Physical & Interfacial Electrochemistry 2013

Home , Hydrodynamic voltammetry, Rotating disk electrode

Physical & Interfacial Electrochemistry 2013.

Lecture 8 Hydrodynamic Voltammetry

Hydrodynamic voltammetry

• Hydrodynamic voltammetry • Examples of hydrodynamic deals with voltammetric electrodes include the rotating measurements conducted under disc electrode (RDE), the conditions where there is rotating ring disc electrode, the controlled hydrodynamic flow of wall jet electrode, the tubular solution near the electrode. electrode and the channel • If convection is applied to the electrode. solution in the vicinity of the electrode then the rate of mass • The transport of reactant and transport is increased which product can in principle be means that faster reactions may calculated quantitatively under be studied. such circumstances by solving the mass transport equations • If the fluid flow is well defined and the relevant hydrodynamic (laminar rather than turbulent), equations either using the rate of mass transport can approximate analytical methods be controlled quantitatively by (for particularly simple varying the solution flow rate. geometries) or, more often, via This is much more convenient numerical simulation (via finite than varying the size of the element modelling). electrode. Also steady state conditions are achieved at hydrodynamic electrodes.

1 http://physchem.ox.ac.uk/~rgc/john/Thesis/1/1.html

Tubular electrode (TE) Rotating disc electrode (RDE)

Channel electrode (CE) Wall Jet electrode (WJE)

Rotating disc electrode (RDE) The reactant is conveyed to the The RDE is constructed from a disk of electrode surface by a electrode material (e.g. gold, glassy combination of two types of carbon or platinum) imbedded in a rod transport : convection and of insulating material (e.g. Teflon). diffusion. Vortex flow in the bulk solution The electrode is attached to a motor continuously brings fresh reactant and rotated at a certain frequency. to the outer edge of the stagnant The movement of rotation leads to a diffusion layer. very well defined solution flow pattern. The reactant diffuses across stagnant layer. The thinner the The rotating device acts as a pump, stagnant layer, the faster the pulling the solution upward and then reactant can diffuse across it and throwing it outward. reach the electrode surface. Faster electrode rotation makes the stagnant layer thinner. Higher rotation rates permit the reactant to diffuse to the electrode faster, resulting in a higher current being measured at the electrode.

2 Rotating-ring-disk electrode (RRDE). RRDE is 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 RRDE

RRDE is a convenient way to measure post- electron transfer reactions of products. The relationship between disk current and ring current depends on rate of movement of product from the disk and is quantified in terms of the Collection Efficiency which can Be computed analytically and depends only on the geometry of the RRDE.

Rotating electrode assembly.

3 Typically, for an aqueous Electrode Distance scales solution D = 10-9 m2s-1 in electrochemistry and  = 10-6 m2s-1 and so ET / H ≈ 0.16. kinetics

1/3 0.1 nm Inner Helmholtz Plane  D  1.61 Outer Helmholtz Plane H  1 nm RDE 10 nm Diffuse Double Layer

0.1 m Aqueous solution 1 m

10 m Diffusion Layer 

0.1 mm

1 mm Hydrodynamic Boundary Layer H

distance

Transport and kinetics Transport via Molecular diffusion in electrochemical systems. only

Diffusion layer (stagnant) Simple diffusion layer Double layer model neglects region  convection effects  and also simplifies c analysis of Fick Interfacial A A k diffusion equations. ET kET D B

Bulk solution Electrode c0 (well stirred)

D c  c Material 0 Hydrodynamic f  flux  layer

4 Transport and kinetics Diffusion layer approximation used. at electrodes. Current density 1.0 i J f   ET & MT nFA nF D

0.5

Net flux D = i / i k   MT D 

 dc  D   0.0 f  D   kET c0  c  c0  kD c  c0 -6 -4 -2 0 2 4 6  dx 0   = F(E-E0)/RT ET c c0   kET kET kDc 1 1 1 1 f    D    kD  kET f kET c kDc

f  kET c0 Normalised 0 kET  k exp    potential

Convective diffusion equation. • In most cases a numerical approach has to be • Material flux near an adopted. electrode surface computed • Commercial software by solving the convective packages utilising finite diffusion equation (this element and finite neglects electromigration difference methods are effects). available to solve the • To do this the velocity convective diffusion and profile in the fluid must be Navier Stokes equations. evaluated using the Navier These include FEMLAB and Stokes equation of FLUENT. hydrodynamics, which is non Convection linear and therefore difficult Diffusion to solve analytically. c • The convective diffusion  D2c  v c equation admits analytical t solutions for only a few problems in electrochemistry such as the rotating disc  2c 1 c  2c c c electrode. D    v  v r 2 r r z2  r r z z

RDE CV eqn.

