Polarography and Voltammetry Lecture 2

Polarization Effects Since we have: Eapplied = Ecell - IR, a plot of current in an electrolytic cell as a function of applied potential should be a straight line with a slope equal to the negative resistance. The observed plot is indeed linear with small currents. However, as the applied voltage increases, the current ultimately begins to deviate from linearity. Cells that exhibit nonlinear behavior at higher currents are said to be polarized, and the degree of polarization is given by an overvoltage, or overpotential.

Note that polarization requires the application of a potential greater than the theoretical value to give a current of the expected magnitude. Thus, the overpotential required to achieve a current of 7.00 mA in the electrolytic cell in previous figure is about - 0.23 V. For an electrolytic cell affected by overvoltage, the equation: (Eapplied = Ecell - IR) then becomes: Eapplied = Ecell - IR + P Note that Ecell and the overpotential, P, have negative values

Polarization is an electrode phenomenon that may affect either or both electrodes in a cell. The degree of polarization of an electrode varies widely. In some instances, it approaches zero (as in a reference electrode), but in others, it can be so large (as in a microelectrode like Hg drop) that the current in the cell becomes independent of potential. Under this circumstance, polarization is said to be complete. Polarization phenomena are conveniently divided into two categories: concentration polarization and kinetic polarization.

Concentration Polarization Concentration polarization occurs because of the finite rate of mass transfer of solute from the solution to the electrode surface. Electron transfer between a reactive species in a solution and an electrode can take place only from a thin film of solution located immediately adjacent to the surface of the electrode; this film is only a fraction of a nanometer in thickness and contains a limited number of reactive ions or molecules. For there to be a steady current in a cell, this film must be continuously replenished with reactant from the bulk of the solution. That is, as reactant ions or molecules are consumed by the electrochemical reaction, more must be transported into the surface film at a rate that is sufficient to maintain the current.

Example of concentration polarization Cd2+ + 2e D Cd(s)

The electrode potential depends on [Cd2 +]s, not [Cd2 +]b, because [Cd2 +]s is the actual concentration at the electrode surface. If [Cd2 +]s = [Cd2+]b, the electrode potential will be that expected from the bulk Cd2+ concentration. When [Cd2+]s does not equal [Cd2+]b, we say that concentration polarization exists.

Concentration polarization occurs when reactant species do not arrive at the surface of the electrode or product species do not leave the surface of the electrode fast enough to maintain the desired current. When this happens, the current is limited to values less than that predicted by the equation: Eapplied = Ecell - IR Reactants are transported to the surface of an electrode by three mechanisms: (1) diffusion, (2) migration, and (3) convection. Products are removed from electrode surfaces by the same mechanisms.

Diffusion When there is a concentration difference between two regions of a solution, ions or molecules move from the more concentrated region to the more dilute. This process, called diffusion, ultimately leads to a disappearance of the concentration difference. The rate of diffusion is directly proportional to the concentration difference. For example, when cadmium ions are deposited at a cathode by a current, the concentration of Cd2+ at the electrode surface [Cd2+]s becomes lower than the bulk concentration.

The difference between the concentration at the surface ([Cd2+]s) and the concentration in the bulk solution [Cd2+]b creates a concentration gradient that causes cadmium ions to diffuse from the bulk of the solution to the surface film. The rate of diffusion is given by: Rate of diffusion to electrode surface = K([Cd2+]b - [Cd2+]s) where [Cd2+]b is the reactant concentration in the bulk of the solution, [Cd2+]s is its equilibrium concentration at the surface of the cathode, and k is a proportionality constant. The value of [Cd2+]s at any instant is fixed by the potential of the electrode and can be calculated from the Nernst equation.

In the present example, we find the surface cadmium ion concentration from the relationship where Ecathode is the potential applied to the cathode. As the applied potential becomes more and more negative, [Cd2+]s becomes smaller and smaller. The result is that the rate of diffusion and thus the current become correspondingly larger until the surface concentration falls to zero, and the maximum or limiting current is reached.

