Shear-Induced Lamellar Rotation Observed in a Diblock Copolymer by in Situ Small-Angle X-ray Scattering

Structural response of an ordered block copolymer melt to uniaxial extensional flow

We report in situ small-angle X-ray scattering (SAXS) studies of a cylindrically ordered styrene-ethylene butylene-styrene (SEBS) triblock copolymer melt subjected to uniaxial extensional flow. The flow is applied by stretching strips of polymer melt using a counter-rotating drum extensional flow fixture housed in a custom oven designed to provide X-ray access. SAXS patterns show two distinct modes of structural response during extensional flow: deformation of the microscopic structure, and re-orientation of PS microdomains towards the flow direction. The d-spacings of the hexagonally ordered domains measured parallel and perpendicular to the flow direction deform affinely until Hencky strains of ∼0.2. Departures in extensional viscosity from linear viscoelastic predictions are observed at similar strain. The azimuthal dependence of the primary diffraction peak reveals a complex re-orientation process whereby PS microdomains rotate toward the stretching direction. At intermediate strains, a '4-point' diffraction pattern indicates the presence of two discrete populations of microdomain orientation, attributed to a buckling instability of microdomains initially oriented perpendicular to the stretching direction. Flow-induced deformation and orientation both relax upon cessation of flow, albeit at very different rates, suggesting that these two modes of structural response are largely decoupled.

Mechanochromic photonic gels

Polymer gels are remarkable materials with physical structures that can adapt significantly and quite rapidly with changes in the local environment, such as temperature, light intensity, electrochemistry, and mechanical force. An interesting phenomenon observed in certain polymer gel systems is mechanochromism - a change in color due to a mechanical deformation. Mechanochromic photonic gels are periodically structured gels engineered with a photonic stopband that can be tuned by mechanical forces to reflect specific colors. These materials have potential as mechanochromic sensors because both the mechanical and optical properties are highly tailorable via incorporation of diluents, solvents, nanoparticles, or polymers, or the application of stimuli such as temperature, pH, or electric or strain fields. Recent advances in photonic gels that display strain-dependent optical properties are discussed. In particular, this discussion focuses primarily on polymer-based photonic gels that are directly or indirectly fabricated via self-assembly, as these materials are promising soft material platforms for scalable mechanochromic sensors.

Measuring relative grain-boundary energies in block-copolymer microstructures

The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0≤θ≤85°) the grain-boundary energy is found to depend on the tilt angle as E(θ)∼θ(x), with 2.5>x≥0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures.

Shear alignment and realignment of sphere-forming and cylinder-forming block-copolymer thin films

In common with many other structured fluids, block copolymers can be effectively oriented by shear. This susceptibility to shear alignment has previously been shown to hold even in thin films, containing as few as two layers of spherical microdomains, or even a single layer of cylindrical microdomains. A phenomenological model has been proposed [M. W. Wu, R. A. Register, and P. M. Chaikin, Phys. Rev. E 74, 040801(R) (2006)] to describe the alignment of such block-copolymer films, yielding the microdomain lattice order parameter as a function of shearing temperature, stress, and time. Here we directly test the central idea of that model, that the grains which are most misaligned with the shear direction are selectively destroyed, to reform in a direction more closely aligned with the shear. Films are first shear aligned from a polygrain state into a monodomain orientation and are then subjected to a second shear, at a variable stress (sigma) and misorientation angle (deltatheta) relative to the monodomain director, allowing the effects of sigma and deltatheta to be independently and systematically probed. For both cylinder-forming and sphere-forming block copolymers, these experiments confirm the basic premise of the model, as the stress required for realignment increases monotonically as deltatheta becomes smaller. For a cylinder-forming block copolymer, we find that the characteristic stress sigma(c) required to realign cylinders from one monodomain orientation to another is indistinguishable from that required to generate a monodomain orientation from the polygrain state. By contrast, the hexagonal lattice of spheres requires a value of sigma(c) more than 3 times as high for reorientation than for generation of the initial monodomain orientation.

Electric field alignment of a block copolymer nanopattern: direct observation of the microscopic mechanism

Using quasi-in-situ scanning force microscopy we study the details of nanopattern alignment in ABC terblock copolymer thin films in the presence of an in-plane electric field. Because of the surface interactions and electric field the lamellae are oriented both perpendicular to the plane of the film and parallel to the electric field. We identified two distinct defect types which govern the orientation mechanism. Ring-like (tori) and open-end defects dominate at the early stage of the orientation process, while mainly classic topological defects (disclinations and dislocations) are involved in long-range ordering at the late stages. Comparison of the time evolution of the defect density with the evolution of the orientational order parameter suggests that tori-defects are essential for the effective reorientation. Further, the quasi-in-situ SFM imaging allowed us to elucidate the influence of the electric field strength on the propagation velocity of the topological defects.

