Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.     

焦化过程半焦孔隙结构时空变化规律的实验研究——孔结构的分形特征及其变化

应用分形理论的概念,结合压汞法测得的半焦孔隙结构数据,建立孔结构分形特征模型,考察了焦化过程中不同焦化温度、不同横向空间位置半焦孔隙结构分形特征及其变化规律。结果表明,孔径大于5μm 的孔不具有分形特征,孔径为20nm～5μm孔的孔隙结构具有分形特征,其分形维数为2.45～2.83,可以用分形维数定量表征孔隙结构;相同空间位置下,半焦孔结构分形维数低温时较高,随温度逐渐升高先减小,然后增大再减小;同一空间位置不同温度下分形维数的变化量较小(< 0.15),表明温度对半焦孔隙结构复杂程度的影响不明显;相同焦化温度下,半焦中心和边缘处的孔结构分形维数大于中间部位,表明中心位置和边缘位置处的孔隙结构要比中间位置处的复杂。     

Probing Ganglia Dissolution and Mobilization in a Water-Saturated Porous Medium using MRI

Magnetic resonance imaging (MRI) is used to probe the evolution of geometric characteristics such as the volume, shape, surface area, and cluster size of octanol ganglia trapped in a model porous medium, in this case a packing of spheres, as they dissolve into a mobile aqueous phase. The resulting pore-scale information is used to assess various assumptions used in existing models of the dissolution process. Dissolution of the ganglia was characterized by a reduction in the overall number of ganglia with little effect on the shape and mean of the volume distribution of the ganglia. This apparently anomalous result is explained by dissolution of the ganglia until they reach a critical size, which is dependent on the structure of the pore space, at which point they are mobilized and subsequently removed from the porous medium. The shape of the entrapped ganglia is characterized by a fractal dimension in the range 2.2-2.3, suggesting that models which assume a Euclidean geometry for the entrapped ganglia are appropriate. No significant change in the shape of entrapped ganglia is observed during dissolution. In agreement with the results of earlier workers, most hydrocarbon ganglia exist as singlets within the pore structure. Copyright 2000 Academic Press.     

Theoretical approach to ion penetration into pores with pore fractal characteristics during double-layer charging/discharging on a porous carbon electrode

The effects of pore fractal characteristics on the kinetics of double-layer charging/discharging on a porous carbon electrode were investigated by using theoretical calculations of potentiostatic current transients (PCTs) and cyclic voltammograms (CVs). Prior to theoretical calculation, it was experimentally evidenced that pore fractality is clearly possessed by the porous carbon electrode. From the analyses of the PCTs and the CVs theoretically calculated at various values of pore fractal dimension dF,pore, inner cutoff length rmin, and outer cutoff length rmax of the pore fractality, it was found that as dF,pore increased, the absolute values of the derivatives of the logarithmic PCTs decreased to 0.5, and the current decayed more slowly with time. The rate capability gamma decreases with increasing dF,pore over the whole scan-rate range, which leads to the lower power density. As rmin increased, the current decayed more rapidly in the later stage of the PCT, which is mainly limited by the smaller pores. On the other hand, as rmax increased, the current decayed more rapidly in the earlier stage of the PCT, which is mainly determined by the larger pores. Moreover, the larger values of rmin and rmax enhance the rate capability gamma as well, but they reduce the double-layer capacitance. The beneficial contribution of the larger pores to the power density competes with the detrimental contribution of those pores to the energy density.     

Evaluation of methods for determining the pore size distribution and pore-network connectivity of porous carbons

The pore size distribution (PSD) and the pore-network connectivity of a porous material determine its properties in applications such as gas storage, adsorptive separations, and catalysis. Methods for the characterization of the pore structure of porous carbons are widely used, but the relationship between the structural parameters measured and the real structure of the material is not yet clear. We have evaluated two widely used and powerful characterization methods based on adsorption measurements by applying the methods to a model carbon which captures the essential characteristics of real carbons but (unlike a real material) has a structure that is completely known. We used three species (CH4, CF4, and SF6) as adsorptives and analyzed the results using an intersecting capillaries model (ICM) which was modeled using a combination of Monte Carlo simulation and percolation theory to obtain the PSD and the pore-network connectivity. There was broad agreement between the PSDs measured using the ICM and the geometric PSD of the model carbon, as well as some systematic differences which are interpreted in terms of the pore structure of the carbon. The measured PSD and connectivity are shown to be able to predict adsorption in the model carbon, supporting the use of the ICM to characterize real porous carbons.     