Migration The process by which ions move under the influence of an electric field is called migration. This process is the primary cause of mass transfer in the bulk of the solution in a cell. The rate at which ions migrate to or away from an electrode surface generally increases as the electrode potential increases. This charge movement constitutes a current, which also increases with potential.

Migration

Migration of analyte species is undesirable in most types of electrochemistry, and migration can be minimized by having a high concentration of an inert electrolyte, called a supporting electrolyte, present in the cell. The current in the cell is then primarily due to charges carried by ions from the supporting electrolyte. The supporting electrolyte also serves to reduce the resistance of the cell, which decreases the IR drop.

Convection Reactants can also be transferred to or from an electrode by mechanical means. Forced convection, such as stirring or agitation, will tend to decrease the thickness of the diffusion layer at the surface of an electrode and thus decrease concentration polarization. Natural convection resulting from temperature or density differences also contributes to the transport of molecules to and from an electrode.

Kinetic Polarization In kinetic polarization, the magnitude of the current is limited by the rate of one or both of the electrode reactions, that is, by the rate of electron transfer between the reactants and the electrodes. To offset kinetic polarization, an additional potential, or overvoltage, is required to overcome the activation energy of the half reaction. Kinetic polarization is most pronounced for electrode processes that yield gaseous products and is often negligible for reactions that involve the deposition or solution of a metal. Kinetic effects usually decrease with increasing temperature and decreasing current density.

These effects also depend on the composition of the electrode and are most pronounced with softer metals, such as lead, zinc, and particularly mercury. In common with IR drop, overvoltage effects cause the application of voltages more negative than calculated to operate an electrolytic cell at a desired current. Kinetic polarization also causes the potential of a galvanic cell to be smaller than the value calculated from the Nernst equation and the IR drop: (Eapplied = Ecell - IR).

Overvoltage or overpotential The electrochemical cell is polarized if its actual potential is different from that expected according to Nernst equation. The extent of polarization is measured as overpotential, P . For an electrode, we have: = Eactual – Ereversible(equilib) Eactual is always smaller than Ereversible, therefore P is always negative. Overpotential, P, always reduces theoretical electrode potential when current is flowing.

The electrode potential can be calculated from Nernst equation: For the reaction: The electrode potential can be calculated from Nernst equation: The measured (actual) electrode potential will be the same as the reversible electrode potential only when [Cd2+]s = [Cd2+]b which is far from being the case, when current is flowing. The difference between the actual and reversible electrode potential is the electrode overvoltage. Cd2+ + 2e D Cd(s)

Eappl = Ec – Ea – IR + (Pcc + Pck) + (Pac + Pak) Or: For an electrolytic cell, the overall equation that describes the contributions of important types of overvoltage and IR drop would be: Eappl = Ec – Ea – IR + (Pcc + Pck) + (Pac + Pak) Or: Eappl = Ecell(reversible) – IR + (Pcc +Pck) + (Pac + Pak) Where Pcc and Pck are cathodic overpotentials resulting from concentration and kinetic polarization, while Pac and Pak are the corresponding anodic overpotentials due to the same factors. Always remember that P carries a negative value

History of Polarography and Voltammetry Developed by Czech chemist Jaroslav Heyrovsky in the year 1922. He received the noble prize in chemistry for this work (1959). In the 1960s and 1970s significant advances were made in all areas of voltammetry (theory, methodology, and instrumentation). This enhanced the sensitivity and expanded the applications of analytical methods. The introduction of low-cost operational amplifiers also facilitated the rapid commercial development of relatively inexpensive instrumentation.

EXAMPLES OF MERCURY ELECTRODES In polarography, mercury is used as a working electrode.  The working electrode is often a Hg drop suspended from the end of a capillary tube. 3 examples of electrodes: 1. HMDE (Hanging mercury drop electrode) we extrude the drop of Hg by rotating a micrometer screw that pushes the mercury from a reservoir through a narrow capillary.

