Discover Top Posts Tagged with #fractal dimension

@matetikus posztja alapján

Magyarország dimenziója 1.126

Nagy-Magyarország dimenziója 1.131

adjátok vissza a dimenzióinkat!

The Coastline Paradox

On the face of it, it is a simple enough: how long is the coastline of the United Kingdom? The answer, though, is far from straightforward. Two of the most respected and renowned data sources come up with wildly different answers, the CIA Factbook putting it at 12,429 kilometres , while the World Resources Institute stating that it is 19,717 km. How can two respected authorities come up with an…

View On WordPress

#Benoit Mandelbrot #fractal dimension #Lewis Richardson #Science

To evaluate the high-grade breast cancer morphological complexity on mammogram. We conducted a retrospective study using an open source data got from figshare repository. These anonymized data were collected and used for a study approved by the institutional review board. Cranio-Caudal and Medio-lateral mammograms and their tumor segmented images from 66 patients subdivided in two groups high histological grade (n=23) low-grade (low and intermediate, n=41). From breast cancer image segmentation, we extracted fractal dimension using Fraclac, plugin of ImageJ software based on box-counting method. For our analysis we used comparatively the fractal dimension from cranio-caudal (CC) and medio-lateral (MLO) images. We summarized the fractal dimension of our cohort using boxplot and performed the Wilcoxon non-parametric statistic for fractal dimension comparison of two groups (High-grade and low-grade). There was not difference between CC (mean ± std= 1.1583±0.067) andmLO (mean ± std =1.1551±0.055) breast cancer fractal dimension. For the high-grade differentiation, CC andmLO images fractal dimension were contributed respectively at a little difference but without statistically difference (P value=0.438 and 0.435). High-grade fractal dimensions mean were respectively 1.142±0.044 and 1.144±0.075 for CC andmLO images against 1.166±0.050 and 1.160±0.057 for low-grade. It had been recorded a lower mean value of fractal dimension for high-grade breast cancer without statistically significant. This finding shows that the high-grade breast cancer tends to have a regular shape.

#Fractal dimension #Box-counting #High grade breast cancer #Mammogram

FRACTAL DIMENSION-SPLIT

#FRACTAL DIMENSION #DEATHCORE #TECHNICAL DEATHCORE #HEAVY METAL #;METAL #2018 EP #TRANSCENDENCE

Fractal Structure of Microcrystalline Cellulose Obtained by Method of Spray Drying-Juniper Publishers

JUNIPER PUBLISHERS- ACADEMIC JOURNAL OF POLYMER SCIENCE

Abstract

In this research, a fractal structure of beads of different sizes obtained by spray-drying of aqueous dispersions of microcrystalline cellulose (MCC) was studied. These beads are formed as a result of aggregation of rod-shaped cellulose nanocrystalline particles (CNP). It was found that increasing the average radius (R) of the formed MCC beads results in increased porosity (P) and reduced density (ρ). The dependences of P and ρ on scale factor (R/r) can be expressed by power-law equations: p=(R/r)k-dp and p-d (R/r)DP-K ,where the fractal dimensions PD= 2.887 andPD=2.986 are close to Euclidean dimension E=3 for three-dimensional space; r=3nm is radius of cellulose nanocrystalline particles, Po = 0.03cm3/g is porosity and d=1.585g/cm3 is true density (specific gravity) of CNP, respectively. Thus, with the increase in the size of formed MCC beads, the order in the packing of the beads is distorted conforming to theory of diffusion-limited aggregation process.

Keywords: Microcrystalline cellulose (MCC); Spray-drying; MCC bead; Size; Porosity; density; Fractal dimension

Introduction

It is known that various natural and artificial objects and phenomena can be considered as fractals, distinctive features of which are scale invariance (self-similarity) and fractional dimension [1,2]. 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 structure or property on scale factor. In particular, the theory of fractals was applied for description of structure and properties of such wide-spread natural biopolymer as cellulose and also of diverse cellulose materials.

For instance, cellulose fibers were studied by a method of low-temperature nitrogen sorption to measure the dependence of cumulative volume on 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 research [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 2.13 to 2.50, whereas sorption of water vapor gave the fractal dimension of pores less than 1.5 due to altering of cellulose structure under effect of water. The study the distribution of nano-scale cellulose aggregates by method of small-angle X-ray scattering permitted to calculate the fractal dimension D=2.10 [5].

The main purpose of this research was to study the fractal characteristics of Microcrystalline Cellulose (MCC) beads with different sizes prepared by method of spray drying, which can be used as excipient in pharmaceutics and medicine, as well as filler in various composite materials.

Experimental

Material

The initial material was chemical grade cotton cellulose (99 % α-cellulose, DP=2700) of Hercules Inc.

Method of preparation beads of MCC

Cotton cellulose was hydrolyzed with boiling 1.5M sulfuric acid at the acid/cellulose ratio 10 for 1h followed by filtration of the acid and washing of MCC on the filter to neutral pH [6]. The resulting wet cake of MCC was diluted with distilled water to obtain 1-5% dispersions, which were disintegrated in Waring blender at 15,000rpm for 10min to break the agglomerates. To produce beads, the aqueous dispersions of MCC were spray-dried using a lab drier of Pilotech at the following conditions: feeding 10ml/min, air pressure 0.2MPa, inlet temperature 120oC and outlet temperature 60oC.