Size exclusion chromatography on porous fractals

Summary Some porous packings used in chromatography have been claimed to be fractals with a scale of sizes a<l<L, where a is a molecular size and L is the size of the largest pores. For a fractal porous packing, the excluded volume for molecules in solution in the vicinity of the packing surface is directly related to D_f, the fractal dimension of the pore surface (2<D_f<3). Since retention in size exclusion chromatography is itself directly related to this excluded volume, the fractal nature of the packing provides a model of retention in this technique. According to this model there is a linear relationship between log R_s and log(1-K_d), where R_s is the hydrodynamic radius of the solute macromolecules and K_d the distribution coefficient. The fractal dimension is derived from the slope of this plot. Size exclusion chromatographic retention data have been analyzed according to the model. It is found that some HPLC packings are fractals with fractal dimensions ranging from about 2.15 to 2.6, depending on the material. Such a large range of D_f values indicates large variations in the selectivities and domains of applications of the different packings. For some classical gel filtration chromatographic gels, the fractal retention model does not seem to apply.Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.     

超级电容器炭电极材料孔结构对其性能的影响

采用无瓶颈的系列酚醛树脂活性炭为电极材料，用氮吸附和恒流充、放电，以及交流阻抗法，研究孔径和孔表面积等孔结构对其性能的影响.结果表明，活性炭电极材料双电层电容与微孔(孔宽度< 2.0 nm)表面和外孔(孔宽度 >2.0 nm)表面都有关系，但主要取决于微孔表面双电层电容.微孔表面比电容为21.4 μF•cm－2，外孔表面比电容< 10 μF•cm－2.外孔表面比电容较低可能是由于空间电荷层的影响.微孔孔径较大的炭材料具有高比电容和良好的高倍率放电的特性.     

Nondestructive technique for the characterization of the pore size distribution of soft porous constructs for tissue engineering

Polymer scaffolds tailored for tissue engineering applications possessing the desired pore structure require reproducible fabrication techniques. Nondestructive, quantitative methods for pore characterization are required to determine the pore size and its distribution. In this study, a promising alternative to traditional pore size characterization techniques is presented. We introduce a quantitative, nondestructive and inexpensive method to determine the pore size distribution of large soft porous solids based on the on the displacement of a liquid, that spreads without limits though a porous medium, by nitrogen. The capillary pressure is measured and related to the pore sizes as well as the pore size distribution of the narrowest bottlenecks of the largest interconnected pores in a porous medium. The measured pore diameters correspond to the narrowest bottleneck of the largest pores connecting the bottom with the top surface of a given porous solid. The applicability and reproducibility of the breakthrough technique is demonstrated on two polyurethane foams, manufactured using the thermally induced phase separation (TIPS) process, with almost identical overall porosity (60-70%) but very different pore morphology. By selecting different quenching temperatures to induce polymer phase separation, the pore structure could be regulated while maintaining the overall porosity. Depending on the quenching temperature, the foams exhibited either longitudinally oriented tubular macropores interconnected with micropores or independent macropores connected to adjacent pores via openings in the pore walls. The pore size and its distribution obtained by the breakthrough test were in excellent agreement to conventional characterization techniques, such as scanning electron microscopy combined with image analysis, BET technique, and mercury intrusion porosimetry. This technique is suitable for the characterization of the micro- and macropore structure of soft porous solids intended for tissue engineering applications. The method is sensitive for the smallest bottlenecks of the largest continuous pores throughout the scaffold that contributes to fluid flow.     

