Negative Dielectric Constant of Photo-conducting Polymers upon Corona-charging

McMaster University

Prepared by: Han YanSupervisor: Dr. Gu Xu

Date: Jan 18th, 2013

1

• Introduction 1. Photoconductors 2. Working Principle of A Laser Printer

• Problem: 1. The Origin of the Unwanted Surface Conduction 2. Why Significant?

• Experiment Details• Results and Discussion

1. Three Possible Explanations2. Negative Dielectric Constant (NDC)

• Summary and Future Work

Outline

2

Introduction: Photoconductor

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•Transparent polymer, electrically insulating in dark•Become hole-conductive upon illumination

•The overall hardcopy market: $80 Billion•An average of 15% annual growth•Laser printers posted the strongest growth up 25 %

PhotoconductorDrum

Laser Light

Problem: The Origin of Unwanted Surface Conduction

4

•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

CTL: charges are transported vertically to annihilate surface charge; relatively thick.

CGL: holes and electrons separated; relatively thin.

Dark RegionLight ExposureDark Region

Holes++ +

++

+ ++

Significance of The Research

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•A long-standing problem since 1980s, cause rapid replacement of drumsa) Yarmchuck (1989) and Keefe (1991) both found the blurred image was caused by

surface conductionb) Tokarski et al. (2007,2008) found another source of the blurred image : corona

related charge accumulation in the CTL.

•NO solution found, due to the unknown mechanism of photoconductor upon Corona charging

Desirable Image

Blurred Image

Experimental: Sample Preparation

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Au Electrode

Spacing between electrodes ~ 1mm

•Interdigitated electrode is used to maximize effective electrode area•Photoconductor: polycarbonate (PC) matrix and diphenylbenzidine (TPD) as charge transporting component

Portable self-made corona chargerSample is charged under high voltage for 30 mins

Photoconductor

Chemical Structure of TPD

Experimental: AC Impedance Spectroscopy (IS)

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Signal(Y) Response(X)

Z（）M

• 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

• Small perturbation I-V curve appears linear

Z()=V()/ I()

• Sine wave voltage perturbation gives sine wave current response

Angular frequency: =2πf

• 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.

Experimental: Step-function IS

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• 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

Z(ω0)=V(ω0)/I(ω0) • I-t relationship is complicated: Z(t) can NOT be integrated directly • However, at any frequency ω0,

Experimental: Step-function IS

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V(t)R

CPower Supply: V(t)=0 when t<0; V(t)=U when t>=0.

= Impedance Representation= Equivalent

Experimental: Measuring Device

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•The rising edge of the voltage source is so sharp that it is below 1 µs.V(t) A

Static ChargesElectrode

Result from Step-function IS: Current Difference Cause by Corona Charging

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•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

Result: Nyquist Plot of Impedance

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}

Equivalent Circuit Modeling: I

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𝑍𝑅 = 𝑅

. Z’

Z’’

R

Z’

Z’’

ω ω

Z’

Z’’

R C L

𝑍𝐶 = 1𝑖𝜔𝐶 𝑍𝐿 = 𝑖𝜔𝐿

0

0

0

Equivalent Circuit Modeling: II

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. .

Z’’

Z’

0 R

ω

Z’

ω

Z’’

R0

Equivalent Circuit Modeling: III

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Z’’

Z’

0 R0

r

R+R0

R0

r C

R

L

. .

ω

ω

Z’’

Z’

0R

C

R

L

. .

ω

ω

ω=(LC)-1/2

ω→0

ω→∞

Result: Equivalent Circuit and Corresponding Elements

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Ro 488 GΩ L1 715 GH L2 19.8 GHR1 1200 GΩ R2 590 GΩ

Co 21.9 pF C1 0.94 pF C2 0.112 pF

r1 332 GΩ r2 190 GΩ

Physically Unlikely

Inductor winding = 0.1Henryelectrosome.com

• 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;

• NO explanation has been given

Similar Inductance Behavior Found in Other Areas: ion conducting polymers

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Roy, S.K. et al. (2007)

Schneider, I.A. et al. (2008)Reversed Imaginary-axis for conventional plot

Similar Inductance Behavior Found in Other Areas: Corrosion

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Cole, K.S. et al. (1941)

•Baril, G. et al. (2001).

•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;

•Hukovic et al. found it in metal electrode anodic dissolution but he stated that the reason was “unclear”.

•No explanation has been given

•Hukovic, M.M. et al. (2002).

Reversed Imaginary-axis for conventional plot

Survey on Possible Explanations

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PossibleAlternative

Explanations

Memristor

Quarts Crystal Resonance

Negative Dielectric Constant(NDC)

1

2

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•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

Possible Explanations 1: Memristor

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Strokov D.B. et al. (2008)

Possible Explanations 1: Memristor

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Inductor

Capacitor

NO Phase Shift Voltage SourceResistorMemristor

Time

I/V

Characteristic current curves of various circuit elements

POSSIBILITY 1 IS TURNED DOWN

0

• 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

Possible Explanation 2: Quartz Crystal Resonance

22electrosome.com

qrbiz.com

Piezoelectric Quartz CrystalResonator

1cm

POSSIBILITY 2 IS TURNED DOWN

Dielectric Polarization

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•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

+ + + + + + + + + + + + + + +

- - - - - - - - - - - - - - -

+ + + + + + + + + + + + + + +

- - - - - - - - - - - - - - -

Dielectric Constant

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•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).

Parallel Metal Plates

+ + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - -

Dielectric

+ + + + + + + + + + + + +

- - - - - - - - - - -

Dielectric Constant

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• 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.

• Capacitors are commonly seen in the equivalent circuit for polymeric materials.

• Dielectric constant ε for a regular polymer is positive.

Possible Explanation 3: Negative Dielectric Constant

In Impedance Result:

Graphically in Nyquist Plot:

If εC<0, Zc has the same form of ZL

Dielectric Constant of the Capacitor is Negative

Const* i= Turn the image 90o counter clock-wisely

Z(Re)

Z(Im)

R

L

C

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∝

C=εA/d and ε=ε*·εoε0=Vacuum Permittivity=Constant

C ε∝

+ve on Im axis

-ve on Im axis

0

Negative Dielectric Constant

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•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.

Ramakrishna, S.A., (2005).

• Plasma are a ‘gas’ of free electrons.

• Metals are a ‘gas’ of free electrons in nuclei

• Assumption : electrons do not interact with each othe

Negative Dielectric Constant: Drude Model I

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Since

Negative dielectric constant are found in plasma:

Solve for ɛ, we have:

Similar situation for metal, slightly different in the governing equation:

N: Electron DensityMe: Electron Mass

Negative Dielectric Constant: Drude Model II

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• 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.

Free Electrons

Electro-magnetic

Waves

Dielectric constant vs normalized frequency =plasma frequency

Metal

Plasma

Dielectric constant is frequency dependant

• 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.

Summary and Future Work

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Thanks for your attendance and attention

Questions?

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