Presentation on theme: "Fundamentals of Electrochemistry"— Presentation transcript:
1Fundamentals of Electrochemistry CHEM*7234 CHEM 720Section 5: Voltammetric Methods
2Voltammetric Methods Historical Electrolysis at DME -1920’s Usually 3-electrode cellsMeasurement of current that results from the application of potential.Different voltammetric techniques are distinguished primarily by the potential function that is applied to the working electrode and by the material used as the working electrode.
3Linear sweep and Cyclic Voltammetry Hydrodynamic Voltammetry Types of VoltammetryPolarographyLinear sweep and Cyclic VoltammetryHydrodynamic VoltammetryPulsed methodsAC Voltammetry (not here)ip = 2.69 x 105 n3/2 A DO1/2 v1/2 COIt is instructive to start with PolarographyVoltammetry at a dropping mercury electrode
4Polarography uses mercury droplet electrode that is regularly renewed during analysis. Applications:Metal ions (especially heavy metal pollutants) - high sensitivity.Organic species able to be oxidized or reduced at electrodes: quinones, reducing sugars and derivatives, thiol and disulphide compounds, oxidation cofactors (coenzymes etc), vitamins, pharmaceuticals.Alternative when spectroscopic methods fail.
5HistoryJaroslav Heyrovský was the inventor of the polarographic method, and the father of electroanalytical chemistry, for which he was the recipient of the Nobel Prize. His contribution to electroanalytical chemistry can not be overestimated. All modern voltammetric methods used now in electroanalytical chemistry originate from polarography.On February 10, 1922, the "polarograph" was born as Heyrovský recorded the current-voltage curve for a solution of 1 M NaOH. Heyrovský correctly interpreted the current increase between -1.9 and -2.0 V as being due to deposition of Na+ ions, forming an amalgam.
6Typical polarographic curves (dependence of current I on the voltage E applied to the electrodes; the small oscillations indicate the slow dropping of mercury): lower curve - the supporting solution of ammonium chloride and hydroxide containing small amounts of cadmium, zinc and manganese, upper curve - the same after addition of small amount of thallium.Swedish king Gustav Adolf VI awards the Nobel Prize to Heyrovský in Stockholm on
7Linear sweep Polarography Potential RampsLinear sweep PolarographyIn order to derive the the current response one must account for the variation of drop area with time:A = 4(3mt/4d)2/3 = 0.85(mt)2/3Density of dropMass flow rate of dropWe can substitute this into Cottrell Equation (see Mass Transport Notes)i(t) = nFACD1/2/ 1/2t1/2
8We also replace D by 7/3D to account for the compression of the diffusion layer by the expanding dropGiving the Ilkovich Equation:id = 708nD1/2m2/3t1/6CI has units of Amps when D is in cm2s-1,m is in g/s and t is in seconds. C is in mol/cm3This expression gives the current at the end of the drop life. The average current is obtained by integrating the current over this time periodiav = 607nD1/2m2/3t1/6C
9The diffusion current is determined by subtracting away the residual current Further improvements can be made by reducing charging currents (see Pulse methods later)E1/2 = E0 + RT/nF log (DR/Do)1/2 (reversible couple)Usually D’s are similar so half wave potential is similar to formal potential. Also potential is independent of concentration and can therefore be used as a diagnostic of identity of analytes. For example
10Good buffering reqd in organic polarography Organic reductions often involve hydrogen ionsR + nH+ + ne RHnGood buffering reqd in organic polarographyMetal ComplexesMLp + ne + Hg M(Hg) + pLDifference between half-wave potential for complexed and uncomplexed metal ion is given by:E1/2(c) - E1/2(free) =RT/nF ln Kd - RT/nF p ln [L] +RT/nF ln (D free/D (c))1/2Stoichiometry can thus be determined by plottingE1/2 versus [L]Also possible to improve resolution between neighbouring waves by carefully choosing ligand and concentration