Fractal calibration in size-exclusion chromatography I. An introduction

The elution behaviour of different polymer-solvent systems in three types of organic columns for SEC has been compared and interpreted. The experimental data show that the classical universal calibration is not accomplished. Deviations from a unique curve are observed due to the binary and ternary interactions between the components of the system (solvent, polymer and gel) which results on secondary mechanisms accompanying the main pure or "ideal" SEC separation mechanism. Both, enthalpic and entropic effects are interpreted in terms of the swelling and crosslinking degrees of the gel packings, and are also related with the fractal characteristics of their surfaces, such as the fractal dimension and the available pore size. Moreover, a relationship between the fractal dimension of the pore surface and the chromatographic distribution coefficient is proposed.     

Surface morphology of nanostructured polymer-based activated carbons

Complementary techniques, including nitrogen adsorption, small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM), have been utilized to characterize the surface features of highly microporous carbon materials prepared from highly aromatic polymers. Nitrogen adsorption measurement interpreted by BET, DR, HK, and NLDFT methods reveals these nanostructured activated carbons exhibit a high surface area of up to 4000 m2/g, a micropore volume up to approximately 1.75 mL/g, and an average pore size of approximately 10-20 angstroms. A modified equation, based on Porod's law, the Debye-Bueche equation, and fractal dimension theories, has been proposed and successfully applied to analyze the SAXS spectra and to extract the porous texture of these unique activated carbons. AFM 3D imaging combined with the Fourier transform technique has been applied to statistically quantify pore sizes on the carbon surface.     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.     

Hydrothermal,microwave and mechanochemical modification of amorphous zirconium phosphate structure

The influence of hydrothermal HTT, microwave MWT and mechanochemical MChT treatments on structure of precipitated amorphous zirconium phosphate has been studied. Using XRF, XRD and DTA-TG techniques, the formation of the low-crystalline zirconium hydrophosphate Zr(HPO₄)₂·H₂O after HTT and MWT has been established. All types of modification promote increase in specific surface area, pore volume and pore size as well as extend the limits of the porous structure parameters variation. MChT of wet gel allow to prepare the samples possessing simultaneously high values of specific surface area, volume and pore size. Total surface acidity significant increases as a result of modification. HTT and MWT as well as MChT of wet gel lead to increasing surface homogeneity as the decrease in fractal dimension for modified samples indicates.     

氩吸附法研究多级孔分子筛的孔结构

采用不同方法分别制备了双介孔分子筛、介微孔分子筛及介孔沸石材料,利用氩吸附法并结合XRD技术表征了多级孔分子筛的孔结构。探讨了适用于多级孔分子筛的孔径分布计算方法,揭示了不同类型吸附等温线与孔径分布、孔型及孔容等之间的关系。研究表明,对于多级孔分子筛、微孔和介孔的孔径分布分别用SF法和BJH法计算较适宜,全孔分析可用NLDFT法计算。通过对TS-1介孔沸石的孔结构分析发现, TPAOH 在改性制备介孔TS-1的过程中起到了生成介孔及促进二次晶化的双重作用。     

污泥活性炭的结构特征及表面分形分析

以城市污水厂污泥为主要原料添加适量添加剂, 采用ZnCl₂化学活化法制备的污泥活性炭, 借助XRD, BET法, FT-IR, SEM等现代分析测试方法结合液相吸附法, 表征结构特征和分析表面分形维数. 结果表明: 在适宜的活化温度、活化时间、ZnCl₂浓度、原料粒度等工艺条件下, 加入少量添加剂制备的污泥活性炭, 最可几孔径分布在4.16 nm左右,平均孔容0.4484～0.5122 mL•g^－1, 比表面积为634.8～748 m²•g^－1, IR峰中出现C—OH, C—H, N＝O, C＝C功能组, 孔结构是具有平行壁的狭缝状介孔结构. 由液相吸附法得到的污泥活性炭分维近似为2, 属于低分维二维表面.     

