





RESOURCES > EIS > CPE > EXPLANATIONS What Causes a CPE?
Surface RoughnessOne physical explanation put forth for CPE behavior is electrode roughness. For a rough, fractal, surface, the fractal dimension (D) of the surface is between 2 and 3: Translated, this means that the surface fills between 2 dimensions (i.e., it's absolutely flat) and 3 dimensions (i.e., the surface fills three dimensions, branching everywhichway through space, and resembling a porous cube.) It has been shown ( Ref 2 ) that for these electrodes, the interfacial impedance (electron transfer or double layer capacitance) is modified by an exponent, n = 1/(D1). For a smooth surface the fractal dimension (D) is 2.0 and n=1: The impedance is unchanged. For a highly contorted surface (D=3), and n=0.5. For a great many real metal or solid electrodes, the measured impedance in the doublelayer region (no faradaic current) follows a power law, such as that for the CPE, with a value of n between 0.9 and 1.0. The phase angle of this "capacitance" is not 90° , but is given by (n*90°). The observed angle is something between 80° (n=0.89) and 90° (n=1.0). When this "capacitance" is in parallel with a chargetransfer resistance (R), the Nyquist plot is the arc of a circle, but with the center of the circle blow the xaxis: It is the "depressed semicircle" shown in the figure on the previous page. This behavior is not seen on a mercury electrode because, as a liquid, it is atomically smooth! 



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REFERENCES
(1) "Impedance Spectroscopy",
JR Macdonald, ed., John Wiley, 1987. Sect. 2.2.3.4.
(2) "Tafel current at fractal electrodes. Connection with admittance spectra,"
WH Mulder, JH Sluyters, T Pajkossy, I Nyikos, J. Electroanal. Chem., 285
(1990)
103.
(3) "An investigation of the
capacitance dispersion on the fractal carbon electrode with edge and basal
orientations," CH Kim, SI Pyun, JH Kim, Electrochimica Acta,
48 (2003) 3455.
(4) "The evaluation of experimental dielectric data of barrier coatings by means of different
models,"
CA Schiller, W Strunz, Electrochimica Acta,
46 (2001) 3619.
(5) "CPE
Analysis by Local Impedance Analysis", JB Jorcin, ME Orazem, N Pebere,
B Tribollet, Electrochimica Acta, 51 (2006) 14731479.
Paper presented at EIS Symposium, Coco Beach, FL, June 2004.
(6) "The
RC time 'constant' at a disk electrode", KB Oldham, Electrochem.
Communications, 6 (2004) 210214.






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