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 McMaster University
Negative Dielectric Constant of Photo-conducting
Polymers upon Corona-charging
Prepared by: Han Yan
Supervisor: Dr. Gu Xu
Date: Jan 18th, 2013
1
Outline
• Introduction
1.
2.
Photoconductors
Working Principle of A Laser Printer
• Problem:
1.
2.
The Origin of the Unwanted Surface Conduction
Why Significant?
• Experiment Details
• Results and Discussion
1.
2.
Three Possible Explanations
Negative Dielectric Constant (NDC)
• Summary and Future Work
2
Introduction: Photoconductor
•The overall hardcopy market: $80 Billion
•An average of 15% annual growth
•Transparent polymer, electrically insulating in dark
•Become hole-conductive upon illumination
•Laser printers posted the strongest
growth up 25 %
Drum
Photoconductor
Laser Light
3
Problem: The Origin of Unwanted Surface Conduction
Dark Region
Light Exposure
+
+
+
+
+ + + +
Dark Region
Holes
CTL: charges are transported
vertically to annihilate
surface charge; relatively
thick.
CGL: holes and electrons
separated; relatively thin.
•It is as a result of the UNWANTED conduction ALONG the photoconductor
surface,
•The DESIRABLE conduction is PERPENDICULAR to the photoconductor surface
•Periphery of letter printed become fussy after repeated charges
4
Significance of The Research
•A long-standing problem since 1980s, cause rapid replacement of drums
a)
Yarmchuck (1989) and Keefe (1991) both found the blurred image was caused by
surface conduction
b)
Tokarski et al. (2007,2008) found another source of the blurred image : corona
related charge accumulation in the CTL.
Desirable Image
Blurred Image
•NO solution found, due to the unknown mechanism of photoconductor
upon Corona charging
5
Experimental: Sample Preparation
Spacing between electrodes ~ 1mm
Au Electrode
•Interdigitated electrode is used to
maximize effective electrode area
•Photoconductor: polycarbonate (PC) matrix
and diphenylbenzidine (TPD) as charge
transporting component
Photoconductor
Chemical Structure of TPD
Portable self-made corona charger
Sample is charged under high voltage for
30 mins
6
Experimental: AC Impedance Spectroscopy (IS)
• To understand the origin of parallel surface conduction, IS is employed
• IS: analysis of electric response of the AC perturbation, non-destructively
• Analysis in frequency domain
M
Signal(Y)
• Small perturbation
Z（）
Response(X)
I-V curve appears linear
• Sine wave voltage perturbation gives sine
wave current response
Angular frequency: =2πf
Z()=V()/  I()
7
Experimental: Step-function IS
•
•
•
•
Insulating material
Huge Resistance
τ=RC is large.
Restriction in using AC: large time constant τ (extremely low resonance frequency).
Low frequency IS: difficult to obtain reliable/reproducible data.
Step-function IS: a step-wise potential signal, includes all frequencies on the
spectrum.
• I-t relationship is complicated: Z(t) can NOT be integrated directly
• However, at any frequency ω0,
Z(ω0)=V(ω0)/I(ω0)
• V(t) and I(t): sum of innumerable simple harmonic oscillations at variable
frequencies, after Fourier transform, V(ω) and I(ω) are obtained
• Step-function IS is theoretically identical to AC IS, only technically more
convenient for sample with large Time Constant
8
Experimental: Step-function IS
V(t)
R
C
Power Supply: V(t)=0 when t<0;
V(t)=U when t>=0.
= Impedance Representation= Equivalent
9
Experimental: Measuring Device
A
•The rising edge of the voltage
source is so sharp that it is
below 1 µs.
V(t)
Static Charges
Electrode
10
Result from Step-function IS: Current Difference
Cause by Corona Charging
•Figure shows the current difference as a result of surface corona charging
•Fourier transform converts I(t) into frequency domain and represents it in
complex form
11
Result: Nyquist Plot of Impedance
}
12
Equivalent Circuit Modeling: I
C
R
1
𝑍𝐶 =
𝑖𝜔𝐶
𝑍𝑅 = 𝑅
Z’’
𝑍𝐿 = 𝑖𝜔𝐿
Z’’
Z’’
Z’
0
0
L
.