11Irreversible systems Heyrovsky-Ilkovich Equation Describes wave shape for reversible systems (with fast electron transfer kinetics)E = E1/2 + RT/nF ln((id - i)/i)Plot E vs log((id - i)/i) gives straight line of slope 0.059/nConvenient way to get nIntercept is half wave potentialIrreversible systemsThe waves are more “drawn out” than for reversible systemsLimiting currents still show a linear function of concentrationShape of polarogram is given by:E = E0 + RT/nF ln (1.35kf((id - i)/i)(t/D)1/2)transfer coefficient forward rate constant
12Charging Currents : first look Drop acts as capacitorDouble layerSince potential change during drop life is very small we can neglect charging changing with potentialcharging thus depends on time and electrode areaic = dq/dt = (E-Epzc)Cdl dA/dtbut A = 4(3mt/4d)2/3 = 0.85(mt)2/3ic = (E-Epzc) Cdl m2/3t-1/3so I(total) = id + ic = kt1/6 + k’t-1/3
13Charging current sets limit of detection Various ways of reducing ite.g., Sample current at end of drop life (TAST polarography)Other methods involve Pulse voltammetry -see later
14Voltammetry The supporting electrolyte Ensures diffusion control of limiting currents by eliminating migration currentsTable: Limiting currents observed for 9.5 x 10-4 M PbCl2 as a function of the concentration of KNO3 supporting electrolyteAt low inert electrolyte concentration, a large fraction of the total current is due to migration current - currents due to electrostatic attraction of ion for electrodeFor sol’n 1, Imigration = = 9.2 A; Idiffusion = 8.45 mA
15Cyclic Voltammetrypotential is continuously changed as a linear function of time. The rate of change of potential with time is referred to as the scan rate (v).cyclic voltammetry, in which 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.advantage that the product of the electron transfer reaction that occurred in the forward scan can be probed again in the reverse scan.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.
17I-E-t surface revisited (see Chronoamp notes) Polarography -constant time E-IChronamp - i -tCV -I-E-t (diagonal cut) -notice wave shapeDiffusional “tails”- governed by mass transportYou can simulate this: for example using the ensemble method of finite differences. See Bard and Faulkner (old edition) Appendix B p675 et seq.
182 conventions in the literature: Sign Conventions:2 conventions in the literature:American - plot cathodic current positive, plot negative potentials decreasing to the right.IUPAC - plot anodic currents positive, plot positive potentials increasing to the right.The slightly illogical American convention arose for historical reasons.IUPAC stands for International Union of Pure & Applied Chemistry.anodiccathodicIUPAC Style
19The Randles-Sevcik equation Reversible systemsip = n F A C (n F v D / R T)1/2n : number of electrons, v scan rate (V / sec),F :Faraday’s constant (96485 C / mol), A : electrode area (cm2), R is the universal gas constant (8.314 J / mol K), T is the absolute temperature (K), and D is the analyte’s diffusion coefficient (cm2/sec). Note that if the temperature is assumed to be 25°C ( K), the Randles-Sevcik equation can be written in a more concise form,ip = (2.687x105) n3/2 v1/2 D1/2 A Cwhere the constant is understood to have units (i.e., 2.687x105 C mol–1 V–1/2).
21ipa= ipc for a reversible couple Peak ratios are often strongly affected by chemical reactions coupled to the redox processSee later and also Organic Electrochemistry (Prof. Houmam)Peak positions are related to formal potential of redox processE0 = (Epa + Epc ) /2Separation of peaks fr a reversible couple is 0.059/n V1-e fast electron transfer thus gives 59mV separationPeak potentials are then independent of scan rate (see previous page)Half-peak potential Ep/2 = E1/2 0.028/nsign is + for a reduction
22shape of voltammogram depends on transfer coefficient () and on a dimensionless parameter = k0 [RT/DF]1/2 is the scan ratefor >7 votammogram is reversiblewhen deviates from 0.5 the voltammograms become asymmetric -cathodic peak sharper as expected from Butler Volmer eqn. = 0.25, = 0.5 =10,1.0.1,0.01
23Ferrocene redox at a 10 m diameter glassy carbon electrode. -why? Microelectrodeswave shape is differentFerrocene redox at a 10 m diameter glassycarbon electrode.-why?
