Investigation of anomalous diffusion and multifractal dimensions in polypyrrole film A. Sharifi-Viand, M.G. Mahjani ⇑ , M. Jafarian Department of Chemistry, Faculty of Science, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran article info Article history: Received 11 October 2011 Received in revised form 5 February 2012 Accepted 10 February 2012 Available online 24 February 2012 Keywords: Anomalous diffusion Fractal dimension Impedance spectroscopy Cyclic voltammetry Polypyrrole abstract The fractal dimensions of polypyrrole (PPy) film electrodeposited on the glassy carbon (GC) electrode formed in the presence of ClO  4 is obtained by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) methods in different film thicknesses and various synthesis temperatures. Atomic force microscopy (AFM) technique was employed to analyze fractal structure of film. Anomalous diffu- sion through the film in which mean squared displacement of particles has not a linear dependence with time (hx 2 i/ t c ) has been discussed and values of c that is the characteristic of anomalous diffusion is obtained by EIS method and then the relation between fractal dimension and anomalous diffusion has been investigated. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Among the conducting polymers, polypyrrole (PPy) has attracted great attention because of its high electrical conductivity and good environmental stability. PPy has been considered as the key mate- rial to many potential applications such as fuel cells [1,2] solar cells [3], batteries [4] corrosion inhibitors [5,6], humidity sensors [7], gas sensors [8], pH sensors [9] and even wastewater treatment [10]. So according to large application of polypyrrole in various fields, deter- mination of real properties of this material will be very useful. One of the main processes that occur during the conducting process in polypyrrole is the diffusion process. Polypyrrole film can trap the diffusing particles due to its porosity and so anomalous diffusion oc- curs. Anomalous diffusion in polypyrrole film has been reported many times, and some of the evidence is available in references, for example first time in 1987 polypyrrole doped by ClO  4 was inves- tigated using Proton Nucleic Relaxation method and some evidence of anomalous diffusion was reported [11]. Furthermore, in 1993 insertion of ClO  4 in polypyrrole film was investigated by EIS method and it was shown that in low potentials anomalous diffusion turns up [12]. In 2002 Bisquert and colleagues investigated the polypyr- role synthesized by galvanostatic method and in this case, the porosity of polymer caused to trap of diffusing particles and caused to anomalous diffusion [13]. When anomalous diffusion is consid- ered some properties will be different from the case of normal diffusion. When normal diffusion occurs, dimension of diffusion coefficient D is cm 2 /s. But in the case of anomalous diffusion the dimension of D will be cm 2 /s c , where c is the characteristic of anom- alous diffusion. Also anomalous diffusion effects on electrochemical properties of polypyrrole and the values of diffusion capacitance C w and resistance R w will be affected. Anomaly behavior is related to the unusual dimension of sur- face geometry, i.e. fractal dimension. Fractal structures are arisen during specific condition of polymerization dynamic and have non-integer dimensions which could be easily calculated [14]. The fractal dimension is characteristic of complex structure which effects surface performance. The Fractal dimension (D f ) is a quan- titative parameter for analyses of fractal objects, which is widely used for different purposes. In addition, it is one of the most impor- tant and useful parameters for analysis of structure of rough sur- faces [15]. In this work fractal dimension of polypyrrole film was calculated by CV, EIS and AFM methods. 2. Experimental 2.1. Materials Pyrrole (C 4 H 5 N, Merck) and potassium perchlorate (KClO 4 , Merck) were used as received without further purification. 2.2. Electrodes and instrumentation All electrochemical measurements were carried out in a con- ventional three electrodes cell powered by a potentiostat/galvano- stat (EG&G, 273A) and a frequency response analyzer (EG&G, 1572-6657/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jelechem.2012.02.014 ⇑ Corresponding author. Tel.: +98 21 22853551; fax: +98 21 22853650. E-mail address: mahjani@kntu.ac.ir (M.G. Mahjani). Journal of Electroanalytical Chemistry 671 (2012) 51–57 Contents lists available at SciVerse ScienceDirect Journal of Electroanalytical Chemistry journal homepage: www.elsevier.com/locate/jelechem