The present work aims at reviewing our current understanding of fractal structures in the frame of colloid aggregation as well as the possibility they offer to produce novel structured materials. In ...particular, the existing techniques to measure and compute the fractal dimension df are critically discussed based on the cases of organic/inorganic particles and proteins. Then the aggregation conditions affecting df are thoroughly analyzed, pointing out the most recent literature findings and the limitations of our current understanding. Finally, the importance of the fractal dimension in applications is discussed along with possible directions for the production of new structured materials.
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•The existing techniques to measure and compute the fractal dimension are summarized•Aggregation conditions affecting the fractal dimension are analyzed•The importance of the fractal dimension in applications is discussed•Possible directions for the production of new structured materials are indicated
Biological semiflexible polymers and filaments such as collagen, fibronectin, actin, microtubules, coiled-coil proteins, DNA, siRNA, amyloid fibrils, etc., are ubiquitous in nature. In biology, these ...systems have a direct relation to critical processes ranging from the movement of actin or assembly of viruses at cellular interfaces to the growth of amyloid plaques in neurodegenerative diseases. In technology and applied sciences, synthetic macromolecules or fibrous objects such as carbon nanotubes are involved in countless applications. Accessing their intrinsic properties at the single molecule level, such as their molecular conformations or intrinsic stiffness, is central to the understanding of these systems, their properties, and the design of related applications. In this Perspective we introduce FiberAppa new tracking and analysis software based on a cascade of algorithms describing structural and topological features of objects characterized by a very high length-to-width aspect ratio, generally described as “fiber-like objects”. The program operates on images from any microscopic source (atomic force or transmission electron microscopy, optical, fluorescence, confocal, etc.), acquiring the spatial coordinates of objects by a semiautomated tracking procedure based on A* pathfinding algorithm followed by the application of active contour models and generating virtually any statistical, topological, and graphical output derivable from these coordinates. Demonstrative features of the software include statistical polymer physics analysis of fiber conformations, height, bond and pair correlation functions, mean-squared end-to-end distance and midpoint displacement, 2D order parameter, excess kurtosis, fractal exponent, height profile and its discrete Fourier transform, orientation, length, height, curvature, and kink angle distributions, providing an unprecedented structural description of filamentous synthetic and biological objects.
Superhydrophobic cotton fabrics were prepared via a facile and environmentally friendly strategy to deposit an organically modified silica aerogel (ormosil) thin film onto the fabrics first, followed ...by polydimethylsiloxane (PDMS) topcoating. The PDMS–ormosil coating displayed a uniform 3D fractal-like structure with numerous loose micro-scale pores, while the PDMS layer increased the binding strength of the hierarchical ormosil film to form a highly robust porous network on the fibers. In comparison with hydrophilic cotton fabrics, the modified cotton fabric exhibited a highly superhydrophobic activity with a water contact angle higher than 160° and a sliding angle lower than 10°. The as-constructed PDMS–ormosil@fabrics are able to withstand 100 cycles of abrasion and 5 cycles of accelerated machine wash without an apparent decrease of superhydrophobicity. In addition, the superhydrophobic cotton fabrics are very stable in strongly acidic and alkaline solutions. Furthermore, the superhydrophobic coating has no or negligible adverse effect on the important textile physical properties of the cotton fabric, such as the strength, air permeability, and flexibility. The composite super-antiwetting fabrics have demonstrated excellent anti-fouling, self-cleaning ability and are highly efficient in oil–water separation for various oil–water mixtures. This facile synthesis technique has the advantages of scalable fabrication of multifunctional fabrics for potential applications in self-cleaning and versatile water–oil separation.