24we now have a brief look at microelectrodes This steady-state current is explained by envisioning that the microelectrode is a "dot" with the diffusion layer being hemispherical in shape extending out into the solution. The amount of ferrocene diffusing to the electrode surface is defined by the volume enclosed by an expanding hemisphere, not a plane projecting into the solution as in the case of a planar electrode.One salient feature of the microelectrode is the small current magnitude, which means that iR loss is negligible even at high scan rates. This allows the determination of kinetic rates of electron transfer that are very fast by going to high scan rates.Also time constant RC is small (see Lecture One) -fast electron transfer can be studiedThe fundamental reason you have met before in the Mass Transport lecturesrecall that diffusional properties depend on the geometry (and size) of the electrodewe now have a brief look at microelectrodes
25Voltammetry at microelectrodes microelectrodes have at least one dimension of the order of micronsIn 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 experimentsmall 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..
26Mass Transportat small electrodes, growth of diffusion layer is initially similar to that at larger electrodes;at longer times, it slows significantly. Thus the size of the diffusion layer at t > 0 is smaller at small electrodes, and the concentration gradient and therefore the rate of (diffusional) mass transport are considerably greater at 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
27so current at microelectrode is a sum of both planar and spherical diffusion magnitude of each will depend on time and size of microelectrodeid = nFADC [ ( 1/Dt)1/2 + 1/r]so:id = C(1/ + 1/r)planar diffusion spherical diffusionThe first term predominates at short times ( <<r ),while the second at a sufficiently long time ( >>r ). is the diffusion layer thickness, .This quantity is defined,for planar semi-infinite diffusion. = (Dt)1/2
28Irreversible and Quasi-Reversible Systems: Macroelectrodes FastSlow
29For 'slow’ reactions (so called quasi-reversible or irreversible electron transfer reactions) the voltage applied will not result in the generation of the concentrations at the electrode surface predicted by the Nernst equation.kinetics of the reaction are 'slow' and thus the equilibria are not established rapidly (in comparison to the voltage scan rate).position of the current maximum, Ep) shifts depending upon the reduction rate constant (and also the voltage scan rate). This occurs because the current takes more time to respond to the the applied voltage than the reversible case.
30Hence, the voltammogram becomes more drawn-out as an decreases. For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated. Totally irreversible systems are characterized by a shift of the peak potential with scan rate:Ep = E° - (RT/nF)[ ln(ko/(D)1/2) + ln anFn/RT)1/2]a is the transfer coefficient and na is the number of electrons involved in the charge-transfer step.Thus, Ep occurs at potentials higher than E°, with the overpotential related to k° and a.Independent of the value k°, such peak displacement can be compensated by an appropriate change of the scan rate.peak potential and the half-peak potential (at 25°C) will differ by 48/an mV.Hence, the voltammogram becomes more drawn-out as an decreases.
31The peak current, given by: ip = (2.99x105)n(ana)1/2ACD1/2n1/2ip is still proportional to the bulk concentration, but will be lower in height (depending upon the value of a).Assuming a = 0.5, the ratio of the reversible- to-irreversible current peaks is 1.27 (i.e. the peak current for the irreversible process is about 80% of the peak for a reversible one).For quasi-reversible systems (with 10-1 > k° > cm/s) the current is controlled by both the charge transfer and mass transport.Shape of the cyclic voltammogram is a function of the ratio k°/(pnnFD/RT)1/2As ratio increases, the process approaches the reversible case. For small values of it, the system exhibits an irreversible behavior. Overall, the voltammograms of a quasi- reversible system are more drawn out and exhibit a larger separation in peak potentials compared to a reversible system.
32First we consider the EC reaction: Reaction mechanismsCyclic voltammetry can be used to diagnose presence of reactions that precede or follow electron transferClassified by ECaffects surface concentrations of electroactive specieschanges in shape of voltammograminfo on intermediatesIntroduction Cyclic voltammetry can be used to investigate the chemical reactivity of species. To illustrate this let us consider a few possible reactions.First we consider the EC reaction:
33The voltammogram will exhibit a smaller reverse peak because the product (R) is chemically removed from the electrode surface.The mass transport equations for this reaction when diffusional transport is dominant are:mass transport equation for (O) is identical to the case when no chemical reaction occursspecies (R) however has an additional term to account for the fact that it is destroyed chemically by a first order reaction. It is possible to gain information about the chemical rate constant kEC by studying the reaction via cyclic voltammetry.
