V Magnetoelectrochemistry Body forces; Is there a ‘concentration gradient’ force ? Lorentz force effects Hydrogen evolution Magnetic field gradient effects Nitrobenzene - a model for magnetoelectrochemistry Planned work MANSE Midterm Review
Staff, Invited Talks, Publications • Lorena Monzon postdoc from January 2009 (previous postdoc Nandu Chaure) • Peter Dunne postgrad • Zhu Diao postgrad • Giovanni Zangari (U.Virginia) Sabbatical visitor Summer 2007 • Damaris Fernandez (U. Santiago) visiting postgrad • Gasparo Varvaro (CNR Rome) visiting postdoc Collaborators . Fernando Rhen (Tyndall, U. Limerick) Ryoichi Aogaki (Samihara Inst, Japan) Talks: Asia Magnetics Society, Pusan 200 ICEPM, Dresden 2009 MANSE Midterm Review
Publications: —Magnetic-field-induced rest potential shift of metallic electrodes in nitric acid solution, M. F. M. Rhen, P. Dunne and J. M. D. Coey, Magnetohydrodynamics 42 395-401 (2006) — Magnetic field induced modulation of anodic area: the rest potential analysis of Zn and Fe. F. M. F. Rhen and J. M. D. Coey, Journal of Physical Chemsitry C 111 3412-3416 (2007) — Inhomogeneous electrodeposition of copper in a magnetic field, Damaris Fernandez and JMD Coey, Electrochemistry Communications, 11 (2009) in press — Design and application of a magnetic field gradient electrode, N. B. Chaure, M. F. M. Rhen and J. M. D. Coey. Electrochemical Communications 9 155-158 (2007) — Enhanced oxygen reduction at composite electrodes producing a large magnetic gradient, NB Chaure and JMD Coey, Journal of the Electrochemical Society, 156 F39-47 (2009); also in Virtual Journal of Nanoscale Science and Technology (Jan 19 2009) — The magnetic concentration gradient force – is it real? J.M.D. Coey, F.M.F. Rhen, P. Dunne and S. McMurray, Journal of Solid State Electrochemistry 11 711-717 (2007) — Levitation in paramagnetic liquids, P. Dunne, J. Hilton and J. M. D. Coey, Journal of Magnetism and Magnetic Materials 316 273-6 (2007) — Magnetic stabilization and vorticity in paramagnetic liquid tubes, J. M. D. Coey, R Aogaki, F Byrne and P Stamenov, Proceedings of the National Academy of Science (submitted) — Magnetic field effect on hydrogen evolution, Z Diao, G. Zangari and J. M. D. Coey, Electrochemical Communications 11 (2009) in press MANSE Midterm Review
Introduction Simple electrochemical cell Cyclic voltametry I ( V ) I = I ( V, t, ω , f, B ) , Chronoamperometry I ( t ) Rotating disc electrode I ( ω ) Potentiostat Impedance spectroscopy I ( f ) Noise spectroscopy V ( t ) Magnetic field Magnetic field perpendicular to the parallel to the Hydrodynamic modeling surface surface B j B Working electrode Counterelectrode Reference electrode - Potentiostatic mode - fixed V - Galvanostatic mode - fixed I MANSE Midterm Review
Body force densities Force driving diffusion RT ∇ c 10 10 N m -3 Lorentz force j x B 10 3 Field gradient force ( μ 0 /2)c χ∇ H 2 10 3 Driving force for natural convection Δρ g 10 2 Viscous drag ρν∇ 2 v 10 2 Magnetic damping σ v x B x B 10 Amperian force ~ μ 0 j 2 l 10 -4 c is the molar concentration, χ is the molar susceptibility MANSE Midterm Review
