Ž . Bioelectrochemistry and Bioenergetics 48 1999 163–169 Modeling the surface phenomena in carbon paste electrodes by low frequency impedance and double-layer capacitance measurements D. Savitri, Chanchal K. Mitra ) Department of Biochemistry, School of Life Sciences, UniÕersity of Hyderabad, Hyderabad, 500 046, India Received 20 August 1998; revised 15 November 1998; accepted 21 November 1998 Abstract Ž . Impedance and capacitance studies have been performed with covalently coupled Glucose oxidase GOD enzyme, covalently coupled Ž . flavin adenine dinucleotide FAD , reconstituted GOD enzyme and blank carbon paste electrodes to study the changes in the electrochemical interfacial properties. Impedance studies were performed using a low frequency impedance technique and the electrochemical surface capacitance was measured by a pulse technique. We have attempted to fit the experimental values to an equivalent circuit model. The Randles’ cell circuit with Warburg impedance modeled well the experimental values and the behavior of the enzyme electrodes. The individual components of the model were calculated and the parameters were explained. The blank paste electrode showed a constant phase element behavior. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Paste electrode; Covalent coupling; Capacitance; Interfacial phenomena; Biosensor 1. Introduction Usually the impedance of a system consisting of an electrode in contact with an electrolyte solution where no faradaic reaction at the electrode surface takes place, i.e., at an ideally polarisable electrode, is represented by an equivalent circuit made up of a resistance R in series with a capacitor C. The resistance represents the bulk liquid part and the capacitance the double layer part of the impedance. This holds true on the assumption that the capacitance between the working electrode and the counter electrode is negligible. If the interfacial capacitance of the counter electrode itself is very large then the representation Ž . X Ž . Y Ž . of cell impedance Z v s Z v q iZ v in the complex plane has the form of a vertical line. For perfectly smooth homogenous electrodes this description works well. How- ever, in the case of solid electrodes marked deviation from this ideal impedance behavior is often observed and in the IP potential region the impedance diagram is again found to be a straight line but rotated clockwise through some angle around the same point in the complex plane relative ) Corresponding author. Tel.: q91-40-3010-814; fax: q91-40-3010- 120; e-mail: ckmsl@uohyd.ernet.in wx to the ideal diagram 1 . In case of paste electrodes, similar wx deviations have been observed 2 . From this phenomenon it may be concluded that the simple picture of a homoge- nous double layer capacity describing the interfacial impedance fails in case of rough surfaces like paste elec- trodes, where the porosity and diffusion also play the limiting factors. Hence the interfacial capacitance has to be replaced by some kind of passive linear element which has Ž .Ž . been named as ‘Constant Phase Element’ CPE Fig. 1A , because it has the peculiar property of causing a frequency independent phase shift between an applied alternating potential and its current response. The phenomenon re- mained unexplained for long time although it was soon recognized that it had to be related to surface inhomogene- ity causing some extra dissipation in the solution which is easily seen to give a deviation from the ideal RC impedance plot. The occurrence of CPE in case of solid and paste electrodes and its absence in case of electrodes like mercury with a homogeneous smooth surface suggests the phenomenon may be due to surface roughness. It has also been suggested that a fractal surface can also lead to a similar behavior but it is practically impossible to relate this surface roughness to the nature of the impedance plot by applying mathematical analysis and most workers have resorted to numerical analysis. 0302-4598r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. Ž . PII: S0302-4598 98 00227-X