Characterization of fractal particles using acoustics, electroacoustics, light scattering, image analysis, and conductivity

Fractals are aggregates of primary particles organized with a certain symmetry defined essentially by one parameter-a fractal dimension. We have developed a model for the interpretation of acoustic data with respect to particle structure in aggregated fractal particles. We apply this model to the characterization of various properties of a fumed silica, being but one example of a fractal structure. Importantly, our model assumes that there is no liquid flow within the aggregates (no advection). For fractal dimensions of less than 2.5, we find that the size and density of aggregates, computed from the measured acoustic attenuation spectra, are quite independent of the assumed fractal dimension. This aggregate size agrees well with light-scattering measurements. We applied this model to the interpretation of electroacoustic data as well. A combination of electroacoustic and conductivity measurements yields sufficient data for comparing the fractal model of the particle organization with a simple model of the separate primary particles. Conductivity measurements provide information on particle surface conductivity reflected in terms of the Dukhin number (Du). Supporting information for the zeta potential and Du can also be provided by electroacoustic measurements assuming thin double-layer theory. In comparing values of Du from these two measurements, we find that the model of separate solid particles provides much more consistent results than a fractal model with zero advection. To explain this, we first need to explain an apparent contradiction in the acoustic and electroacoustic data for porous particles. Although not important for interpreting acoustic data, advection within the aggregate does turn out to be essential for interpreting electrokinetic and electroacoustic phenomena in dispersions of porous particles.     

Morphological behavior of spherically granulated hydrated zirconium dioxide during its chemical and hydrothermal treatments

Hydrated zirconium dioxide samples were synthesized via original sol–gel route by two-step neutralization of zirconium oxychloride. Spherical granules of zirconia materials were prepared using a well-known “oil-drop” method. By the use of low temperature nitrogen adsorption, it is shown that surface fractal dimension of synthesized xerogels strongly depends on synthesis conditions, chemical and hydrothermal treatments. It is established that the change of synthesis conditions allows to obtain zirconium containing materials with developed porous structure: BET surface area—250–450 m²/g, pore diameter—2.0–4.2 nm, surface fractal dimension—2.28–2.63. It is shown that surface fractal dimension is an important parameter allowing to control the final properties of synthesized material and to determine the reasons of non-reproducibility of adsorptive, catalytic and other physical and chemical properties of zirconium containing oxides from synthesis to synthesis.     

Sulfur-doped CMK-5 with expanded lattice for high-performance lithium ion batteries

Heteroatom-doped porous carbon materials are very attractive for lithium ion batteries (LIBs) owing to their high specific surface areas, open pore structures, and abundant active sites. However, heteroatom-doped porous carbon with very high surface area and large pore volume are highly desirable but still remain a big challenge. Herein, we reported a sulfur-doped mesoporous carbon (CMK-5-S) with nanotubes array structure, ultrahigh specific surface area (1390 m²/g), large pore volume (1.8 cm³/g), bimodal pore size distribution (2.9 and 4.6 nm), and high sulfur content (2.5 at%). The CMK-5-S used as an anode material for LIBs displays high specific capacity, excellent rate capability and highly cycling stability. The initial reversible specific capacity at 0.1 A/g is as high as 1580 mAh/g and simultaneously up to 701 mAh/g at 1 A/g even after 500 cycles. Further analysis reveals that the excellent electrochemical storage performances is attributed to its unique structures as well as the expanded lattice by sulfur-doping.     

Further Insights into the Porous Structure of TEOS Derived Silica Gels

The porous structure of TEOS derived silica gels was studied using nitrogen adsorption at 77 K. Silica gels were prepared using TEOS, H₂O and ethanol for different molar ratios. No catalyst was used in this study. Silica gels were also heat treated up to 1000°C. The nitrogen sorption isotherms were analyzed by two models: Fractal and Percolation Theories. Using the fractal analysis approach, the surface roughness of the porous structure of silica gels was determined. The surface fractal dimension depends on the hydrolysis conditions and heat treatment. The surface fractal dimension decreases with increasing H₂O/TEOS molar ratio or heating temperature. For the silica gels studied, the surface fractal dimension changed from 2.6 to 2.5 after heating the gels, and from 2.4 to 2.6 with decreasing H₂O/TEOS ratio.Using the Percolation theory, we have determined the connectivity of the porous structure of silica gels. The extent of sorption hysteresis of the nitrogen isotherms reflects the connectivity of the pore network. The mean coordination number (connectivity) Z, and the linear dimension of the network, L, have been calculated from the hysteresis of the isotherms. For the as-prepared silica gels, Z was about 8 and L close to 2. On heating the gels, Z decreases to 4 and L increases to 7, results which are in accordance with the collapse of the porous network.