Is there a concentration gradient force ? E = - ( μ 0 /2)c χ H 2 F = - ∇ E = ( μ 0 /2)c χ∇ H 2 + ( μ 0 /2) χ H 2 ∇ c The force density acting on a non-uniformly magnetized material is most easily calculated from the Coulomb model: f = µ 0 q m H 0 F = - µ 0 ( ∇ . M ) H 0 q m is magnetic ‘charge’ ⇒ but B = µ 0 ( H + M ) and ∇ . B = 0 0 = ∇ .( H + M ) ∇ . H = - ∇ . M F = µ 0 ( ∇ . H ) H 0 but the applied field H 0 is uniform, so the force is zero when the demagnetizing field is H m = - N M = N χ H is negligible. MANSE Midterm Review
Electrolyte susceptibility Susceptibility of ionic solutions is the sum of the contributions of the ions and that of the water; χ water = -9.0 10 -6 χ = χ water + c χ mol Susceptibility of ions at 295 K Ion Configuration S p eff 2 χ mol χ (m 3 mol -1 ) (1- molar) Ti 3+ V 2+ Cu 2+ 3d 1 , 3d 9 1/2 3 15.7 10 -9 6.7 10 -6 V 3+ , Ni 2+ 3d 2 , 3d 8 1 8 41.9 32.9 Cr 3+ , Co 2+ 3d 3 , 3d 7 3/2 15 78.6 69.6 Mn 3+ , Fe 2+ 3d 4 , 3d 8 2 24 125.7 116.7 Mn 2+ , Fe 3+ 3d 5 5/2 35 183.3 174.3 χ Is at most ~ 10 -4 Hence the B demagnetizing field is negligible Ferrofluid H m / H 0 ≈ 0.1 MANSE Midterm Review
Lorentz force effects The Lorentz force F = j x B is responsible for most of the observed magnetic field effects in electrochemistry — the magnetohydrodynamic (MHD) effect. A current density of 1 mA Electrodeposition of Cu mm -2 in a field of 1 tesla gives a body force of 10 3 N m -3 . The Lorentz force can be expected to significantly modify the pattern of convection and flow in electrochemical cells. MANSE Midterm Review
E δ d l c = c ∞ e c t Solution r o c = 0 d e c oncentration gradient is ~ linear over the diffusion layer δ δ d ~ 0.1 mm δ h ~ 1 mm MANSE Midterm Review
The effect of the magnetic field on the mass transport (copper deposition rate) is equivalent to gentle stirring 0.1 M M CuSO CuSO 4 , , B B vertical, H H c/a c/a (b) (b) 3.5 3.5 3.0 3.0 J = j 0 + a B 0.35 j in j MEAS shift in 2.5 2.5 Normalized shift 2.0 2.0 1.5 1.5 - - 40 40 mV mV 1.0 1.0 - - 200 200 mV mV - - 550 550 mV mV 0.5 0.5 0.0 0.0 0 1 2 3 4 5 B, B, Tesla MANSE Midterm Review
B = 0.3 T Velocity profile Electrode v v v v The Aogaki Cell Vortex at the electrode edge. B j z y x J = j 0 + a B n n = 1/3 MANSE Midterm Review
Rest potential shift 0.1 Magnetic field can shift the rest potential of magnetic and nonmagnetic electrodes ) |j| (A cm 0.01 The effect is related to corrosion -2 1.5 T At the rest potential, there are compensating 1E-3 0 T cathodic and anodic currents. When the cathodic current is mass-transport limited, Iron pH 1 1E-4 the primary mechanism is a small-scale stirring produced by the Lorentz force; -0.4 -0.3 -0.2 -0.1 0.0 ‘Micro MHD effect’. E vs. SHE (V) Anodic Evans diagram Cathodi j L (B) Ln| j| c B Cathodi j L (0) c E E a E 0 (0) E 0 (B) E c MANSE Midterm Review
