2014/12/20

Static-Tribo-Electricity of Powder

Technical Committee on Simulation Technology Technical Committee on Toner Technology

Masami KADONAGA(Ricoh co.)

Anatomy of Toner Adhesion with

SPM Measurement and

Electrostatic Simulation

Imaging Society of Japan

Jun HIRABAYASHI(Canon Inc.)

-Colaborators-

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. ）

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 ）

Experiment and DiscussionT.Tanaka（ Canon ）

SPM Measurement and Discussion

Estimation of Charge, Simulation and Discussion

2

Agenda

2. Objective

1. Introduction

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

1

6. Conclusion

Electrostatic AdhesionMeasurement 1 nN ～ 50nN50nN50nN50nN ～100nN

Theory（Mirror Force) ～ 2nN2nN2nN2nN ～

20

2

4 D

qFe πε

=

Theory(Mirror Force)

-q

＋q

Metal(Grounded)

D

(ex) Q=2.51fC D=6μm⇒1.55nN-10 -9 -8 -7 -6

Log10F

Fre

q.

Measurement

Average:30nN

10nN1nN 100nN0.1nN

2

Measurements indicate forces on the order of Measurements indicate forces on the order of Measurements indicate forces on the order of Measurements indicate forces on the order of 10x10x10x10x larger than larger than larger than larger than

what would be predicted from the mirror force theory.what would be predicted from the mirror force theory.what would be predicted from the mirror force theory.what would be predicted from the mirror force theory.

SPM

Potential

Measurement

Charge

Distribution

on a Toner

Estimation

of

Charge

Estimation of Adhesion

(Simulation)

Adhesion

Measurement

Adhesion f orce of par t ly charged toners

T. Tanaka (2013)

>

SPM potential

T. Tada (2013) Our Study

3

M. Kadonaga(2014)

J. Hirabayashi (2014)

Big Picture of Adhesion Analysis

Step２： Estimation of adhesion with

the charge distribution

To investigate adhesion mechanism

with SPM and simulation

Step1 ：Estimation of charge distribution

with SPM measurement

4Objective

Step 3： Analysis of adhesion with simulation

5

Step1：Estimation of charge distribution

with SPM measurement

Jun HIRABAYASHI(Canon Inc.)

CarrierToner

+ +

SampleToner Charging 6

polystyrene particle

Fumed Silica

(Negative)

ISJ standard carrier Model Toner

Mixing and Charging

Carrier

Toner

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Additive

5µm

5µm

+ +

Sample

Carrier

Toner

Toner Charging 6

Soken chemical & Engineering SX500H( polystyrene particle)

AEROSIL

Fumed Silica (Nega)RY 200 (0.5部)

ISJ standard carrier N-02 (T/D:5%)

Toner Q=2～3 ｆC D=6μｍ

SampleMeasurement with SPM 6

Surface form and Potential

2.5 μm

2.5 μm

Polystyrene + Additive(Silica)

ISJ Standard Carrier

Mixed and toner is charged.

40 nmToner

SPM(2013：Canon Tada)

Grounded Metal

�

We should estimate a charge distribution from We should estimate a charge distribution from We should estimate a charge distribution from We should estimate a charge distribution from

the potential distribution.the potential distribution.the potential distribution.the potential distribution.

Charge Estimation using de-Convolution with System Response

× ＝

Point ChargePotential

System

Response

＝

Estimated

ChargeMeasured Potential -1

×

Inverse ofSystem

Response

Theoretically speaking, we can estimate charge Theoretically speaking, we can estimate charge Theoretically speaking, we can estimate charge Theoretically speaking, we can estimate charge

distribution with a system response.distribution with a system response.distribution with a system response.distribution with a system response.

7

System response: Relation between charge and potential

Estimation of System Response

Electrostatic simulation of SPM is carried out.

System response is estimated from a 3DSystem response is estimated from a 3DSystem response is estimated from a 3DSystem response is estimated from a 3D----electrostatic electrostatic electrostatic electrostatic

simulation of SPM.simulation of SPM.simulation of SPM.simulation of SPM.

8

System Response

Toner: Flat plane with 6µm thick(ε=3)80 µm

SPM model SPM system response

Relation between the position of a charge and induced potential of the probe is obtained.

9Estimation of Charge Distribution

＝

Estimated Charge

-1

× ＝

Potential Inverse of System

Response Estimated Charge

Charge distribution on a small area is obtained.Charge distribution on a small area is obtained.Charge distribution on a small area is obtained.Charge distribution on a small area is obtained.