We studied the effects of shear and its history on suspensions of carbon black (CB) in lithium ion battery electrolyte via simultaneous rheometry and electrical impedance spectroscopy. Ketjen black ...(KB) suspensions showed shear thinning and rheopexy and exhibited a yield stress. Shear step experiments revealed a two time scale response. The immediate effect of decreasing the shear rate is an increase in both viscosity and electronic conductivity. In a much slower secondary response, both quantities change in the opposite direction, leading to a reversal of the initial change in the conductivity. Stepwise increases in the shear rate lead to similar responses in the opposite direction. This remarkable behavior is consistent with a picture in which agglomerating KB particles can stick directly on contact, forming open structures, and then slowly interpenetrate and densify. The fact that spherical CB particles show the opposite slow response suggests that the fractal structure of the KB primary units plays an important role. A theoretical scheme was used to analyze the shear and time-dependent viscosity and conductivity. Describing the agglomerates as effective hard spheres with a fractal architecture and using an effective medium approximation for the conductivity, we found the changes in the derived suspension structure to be in agreement with our qualitative mechanistic picture. This behavior of KB in flow has consequences for the properties of the gel network that is formed immediately after the cessation of shear: both the yield stress and the electronic conductivity increase with the previously applied shear rate. Our findings thus have clear implications for the operation and filling strategies of semisolid flow batteries.
•Silica fume homogenizes concrete matrix and refines pore structure.•Meso and coarse porosities have contrary effects on strength.•Permeability and threshold pore size follow the Katz-Thompson ...equation.•Increasing fractal dimension tends to decrease strength but increase permeability.
In this study, we focused on the correlations among the fractal dimension, compressive strength, and permeability of concrete incorporating silica fume. The fractal dimension was calculated from SEM images by using a box-counting method, and the pore structure, compressive strength, and permeability were tested by mercury intrusion, compression and water penetration tests, respectively. Results show that increasing silica fume content improves compressive strength but decreases permeability and fractal dimension. The filling of available space, the promotion of heterogeneous nucleation of cement hydrates and the pozzonlanic reaction of silica fume itself, which densifies and homogenizes concrete microstructures, account for the effects of silica fume on the strength, permeability, and fractal dimensions of concrete. Compressive strength shows no appealing correlations with total porosity, but decreases as median pore size increases. Increasing meso porosity tends to strengthen concrete, whereas coarse pores are always harmful to compressive strength. The relationship between permeability and threshold pore size roughly follows the Katz-Thompson relation. Increasing fractal dimension can linearly depress compressive strength but nonlinearly promote permeability.
Self-assembled DNA nanostructures enable nanometre-precise patterning that can be used to create programmable molecular machines and arrays of functional materials. DNA origami is particularly ...versatile in this context because each DNA strand in the origami nanostructure occupies a unique position and can serve as a uniquely addressable pixel. However, the scale of such structures has been limited to about 0.05 square micrometres, hindering applications that demand a larger layout and integration with more conventional patterning methods. Hierarchical multistage assembly of simple sets of tiles can in principle overcome this limitation, but so far has not been sufficiently robust to enable successful implementation of larger structures using DNA origami tiles. Here we show that by using simple local assembly rules that are modified and applied recursively throughout a hierarchical, multistage assembly process, a small and constant set of unique DNA strands can be used to create DNA origami arrays of increasing size and with arbitrary patterns. We illustrate this method, which we term 'fractal assembly', by producing DNA origami arrays with sizes of up to 0.5 square micrometres and with up to 8,704 pixels, allowing us to render images such as the Mona Lisa and a rooster. We find that self-assembly of the tiles into arrays is unaffected by changes in surface patterns on the tiles, and that the yield of the fractal assembly process corresponds to about 0.95
for arrays containing m tiles. When used in conjunction with a software tool that we developed that converts an arbitrary pattern into DNA sequences and experimental protocols, our assembly method is readily accessible and will facilitate the construction of sophisticated materials and devices with sizes similar to that of a bacterium using DNA nanostructures.
•A model is built for the effective electrolyte diffusion in porous media.•Effects of microstructural and electrokinetic parameters are analyzed.•Good agreement between our present model and results ...is observed.
Electrolyte diffusion in electrolyte solutions exists in various areas including rechargeable batteries, soil physics and chemical engineering. In this paper, a fractal model based on the capillary model and fractal theory of porous media is proposed to quantify the effective electrolyte diffusivity in porous media with consideration of the electrical double layer (EDL) effects. The present model explicitly relates to the micro-structural parameters of porous media and electrokinetic parameters. To validate this model, a comparison is carried out with experimental data and semi-analytical model results, and yields satisfying agreement. Besides, the influences of the parameters (the porosity, equivalent particle diameter, ratio of the minimum pore radius to the maximum pore radius, molar concentration, zeta potential, and dimensionless parameter β) are discussed in details.
