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Static-Tribo-Electricity of Powder
2014/12/20
Anatomy of Toner Adhesion with
SPM Measurement and
Electrostatic Simulation
Imaging Society of Japan
Technical Committee on Simulation Technology
Technical Committee on Toner Technology
Masami KADONAGA(Ricoh co.)
Jun HIRABAYASHI(Canon Inc.)
-ColaboratorsExperiment and Discussion
2
T.Tanaka（ Canon ）
SPM Measurement and Discussion
ISJ：Technical Committee on Toner Technology
T. TADA （ Canon ）、 T. UEHARA （ TREK ）、 H. OHTA （ KYOCERA ）、
M. KIMURA （ Fuji Xerox ）、 T. KUBO （ Kao ）、 H. KOBAYASHI
（ Powdertech ）、 N. SAWAYAMA （ RICOH ）、 C. SUZUKI（ Fuji Xerox ）、 D.
HARADA （ CLARIANT ）、 K. HOSHINO （ CHIBA Univ. ）、 Y. HOSHINO
（TOKYO DENKI Univ. ）
Estimation of Charge, Simulation and Discussion
ISJ：Technical Committee on Simulation Technology
J. HIRABAYASHI（ Canon ）、H. KAWAMOTO（ Waseda Univ. ）、 N.
NAKAYAMA （ Fuji Xerox ）、 M. NAKANO （ Canon ）、 T. KAGAWA
（ KONICA MINOLTA ）、 T. ITOH （ Fuji Xerox ）、 M. MAEDA （ brother）、 S.
HASEBE （ Fuji Xerox ）、 J. MURAKOSO （ FUJITSU ）
Agenda
1
1. Introduction
2. Objective
3. Estimation of Charge Distribution with
SPM Measurement
4. Estimation of Adhesion with Charge
Distribution obtained from SPM Measurement
5. Analysis of Toner Adhesion with Simulation
6. Conclusion
Electrostatic Adhesion
2
Measurement
1 nN ～ 50nN ～100nN
Theory（Mirror Force)
～ 2nN ～
Theory(Mirror Force)
Measurement
＋q
Freq.
D
-q
Average:30nN
Metal(Grounded)
Fe =
0.1nN
-10
1nN
-9
10nN
100nN
-8
-7
-6
Log10F
q2
4 πε 0 D 2
(ex) Q=2.51fC D=6μm⇒1.55nN
Measurements indicate forces on the order of 10x larger than
what would be predicted from the mirror force theory.
Big Picture of Adhesion Analysis
3
SPM potential
SPM
Adhesion f orce of
par t ly charged t oner s
Our Study
Potential
T. Tada (2013)
Measurement
>
T. Tanaka (2013)
Adhesion
Measurement
Estimation of
Adhesion
(Simulation)
M. Kadonaga
(2014)
Estimation
of
Charge
Charge
Distribution
on a Toner
J. Hirabayashi
(2014)
Objective
4
To investigate adhesion mechanism
with SPM and simulation
Step1 ：Estimation of charge distribution
with SPM measurement
Step２： Estimation of adhesion with
the charge distribution
Step 3： Analysis of adhesion with simulation
5
Step1：Estimation of charge distribution
with SPM measurement
Jun HIRABAYASHI(Canon Inc.)
Sample
Toner Charging
6
Model Toner
ISJ standard carrier
polystyrene particle
+
+
Additive
Fumed Silica
(Negative)
5µm
Mixing and Charging
Toner
Carrier
Carrier
Toner
Toner Charging
6
Sample
+
+
5µm
ISJ standard carrier
N-02 (T/D:5%)
Carrier
Toner
AEROSIL
Fumed Silica (Nega)
RY 200 (0.5部)
Soken chemical &
Engineering SX500H
( polystyrene particle)
Measurement with SPM
Sample
6
ISJ Standard Carrier
Mixed and toner is charged.
Toner Q=2～3 ｆC
D=6μｍ
Polystyrene + Additive(Silica)
Surface form and Potential
40 nm
Toner
2.5 μm
Grounded
Metal
SPM(2013：Canon Tada)
2.5 μm
We should estimate a charge distribution from
the potential distribution.
