1. On Counter-Charges in Development Rollers for Electrophotography
NIP22
NIP-22 Denver, September. 2006
On Counter-Charges in Development Rollers for Electrophotography
Inan Chen and Ming-Kai Tse
Quality Engineering Associates (QEA), Inc.
Burlington, MA, USA

2. Counter-Charges in Development Rollers for Electrophotography
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Counter-Charges in Development Rollers for Electrophotography
Latent images developed by moving Charged Toners
- Extensively studied.
Counter-charges : Little attention
- Reside in carrier beads (2-component development),
or development rollers (Single-Component Dev.)
Objectives:
Quantitative analyses of roles of counter-charges
in Toner-charging and Toner-deposition in SCD
Requirements for ideal roller coating materials,
and characterization method for SCD rollers
In electrophotography, latent images are developed by moving charged toners from their supplier to the photoreceptors. Extensive works on the measurements and analyses of toner motion have been reported in the literature.
In contrast, little attention has been paid to the motion of counter-charges that reside in the carrier beads in two-component development, or in the development rollers in single-component development (SCD).
The objective of this paper is to quantitatively analyze the roles of counter-charges in the toner-charging and toner-deposition steps in SCD, and determine the requirements for ideal roller coating materials, and characterization method for Roller characterization.

3. Single-Component Development (SCD)
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Single-Component Development (SCD)
1. Development Rolls:
Conductive elastomer core
Semi-insulator Coating MB
Dev.
Roll PR VB
2. Toner Charging at
Metering Blade (MB):
Charges supplied to toner,
Counter-charges to Roll coating
3. Toner deposition:
Charged toners move to PR,
Counter charges impede toner motion,
must be removed (neutralized)
to improve deposition efficiency
1. In SCD, the development rolls consist of a conductive elastomer core surrounded by a semi-insulator coating layer.
2. Toners are charged as they pass through the metering blade. At the same time, counter-charges are induced in the roller coating layer.
3. In the deposition step, toners move toward the PR, counter-charges impede this toner motion, and must be removed, or neutralized in order to improve the deposition efficiency.

4. Single-component Development
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Single-component Development
Induction at charging, and
Neutralization at deposition of Counter Charges
Charge injection and transport
in Semi-insulator Coating layer
Charge-Transport Model
Non-Ohmic nature
Applied and reported :
Roller charging of PR (NIP21)
Electrostatic toner transfer (NIP16, 20, ICIS’06)
Liquid development (J. App. Phy. 80, 6796)
Counter-charges in SCD (This talk)
This Induction and Neutralization of counter charges
are achieved by charge injection and transport in the semi-insulator coating layer.
We have developed a charge-transport model, which considers the non-Ohmic nature of charge injection and transport in the semi-insulating overcoat layer.
The model has been applied to Roller charging of PR’s, Electrostatic transfer of toners to media, and Liquid development, and reported at previous conferences and journal.
Today, we’ll apply the model to investigate the induction and neutralization of counter-charges in SCD.

5. Charge Transport Model
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Charge Transport Model
Semi-insulators characterized by 3 parameters
1. Densities of mobile charges, qp(y, t), qn(y, t),
Initial (intrinsic) value: qi = qp(y, 0) = –qn(y, 0)
2. Charge mobility: m(E) - field dependent
3. Charge injection strength s
Injection currents from boundary at y
Ji = sE(y), E(y) = field at y ( = 0 or L)
Continuity eq. q(y, t)/t = – (mqE)/y
Poisson’s eq. E(y, t)/y = (qp + qn)/e
Results for SCD charging and deposition
sp, sn
– – – – – – y L
In this model, the charge transport in semi-insulating layer is characterized by 3 parameters:
1. Density of mobile positive and negative charges, qp and qn, having the initial, or intrinsic value: qi;
2. The charge mobility m, generally field dependent. The product of m and qi is the conductivity s.
And the third is the charge injection strength s. The injection current Ji from the layer boundary at y is given by the product of s and the field E at y.
The continuity equation and Poisson’s equation are used to calculate the time and spatial variations of q and E.
The numerical results for SCD charging and deposition steps are discussed in the following slides.

