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

Characterization of the dynamics of block copolymer microdomains with local morphological measures

We investigate the structure formation in thin films of cylinder forming block copolymers. With in situ scanning probe microscopy image sequences can be recorded with high temporal (2 min per frame) and spatial (10 nm) resolution. We compare different image processing methods for quantitative analysis of the large amount of data. Computing local Minkowski functionals yields local geometrical and morphological information about the observed structures and enables us to track their evolution with time. An alternative characterization method is to reduce the gray scale images to their skeleton and to classify and count the branching points of the skeletonized structure. We tracked the temporal evolution of these measures and computed correlation functions.

Directed copolymer assembly on chemical substrate patterns: a phenomenological and single-chain-in-mean-field simulations study of the influence of roughness in the substrate pattern

The directed assembly of lamella-forming copolymer systems on substrates chemically patterned with rough stripes has been studied using a Helfrich-type, phenomenological theory and Single-Chain-in-Mean-Field (SCMF) simulations. The stripe period matches that of the lamellar spacing in the bulk. The effect of the line edge roughness (LER) of the substrate pattern on the microphase-separated morphology was investigated considering two generic types of substrate LER with a single characteristic wavelength imposed on the edges of the stripes: undulation and peristaltic LER. In both cases, the domain interfaces are pinned to the rough stripe boundary at the substrate and, thus, are deformed. We study how this deformation decays as a function of the distance from the substrate. The simple theory and the SCMF simulations demonstrate that one of the basic factors determining the decay of the roughness transferred into the self-assembled morphology is the characteristic LER wavelength of the substrate pattern; i.e., the distance over which the roughness propagates away from the substrate increases with wavelength. However, both approaches reveal that, for a quantitative understanding of the consequences of substrate LER, it is important to consider the interplay of the pattern wavelength with the other characteristic length scales of the system, such as the film thickness and the bulk lamellar spacing. For instance, in thin films, the induced deformation of the lamellar interface decays slower with distance from the patterned surface than in thicker films. It is shown that the phenomenological theory can capture many of the same qualitative results as the SCMF simulations for copolymer assembly on substrate patterns with LER, but, at the same time, is limited by an incomplete description of the constraints on the polymer chain conformations imposed by the substrate.

Kinetic pathways of gyroid-to-cylinder transitions in diblock copolymers under external fields: cell dynamics simulation

Using cell dynamics simulation we investigate the cubic gyroid morphology of block copolymer melts under simple shear flow and electric field. The electric field should be stronger than a certain critical value to induce transition to a cylindrical phase. In the case of simple steady shear the gyroid-to-cylinder transition was observed even for a very weak shear. Quantitative analysis of pathways of gyroid-to-cylinder transition is performed by means of Minkowski functionals. We found that the kinetics of the gyroid-to-cylinder transition are different under electric field and shear flow. Moreover, the gyroid structure under different strengths of electric field shows different pathways. Different types of intermediates such as five-, four-fold connections and "winding" cylinders are found for different pathways.

Visualizing the dynamics of complex spatial networks in structured fluids

We present a data reduction and visualization approach for the microdomain dynamics in block copolymers and similar structured fluids. Microdomains are reduced to thin smooth lines with colored branching points and visualized with a tool for protein visualization. As a result the temporal evolution of large volume data sets can be perceived within seconds. This approach is demonstrated with simulation results based on the dynamic density functional theory of the ordering of microdomains in a thin film of block copolymers. As an example we discuss the dynamics at the cylinder-to-gyroid grain boundary and compare it to the epitaxial cylinder-to-gyroid phase transition predicted by Matsen [Phys. Rev. Lett. 80, 4470 (1998)].

Nanoscale compositional mapping with gentle forces

Microscopists have always pursued the development of an instrument that combines topography and materials properties analyses at the highest resolution. The measurement of the tiny amount of energy dissipated by a vibrating tip in the proximity of the sample surface has provided atomic force microscopes with a robust and versatile method to determine the morphology and the compositional variations of surfaces in their natural environment. Applications in biology, polymer science and microelectronics illustrate the potential of phase-imaging force microscopy for nanoscale analysis.

Automatization of nanotomography

An approach for automated nanotomography, a layer-by-layer imaging technique based on scanning probe microscopy (SPM), is presented. Stepwise etching and imaging is done in situ in a liquid cell of an SPM. The flow of etching and rinsing solutions after each etching step is controlled with solenoid valves which allow for an automated measuring protocol. The thermal drift and the drift of the piezo scanner is corrected by applying offsets calculated from the cross correlation coefficients between successive images. As an example, we have imaged human bone with approximately 10 nm resolution using tapping mode SPM and successive etching with hydrochloric acid.

Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.

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.

General theory of amplitude-modulation atomic force microscopy

We present a general analytical theory that enables one to determine accurately the unknown tip-sample interactions from the experimental measurement of the amplitude and phase of the oscillating tip in amplitude-modulation atomic force microscopy (AM-AFM). We apply the method to the known Lennard-Jones-type forces and find excellent agreement with the reconstructed results. AM-AFM, widely used in air and liquid, is now not only an imaging tool but also a quantitative force measurement tool.

Rapid transitions between defect configurations in a block copolymer melt

With in situ scanning force microscopy, we image the ordering of cylindrical microdomains in a thin film of a diblock copolymer melt. Tracking the evolution of individual defects reveals elementary steps of defect motion via interfacial undulations and repetitive transitions between distinct defect configurations on a time scale of tens of seconds. The velocity of these transitions suggests a cooperative movement of clusters of chains. The activation energy for the opening/closing of a connection between two cylinders is estimated.

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.

Detailed Structure of Diamond-Type Lipid Cubic Nanoparticles

Supramolecular three-dimensional self-assembly of nonlamellar lipids with fragments of the protein immunoglobulin results in a bicontinuous cubic phase fragmented into nanoparticles with open water channels (cubosomes). The structure of the diamond-type cubic nanoparticles is characterized experimentally by freeze-fracture electron microscopy, and it is mathematically modeled with nodal surfaces emphasizing the fluid-like undulations of the cubosomic interfaces. Based on scaling-up and scaling-down approaches, we present stable and intermediate-kind nanoparticles resulting from the cubosomic growth. Our results reveal the smallest stable diamond-type cubosomic entity that can serve as a building block of more complex nanostructured fluid drug delivery vehicles of therapeutic proteins. The evidence presented for lipid-bilayer undulations in the surface region of the protein/lipid cubosomes could have important consequences for possible applications of these hierarchically organized porous nanoparticles.

Directed Assembly of Block Copolymer Blends into Nonregular Device-Oriented Structures

Self-assembly is an effective strategy for the creation of periodic structures at the nanoscale. However, because microelectronic devices use free-form design principles, the insertion point of self-assembling materials into existing nanomanufacturing processes is unclear. We directed ternary blends of diblock copolymers and homopolymers that naturally form periodic arrays to assemble into nonregular device-oriented structures on chemically nanopatterned substrates. Redistribution of homopolymer facilitates the defect-free assembly in locations where the domain dimensions deviate substantially from those formed in the bulk. The ability to pattern nonregular structures using self-assembling materials creates new opportunities for nanoscale manufacturing.