The semicircle only occurs for ideal circuits containing a single time constant (simple RC circuit, for example).  The linear component indicates a frequency regime where the device response maintains a constant phase.  In electrochemistry, this could be indicative of diffusion limited processes, such as ionic conduction for example.  How this specifically applies to your experiments, I'm not sure.  Hope this helps.

Hossein,

  This is what we're trying to explain.  The complete semi circle only occurs for ideal circuits with a single time constant.  That your data doesn't look that way isn't surprising, it just indicates a deviation from the ideal, simplified case.  This means that the AC response of your super capacitor isnt well-described by a capacitance with a resistance in series for all frequencies that you've measured.  That linear region indicates your circuit model needs to include additional components (resistance, capacitance) in order to reflect the behavior of your super cap.  This Nyquist plot is not uncommon in electochemistry experiments and is often associated with diffusive processes.

Thank you so much.

Try to evaluate the frequency range where the RC circuit is active and where the diffusion predominates (for your graph).

Look at and compare two EIS records with:

- two separate and complete semicircles and 

- two superposed semicircles.

You may simulate them with physical resistors and capacitors. 

If you understand and accept that the separation is the exception , not the rule the situation will be more clear.

Can anyone explain why the linear part will have some slope instead of exact vertical or horizontal line. Is there any physical significance for that too?

Thanks

What's its equivalent circuit?