5 c c  2c v r  v z  D 2 r z z

vCrzr  2 vCzz  Normal diffusion C  0.513/2  1/2

2  c 2 c c D 2 Cz  Crz z z r Normal Radial convection convection

Either of these equations may be solved analytically for a Number of well defined geometries such as RDE, RRDE, ChE TE etc.

The whole disc acts as a pump, sucking solution towards it, spinning the solution around and then flinging it out sideways.

z    z  H 

23/21/222 vaz  0.51  zCz  Velocity profiles near RDE 3/2 1/2 varr 0.51   rzCrz  Surface.

6 Convective diffusion equation : Rotating disc electrode (RDE)

Neglect radial Fluid velocity profile (approximate) Diffusion & Steady state time independent Convection. 2 equation.  c 2 c D Cz 3/ 2 1/2 radial z 2 z C  0.51 

Convective diffusion equation expressed in cylinderical polar co-ordinates (r,z,) Rotation frequency (Hz) normal rcc    = 2f angular  c r 00  r Angular velocity (rad/s) zcc   Normalised distance  c zfDkc0   ET 0 1/3 1/3  z   zC D x  r cos y  rsin  z  z z0 r  00   2 z    cc   3 cc0 exp  d 2 2 1 y  0   r  x  y   tan    0 3 x  Reactant concentration profile near RDE

C = convective constant

c c  c c  c   0  0   1/3 1/3 1/6 1/2 1/3 z z 0 KC D 1.288  1. 2 5   D c  c  0 1. 61 1/6 D1/3 1/2

K = 31/3 (4/3) = 1.288.  Nernst diffusion layer  c cc 0 Approximation.   z z0  Diffusion layer thickness for RDE (Levich) KC1/3 D 1/31.61 D 1/3 1/6 1/2 a c i  2nFD  dr Levich equation L    0 z z 0 Diffusion limited Current.  0.62nFa 2 D2/3 1/6c1/2

7 Transport and kinetics at electrodes. A A k kET D Linear Plot: B B 11/2  fvs  i kkcET D fkc ET 0  Kinetic info (k ,k0) got nFA kET k D ET from intercept  c 11 Diffusion coefficient got  from slope. fk ET k D

D kD can be computed k D  accurately provided k  k 0 exp    ET 1/3 1/ 6 1/ 2 Convective-diffusion   0.643D   equation can be solved. Specific result for RDE, RRDE geometry. D 2/3 1/6 1/2 2/3 1/6 1/2 kDD 0.62  1.55 DW  ZD Hz Rad s-1

The Rotating Disc Electrode . • RDE has well defined hydrodynamic flow to electrode surface . • Fluid velocity profile near Insulating mantle disc well defined . • Transport of reactant to Angular surface obeys steady state velocity Convective diffusion equation  which may be rigorously solved . • Rate of material transport depends in a well defined Disc manner on the rotation speed D of the electrode . k  D  1/3 1/ 6 1/ 2   0.643D    = kinematic viscosity -1  = rotation speed (Hz) kD= diffusive rate constant (cms ) D = substrate diffusion coefficient  = Nernst diffusion layer thickness

8 Levich equation. Veniamin Grigorievich (Benjamin) Levich.

a c i  2nFD dr Levich equation L    0 z z 0 1/ 2  0.62nFa 2 D2/3 1/6c1/2 iL  SL

Levich slope 2 2/3 ∞ -1/6 SL = 0.62nFa D c 

w1/2

9 Data Analysis using the RDE. Low  • Apply constant potential to electrode. 1/i • Measure limiting current i at various  rotation speeds . High  • Plot 1/i versus  -1/2 . • Kinetic information obtained from S intercept corresponding to infinite KL rotation speed . • Transport information obtained I from slope . KL  -1/2

 nFAc 1/2 SIKL KL iL Koutecky-Levich Plot . 1 IKL  kET Diffusion coefficient calculated 1 from slope, ET rate constant SBKL  calculated from intercept. B Levich constant 1.55D2/3  1/ 6

http://physchem.ox.ac.uk/~rgc/john/Thesis/1/1.html

Variable Method Controls Parameter Steady-state voltammetry Potential Rate of electrochemical kinetics Linear-sweep/cyclic Potential and Rate of electrochemical kinetics voltammetry time and mass transport Potential-step Time Rate of mass transport chronoamperometry† Transport-limited current: Jet velocity Rate of mass transport wall-jet Flow rate, Transport-limited current: (electrode Rate of mass transport channel flow cell length) Transport-limited current: Radius Rate of mass transport microdisc electrode Transport-limited current: Rotation speed Rate of mass transport RDE

Object of most voltammetric experiments is to record current flowing as a function of rate of mass transport and/or electrochemical kinetics (which have an associated time scale).

