Liquid crystalline fractals: dilatation invariant growth structures in the phase ordering process of 'banana-phases' 

Fractal growth structures are known to be exhibited by numerous systems in condensed matter physics, mostly forming under non-equilibrium conditions. Materials of the 'soft condensed matter' class, including colloids and polymers, are especially rich in fractal growth phenomena. It thus seems surprising that only very few reports on fractal structures in liquid crystals have been given. The likely reason is that conventional calamitic liquid crystals do not exhibit fractal growth aggregates. In contrast, the recently reported bent-core molecules, constituting the so-called liquid crystalline 'banana-phases', do in fact undergo a phase ordering process via aggregates of fractal dimensionality. In this paper the phase ordering process from the isotropic liquid to the liquid crystalline state, as well as the transition from the liquid crystal to the crystalline state, is characterized in terms of fractal dimensions of growth aggregates. Systematic investigations of the phase formation process of different 'banana-phases' as a function of time, aggregate size, cell gap, quench depth and quench rate suggest a general phase ordering process via a percolation mechanism.