Phase-field modeling of the formation of lamellar nanostructures in diblock copolymer thin films under inplanar electric fields

Recent experiments show that external inplanar electric field can be employed to guide the molecular self-assembly in diblock copolymer (BCP) thin films to form lamellar nanostructures with potential applications in nanotechnology. We study this self-assembly process through a detailed coarse-grained phase-separation modeling. During the process, the free energy of the BCP films is modeled as the Ginzburg-Landau free energy with nonlocal interaction and electrostatic coupling. The resulting Cahn-Hilliard (CH) equation is solved using an efficient semi-implicit Fourier-spectral algorithm. Numerical results show that the morphology of order parameter formed in either symmetric or asymmetric BCP thin films is strongly influenced by the electric field. For symmetrical BCPs, highly ordered lamellar nanostructures evolved along the direction of the electric field. Phase nucleation and dislocation climbing in the BCP films predicted by the numerical simulation are in a good agreement with those observed in recent BCP electronanolithography. For asymmetrical BCPs, numerical simulation shows that nanodots are guided to align to the electric field. Furthermore, in the case of high electric field, nanodots formed in asymmetrical BCPs may further convert into highly ordered lamellar nanostructures (sphere-to-cylinder transition) parallel to the electric field. Effects of the magnitude of electric field, BCP asymmetry, and molecular interaction of BCPs on the self-assembly process are examined in detail using the numerical scheme developed in this study. The present study can be used for the prediction of the formation of nanostructures in BCP thin films and the quality control of BCP-based nanomanufacturing through optimizing the external electric fields.

A rheo-optical apparatus for real time kinetic studies on shear-induced alignment of self-assembled soft matter with small sample volumes

In soft materials, self-assembled nanoscale structures can allow new functionalities but a general problem is to align such local structures aiming at monodomain overall order. In order to achieve shear alignment in a controlled manner, a novel type of rheo-optical apparatus has here been developed that allows small sample volumes and in situ monitoring of the alignment process during the shear. Both the amplitude and orientation angles of low level linear birefringence and dichroism are measured while the sample is subjected to large amplitude oscillatory shear flow. The apparatus is based on a commercial rheometer where we have constructed a flow cell that consists of two quartz teeth. The lower tooth can be set in oscillatory motion whereas the upper one is connected to the force transducers of the rheometer. A custom made cylindrical oven allows the operation of the flow cell at elevated temperatures up to 200 degrees C. Only a small sample volume is needed (from 9 to 25 mm(3)), which makes the apparatus suitable especially for studying new materials which are usually obtainable only in small quantities. Using this apparatus the flow alignment kinetics of a lamellar polystyrene-b-polyisoprene diblock copolymer is studied during shear under two different conditions which lead to parallel and perpendicular alignment of the lamellae. The open device geometry allows even combined optical/x-ray in situ characterization of the alignment process by combining small-angle x-ray scattering using concepts shown by Polushkin et al. [Macromolecules 36, 1421 (2003)].

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.

Shear-induced undulation of smectic-A: Molecular Dynamics simulations vs. analytical theory

Experiments on a variety of systems have shown that layered liquids are unstable under shear even if the liquid layers are planes of constant velocity. We investigate the stability of smectic- A like liquids under shear using Molecular Dynamics simulations and a macroscopic hydrodynamic theory (including the layer normal and the director as independent variables). Both methods show an instability of the layers, which sets in above a critical shear rate. We find a remarkable qualitative and reasonable quantitative agreement between both methods for the spatial homogeneous state and the onset of the instability.

Shear-induced instabilities in layered liquids

Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic-A-like systems, we consider an extended formulation of smectic-A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normal p(circ)) and the director n(circ) of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in nonequilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle between n(circ) and p(circ), which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers. We generalize our earlier approach [G. K. Auernhammer, H. R. Brand, and H. Pleiner, Rheol. Acta 39, 215 (2000)] and include the cross couplings with the velocity field and the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of various material parameters on the instability. Comparing our results to recent experiments and molecular dynamic simulations, we find a good qualitative agreement.

Microscopic mechanisms of electric-field-induced alignment of block copolymer microdomains

We investigate the microscopic mechanisms responsible for microdomain alignment in block copolymer solutions exposed to an electric field. Using time-resolved synchrotron small-angle x-ray scattering, we reveal two distinct processes, i.e., grain boundary migration and rotation of entire grains, as the two dominant microscopic mechanisms. The former dominates in weakly segregating systems, while the latter is predominant in strongly segregated systems. The kinetics of the processes are followed as a function of polymer concentration and temperature and are correlated to the solution viscosity.