10 ‘Levich’ type equations for various types of hydrodynamic electrodes.

Geometry Limiting Current

RDE47

WJE28

MJE48,49

ChE50,51

Tube Electrode (TE)

The TE system consists of an annular electrode that is inserted into the length of a cylinderical tube down which the solution under study flows. The volume flow rate Vf is Since the flow is laminar chosen to ensure laminar The diffusion layer thickness flow of solution in the tube. Increases with the Because of friction with the Distance x downstream tube walls, the velocity of From the upstream edge of the liquid v in the tube varies in Tube electrode and  ~ x1/3. a parabolic manner with the The mass transport controlled distance r from the tube flux varies as x-1/3 across the centre. electrode surface and so the TE Velocity at tube centre is not uniformly accessible.

Tube radius

11 Transport to the TE is given by the convective diffusion equation written in terms of axial (x) and radial (r) coordinates. Levich assumed that the fluid flow pattern is linear close to the electrode surface Leveque approximation and vx is given by the Leveque approximation. If axial and radial diffusion effects are neglected then the CD equation can be solved to obtain a well defined expression for the limiting current which will be valid when the diffusion layer is sufficiently thin in comparison with the TE Levich equation tube radius. 2/3 1/3  The Levich equation is derived by assuming iL  5.43nF(D xE ) V f c that fluid flow is sufficiently fast such that diffusion in the direction of Electrode convective flow can be neglected, and that convection length is sufficient to ensure that the concentration TE slow flow limit gradient of reactive species near the electrode surface can be linearised. i  nFV c Note that limiting current does not depend on L f radius of tube  or on the solvent viscosity. Slow flow or long electrode conditions produces a more simple expression for the limiting current. TE geometry used in Complete expression for TE response for all values Electrochemical ESR of Vf only obtained numerically. Measurements.

Channel Electrode (ChE)

The channel electrode (ChE) is closely related to the Tube electrode. It consists of an electrode embedded in one wall of a rectangular duct down which solution flows. Advantages include: • flow through facilitates continuous monitoring in analytical applications following chromatographic separation. • Well defined hydrodynamics permits rigorous mechanistic investigation of reactions via Voltammetric techniques. • Channel geometry can be readily used in spectroelectrochemistry (IR, UV/VIS, ESR, fluorescence). • Double electrode collector/generator experiments readily done.

12 Cooper, Compton

13 Double hydrodynamic electrodes : Generator-Collector Experiments.

Hydrodynamic electrode systems useful for Generator-Collector (detector) experiments where the intermediate/product generated at an upstream generator electrode is detected at a downstream collector electrode.  RRDE Geometry Gap r z Ring

Ring r1 r2 r3 Disc Gap r = 0 downstream upstream downstream

Fraction of B which reaches collector/ detector - Generator : A + n1e  B electrode is always less than unity, - Collector : B + n2e  P since some B is lost to bulk solution in transit from generator to collector electrode.

14 Double Hydrodynamic Electrode Collection efficiency.

  nI1 D 2/3 2/3     NF0  11111   F   F    nI2 G   

3 1/21 1/3 1/3 33211 1   F  ln tan   41 2 341/2  

, are functions only of electrode geometry and are independent of mass transport and electrode kinetics.

RRDE, WTRDE WJRDE TDE, CDE

3339/8 9/8 9/8 rr r  rr r   221 3 221 3 221 3         rrr111   rrr111   111

15 (a) Ring currents recorded with the Pt ring being potentiostated at

0.95 V, at which the H2O2 could be oxidized to O2 if it is generated at the disk. (b) Potentiodynamic oxygen reduction current recorded ot ploycrystalline Pt disk in 0.1 M

HClO4 in a RRDE assembly.

16 R.G. Compton, G.M. Stearn. Other double hydrodynamic electrode systems.