Growth and Formation of Diffusion-Limited-Aggregation Crystal Pattern
This chapter described that the DLA crystal patterns have been characterized by optical microscope (OPM), scanning electron microscope (SEM), transmission electron microscope (TEM), X-ray diffractometer (XRD), Fourier transform infrared spectroscopy (FT-I
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Growth and Formation of Diffusion-Limited-Aggregation Crystal Pattern
2.1
Introduction
In nature, so many things around us have been created and designed beautifully but still most of them have appeared spontaneously such as living beings or snowflakes. The mechanism of pattern formation in nature, which is apparently produced via spontaneous processes that generate complex shapes and well-ordered structures, usually lies in the range of molecular as well as micro/nano scale. Some examples of nature which prefer symmetry like mountains, snowflakes, branches of trees, shores of continent, and so forth are some eye-catching examples of symmetrical structures in nature. More patterns of self-similar structures encountered by mankind are cancer, piles, and so forth. Retinal circulation of the normal human retinal vasculature is, also, statistically self-similar and fractal. Hence fractals are one of the most important topics in biology and medical fields, which generally cover the study of (a) the understanding of spatial shape and branching structure, and (b) the analysis of time varying signal. By knowing the branching structures of tissues and organs, biologists use this to discriminate between normal and pathological structures. In 1981, Witten and Sander [1] proposed that diffusion-limited aggregation (DLA) describes a rule-based process which has been used to model many physical, biological, and social phenomena. According to the proposed theory in two dimensions it is easy to explain, a “particle” is placed randomly in the plane and undergoes a random walk until either it encounters an existing structure—initially a fixed random particle or seed—in which case it adheres, or its time limit expires and dies. The dendritic growth that results from the release, over time, of many particles has seen widespread application. Among the dendrite structure DLA has been used to model electrodeposition [2], urban cluster growth [3], root system growth [4], and even aspects of string theory [5]. There is much interest in DLA structure formation due to its importance and its interconnection with mathematics by its
© The Author(s) 2016 R. Srivastava et al., Growth and Form of Self-organized Branched Crystal Pattern in Nonlinear Chemical System, SpringerBriefs in Molecular Science, DOI 10.1007/978-981-10-0864-1_2
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2 Growth and Formation of Diffusion-Limited-Aggregation Crystal Pattern
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Fig. 2.1 Growth pathways of DLA pattern in ADA/EAA/Ce+4/[Fe(Phen)3]+2/BrO3/H2SO4 system. Composition [ADA] = 0.0461 M, [EAA] = 0.1212 M, [Ce+4] = 0.00486 M, [Fe(Phen)3]+2 = 0.0038 M, [BrO3] = 0.0553 M, [H2SO4] = 0.42 M at 30 °C Petri dish (i.d) = 9.1 cm. The caption L and S denotes liquid phase and solid phase, respectively
fractal-like nature [4], with significant attempt having been devoted to measuring the fractal dimension of DLA formations [6]. Initially a Petri dish is used to keep an aliquot of homogenous red-color reaction solution which abruptly transforms into a blue-color solution in f
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