Sains Malaysiana 40(1)(2011): 75–78

Ion Conductive Polymer Electrolyte Membranes and Simulation of Their Fractal Growth Patterns

(Membran Polimer Elektrolit Konduksian Ion dan Simulasi Pola-pola Pertumbuhan Fraktal)

S. Amir^1, *, S.A. Hashim Ali² & N.S. Mohamed¹

¹Pusat Asasi Sains, University of Malaya

50603 Kuala Lumpur, Malaysia

²Institute of Mathematical Sciences, Faculty of Science

University of Malaya, 50603 Kuala Lumpur, Malaysia

Received: 7 December 2009 / Accepted: 15 July 2010

ABSTRACT

Due to their high ionic conductivity, solid polymer electrolyte (SPE) systems have attracted wide spread attention as the most appropriate choice to fabricate all-solid-state electrochemical devices, namely batteries, sensors and fuel cells. In this work, ion conductive polymer electrolyte membranes have been prepared for battery fabrication. However, fractals were found to grow in these polymer electrolyte membranes weeks after they were prepared. It was believed that the formation of fractal aggregates in these membranes were due to ionic movement. The discovery of fractal growth pattern can be used to understand the effects of such phenomenon in the polymer electrolyte membranes. Digital images of the fractal growth patterns were taken and a simulation model was developed based on the Brownian motion theory and a fractal dialect known as L-system. A computer coding has been designed to simulate and visualize the fractal growth.

Keywords: Fractal; polymer electrolytes; simulation

ABSTRAK

Disebabkan kekonduksian ionik yang tinggi, sistem polimer elektrolit pepejal (SPE) telah menarik perhatian meluas sebagai pilihan paling sesuai untuk memfabrikasi alat elektrokimia keadaan pepejal sepenuhnya, iaitu bateri, pengesan dan sel bahan bakar. Dalam kerja penyelidikan ini, membran polimer elektrolit konduksian ion telah disediakan untuk penyediaan bateri. Bagaimanapun, fraktal telah didapati tumbuh dalam membran polimer elektrolit ini beberapa minggu selepas disediakan. Adalah dipercayai pembentukan agregat fraktal dalam membran ini ialah disebabkan oleh pergerakan ion. Penemuan corak pertumbuhan fraktal boleh digunakan bagi memahami kesan fenomena pergerakan ion dalam membran polimer elektrolit. Imej-imej digital pola-pola pertumbuhan fraktal telah diambil dan satu model simulasi dibangunkan berasaskan teori pergerakan Brown dan dialek fractal dikenali sebagai L-sistem. Pengekodan komputer telah direkabentuk bagi mensimulasi dan menggambarkan pertumbuhan fraktal.

Kata kunci: Elektrolit polimer; fraktal; simulasi

REFERENCES

Amir, S. 2008. Modeling and Simulation of Fractal Growth Pattern, M.Phil. Thesis, University of Malaya.

Amir, S., Mohamed, N.S. & Hashim Ali. S.A. 2007. Simulation of the Fractal Patterns in Polymer Membranes. Proceeding in IEECI 2007: 919-922.

Amir, S., Mohamed, N.S. & Hashim Ali, S.A. 2008. Simulation of Complex Geometric Patterns in Polymer Films. Matematika, Special Edition, Part 1: 207-211.

Amir, S., Mohamed, N.S. & Hashim Ali, S.A. 2010. Simulation model of the fractal patterns in ionic conducting polymer films. Cent. Eur. J. Phys. 8(1): 150-156.

Barkey, D. 1991. Morphology selection and the concentration boundary layer in electrochemical deposition. J. Electrochem. Soc. 138: 2912-2917.

Chandra, A. 1996. Anion clustering and fractal pattern growth in ion conducting polymeric matrix. Solid State Ionics 86-88: 1437-1442.

Chandra, A. & Chandra, S. 1994. Experimental observation of large-size fractals in ion-conducting polymer electrolyte films, Physical Review B 49(1): 633-636.

Harun, M.H., Saion, E., Kassim, A., Yahya, N. & Mahmud, E. 2007. Conjugated conducting polymers: A brief overview. UCSI Academic Journal: Journal for the Advancement of Science & Arts 2: 63-68.

Horie, K., Barón, M., Fox, R.B., He, J., Hess, M., Kahovec, J., Kitayama, T., Kubisa, P., Maréchal, E., Mormann, W., Stepto, R.F.T., Tabak, D., Vohlídal, J., Wilks, E.S. & Work, W. J. 2004

Definitions of terms relating to reactions of polymers and to functional polymeric materials (IUPAC Recommendations 2003). Pure Appl. Chem. 76(4): 889-906.

Kaufmann, J.H., Nazzal, A.I. & Melroy, O.R. 1987. Onset of fractal growth: Statics and dynamics of diffusion-controlled polymerization. Phys. Rev. B 35: 1881-1890.

Kleinert, H. 2004. Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. 4th edition. Singapore: World Scientific.

Mohamed, N.S. & Arof, A.K. 2001. Fractal like dendritic crystals of lithium tetrafluoroborate in chitosan acetate films. Malaysian Journal of Analytical Sciences 6(1): 71-74.

Okubo, S., Mogi, I., Kido, G. & Nakagawa, Y. 1993. Effect of high magnetic fields on fractal growth of silver metal-forest. Fractals 1: 425-429.

Prusinkiewicz, P. & Lindenmayer, A. 2004. The Algorithmic Beauty of Plants. Springer-Verlag.

Stephan, A.M. 2006. Review on gel polymer electrolytes for lithium batteries. European Polymer Journal 42(1): 21-42.

Suki, M.N., Mohamed, N.S., Hashim Ali, S.A. & Zainuddin, R. 2007. The role of image processing in measuring fractal dimension. Malaysian Journal of Science: 23-33.

Witten Jr, T.A. & Sander, L.M. 1981. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47: 1400-1403.

*Corresponding author; email:shahizat@um.edu.my