usually the Oxide layer, the coating layer or any physical layer on the surface of the metal prevents the flow of direct current, which makes running a conventional LPR test difficult, yet  corrosion takes place below those layers which means there is a corrosion current passing through them. EIS depend on passing alternative current for which these layers play the role of the capacitor isolation middle layer , and thus by passing the AC in the cell the impedance of this layer (how much it resists the flow of current) can be determined. Providing the open circuit   potential  is known, we can easily determine the corrosion current . This idea is good to study the resistivity  of coating or passivation layers to corrosion ...

Fine oxide or ppt. particles will grow as corrosion on the metal surface proceeds. With time swelling capacity of these fine compact deposits are reduced. Basically these highly fine and porous particles are hydrophobic. Though hydrophobic, the fine deposits are enough porous to water penetration. Hence CPE (~Qn) of these particles may be similarly defined as that of the coating.

A suggestion: For corrosion studies one just follow the CPE-coat magnitude. The smaller (nano-pico i.e. very small current flowing to corrode the substrate surface) the value the better is the coating. But one must also follow the shift in the mid frequency EIS Bode phase angle plot.

Dear Wadah Jawich and Narinder Mehta,

Thank you for your answers, they are very enlightening

So let me confirm, that in general, the smaller value of capacitance would mean smaller current flow occured, which indicate better corrosion protection properties provided by the coating.

Also regardless of that, resistance value was more significant as compared to capacitance.

Is this right??

In a way you are right that "the smaller value of capacitance would mean smaller current flow occurs, which indicate better corrosion protection properties provided by the coating.

However, one should know that the EIS is mainly used to study the electrochemical behavior of cases such as ;an  interface between solid metal & aqueous solution; an interface between an oxide layer on a solid metal and aqueous solution; an interface between a coated layer on a solid metal and aqueous solution; an interface between an inhibited layer on a solid metal and aqueous solution and so on.   The purpose of the use of  EIS because one can control the A.C current due to the subtleness of the interfaces.   Therefore, Opposite charges which form across an interface; for instance, the interface between an oxide layer on a solid metal and aqueous solution    would lead to the formation of the capacitance.   The smaller the opposite charges across the interface the smaller the value of the capacitance.   Consequently, the smaller the flow of the current would occur,which indicates better corrosion protection properties provided by the formation of the oxide layer.   

Dear Muhammad,

I understand that your system is some specific oxide layer growing on a given metal substrate. If that is the case, then I have the following comments :

1. In the first approximation, it is correct that the EIS response of this system can be modelled by a single resistor "R" in parallel with a single capacitor "C".

The real part of the measured impedance Z1(w) at low frequencies w (w->0; here becomes Z1 frequency independent) is the resistance R of the oxide layer.  

The imaginary part of the measured impedance Z2(w) is directly related to the real part of the measured complex capacitance [ impedance: Z(w)=Z1(w)+I*Z2(w); admittance: Y(w)=1/Z(w) ; capacitance: C(w)= (1/i*w)*Y(w) ]. If the real part of the measured complex capacitance C1(w) is frequency independent, then it is THE GEOMETRICAL CAPACITANCE OF THE OXIDE LAYER. This IS THE PHYSICAL MEANING of the modelled capacitor C in your R,C equivalent circuit. C=eps*(oxide area/oxide thickness), where eps is the dielectric constant of the oxide layer.

2.  The measured/deduced value of the model capacitor "C" IS INDEPENDENT of the current through the oxide (the model resistor "R" ) !! It only changes if eps  and/or the thickness of the oxide layer change with time.

3. In a perfect oxide, the R->infinity (no dc current), but the "corrosion oxides" are not perfect and therefore one observes both finite and possibly time changing R and time changing eps . This is observed as frequency dependent C1(w)~ws (power law dependence and the R,C model has to be extended by introducing a third parallel element (sometimes called constant phase element). This is probably what you see in your data.

I hope this will help you on the way.

With best regards

Petr

3.

Dear  Khaled J. Habib and  Petr Viscor

Thank you for your answers.

I take that the capacitance value is only dependent on the geometry/morphology of the oxide, and not dependent on the current flow/resistance.

In the system that i am working on, the mostly used equivalent circuit model in previous investigations involves two pairs of R-C (or R-CPE) in parallel, instead of one pair. This was attributed to the significant morphological difference between inner and outer part of the oxide coating.

In this case, is it proper to use each values of "outer part" and "inner part" capacitance value to calculate the thickness of each part? Or am i missing some point here?

Regards,

Oxides of few metals such as Ru, Co,  Ni, Mn and others are used as supercapacitor. The pseudocapacitance occurs in the oxide layer. In fact oxide on Al is used as commercial capacitor. In CV you might have seen oxidation and reduction peaks. Underneath metal acts as current collector. The EIS exhibits accordingly.

Dear Muhammad,

first, a point to clarify: If your oxide is indeed spatially inhomogeneous, meaning that dielectric constant and the resistivity/conductivity change within the oxide in a reasonably "sharp" fashion (spatial scale < oxide thickness), then it might be that the equivalent R,C model should consist of two R,C terms, each being a parallel connection of resistance R and capacitance C. BUT THESE TWO TERMS ARE CONNECTED IN SERIES, NOT IN PARALLEL !!! They simply represent the oxide layer as consisting of two oxide sub-layers on top of each other. Any other topology is non-physical, being just an arbitrary R,C network with no connection to physical reality.

If that is the case, then you are right and the two capacitors are indeed related directly to the thicknesses of the respective sub-layers. BUT BE AWARE, now the actual experimentally observed values of the respective C's (remember, the flat parts of C1(w) and C2(w) !) do depend on the modelled resistances ! You should probably try it for yourself, the resulting impedance of such a network (two parallel R,C terms in series) is analytical and you will see immediately how the "measured" C1 and C2 depend on the values of R1 and R2.

The last thing is the "constant phase element". It might be that there are indeed slow polarisations of universal type (see the books by  Andrzej K. Jonscher). The typical and rather fatal error occurring in the literature is that one does not recognise the importance of establishing, where spatially, these processes occur !! The constant phase element might be in the first sub-layer (Havrilliak's universal capacitor Cuniv(w), in parallel with the corresponding spatial R,C), it can be in the second sub-layer, or it can be in both. If one does not have a reasonably clear physical picture, then only fitting of the data with different topologies of Cuniv(w) can resolve the problem.

With best regards

Petr