Sieve analysis

MCC beads of different sizes were separated by screening through sieves with mesh of 80-100, 140-170, 230-270 and 450-635. The average radius of the beads was shown in the Table 1. With rise of the concentration of MCC dispersion from 1 to 5%, an increase in the yield of larger beads was observed.

Scanning electron microscopy

Shape of MCC beads were investigated by electron microscope Hitachi S-4700.

Wide-angle X-ray scattering (WAXS)

Nanostructure of MCC beads was investigated by WAXS method using Rigaku-Ultima Plus diffractometer (CuKa - radiation, l=0.15418nm) [7, 8]. Lateral size (L) of cellulose nanocrystalline particles (CNP) in direction perpendicularly to [200] planes of crystalline unit cell were calculated by modified Scherrer equation taking into account the contribution of instrumental factor and lattice distortions to width of crystalline peak. Minimum radius of CNP was calculated as follows: r = 0.5L.

Sorption method

Sorption of hexane vapor by MCC beads was measured at 25oC with the use of a vacuum Mac-Ben apparatus having helical spring quartz scales [9]. The porosity [p,cm3/g] the beads was calculated by the equation:

where V is total volume of pores (cm3 ) measured at relative vapor pressurep/p0 m is mass of the dry sample (g).

Results and Discussion

SEM studies showed that spray-dried MCC beads have ellipsoidal or spherical shape and contain small rod-like particles (Figure 1). As known, cellulose is semicrystalline linear polysaccharide that consists of elementary nanofibrils and their bundles called microfibrils [10]. Furthermore, each nano-scale fibril is built of ordered rod-like nanocrystallites and low ordered amorphous nanodomains. The three-dimensional ordered nanocrystallites are strong and inaccessible structural elements. As against, the low-ordered amorphous domains are weak and accessible segments of the fibrils. Therefore, cleavage of amorphous domains at the acid hydrolysis leads to formation of rod-shaped nanocrystalline particles (CNP). As a result of spraydrying, the rod-shaped CNP are aggregated by their side surfaces and forms micron sized beads of microcrystalline cellulose with various average radius.

The structural studies showed that CNP isolated from plant biomass have lateral sizes of 4-8nm and length of 100-200nm [11]. As it follows from WAXS results, the average lateral size (L) of CNP made of cotton cellulose is 6nm and their average radius (r) is 3nm or 0.003μm (Table 2).

The study of vapor sorption of inert organic liquid (hexane) revealed that the porosity of MCC beads varies in the range from 0.0757 to 0.0931 cm3/g (Table 3). Moreover, when the average size of the beads increases, their porosity rises.

The dependence of porosity (P) on scale factor (R/r) can be expressed by a power-law function:

where Po is porosity of CNP, DP is fractal dimension; E=3 is Euclidean dimension for three-dimensional space.

After logarithmizing of the function (2), a linear graph was drawn (Figure 2), from which the values of Po = 0.03 [cm3/g]=2.887 were found.

Along with porosity, it is also possible to calculate the density of MCC beads, as follows:

where Vc = d-1 is specific volume of CNP having crystallinity about 80% and true density (specific gravity) d=1.585g/cm3 [10].

Using ρ values and scale factor [R/r](Table 3), the linear dependence can be obtained (Figure 3) by logarithmizing of the function:

From the linearized graph (Figure 3), the value of Dρ =2.986 was calculated.

The results have shown that the small beads contain more densely packed aggregates of CNP than the large MCC beads. According to DLA-theory [2, 12-14], such structural feature indicates that the formation of MCC beads occurs via diffusionlimited aggregation process.

Conclusion

Rod-shaped crystalline nanoparticles (CNP) of cotton cellulose with radius r = 3 nm have a compact packing with high true density (specific gravity) d=1.585g/cm3 and negligible porosity Po=0.03 cm3/g During spray-drying a lateral aggregation of rod-shaped CNP occurs. Moreover, with the development of aggregation process of CNP and increase in size of the formed MCC beads, the order in the packing is distorted conforming to theory of diffusion-limited aggregation process. Consequence of this phenomenon is increase in porosity and decrease in density with the rise in size (average radius R) of the beads. The dependences of porosity (P) and density (ρ) on scale factor (R/r) can be expressed by the following power-law equations:

where the fractal dimensions DP = 2.887 and Dρ = 2.986 are close to Euclidean dimension E=3 for three-dimensional space.

For more Open Access Journals in Juniper Publishers please click on: https://juniperpublishers.com

For more articles in Academic Journal of Polymer Science please click on: https://juniperpublishers.com/ajop/index.php

For more Open Access Journals please click on: https://juniperpublishers.com

#Microcrystalline cellulose (MCC)#Spray-drying #MCC bead #Porosity #Fractal dimension