Measuring relative grain-boundary energies in block-copolymer microstructures

Understanding grain-boundary energies in block-copolymer systems remains a key challenge in polymer physics. Prior research has shown that grain boundaries influence microstructure evolution in inorganic materials. However, the relationship between tilt angle and grain-boundary energy in block-copolymers is not well established. This uncertainty drives the need for precise measurements in strongly segregated systems. No prior work had resolved the scaling behavior of grain-boundary energy across a wide tilt-angle range. The transition between different grain-boundary morphologies is also poorly understood. Existing models often assume a linear dependence on tilt angle, but this may not apply universally. The inverse relationship between grain-boundary energy and frequency is a known phenomenon in inorganic systems. That uncertainty motivated this study to clarify the energy-misorientation relationship in block-copolymers.

This study aimed to determine how grain-boundary energy varies with tilt angle in a strongly segregated lamellar block copolymer. The researchers focused on symmetric tilt grain boundaries and their behavior at triple junctions. They sought to identify the scaling relationship between energy and tilt angle. The specific problem addressed was the lack of empirical data on grain-boundary energy at large misorientations. The motivation stemmed from the need to understand microstructure evolution in block-copolymer systems. Prior assumptions about linear scaling were not supported by experimental evidence. The study also aimed to clarify the structural transition between chevron and omega morphologies. The researchers proposed that boundary energy plays a key role in grain coarsening, similar to inorganic systems.

The researchers analyzed dihedral angles at grain-boundary triple junctions to estimate grain-boundary energies. They used a strongly segregated lamellar block copolymer as the model system. The tilt-angle range was divided into low, intermediate, and large misorientation categories. For each category, they measured the dihedral angles and calculated the corresponding energies. The scaling behavior of energy with tilt angle was determined using power-law analysis. The transition between chevron and omega morphologies was identified through structural observations. The inverse relationship between energy and frequency was tested using statistical methods. The experimental uncertainty was quantified to assess the validity of the energy-angle independence at large misorientations.

The study found that grain-boundary energy scales with tilt angle as E(θ)∼θ(x), where 2.5 > x ≥ 0 for low and intermediate misorientations. At large misorientations, the energy was independent of tilt angle within experimental uncertainty. The transition between the two scaling regimes occurred at a tilt angle of approximately 85°. The chevron morphology dominated at lower angles, while the omega morphology appeared at higher angles. The inverse relationship between energy and frequency was confirmed across all tilt angles. The energy-misorientation relationship was not linear, as previously assumed. The structural transition was linked to changes in grain-boundary morphology. These findings suggest that boundary energy significantly influences grain coarsening in block-copolymer systems.

The authors concluded that grain-boundary energy in block-copolymers depends on tilt angle in a non-linear manner. The energy scales with a power law for low and intermediate misorientations. At large misorientations, the energy becomes independent of tilt angle. The transition between scaling regimes corresponds to a change in grain-boundary morphology. The inverse relationship between energy and frequency supports the role of boundary energy in grain coarsening. The findings align with observations in inorganic polycrystalline systems. The study provides empirical evidence for the energy-misorientation relationship in block-copolymers. The researchers propose that boundary energy is a key parameter during microstructure evolution.