Impedance studies on polycarbazole bioelectrodes: Evidence of an electrode-side nonlinearity quantifiable by a Hamiltonian quaternion formalism that preserves Kramers-Kronig relations

PHYS 523

Marc Ovadia, movadia@uic.edu1, Daniel H. Zavitz, dzavit1@uic.edu2, Yobani P. Kayinamura, ypk@georgetown.edu3, and J. Faye Rubinson, jfr@georgetown.edu3. (1) Department of Bioengeering, The University of Illinois-Chicago, 851 S. Morgan, Chicago, IL 60607, (2) Department of Chemistry, University of Illinois at Chicago, (3) Department of Chemistry, Georgetown University, 36&O street, Washington DC, DC 20057
Nonlinear response to sinusoidal electrification is a rarely observed phenomenon for electrically conductive interfaces. Where this has been observed in biological interfaces, it has been attributed to tissue-side phenomena, and time-domain analysis has been applied (Ovadia et al. Chemical Physics Letters 2006; 424: 285 – 288). In the present abstract we report the observation of nonlinear response attributable to electrode-, or virtual-electrode phenomena, in an exemplar of the important new class of electrically conductive highly conjugated polymer (organic) electrodes, viz. linear polycarbazole. While other members of this class manifest a quantifiable impedance in the complex number field (which may include Warburg response where complex Z = ZW∞ and resistive behavior where Z = ZHl [Hl means Halbleiter; Cf. Ovadia et al. Chemical Physics Letters 2006; 419: 277–287]) the polycarbazole manifests no definable impedance due to essential nonlinearity. There is no formal description available for this type of pseudoconductivity. We introduce a quaternion formalism for impedance and pseudoimpedance Z⊂T=a+bi+cj+dk [where a,b,c,d are real and i2=j2=k2=-1 and jk=i] that adequately and successfully describes all conductivity (c=d=0) and pseudoconductivity presently known, and which reduces to the complex field for ordinary conductivity. In this formalism, the normalized impedance of a capacitor is Z=i, the polycarbazole pseudoimpedance determined experimentally Z⊂T(polycarbazole)=k, that of a resistance is Z=1 and that of the Warburg impedance ZW∞=√i=i½. The non-Abelian character of Z⊂T implies that the Onsager relation will fail for some such interfaces. Remarkably, certain Kramers-Kronig relations (Hilbert transformation not only in the complex but also in the [j,k] plane) still hold for certain experimental setups. Computation of the energy integral ∫D.Edt reveals that charge transport through such an element is lossless, similar to conduction in an ordinary capacitance.
 

PHYS Poster Session - General Theory
7:30 PM-10:00 PM, Wednesday, April 9, 2008 Morial Convention Center -- Hall A, Poster

Division of Physical Chemistry

The 235th ACS National Meeting, New Orleans, LA, April 6-10, 2008