Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids

The 3D profile surface parameter H _q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H _q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H _q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.     

Surface fractal analysis of pore structure of high-volume fly-ash cement pastes

The surface fractal dimensions of high-volume fly-ash cement pastes are evaluated for their hardening processes on the basis of mercury intrusion porosimetry (MIP) data. Two surface fractal models are retained: Neimark's model with cylindrical pore hypothesis and Zhang's model without pore geometry assumption. From both models, the logarithm plots exhibit the scale-dependent fractal properties and three distinct fractal regions (I, II, III) are identified for the pore structures. For regions I and III, corresponding to the large (capillary) and small (C-S-H inter-granular) pore ranges respectively, the pore structure shows strong fractal property and the fractal dimensions are evaluated as 2.592-2.965 by Neimark's model and 2.487-2.695 by Zhang's model. The fractal dimension of region I increases with w/b ratio and hardening age but decreases with fly-ash content by its physical filling effect; the fractal dimension of region III does not evolve much with these factors. The region II of pore size range, corresponding to small capillary pores, turns out to be a transition region and show no clear fractal properties. The range of this region is much influenced by fly-ash content in the pastes. Finally, the correlation between the obtained fractal dimensions and pore structure evolution is discussed in depth.     

气体吸附法测定二氧化硅干凝胶的分形维数

提出了一种方便、科学有效的利用气体吸附法测定二氧化硅干凝胶等多孔材料分形维数（表面分形维数和孔分布分形维数）的方法，不需要进行一系列的吸附/脱附实验，只需要利用单一气体的一次吸附/脱附实验得出的样品孔分布、比表面数据，与不同的标尺进行关联，即可同时获得表面分形维数和孔分布分形维数.通过误差分析和校正，保证了结果的可靠性.用上述方法测定了二氧化硅干凝胶的分形维数，以FHH法和SAXS法对所得结果进行了比较和验证，并对吸附/脱附过程所得结果的差异进行了初步分析. 关键词： 分形维数 气体吸附 二氧化硅 干凝胶     

Dielectric constant of porous ultra low-k dielectrics by fractal-Monte Carlo simulations

The effective dielectric constant of porous ultra low-k dielectrics is simulated by applying the fractal geometry and Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for effective dielectric constant are derived. The proposed model for the effective dielectric constant is expressed as a function of the dielectric coefficient of base medium and the volume fractions of pores and base medium, fractal dimension for pores, the pore size, as well as random number. The Monte Carlo simulations combined with the fractal geometry are performed. The predictions by the present simulations are shown in good accord with the available experimental data. The proposed technique may have the potential in analyzing other properties such as electrical conductivity and thermal conductivity in porous ultra low-k dielectrics.     

Characterization of electrodeposited nickel film surfaces using atomic force microscopy

Microstructures of nickel surfaces electrodeposited on indium tin oxides coated glasses are investigated using atomic force microscopy. The fractal dimension D and Hurst exponent H of the nickel surface images are determined from a frequency analysis method proposed by Aguilar et al. [J. Microsc. 172 (1993) 233] and from Hurst rescaled range analysis. The two methods are found to give the same value of the fractal dimension D∼2.0. The roughness exponent α and growth exponent β that characterize scaling behaviors of the surface growth in electrodeposition are calculated using the height-difference correlation function and interface width in Fourier space. The exponents of α∼1.0 and β∼0.8 show that the surface growth does not belong to the universality classes theoretically predicted by statistical growth models.     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Evolution of pore and surface characteristics of silica xerogels during calcining

This paper has investigated the effect of calcining temperature (600-1000°C) on the mesopore structure and surface fractal dimension of silica xerogels derived from two-step acid-base-catalyzed TEOS (tetraethyl orthosilicate) systems. Two base contents were adopted in the base step. FE-SEM (field emission gun-scanning electron microscopy) observation and XRD (X-ray diffraction) analysis indicate that gel coarsening, agglomeration and sintering occurred successively with increasing temperature, and those prepared with higher base content exhibit easier agglomeration, lower sintering temperature and weaker crystallizability. Percent mesoporosity and surface fractal dimensions evaluation via image analysis methods shows that the mesoporosity of those prepared with lower base content increases below 700°C and decline at higher temperatures, while the surface fractal dimension appears to decrease above 800°C.     

Fractal Analysis of Surface Roughness of Particles in Porous Media

A fractal dimension for roughness height （RH） is introduced to characterize the degree of roughness or disorder of particle surface characters which significantly influence physical-chimerical processes in porous media. An analytical expression for the fractal dimension of RH on statistically self-similar fractal surfaces is derived and is expressed as a function of roughness parameters. The specific surface area （SSA） of porous materials with spherical particles is also derived, and the proposed fractal model for the SSA of particles with rough surfaces is expressed as a function of fractal dimension for RH and fractal dimension for particle size distribution, relative roughness of particle surface, and ratio of the minimum to the maximum particle diameters of spherical particles.     

An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks

In this paper, an analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks is presented. A dual-domain model is applied to simulate the heterogeneous porous media embedded with a constructal tree network based on the fractal distribution of pore space and tortuosity nature of flow paths. The analytical expressions for seepage velocity, pressure drop, local and global permeability of the network and binary system are derived, and the transport properties for the optimal branching structure are discussed. Notable is that the global permeability (K_n) of the network and the volume fraction (f_n) occupied by the network exhibit linear scaling law with the fractal dimension (D_p) of channel diameter bylogK_n∼0.46D_p and logf_n∼1.03D_p, respectively. Our analytical results are in good agreement with the available numerical results for steady-state soil vapor extraction and indicate that the fractal dimension for pore space has significant effect on the permeable properties of the media. The proposed dual-domain model may capture the characteristics of heterogeneous porous media and help understanding the transport mechanisms of the radial flow in the media.