6. Toner Charging in SCD (1)
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Toner Charging in SCD (1)
–VB
Metering Blade
– – Toner – – QT
Roll-Coating QR yR yT LR s
Toner Coating
Thickness: LT LR
Permittivity: eT eR
Bias voltage VB
Toner charge density:
QT(t) = [VB – QR(t)DR – UR(t)]/(DT/2 + DR) (D = L/e = 1/C)
QR(t) = Interface charge density
UR(t) = 0LR dy0y’(qP + qN)dy’/eR
Transport equations, calculate QR(t), UR(t)  QT(t)
In the toner charging step, the charging nip is represented by this layer geometry.
A bias voltage VB is applied across the toner and the coating layers.
The toner charge density QT can be expressed as a function of the bias voltage VB, the interface charge density QR, and the integral of positive and negative charge densities in the roll-coating layer UR.
The counter-charges contribute to the interface charge QR and the integral UR.
The Charge transport equations are used to calculate QR and UR as functions of time, which in turn, give the time dependence of toner charge density QT.
} Counter-charges

7. Toner Charging in SCD (2)
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Toner Charging in SCD (2)
Growth of toner charge QT(t)
with time
Dependence on
Injection Strength s
very significant at
t  100to
High speed printing
-- short charging time:
high s important
This figure shows numerical examples of the growth of toner charge with time, and its dependence on the strength s of charge injection from the bias into the roller coating.
It can be seen that the s dependence is very significant at times of about 100 time units. Here, the unit of time is normalized to the layer thickness, charge mobility and the bias voltage, and has a typical value of 10 msec.
This suggests that as the print speed increases, and the charging time becomes shorter it becomes more important to have a good injection from the bias electrode.
Units:
to = LR2/moVB  10 msec
so = moqo = eo/to  3x10–11 S/cm
qo= eoVB/LR  3x10–6 C/cm3

8. Toner Charging in SCD (3)
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Toner Charging in SCD (3)
Dependence on mobility mp, mn
in RC
For QT< 0
Smaller pos mobility mp
has significant effect (A, B, C)
Insensitive to neg mn (A, D)
Build-up of counter-charge
mostly from injection of
pos charge from VB,
not from depletion of
neg charge in coating layer
This figure shows the effects of charge mobilities, mp and mn on the growth of toner charge density.
Assuming the toner charge is negative and the counter-charge is positive, then, when the positive charge mobility mp is decreased, as in curves A, to B, and to C, it has significant effect on the charging rate.
On the other hand, the charging is rather insensitive to the negative charge mobility mn, as we can see by comparing curves A and D, which differs in the negative charge mobility.
This indicates that the build-up of counter-charges comes mostly from the injection of positive charge from the bias, and not from the depletion of negative charge in the coating layer.
Units
Mobility: mo  10–5 cm2/ Vs
Time: to = LR2/moVB  10–2 sec
Chg density: qo= eoVB/LR2
 3x10–6 C/cm3

9. Toner Deposition in SCD (1)
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Toner Deposition in SCD (1)
Fields and Voltages in layers
Photoreceptor: EP, VP
Toner-layer: ET(y), VT
Roller coating: ER(y), VR
Bias voltage: -VB = VP + VT + VR
Gauss’ theorem relates charges QP, QR, QT to E’s
Field in toner layer:
ET(y, t) = ET0 + (QT/e)(y/LT) (detail in Proc. paper)
= func.[VB, QP, QT, QR(t), UR(t), L’s, e’s]
Injection & transport of Counter-charges in RC
contribute to QR(t), UR(t) QT
Now, for toner-deposition:
This figure shows a layer geometry of the development nip, consisting of the photoreceptor, the toner and the roller coating layers.
The applied bias voltage VB is equal to the sum of the three layer voltages.
The Gauss theorem relates the layer charges to the fields.
Then, the field in the toner layer ET can be expressed as a function of the bias voltage VB; the charge densities QP, QT and QR; the integral of mobile charge densities in the coating layer UR, and the layer thickness and permittivity.
The injection and transport of counter charges contribute to QR and UR.

10. Toner Deposition in SCD (2)
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Toner Deposition in SCD (2)
Negative toner deposition: ET(y, t) > 0
Demarcation line at y = YD
ET > 0 for y < YD
ET < 0 for y > YD
ET(YD) = ET0 + (QT/eT)(YD/LT) = 0
Deposition efficiency:
YD/LT = – eTET0/QT
= func.[VB, QP, QT, QR(t), UR(t), L’s, e’s] (in proc. paper)
QR(t), UR(t) from Transport Eqs.
Time evolution of Deposition efficiency YD/LT
–LP PR
Roll Coating (RC)
–VB
– – Toner – QT QP LT y QR YD
For negatively charged toners to be deposited on the PR, a positive ET is required.
If a demarcation line at y = YD separates the toner layer with positive ET(yT) from that with negative ET(yT),
then ET at YD is = 0, and the ratio of YD to the total toner thickness LT can
can represent the efficiency of deposition.
We can calculate the contribution of counter-charges to QR and UR as functions of time from the charge transport equations, and examine the time evolution of the deposition efficiency YD/LT.

