Chronopotentiometry (CP)

Posted 1/4/2016 in Uncategorized

This article is part of the AfterMath Data Organizer Electrochemistry Guide

This is a galvanostatic method in which the current at the working electrode is held at a constant level for a given period of time. The working electrode potential and current are recorded as a function of time.

Synonyms: constant current electrolysis

Detailed Description

Like most other electrochemical techniques, this experiment begins with an induction period. During the induction period, a set of initial conditions which you specify is applied to the electrochemical cell and the cell is allowed to equilibrate to these conditions. Data are not collected during the induction period.

After the induction period, the current applied to the electrode is stepped to the value you specified for the duration of the experiment. The instrument's galvanostat circuit maintains the current at a steady level while measuring the potential of the working electrode. Throughout the electrolysis period, the potential and current at the working electrode are recorded at regular intervals based on the number of intervals you choose.

The experiment concludes with a relaxation period. During the relaxation period, a set of final conditions which you specify is applied to the electrochemical cell and the cell is allowed to equilibrate to these conditions. Data is not collected during the relaxation period.

At the end of the relaxation period, the post-experiment idle conditions are applied to the cell, and the instrument returns to the idle state.

Potential is plotted as a function of time.

Parameter Setup

The parameters for this method are arranged on two tabs on the setup panel. The Basic tab contains the parameters relating to the electrolysis. An additional tab for Post Experiment Idle Conditions is common to all of the electrochemical techniques supported by the AfterMath software.

Basic Tab

You can click on the “I Feel Lucky” button (located at the top of the setup) to fill in all the parameters with typical default values (see Figure 1). You will no doubt need to change the Current and Duration in the Electrolysis period box to values which are appropriate for the electrochemical system being studied. You may also want to change the Number of intervals in the Sampling Control box.

Figure 1: Basic Chronopotentiometry Setup

The Electrode Range on the Basic tab is used to specify the expected range of potentials. The potential of the electrode is dictated according to the Nernst equation, assuming a fully reversible system (see Theory section below), and will change to the value necessary to maintain the specified current. Therefore, if the choice of potential range is too small, actual potential may go off scale and the results will be truncated. If the potential range is too large, the potentiogram may have a noisy, choppy, or quantized appearance. Please see the ugly duckling webpage for an analogous situation in a voltammogram.

Some Pine potentiostats (such as the WaveNow and WaveNano portable USB potentiostats) have potential autoranging capability. To take advantage of this feature, set the electrode range parameter to “Auto”. This allows the potentiostat to choose the potential range “on-the-fly” while the chonopotentiogram is being acquired.

The waveform that is applied to the electrode is a simple pulse to the Current listed in the Electrolysis period box (see Figure 2). Note that the flat portions before and after the current pulse are the induction and relaxation periods, respectively.

Figure 2 : Waveform

Post Experiment Conditions Tab

After the Relaxation Period, the Post Experiment Conditions are applied to the cell. Typically, the cell is disconnected but you may also specify the conditions applied to the cell. Please see the separate discussion on post experiment conditions for more information.

Typical Results

The typical chronopotentiogram for a $2.5 \; mM$ solution of Ferrocene in $0.1 \; M \; Bu_4NClO_4/MeCN$ shows a plot similar to a titration (see Figure 3). Initially, the potential is slightly rising until nearly all of the ferrocene at the electrode is consumed, at which point the potential rises rapidly through an inflection point, followed by a trailing off of the potential after the inflection point.

Figure 3: Typical Results

The addition of a Baseline Tool (Tangent type) can be added to find the inflection point, the point at which the slope of the plot is greatest (see Figure 4). The potential at $1/2$ of the inflection point is approximately the $E^0$ for the species of interest ( $0.532 \; V \; vs. \; Ag/AgCl_{(aq)}$ ). Two additional Crosshair tools have been added to the plot to show the time at the inflection point and the time of $1/2$ of the inflection point.

