Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

• Published in: Gels Vol. 7; no. 2; p. 46
• Main Authors: Nasr, Pedram, Leung, Hannah, Auzanneau, France-Isabelle, Rogers, Michael A
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 14.04.2021; MDPI
• Subjects: 1,3:2,4-Dibenzylidene sorbitol; Agglomeration; Cayley Tree; Crystallization; Euclidean geometry; fractal dimension; Fractal geometry; Fractal models; fractality; Fractals; Morphology; Polyethylene glycol; self-assembled fibrillar networks (SAFiNs); Self-assembly; Self-similarity; solvent viscosity; Solvents; Sorbitol; Viscosity; supercooling; 1,3:2,4-Dibenzylidene sorbitol; crystallization; fractal dimension; solvent viscosity; Cayley Tree; fractality; self-assembled fibrillar networks (SAFiNs)
• ISSN: 2310-2861; 2310-2861
• DOI: 10.3390/gels7020046

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle-cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.