The Ohmic Impedance Contribution to the Indirect Impedance Measurement
Authors: Alexander Christopher L. , Orazem Mark E. 
Published: February 2020

Studies have shown that the application of an electric field to the surface of an electrolytic medium can indirectly polarize a metal within the solution.1,2,3 Based on this concept, an indirect impedance measurement may be used to assess the properties of a conductive element contained within a resistive medium without a direct connection to the conductive element.
The indirect impedance technique was studied by Zhang et al.4 to determine the location and the condition of steel rebar within concrete slabs. They were able to determine qualitatively that the measured surface impedance was a function of the corrosion state of the steel as well as the resistance of the concrete. However, extracting the true impedance of the conductive element from the impedance of the whole system was difficult.
The simplest way to interpret impedance measurements is to use equivalent circuits containing physically meaningful components to fit the data. Andrade et al.5 used results of finite element models to propose an analogue circuit that accounts for the polarization behavior of the steel and the properties of the mortar in which the steel is embedded. They determined that a suitable circuit must contain a parallel, as well as, a series resistance term associated with the resistivity of the concrete in relation to the impedance of the steel.
The disadvantage of using circuits containing passive elements is the inability to account for the effects of nonuniform current distributions and ill-defined geometries. Newman6 showed that the geometry of a disk electrode embedded within an insulating plane causes the apparent capacitance to be frequency dependent. Huang et al.7 provided an explanation for this by showing that the ohmic contribution to the impedance becomes complex at high frequencies due to the nonuniform current distribution. Therefore the use of equivalent circuits to fit the impedance of disk electrodes is only valid below a characteristic frequency dependent on the radius of the disk.
A ﬁnite-element model has been developed to calculate the frequency-dependent potential distribution through a cylindrical grout specimen representing a section of a structural bridge tendon containing one axially-located steel strand. Impedance simulations were performed at diﬀerent steel corrosion states while incorporating the kinetics at the current-injecting electrodes. The idea of an ohmic impedance was used to account for the unusual geometry of the indirect impedance in application to corrosion detection in structural bridge tendons. The indirect impedance was found to include two separate contributions of the grout resistivity. There is an ohmic impedance associated with the grout that is in parallel to the steel and another ohmic impedance associated with the grout that is in series to the steel. By understanding the exact influence the grout has on the indirect impedance, a method may be devised to extract the properties of the steel and determine the corrosion rate.

References

C. Andrade, I. Martnez, “Metal corrosion rate determination of diﬀerent solutions and reinforced concrete specimens by means of a noncontacting corrosion method,” Corrosion
66 (2010) pg. 056001-056001.

P. J. Monteiro, H. Morrison, Non-destructive method of determining the position and condition of reinforcing steel in concrete, 1999. US Patent 5,855,721.

M Keddam, X. R. Novoa, V. Vivier, “The concept of floating electrode for contact-less electrochemical measurements: Application to reinforcing steel-bar corrosion in concrete,” Corrosion Science,
51 (2009) pg. 1795-1801.

J. Zhang, P. J. Monteiro, F.H. Morrison, “Noninvasive surface measurement of corrosion of reinforcing bar in concrete: Part I Experimental results”, ACI Materials Journal,
98 (2001) pg. 116-125.

C. Andrade, J. Sanchez, I. Martinez, N. Rebolledo, Analogue circuit of the inductive polarization resistance,” Electrochimica Acta
56 (2011) pg. 1874-1880.

J. S. Newman, Frequency dispersion in capacity measurements at a disk electrode, Journal of the Electrochemical Society 117 (1970) 198–203.

V. M. W. Huang, V. Vivier, M. E. Orazem, N. Pbre, B. Tribollet, “The apparent constant-phase-element behavior of a disk electrode with faradaic reactions a global and local impedance analysis,” Journal of the Electrochemical Society
154 (2007) C99-C107.