I am assuming you are using high frequencies impedance measurements. You should be able to tell the difference between different solutions concentrations. Need to use platinum, get rid of the oxygen in the electrolyte and you should be fine. By the way, a conductimeter just do that.

Energy Storage Materials, 2018, 10: 85-91

This work from Prof. Yuguo Guo's group may be helpful. The method to measure the ionic conductivity of the electrolyte was described in the experimental part. You can also search some papers on quasi solid state electrolytes.

In addition to the above answers I would recommend you to read this good manual http://www.analytical-chemistry.uoc.gr/files/items/6/618/agwgimometria_2.pdf

As to the discrepancy between two different standard solutions. Make sure that the salts are of analytical grade quality at least.

I've read in a couple of articles that you are actually supposed to calibrate your device with a calibrating solution having a conductivity in range of what you want to measure. It means that I cannot expect that my cell gives me the same cell constant as for conductivity solutions of 1413, 5000 and 12880 uS/cm as they are so deviated from one another.

http://www.naptprogram.org/files/napt/publications/method-papers/1998-measurement-of-conductivity.pdf

http://www.crisoninstruments.com/site/pdfs_en/07/crison_en_7_1.pdf

I once had a supervisor that I saw twice in one year!

The four-electrode mode[1], technique (Z4e)[2], is an essential setup for your task; the Working Sense lead (WSLE) is decoupled from the working[3] electrode (WE), as the Reference lead.  In a 4-electrode technique, the potentials for any electrochemical reactions, that are occurring at the working (and counter) electrode(s), are not being measured; what is measured is the effect of an applied current[4] in the solution itself[2,3] or some barriers (always, in the solution[2,4]).

1. Two, Three and Four Electrode Experiments : Four-Electrode Experiments https://www.gamry.com/application-notes/electrodes-cells/two-three-and-four-electrode-experiments/

2. This technique is, relatively, a peculiar approach in applied electrochemistry, but if you want to measure the conductivity of even more complex and/or composite solutions such as (sensor for) wine, blood, ferrofluids, etc., as well as to give you a good answer for your task, then it (Z4e) is a crucial technique.

3. Ignore some destructive potential barriers on the working (and the counter) electrode(s). Also, some possible potential barriers in middle measuring (Pt wire) same electrodes are "relatively guiltless", since they are the same material, and no (applied, e.g. external) current is passing from them.

4. The Voltage due to the current i, in the solution, is measured from the (incremental) differential V (dV, middle electrodes), without (a contribution from) any destructive potential barriers in the useful, commonly used, frequency band(s). For the same (middle) electrodes, dV is a reliable signal for EIS (of the solution). Note: select a four-electrode mode, in EIS (Z=dV/di).

Dear Shahabeddin Dayani, ask, please, from your supervisor(s) to approve (your next plans and) the techniques, that you will implement, actually, in order to obtain the conductivity measurements of your solutions.

Dear Ioannis Samaras,

I speak regulary with my supervisor about this issue , and we found a paper today about this issue that put us one step ahead, I will add how to solve this problem in future to this question.

Thanks for your answer

After almost 4 month of dealing with different resources , papers, and expperiments, I shall answer to this question which was first aske by myslef :

Cell Constant is NOT a purely geometrical factor. It strongly depends on the concenteration of the electrolyte since a change in concenteration leads to the change in double layer capacitance of the electrochemical cell.

If you need more evidence and more explanations , I would be more than happy to answer your emials

I see only now this long discussion and I don't agree with the final conclusion: "Cell Constant is NOT a purely geometrical factor. It strongly depends on the concentration of the electrolyte ". It means that this constant is not... constant. Or, in the common/reference method (using a conductivity cell and a conductivity meter) the linearity of the response is considered a verified issue and thus only one standard solution is used for calibration. It means that the cell constant is ...constant on a large range of standard solutions concentration.

I suggest the following conditions to verify** if EIS is comparable with the reference method:

- use a professional conductivity cell (platinized platinum*, 4 electrodes)

- the applied DC: 0 V (not OCP)

- useful frequency range: 25...1000 Hz

- temperature control is critical

The measurement of the conductivity by EIS on a standard solution is not an electrochemical experiment, but a physical one.

* https://assets.fishersci.com/TFS-Assets/LSG/manuals/D15988~.pdf

** Article A New system for Measuring Electrical Conductivity of Water ...

As Cornel Radu, for professional conductivity cells' conditions (4 same Pt-electrodes, 1kHz) the "Cell Constant" is a useful constant, and it does not depend on the concentration of (common) electrolytes.

The assumptions of the final conclusion, where the cell constant was made dependent on the concentration, is a bit of a setback. Constants are made to exactly compensate such variations in the parameters.

The following work describes the classical methods for the determination of the conductivity of electrolyte solutions. Many of the techniques and precautions needed also apply to impedance spectroscopy, which is now more common. Simple resistance meters operating at a single frequency and without any balancing of the capacitance, can not be used in serious laboratory work.

Spiro, M. Conductance and Transference Determinations. In Physical Methods of Chemistry, 2nd ed., Vol. 2, Electrochemical Methods; B. W. Rossiter and J. F. Hamilton, eds.; John Wiley and Sons Inc.: New York, 1986; Chapter 8.

Hello again everyone,

thanks for the discussion and answers . Unfortunately due to a lot of work pressure I couldnt respond to the answers for a long time .

Ill upload a part of my master thesis , sorry that I cannot upload the whole part due to copy right issues .

long story short, in design of a conductivity sensor surface porosity and the resistor of the cable shall be obsrved very accurately . the range of the sensor , hence , the range in which measured cell constant vs. conductivity doesnt change is highly related to surface, cable impedance and measured impedance. Although, Cell constant (theoretical and geometrically defined) is always constant, one should always consider the measured cell constant .

Please read the attached document and give me your feedback .

Cheers.

Using a three-electrode conductivity cell for dilute solutions