Kinetic pathways of sphere-to-cylinder transition in diblock copolymer melt under electric field.

Phase transition from body-centered-cubic spheres to cylinders in a diblock copolymer melt under an external electric field is investigated by means of real-space dynamical self-consistent field theory. Different phase transition kinetic pathways and different cylindrical domains arrangements of the final phase are observed depending on the strength and direction of the applied electric field. Various transient states have been identified depending on the electric field being applied along [111], [100], and [110] directions. The electric field should be above a certain threshold value in order the transition to occur. A "dynamic critical exponent" of the transition is found to be about 3/2, consistent with other order-order transitions in diblock copolymers under electric field.

The phases in a non-ionic surfactant (C12E6)-water ternary system: a coarse-grained computer simulation.

A dissipative particle dynamics computer simulation is used to investigate the ability of small oil molecules (hexane, dodecane, and octadecane) to control phase structures in nonionic surfactant-water systems. The model is successfully tested against the experimental results for binary and ternary systems where the third components are "swelling" and "penetrating" oils. The experimentally observed phases present in such systems were successfully modeled. In addition, the simulations show the locations of the oil molecules within the bilayer and the surfactant chain conformation. While the simulations confirm much of what is expected from experiment and theoretical models, evidence is found for the terminal methyl end of the surfactant molecules being located slightly closer to the interfacial region than other groups in the same chain.

Block copolymers confined in a nanopore: pathfinding in a curving and frustrating flatland.

We have studied structure formation in a confined block copolymer melt by means of dynamic density functional theory. The confinement is two dimensional, and the confined geometry is that of a cylindrical nanopore. Although the results of this study are general, our coarse-grained molecular model is inspired by an experimental lamella-forming polysterene-polybutadiene diblock copolymer system [K. Shin et al., Science 306, 76 (2004)], in which an exotic toroidal structure was observed upon confinement in alumina nanopores. Our computational study shows that a zoo of exotic structures can be formed, although the majority, including the catenoid, helix, and double helix that were also found in Monte Carlo nanopore studies, are metastable states. We introduce a general classification scheme and consider the role of kinetics and elongational pressure on stability and formation pathway of both equilibrium and metastable structures in detail. We find that helicity and threefold connections mediate structural transitions on a larger scale. Moreover, by matching the remaining parameter in our mesoscopic method, the Flory-Huggins parameter chi, to the experimental system, we obtain a structure that resembles the experimental toroidal structure in great detail. Here, the most important factor seems to be the roughness of the pore, i.e., small variations of the pore radius on a scale that is larger than the characteristic size in the system.

Scaling behavior of the reorientation kinetics of block copolymers exposed to electric fields.

We have followed the reorientation kinetics of various block copolymer solutions exposed to an external electric DC field. The characteristic time constants follow a power law indicating that the reorientation is driven by a decrease in electrostatic energy. Moreover, the observed exponent suggests an activated process in line with the expectations for a nucleation and growth process. When properly scaled, the data collapse onto a single master curve spanning several orders of magnitude both in reduced time and in reduced energy. The power law dependence of the rate of reorientation derived from computer simulations based on dynamic density functional theory agrees well with the experimental observations. First experiments in AC electric fields at sufficiently high frequencies confirm the notion that the reorientation process is dominated by differences in the dielectric constants rather than by mobile ions.

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.

Influence of initial order on the microscopic mechanism of electric field induced alignment of block copolymer microdomains.

We investigate the mechanism of microdomain orientation in concentrated block copolymer solutions exposed to a dc electric field by in situ synchrotron small-angle X-ray scattering (SAXS). As a model system, we use concentrated solutions of a lamellar polystyrene-b-polyisoprene block copolymer in toluene. We find that both the microscopic mechanism of reorientation and the kinetics of the process strongly depend on the initial degree of order in the system. In a highly ordered lamellar system with the lamellae being aligned perpendicular to the electric field vector, only nucleation and growth of domains is possible as a pathway to reorientation and the process proceeds rather slowly. In less ordered samples, grain rotation becomes possible as an alternative pathway, and the process proceeds considerably faster. The interpretation of our finding is strongly corroborated by dynamic self-consistent field simulations.

