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

Quenching a system below the isotropic-to-liquid-crystal phase transition, one would intuitively expect a random distribution of liquid crystal nuclei growing in the isotropic melt. By fractal dimensional analysis it is demonstrated that the germ distribution is, in fact, not completely random, but rather fractally homogeneous. The fractal dimension was determined as a function of time as the quench depth and sample dimension were varied. The results show that the germ distribution obtained after completing the short-term nucleus growth process as well as late-time coarsening, is independent of the quench depth and sample dimension, which suggest a spatial correlation of germs due to a direct interaction between nuclei.