An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures

Pore Structure and Fractal Dimension in Marine Mature Silicon-Rich Shale of the Dalong Formation in Western Hubei

How shale reservoirs and gas contents are affected by the pore structure of shale is very important. Low-temperature nitrogen isothermal adsorption experiments were conducted by us to investigate the pore structure of the Dalong Formation shale. We measured the specific surface area and fractal dimension of the pores and also considered the mineral fraction and organic matter content of the rock. The results show that the Dalong Formation shale contains a lot of organic carbon, with a total organic carbon (TOC) value between 1.20 and 10.82% (mean: 5.02%). Quartz and clay minerals are the main components of the shale, with quartz making up 40.30 to 85.60% (mean: 67.21%) and clay minerals making up 9.20 to 34.10% (mean: 20.26%) of the shale. Most of the pore space in the shale of the Dalong Formation is formed by intragranular and intergranular pores, organic matter pores, and some microfissures. The pore structure is complex, with parallel-plate and ink-bottle pores being the most common types. Most of the pores are 0-2 or 2-5 nm in size. D1 and D2 are the fractal dimensions, with averages of 2.66 and 2.81, respectively. D1 can range from 2.55 to 2.78, while D2 can range from 2.66 to 2.94. The TOC content, mineral composition, and pore structure characteristics determine the fractal dimension. Higher levels of the TOC content, quartz mineral content, and specific pore surface area result in a higher fractal dimension, while higher levels of feldspar content result in a lower one. There is no apparent correlation to clay minerals or other mineral compositions.

Pectin Nanoporous Structures Prepared via Salt-Induced Phase Separation and Ambient Azeotropic Evaporation Processes

Polysaccharide nanoporous structures are suitable for various applications, ranging from biomedical scaffolds to adsorption materials, owing to their biocompatibility and large surface areas. Pectin, in particular, can create 3D nanoporous structures in aqueous solutions by binding with calcium cations and creating nanopores by phase separation; this process involves forming hydrogen bonds between alcohols and pectin chains in water and alcohol mixtures and the resulting penetration of alcohols into calcium-bound pectin gels. However, owing to the dehydration and condensation of polysaccharide chains during drying, it has proven to be challenging to maintain the 3D nanoporous structure without using a freeze-drying process or supercritical fluid. Herein, we report a facile method for creating polysaccharide-based xerogels, involving the co-evaporation of water with a nonsolvent (e.g., a low-molecular-weight hydrophobic alcohol such as isopropyl or n-propyl alcohol) at ambient conditions. Experiments and coarse-grained molecular dynamics simulations confirmed that salt-induced phase separation and hydrogen bonding between hydrophobic alcohols and pectin chains were the dominant processes in mixtures of pectin, water, and hydrophobic alcohols. Furthermore, the azeotropic evaporation of water and alcohol mixed in approximately 1:1 molar ratios was maintained during the natural drying process under ambient conditions, preventing the hydration and aggregation of the hydrophilic pectin chains. These results introduce a simple and convenient process to produce 3D polysaccharide xerogels under ambient conditions.

Investigation on Adsorption Pore and Fractal Analyses of Low-Rank Coals in the Northern Qaidam Basin

