Instrumental limitations high impedances

With appropriate calibration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to zero concentration yield the intrinsic storage and loss moduli [Gr] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instrument provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 Hz. High frequency (20 to 500 K Hz) viscoelastic properties can be measured with another instrument, the high frequency torsional rod apparatus (HFTRA) (294). 

For RF measurements, another class of instruments is available. Modem high-end network analyzers range up to 110 GHz. These instmments use reflexion measurements to determine ratios of inserted to reflected power. Because of the use of directional couplers, the lower frequency limit will typically not go below a few kHz. To obtain complex impedance values, a vector network analyzer (VNA) is needed, because scalar network analyzers give absolute values only. Measurements can be conducted very fast... 

FRAs provide a very convenient, high-precision, wide-bandwidth method of measuring impedances in electrochemical systems. Commercial instruments are available which provide up to 4 digits of precision in the real and imaginary components, in frequency ranges covering 10 to lO Hz. These are direct-measuring devices and therefore are not susceptible to limitations on imposed potentiostat control. 

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