Motion of a Transverse/Parallel Grain Boundary in a Block Copolymer under Oscillatory Shear Flow

Evolution of unique nano-cylindrical structure in poly(styrene-b-isoprene-b-styrene) prepared under "dynamic packing injection moulding"

This work reports the evolution of ordered nano-cylindrical structures in a thermoplastic elastomer, poly(styrene-b-isoprene-b-styrene) (SIS), utilizing a newly designed processing technique, so-called "dynamic-packing injection moulding". In this injection moulding technique, controlled oscillating shears with different shear cessation times under constant pressure were applied on the moulded samples during cooling. It was found that these additional controlled oscillating shears resulted in a change of orientation in skin-core structures in these samples, compared with corresponding "reference" samples processed via traditional injection moulding (without controlled oscillating shears). For the "reference" samples, a highly oriented PS cylindrical structure combined with relatively weak lateral ordering was observed in their skin layers, whereas the lateral ordering of the PS nano-cylinders gradually disappeared when entering the core region. On the other hand, for the SIS samples obtained via "dynamic-packing injection moulding", the orientation of the PS nano-cylinders in the skin layers was similar to the case of the "reference" sample due to their extremely fast cooling rate. However, the lateral ordering of these cylinders had been extended to the core region. With an increase in the cessation time, the lateral ordering of the PS nano-cylinders was further improved and finally resulted in hexagonal lateral packing along the flow direction in the mould. Furthermore, a mixture of parallel/perpendicular orientation of the cylinders relative to the flow direction was found, particularly when the cessation time was short (such as 3 s). We speculated that this specific perpendicular orientation was a transient state for development of a final parallel orientation aligned with the flow direction with increasing cessation time, accompanied by a further enhancement of the nano-cylindrical parallel orientation. This study could provide a better understanding of the shear and relaxation effects on the structural evolution of this class of thermoplastic elastomers, enhancing supramolecular ordered cylindrical orientation in the core region, and paving a way to tune the nano-structures of block copolymers via this new processing technique to achieve desired properties.

Microphase separation in comblike liquid-crystalline diblock copolymers

The interplay between liquid crystallinity and microphase separation in comblike liquid-crystalline diblock copolymers is examined via a Brazovskii-type phenomenological model using both analytical and numerical calculations. For symmetric diblock copolymers we determine a critical electric field that is required to tilt the orientation of the constituent liquid crystals of the polymer side chains in the microphase-separated lamellar state. Such electrically induced reorientation of the liquid-crystal molecules can lead to substantially large changes of lamellar periodicity. Our numerical results show that highly aligned polymer lamellar domains can self-assemble when the liquid-crystal ordering precedes microphase separation, and that weak electric fields can be used to direct the self-assembly process due to the dielectric anisotropy of the liquid-crystal side chains. We also find that phase separation of asymmetric diblock copolymers can coexist with a network of liquid-crystal nematic orientations, with domain morphology depending on the details of copolymer and liquid-crystal coupling.

Novel mechanical properties in lamellar phases of liquid-crystalline diblock copolymers

Structural properties of flexible nematic diblock copolymers in the lamellar phase are investigated using a mean-field model. We address two complementary questions on the mechanics of the system: 1) How does the nematic order affect the elasticity of the one-dimensional solid? 2) What effect does the block copolymer microstructure has on the orientation of the nematic director? In the limit when the microstructure does not influence the nematic director orientation we predict a soft lamellar compression mode. When the microstructure does influence the nematic director orientation, small compressions lead to conventional elasticity, until a critical strain is reached, where there is then a transition to a softer response. On the other hand, we show that an identifiable lamellar symmetry provides a direction along which the nematic director prefers to align. Our model provides avenues to explore nonlinear properties of flexible diblock copolymers in which the monomers on both sides have mesogenic side groups.

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.

Tilt grain boundary instabilities in three-dimensional lamellar patterns

We identify a finite wave-number instability of a 90 degrees tilt grain boundary in three-dimensional lamellar phases which is absent in two-dimensional configurations. Both a stability analysis of the slowly varying amplitude or envelope equation for the boundary, and a direct numerical solution of an order parameter model equation are presented. The instability mode involves two-dimensional perturbations of the planar base boundary, and is suppressed for purely one-dimensional perturbations. We find that both the most unstable wave numbers and their growth rate increase with epsilon , the dimensionless distance away from threshold of the lamellar phase.

Shear-induced grain boundary motion for lamellar phases in the weakly nonlinear regime

We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn dissipated by net motion of the boundary toward the transverse region. The observed boundary motion is a combination of rigid advection by the flow and order parameter diffusion. The latter includes break up and reconnection of lamellae, as well as a weak Eckhaus instability in the boundary region for sufficiently large strain amplitude that leads to slow wave number readjustment. The net average velocity is seen to increase with frequency and strain amplitude, and can be obtained by a multiple scale expansion of the governing equations.