Corrosion 0.00 0 vs. SHE (V) Corrosion of Fe in 1M KHO 3 pH = 1 -0.05 0 H = 1.5 T µ µ 0 H (T) Rate (nm s -1 ) 0 H = 0 T 0 17.0 µ -0.10 E 1.5 29.2 -0.15 0 150 300 450 600 750 Time (s) Magnetic field can inhibit the corrosion of copper or silver in acid The corrosion of both copper and silver in nitric acid involves a catalyst HNO 2 and formation of a passive oxide layer. Magnetic field (or electrode rotation) helps to remove the HNO 2 catalyst from the vicinity of the electrode, thereby reducing corrosion. The driving force is the Lorentz force, producing the micro MHD effect. The lengthscale of the local electrochemical cells, for micro-MHD effect, is ~ 10 microns. MANSE Midterm Review
B Hydrogen V Galvanostatic - 10 mA t 1/f 2 1/f 2 noise characteristic of a coalescece penomemon Field reduces average bubble size by half - 45 to 24 microns; twist off effect Overpotential for hydrogen generation reduced by 10 % MANSE Midterm Review
Magnetic field gradient effects With suitably designed field gradient F = (1/ µ 0 ) c χ∇ B 2 electrodes it is possible to create very large magnetic field gradients, and exert force Field gradient force densities of up to 10 6 N m -2 , which can have important effects in confining reagent 60-70 60-70 µ m species at the electrode surface. Free alumina membrane template Alumina membrane template with back metallic contact Pt Electrodeposited alloy into the membrane 500 nm 500 nm 1 1 µ m MANSE Midterm Review
MANSE Midterm Review
B Model oxygen reduction reaction. Borate buffer pH 8.4 ∇ B MANSE Midterm Review
Data from chronoamperometry experiments. Cobalt nanowires in Current density (A m -2 ) (Chronoamperometry) Electrode Rotat- an applied field Cathode ion Air-saturated borate bath Oxygenated borate bath produce much rate 0.0 T 0.4 T Enhanc 1.0 T Enhanc 0.0 T 0.4 T Enhanc 1.0T Enhanc enhanced B ∇ B close (rpm) ement ement ement ement 0 1.2 1.7 41.0 6.0 330.0 4.0 20.0 400.0 27.0 575.0 to the Pt electrode A 500 5.2 7.5 44.0 12.0 130.0 12.5 40.0 220.0 50.0 300.0 surface. Pt/cobalt 1000 7.5 10.0 34.0 16.0 113.0 17.0 50.0 194.0 70.0 310.0 nanowire 2000 9.0 14.0 55.0 22.0 144.0 22.0 62.0 180.0 87.0 295.0 eletrode 3000 11.0 17.0 55.0 27.0 145.0 26.0 68.0 160.0 100.0 284.0 (47) (135) (189) (297) 0 2.4 3.3 37.0 3.4 41.0 2.6 3.7 26.0 3.0 16.0 B 500 4.0 5.0 25.0 5.0 25.0 4.8 5.5 15.0 5.8 21.0 Pt/cobalt 1000 4.5 5.5 22.0 5.6 24.0 6.0 7.5 25.0 8.0 33.0 film 2000 5.6 6.8 21.0 6.9 23.0 7.6 11.0 44.0 11.8 55.0 electrode 3000 6.1 7.3 20.0 7.5 23.0 8.7 12.0 38.0 13.0 50.0 (22) (24) (31) (40) 0 0.2 0.2 0.0 0.2 0.0 1.5 1.7 13.0 1.8 20.0 C 500 1.2 1.5 7.0 1.6 14.0 5.0 5.2 4.0 5.2 4.0 Pt 1000 2.2 2.3 5.0 2.3 5.0 6.7 7.0 5.0 7.5 12.0 electode 2000 2.8 3.1 10.0 3.1 10.0 8.7 9.0 4.0 9.5 10.0 3000 3.6 3.7 3.0 3.8 5.0 11.0 11.5 4.0 11.5 5.0 More than 10 x (6) (9) (4) (8) current enhancement MANSE Midterm Review
Electrode A Electrode C This is not a mass transport effect, as it is independent of electrode rotation speed MANSE Midterm Review
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