Potential from SPM

-1

×

Estimation of Charge on the Whole Surface of a Toner

Copy

Sphere Mapping

Expand to Cube

Projection to Sphere

Charge on

a small area

10

Charge distribution on the whole surface Charge distribution on the whole surface Charge distribution on the whole surface Charge distribution on the whole surface

of a toner is obtained.of a toner is obtained.of a toner is obtained.of a toner is obtained.

Step1：Estimation of charge distribution

with SPM measurement

11Estimation of Charge on the whole surface of a Toner

Q=2.5fC

shows non-uniform charging!

Masami KADONAGA（Ricoh）

12

Step２： Estimation of adhesion with

the charge distribution

①Mesh Making/Setting Toner ②Setting Charge

③Electrostatic Calculation ④Estimation of Adhesion to a Grounded Plane with Maxwell Stress Tensor

Simulation Model (FDM)13

Adhesion with Charge Distribution Estimated from SPM Measurement 14

Appropriate adhesion is obtained with the charge Appropriate adhesion is obtained with the charge Appropriate adhesion is obtained with the charge Appropriate adhesion is obtained with the charge

distribution obtained from distribution obtained from distribution obtained from distribution obtained from Step1Step1Step1Step1....

Electrostatic Simulation Q=2.5fC

Adhesion:135nN

Result

(Mirror Force:1.6nN)

Estimation of Adhesion

Charge Distribution Estimated from Step1 Deposit on the

grounded plane

Rotated Toner(N=100)

Appropriate distribution of adhesion is obtained.Appropriate distribution of adhesion is obtained.Appropriate distribution of adhesion is obtained.Appropriate distribution of adhesion is obtained.

15

Adhesion with Rotated Charge Distribution

Average:68nN(N=100)

16

offers an appropriate

adhesion value!

Step２： Estimation of adhesion with

charge distribution

Masami KADONAGA（Ricoh）

17

Step 3： Analysis of adhesion with simulation

Anatomy of Adhesion

Calculate adhesion

18

Artificial charge-distributions are made by random number.

SPM measurements and estimations of charge are laborious work・・・・

23

N=1000 q=3.4fC With Charge Patch on the South Pole

Average Adhesion27nN(N=1000)

Estimated Adhesion of Artificial Toner

Appropriate adhesion is obtained with artificial toners.Appropriate adhesion is obtained with artificial toners.Appropriate adhesion is obtained with artificial toners.Appropriate adhesion is obtained with artificial toners.

19

FE（Whole Toner）

FEN（Northern Hemisphere) ＜＜ FES（Southern Hemisphere)

1.7fC F= 22nN1.7fC F= 0.89nN

3.4fC F= 27nN

Effect of Location of Charge Patch21

FEN（Northern Hemisphere) FES（Southern Hemisphere)

Charge of Southern Hemisphere is dominant.Charge of Southern Hemisphere is dominant.Charge of Southern Hemisphere is dominant.Charge of Southern Hemisphere is dominant.

Num.of Charge Patch/Size v.s. Adhesion 22

Q=3.4fC, N=100

Patch Radius:0.4μｍ Q=3.4fC Patch Radius:0.5μｍ Q=3.4fC

Patch Radius:1μｍ Q=3.4fC Patch Radius:1.5μｍ Q=3.4fC

26NonNonNonNon----uniform charging enhances adhesion.uniform charging enhances adhesion.uniform charging enhances adhesion.uniform charging enhances adhesion.

23Num.of Charge Patch/Size v.s. Adhesion

Num.of Charge Patch(Average)

Aver

age

Adhes

ion[n

N]

With South-Pole Charge Q=3.4fC, N=100

Uniform ChargingNon-Uniform Charging

Conclusion24

Step２： Estimation of adhesion with

the charge distribution

Step1：Estimation of charge distribution

with SPM measurement

Step 3： Anatomy of adhesion with simulation

offers an appropriate adhesion

value!

shows non-uniform charging!

Charge of Southern Hemisphere

is dominant.

SPM

Potential

Measurement

Charge

Distribution

on a Toner

Estimation

of

Charge

Estimation of Adhesion

(Simulation)

Adhesion

Measurement

Adhesion f orce of par t ly charged toners

T. Tanaka (2013)

>

SPM potential

T. Tada (2013) Our Study

3

M. Kadonaga(2014)

J. Hirabayashi (2014)

Big Picture of Adhesion Analysis