Electrochemistry MAE- 212

1. Electrochemistry MAE-212 Dr. Marc Madou, UCI, Winter 2014 Class III Transport in Electrochemistry (I)

2. Table of Content • Interface structure • Two-electrode cells and three-electrode cells • Cyclic voltammetry • Diffusion • Convection • Migration

3. 1-10 nm Electrode surface Solvated ions l l l l l l IHL OHL Interface structure • The double-layer region is: • Where the truncation of the metal’s • Electronic structure is compensated for • in the electrolyte. • 1-10 nm in thickness • ~1 volt is dropped across this region… • Which means fields of order 107-8 V/m “The effect of this enormous field at the electrode-electrolyte interface is, in a sense, the essence of electrochemistry.”

4. Electrolytic cell (example): Au cathode (inert surface for e.g. Ni deposition) Graphite anode (not attacked by Cl2) Two electrode cells (anode, cathode, working and reference or counter electrode) e.g. for potentiometric measurements (voltage measurements) (A) Three electrode cells (working, reference and counter electrode) e.g. for amperometric measurements (current measurements)(B). Non-polarizable electrodes: their potential only slightly changes when a current passes through them. Such as calomel and H2/Pt electrodes Polarizable electrodes: those with strongly current-dependent potentials. A criterion for low polarizability is high exchange current density Two-electrode and three-electrode cells

5. Two-electrode and three-electrode cells

6. Two-electrode and three-electrode cells • Inert metals (Hg, Pt, Au) • Polycrystalline • Monocrystals • Carbon electrodes • Glassy carbon • reticulated • Pyrrolytic graphite • Highly oriented (edge plane, ) • Wax impregnated • Carbon paste • Carbon fiber • Diamond (boron doped) • Semiconductor electrodes (ITO) • Modified electrodes Potential window available for experiments is determined by destruction of electrode material or by decomposition of solvent (or dissolved electrolyte)

7. At equilibrium the exchange current density is given by: The reaction polarization is then given by: The measurable current density is then given by: For large enough negative overpotential: Two-electrode and three-electrode cells: activation control (Butler-Volmer) (Tafel law)

8. Two-electrode and three-electrode cells: activation control • With a symmetry coefficient a >0.5 the activation energy for the reduction process is decreased while the activation energy for the oxidation process is increased. • At a=0.5 the curve is symmetrical in that the anodic and cathodic portions are equivalent.The dotted blue curve is the result of the same equation but with a=0.6. The dashed green curve has a=0.7.

9. Two-electrode and three-electrode cells: activation control • Tafel plot: the plot of logarithm of the current density against the over potential. • Example: The following data are the cathodic current through a platinum electrode of area 2.0 cm2 in contact with an Fe 3+, Fe 2+ aqueous solution at 298K. Calculate the exchange current density and the transfer coefficient for the process. Slope is a and intercept is a (=lnie). • In general exchange currents are large when the redox process involves no bond breaking or if only weak bonds are broken. • Exchange currents are generally small when more than one electron needs to be transferred, or multiple or strong bonds are broken.

10. Transport in Electrochemistry • The rate of redox reactions is influenced by the cell potential difference. • However, the rate of transport to the surface can also effect or even dominate the overall reaction rate and in this class we look at the different forms of mass transport that can influence electrolysis reactions. • There are three forms of mass transport which can influence an electrolysis reaction: • Diffusion • Convection • Migration

11. Diffusion • In essence, any electrode reaction is a heterogeneous redox reaction. If its rate depends exclusively on the rate of mass transfer, then we have a mass-transfer controlled electrode reaction. If the only mechanism of mass transfer is diffusion (i.e. the spontaneous transfer of the electroactive species from regions of higher concentrations to regions of lower concentrations), then we have a diffusion controlled electrode reaction. • Diffusion occurs in all solutions and arises from local uneven concentrations of reagents. Entropic forces act to smooth out these uneven distributions of concentration and are therefore the main driving force for this process. • For a large enough sample statistics can be used to predict how far material will move in a certain time - and this is often referred to as a random walk model where the mean square displacement in terms of the time elapsed and the diffusivity:

12. Diffusion • The rate of movement of material by diffusion can be predicted mathematically and Fick proposed two laws to quantify the processes. The first law: this relates the diffusional flux Jo (ie the rate of movement of material by diffusion) to the concentration gradient and the diffusion coefficient Do. The negative sign simply signifies that material moves down a concentration gradient ie from regions of high to low concentration. However, in many measurements we need to know how the concentration of material varies as a function of time and this can be predicted from the first law. • The result is Fick's second law: in this case we consider diffusion normal to an electrode surface (x direction). The rate of change of the concentration ([O]) as a function of time (t) can be seen to be related to the change in the concentration gradient. • Fick's second law is an important relationship since it permits the prediction of the variation of concentration of different species as a function of time within the electrochemical cell. In order to solve these expressions analytical or computational models are usually employed.

