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.

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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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Thank you!

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AcknowledgementNational Science FoundationThe Faculty of Engineering at The University of Georgia.My advisor Dr. Guigen ZhangAll my group members