The northern Qaidam Basin has abundant coal and coalbed methane (CBM) resources, and quantitative evaluation of adsorption pore characteristics has great significance for optimum selection of CBM-favorable areas. Based on vitrinite reflectance, coal maceral, proximate analysis, low-temperature N2 adsorption, and methane isothermal adsorption experiments, the heterogeneities of adsorption pores (pore diameter <100 nm) were quantitatively characterized, and relationships between fractal dimensions and physical parameters of low-ranked coal reservoirs were revealed. The results show that the micropore volume percentage ranges between 33.70 and 86.44% with an average of 64.94%. Based on N2 adsorption/desorption curves and pore diameter distribution characteristics, the adsorption pore structures of low-ranked coals were divided into 3 types. According to the FHH model, fractal dimension D1 (relative pressure between 0 and 0.5) and D2 (relative pressure between 0.5 and 1) were calculated. Fractal dimension D1, representing adsorption pore surface area, ranges from 2.001 to 2.345, with lower values. Fractal dimension D2 (adsorption pore structure) is from 2.641 to 2.917, with relatively high values, which has a decreasing tendency from west to east in the study area. There are positive relationships between fractal dimension D1 and Langmuir volume and specific surface area, whereas negative correlations are found between fractal dimension D2 and Langmuir pressure, ash yield, moisture content, volatile content, and average pore diameter. Combined with the related data for middle- and high-rank coals, the characteristics of pore surface and methane adsorption capacity can be analyzed based on the variation of vitrinite reflectance. Furthermore, the complexity of pore structure can also be predicted according to the averaged pore size and micropore content to some degree.

Characterization on Structure and Fractal of Shale Nanopore: A Case Study of Fengcheng Formation in Hashan Area, Junggar Basin, China

The Lower Permian Fengcheng Formation in Halaalate Mountain in the Junggar Basin has enormous potential for shale oil, while few investigations on quantifying pore structure heterogeneity have been conducted. Thus, total organic carbon (TOC), X-ray diffraction (XRD), scanning electron microscopy (SEM), and low-temperature N2 adsorption tests were conducted on the shales collected from the HSX1 well in the Hashan region to disclose the microscopic pore structure and its heterogeneity. Results show that the selected shales mainly consist of quartz, plagioclase, calcite, and clay minerals. The primary pore types are intergranular pores in quartz and carbonate and intragranular pores in clays, while organic matter (OM) pores are rare. Typical types of H2 and mixed H2-H3 were observed. Type H3 shale pore size distributions (PSD) are unimodal, with a peak at about 70 nm, while Type H2-H3 shales are bimodal, with peaks at about 70 nm and 3 nm, respectively. Type H3 shales have lower D2 than Type H2-H3 shale, corresponding to weaker pore structure heterogeneity. Multifractal analyses indicate that macropores in Type H3 shales have stronger heterogeneity with large D10−D0 ranges, while minor D−10−D0 ranges mean weaker heterogeneity of micro- and mesopores, and so do Types H2-H3 shales. The higher the contents of plagioclase and clay minerals, the more heterogeneous the micro- and mesopores are; a larger content of quartz leads to more heterogeneous macropores. Specific surface area, micro-, and mesopores contents positively correlate to D2, while average pore diameter and macropores are on the contrary, thus the higher the content of micro- and mesopores and the specific surface area, the lower the content of macropores and average pore diameter, the more complex the microscopic pore structure of shale. Micro- and mesopores control the heterogeneity of shale pore development with a great correlation of D−10−D0 and D−10−D10, and D2 can effectively characterize the heterogeneity of a high porosity area with a strong correlation of D2 and D0−D10.

Study on Pore Structure and Fractal Characterization during Thermal Evolution of Oil Shale Experiments

In order to better study the characteristics of the pore structure and to explore the influence factors of its fractal dimensions during the thermal evolution of oil shale, the immature oil shale (T _max = 433 °C, TOC = 28.00%) of the Ordos Basin Extension Group was selected to simulate the whole thermal evolution process from immature to over mature in a semiopen system. Organic geochemical data show that the thermal simulation hydrocarbon generation threshold is between 300 and 400 °C. According to AIP-SEM observation, the pore types of the samples are different in different thermal simulation stages. The fractal dimensions are calculated by low-temperature N₂ adsorption data using the fractal Frenkel-Halsey-Hill fractal model. The average surface fractal dimension (D ₁) is 2.26, indicating that the pore (<4 nm) surface is relatively smooth. The average pore structure fractal dimension (D ₂) is 2.49, indicating that the pore (>4 nm) structure is complex. Through the exploration of the relationship between fractal dimensions and organic geochemistry, whole rock X-ray diffraction, and N₂ adsorption data, it is found that fractal dimensions have different degrees of correlation with thermal maturity, mineral composition, TOC content, and pore parameters. Through comprehensive research, it shows that hydrocarbon generation and expulsion, oil and gas cracking, and organic matter carbonization have important effects on the pore structure and fractal characteristics of oil shale.

