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.

We have used a dynamic density functional theory ͑DDFT͒ for polymeric systems, to simulate the formation of micro phases in a melt of an asymmetric block copolymer, A n B m ( f A ϭ1/3), both in the bulk and in a thin film. In the DDFT model a polymer is represented as a chain of springs and beads. A spring mimics the stretching behavior of a chain fragment and the spring constant is calculated with the Gaussian chain approximation. Simulations were always started from a homogeneous system. We have mainly investigated the final morphology, adopted by the system. First, we have studied the bulk behavior. The diblock copolymer forms a hexagonal packed array of A-rich cylinders, embedded in a B-rich matrix. Film calculations have been done by confining a polymer melt in a slit. Both the slit width and surface-polymer interactions were varied. With the outcomes a phase diagram for confined films has been constructed. Various phases are predicted: parallel cylinders (C ʈ ), perpendicular cylinders (C Ќ ), parallel lamellae (L ʈ ), and parallel perforated lamellae (CL ʈ ). When the film surfaces are preferentially wet by either the A or the B block, parallel oriented microdomains are preferred. A perpendicular cylindrical phase is stable when neither the A nor B block preferentially wets the surfaces. The predicted phase diagram is in accordance with experimental data in the literature and explains the experimentally observed differences between films of asymmetric block copolymers with only two parameters: the film thickness and the energetic preference of the surface for one of the polymer blocks. We have also observed, that confinement speeds up the process of long range ordering of the microdomains.

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.

The influence of confinement on morphology formation in copolymer systems is an important area of interest in theoretical research. We apply dynamic density functional theory to investigate the effect of pores on the morphology formation in a symmetric diblock copolymer system. The pore is represented by a perfect cylindrical tube. Porous systems are important in biology and are gaining interest for applications in nanotechnology. We show that for the pore sizes under investigation two equilibrium morphologies are possible depending on the surface interaction: a perpendicular or slab morphology and a parallel or multiwall tube morphology. The latter is referred to in the article as dartboard morphology. In the dynamic pathway towards this morphology an intermediate metastable helical phase is found. An important observation is that, for a wide range of pore radii and variations of polymer chain length, no mixed parallel/perpendicular morphologies were found: All observed morphologies are insensitive to the pore diameter.

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.

Volume 36, Number 21

A dynamic density functional theory for polymeric systems has been used to investigate the influence of surface fields on the morphology of thin films of asymmetric diblock copolymers, which form cylinders in a bulk system. We have found that noncylindrical structures become stable when one of the blocks is strongly attracted by the surfaces. When the interaction between the surface and the polymer was increased, two transitions occur: (a) from parallel oriented cylinders to parallel oriented perforated lamellae (C | f CL|) and (b) from this perforated lamellae to lamellae (CL| f L|). It has also been observed that the microstructure becomes much more sensitive to the film thickness in the case where the surfaces strongly attract one of the polymer blocks. The influence of the surfaces seems to be limited to a region with a size of the order of one domain-domain distance.

We simulate the microphase separation dynamics of aqueous solutions of the triblock polymer surfactants (ethylene oxide)13(propylene oxide)30(ethylene oxide)13 and (propylene oxide)19(ethylene oxide)33(propylene oxide)19 by a dynamic variant of mean-field density functional theory for Gaussian chains. This is the first 3D mesoscale model for the dynamic behavior of specific complex polymer solutions. Different mesoscale structures (micellar, hexagonal, bicontinuous, and lamellar and dispersed coexisting phases) are formed depending on composition. The numerical results are in good agreement with experiment. The intermediate hexagonal and bicontinuous phases of (ethylene oxide)13(propylene oxide)30(ethylene oxide)13 solution retain a rich defect structure. Concentrated solution (60%) of (propylene oxide)19(ethylene oxide)33(propylene oxide)19 shows the onset of macrophase separation, with small water droplets dispersed throughout the system. We confirm the experimental observation that the lamellar phase formation does not depend on the block sequence. Quenched from homogeneous state, the kinetics of each system consists of a fast local aggregation stage and subsequent slow rearrangement by defect annihilation. We conclude that the simulation method is a valuable tool for description of 3D morphology formation in a wide variety of complex polymer liquids.