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#
Inaccuracy of corrosion current determination in presence of ohmic drop *Corrosion – Application Note 48*

Latest updated: March 28, 2024
**Abstract**

Ohmic drop is one of the error factors leading to an inaccuracy in the corrosion rate measurement. This factor, resulting from a low conductivity of a solution, has the effect to decrease the measured corrosion current and so leads to underestimating the true corrosion rate of a material.

In this application note a special dummy cell (Test Box #3-2), built to mimic a linear electrochemical system, was tested in order to study the effect of Ohmic drop on the measured corrosion parameters. The corrosion rate and Tafel parameters were estimated using Ohmic drop compensation with four techniques available in EC-Lab software. A good correlation between the corrosion parameters obtained with the four methods was obtained.

## Introduction

### Ohmic drop

The effect of the ohmic drop on electrochemical measurements was presented in Application note #27 [1]. The ohmic drop $R_\Omega I(t)$, due to the resistance $R_\Omega$ of the electrolyte between the working electrode and the reference electrode, is given by (Fig. 1) [1]:

$$V(t) = E(t) + R_\Omega I(t) \tag{1}$$

Where $V(t)$ is the potential applied by the potentiostat and $E(t)$is the potential seen by the working electrode.

Figure 1: Scheme of the ohmic drop in a standard three-electrode set-up ($V(t)$: potential applied by the potentiostat; $E(t)$: potential at the electrode and $R_\Omega I(t)$): ohmic drop) [1].

This note presents the error made when corrosion currents are determined in presence of an ohmic drop. The following part describes this inaccuracy.

### Corrosion current measurement in presence of an ohmic drop

It is convenient to use a dummy cell of known $I$ *vs.* $E$ characteristics to check the different methods used to measure corrosion parameters. The test box #3-2, which is the second circuit of the test box #3, presented in Application note #9 [2] was used*vs. * $E$ curve of the test box #3-2 is shown in Fig. 2. Tafel straight lines are observable over 250 mV on each side of the corrosion potential and the Tafel Fit analysis gives $I_\text{corr}$=33 nA, $\beta_\text{a}$=61.5 mV and $\beta_\text{c}$=61.4 mV (Fig. 2).

Figure 2: Steady-state curves $\text{log}|I|$ *vs. * $E$ for the test box #3-2 without ohmic drop, and Tafel Fit. $I_\text{corr}$=33 nA, $\beta_\text{a}$=61.5 mV, $\beta_\text{c}$=61.4 mV.

The effect of the ohmic drop is simulated by adding a 2 kΩ resistance in series with the test box #3-2 on the WE side. The results obtained by Tafel Fit depend on the potential range chosen to plot the Tafel lines. When a 2 kΩ resistance is added in series, the Tafel lines can only be observed over a 100 mV potential range on both the anodic and cathodic part of the curve (Fig. 3). The results of the Tafel Fit analysis now given for the potential range chosen in Fig. 3, with a 2 kΩ resistance in series, $I_\text{corr}$=44 nA, $\beta_\text{a}$=69.4 mV and $\beta_\text{c}$=68.6 mV.

Figure 3: Steady-state curves $\text{log}|I|$ *vs. * $E$ for the test box #3-2 with ohmic drop, and Tafel Fit. $I_\text{corr}$=44 nA, $\beta_\text{a}$=69.4 mV and $\beta_\text{c}$=68.6 mV

In the remaining part of the note, the ZIR ohmic drop compensation technique will be used and tested for all the methods available in EC-Lab®: Stern Method (Tafel Fit), Stern and Geary method, VASP (VASP Fit) and CASP (CASP Fit).

## ZIR Technique

The ZIR technique is described in the Application note #29 [3]. The resistance of the solution is determined by carrying out an impedance measurement at one single frequency, by default 100 kHz. This frequency can be changed by the user.

$$R_\Omega = \text{Re}Z(f_\text{ZIR}) \tag{2}$$

The ZIR technique has to be set before the technique that needs to be corrected (Fig. 4). A compensation value of 85% was chosen. Please note that this is a software compensation.

Figure 4: Linking of ZIR and LP techniques.

## STERN Method (TAFEL Fit)

The curves $\text{log}|I|$ *vs. * $E$ measured on the test box #3-2 with a series resistance of 2 kΩ with or without using ZIR technique are shown in Fig. 5. Using ZIR technique enlarges the potential range where Tafel lines can be seen and facilitates the determination of corrosion parameters. Using Tafel Fit analysis with ZIR technique we obtain $I_\text{corr}$=37 nA, $\beta_\text{a}$=68.4 mV and $\beta_\text{c}$=69.5 mV.

Figure 5: Steady-state curves $\text{log}|I|$ *vs. * $E$ with ohmic drop (RΩ=2 kΩ, blue curve), and ZIR correction (red curve), $I_\text{corr}$=37 nA, $\beta_\text{a}$=64.7 mV and $\beta_\text{c}$=64.5.

## Stern and Geary method

In the case of a corrosion reaction without adsorption or diffusion limitation, the value of $R_\text{p}$ cannot be measured using the micropolarisation method [4] in the presence of ohmic drop. Only the sum $R_\text{p}$+$R_\Omega$ can be measured with this method. It would be possible to measure $R_\text{p}$ by linking ZIR and micropolarisation (LP) techniques. It is easier to plot the diagram of the impedance at the rest potential (Fig. 6) and directly determine $R_\text{p}$ and $R_\Omega$.

The Nyquist diagram shown in Fig. 6 was measured on the test box #3-2 with a resistance of 90 kΩ in series.

Figure 6: Nyquist diagram of the impedance of the test box #3-2 measured at the rest potential (x) and theoretical diagram of a R1+R2/C2 circuit (line) with R1=90.2 kΩ, R2=400.5 kΩ and C2=0.467 µF.

