Double flip of orientation for a lamellar diblock copolymer under shear

The relationship between structure and rheology in a three-dimensional sheared lamellar mesophase

The evolution of a lamellar mesophase from an initially disordered state under shear is examined using simulations of a mesoscale model based on a concentration field ψ that distinguishes the hydrophilic and hydrophobic components. The Landau-Ginzburg free-energy functional is augmented by a term that is minimised for sinusoidal modulations in the concentration field with wavelength λ = (2π/k), and the dynamical equations are the model H equations. The structure and rheology are determined by the relative magnitudes of the diffusion time for coarsening, (λ²/D) and the inverse of the strain rate ^-1, and the Ericksen number, which is the ratio of the shear stress and the layer stiffness. When the diffusion time is small compared with the inverse of the strain rate, there is a local formation of misaligned layers, which are deformed by the imposed flow. There is near-perfect ordering with isolated defects at low values of the Ericksen number, but the defects result in a significant increase in viscosity due to the high layer stiffness. At high values of the Ericksen number, the concentration field is deformed by the mean shear before layers form via diffusion. Cylindrical structures aligned along the flow direction form after about 8-10 strain units, and these evolve into layers with disorder through diffusion perpendicular to the flow. The layers are not perfectly ordered, even after hundreds of strain units, due to the creation and destruction of defects via shear. The excess viscosity is low because the layer stiffness is small compared with the applied shear at a high Ericksen number. This study provides guidance on how the material parameters and imposed flow can be tailored to achieve the desired rheological behaviour.

Nonlinear behavior of nematic platelet dispersions in shear flow

Dispersions of platelets in the nematic phase are submitted to large amplitude oscillatory shear flow and probed by high temporal resolution small angle x-ray scattering. The response displays rich dynamic and structural behavior. Under small amplitude deformations we observe an elastic response, while structurally symmetry is broken: a preferential direction of deformation is selected which induces off-plane orientation of the platelets. We associate the elastic responses with the tilting director of the platelets towards the flow direction at all strain amplitudes. At large strain amplitudes there is a yielding transition between elastic and plastic deformation, accompanied by a flipping of the director. At intermediate strain amplitudes the director has a rich dynamic behavior, illustrating the complex motion of platelets in shear flow. These observations are confirmed by steady-shear flow reversal experiments, which underline the unique character of sheared nematic platelet dispersions.

Nonequilibrium molecular dynamics simulation study on the orientation transition in the amphiphilic lamellar phase under shear flow

By the extensive large-scale nonequilibrium molecular dynamics simulation on an effective generic model-A2B2 tetramer for amphiphiles, we investigate the shear-induced parallel to perpendicular orientation transition in the lamellar phase as a function of segregation degree and shear rate. Under low rate shear flow the evolution of parallel lamellar configurations at different segregation strengths shows a similar kinetic pathway independent of the segregation degree. While under high rate shear flow in which the lifetime of undulation instability exceeds the characteristic time of the applied shear flow, the kinetic pathway of the shear-induced parallel-to-perpendicular orientation transition in lamellar systems is the segregation degree dependent. Comparing the temporal mesoscopic domain morphology, the microscopic chain conformation, and macroscopic observable-viscosity changes with the experimentally proposed mechanisms, we find that the undulation instability, partial breakup of monodomain, grain rotation, and recombination combined with defect migration and annihilation are the kinetic pathway for the parallel-to-perpendicular orientation transition in the lamellar phase in or near the intermediate segregation limit, and that the undulation instability, domain dissolution, and reformation along the preferred direction combined with defect migration and annihilation are the kinetic pathway for the parallel-to-perpendicular orientation transition in the lamellar phase close to the order-to-disorder phase transition point. A detailed underlying microscopic picture of the alignment process illustrates that the orientation transition is driven by the alignment of molecules with shear flow. The orientation diagram that characterizes the steady-state orientations as a function of shear rate and attractive potential depth is built, in which the attractive potential depth takes the role of an inverse temperature, somewhat like the Flory-Huggins interaction parameter. The microscopic mechanism of the critical orientation transition condition is discussed.

Dissipative particle dynamics study on the morphology changes of diblock copolymer lamellar microdomains due to steady shear

The morphology changes of linear diblock copolymer lamellar microdomains under uniform simple shear are studied via the dissipative particle dynamics technique. The parallel and perpendicular reorientations of the lamellae are observed in the simulations, and two different reorientation mechanisms, under small and large shear rates respectively, are proposed. The parallel-to-perpendicular transition is also observed and the kinetics is discussed. Sinusoidal and chevron instabilities due to the shear are found. After relaxation the peculiar "bidirectionally undulating" instability is obtained.

Orientation selection in lamellar phases by oscillatory shears

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shears. The resulting secondary flows break the degeneracy between the parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.

