There is any relationship between Dielectric measurement, AC conductivity and Impedance spectroscopy at room temperature.
From the impedance spectroscopy itself you can derive all these parameters.
Read "Impedance Spectroscopy Theory, Experiment, and Applications" by J. Ross Macdonald for deep understanding.
complex cond = j*angular frequency * complex permittivity
Yes, any of these quantities can convert to the others. The impedance is obtained by Z* = U*/I*, and the equivalent parallel capacitance by Cp* = 1/jωZ*. The complex permittivity ε* = ε’ - jε’’ = Cp*/C0, where ε’ is the dielectric constant, ε’’ is the dielectric loss, and C0 is the vacuum capacitance (or the geometric capacitance, i.e., the capacitance of the vacuum with the same geometry of the sample). The complex conductivity σ* = σ’ + jσ’’ = jωε0ε*, where ε0 is the dielectric constant of the vacuum and σ’ is the conductivity.
This paper may be more helpful with the discussion, https://doi.org/10.1063/1.5081842.
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