Chrono Amperometry with RCB200 (position D) – Time constant determination

Files:
RCB200-D .EXP
RCB200-D Extract 014.CRV

Abstract

A Chrono Amperometry with data acquisition rate of one point every 500µs is used to determine the time constant of a RC circuit and the values of R and C are then calculated.
This method cannot be run with a VoltaLab 10 (data acquisition rate is less than 20 ms).

RCB200 with WORK connected to position D and functional ground connected to the potentiostat rear panel. The RCB200 contains resistor at 1% and capacity at 10%.
R1R2C = 1.21 kOhm ±1% +[(4.99kOhms ±1% )//(4.7nF ±10%)]+[(4.99kOhms ±1% )//(4.7nF ±10%)]

The experiment imposes +1000 mV during 0.025 + 0.025 = 0.05 seconds. Acquisitions are made every 500 µsec, so 100 measurements are recorded. 1 mA is the fixed measurement range.

Display: Type = Normal X = Time Y1 = log(Current) Y2 = No

According to [1] the linear regression of the first points gives a slope which is equal to -1/(2.3*tau). This slope, tau, is the time constant of a system R1+R2//C2 because the first capacity is negligible regarding the time resolution.
Here, R1=6200 Ohms R2=10000 Ohms and C2=1µF
The theoretical slope is -(R1+R2)/(R2*R1*C*2.3) = -(10000+6200)/(10000*6200*0.000001*2.3) = -113.6

Linear regression----------------------- 01-09-1999, 16:08:56
X min. : 0.001
X max. : 0.005
Mode : y=f(x)
Result : y(log ) = -109.522*x(sec.) -4.017
x(y=0) = -0.0366805
Coefficient : 0.999928

We find a experimental slope of (-109.5) which is in good accordance with the theoretical value (-113.6).
At t=0 the capacity is like a short circuit and the current is made by R. We can calculate the current at t=0 from the linear regression.
I(t=0)= 10^(-4.017) = 96.16 µA then R1 = 1000/(96.16+61) = 6.36 kOhms
I(t>>0)= 61 µA = 1000 /(R1+R2) then R1 + R2 = 1000/61 = 16.39 kOhms ==> R2 = 10.03 kOhms
C= (R1+R2)/(R1*R2*2.3*tau) = 16390/(6360*10030*2.3*109.522) = 1.02 µF

A time constant can be determined with a DC measurement thanks to the 500µs resolution.

[1] A tutorial on impedance spectroscopy. Mark E ORAZEM, paper n°302 CORROSION 98.Chrono

Note:
If you perform calculations from a curve which you have obtain experimentally you must use the Linear Extraction tool to subtract the stationary current from the experimental curve prior to the calculations. The DC current can be determined as the stationary current and you can use the offset function of the linear extraction tool.