Blends Of AB Diblock Copolymers Research Articles

Bicontinuous microemulsion in binary blends of complementary diblock copolymers.

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.

Complex Phase Behavior in Binary Blends of AB Diblock Copolymer and ABC Triblock Terpolymer

Blending block polymers with different block compositions provides an opportunity to create nanostructures that are not accessible from neat block copolymer melts. In this study, we investigate the equilibrium phase behavior in binary blends composed of an AB diblock copolymer and an ABC triblock terpolymer, using self-consistent field theory (SCFT). Blending these simple linear block polymers results in complex phase behaviors, including unusual core–shell network phases with asymmetric core and shell volume fractions and a new cylinder-in-O70 hybrid network phase. The phase diagrams with respect to segregation strength and blend composition reveal an unexpected morphological richness, including 15 ordered phases, illustrating the potential inherent in blending these relatively simple components.

Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation.

Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, , depends on a composition field, , that controls the segregation of the unlike components and a pressure field, , that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which fluctuates while tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).

Instability of the Microemulsion Channel in Block Copolymer-Homopolymer Blends.

Field theoretic simulations are used to predict the equilibrium phase diagram of symmetric blends of AB diblock copolymer with A- and B-type homopolymers. Experiments generally observe a channel of bicontinuous microemulsion (BμE) separating the ordered lamellar (LAM) phase from coexisting homopolymer-rich (A+B) phases. However, our simulations find that the channel is unstable with respect to macrophase separation, in particular, A+B+BμE coexistence at high T and A+B+LAM coexistence at low T. The preference for three-phase coexistence is attributed to a weak attractive interaction between diblock monolayers.

Bicontinuous Double-Diamond Structures Formed in Ternary Blends of AB Diblock Copolymers with Block Chains of Different Lengths

We report on the formation of a bicontinuous double diamond (DD) structure in ternary blends of poly(styrene-b-isoprene) (SI) diblock copolymers with chains of different lengths merely in a polyisoprene block. Certainly, the materials revealing the DD structure with mesoscopic length scale have strongly been expected due to high potential for applications; however, it is difficult to form owing to thermodynamically evident disadvantages such as wider surface area and larger domain thickness variation, particularly for monodisperse copolymers. The DD structure was successfully formed for ternary blends composed of three parent diblock copolymers; SI-L (M = 190k, φs = 0.46), SI-G (M = 151k, φs = 0.62), and SI-C (M = 124k, φs = 0.73), resulting in covering the overall composition range 0.57 ≤ φs ≤ 0.60, where φss denotes volume fractions of polystyrene blocks. Four-branched double network structure with space group symmetry of Pn3m was clearly proved by transmission electron microscopy (TEM) observation aid...

Soft Confinement-Induced Morphologies of the Blends of AB Diblock Copolymers and C Homopolymers.

Self-assembly behavior of the blends of AB diblock copolymers and C homopolymers in soft confinement is studied by using a simulated annealing method. Polymer solution droplets in a poor solvent environment realize the soft confinement. Several sequences of soft confinement-induced copolymer aggregates with different shapes and internal structures are predicted as functions of the size of confinement, the number ratio of AB diblock copolymers to C homopolymers, the volume fraction of blocks, the selectivity of confinement's surface, the incompatibility between blocks, and the competition between two block-homopolymer interactions. Simulation results demonstrate that those factors are able to tune the morphology of the aggregates precisely. We anticipate the rules achieved here is helpful to fabrication of polymeric particle with predesigned morphology.

Modeling Hydrogen Bonding in Diblock Copolymer/Homopolymer Blends

Blends of AB-diblock copolymers and C-homopolymers (AB/C), in which A and C are capable of forming hydrogen bonds, are used as a model system to examine and validate two approaches for modeling the effects of hydrogen bonding on the phase behavior of polymeric systems. The first model assumes a negative Flory–Huggins parameter between the A/C monomers. This attractive-interaction model reproduces qualitatively correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C-homopolymers. The second model assumes that hydrogen bonding leads to A/C complexation. The interpolymer-complexation model predicts correctly the order–order phase transition sequences and the decrease of lamellar spacing at strong hydrogen bonding. The results demonstrate that hydrogen bonding of polymers should be modeled by the interpolymer-complexation model.

The Plumber’s Nightmare Phase in Diblock Copolymer/Homopolymer Blends. A Self-Consistent Field Theory Study.

Using self-consistent field theory, the Plumber’s Nightmare and the double diamond phases are predicted to be stable in a finite region of phase diagrams for blends of AB diblock copolymer (DBC) and A-component homopolymer. To the best of our knowledge, this is the first time that the P phase has been predicted to be stable using self-consistent field theory. The stabilization is achieved by tuning the composition or conformational asymmetry of the DBC chain, and the architecture or length of the homopolymer. The basic features of the phase diagrams are the same in all cases studied, suggesting a general type of behavior for these systems. Finally, it is noted that the homopolymer length should be a convenient variable to stabilize bicontinuous phases in experiments.

New Fast SCFT Algorithm Applied to Binary Diblock Copolymer/Homopolymer Blends

We present an efficient strategy for mapping out the classical phase behavior of block copolymer systems using self-consistent-field theory. With our new algorithm, the complete solution of a classical block copolymer phase can be evaluated typically in a fraction of a second on a single-processor computer, even for highly segregated melts. This is accomplished by implementing the standard unit-cell approximation for the cylindrical and spherical phases and solving the resulting equations using a Bessel function expansion. Here the method is used to investigate blends of AB diblock copolymer and A homopolymer, concentrating on the situation where the two molecules are of similar size.

Phase Behavior of Block Copolymer/Homopolymer Blends

We examine weakly segregated blends of AB diblock copolymer and A homopolymer with similar degrees of polymerization. The relative stability of numerous phases is examined and phase diagrams are constructed using self-consistent field theory. While the pure diblock system is only found to exhibit the body-centered cubic (spherical), hexagonal (cylindrical), bicontinuous Ia3d cubic (gyroid), and lamellar ordered phases, we find that the addition of homopolymer stabilizes close-packed spherical, bicontinuous Pn3m cubic (double-diamond), and hexagonally-perforated (catenoid) lamellar phases. We find that, in general, the minority-component region of a microstructure can only accommodate a limited amount of homopolymer before macrophase separation occurs. On the other hand, the majority-component regions can swell indefinitely with the addition of homopolymer, eventually resulting in an unbinding transition. We associate the region of highly-swollen microstructures with the micellar region observed in real systems. For the lamellar and hexagonal phases, we examine the distribution of homopolymer within the microstructure, and for the lamellar phase, we calculate the effect of homopolymer on the dimensions of the A- and B-rich microdomains.