) films. The persistence of the metastable structures was attributed to the slow reorganization of the polymer chains in the absence of solvent

Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers

We compute phase diagrams for $A_nB_m$ starblock copolymers in the strong-segregation regime as a function of volume fraction $\phi$, including bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as candidate structures. We present the details of a general method to compute free energies in the strong segregation limit, and demonstrate that the gyroid G phase is the most nearly stable among the bicontinuous phases considered. We explore some effects of conformational asymmetry on the topology of the phase diagram.Comment: 14 pages, latex, 21 figures, to appear in Macromolecule

Interfaces in Diblocks: A Study of Miktoarm Star Copolymers

We study AB$_n$ miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by implementing a numerically exact self-consistent field theory to probe the phase diagram and the shape of the AB interface.Comment: 12 pages, 11 included figure

The non-centrosymmetric lamellar phase in blends of ABC triblock and ac diblock copolymers

The phase behaviour of blends of ABC triblock and ac diblock copolymers is examined using self-consistent field theory. Several equilibrium lamellar structures are observed, depending on the volume fraction of the diblocks, phi_2, the monomer interactions, and the degrees of polymerization of the copolymers. For segregations just above the order-disorder transition the triblocks and diblocks mix together to form centrosymmetric lamellae. As the segregation is increased the triblocks and diblocks spatially separate either by macrophase-separating, or by forming a non-centrosymmetric (NCS) phase of alternating layers of triblock and diblock (...ABCcaABCca...). The NCS phase is stable over a narrow region near phi_2=0.4. This region is widest near the critical point on the phase coexistence curve and narrows to terminate at a triple point at higher segregation. Above the triple point there is two-phase coexistence between almost pure triblock and diblock phases. The theoretical phase diagram is consistent with experiments.Comment: 9 pages, 8 figures, submitted to Macromolecule

Phase diagram for diblock copolymer melts under cylindrical confinement

We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders are eliminated. Our results are consistent with experiments, but we also predict phases yet to be observed.Comment: 12 pages, 3 figures. submitted to Physical Review Letter

Partial integration and local mean-field approach for a vector lattice model of microemulsions

A vector model on the simple cubic lattice, describing a mixture of water, oil, and amphiphile, is considered. An integration over the amphiphile orientational degrees of freedom is performed exactly in order to obtain an effective Hamiltonian for the system. The resulting model is a three-state (spin-1) system and contains many-site interaction terms. The analysis of the ground state reveals the presence of the water-oil-rich phase as well as the amphiphile-rich and the cubic phases. The temperature phase diagram of the system is analyzed in a local mean-field approach, and a triple line of water-rich, oil-rich, and microemulsion coexistence is obtained. For some values of the model parameters, lamellar phases also appear in the system, but only at finite temperature. The Lifshitz line is determined in a semianalytical way in order to locate the microemulsion region of the disordered phase

Block Copolymer at Nano-Patterned Surfaces

We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the alignment and orientation of lamellar phases. The calculations are done within self-consistent field theory (SCFT), where the semi-implicit relaxation scheme is used to solve the diffusion equation. Two specific set-ups, motivated by recent experiments, are investigated. In the first, the film is placed on top of a surface imprinted with long chemical stripes. The stripes interact more favorably with one of the two blocks and induce a perpendicular orientation in a large range of system parameters. However, the system is found to be sensitive to its initial conditions, and sometimes gets trapped into a metastable mixed state composed of domains in parallel and perpendicular orientations. In a second set-up, we study the film structure and orientation when it is pressed against a hard grooved mold. The mold surface prefers one of the two components and this set-up is found to be superior for inducing a perfect perpendicular lamellar orientation for a wide range of system parameters