Protein Immobilization on Heterogeneous (SiO2/ZnO) Hollow-Mesoporous Nanocapsules Prepared by Imprinting CPMV: Drug Delivery and Possibility of Immunological Applications

Herein, we report the protein immobilization and stability studies of heterogeneous hollow mesoporous nanocapsules (Hhmn) for drug and protein delivery. The final results of the diverse precursors such as TEOS, TMOS, APTES, and zinc acetate on the formation of the hollow-mesoporous architecture of nanocapsules have been assimilated in this work. Three types of Hhmn of various sizes were synthesized. Among the three Hhmn, sample I and II nanocapsules were synthesized in the presence of zinc acetate and were identified to be amorphous in nature. Sample III nanocapsules synthesized in the absence of zinc acetate were analogous to the other two synthesized samples. Physiochemical analysis showed the formation of zinc phosphate in the silica matrix for the samples when synthesized with zinc acetate. Specific surface area analysis revealed that sample III has a relatively higher specific surface area. Further, the drug/dye loading and release capacity for the nanocapsules were studied using doxorubicin (DOX) and imatinib mesylate (IM) as model anticancerous drugs and rhodamine 6G as a model dye. Among the synthesized nanocapsules, sample III was shown to have a higher loading capacity for DOX (∼128 μg). From the release kinetic studies of drug/dye, sample III nanocapsules demonstrate a controlled release pattern of DOX and IM. Additionally, protein adsorption and stability studies of samples I and II revealed that the BSA adsorption capacity increases with the increase in the initial concentration of BSA. Furthermore, analysis of the release profiles of BSA and OVA leads to the conclusion that the heterogeneous nanocapsules show a higher loading capacity and sustained release pattern toward OVA. These properties of the nanocapsules highlight their path to immunological applications.

Investigation of Fractal-like Characteristics According to New Kinetic Equation of Desorption

Most of the adsorbents have porous structures and a suitable kinetic model is essential for studying these systems. The kinetic Langmuir model is one of the first theoretical models, which can be used for desorption studies. In the present research, the fractal-like concept was added to the kinetic Langmuir model of desorption. A new integrated kinetic Langmuir equation was provided to investigate the rate of desorption from a solid surface. The preferred characteristic of the provided rate equation is the application of the fractal concept for the kinetic study of the desorption process from porous surfaces. The derivation of a new equation was confirmed using the generated data. The fractal-like concept for some experimental desorption studies was obtained. This parameter can show how the porous structure of an adsorbent can affect the desorption kinetics.

Biomimicked and CPMV-Imprinted Hollow Porous Zinc Phosphate Nanocapsules and Their Therapeutic Efficiency

Hollow zinc phosphate nanocapsules (hZPNCs) are an alloplastic biomaterial that has been synthesized to deliver chemotherapeutic drugs in a sustained manner. A very simple one-pot synthesis approach has been employed to synthesize hZPNCs by using cowpea mosaic virus (CPMV) in the presence of phosphate buffer (PBS) (0.01 M PBS, pH ∼7.2) with zinc acetate precursor. The synthesis mechanism of hZPNCs relies on the basis of biomineralization, where the precursor molecules initiate mineralization with the help of amino acid residues present on the CPMV capsid. The synthesized hollow nanocapsules were of diameter ∼50-60 nm and porous shell with thickness of ∼4 nm. The cavity performed as a reservoir for the anticancer drugs (DOX and IM). The release kinetic studies show the positive aspect of hZPNCs to be labeled as drug delivery cargo for sustained delivery. In vitro cytotoxic studies of hZPNCs and hZPNCs-chemo drugs on HEK293, HEPG2, and K562 cells were performed. The cytotoxic studies show that hZPNCs-DOX and hZPNCs-IM arrest the cell cycle of carcinoma cells (HEPG2 and K562 cells) at relatively low IC₅₀ and that the inhibition efficiency is dosage dependent. Furthermore, through HRTEM, in vitro cellular interactions of carcinoma cells with hZPNCs and chemo drug-loaded hZPNCs were confirmed by the cryo-sectioning of cells before and after the incubation. These studies revealed the likely endocytic pathway for the nanocapsules entering the cell and executing the specific action of delivering the anticancer drugs. Together, these results reveal the hZPNCs as potential sustained drug delivery agents.

