Calculating Surface Fractal Dimensions of Adsorbents

Neimark, Alexander V.

doi:10.1177/026361749000700402

Cited by 107 publications

(38 citation statements)

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“…Its fractal dimension is associated with other structures and performance parameters. Various approaches have been proposed in the literature to evaluate the fractal dimension, such as the yard stick method [10] , the gas adsorption method [11][12][13] , the thermodynamic method [14,15] , mercury porosimetry [16] , the small angle X-ray diffraction method [17] , the nuclear magnetic resonance (NMR) method [18] and the scanning electronic microscope (SEM) method [19] . Generally, the most popular method is the gas adsorption method which often uses nitrogen, carbon dioxide and water vapor as adsorbates.…”

Section: Introductionmentioning

confidence: 99%

Surface pore tension and adsorption characteristics of polluted sediment

Fang

Chen

2008

Sci. China Ser. G-Phys. Mech. Astron.

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Most natural sediment particles have numerous pores and a complex surface texture which facilitates their adsorption of contaminants. Particle surface structure, therefore, is an important instrumental factor in the transport of contaminants, especially in water environments. This paper reports on the results of adsorption-desorption experiments to analyze polluted sediment surface pore tension characteristics performed on samples from the bottom of Guanting Reservoir. In our analysis, the Frenkel-Halsey-Hill (FHH) equation is applied to calculate the fractal dimensions of particles to quantify the surface roughness and pore tension characteristics. The results show that the surface fractal dimensions of sediment particle surfaces normally measure from 2.6 to 2.85. The volume of pores smaller than 10 nm changes significantly after being contaminated with pollutants and the fractal dimension decreases because the pores adsorb the contaminants. sediment pollution, pore distribution, fractal dimension, adsorption mechanics

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Section: Introductionmentioning

confidence: 99%

Surface pore tension and adsorption characteristics of polluted sediment

Fang

Chen

2008

Sci. China Ser. G-Phys. Mech. Astron.

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“…Both methods assume the applicability of the Washburn equation (22). The first method supposes a fractal pore size distribution (23)(24)(25)(26) while the other one, the so-called thermodynamic method, supposes a fractal pore surface (27)(28)(29)(30). In this work we will use the thermodynamic method, as it appears more straightforward for calculations.…”

Section: Methodsmentioning

confidence: 99%

Fractal Characterization of Wide Pore Range Catalysts: Application to Pd–Ag/SiO2 Xerogels

Blacher

Heinrichs

Sahouli

et al. 2000

Journal of Colloid and Interface Science

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“…Natural objects display the fractal behavior in a limited range of scales (Neimark, 1990;Pfeifer and Obert, 1889). For many porous systems, the fractal behaviour has been represented as a power law relationship between a perimeter P (surface area, porosity) and the radius r:…”

Section: Appendixmentioning

confidence: 99%

Effect of pH and zinc stress on micropore system of rye roots

Szatanik-Kloc¹

2012

International Agrophysics

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A b s t r a c t. After zinc stress the total micropore volume decreased remarkably while the average micropore radius increased remarkably for the rye roots. Pore size distribution functions of the roots after the additional zinc application showed the decrease of the small micropore fraction from ca 2 to 10 nm and the increase of the large micropore from ca 22 to 50 nm. The root surface pores were fractal. After the stress pore fractal dimension increased. The changes of the microporosity observed in the roots surface can be related to the high content of zinc in the cell wall and/or due to the shortage of Ca +2 the intercellular spaces particularly in the tissues of seminal cortex of the studied roots might have grown.K e y w o r d s: rye roots, micropore, zinc stress, pH, fractal dimension INTRODUCTION Plant roots are highly porous. It has been demonstrated that the porous structure exists in the fibre -vascular bundles of the roots in the secondary xylem which transports water and mineral salts from the roots to the shoot (active transport) and in the phloem which transports products of the photosynthesis (Evert and Eichhorm, 2006). The active transport precedes the passive transport in which water and ions are transported through apoplasts (cell walls and intercellular spaces) of the cells that build the epidermis and the primary cortex of the root. The porous structure of the apoplasts of these tissues has been shown (Carpita, 1982;Carpita et al., 1979;Fleischer et al., 1999). Pores of such dimensions can also be measured by eg osmotic permeability (Carpita et al., 1979) or microscopy. Such pores are important for ionic and molecular transport processes (Clarkson, 1991;Canny, 1995).The adsorption -desorption methods as describing water vapour condensation process occurring in the pores us to estimate various pore parameters as: volume, distribution of sizes, average radii and/or fractal dimensions. Using water vapour desorption data pores from~1 to a few tens of nanometers in radius can be detected and characterized. However, it remains unclear whether the water desorption technique provides results compatible with other methods. The differences may arise, among others, from various water status of the investigated root sample. The geometry of biological materials strongly depends on moisture (swelling, irreversible shrinking after drying etc.). Also in the indirect experimental methods eg osmotic permeability or water vapour desorption) the results depend strongly on the assumptions applied in calculations. The geometric structure of the surface or the pore system may be highly irregular. The geometrical shape of many natural objects is self-similar at different scales of observation, which can be characterized by the fractal dimension, D (Pfeifer and Obert, 1989;Soko³owska, 2009). In this paper, a fractal model of polymolecular adsorption-desorption was used to test how self -similarity of root surfaces was altered by Zn toxicity (detailed in the Appendix). Zinc is absorbed by the plants as the microelem...

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Calculating Surface Fractal Dimensions of Adsorbents

Cited by 107 publications

References 8 publications

Surface pore tension and adsorption characteristics of polluted sediment

Surface pore tension and adsorption characteristics of polluted sediment

Fractal Characterization of Wide Pore Range Catalysts: Application to Pd–Ag/SiO2 Xerogels

Effect of pH and zinc stress on micropore system of rye roots

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