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arXiv · 2306.11672

Critical percolation in the ordering kinetics of twisted nematic phases

Renan A. L. Almeida
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Abstract

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds towards a broken $\mathbb{Z}_2$-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale $t_{\textrm{p}}$. At this time, exact formulae for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.

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BibTeXRIS

Renan A. L. Almeida. 2023-06-20. Critical percolation in the ordering kinetics of twisted nematic phases. https://doi.org/10.1103/physrevlett.131.268101

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