Full‐Scale Pore Structure and Fractal Dimension of the Longmaxi Shale from the Southern Sichuan Basin: Investigations Using FE‐SEM, Gas Adsorption and Mercury Intrusion Porosimetry

Pore structure determines the gas occurrence and storage properties of gas shale and is a vital element for reservoir evaluation and shale gas resources assessment. Field emission scanning electron microscopy (FE‐SEM), high‐pressure mercury intrusion porosimetry (HMIP), and low‐pressure N2/CO2 adsorption were used to qualitatively and quantitatively characterize full‐scale pore structure of Longmaxi (LM) shale from the southern Sichuan Basin. Fractal dimension and its controlling factors were also discussed in our study. Longmaxi shale mainly developed organic matter (OM) pores, interparticle pores, intraparticle pores, and microfracture, of which the OM pores dominated the pore system. The pore diameters are mainly distributed in the ranges of 0.4–0.7 nm, 2–20 nm and 40–200 μm. Micro‐, meso‐ and macropores contribute 24%, 57% and 19% of the total pore volume (PV), respectively, and 64.5%, 34.6%, and 0.9% of the total specific surface area (SSA). Organic matter and clay minerals have a positive contribution to pore development. While high brittle mineral content can inhibit shale pore development. The fractal dimensions D1 and D2 which represents the roughness of the shale surface and irregularity of the space structure, respectively, are calculated based on N2 desorption data. The value of D1 is in the range of 2.6480–2.7334 (average of 2.6857), D2 is in the range of 2.8924–2.9439 (average of 2.9229), which indicates that Longmaxi shales have a rather irregular pore morphology as well as complex pore structure. Both PV and SSA positively correlated with fractal dimensions D1 and D2. The fractal dimension D1 decreases with increasing average pore diameter, while D2 is on the contrary. These results suggest that the small pores have a higher roughness surface, while the larger pores have a more complex spatial structure. The fractal dimensions of shale are jointly controlled by OM, clays and brittle minerals. The TOC content is the key factor which has a positive correlation with the fractal dimension. Clay minerals have a negative influence on fractal dimension D1, and positive influence D2, while brittle minerals show an opposite effect compared with clay minerals.

Nanopore Structure and Fractal Characteristics of Lacustrine Shale: Implications for Shale Gas Storage and Production Potential