Charge Estimation using de-Convolution 7
with System Response
System
Response
Point Charge
×
Potential
＝
System response: Relation between charge and potential
Estimated
Charge
Inverse of
System
Response
Measured Potential
＝
×
Theoretically speaking, we can estimate charge
distribution with a system response.
-1
Estimation of System Response
8
Electrostatic simulation of SPM is carried out.
Relation between the position of a charge and induced
potential of the probe is obtained.
SPM model
SPM system response
System
Response
Toner: Flat plane with 6µm thick(ε=3)
80 µm
System response is estimated from a 3D3D-electrostatic
simulation of SPM.
Estimation of Charge Distribution
Inverse of
System
Response
Potential
-1
9
Estimated Charge
＝
×
Estimated Charge
Potential from SPM
-1
×
＝
Charge distribution on a small area is obtained.
Estimation of Charge on the Whole
Surface of a Toner
Charge on
a small area
Copy
Projection to Sphere
10
Expand to Cube
Sphere Mapping
Charge distribution on the whole surface
of a toner is obtained.
Estimation of Charge on the whole
surface of a Toner
Q=2.5fC
Step1：Estimation of charge distribution
with SPM measurement
shows non-uniform charging!
11
12
Step２： Estimation of adhesion with
the charge distribution
Masami KADONAGA（Ricoh）
Simulation Model (FDM)
①Mesh Making/Setting Toner
③Electrostatic Calculation
②Setting Charge
13
④Estimation of Adhesion to a Grounded
Plane with Maxwell Stress Tensor
Adhesion with Charge Distribution
Estimated from SPM Measurement 14
Charge Distribution
Estimated from Step1
Deposit on the
grounded plane
Result
Electrostatic
Simulation
Estimation of
Adhesion
Q=2.5fC
Adhesion:135nN
(Mirror Force:1.6nN)
Appropriate adhesion is obtained with the charge
distribution obtained from Step1.
Step1.
Adhesion with Rotated Charge Distribution
Rotated Toner(N=100)
15
Average:68nN
(N=100)
Appropriate distribution of adhesion is obtained.
16
Step２： Estimation of adhesion with
charge distribution
offers an appropriate
adhesion value!
17
Step 3： Analysis of adhesion with simulation
Masami KADONAGA（Ricoh）
Anatomy of Adhesion
18
SPM measurements and estimations of charge are
laborious work・・・・
Artificial charge-distributions are made by random number.
Calculate adhesion
Estimated Adhesion of Artificial Toner
19
N=1000 q=3.4fC With Charge Patch on the South Pole
Average Adhesion
27nN(N=1000)
Appropriate adhesion is obtained with artificial
toners.
23
Effect of Location of Charge Patch
FE（Whole Toner）
21
3.4fC F= 27nN
FEN（Northern Hemisphere)
1.7fC F= 0.89nN
FES（Southern Hemisphere)
1.7fC F= 22nN
FEN（Northern Hemisphere) ＜＜ FES（Southern Hemisphere)
Charge of Southern Hemisphere is dominant.
Num.of Charge Patch/Size v.s. Adhesion 22
Patch Radius:0.4μｍ Q=3.4fC
Patch Radius:0.5μｍ Q=3.4fC
Patch Radius:1.5μｍ Q=3.4fC
Patch Radius:1μｍ Q=3.4fC
Q=3.4fC, N=100
Num.of Charge Patch/Size v.s. Adhesion 23
Average Adhesion[nN]
With South-Pole Charge Q=3.4fC, N=100
Non-Uniform Charging
Uniform Charging
Num.of Charge Patch(Average)
NonNon-uniform charging enhances adhesion.
26
Conclusion
24
Step1：Estimation of charge distribution
with SPM measurement
shows non-uniform charging!
Step２： Estimation of adhesion with
the charge distribution
offers an appropriate adhesion
value!
Step 3： Anatomy of adhesion with simulation
Charge of Southern Hemisphere
is dominant.
Big Picture of Adhesion Analysis
3
SPM potential
SPM
Adhesion f orce of
par t ly charged t oner s
Our Study
Potential
T. Tada (2013)
Measurement
>
T. Tanaka (2013)
Adhesion
Measurement
Estimation of
Adhesion
(Simulation)
M. Kadonaga
(2014)
Estimation
of
Charge
Charge
Distribution
on a Toner
J. Hirabayashi
(2014)

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