2. DME (dropping mercury electrode) mercury drops form at the end of the capillary tube as a result of gravity. Unlike the HMDE, the mercury drop of a DME grows continuously—as mercury flows from the reservoir under the influence of gravity—and has a finite lifetime of several seconds (2-5s). At the end of its lifetime the mercury drop is dislodged, either manually or on its own, and replaced by a new drop. 3. SMDE (static mercury drop electrode) uses a solenoid driven plunger to control the flow of mercury. Activation of the solenoid (a device that converts electrical energy into mechanical movement) momentarily lifts the plunger, allowing mercury to flow through the capillary and forming a single, hanging Hg drop

Two versus three electrode cells There are some problems associated with two electrode cells: To study the behavior of analyte at the electrode/electrolyte interface we require both potential and current to be monitored. A 2-electrode cell gives the current flowing between the two electrodes however, none of the electrode potential is fixed and thus cannot know at which potential (vs a reference) a reaction occurs. In the two electrode case, we are measuring the characteristics of the whole cell including the counter electrode and the electrolyte. In a two electrode system we never know where the interfacial potential difference occurs if the cell voltage is changed; it might be on both electrodes and not at the one of interest. In organic solvents the IR drop can be considerable.

Three electrodes cells A 3 electrode cell is necessary, because the reference electrode must not take part in the redox reaction. Otherwise, the measured potential will be inaccurate. A 3 electrode cell is necessary to measure the current voltage characteristics of the working/sample electrode only. The counter electrode's role is essentially to ensure that current does not run through the reference electrode, since such a flow would change the potential of the reference electrode. That is why the CE surface is much larger than the working electrode or the reference electrode. The three-electrode setup is necessary in the case where the correct value of polarization potential of the working electrode is to be determined.

The optimum interval between drops for most analyses is between 2 and 5 seconds.

Control Circuit

Direct Current polarography (DCP) The earliest voltammetric experiment was normal polarography at a dropping mercury electrode. In normal polarography the potential is linearly scanned, producing voltammograms (polarograms) such as that shown in figure below. This technique is discussed above and usually called Direct Current polarography (DCP)

Classical DC polarography

Polarogram

Imax is the maximum current and is also called the limiting current)  ir (residual current) which is the current obtained when no electrochemical change takes place.    iav (average current) is the current obtained by averaging current values throughout the life time of the drop id (diffusion current) which is the current resulting from the diffusion of electroactive species to the drop surface.

Analyte is either reduced (most of the cases) or oxidized at the surface of the mercury drop. The current–carrier auxiliary electrode is usually a platinum wire. SCE or Ag/AgCl reference electrode is used. The potential of the mercury drop is measured with respect to the reference electrode.

Polarogram in more details A graph of current versus potential in a polarographic experiment involving Cd2+ reduction is shown below: Cd2+ + 2e D Cd(s)

When the potential is only slightly negative with respect to the calomel electrode, essentially no reduction of Cd2+ occurs. Only a small residual current flows. At a sufficiently negative potential, reduction of Cd2+ commences and the current increases. The reduced Cd dissolves in the Hg to form an amalgam.

After a steep increase in current, concentration polarization occurs After a steep increase in current, concentration polarization occurs. The rate of electron transfer becomes limited by the rate at which Cd2+ can diffuse from bulk solution to the surface of the electrode. The magnitude of this diffusion current Id is proportional to Cd2+ concentration and is used for quantitative analysis. The upper trace in the figure above is called a polarographic wave.

When the potential is sufficiently negative around ‑1 When the potential is sufficiently negative around ‑1.2 V, reduction of H+ begins and the curve rises steeply. At positive potentials (near the left side of the polarogram), oxidation of the Hg electrode produces a negative current. By convention, a negative current means that the working electrode is behaving as the anode with respect to the auxiliary electrode. A positive current means that the working electrode is behaving as the cathode.

The oscillating current in the previous figure above is due to the growth and fall of the Hg drops. As the drop grows, its area increases, more solute can reach the surface in a given time, and more current flows. The current increases as the drop grows until, finally, the drop falls off and the current decreases sharply.

Half-wave Potential, E1/2 Half wave potential, E1/2 is an important feature that can be derived from the plarogram. It is the potential corresponding to one half the diffusion current i.e. id/2. El/2 is a characteristic value for each element and thus used for qualitative analysis.