In order to better understand nanopore structure and fractal characteristics of lacustrine shale, nine shale samples from the Da’anzhai Member of Lower Jurassic Ziliujing Formation in the Sichuan Basin, southwestern (SW) China were investigated by total organic carbon (TOC) analysis, X-ray diffraction (XRD) analysis, field emission scanning electron microscopy (FE-SEM), and low-pressure N₂ adsorption. Two fractal dimensions D₁ and D₂ (at the relative pressure of 0–0.5 and 0.5–1, respectively) were calculated from N₂ adsorption isotherms using the Frenkel–Halsey–Hill (FHH) equation. The pore structure of the Lower Jurassic lacustrine shale was characterized, and the fractal characteristics and their controlling factors were investigated. Then the effect of fractal dimensions on shale gas storage and production potential was discussed. The results indicate that: (1) Pore types in shale are mainly organic-matter (OM) and interparticle (interP) pores, along with a small amount of intraparticle (intraP) pores, and that not all grains of OM have the same porosity. The Brunauer–Emmett–Teller (BET) surface areas of shale samples range from 4.10 to 8.38 m²/g, the density-functional-theory (DFT) pore volumes range from 0.0076 to 0.0128 cm³/g, and average pore diameters range from 5.56 to 10.48 nm. (2) The BET surface area shows a positive correlation with clay minerals content and quartz content, but no obvious relationship with TOC content. The DFT pore volume shows a positive correlation with TOC content and clay minerals content, but a negative relationship with quartz content. In addition, the average pore diameter shows a positive correlation with TOC content and a negative relationship with quartz content, but no obvious relationship with clay minerals content. (3) Fractal dimension D₁ is mainly closely associated with the specific surface area of shale, suggesting that D₁ may represent the pore surface fractal dimension. Whereas fractal dimension D₂ is sensitive to multiple parameters including the specific surface area, pore volume, and average pore diameter, suggesting that D₂ may represent the pore structure fractal dimension. (4) Shale with a large fractal dimension D₁ and a moderate fractal dimension D₂ has a strong capacity to store both adsorbed gas and free gas, and it also facilitates the exploitation and production of shale gas.

Scattering from surface fractals in terms of composing mass fractals

It is argued that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of a surface fractal is shown to be a sum of the amplitudes of the composing mass fractals. Various approximations for the scattering intensity of surface fractals are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of a power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensityI(q) ∝ q^{D_{\rm s}-6}, where 2 <Ds< 3 is the surface-fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution dN(r) ∝r−τdr, withDs= τ − 1. The distribution is continuous for random fractals and discrete for deterministic fractals. A model of the surface deterministic fractal is suggested, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and its scattering properties are studied. The present analysis allows one to extract additional information from SAS intensity for dilute aggregates of single-scaled surface fractals, such as the fractal iteration number and the scaling factor.

Application of the Discrete Wavelet Transform to SEM and AFM Micrographs for Quantitative Analysis of Complex Surfaces

The discrete wavelet transform (DWT) has found significant utility in process monitoring, filtering, and feature isolation of SEM, AFM, and optical images. Current use of the DWT for surface analysis assumes initial knowledge of the sizes of the features of interest in order to effectively isolate and analyze surface components. Current methods do not adequately address complex, heterogeneous surfaces in which features across multiple size ranges are of interest. Further, in situations where structure-to-property relationships are desired, the identification of features relevant for the function of the material is necessary. In this work, the DWT is examined as a tool for quantitative, length-scale specific surface metrology without prior knowledge of relevant features or length-scales. A new method is explored for determination of the best wavelet basis to minimize variation in roughness and skewness measurements with respect to change in position and orientation of surface features. It is observed that the size of the wavelet does not directly correlate with the size of features on the surface, and a method to measure the true length-scale specific roughness of the surface is presented. This method is applied to SEM and AFM images of non-precious metal catalysts, yielding new length-scale specific structure-to-property relationships for chemical speciation and fuel cell performance. The relationship between SEM and AFM length-scale specific roughness is also explored. Evidence is presented that roughness distributions of SEM images, as measured by the DWT, is representative of the true surface roughness distribution obtained from AFM.

SAXS investigation of nanoporous structure of thermal-modified carbon materials

The article investigates the effect of thermal modification of porous carbon material (PCM), obtained from plant feedstock, on its morphology and fractal structure by small-angle X-ray scattering (SAXS) method. The analysis of the scattering intensity curves serve the basis for calculating the parameters of the PCM porous structure: the Porod constant, the Porod invariant, average pore radius, specific surface area, and mass and surface fractal dimensions. It has been found out that the PCMs obtained have fractal structure, formed from mass and surface fractals, the sizes of which increase at the growth of temperature and modification time.

PACS

81.05.Uw; 61.05.cf; 82.47.Aa.