The spatial organization of chromatin critically affects genome function. Recent chromosome-conformation-capture studies have revealed topologically associating domains (TADs) as a conserved feature ...of chromatin organization, but how TADs are spatially organized in individual chromosomes remains unknown. Here, we developed an imaging method for mapping the spatial positions of numerous genomic regions along individual chromosomes and traced the positions of TADs in human interphase autosomes and X chromosomes. We observed that chromosome folding deviates from the ideal fractal-globule model at large length scales and that TADs are largely organized into two compartments spatially arranged in a polarized manner in individual chromosomes. Active and inactive X chromosomes adopt different folding and compartmentalization configurations. These results suggest that the spatial organization of chromatin domains can change in response to regulation.
This paper presents a novel fractal solution to investigate the permeability and the Kozeny-Carman (KC) constant of fibrous porous media made up of solid particles and porous fibers. The proposed ...model has been verified with satisfying agreements of the permeability and KC constant of fibrous porous media obtained by our model and those obtained by experimental data, analytical solution, and numerical simulation reported in literature. The results demonstrate that 1) an increase in particle diameter leads to an increase in the absolute permeability; 2) an increase in the tortuosity fractal dimension leads to an increase in the KC constant and decreases in the dimensionless permeability and absolute permeability; 3) an increase in the porosity results in increases in the dimensionless permeability and absolute permeability of the fibrous porous media; 4) increases in the fiber diameter yields an increase in the absolute permeability of fibrous porous media. The proposed fractal model explicitly relates the KC constant and the permeability to the microstructural parameters of the fibrous porous media, and consequently facilitating the understanding of the detailed physical mechanisms for fluids transport through fibrous porous media.
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•A novel fractal solution for permeability and KC constant is obtained.•The effects of micro-structural parameters on permeability are discussed.•Good agreement between the model predictions and experimental data are found.
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•Fractal characteristics of coals were analyzed using SEM and gas adsorption.•Both VL and PL were considered when assessing the adsorption capacity of coals.•Coalification has ...significant effect on the fractal dimensions of coal samples.•D1 and D2 have different impacts on CH4 adsorption.
Coal is a porous medium with fractal characteristics. In order to investigate the effect of fractal dimensions on methane adsorption capacity, fractal characteristics of 11 coal samples were analyzed, using scanning electron microscopy (SEM) and low-pressure nitrogen gas adsorption (LP-N2GA). Data from SEM image analysis and LP-N2GA experiments were applied to assess the heterogeneities of pore distribution (D1) and the irregularities of coal surface (D2) on the basis of box-counting method and Frenkel–Halsey–Hill (FHH) theory, respectively. The relationship between fractal dimensions and coalification was investigated. Based on the physical description of fractal surfaces and pore distributions, the influence of fractal dimensions (both D1 and D2) on CH4 adsorption characteristics was also discussed. The results indicate that these coal samples have different CH4 adsorption characteristics and fractal geometries, with D1 ranging between 1.5380 and 1.8267, and D2 varying from 2.2656 to 2.6541. The U-shaped curve relationship between D values (including D1 and D2) and volatile matter (Vdaf) is observed, demonstrating that coalification makes coal surfaces and pore networks comparatively smoother and more regular for lower rank coals (Vdaf>15%), but rougher and more complex for higher rank coals (Vdaf<15%). The Langmuir volume (VL) shows a positive linear correlation with the fractal dimension D2 values, but little correlation with D1 values. While, the Langmuir pressure (PL) is affected by both D1 and D2. Fractal dimensions comprehensively reflect the difference in physical properties of coal, which can be used to evaluate CH4 adsorption capacity. Fractal analysis is of great significance for better understanding of the surface irregularity and methane storage capacity of a coal reservoir.
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