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Tilt grain boundaries in a diblock copolymer ordered nanocomposite lamellar phase
17.M. K. Gaines, S. D. Smith, J. Samseth, M. R. Bockstaller, R. B. Thompson, K. O. Rasmussen, and R. J. Spontak, Soft Matter 4, 1609 (2008).
27.Packing frustration is the tendency of block copolymer systems to form interfaces of equal thickness, thus preventing undue stretching of polymer molecules and reducing the conformational entropy contribution to the free energy (Ref. 31). This effect is balanced by the tendency to reduce interfacial energies which would, in the absence of packing frustration, promote structures of constant mean curvature (Ref. 32).
29.A lamellar phase is first stabilized within the calculation box, oriented in a diagonal fashion with respect to the box, using periodic boundary conditions. Then, the boundary conditions of two opposite sides of the box are changed from periodic to reflecting and the structure is reconverged. Only the upper (lower) half of the box is needed to show one tilt grain boundary thus formed, although it is repeated (reflected) to best illustrate the entire tilt structure.
30.For simplicity, only two contours are shown in Fig. 3. In fact, a nonzero probability of finding particles exists away from the kinks, similar to Fig. 2 but to a much smaller extent. The bulk condition of the lamellae would be that found in Figs. 2 and 3 near the boundaries (away from the kinks). Thus, the systems in these figures, or between panels in each figure, would not correspond to exactly the same overall volume fraction. A comparison between the figures is still appropriate given the qualitative nature of the study in that the trends are still valid. For a quantitative comparison, one should vary the overall particle volume fractions to find equal chemical potentials. A grand canonical formalism would be more convenient for such a study.
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