Low temperature and template-free synthesis of hollow hydroxy zinc phosphate nanospheres and their application in drug delivery

Hollow hydroxy zinc phosphate nanospheres (HZnPNSs) with sizes of 30-50 nm and wall thicknesses of about 7 nm were synthesized using a template-free method through wet precipitation of Zn(NO3)2·6H2O and (NH4)2HPO4 at temperatures of 0, 10, and 20 °C. The crystal structures, morphologies, sizes and pore properties, Zn/P molar ratios, and thermal stability properties of nanoparticles have been carefully examined. The methyl-thiotetrazole assay measurements proved the low cell cytotoxicity of the material. The protein adsorption of negatively charged bovine serum albumin (BSA) and positively charged lysozyme on HZnPNSs was also investigated. The results showed that HZnPNSs had high protein adsorption affinity. Furthermore, anticancer doxorubicin as a model drug was used to evaluate the entrapment efficiency and drug loading capacity of HZnPNSs, which showed high loading capacity (>16 wt %) for doxorubicin. The confocal laser scanning microscope observations showed that the drug could be efficiently delivered into cells.

Surface analysis of cryofixation-vacuum-freeze-dried polyaluminum chloride–humic acid (PACl–HA) flocs

The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryofixation-vacuum-freeze-drying method. The FTIR spectra show that some characteristic functional groups in polyaluminum chloride (PACl), humic acid (HA), and kaolin still existed in the dried flocs. X-ray diffractometry (XRD) patterns indicate that these flocs are amorphous. Nitrogen adsorption-desorption isotherms were obtained for different samples of the dried PACl-HA flocs. The BET specific surface area, BJH cumulative absorbed volume and BJH desorption average pore diameter of them were determined. The peak values of 8.4-11.2 nm (pore diameter) for pore size distribution (PSD) curves indicate that the pores of the dried flocs are mostly mesopores. The surface fractal dimensions D(s) and the corresponding fractal scales determined from both SEM images and nitrogen adsorption-desorption data sets reveal the multi-scale surface fractal properties of the dried PACl-HA flocs, which exhibited two distinct fractal regimes: a regime of low fractal dimensions (2.07-2.26) at higher scales (23-387 nm), mainly belonging to exterior surface scales, and a higher fractal dimensions (2.24-2.37) at lower scales (0.80-7.81 nm), falling in pore surface scales. Both HA addition and kaolin reduction in dried floc can decrease the irregularity and roughness of external surface. However, for the irregularity and roughness of pore surface, the addition of HA or kaolin in dried floc can increase them. Furthermore, some difference was found between the pore surface fractal dimensions D(s) calculated from nitrogen adsorption and desorption data. The pore surface D(s) values calculated through thermodynamic model were much greater than three.

A study on electrophoretic deposition of Ni nanoparticles on pitted Ni alloy 600 with surface fractality

In the present work, the electrophoretic deposition of Ni nanoparticles used for self-repairing of pits in organic suspension was investigated on pitted fractal Ni alloy 600 with respect to surface fractality of the pits. For this purpose, Ni nanoparticles prepared by levitation-gas condensation were dispersed into an ethanol solution with the addition of a dispersant. Four kinds of pitted fractal specimens with different surface fractal dimensions dF,surf were prepared by applying various anodic potentials above pitting potential to alloy 600 in aqueous 0.1 M NaCl solution. From the scanning electron microscopy (SEM) images, it was observed that the pits repaired under applied electric field E of 100 V cm-1 comprised more agglomerates of Ni nanoparticles than those repaired under E of 20 V cm-1. This suggests that the higher the value of E is, the more agglomerates of Ni nanoparticles are deposited on the specimen due to more depletion of OH- in suspension near the specimen surface. Moreover, the specimen with higher dF,surf gave a higher value of electrophoretic current Ip than one with lower dF,surf due to the increased electrochemical active area Aea of the specimen. From the above, it is concluded that the surface irregularities of the pit enhance the deposition of Ni nanoparticles on pitted fractal specimen during electrophoretic deposition.

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.