COMSOL - Classical Models of the Interface between an Electrode and Electrolyte...
Transcript of COMSOL - Classical Models of the Interface between an Electrode and Electrolyte...
-
Classical Models of the Interface between an Electrode and Electrolyte
M.Sc. Ekaterina GongadzeFaculty of Informatics and Electrical Engineering
Comsol ConferenceMilano 200913 10 2009
Interdisziplinäre Fakultät Fakultät für Informatik und Elektrotechnik Medizinische FakultätMathematisch-Naturwissenschaftliche Fakultät Fakultät für Maschinenbau und Schiffstechnik
13.10.2009
Presented at the COMSOL Conference 2009 Milan
-
Outline
MotivationElectrical Double Layer (EDL)y ( )EDL Models
• Classical ModelsClassical ModelsEDL Capacitance ComparisonF t G lFuture Goals
2
-
Motivation
Implant & Body Implant & Body FluidsFluidsFluidsFluids
Electrical Electrical
Double LayerDouble Layer
3
Source: Lüthen et al. (2005),Biomaterials 26
-
Electrical Double Layer (EDL)
• What?
The interface between a charged surface and an electrolyte
• How big?
Thickness: 0.1 - 100 nm (~ ionic strength of the solution)
• Where?
Implant´s surfaceElectrolyte batteryElectrolyte battery In microsystems, around charged nanoparticles (biomolecules, latex beads…)Aurora, solar corona, pulsars
4
-
Distribution of Ions
D t i d b th f tDetermined by three factors:
• electrostatic (Coulombic) forceselectrostatic (Coulombic) forces • diffusion• specific interactionsp
5
-
Helmholtz Model
Potential profile determined by Poisson’s equation: q
022
02
2
dxd
dxd
r
022
02
2
dxd
dxd
r
εr relative permittivity of medium
ε0 permittivity of free space
ρ space charge density
φ electric potentialφ electric potential
x distance tangential to the electrode‘s surface
d diameter of the solvated counter
6
d diameter of the solvated counter ion
-
Gouy-Chapman Model
Assumptions:
• ions as point-like charges• dilute ionic solution• continuum dielectric solvent• continuum dielectric solvent
7
-
Stern Model
Helmholtz layerHelmholtz layer+
Diffuse double layery
Total capacitance:
CH and Cdiffuse in series:
)(111
0diffuseHd CCC
8
-
Numerical Simulation
• Geometry and Subdomain Settings
Gouy-Chapman Model:Linearized Poisson BoltzmannSubdomain Settings Linearized Poisson-Boltzmann Equation:
zekTn sinh8
2/10
whereElectrolyte:
NaCl
Ele
ctro
de
Ø 2
0 nm
kTx r 2
sinh0
k Boltzmann constant
20 nm0.3 nm 0.3 nm
E k Boltzmann constante unit chargezi ion i charge numberc concentration of ion i
Helmholtz Model:Poisson Equation:
02d
ci concentration of ion iT temperatureni0 number of ion i in bulk
9
02 dx
-
Numerical Simulation (2)
Stern Model: • Boundary conditions
Subdomain 1:
02d
symmetry
Subdomain 2:
02 dx
continuity
pote
ntia
l
pote
ntia
l
dom
ain
1
dom
ain
2
kTzekTn
x 2sinh8
2/10
El.
p
El.
Sub
d
Sub
d
kTx r 20 symmetry
10
-
Postprocessing
• Capacitance computation
i
ndADQ 0QC
where Q – free electric charge dA i i fi i i l
H l h lt G St M d l E i t
QC dA - vector representing an infinitesimal element of area D0 - electric displacement field
Helmholtz Model
Gouy-Chapman Model
Stern Model Experiment
C [µF/cm2] 231 41 77 16 57 92 6Cdl [µF/cm2]analytical
231.41 77.16 57.92 6
Cdl [µF/cm2]i
231.69 77.03 57.61 6
11
numerical
-
Classical Models – an overview
Assumptions:• ions as point like charges
Disadvantages:
i t t d i t h• ions as point-like charges• dilute ionic solution• continuum dielectric solvent
• ions treated as point charges• only significant interactions -
Coulombic ones• constant electrical permittivity
Advantages:• Simple implementation • Analytical solution
• not time-dependent• infinite concentration of counter-
ions near the charged surface• inhomogeneity of the charge • Analytical solution o oge e y o e c a gedistribution not included• finite size & shape anisotropy of
molecules not incorporated• distorted structure by steric effectdistorted structure by steric effect
& hydration force not included• overlapping problem
12
-
Summary & Outlook
• Importance of EDL
• Classical Models
• Need of a Sophisticated M d lModel
• Modelling of a non-planar electrode‘s surface
13
Source: Lange, R. et al (2009), Material and cell biological investigations on structured biomaterial surfaces with regular geometry, IBI 2009