R
ω
ω
Z’
0
Z’
13
Equivalent Circuit Modeling: II
.
Z’’
0
.
Z’’
R
R
0
Z’
ω
Z’
ω
14
Equivalent Circuit Modeling: III
ω
Z’’
ω
Z’’
ω=(LC)-1/2
0
ω→0
R
ω→∞
Z’
0
R0
ω
R+R0
ω
r
L
L
.
R
C
Z’
.
R0
R
.
r
.
C
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Result: Equivalent Circuit and Corresponding Elements
Physically Unlikely
Ro
Co
488 GΩ
21.9 pF
L1
715 GH L2
19.8 GH
R1
1200 GΩ
R2
590 GΩ
C1
0.94 pF
C2
0.112 pF
r1
332 GΩ
r2
190 GΩ
Inductor winding = 0.1Henry
electrosome.com
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Similar Inductance Behavior Found in Other Areas: ion
conducting polymers
•
Chen et al. in 2002 believed that it was a
result of oxidation/reduction reaction but NO
prove was given;
•
Schneider et al. in 2008 believed that cycle of
hydration and dehydration caused the
unpredicted inductor BUT it was found in other
systems without water hydration;
•
Le Canut et al. in 2009 simply considered it as
artefect and didn’t want to discuss further;
•
Nanda et al. in 2011 claimed it can NOT be
explained;
Roy, S.K. et al. (2007)
• NO explanation has been given
Reversed Imaginary-axis for conventional plot
Schneider, I.A. et al. (2008)
17
Similar Inductance Behavior Found in Other Areas:
Corrosion
•Cole et al. in 1941 found this mysterious
inductor on a squid giant axon and gave
no explanation;
•Baril et al. in 1975 found this in Iron
corrosion system and believed that it
was as a result of Redox reaction;
Cole, K.S. et al. (1941)
•Hukovic et al. found it in metal
electrode anodic dissolution but he
stated that the reason was “unclear”.
•No explanation has been given
•Baril, G. et al. (2001).
Reversed Imaginary-axis for conventional plot
•Hukovic, M.M. et al. (2002).
18
Survey on Possible Explanations
1
Possible
Alternative
Explanations
3
Memristor
2
Quarts Crystal Resonance
Negative Dielectric Constant(NDC)
19
Possible Explanations 1: Memristor
•Memristor was originally envisioned in
1971 by circuit theorist Leon Chua;
•Recent progress reported from Nature
(2008,2010), Physical Review B (2008)
•It is currently under development by
various teams including Hewlett-Packard for
nanoelectronic memories, computer logic,
and neuromorphic computer architectures
•Non-linear element: impedance change as
a function of voltage/current applied
Strokov D.B. et al. (2008)
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Possible Explanations 1: Memristor
I/V
NO Phase Shift
Voltage Source
Resistor
Memristor
0
Inductor
Capacitor
Time
Characteristic current curves of various circuit elements
POSSIBILITY 1 IS TURNED DOWN
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Possible Explanation 2: Quartz Crystal Resonance
• Piezoelectric quartz crystal distorts when an electric field is applied;
• Field removed, it returns to its previous shape
• Energy is transformed back and forth;
Electric
Mechanical
• A non-physical inductor is found in its equivalent circuit ;
• Resonance frequency: ω2=1/L1C1, size dependent;
• Resonance frequency of sample in figures below: Mega Hertz;
• Resonance frequency at 1 hertz, magnitude of size: ~100 meters
Piezoelectric
Quartz Crystal
Resonator
1cm
electrosome.com
POSSIBILITY 2 IS TURNED DOWN
qrbiz.com
22
Dielectric Polarization
+++++++++++++++
+++++++++++++++
---------------
---------------
•Dielectrics: electrically insulating but polarizable;
•NO external field: dipoles oriented randomly: electronically NEUTRAL
•Polar dipoles REORIENT themselves slowly by external field;
•Dipoles ALIGNED so that the internal field can CANCEL part of the external field
•Dielectric constant measures how EASILY dipoles are aligned by external field:
higher ɛ
easy polarization
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Dielectric Constant
+ + + + + + + + + + + + + + +
- - - - - - - - - - Dielectric
+ + + + + + + + + + + + +
- - - - - - - - - - - - - - - - -
Parallel Metal Plates
•Upon insertion, free charge on plates maintained constant: q0 ;
•At molecular level, alignment of dipole moments inside the dielectric
decrease potential over metal plates;
•Total charge that contributes to the voltage: q1= q0 /ε;
•Polarization(P) == Surface Density of the Polarized Charge (σ0-σ1).