11. Toner Deposition in SCD (3)
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Toner Deposition in SCD (3)
Deposition efficiency YD/LT vs. time
Dependence on strength s
of injection into RC from VB
Significant effects
due to small s,
in time 10 < t <100
Time unit:
to = LR2/moVB  10 msec
This figure shows examples of calculated deposition efficiency. In particular, it shows the dependence on the strength of charge injection into the coating layer from the bias.
We can see a significant effect of reduced injection s in the time ranges from 10 to 100 time units.
Here, the normalized time unit, as mentioned before, has a value of the order of 10 msec, in typical applications.

12. pos and neg charges in SCD roller-coating
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Toner Deposition in SCD (4)
Charge mobility (mP, mN) dependence of YD/LT (QT< 0)
Neg. mn reduced (A B C)
 Significant decrease
Pos. mp reduced (A D)
 No effects
Neutralize Counter-charge
requires negative charge
injection and transport
 opposite to polarity
required at charging
This figure shows the dependence of deposition efficiency (of negative toners) on the charge mobilities.
We can see that when the negative mobility mn is reduced, as in curves A to B to C, there is a significant decrease in the deposition efficiency. But, there is little effect if the positive mobility is small, as in curve D
This suggests that the neutralization of counter-charges requires the injection and transport of negative charges from the bias. This polarity is opposite to that required at the charging step.
Therefore, we can conclude that to achieve efficient charging and deposition, it requires a good injection and transport for both positive and negative charges in the SCD roller coating.
For efficient charging & deposition, it requires good injection (s) and transport (m) for both
pos and neg charges in SCD roller-coating

13. Summary and Conclusions (1)
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Summary and Conclusions (1)
In SCD, Counter Charges in semi-insulator coating
Induced at toner Charging, and
Neutralized at toner Deposition steps
Analyses: Charge-Transport model
Good bi-polar charge injection and transport
e.g., for negative toners,
Pos. charge inject. & transport for Charging
Neg. charge inject. & transport for Deposition
Process time > 100 to (to = LR2/mVB)
High speed printing requires high mobility m (+ and –)
Dev. Roller performance can’t be evaluated properly
with closed-circuit resistance measurements
In summary, we have shown that counter-charges in the semi-insulator coating layer must be efficiently induced at the charging step, and efficiently neutralized at the deposition step.
Our analyses based on charge-transport model indicate that this requires good bi-polar charge injection and transport.
For example, if the toner charge is negative, positive charge injection is required for charging, and negative charge injection for deposition.
In addition, we find that the process takes more than 100 time units. The definition of time unit suggests that for high speed printing with short process time, high mobilities m, for both positive and negative charges are very desirable.
Because of these complex requirements, the performance of roller coatings cannot be evaluated properly with the conventional method of closed-circuit resistance measurements.

14. Summary and Conclusions (2)
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Summary and Conclusions (2)
Alternative evaluation method:
Electrostatic Charge Decay (ECD) technique
(NIP-11, 15, 16, 17; ICIS’02; JHC-00, 02, 05)
Open-circuit voltage decay
- simulating actual process in Electrophotography
Field applied by Corona charging
- Scan and map large area,
efficient, non-destructive
Applied to transfer belts, paper,
charge rolls, dev- rolls, PR
Consistently predict device performance
We have developed an alternative evaluation method known as ECD, introduced at previous conferences.
This technique is based on measurements of open-circuit voltage decay, simulating the actual process in EP.

15. ECD Data for Intermediate Transfer Belt
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ECD Data for Intermediate Transfer Belt
Voltage *
The output data can be displayed as single-track curves or color-coded maps.
The sample can be in the shapes of rolls, sheets or belts as shown in these photographs.
For more details, please visit Exhibit booth # 210
Rolls and Belts Testing Fixture
Exhibit Booth #210
© 2005 Quality Engineering Associates (QEA), Inc. All Rights Reserved

16. Thank you for your attention Please visit Exhibition Booth #210
NIP22
NIP-22 Denver, September. 2006
Thank you for your attention Please visit Exhibition Booth #210
Inan Chen and Ming-Kai Tse
Quality Engineering Associates (QEA), Inc.
Burlington, MA, USA