Simulating the Electrical Double Layer Guigen Zhang, Ph.D.

Transcription

1 Presented at the COMSOL Conference Boston Simulating the Electrical Double Layer Guigen Zhang, Ph.D. Dept. of Bioengineering, Dept. of Electrical & Computer Engineering Institute for Biological Interfaces of Engineering Clemson University

2 Overview The drive to make supercharge capacitors Electrochemical based capacitor The structure of electrical double layer (EDL) The effect of EDL structure on electron transfer The EDL capacitor Conclusions

3 Making Supercharge Capacitors 3. Capacitance ( F) Flat Overpotential (mv) Capacitance ( F) 6 The Electrochemical Society Interface, Fall 8 8 Nano Overpotential (mv)

4 Electrochemical Based Capacitor This topic has been a major interest in electrochemistry for about a century D. C. Grahame, 947. In 997, the Electrochemical Society sponsored a symposium on the double layer to recognize the 5 th anniversary of Grahame s seminal work C A/ d

5 Electrical Double Layer (EDL) The EDL structure Helmholtz Model GouyChapman Model Ψ OHP C A d x Diffuse zone x Problems with the classic theories on electrical double layer (EDL):. No electron transfer across the electrode/solution interface. Boltzmann distributions for ions in the solution 3. Electroneutrality GouyChapmanStern Model Stern Plane OHP, PET Diffuse layer Compact layer Gouy plane x Bulk solution

6 Modeling the EDL Using COMSOL A Mass transport by diffusion and electromigration NernstPlanck equation Electrostatics Poisson equation ci t Reversible/irreversible systems ButlerVolmer kinetics zif ( Di ci Dici V ) RT ( V ) In the compact layer: In the solution: z c i i i Axis of inplane symmetry r IHP OHP r Axis of Electrolyte axisymmetry u r u v l l v k b O z e k f R k b z ' k f k exp[ F ( Et V E ) / RT ] ' k exp[( ) F( Et V E ) / RT ]

7 Modeling Using COMSOL Dielectric constant inside the compact layer cosh [S ( r r )], cos [S( l l r r)],, B l a b c r r r r r r r l l l l r l IHP OHP Dielectric constant (x) Electrode surface PET Electrolyte r r l Distance (x) Radial Distance (r) r l l

8 The Size Factor of the EDL Potential (V) A nm nm Potential (V) B Diffuse Layer Potential Concentration nm nm Diffuse Layer Concentration (mm) rr (nm) (rr )/ diffuse diffuse nm.8 (nm), nm 4.5 (nm) diffusion diffusion nm 4 (nm), nm 8 (nm) ~3% ~.5%

9 EDL Effect on Electron Transfer i/i dl i/i dl Insert..... EE ' (V) Insert Diffusion z= z= Electrode Radius (mm) nm nm 5nm nm nm z = z = Diffusion i/i dl Diffusion.nm.4nm.7nm Potential (V) Potential 3.4 Concentration (rr )/ Concentration (mm) EE ' (V) EE ' (V) Effect of electrode size Effect of compact layer thickness Note: Diffusion represents the case in which the EDL effect is not considered.

10 Effects of EDL Potential (V) Potential Concentration.33nm.44nm.55nm.66nm 3 Concentration (mm) Potential (V).3.. Potential Concentration ES=6 ES= ES=8 ES=4 3 Concentration (mm) Distance into Solution from PET (nm) Distance into Solution from PET (nm) Potential (V) Potential Concentration. M.5 M.5 M 5. M 4 3 Concentration (mm) Potential (V).3.. Potential Concentration.5 nm. nm 5. nm. nm Flat 4 3 Concentration (mm) Distance into Solution from PET (nm) Distance into Solution from PET (nm)

11 EDL Capacitance 6 Size effect Capacitance ( F/cm ) y=4.8.66x/(.4x) C r E Radius of Electrode (nm)

12 EDL Capacitance 4 Dielectric effect Capacitance ( F/cm ) B a b c IHP OHP Dielectric constant (x) Electrode PET surface Electrolyte r r Distance l (x) r l l Radial Distance (r) Dielectric Constant at Electric Satuaration

13 EDL Capacitance 4 Thickness effect Capacitance ( F/cm ) Thickness of Compact Layer (nm)

14 EDL Capacitance 7. Electrolyte effect Capacitance ( F/cm ) Concentration of Supporting Electrolyte (M)

15 EDL Capacitance: A Surprise C A/ d Capacitance ( F/cm ) With ET without ET FEM Overpotential (V) D. C. Grahame, 947. Capacitance (C/C PZC ) MD Overpotential (V)

16 Conclusions EDL capacitance varies as a function of Dielectric constant Compact layer thickness Electrode size Electrolyte concentration When redox is allowed, the capacitancepotential curve exhibits a dip feature near the potential of zero charge This study shed some new light into enhancing the supercharge capacitors

17 Acknowledgement National Science Foundation Bill & Melinda Gates Foundation Thank You!