34EC reaction for reversible electron transfer reaction and rate constant kEC is extremely large. back peak height kEC.
35wave shifts as kEC increases results from the desire of the electrochemical system to set up an equilibrium controlled by the applied voltage.for reversible electron transfer reactions the ratio of (O) and (R) at the surface can be predicted by the Nernst equation at any particular value of applied voltage.chemical reaction removes (R) so when this happens the applied voltage forces more (O) to convert to (R) electrochemically to restablish the required ratio.As more (O) is converted to (R) this results in the flow of more current and the wave begins to shift anodically (for a reduction).E = E0 +RT/nF ln [O]/[R]
40Adsorption in cyclic voltammetry Repetitive voltammograms for micromolar riboflavin at a HMDEnote peak separation is smaller than for solution phase coupleif it is ideal then separation = 0peak half-width = 90.6/n mVpeak current is directly proportional to surface coverage () and scan rateip = (n2F2A)/4RTPeak area also gives coverageQ =nFA can be used to determine area occupied by molecule - can give orientational information
41Rotating Disk Voltammetry important advance in voltammetryrotating disk electrode (RDE)and later the rotating ring-disk electrode (RRDE) by Levich and co-workers in the former Union of Soviet Socialist Republics. Although steady-state voltammograms had previously been obtained for stirred solutions most of these voltammograms were not amenable to rigorous mathematical treatments.RDE shows hydrodynamic behavior that could be treated mathematicallyallowed the RDE to be applied to solution and kinetic studies. and rapid homogeneous reactions under steady-state conditionsRDE is constructed from a disk of electrode material (e.g. gold, glassy carbon or platinum) imbedded in a rod of insulating material (e.g. Teflon). The electrode is attached to a motor and rotated at a certain frequency. The movement of rotation leads to a very well defined solution flow pattern. The rotating device acts as a pump, pulling the solution upward and then throwing it outward.
42The Levich EquationVeniamin Grigorievich (Benjamin) Levich was a leading scientist in electrochemical hydrodynamics, - invented and developed by him. The famous Levich equation describing a current at a rotating disk electrode is named after him.It is important to note that the layer of solution immediately adjacent to the surface of the electrode behaves as if it were stuck to the electrode. While the bulk of the solution is being stirred vigorously by the rotating electrode, this thin layer of solution manages to cling to the surface of the electrode and appears (from the perspective of the rotating electrode) to be motionless. This layer is called the stagnant layer in order to distinguish it from the remaining bulk of the solution.
43Analyte is conveyed to the electrode surface by a combination of two types of transport. vortex flow in the bulk solution continuously brings fresh analyte to the outer edge of the stagnant layer.analyte diffuses across stagnant layer. The thinner the stagnant layer, the faster the analyte can diffuse across it and reach the electrode surface.Faster electrode rotation makes the stagnant layer thinner. faster rotation rates permit the analyte to diffuse to the electrode faster, resulting in a higher current being measured at the electrode.The act of rotation drags material to the electrode surface where it can react. Providing the rotation speed is kept within the limits that laminar flow is maintained then the mass transport equation is given bywhere the x dimension is the distance normal to the electrode surface. It is apparent that the mass transport equation is now dominated by both diffusion and convection and both these terms effect the concentration of reagent close to the electrode surface. Therefore to predict the current for this type of electrode we must solve this subject to the reactions occurring at the electrode.
44Rotated disk voltammetry is similar to cyclic voltammetry in that the working electrode potential is (slowly) swept back and forth across the formal potential of analyte.The Levich equation This equation takes into account both the rate of diffusion across the stagnant layer and the complex solution flow pattern. In particular, the Levich equation gives the height of the sigmoidal wave observed in rotated disk voltammetry. The sigmoid wave height is often called the Levich current, iL, and it is directly proportional to the analyte concentration, C. The Levich equation is written as:iL = (0.620) n F A D2/3 w1/2 v–1/6 Cwhere w is the angular rotation rate of the electrode (radians/sec) and v is the kinematic viscosity of the solution (cm2/sec). The kinematic viscosity is the ratio of the solution's viscosity to its density.
