scholarly journals Evaluation and comparison of bentonite surface fractal dimension and prediction of swelling deformation: Synchrotron radiation SAXS and N2-adsorption isotherms method

2021 ◽  
Vol 269 ◽  
pp. 121331
Author(s):  
Lei Peng ◽  
Bing Chen ◽  
Yongjian Pan
2010 ◽  
Vol 9 (1) ◽  
pp. 13-17
Author(s):  
Silvester Tursiloadi

A technique to determine the surface fractal dimension of mesoporous TiO­2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO­2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted.  Mesoporous TiO­2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH) theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS  values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation.     Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania


Author(s):  
Zofia Sokołowska ◽  
Mieczysław Hajinos ◽  
Christian Hoffmann ◽  
Manfred Renger ◽  
Stefan Sokołowski

2009 ◽  
Vol 25 (1) ◽  
pp. 103-115
Author(s):  
J. L. Liou ◽  
J. F. Lin

AbstractThe cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). The contact parameters, including the total contact force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing the mean separation (d*). The initial plasticity index before contact deformation (ψ)0 is also a factor of importance to the predictions of the contact load (F*t) and contact area (At*) between the model of variable D and G, non-Gaussian asperity heights and circular contact area and the present model of variable D and G, non-Gaussian asperity heights and fractal contact area.


2002 ◽  
Vol 31 (1) ◽  
pp. 76-77
Author(s):  
Zheng-Hong Huang ◽  
Feiyu Kang ◽  
Jun-Bing Yang ◽  
Kai-Ming Liang ◽  
Hui Zhao ◽  
...  

2012 ◽  
Vol 212-213 ◽  
pp. 236-240 ◽  
Author(s):  
Yin Jun Zhou ◽  
Fei Li ◽  
Li Chen ◽  
Zhong Wu Jin ◽  
Jun Wang

Fractal theory is used to describe river bed form. Based on improvements in some aspects of Surface area – Scale Method, such as, estimation of surface area, boundary treatment and so on, the calculation method of surface fractal dimension with irregular boundary is obtained, and the new method has good application on the bed surface fractal dimension calculation. The fractal characteristics of river bed surface morphology are discussed by combination with river-pattern, river regime, river process and changes of BSD. BSD can be used to study some related problems, such as analysis of river regime, distinction of river pattern, calculation of river resistance and so on.


2010 ◽  
Vol 97 (8) ◽  
pp. 084101 ◽  
Author(s):  
Yongping Chen ◽  
Chengbin Zhang ◽  
Mingheng Shi ◽  
George P. Peterson

1991 ◽  
Vol 87 (1) ◽  
pp. 179 ◽  
Author(s):  
Katsumi Kaneko ◽  
Mutsumi Sato ◽  
Takaomi Suzuki ◽  
Yoko Fujiwara ◽  
Keiko Nishikawa ◽  
...  

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