2021
DOI: 10.3390/gels7020046
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Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Abstract: 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 a… Show more

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Cited by 6 publications
(4 citation statements)
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“…Transmission electron microscopy (TEM) imaging (see Figure 2C) showed the formation of eADF4(C16) nanofibrils with diameters of 9.0 ± 1.0 nm ( n = 20), indicating fractal fibrillar growth upon protein self‐assembly and consequent gelation. [ 26 ] Liu and Sawant adapted Avrami's equation for the case of time‐dependent fractal growth, replacing n with the fractal dimension D f . [ 27 ] Interestingly, besides the significantly increased rate constant k , a decrease in D f from 2.85 to 2.34 was observed (Figure 2B).…”
Section: Resultsmentioning
confidence: 99%
“…Transmission electron microscopy (TEM) imaging (see Figure 2C) showed the formation of eADF4(C16) nanofibrils with diameters of 9.0 ± 1.0 nm ( n = 20), indicating fractal fibrillar growth upon protein self‐assembly and consequent gelation. [ 26 ] Liu and Sawant adapted Avrami's equation for the case of time‐dependent fractal growth, replacing n with the fractal dimension D f . [ 27 ] Interestingly, besides the significantly increased rate constant k , a decrease in D f from 2.85 to 2.34 was observed (Figure 2B).…”
Section: Resultsmentioning
confidence: 99%
“…Previous studies have reported that two growth modes of gel networks (bulb growth mode and fiber growth mode) can control the gel properties [ 16 ]. The Avrami model has been widely used to analyze the dynamics of small and macromolecular polymers, in which the obtained kinetic parameters are closely related to the growth dimension and the nucleation mechanism, establishing a relationship between dynamics and gel structures [ 17 , 18 ]. According to the difference in the Avrami factor, the process of fiber network structure is studied from one-dimensional growth to the whole fiber network.…”
Section: Introductionmentioning
confidence: 99%
“…This fact has inspired a variety of applications of the Avrami model that have stretched far beyond the process of crystallization. Some examples include: gelation [3][4][5], the adsorption of solutes [6][7][8] and…”
Section: Introductionmentioning
confidence: 99%