Abstract
In this research, the fractal structure of beads of different sizes obtained by the spray-drying of aqueous dispersions of microcrystalline cellulose (MCC) was studied. These beads were formed as a result of the aggregation of rod-shaped cellulose nanocrystalline particles (CNP). It was found that increasing the average radius (R) of the formed MCC beads resulted in increased specific pore volume (P) and reduced apparent density (ρ). The dependences of P and ρ on the scale factor (R/r) can be expressed by power-law equations: P = Po (R/r)E−Dp and ρ = d (R/r)Dd−E, where the fractal dimensions Dp = 2.887 and Dd = 2.986 are close to the Euclidean dimension E = 3 for three-dimensional space; r = 3 nm is the radius of the cellulose nanocrystalline particles, Po = 0.03 cm3/g is the specific pore volume, and d = 1.585 g/cm3 is the true density (specific gravity) of the CNP, respectively. With the increase in the size of the formed MCC beads, the order in the packing of the beads was distorted, conforming to theory of the diffusion-limited aggregation process.
Highlights
It is known that various natural and artificial objects and phenomena can be considered as fractals, distinctive features of which are scale invariance and fractional dimension [1,2].The theory of fractals is widely used in engineering, mathematics, biology, physics, chemistry, and other areas
Can be expressed by power-law equations: P = Po (R/r)E−D p and ρ = d (R/r)D d −E, where the fractal dimensions Dp = 2.887 and Dd = 2.986 are close to the Euclidean dimension E = 3 for three-dimensional space; r = 3 nm is the radius of the cellulose nanocrystalline particles, Po = 0.03 cm3 /g is the specific pore volume, and d = 1.585 g/cm3 is the true density of the CNP, respectively
Cellulose fibers were studied by a method of low-temperature nitrogen sorption to measure the dependence of the cumulative volume on the radius of various pores expressed by the power-law function, from which the fractal dimension from 2.88 to 2.95 was determined [3]
Summary
The theory of fractals is widely used in engineering, mathematics, biology, physics, chemistry, and other areas. According to this theory, the fractal dimension (D) of an object can be determined by logarithmization of power-law dependence of a structure or property on the scale factor. The theory of fractals was applied to describe the structure and properties of such wide-spread natural biopolymers as cellulose as well as diverse cellulose materials. Cellulose fibers were studied by a method of low-temperature nitrogen sorption to measure the dependence of the cumulative volume on the radius of various pores expressed by the power-law function, from which the fractal dimension from 2.88 to 2.95 was determined [3]. In another study [4], the fractal structure of pores in various cellulose materials was studied by nitrogen and water vapor sorption methods; in the case of nitrogen sorption the fractal dimension of pores was from
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