Density and concentration field description of nonperiodic structures

Details Density and concentration field description of nonperiodic structures Density and concentration field description of nonperiodic structures

2011-08-22

arxiv.org/abs/1108.4444v1

Phys. Rev. E 84, 051505 (2011)

Physics

Condensed Matter

Soft Condensed Matter

16 pages, 16 figures

Scientific paper

10.1103/PhysRevE.84.051505

We propose a simple nonlocal energy functional that is suitable for the continuum field characterization of nonperiodic and localized textures. The phenomenological functional is based on the pairwise direction-dependent interaction of field gradients that are separated by a fixed distance. In an appendix, we describe the numerical minimization of our functional. On that basis, we investigate the kinetic evolution of thread-like stripe patterns that are created by the functional when we start from an initially disordered state. At later stages, we find a coarse-graining that shows the same scaling behavior as was obtained for the Cahn-Hilliard equation. In fact, the Cahn-Hilliard model is contained in our characterization as a limiting case. A slight modification of our model omits this coarse-graining and leads to nonperiodic stripe phases. For the latter case, we investigate the temporal evolution of the defects (end points) of the thread-like stripes. In view of possible applications of this functional, we discuss a possible characterization of polymeric systems and vesicles. The statistics of the growth of the thread-like structures is compared to the case of step-growth polymerization reactions. Furthermore, we demonstrate that the functional may be applied for the study of vesicles in a continuum field description. Basic features, such as the tendency of tank-treading in simple shear flows and parachute folding in pipe flows, are reproduced.

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