24
Dielectric Constant
• σ0 and σ1 are the surface densities of free
and total charges and they define electric
displacement D and electric field E;
• Consequently, an application of an electric
field leads to polarization.
• A positive dielectric constant meaning
displacement is in the same direction as
the applied field.
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∝
Possible Explanation 3: Negative Dielectric Constant
C=εA/d and ε=ε*·εo
ε0=Vacuum Permittivity=Constant
C∝ε
Graphically in Nyquist Plot:
• Capacitors are commonly seen in the
equivalent circuit for polymeric materials.
Const* i= Turn the image 90o
counter clock-wisely
Z(Im)
• Dielectric constant ε for a regular polymer
is positive.
L
In Impedance Result:
+ve on Im axis
R
0
Z(Re)
-ve on Im axis
C
If εC<0, Zc has the same form of ZL
Dielectric Constant of the Capacitor is Negative
26
Negative Dielectric Constant
Ramakrishna, S.A., (2005).
•Observed were NOT inductors. They were capacitors with negative dielectric constant (NDC)
•NDC stands for a induced field with OPPOSTITE direction than the original field
•Two capacitors in a circuit, one filled with a POSITIVE dielectric and the other filled with a
NEGATIVE dielectric material, can become an LC resonance ω2=1/LC
•If ε*of our the photoconductor is negative, we would expect a phase shift of the induced
current curve to the right on the I(t)/V(t) characteristic curve for a capacitor, which is
equivalent to an INDUCTOR.
27
Negative Dielectric Constant: Drude Model I
Negative dielectric constant are found in plasma:
Since
• Plasma are a ‘gas’ of free
electrons.
• Metals are a ‘gas’ of free
electrons in nuclei
• Assumption : electrons do
not interact with each
othe
Solve for ɛ, we have:
N: Electron Density
Me: Electron Mass
Similar situation for metal, slightly different in the governing equation:
28
Negative Dielectric Constant: Drude Model II
Metal
Plasma
Dielectric constant vs normalized frequency
=plasma frequency
Dielectric constant is frequency dependant
•
•
Free
Electrons
•
The plasma frequency is
derived in Drude Model
Conclusion 1: ω>ωp, free
electron could NOT respond
fast enough, wave transmitted.
Conclusion 2: ω<ωp, wave
mostly reflected, propagates
shallow in the metal, oscillates
slowly enough for the
electrons to follow.
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Summary and Future Work
• To find out the origin of surface conduction on photoconducting polymer
surface that causes blurred image edge.
• Due to sample’s large time constant, AC IS could not obtain reliable data,
step-function IS was employed.
• Fourier transformed step-function IS data revealed physically unlikely
inductors.
• Negative dielectric constant in corona charged photo-conductor surface is
proposed to be the explanation.
• To understand the nature of NDC in photoconducting polymer.
•
To build a model for the negative dielectric constant upon corona
exposure.
• Additionally, the understanding of NDC material at low frequency may
provide possible means to make coil-less inductor.
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Thanks for your attendance and attention
Questions?
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