Shear-induced parallel-to-perpendicular orientation transition in the amphiphilic lamellar phase: A nonequilibrium molecular-dynamics simulation study

The present work is devoted to a study of the shear-induced parallel-to-perpendicular orientation transition in the lamellar system by the large-scale nonequilibrium molecular-dynamics (NEMD) simulation. An effective generic model-A2B2 tetramer for amphiphilies is used. The NEMD simulation produces unambiguous evidence that undulation instability along the vorticity direction sets in well above a critical shear rate and grows in magnitude as the shear rate is further increased. At a certain high shear rate, the coherent undulation instability grows so large that defects are nucleated and the global lamellar monodomain breaks into several aligned lamellar domains. Subsequently layers in these domains rotate into the perpendicular orientation with the rotation of chains towards the y direction, merge into a global perpendicular-aligned lamellar monodomain, and organize into a perfect well-aligned perpendicular lamellar phase by the migration and annihilation of edge dislocations and disclinations. The macroscopic observable viscosity as a function of time or shear rate is correlated with the structural response such as the mesoscopic domain morphology and the microscopic chain conformation. The onset of undulation instability concurs with the start-up of shear-thinning behavior. During the orientation transformation at the high shear rate, the complex time-dependent thixotropic behavior is observed. The smaller viscosity in the perpendicular lamellar phase gives an energetic reason for the shear-induced orientation transition.

Aggregation of Poly(ethylene oxide)−Poly(propylene oxide) Block Copolymers in Aqueous Solution: DPD Simulation Study

The dissipative particle dynamics (DPD) simulation method was applied to simulate the aggregation behavior of three block copolymers, (EO)16(PO)18, (EO)8(PO)18(EO)8, and (PO)9(EO)16(PO)9, in aqueous solutions. The results showed that the size of the micelle increased with increasing concentration. The diblock copolymer (EO)16(PO)18 would form an intercluster micelle at a certain concentration range, besides the traditional aggregates (spherical micelle, cylindrical micelle, and lamellar phase); while the triblock copolymer (EO)8(PO)18(EO)8 would form a spherical micelle, cylindrical micelle, and lamellar phase with increasing concentration, and (PO)9(EO)16(PO)9 would form intercluster aggregates, as well as a spherical micelle and gel. New mechanisms were given to explain the two kinds of intercluster micelle formed by the different copolymers. It is deduced from the end-to-end distance that the morphologies of the diblock copolymer and triblock copolymer with hydrophilic ends were more extendible than the triblock copolymer with hydrophobic ends.

Shear alignments in three-dimensional simulations of lamellar phases

Experiments studying layer orientation of sheared lamellar phases have consistently observed not only the seemingly obvious parallel orientation (with layers parallel to the shear plane), but also the so called perpendicular orientation (with layer normals along the vorticity direction) at the condition of higher shear frequencies and near the lamellar phase transition. We find that three-dimensional simulations of a deterministic mesoscopic dynamical equation (without thermal fluctuations) under the convection of simple shear flows have shown exactly such a dependence. The simulations show the important role played by the transverse orientation (layer normal along the velocity direction) and highlight the mechanism of the shear alignment being the competition between the shear frequency and the mesoscopic time scale of pattern organization.

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.

Grazing incidence small-angle X-ray scattering: an advanced scattering technique for the investigation of nanostructured polymer films

Hamburg workshop on the "application of synchrotron radiation in chemistry"With grazing incidence small-angle X-ray scattering (GISAXS) the limitations of conventional small-angle X-ray scattering with respect to extremely small sample volumes in the thin-film geometry are overcome. GISAXS turned out to be a powerful advanced scattering technique for the investigation of nanostructured polymer films. Similar to atomic force microscopy (AFM), a large interval of length between molecular and mesoscopic scales is detectable with a surface-sensitive scattering method. While with AFM only surface topographies are accessible, with GISAXS the buried structure is also probed. Because a larger surface area is probed, GISAXS also has a much larger statistical significance compared to AFM. Due to the high demand on collimation, GISAXS experiments are based on synchrotron radiation. Nanostructures parallel and perpendicular to the sample surface observable in thin poly(styrene- block-isoprene) diblock copolymer films are presented as an example of the possibilities of GISAXS.

Phase separation of a polymer blend driven by oscillating particles

We study the possible formation of ordered structures of a binary polymer blend by introducing mobile particles in a periodically oscillating driving field. The particles which have a preferential attraction to one of the immiscible phases, will significantly perturb the phase separation of the system and breakup the isotropy of the system, so that some interesting structures such as lamellar and cylinder phases are observed by appropriate selection of the simulation parameters. We examine in detail the dependence of formed morphology and domain size on the oscillating fields, the relative composition of mixtures, the diffusion coefficient, and quench depth, and then discuss how to realize stable and highly ordered structures.

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.

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melts under reciprocating shear flow. We show that, similar to the steady shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the [parallel]--> [perpendicular] transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.