Figure 4 : Worked up Results

In the second example, chronopotentiometry has been used to reduce $Ag^+$ onto a Pt electrode, as you might do in calibrating an Electrochemical Quartz Crystal Microbalance. The application of a cathodic current for a specified period of time reduces $Ag^+$ on the surface of the electrode as $Ag^0$ (see Figure 5, parameters were: $400 \;\frac{\mu A}{cm^2}$ cathodic current, $2 \; mm$ Pt WE, $0.05 \; M \; AgNO_3, \; 0.5 \; M \; HNO_3$ ). The current can be integrated to obtain a charge which can be correlated to the mass deposited on the electrode on the face of the quartz crystal (see Figure 6, parameters were the same as Figure 5). Note that since the potential is plotted against a $Ag^0$ quasireference electrode, the entire face of the platinum electrode is covered once the measured potential drops to roughly zero.

Figure 5: Silver Ion Deposition

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Figure 6 : Silver Ion Deposition Applied Electrolysis Current

Theory

The section presented here is common to both CP and CRP and is only a brief introduction to the theory of chronopotentiometry. If you use CP for electrolysis, please see the theory section of BE for a detailed discussion.

Please see Bard and Faulker¹ for a more detailed description of CP. CP is a technique that, like CV, can be utilized to calculate a concentration or a diffusion coefficient. Consider a reaction $O + e^- \rightarrow R$ with a formal potential $E^{0'}$ . As a current is applied to the working electrode, $O$ begins getting reduced at the electrode surface, producing $R$ . The potential of the electrode, $E$ , moves to values characteristic of the $O/R$ couple, based on a time-based Nernstian relation. As the concentration of $O$ drops to zero at the electrode surface the potential starts to rapidly increase to more negative values. The resulting $E-t$ curve is much like a potentiometric titration with a transition time (analogous to an equivalence point), $\tau$ . The potential at one half $\tau$ is $E^{0'}$ . The transition time is related to the concentration and diffusion coefficient of $O$ through the expression

$\tau^{3/2} = {\frac{2C_0^*nFAD_0^{1/2}}{3\beta}}$

where $C_0^*$ is the concentration of $O$ ( $mol/cm^3$ ), $n$ is the number of electrons, $F$ is Faraday's Constant ( $96485 \; C/mol$ ), $A$ is the electrode area ( $cm^2$ ), $D$ is the diffusion coefficient ( $cm^2/s$ ) and $\beta$ is the sweep rate ( $A/s$ ).

For rapid electrode kinetics, the time-based Nernstian equation is

$E = E_{\tau/4}+\frac{RT}{nF} \; ln\left({\frac{\tau^{1/2}-t^{1/2}}{t^{1/2}}}\right)$

where $E_{\tau/4}$ is equal to

$E_{\tau/4} = E^{0'} - \frac{RT}{2nF} ln \frac{D_O}{D_R}$

Finally, plotting $E \; vs \; ln\left({\frac{\tau^{1/2}-t^{1/2}}{t^{1/2}}}\right)$ should give a straight line with slope of $RT/nF$ for a reversible $E-t$ curve.

Application

The first example shows how CP is used to measure diffusion coefficients. Le et al.² applied a current to a membrane to generating concentration polarizations between bulk solutions and anion exchange membranes. The potential drop across the membrane is monitored as a function of time. By determining the transition time (point of inflection) they were able to calculate diffusion coefficients for several chloride salts in $0.1 \; M$ solutions. An exquisite example, considering the authors were able to determine diffusion coefficients of non-redox active species.

In the second example, Nagaraju and Lakshminarayanan³ used CP to grow mesoporous Au films for use for electro-oxidation of alcohols in alkaline media. The researchers showed that varying the current density and deposition times gave different surface areas. These films were then used to electro-oxidize methanol or ethanol, indicating that they could be used in direct alcohol alkaline fuel cells.

References

1. Faulkner, L. R.; Bard, A. J. Controlled-Current Techniques, Electrochemical Methods: Fundamentals and Applications, 2^nd ed.; Wiley: New Jersey, 2000; 305-330.

2. Le, X. T.; Viel, P.; Tran, D. P.; Grisotto, F.; Palacin, S. J. Phys. Chem. B, 2009, 113, 5829–5836

3. Nagaraju D. H.; Lakshminarayanan, V. J. Phys. Chem. C, 2009, 113, 14922–14926.

Additional Resources

Links: Electrochemist's Guide, AfterMath User's Guide, AfterMath Main Support Page

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