Siti Aishah Hashim Ali

Simulation model of the fractal patterns in ionic conducting polymer films

Normally polymer electrolyte membranes are prepared and studied for applications in electrochemical devices. In this work, polymer electrolyte membranes have been used as the media to culture fractals. In order to simulate the growth patterns and stages of the fractals, a model has been identified based on the Brownian motion theory. A computer coding has been developed for the model to simulate and visualize the fractal growth. This computer program has been successful in simulating the growth of the fractal and in calculating the fractal dimension of each of the simulated fractal patterns. The fractal dimensions of the simulated fractals are comparable with the values obtained in the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.

Characterization of PVDF-HFP-LiCF3SO3-ZrO2 Nanocomposite Polymer Electrolyte Systems

Nanocomposite polymer electrolytes were prepared by incorporating different amounts of zirconium oxide (ZrO2) nanofiller to poly(vinylidene fluoride-co-hexafluoropropylene)-lithium trifluoromethane sulfonate (PVDF-HFP-LiCF3SO3). X-ray diffraction (XRD) study has been carried out to investigate the structural features of the electrolyte films while a.c. impedance spectroscopy has been performed to investigate their electrical properties. The conductivity of nanocomposite polymer electrolyte systems is influenced by nanofiller concentration. The increase in conductivity is attributable to the increase in the fraction of amorphous region and the number of charge carriers and vice versa. The highest conductivity obtained is in the order of 10-3 S cm-1 for the system dispersed with 5 wt% of ZrO2 nanofiller.

Simulation Model of Multiple Cluster Fractals Cultured in Nanocomposite Polymer Electrolyte Film

This work contributes to the melioration of the modeling and simulation of laboratory cultured fractals using poly (vinylidene fluoride-co-hexafluoropropylene)/poly (ethyl methacrylate)-ammonium trifluorome-thanesulfonate nanocomposite polymer electrolyte films as the media of growth. Main focus is given to fractals and fractal growth models particularly DLA (Diffusion Limited Aggregation). The DLA cluster formed through DLA is formed by particles moving in Brownian motion (diffusion) which meet and stick together randomly (aggregation) to form the cluster. The simulation of multiple cluster fractals is done using DLA methods incorporating different parameters such as its sticking coefficient, lattice geometry and number of particles. To compare the simulation with the real patterns obtained, one vital aspect would be the calculation of their fractal dimension values. The computer program developed is able to calculate the fractal dimension value of each of the simulated fractal patterns. Suitable fractal dimension calculation method is employed according to its usefulness and efficiency. Fractal growth modeling and simulation such as done here can contribute to the understanding of other related studies concerning fractal growth found in areas including medical (nervous systems, cancer growth and more).

Ion Conductive Polymer Electrolyte Membranes and Fractal Growth

It has been widely accepted that Euclidean geometry plays an important role in shaping the way natural forms are viewed in science and mathematics, arts and even the human psyche (Hastings & Sugihara, 1993). This happens because man always seeks to find simplicity and order in nature, and often makes approximation on natural forms that may be essentially complex and irregular. Hence, leaves are roughly ellipses, planets are spheres and spruce trees are cone-shaped. However, shapes such as coastlines, fern leaves and clouds are not easily described by traditional Euclidean geometry. Nevertheless, they often possess a remarkable invariance under changes of magnification. With a certain scale of magnification, the pattern is seen as repeating itself. Since the term ‘fractal’ was first coined by Mandelbrot (Mandelbrot, 1983), study of fractals has increasingly become an interest for scientists and mathematicians. Consequently many researchers study the growth and shapes of fractals through theoretical modeling and computer simulations of fractal patterns. Simulation model of fractal patterns found in polymer electrolyte membranes provides another interesting perspective in the study of ion conductive polymer membranes. The characteristics and scientific aspects of the model have been studied and computer program s to simulate the growth of the patterns have been developed. Fractal aggregates especially diffusion-limited aggregate involve the random walk of particles and their subsequent sticking (Chandra & Chandra, 1994). To obtain fractal aggregates in laboratory framework, a system with particles in random walk is required. In most polymer electrolytes, the anions as well as the cations are found to be mobile and thus can be considered as a natural framework for fractal growth. The polymers act as a host while the inorganic salts dissociate in them to provide the ions necessary for conduction. According to Chandra (1996), fractals formed in the PEO-NH4I polymer electrolyte films are principally due to the random walk and subsequent aggregation of iodine ions. In other research as well, Fujii et al. (1991) have successfully carried out fractal dimension calculations of dendrite, of fractal patterns observed on the surface of a conducting polymer polypyrrole, after an ‘undoping’ process. Recent studies of fractals in polymers that involved modeling and/or simulation include Janke & Schakel (2005), Lo Verso et al. (2006) and Marcone et al. (2007). On the other hand, Rathgeber et al. (2006) have done some work on theoretical modeling and experimental studies of dendrimers. There have also been experimental studies of crystal pattern transition from dendrites through fourfold-symmetric structures to faceted crystals of ultra thin poly(ethylene oxide) films which were carried out by Zhang et al. (2008). These research

Modeling of Tumor Growth Based on Adomian Decomposition Method

Modeling of a growing tumor over time is extremely difficult. This is due to the complex biological phenomena underlying cancer growth. Existing models mostly based on numerical methods and could describe spherically‐shaped avascular tumors but they cannot match the highly heterogeneous and complex shaped tumors seen in cancer patients. We propose a new technique based on decomposition method to solve analytically cancer model.