Phase angle applied potential

Further, if within the electrical circuit the ohmic resistance R can be neglected, the ic wave leads to the potential by 90°, as is known, which means that shows a positive 7t/2 phase angle shift ( between tt/2 and zero. Our main objective in AC polarography, however, is the faradaic current, so a separating condenser is placed between the amplifier and normal resistor in order to filter out the d.c. current and to evaluate the ac current component. As we want to understand the relationship between idc(i ) and iac(i ) as a function of Edc and Eac applied, we may consider Fig. 3.41(a) and (b). 

If a fixed frequency sinusoidal perturbation is applied at a succession of fixed d.c. potentials, we can register the resulting alternating current and its phase angle vs. the d.c. potential. The form of the curves obtained gives information about the kinetics, and can also be used for analytical... 

The angle 8e describes the deviation of the phase shift between current and applied potential from the ideal value of 90°. Its projection on the real part of the total impedance Z therefore describes the ohmic part of the capacitor characteristic corresponding to a series resistance in the equivalent circuit. In practice, this number is used to specify the polarization losses of a capacitor. Analogously, the total loss factor tan 8C of a capacitor is defined by the ratio of the real and imaginary part of the total impedance Z. In addition to the polarization loss, this number considers unavoidable resistances due to lead wires and losses due to an imperfect insulation, plus the capacitive inductance I ... 

It is noted that the equivalent circuit in Fig. 6.18 has been normalized with respect to specimen (WE) area. Therefore, external current density is shown, iex = Iex/A, and the dimensions of the impedances are electrical resistance times specimen area (e.g., ohm-m2). To analyze this ac circuit, the potential, current density, and impedances will be treated as vectors (again indicated by bold type), which will be represented by complex numbers. The analysis first will provide the equivalent impedance of the circuit, Z, and then the phase angle, 8, of the impedance with respect to the applied potential, (Eexp - Ecorr). 

Recall that in a purely capacitive circuit element, the phase angle between the current and applied potential is 0 = Jt/2 and Z2 = -jXc, where Xc is the capacitive reactance, in this case normalized with respect to the specimen area (ohm-m2). Xc is equal to 1/toC, where (0 is the angular frequency (radians/s, that is, (0 = 27tf, where f is frequency in cycles/s or Hertz) and C is the normalized capacitance (farad/m2). In a purely resistive circuit element (e g., Rp and Rs), the current is exactly in phase with the applied potential (0 = 0) thus, Z3 = Rp and Z3 = R, where, again, Rp and Rs are normalized with respect to specimen area (ohm-m2). Upon substitution of Eq 6.61 to 6.63 into Eq 6.60, the equivalent circuit impedance is determined to be ... 

Figure 5, EIS curves showing phase angle change with frequency for 100 nm-thickpoly(3-methylthiophene) film in 0,1 MLiClO at different applied potentials, -0.5 V(a), 0.0 V(b), 1.2 V(c).

The AC polarographic wave can be distorted, if the resistance of the electrolytic cell is not minimized. The product of the solution resistance, Rs and the alternating current, results in the potential drop Iac s which causes the decrease of the amplitude of the applied AC potential and affects the phase angle between E c and Iac- The consequences are the broadening and the lowering of the AC peaks. 

This means that the phase angle 0 is zero. For a capacitor, we need to apply the definition of capacitance, C, from the relation between the potential, E, across the plates to the charge q residing on the plates ... 

Ac voltammetry is one of the techniques based on the analysis of faradaic impedance. A low-amplitude sinusoidal voltage (E ) is applied to the working electrode, which is also biased at some dc potential (E ) with respect to the reference electrode. Because of the difference in the time scale, the ac component of the total current can be readily separated from the dc component. The kinetic parameters can be extracted either from the amplitude of ac current, which is measured as a function of E, or from the phase angle between the ac current and ac voltage, [Pg.645]

DIELECTRIC PHASE ANGLE The angular difference in phase between the sinusoidal alternating potential difference applied to a dielectric and the component of the resulting alternating current having the same period as the potential difference. 

---