Theory of T junctions and symmetric tilt grain boundaries in pure and mixed polymer systems

Abstract

We apply self-consistent-field theory to T junctions and symmetric tilt grain boundaries in block copolymer systems with and without the addition of homopolymer. We find that, in the absence of homopolymer, T junctions have a larger free energy per unit area than that of the symmetric tilt junctions with which they compete except for a range of angles between about 100°and 130°. With the addition of homopolymer, this range increases. These results are quite consistent with experiment. As the angle between grains increases towards 180°, the T junction undergoes a morphological change somewhat similar to that which occurs in symmetric tilt grain boundaries. At the onset of this change, the free energy per unit area decreases markedly.

Kinetics of directed self-assembly of block copolymers on chemically patterned substrates

“…5 is much larger than the tension of the internal AB interface, γ AB R e0 2 /k B T √N ≈ χN/6 and therefore even the liquid of segments will wet the corresponding lines of the chemical pattern. The grain boundary tension typically adopts much smaller values [19,20]. Eventually the misaligned top grain becomes so thin that the shifted stripes break up into spots [9], and defect-free standing lamellae are established at t = 14000 SMC ≈ 1.1τ .…”

“…/R e0 2 [19,20] and the typical defect area is of the order of a few lamellar spacings L 0 times the film thickness…”

Tilt grain boundaries in a diblock copolymer ordered nanocomposite lamellar phase

“…4 In block copolymers, grain boundaries have been studied both experimentally and theoretically (see, for example, Refs. [5][6][7][8][9][10]). An experimental study by Listak and Bockstaller 11 represents the first attempt to understand grain boundary formation in block copolymer nanocomposites.…”

“…Listak and Bockstaller hypothesized that particles locate where they do because they relieve packing frustration and allow the polymer to stretch less, just as in the case of added homopolymers. 4,9,10 An advantage of using nanoparticles is that they can be eas ily distinguished from the polymer and provide a map of regions of high packing frustration. The present theoretical results provide evidence in support of the hypothesis of Listak and Bockstaller, reproducing their regions of highest particle aggregation but also predicting particle locations in other places they did not observe, locations that are also regions of high packing frustration in diblock copolymer tilt grain boundaries.…”

Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

“…For controlling the self-assembled structures and improve the material characteristics for applications in nanoscale device manufacturing, one would like to understand the properties of defects and the structure and thermodynamics of grain boundaries [181][182][183][184][185][186], where domains with different orientations of the periodic structure meet, or interfaces between coexisting morphologies.…”