Dynamics of Shear Alignment in a Lamellar Diblock Copolymer:  Interplay of Frequency, Strain Amplitude, and Temperature

Abstract

Rheo-optical methods are used to examine the combined effect of shear frequency, strain amplitude, and temperature on the direction and kinetics of flow-induced alignment in lamellar block copolymers. The development of shear-induced alignment in a nearly symmetric polystyrene−polyisoprene diblock (ODT ≃ 164 °C) is recorded in real time using flow birefringence as a probe of the transient lamellar orientation distribution. As alignment progresses during large amplitude oscillatory shearing, the birefringence shows an initial “fast” and a later “slow” change. While increasing strain amplitude (γo) generally speeds both the fast and the slow processes, below a critical γo the slow process is not observed and a well-aligned state is not achieved. The transient birefringence observed at a particular frequency and temperature, but different strain amplitudes, can be partially superposed by scaling time with However, the “fast” and “slow” processes require different values of n(ω). Estimates of n(ω) show that effects of strain are highly nonlinear and stronger than the simple rescaling of time in terms of either cumulative strain (∼tγo) or cumulative flow energy The effect of temperature enters most strongly through the shift of time scale of molecular relaxations (aT ).

Shear-induced instabilities in layered liquids

“…In some of the systems a third regime is observed at even higher shear rates with a parallel orientation [5,10]. If the starting point is rather a randomly distributed lamellar phase, the first regime is not observed [1,4,12,16]. This last point illustrates that experiments on layered liquids depend on the history of the sample.…”

“…In this appendix we describe the key ingredients of a suitable Maple program. A good starting point for such an approach are the balance equations for the unknown quantities (16, 18 -20, 27, and 28) along with the energy density (1) in the appropriate approximation. These equations are entered directly in Maple, with the unknown quantities being functions of time and the spatial coordinates.…”

Ion Conduction in Microphase-Separated Block Copolymer Electrolytes

“…25 The degree of alignment can be controlled by manipulating variables such as the molecular weight, volume ratio of polymer segments, viscoelastic properties of each polymer component, shear rate (or shear frequency for dynamic shearing), force amplitude, and force direction. 21,22,[26][27][28][29] In one example, Albalak, et al, 25 reported a roll-casting technique to align poly(styrene-block-butadiene-blockstyrene) in the through-plane direction using constant shear. Shear and compression alignment techniques were also successfully applied to the BCE poly(styrenesulfonate-block-methylbutelyne) by Park, et al 12 Although the origin of assembly in mechanical alignment is ascribed to the differences in mechanical properties of each domain, the explicit theory behind the mechanism is still debated.…”

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

“…A third alignment direction, the so called transverse orientation in which the lamellar normal is parallel to the shear direction, has been found to coexist with parallel orientation for entangled poly(styrene-b-ethylenepropylene) (S-EP) diblock copolymer at high frequency and in the strong segregation limit [10]. Other studies have focused on the kinetics of global alignment and have shown that the ordering rate increases with shear frequency, strain amplitude, and temperature [8,11]. Experiments on PS-PI diblocks further show nonlinear effects of the strain amplitude on the alignment rate, and that the time scale for the development of alignment exhibits a power law dependence on the strain amplitude, with an exponent equal to −3 or −5 depending on the stage of alignment and in different frequency regimes [11].…”

“…Other studies have focused on the kinetics of global alignment and have shown that the ordering rate increases with shear frequency, strain amplitude, and temperature [8,11]. Experiments on PS-PI diblocks further show nonlinear effects of the strain amplitude on the alignment rate, and that the time scale for the development of alignment exhibits a power law dependence on the strain amplitude, with an exponent equal to −3 or −5 depending on the stage of alignment and in different frequency regimes [11]. Furthermore, many experiments have indicated that the motion of topological defects plays an important role in the global alignment of microdomains under shear, including the evolution of kink band defects and tilt boundaries [12], as well as the migration and annihilation of partial focal conic defects, boundaries, and tilt walls [8,13].…”