Fractal Growth Patterns in Liquid Crystals

Abstract

Bent‐core mesogens, the ”banana liquid crystals”, represent a fascinating, novel class of materials with suprising physical properties. During the phase‐ordering process of the liquid crystal from its isotropic melt, fractal growth patterns form (see the picture, in which such a crystal phase, in black, is nucleated from an air bubble, central circle). The fractal growth patterns are qualitatively different from the growth patterns observed for ordinary rodlike liquid crystal molecules.

Effects of Cyclic Heating and Cooling on the Banana-Phase Growing Behaviors of Banana-Shaped Liquid Crystal 1,3-Phenylene-bis[4-(4-octyl phenylimino)methyl]benzoate

“…From the recorded textures for B2 and b3 phases, it is obvious that the aggregates are characteristic of fractals. At this point, our results are in agreement with those reported by Dierking[3,4].…”

Effects of Cyclic Heating and Cooling on the Banana-Phase Growing Behaviors of Banana-Shaped Liquid Crystal 1,3-Phenylene-bis[4-(4-octyl phenylimino)methyl]benzoate

“…From the recorded textures for B2 and b3 phases, it is obvious that the aggregates are characteristic of fractals. At this point, our results are in agreement with those reported by Dierking[3,4].…”

A dynamical model for fractal and compact growth in supercooled systems

“…The theoretical investigation presented above was originally motivated by the observation of contrasting patterns for the growth of liquid crystal phases out of a supercooled amorphous melt (figure 1). As observed via polarising microscopy and digital-image acquisition ( figure 7), standard nematic liquid crystals exhibit compact growth of circular domains (figure 1(a)), while the B2 phase of a bent-core liquid crystal and the smectic C phase of a calamitic liquid crystal grow in the form of irregular fractal-like structures [13][14][15][16][17][18]21] ( figure 1(b)) with an observed dimension very close to that of percolation clusters. Experiments suggest a correlation between relaxation slowdown [26][27][28] and fractal growth for bent-core smectics and calamitic smectics, with relaxation frequencies  …”

“…is the number of boxes of side length d as occupied by the cluster. The same approach has been employed to characterize the fractal dimensions of experimental clusters [13][14][15][16][17][18].…”

Chirality Synchronization of Hydrogen‐Bonded Complexes of Achiral N‐Heterocycles

“…The transmission of chirality over macroscopic ranges (ca. 10 μm) could be explained by the slow formation of the primary seeds, coupled with rapid dendritic growth, transferring chirality (helicity) over macroscopic distances, but limiting periodic order to the nanometer range. As the size of the uniformly aligned areas is much smaller than the wavelength of light, an amorphous optically isotropic phase results.…”

Effects of Cyclic Heating and Cooling on the Banana-Phase Growing Behaviors of Banana-Shaped Liquid Crystal 1,3-Phenylene-bis[4-(4-octyl phenylimino)methyl]benzoate

“…From the recorded textures for B2 and b3 phases, it is obvious that the aggregates are characteristic of fractals. At this point, our results are in agreement with those reported by Dierking[3,4].…”

A dynamical model for fractal and compact growth in supercooled systems

“…The theoretical investigation presented above was originally motivated by the observation of contrasting patterns for the growth of liquid crystal phases out of a supercooled amorphous melt (figure 1). As observed via polarising microscopy and digital-image acquisition ( figure 7), standard nematic liquid crystals exhibit compact growth of circular domains (figure 1(a)), while the B2 phase of a bent-core liquid crystal and the smectic C phase of a calamitic liquid crystal grow in the form of irregular fractal-like structures [13][14][15][16][17][18]21] ( figure 1(b)) with an observed dimension very close to that of percolation clusters. Experiments suggest a correlation between relaxation slowdown [26][27][28] and fractal growth for bent-core smectics and calamitic smectics, with relaxation frequencies  …”

“…is the number of boxes of side length d as occupied by the cluster. The same approach has been employed to characterize the fractal dimensions of experimental clusters [13][14][15][16][17][18].…”

Chirality Synchronization of Hydrogen‐Bonded Complexes of Achiral N‐Heterocycles

“…The transmission of chirality over macroscopic ranges (ca. 10 μm) could be explained by the slow formation of the primary seeds, coupled with rapid dendritic growth, transferring chirality (helicity) over macroscopic distances, but limiting periodic order to the nanometer range. As the size of the uniformly aligned areas is much smaller than the wavelength of light, an amorphous optically isotropic phase results.…”

Effects of Cyclic Heating and Cooling on the Banana-Phase Growing Behaviors of Banana-Shaped Liquid Crystal 1,3-Phenylene-bis[4-(4-octyl phenylimino)methyl]benzoate

“…From the recorded textures for B2 and b3 phases, it is obvious that the aggregates are characteristic of fractals. At this point, our results are in agreement with those reported by Dierking[3,4].…”

A dynamical model for fractal and compact growth in supercooled systems

“…The theoretical investigation presented above was originally motivated by the observation of contrasting patterns for the growth of liquid crystal phases out of a supercooled amorphous melt (figure 1). As observed via polarising microscopy and digital-image acquisition ( figure 7), standard nematic liquid crystals exhibit compact growth of circular domains (figure 1(a)), while the B2 phase of a bent-core liquid crystal and the smectic C phase of a calamitic liquid crystal grow in the form of irregular fractal-like structures [13][14][15][16][17][18]21] ( figure 1(b)) with an observed dimension very close to that of percolation clusters. Experiments suggest a correlation between relaxation slowdown [26][27][28] and fractal growth for bent-core smectics and calamitic smectics, with relaxation frequencies  …”

“…is the number of boxes of side length d as occupied by the cluster. The same approach has been employed to characterize the fractal dimensions of experimental clusters [13][14][15][16][17][18].…”

Chirality Synchronization of Hydrogen‐Bonded Complexes of Achiral N‐Heterocycles

“…The transmission of chirality over macroscopic ranges (ca. 10 μm) could be explained by the slow formation of the primary seeds, coupled with rapid dendritic growth, transferring chirality (helicity) over macroscopic distances, but limiting periodic order to the nanometer range. As the size of the uniformly aligned areas is much smaller than the wavelength of light, an amorphous optically isotropic phase results.…”