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The current-voltage relationship of an electrochemical investigation contains essential information of the electrode-electrolyte interface. However, the accuracy of data always bother the electrochemists for the correct evaluation of interfacial properties. While the accurate measurement of current is reasonably straightforward, measuring potential across the interface is impossible as the potential measuring probe in the electrolyte can not measure the potential at the solution side. Therefore, the potential difference is measured across the working electrode and reference electrode in a typical three-electrode setup. Since these electrodes are at a finite distance to each other in the electrolyte solution, an additional potential drop is observable due to the current flowing through the electrolyte with non-zero resistance. This drop in potential is known as IR drop, the effect of which must be compensated in electrochemical measurements.

Consider a typical three-electrode system that consists of an equipotential working electrode and ideally polarizable reference electrode as shown in the schematic. The equivalent circuit associated with the system gives a deep insight into electronic current flow through the circuit. Let assume that the currents I and I* are flowing through the working and reference electrodes, respectively. Since the reference electrode is an ideally polarizable electrode, no current will pass through it, and hence, the current I  will flow through the counter electrode and be measured by the workstation. The notations in the schematic are defined below:

R_w = Charge transfer resistance across the interface of the working electrode

C_w = Double-layer capacitance across the interface of the working electrode

R_u = Uncompensated resistance

R_b = Salt bridge resistance

Z_Ref = Impedance of reference electrode

R_S = Solution resistance

R_C = Charge transfer resistance across the interface of the counter electrode

C_C = Double-layer capacitance across the interface of counter electrode

 

We know that all the workstations can control/measure the potential between point R and W. Therefore, it can be written as:

V_measured=V_W-V_R                    (1)

Since the actual potential difference should be calculated at the electrode-electrolyte interface, we can write the potential difference at the interface as

V_actual=V_s-V_l                              (2)

Where V_s and V_l  are the potentials of a solid electrode and liquid electrolyte at the interface. Since the working electrode is an equipotential surface,  V_s  will be equal to V_w. Therefore equation 2 can be written as

V_actual=V_W-V_l                            (3)

Applying Kirchhoff’s second law between point L and R:

V_l-V_R= I.R_u-I*.R_b-I*.Z_Ref+V_OC                             (4)

where, V_OC  is the Fermi level difference of working and reference electrodes. Therefore,

V_l-V_R= I.R_u+V_OC                   (5)

Rearranging equation 5 results into

V_l= V_R+I.R_u+V_OC                   (6)

Combining equation 3 and 6 results into

V_actual=V_W-V_R-I.R_u-V_OC              (7)         

or

V_actual=V_measured-I.R_u-V_OC           (8)         

At the right-hand side of the equation, all the parameters are directly measurable except R_u. Therefore, V_actual can be calculated if we know R_u. The easiest way to calculate the  V_actual is by elimination of potential drop due to uncompensated resistance. This can be achieved either by increasing the conductivity of electrolyte (through the addition of supporting electrolyte) or by decreasing the distance between reference and the working electrode (typically through a lugging capillary). However, these methods can result in erroneous measurements. For example, the use of supporting electrolytes can disturb the double layer. Though supporting electrolytes do not participate in the electrochemical reaction, they may also affect the adsorption/desorption kinetics of electroactive species. Therefore, IR compensation through experimental methods is a better tactic to deal with the problem. These methods are described below:

1. Measurement through AC technique: In this technique, a variable frequency signal is passed through the cell, typically using the EIS technique. The low-frequency signal accounts for the potential drop across both R_u and R_C whereas the high-frequency signal accounts for potential drop only across R_u. The variation of resistance with frequency (Bode plot) is plotted, which determine the R_u.
2. Measurement through DC technique: In this technique, a transient current interrupt is applied for the duration of 10µs-30ms across the electrochemical cell. Simultaneously, The voltage ( V_measured ) is recorded just before and just after the current interruption. During such a short span, an instantaneous voltage drops ( V _u ) is observable across R_u which accounts for the IR compensation. The V_actual  is calculated by subtracting V _u  from V_measured . Afterward, a gradual potential drop is observed across R_f  due to slow discharge of C_f  which is observable only if we record the signal for a longer time; however, not of our interest. Unlike the previous method, this method provides a dynamic IR correction which means that the system automatically compensates the changes for varying  R_u.

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