Classical Models of the Interface between an Electrode and Electrolyte. M.Sc. Ekaterina Gongadze

Size: px

Start display at page:

Download "Classical Models of the Interface between an Electrode and Electrolyte. M.Sc. Ekaterina Gongadze"

Katrina Price
5 years ago
Views:

Ekaterina Gongadze Faculty of Informatics and Electrical Engineering Comsol Conference Milano 009 13.10.

1 Presented at the COMSOL Conference 009 Milan Classical Models of the Interface between an Electrode and Electrolyte M.Sc. Ekaterina Gongadze Faculty of Informatics and Electrical Engineering Comsol Conference Milano Interdisziplinäre Fakultät Fakultät für Informatik und Elektrotechnik Medizinische Fakultät Mathematisch-Naturwissenschaftliche Fakultät Fakultät für Maschinenbau und Schiffstechnik

2 Outline Motivation Electrical Double Layer (EDL) EDL Models Classical Models EDL Capacitance Comparison Future Goals

3 Motivation Implant & Body Fluids Electrical Double Layer Source: Lüthen et al. (005), Biomaterials 6 3

Implant s surface Electrolyte battery In

4 Electrical Double Layer (EDL) What? The interface between a charged surface and an electrolyte How big? Thickness: nm (~ ionic strength of the solution) Where? Implant s surface Electrolyte battery In microsystems, around charged nanoparticles (biomolecules, latex beads ) Aurora, solar corona, pulsars 4

5 Distribution of Ions Determined by three factors: electrostatic (Coulombic) forces diffusion specific interactions 5

6 Helmholtz Model Potential profile determined by Poisson s equation: d dx r 0 d dx 0 d dx r 0 d 0 dx ε r ε 0 relative permittivity of medium permittivity of free space ρ space charge density φ electric potential x distance tangential to the electrode s surface d diameter of the solvated counter ion 6

7 Gouy-Chapman Model Assumptions: ions as point-like charges dilute ionic solution continuum dielectric solvent 7

8 Stern Model Helmholtz layer + Diffuse double layer Total capacitance: C H and C diffuse in series: 1 C d 1 C H C 1 diffuse ( 0 ) 8

9 Numerical Simulation Geometry and Subdomain Settings Electrode Electrolyte: NaCl Ø 0 nm 0 nm 0.3 nm 0.3 nm Helmholtz Model: Poisson Equation: d 0 dx Gouy-Chapman Model: Linearized Poisson-Boltzmann Equation: 1/ 0 8kTn ze sinh x r 0 kt where k Boltzmann constant e unit charge z i c i T n i 0 ion i charge number concentration of ion i temperature number of ion i in bulk 9

10 Numerical Simulation () Stern Model: Boundary conditions Subdomain 1: d 0 dx Subdomain : 1/ 0 8kTn ze sinh x r 0 kt El. potential Subd domain 1 Subd domain symmetry continuity symmetry potential El. 10

displacement field Hl Helmholtz hlt Gouy- Stern Model Experiment Model Chapman

11 Postprocessing Capacitance computation Q D0 C i Q nda where Q free electric charge da - vector representing an infinitesimal i i element of area D 0 - electric displacement field Hl Helmholtz hlt Gouy- Stern Model Experiment Model Chapman Model C dl [µf/cm ] analytical C dl [µf/cm ] numerical

12 Classical Models an overview Assumptions: ions as point-like charges dilute ionic solution continuum dielectric solvent Advantages: Simple implementation Analytical solution Disadvantages: ions treated t as point charges only significant interactions - Coulombic ones constant electrical permittivity not time-dependent infinite concentration of counterions near the charged surface inhomogeneity oge e of the charge distribution not included finite size & shape anisotropy of molecules not incorporated distorted structure by steric effect & hydration force not included overlapping problem 1

13 Summary & Outlook Importance of EDL Classical Models Need of a Sophisticated Model Modelling of a non-planar electrode s surface Source: Lange, R. et al (009), Material and cell biological investigations on structured biomaterial surfaces with regular geometry, IBI

Lecture 3 Charged interfaces

Lecture 3 Charged interfaces rigin of Surface Charge Immersion of some materials in an electrolyte solution. Two mechanisms can operate. (1) Dissociation of surface sites. H H H H H M M M +H () Adsorption