Multipod structures of lamellae‐forming diblock copolymers in three‐dimensional confinement spaces: Experimental observation and computer simulation

The three‐dimensional (3D) confinement effect on the microphase‐separated structure of a diblock copolymer was investigated both experimentally and computationally. Block copolymer nanoparticles were prepared by adding a poor solvent into a block copolymer solution and subsequently evaporating the good solvent. The 3D structures of the nanoparticles were quantitatively determined with transmission electron microtomography (TEMT). TEMT observations revealed that various complex structures, including tennis‐ball, mushroom‐like, and multipod structures, were formed in the 3D confinement. Detailed structural analysis, showed that one block of the diblock copolymer slightly prefers to segregate into the particle surface compared with the other block. The observed structures were further elaborated using cell dynamics computer simulation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1702–1709     

Kinetic pathways of sheared block copolymer systems derived from Minkowski functionals

We employ Minkowski functionals to analyze the kinetics of pattern formation under an applied external shear flow. The considered pattern formation model describes the dynamics of phase separating block copolymer systems. For our purpose, we have chosen two block copolymer systems (a melt and a solution) that exhibit a hexagonal cylindrical morphology as an equilibrium structure. Our main objective is the determination of efficient choices for the treshold values that are required for the calculation of the Minkowski functionals. We find that a minimal set of two treshold values (one from which should be equal to an average density value and another to a higher density value) is sufficient to unraffle the phase separation kinetics. Given these choices, we focus on the influence of the degree of phase separation, and the instance at which the shear is applied, on the kinetic pathways. We also found a remarkable similarity of the time evolution of Euler characteristic and the segregation parameter for the average density choice.     

Simulations of Electric Field Induced Lamellar Alignment in Block Copolymers in the Presence of Selective Electrodes

Computer simulations have been performed for electric field induced parallel‐perpendicular lamellar phase transition in the presence of electrodes. The simulations are based on the dynamic density functional theory. Here we provide the extension of earlier work in two dimensions (2D) to three dimensions (3D). The result is a vivid picture of the transitions through defect creation and collision.

Observed change in lamellar alignment with applied electric field.     

Dynamics of terrace formation in a nanostructured thin block copolymer film

We have used dynamic self-consistent field (DSCF) theory to investigate the structural evolution of an ABA block copolymer thin film placed between a solid substrate and a free surface. In line with the few existing theoretical studies for pure homopolymers and mixtures, the free interface is introduced by a void component. In our calculations, the free surface experiences surface roughening and eventually the formation of terraces, as in the experiments. The kinetic pathway of the microstructures was compared to findings of an existing detailed experimental study (Knoll, A.; Lyakhova, K. S.; Horvat, A.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Nat. Mater. 2004, 3, 886) and was found to be equivalent in detail. This corroborates our assumption in this earlier work that the pathway due to changing film thickness is similar to a pathway due to changing surface energetics. Moreover, our calculations show for the first time that microstructural transitions are a driving force of polymer/air interface curving and the formation of terraces.     

Large scale simulation of block copolymers with cell dynamics

Cell dynamics simulation (CDS) is a fast method to simulate kinetic processes in phase separating systems of large sizes. We review this method applied to block copolymer systems and illustrate it on a set of physical phenomena occurring in these systems. Achievements of CDS demonstrate, that the method can describe such complex phenomena rather well and therefore, is a complementary method to other more elaborate but slow techniques to which it can serve as a precursor.     

Mechanism of the transition between lamellar and gyroid phases formed by a diblock copolymer in aqueous solution

The mechanism of the transition from a lamellar phase to a gyroid phase in an aqueous solution of a diblock copolymer has been studied by time-resolved synchrotron small-angle X-ray scattering. The transition occurs via a metastable perforated lamellar structure. The perforations initially have liquidlike ordering before developing hexagonal packing. The transient phase of irregularly perforated layers is revealed by the development of diffuse scattering peaks, just below the Bragg peaks of the lamellar structure. The diffuse scattering is modeled by Monte Carlo simulations of perforated layers. Following the formation of perforations, Bragg peaks characteristic of a hexagonal structure signal an ordering into a hexagonal lattice (with the concomitant loss of diffuse scattering). Computer simulations based on a dynamic density functional model reproduce these features. The hexagonal perforated lamellar phase is rapidly replaced by the gyroid phase. The domain spacing of the gyroid phase is larger than that of the perforated lamellar structure. The perforated lamellar and gyroid phases coexist for a defined period. The reverse transition from gyroid to lamellae occurs directly, with no transient or metastable intermediates.     

Phase behavior in thin films of cylinder-forming ABA block copolymers: mesoscale modeling

The phase behavior of cylinder-forming ABA block copolymers in thin films is modeled in detail using dynamic density functional theory and compared with recent experiments on polystyrene-block-polybutadiene-block-polystyrene triblock copolymers. Deviations from the bulk structure, such as wetting layer, perforated lamella, and lamella, are identified as surface reconstructions. Their stability regions are determined by an interplay between surface fields and confinement effects. Our results give evidence for a general mechanism governing the phase behavior in thin films of modulated phases.     

Defect evolution in block copolymer thin films via temporal phase transitions

We study the details of the defect dynamics in thin films of a cylinder-forming polystyrene-block-polybutadiene (SB) diblock copolymer melt. The high temporal resolution of in-situ scanning force microscopy (SFM) uncovers elementary dynamic processes of structural rearrangements on time scales not accessible so far. Short-term interfacial undulations and the formation of transient phases (spheres, perforated lamellae, and lamellae) are observed. We demonstrate that the well-known structural defects are annihilated by short-term phase transitions into what may be considered excited states. These temporary phase transitions are reproduced in simulations based on dynamic self-consistent field theory. We discuss the role of the observed structural evolution in the context of the equilibrium phase behavior in SB thin films.