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Thesis (pdf) - Espci

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2<br />

Probing elastic anisotropy from defect dynamics in<br />

Langmuir Monolayers<br />

2.1 Introduction<br />

The study of topological defects is of general relevance in many areas of<br />

physics and biology, ranging from cosmology to superfluid helium or cell<br />

division. An important motivation arises from the universality of the defects,<br />

which occur in any system with order parameter. Their main properties are<br />

independent of the underlying physics, determined only by symmetries, the<br />

dimension of the order parameter and the defect charge. This universality has<br />

been lately exploited by condensed matter systems such as liquid crystals<br />

which allow to perform relatively easy experiments yielding knowledge in<br />

completely different physical areas.<br />

Of particular interest is the study of the motion of a defect, and the interaction<br />

and annihilation dynamics of defect pairs, which have been extensively<br />

studied by several groups (Ryskin and Kremenetsky, 1991; Svenˇsek<br />

and ˇZumer, 2002; Blanc et al., 2005). A remarkable feature of defect pairs annihilation,<br />

both observed experimentally and numerically, although not fully<br />

understood, is the enhanced mobility of the positively charged defect with respect<br />

to its negative counterpart. Elastic anisotropy (inequality of the elastic<br />

constants) and hydrodynamic effects arising from defect motion (backflow)<br />

have been shown to generically contribute to explain this asymmetry. In fact,<br />

the latter is dominant in the context of bulk (3-d) liquid crystals (Tóth et al.,<br />

2002; Svenˇsek and ˇZumer, 2002; Oswald and Ignés-Mullol, 2005; Blanc<br />

et al., 2005), thus hindering the possibility to develop a simple method to<br />

quantitatively relate material elasticity to defect dynamics, which would be<br />

an interesting alternative to traditional methods to determine the elastic constants<br />

(de Gennes and Prost, 1995; Oswald and Ignés-Mullol, 2005).

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