This Nyquist diagram can be fitted using ZFit [5] for the R1+(R2/C2) circuit. We obtain $R_\text{p}$ = R2 = 400.5 kΩ and $R_\Omega$ = R1 = 90.2 kΩ. The value of $I_\text{corr}$ can be determined using the Stern and Geary relationship:

$$I_\text{corr} = \frac{\beta_\text a \beta_\text c}{R_{\text{p},E_\text{corr}} (\beta_\text a + \beta_\text c) \text{ln} \,10} \tag{3}$$

And $\beta_\text a$ = 61.5 mV and $\beta_\text c$ = 61.4 mV found previously by Tafel Fit analysis without ohmic drop (cf I – 2). We obtain $I_\text{corr}$ = 33.3 nA.

## VASP method

The VASP method is described in the Application note #36 [6]. The VASP technique consists of the determination of the change of the measured polarization resistance $R_\text{p}$ with the potential amplitude variation $\delta E$.

Fig. 7 shows the $R_\text{p}$ *vs.* $\delta E$ curves plotted i) without ohmic drop, ii) with a resistance, iii) with ohmic drop compensation by ZIR method at 85%

Figure 7: VASP on test box #3-2 without ohmic drop (blue curve), with a resistance in series of $R_\Omega$=90 kΩ (red curve), and with ZIR compensation at 85% (green curve).

The following relationship [7,6] cannot be used in the presence of ohmic drop.

$$\frac{1}{R_{\text p}}=I_\text{corr} \sum^\infty_{k=0} \frac{b_\text a ^{2k+1}+b_\text c ^{2k+1}}{2^{2k} k!(k + 1)!} \delta E^{2k} \tag{4}$$

But it is possible to use the experimental result obtained with ZIR compensation (green curve in Fig. 7). The obtained values are: $I_\text{corr}$=41.3 nA and $\beta_\text a$=$\beta_\text c$=72 mV.

## CASP method

The CASP method analyses the non-linear response of an electrochemical system subjected to a sinusoidal potential of constant amplitude and frequency [8].

Figure 8 shows the current response for test box #3-2 without ohmic drop, with a resistance in series of $R_\Omega$=90 kΩ, and with MIR compensation at 85%. In the MIR technique, the value of the resistance that needs to be compensated is manually entered.

Figure 8: CASP on test box #3-2 without ohmic drop (green curve), with a resistance in series of $R_\Omega$=90 kΩ (blue curve), and with MIR compensation at 85% (red curve). $\delta E$=40 mV, $f$=0.1 Hz.

MIR and ZIR can both be linked to CASP (and to the other techniques too). If the value of the ohmic drop is known, MIR can be used. The frequency $f$=0.1 Hz is low enough to allow the measurement of $R_\text{p}$ as it is shown in Fig. 6. The obtained values with the CASP analysis tool are:

- Without ohmic drop: $I_\text{corr}$=31 nA, $\beta_\text a$=56.9 mV, and βc=55.6 mV,
- With ohmic drop: $I_\text{corr}$=40.3 nA, $\beta_\text a$=89.0 mV, and $\beta_\text c$=87.7 mV,
- With ohmic drop and ZIR (85%): $I_\text{corr}$=33.9 nA, $\beta_\text a$=64 mV, and $\beta_\text c$=62.7 mV.

## Conclusion

The values of the corrosion parameters obtained with the Test Box #3-2 with all the different methods are shown in Tab. I. This application note showed that the methods available in EC-Lab^{®} to determine the corrosion rates (Tafel Fit, Stern and Geary, VASP, CASP) can be used to determine the corrosion rate of a system in presence of ohmic drop.

Table I: Summary of the parameter values. $R_\Omega$ means that an ohmic drop is added. The method of compensation is stated before the technique.

Technique | $I_\text{corr}$/nA | $\beta_\text a$/mV | $\beta_\text c$/mV |

Tafel Fit | 33 | 61.4 | 61.5 |

Tafel Fit, $R_\Omega$ | 44 | 69.4 | 68.2 |

ZIR, Tafel Fit, $R_\Omega$ | 37 | 64.7 | 64.5 |

Stern, Geary | 27.2 | – | – |

EIS, Stern, Geary, $R_\Omega$ | 33.3 | – | – |

VASP | 35.8 | 61.6 | 61.6 |

VASP, $R_\Omega$ | 57.2 | 120.8 | 120.8 |

ZIR, VASP, $R_\Omega$ | 41.3 | 72 | 72 |

CASP | 31 | 56.9 | 55.6 |

CASP, $R_\Omega$ | 40.3 | 89.0 | 87.7 |

MIR, CASP $R_\Omega$ | 33.9 | 64.0 | 62.7 |

This table shows the error introduced by the ohmic drop in the measurement of the corrosion rates. This error can be up to ≈40% (VASP). It is also clear that ohmic drop compensation techniques are highly efficient at reducing this error down to ≈10% (Tafel Fit).

*Data files can be found in :*

*C:\Users\xxx\Documents\EC-Lab\Data\Samples\Corrosion\AN48_*

## References

1) Application note #27 “Ohmic drop, part I: Effect on measurements”

2) Application note #9 “Linear *vs.* non-linear systems in impedance measurements.

3) Application note #29 “Ohmic drop, Part III: Suitable use of the ZIR techniques ?”

4) Application note #10 “Corrosion current measurement for an iron electrode in an acid solution”

5) Application note #14 “ZFit and equivalent electrical circuits”

6) Application note #36 “VASP: an innovative and exclusive technique for corrosion monitoring”

7) J.-P. Diard, B. Le Gorrec, and C. Montella, Corros. Sci. 40, (1998) 495.

8) Application note #37 “CASP: a new method for the determination of corrosion parameters”