2-dimensional fractally homogeneous distribution of liquid crystalline nuclei in the isotropic melt

Quenching system below the isotropic to liquid-crystal phase transition, on e would intuitively expect random distribution of liquid crystal nuclei gro wing in the isotropic melt. By fractal dimensional analysis it is demonstra ted that the germ distribution is, in fact, not completely random, but rath er fractally homogeneous. The fractal dimension was determined as a functio n of time as the quench depth and sample dimension were varied. The results show that the germ distribution obtained after completing the short-term n ucleus growth process as well as late-time coarsening, is independent of th e quench depth and sample dimension, which suggest spatial correlation of g erms due to direct interaction between nuclei.