Modeling of the fractal-like adsorption systems based on the diffusion limited aggregation model

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment

A growth model combined with diffusion-limited aggregation (DLA) and oriented attachment (OA) is developed for deducing quantitative understanding of the growth process of pine-needle like structures. We define the completely random parameters for describing the realistic Brownian motion in DLA. The results indicate that the cluster by DLA changes from random branches to regular needles by the introduction of OA. And the cluster of DLA and OA has a fractal dimensionality of about 1.0 during the whole growth process. The maximum length of needels (L max) depends on the number of particles (N p). They satisfy the relation L max = aN p b (a and b are constant) over the whole range. The model has also been used to describe the formation of needles on a line, plane and sphere. The growth of needles has obvious steric hindrance from the outer needles. In particular, only one needle grows in the later period in the plane.

Finite dimension and particle heterogeneous DLAs

We study heterogeneous Diffusion Limited Aggregates (DLAs) i.e. those formed by a mixture, in different proportions, of 4-legged and 2-legged particles. We fixed the total number of particles, let the proportions vary, and computed their finite dimension, a recent addition to the list of "fractal" dimensions. At one extreme, when all particles are 4-legged, the corresponding DLAs are complex, fractal structures whose appearance resembles very much that of the DLAs that occur in Nature. At the other extreme, when almost all particles are 2-legged, the DLAs lose much of their complexity and acquire long rectilinear stretches so that their appearance resembles more and more the structure of the underlying lattice. We expected the complexity in between would decrease monotonically, and this would be reflected in the finite dimension of the corresponding DLAs. However, the finite dimension first increases and then, when the proportion of 4-legged to 2-legged particles is about 30 to 70, starts decreasing. In the paper, we study and explain the mechanisms behind this unexpected, counter-intuitive behaviour.

A critical review of various adsorbents for selective removal of nitrate from water: Structure, performance and mechanism

Nitrate is ubiquitous pollutant due to its high water solubility, usually contributing to eutrophication, and posing a threat to aquatic ecosystem and human health. Adsorption approach has been widely used for nitrate removal because of the simplicity, easy operation, and low cost. Adsorbent plays a key role in the adsorptive removal of nitrate. The adsorption performance and adsorption mechanism are determined by the structural feature of adsorbent that is dependent on the preparation method. In this review, various types of adsorbents for nitrate removal were systematically summarized, their preparation, characterization, and adsorption performance were evaluated; the factors influencing the nitrate adsorption performance were discussed; the adsorption isotherm models, kinetic models and thermodynamic parameters were examined; and the possible adsorption mechanisms responsible for nitrate adsorption were categorized; the possible correlation of adsorbent structure to adsorption performance and adsorption mechanism were explained; the potential applications of adsorbents were discussed; finally, the strategies for improving adsorption capacity and selectivity towards nitrate, the challenges and future perspectives for developing novel adsorbent were also proposed. This review will deepen the understanding of nitrate removal by adsorption process and help the development of high-performance adsorbents for selective nitrate removal from water and wastewater.

Adsorption of interacting particles on bivariate diffusion-limited aggregates

The adsorption of pairwise interacting particles on fractal surfaces has been studied by grand canonical Monte Carlo simulations. The substrate is built from a mixture of two types of objects: (i) objects with two bonds and (ii) objects with four bonds. These objects move on a square lattice, according to diffusion-limited aggregation (DLA) rules, and stick to each other only if they have a free bond pointing at each other and, of course, are first neighbors of each other. The resulting substrate, which is named as bivariate diffusion-limited aggregate (BDLA), is a fractal structure composed by two bonds units with fraction [Formula: see text] and four bonds units with concentration [Formula: see text]. Different surface morphologies are obtained by varying [Formula: see text] and [Formula: see text]. In the limit case of [Formula: see text] and [Formula: see text], the standard DLA model is recovered. In addition, repulsive lateral interactions between adsorbed particles are considered. Adsorption isotherms and differential heats of adsorption are calculated for different values of the parameters of the system. In the case of high repulsive couplings, a wide variety of structural orderings are observed in the adlayer. The main characteristics of these ordered phases are discussed in terms of the topological properties of the bivariate aggregates.

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.