Orthogonal fields: a path to long-range three-dimensional order in block copolymers.

Large-scale computer simulations show that two orthogonal external fields can control the orientation of lamellar microdomains in diblock copolymers in three dimensions and lead to an enhanced long-range ordering.

Design of chimaeric polymersomes.

We discuss the development of hierarchical polymer particles, or variegated polymersome composites, in which at least two different components are phase separated within one polymersome chimaera. We briefly discuss the present status in experimental polymersome research, and then discuss a speculative design strategy, based on mesoscopic simulations with a dynamical variant of polymer self-consistent field theory (Mesodyn). The main conclusion is that the counter-intuitive co-assembly of demixing block copolymers is the key in controlling hierarchical structures on a mesoscopic scale. This is the classical paradox of a chimaera: the constituents live in the same scaffold, but apart. Block copolymers beyond a certain length will always split the assembly, and without further precautions, polymer based chimaerae are intrinsically unstable. To this end, we propose the application of a branched block copolymer as composite compatibilizer, glueing the separate domains together, and thereby stabilizing the chimaeric polymersome.

Direct imaging and mesoscale modelling of phase transitions in a nanostructured fluid.

The kinetics of phase transitions is essential for understanding pattern formation in structured fluids. These fluids play a key role in the morphogenesis of biological cells, and they are very common in pharmaceutical products and plastic materials. Until now, it has not been possible to follow phase transitions in structured fluids experimentally in real time and with high spatial resolution. Previous work has relied on static images and indirect experimental evidence from spatially averaging scattering experiments. Simulating the processes with computer models is a further challenge because of the multiple time and length scales involved. Our movies based on in situ scanning force microscopy show the time sequence of the elementary steps of a phase transition in a fluid film of block copolymer from the cylinder to the perforated lamella phase. The movies validate a versatile simulation model that gives physical insight into the nature of the process. Our approach provides a means of improving the study and understanding of pattern formation processes in nanostructured fluids. We expect a significant impact on nanotechnology where block copolymers serve as self-organized templates for the synthesis of inorganic nanostructured materials.

Nematic-amorphous polymer interfaces in the presence of a compatibilizer.

We introduce and apply a variant of a dynamic self-consistent field simulation in two dimensions to predict the structure of interfaces between a nematic and an amorphous polymer compatibilized by a diblock copolymer. First, we investigate the effect of the nematic order on the polymer polymer interface without compatibilizer. Then we include the compatibilizer and consider two interfacial setups previously used in experiments, i.e., the bilayer setup and the trilayer setup. In the bilayer setup the diblock copolymer is mixed into the amorphous homopolymer and migrates to the interface in the course of the simulation forming a layered structure. We compare the amount of copolymer at the interface for initial concentrations of the copolymer below and above the critical micelle concentration. In the trilayer setup the initial thickness of the diblock copolymer is varied. The resulting interfacial morphology evolves in the competition between the lamellar structure induced by the interface and a micellar structure, which is intrinsic to the copolymer.

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.

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.

Role of dissimilar interfaces in thin films of cylinder-forming block copolymers.

We study the effect of dissimilar interfaces on the phase behavior of cylinder forming block copolymers in thin films by means of dynamic density-functional theory. In this article, we show that dissimilarity of the interfaces induces hybrid structures. These structures appear when the surface fields at the two interfaces stabilize different surface structures and/or reconstructions. We propose a general classification of hybrid structures and give an unifying description of phase behavior of cylinder forming block copolymer films. Our results are consistent with experimental observations.

Phase behavior in thin films of cylinder-forming block copolymers.

We have experimentally determined a phase diagram for cylinder-forming polystyrene-block-polybutadien-block-polystyrene triblock copolymer in thin films. The phase behavior can be modeled in great detail by dynamic density functional theory. 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.

Influence of confinement on the orientational phase transitions in the lamellar phase of a block-copolymer melt under shear flow.

In this paper, we incorporate some real-system effects into the theory of orientational phase transitions under shear flow [M. E. Cates and S. T. Milner, Phys. Rev. Lett. 62 1856 (1989) and G. H. Fredrickson, J. Rheol. 38, 1045 (1994)]. In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates, the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behavior. At lower temperatures, the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behavior might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.