THE EFFECT OF ELECTRICAL DOUBLE LAYER ON THE ELECTROCHEMICAL PROCESSES OF NANOMETER
INTERDIGITATED ELECTRODES
Xiaoling Yang1 and Guigen Zhang1,2,3
1Micro/Nano Bioengineering Laboratory, 2Nanoscale Science and Engineering Center, 3Faculty of Engineering
The University of Georgia, Athens, GA 30602
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Nanotechnology in Biological Engineering II
Motivation
• Electrochemical sensor plays an important role in clinical diagnosis:
Features: High Sensitivity, Real‐time detection, Simple operation
• Micro/nano interdigitated electrodes (Micro/Nano IDEs) based electrochemical biosensors are getting more and more popular:
Features: small dimension, low sample volume, low cost
Application: Glucose sensor, immune sensor, gas sensor
2
Motivation
• Problem:
For sensing purpose, IDEs measure faradic current
When the electrodes get to nanometer scale, the faradic responseat electrode may be affected by electrical double layer (EDL).
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EDL Effect on Single Electrodes
reactant Concentration
Potential
Diffuse Layer
Diffusion Layer
reactant Concentration
Potential
Diffuse LayerDiffusion Layer
Micro electrodes: diffusion only Nano electrodes: diffusion and electromigration
EDL formation: A charged electrode can attract oppositely charged species in the solution and forms EDL (compact layer and diffuse layer)
Compact Layer
+
+
Diffuse layer
Bulk Solution
OHP
-----------
x
-
-
Gouy Plane
+
+-
-
+
+
-+
+
+
EDL effect
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EDL Effect on Nano‐IDEsy
x1xIHP OHP OHP IHP
µ
0r
1r 2r
Symm Symm
Diffuse Layer
Diffuse Layer
reactant Concentration
Potential
Diffuse LayerDiffusion Layer
Diffuse layer and diffusion layer overlap
Diffuse layers overlap at two electrodes of nano-IDEs
For a widespread application of nano-IDEs, it is imperative to elucidate the effect of the EDL on the faradic reactions of nano-IDEs. But this problem is too complicated to be solved by analytical means.
5
Objective
• To investigate the EDL effect on the faradic reaction of nano‐IDEs by a fully numerical method developed using COMSOL Multiphysics
6
• In this study we expand previous method to further address the issue at nano‐IDEs.
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*Yang, X.; Zhang, G. Nanotechnology 2007, 18, 335201-335209
Model Development
Electrolyte
G G GC C C
y
1xOHP IHPIHP OHP
xG C
• Previously our group developed a fully numerical method by COMSOL Multiphysics using Nernst‐Plank‐Poisson equation to simulate EDL affected faradic reaction at single nanometer electrodes.*
r =1nm
Electrolyte
• Potential at electrode and bulk solution
– EG = 0.3V to ‐0.4V at 20mV/s;
– EC = 0.3V
– Eb = 0V
• Current Flux
Butler‐Volmer Equation
• Oxidized species (OS) and Counter ion : 5mM
• Reduced species: 0mM
• Supporting electrolyte (SE):
SE is excess CSE = 500mM
Initial Concentrations Boundary Conditions
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1z
b
fz ReO −− ⎯→←+
y
1xOHPIHPIHPOHPxECEG
V V
Eb
R0
0
O0
0bf
cRTEVEF1k
cRTEVEFkJJ
⋅−−−⋅−
⋅−−−⋅=−=
]/)()exp[(
]/)(exp['
'
α
α
V: potential at OHP, i.e. the Position of Electron Transfer
Model Development
• Potential distribution– Poisson equation
• Mass transport– Nernst‐Plank equation
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)( VcDRT
FzcD
tc
jjj
jjj ∇+∇∇=
∂∂
y
1xOHP IHPIHP OHP
x
∑=j
jjczρ
0=ρ0=ρ
ρεε −=∇∇ )( V0
61 =ε
782 =ε
Assume: perfectly smooth electrode surface; no specific adsorption
‐‐‐ Governing Equations
Model Development
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2ε
1ε
Radial Distance (r)
PET
r0 + l1 + l2
a b c
r0 r0 + l1
IHP OHP
B
Electrode surface
Electrolyte
2ε
1ε
Radial Distance (r)
PET
r0 + l1 + l2
ε
EDL Effect and the Charge Valences of Redox Species
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Potential (V)-0.4 -0.2 0.0 0.2 0.4
Cur
rent
Den
sity
(kA
/m2 )
-60
-40
-20
0
20
40
60
Diffusionz = -1z = +1
Generator
Collector
EDL affected voltammetric curve deviated from diffusion controlled case, when inter‐electrode spacing wgap = 4nm
OHP IHPIHP OHP
4nm
EDL Effect with Changing Gap Spacing
limiting current and wgap
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Potential Distribution at wgap = 4nm & 16nm
More diffuse layer overlap have more EDL effect!
Distance/(wgap - 2µ)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Pot
entia
l (V
)
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
wgap =4nmwgap = 16nmEG =0.3V, EC =0.3VEG = -0.4V, EC = 0.3V
BOHP IHPIHP OHP
wgap(nm)4 16 64
Lim
iting
Cur
rent
(kA
/cm
2 )-40
-30
-20
-10
0
10
20
30
40
Diffusionz = -1z = +1Generator
Collector
A
EDL Effect and Supporting Electrolyte
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Potential (V)-0.4 -0.2 0.0 0.2 0.4
Cur
rent
(kA/
cm2 )
-40
-30
-20
-10
0
10
20
30
40Diffusion500 mM0 mM
Generator
Collector
A
z = -1
z = -1
Potential (V)-0.4 -0.2 0.0 0.2 0.4
Cur
rent
(kA/
cm2 )
-100
0
100
200
Diffusion500mM0 mM
Generator
Collector
B
z = +1
z = +1
The voltammetric curve deviate significantly from diffusion controlled case when supporting electrolyte is absent in the solution.
Conclusion
• The effect of EDL on the voltammetric performance of nano IDEs is dependent on – The charge valence of redox species– The gap spacing between electrodes– The concentration of supporting electrolyte
• This work demonstrates that a complete computer‐modeling approach is well suited for elucidating the electrochemical processes of electrodes with complex geometries when faradic reactions and the EDL effect are of concerns.
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