13. Diffusion • The thickness of the Nernst diffusion layer varies within the range 0.1-0.001 mm depending on the intensity of convection caused by agitation of the electrodes or electrolyte. • According to the definition of the Nernst diffusion layer the concentration gradient may be determined as follows: Where: C0 - bulk concentration;Cc - concentration of the ions at the cathode surface;c - thickness of the Nernst diffusion layer. • Therefore the flux of ions toward the cathode surface: • Each ion possesses an electric charge. The density of the electric current formed by the moving ions: Where: F - Faraday’s constant, F = 96485 Coulombs; z - number of elementary charges transferred by each ion. • The maximum flux of the ions may be achieved when Cc=0 therefore the electric current density is limited by the value:

14. From activation control to diffusion control: Concentration difference leads to another overpotential i.e. concentration polarization: Using Faraday’s law we may write also: At a certain potential Cs=0 and then: Diffusion • Homework II: derive the identity:

15. Cyclic Voltammetry • In voltammetry the potential is continuously changed as a linear function of time. The rate of change of the potential with time is referred to as the scan rate (v). • In Cyclic voltammetry,the direction of the potential is reversed at the end of the first scan. Thus, the waveform is usually of the form of an isosceles triangle. • Cyclic voltammetry is a powerful tool for the determination of formal redox potentials, detection of chemical reactions that precede or follow the electrochemical reaction and evaluation of electron transfer kinetics. • An advantage is that the product of the electron transfer reaction that occurred in the forward scan can be probed again in the reverse scan.

16. Diffusion: Cyclic voltammetry • Scan the voltage at a given speed (e.g. from + 1 V vs SCE to -0.1 V vs SCE and back at 100 mV/s) and register the current . • At low current density, the conversion of the electroactive species is negligible. • At high current density the consumption of electroactive species close to the electrode results in a concentration gradient. • Concentration polarization: The consumption of electroactive species close to the electrode results in a concentration gradient and diffusion of the species towards the electrode from the bulk may become rate-determining. Therefore, a large overpotential is needed to produce a given current. • Polarization overpotential: ηc Ferricyanide

17. Diffusion: Cyclic voltammetry • The thickness of the Nernst diffusion layer (illustrated in previous slide) is typically 0.1 mm, and depends strongly on the condition of hydrodynamic flow due to such as stirring or convective effects. • The Nernst diffusion layer is different from the electric double layer, which is typically less than 1 nm.

18. Diffusion: Cyclic voltammetry (also polarography)

19. Diffusion: Microelectrodes Microelectrode: at least one dimension must be comparable to diffusion layer thickness (sub μm upto ca. 25 μm). Produce steady state voltammograms. Converging diffusional flux Advantages of microelectrodes: • fast mass flux - short response time (e.g. faster CV) • significantly enhanced S/N (IF / IC) ratio • high temporal and spatial resolution • measurements in extremely small environments • measurements in highly resistive media

20. Diffusion: Microelectrodes • Microelectrodes have at least one dimension of the order of microns • In a strict sense, a microelectrode can be defined as an electrode that has a characteristic surface dimension smaller than the thickness of the diffusion layer on the timescale of the electrochemical experiment • Small size facilitates their use in very small sample volumes. - opened up the possibility of in vivo electrochemistry. This has been a major driving force in the development of microelectrodes and has received considerable attention..

21. Diffusion: Microelectrodes • At short times size of the diffusion layer is smaller than that of the electrode, and planar diffusion dominates--even at microelectrodes. • At very short time scale experiments (e.g., fast-scan cyclic voltammetry) a microelectrode will exhibit macroelectrode (planar diffusion) behavior. • At longer times, the dimensions of the diffusion layer exceed those of the microelectrode, and the diffusion becomes hemispherical. The molecules diffusing to the electrode surface then come from the hemispherical volume (of the reactant-depleted region) that increases with time; this is not the case at macroelectrodes, where planar diffusion dominates

22. Convection • Convection results from the action of a force on the solution. This can be a pump, a flow of gas or even gravity. There are two forms of convection the first is termed natural convection and is present in any solution. This natural convection is generated by small thermal or density differences and acts to mix the solution in a random and therefore unpredictable manner. In the case of electrochemical measurements these effects tend to cuase problems if the measurement time for the experiment exceeds 20 seconds. • It is possible to drown out the natural convection effects from an electrochemical experiment by deliberately introducing convection into the cell. This form of convection is termed forced convection. It is typically several orders of magnitude greater than any natural convection effects and therefore effectively removes the random aspect from the experimental measurements. This of course is only true if the convection is introduced in a well defined and quantitative manner.

23. Convection • If the flow is controlled, after a small lead in length, the profile will become stable with no mixing in the lateral direction, this is termed laminar flow. • For laminar flow conditions the mass transport equation for (1 dimensional) convection is predicted by: where vx is the velocity of the solution which can be calculated in many situations be solving the appropriate form of the Navier-Stokes equations. An analogous form exists for the three dimensional convective transport. • When an electrochemical cell possesses forced convection we must be able to solve the electrode kinetics, diffusion and convection steps, to be able to predict the current flowing. This can be a difficult problem to solve even for modern computers.

24. Migration • The final form of mass transport we need to consider is migration. This is essentially an electrostatic effect which arises due the application of a voltage on the electrodes. This effectively creates a charged interface (the electrodes). Any charged species near that interface will either be attracted or repelled from it by electrostatic forces. The migratory flux induced can be described mathematically (in 1 dimension) as: • The contribution of migration is typically avoided by adding a lot of indifferent electrolyte. • See example: Nanogen DNA chip.

25. Calculate the potential of a battery with a Zn bar in a 0.5 M Zn 2+ solution and Cu bar in a 2 M Cu 2+ solution. Show in a cyclic voltammogram the transition from kinetic control to diffusion control and why does it really happen ? Derive how the capacitive charging of a metal electrode depends on potential sweep rate. What do you expect will be the influence of miniaturization on a potentiometric sensor and on an amperometric sensor? Homework