Hello, 

In real world, electrical circuits / systems are composed of capacitors (C) and inductors (L) beside of resistors (R). AC current is useful to probe C and L and it can also excite R. Also depending on frequency the behavior of C / L will change and DC can not probe this behavior. 

The 5 mV AC is chosen keeping in mind the pseudo linear behavior of the system. Too low value will generate a noisy response where as too high will make the response non linear. 

Please consult the books by Bard and Orazem for in depth understanding.

Thanks

I am not sure about an answer to the 2nd question. But I think that your working electrode suffered some reaction during the 1st EIS which changed its interaction with the electrolyte.

What is your VDC (?) voltage value[1-3] during your battery's EIS test?

1.  Check your VDC value in your actual schedule file.

2.  An extremely LOW value of VDC~0 is a reasonable (erroneous) value, that might be a probable cause[3], for the accidental decreasing battery's OCV, from 3V to 0.2V, after a wrong EIS test. The battery's OCV should never change during a common (quasi-potentiostatic) EIS test,

3.  A normally LOW VAC value might be unfairly intermixed with a normally HIGH VDC in a EIS for a battery.

Thank you  very much Agnivo for your comments. 

Dr. Samaras thank you very much  for your suggestions. You pointed out the exact cause for the  problem. VDC was low. I completely agree of the fact that OCV should remain same after EIS test.  As you mentioned in point 3, i was wondering about choosing the value of VAC and VDC for a EIS test. On what basis should we decide those parameters? 

The amplitude of the sinus voltage preset value (VAC,  say,  VAC : [1 to 5] mV) is very low, as common wisdom[1]. On the other hand, the DC component Voltage source, or else, known as the offset (VDC) of the composite sinus V-source (= VDC + VAC sin[wt] ), is preset near the OCV (of the battery, iDC~0A), during a common EIS measurement, for a single freq. scan range.

1.  The AC voltage source amplitude (VAC) must be set as low, as possible,  for a long list of exp. sophistications.

Thank you Dr. Samaras for your suggestions. With change in VDC i noted there will be change in impedance thus the EIS curve will be slightly different. Even the same technology battery made from the same sample will have different OCV .  So i was wondering how can we compare the EIS curve of two batteries which have different OCV? I appreciate if you can provide any references Dr. Samaras. Thank you !!

Yes, even the "same" technology battery... might have different OCV, as well as different SOC[1] ;  then, an alternative to, frequently used AC-Voltage-mode, an AC-current mode of an EIS  ( isource= 0DC + iAC sin[wt] ), if available, is more adaptable[2] for this (class of) task, you are asking for.

1.   "Li-ion dynamics and state of charge estimation"      http://www.sciencedirect.com/science/article/pii/S0960148116305213

2.   There exist an "OCV free" mode, using an AC-current source mode of EIS, that is not used regularly.

Thank you Dr. Samaras, i was wondering if i provide the source with 0DC + iACsin[wt], won't the 0 DC current have effect on OCV as it is the case with DC voltage mode? 

The alternative AC-current mode of an EIS (i= iDC + iAC sin[wt] ) with : iDC[1] ~ 0(uA/cm2), has never[2] an effect on the OCV of the cell.

1.  Maybe you want to ask some help from a technician, in order to make a checkup for the actual value of the "iDC_0 zero" (or zero offset calibration), in all current mode ranges : iDC_0 ~ 0.

2.  Keep low the amplitude iAC value; start with iAC ~ 1(uA/cm2), a fair AC-current amplitude value, for many cases of common lab. battery cells. In case of noise, increase it, up to 100(uA/cm2), if possible, under a brief oscilloscope[3] supervision (so that : VAC