Fractal analysis of optical textures for quantitative phase characterization of hydrogen-bonded liquid crystals

In the present study, fractal analysis was employed to quantitatively investigate the thermotropic phase behavior of hydrogen-bonded liquid crystals: p, n-alkyl benzoic acid: p-(p′-octyloxy benzylidene)-p-cyanoaniline (nBA:OBCA, n = 6, and 7). Temperature-dependent liquid crystal textures obtained from polarized optical microscopy were quantitatively investigated using fractal analysis, which reflects the degree of structural complexity associated with domain boundaries and textural features. Here, fractal analysis parameters fractal dimension, lacunarity, and edge density were evaluated to characterize spatial complexity, texture heterogeneity, and boundary distribution within different liquid crystal phases. The magnitude and temperature-dependent variation of these parameters provide quantitative structural evidence for differentiating the liquid crystalline phases. Furthermore, first-derivative analysis of fractal dimension was performed to identify the thermotropic phase transitions. The results demonstrate that fractal analysis of polarizing optical microscopic textures provides a reliable, objective, and structurally sensitive approach for quantitative phase characterization of liquid crystals.