45results for a series of rotated disk voltammograms taken at different scan rates. a Levich study. The limiting current (or Levich current) is measured and plotted against the square root of the rotation rate, producing a Levich plot. Note that the experimental rotation rate, f , is measured in RPM and must be converted to the angular rotation rate, w, so that it has units of radians per secondin experiment shown the electrode area, A, was cm2, the analyte concentration, C, was x10–6 mol/cm3, and the solution had a kinematic viscosity, v, equal to cm2/sec. After careful substitution and unit analysis, you can solve for the diffusion coefficient, D, and obtain a value equal to x10–6 cm2/s.
46The kinematic viscosity is the ratio of the absolute viscosity of a solution to its density. Absolute viscosity is measured in poises (1 poise = gram cm–1 sec–1). Kinematic viscosity is measured in stokes (1 stoke = cm2 sec–1). Extensive tables of solution viscosity and more information about viscosity units can be found in the CRC Handbook of Chemistry and Physics.
47Rotating Ring Disk Voltammetry Rotating-ring-disk electrode: A variant of the rotating-disk electrode which includes a second electrode - a concentric ring electrode - that is placed outside the disk and used to analyze the species generated on the disk. The ring is electrically insulated from the disk so that their potentials can be controlled independently. Abbreviated as RRDEconvenient way to measure post-electron transfer reactions of productsrelationship between disk current and ring current depends on rate of movement of product from the disk
48only a fraction of disc products will reach ring each ring-disk electrode must be calibrated with a well-behaved reversible couple to determine the collection efficiency (N)N= iR / iDcouples used - ferri/ferocynadide, quinone/hydroquinoneefficiency depends on electrode geometry (radii of disk and ring)Example: peroxide- study of post electron transferrapid disproportionationelectrochem HOOH - e HOOfollowed by HOO + HOO HOOH + O2we now look at cyclic voltammetry and RRDE study
49CV in MeCNdiskRingCV: ipa increases with [HOOH] (A to D)ipa proportional to square root of scan ratenote plateau in wave after peak - indicative of secondary redox process
50b: Ring currentsRHS: cathodic scanA ED is disconnected: B ED is at +2.6V vs SCEproducts can be characterized by scanning ring from +1 to -2Vfirst wave at 0.4V is indicative of HOO
51If 1/ N (collection efficiency) is plotted against [HOOH] then: HOO disproportionation rate constant can be calculated if:1. Oxidation of HOOH is diffusion controlled (seescan rate dependence of ipa2 the only decay path for HOO is disproportionation while moving from disk to ring
52disproportionation of HOO follows simple second order rate law: 1/[HOO ]t - 1/[HOO ]0 =ktconc on inneredge of ringconc at disk: zero timeexperimental collection efficiencies when compared to theoretical N make it possible to relate the two HOO concentrations[HOO ]t = N(exp)/N [HOO ]0and so:1/N(exp) = 1/N + kt/N [HOOH]plot 1/N vs [HOOH] gives k
53Pulse Methods: as promised Examples below refer to polarography but are applicable to other votammetric methods as wellall attempt to improve signal to noiseusually by removing capacitive currentsNormal Pulse Polarographycurrent measured at a single instant in the lifetime of each drop.higher signal because there is more electroactive species around each drop of mercury.somewhat more sensitive than sampled DC and regular polarography.data obtained have the same shape as a regular LSV.
54A modification on NPP is Differential Pulse Polarography (DPP) current measured twice during the lifetime of each dropdifference in current is plotted.Results in a peak-shaped feature, where the top of the peak corresponds to E1/2, and the height gives concentrationThis shape is the derivative of the regular LSV data. DPP has the advantage of sensitive detection limits and discrimination against background currents. Traditionally, metals in the ppm range can be determined with DPP.
55note -small currents but almost devoid of capacitive contribution derivative improves contrast between overlapping waves
56Square Wave Voltammetry advantage of square wave voltammetry is that the entire scan can be performed on a single mercury drop in about 10 seconds, as opposed to about 5 minutes for the techniques described previously. SWV saves time, reduces the amount of mercury used per scan by a factor of 100. If used with a pre- reduction step, detection limits of 1-10 ppb can be achieved, which rivals graphite furnace AA in sensitivity.data for SWV similar to DPPheight and width of the wave depends on the exact combination of experimental parameters (i.e. scan rate and pulse height