CHARGING CHARACTERIZATION OF COLLOIDAL DISPERSIONS BY A

PLATE-OUT CELL

IS&T NIP15

October 17-22, 1999

James Wang, Fa-Gung Fan, Richard Blum

Xerox Corporation

11/96, file: LTM_NHT.PPT

Liquid Toner Chemical Model: The Anatomy of anLiquid Toner Chemical Model: The Anatomy of an

InkInk

+

+

+

+ -

-

-

--

+

Inverse

Micelle

Liquid Inks Contain:

1) Charged toner particles: Field dependent

2) Co-Ions: charged micelle with same polarityof toner

3) Counter-Ions: charged micelle with oppositepolarity of toner

4) Carrier Liquid

Big Picture

Work Process to Study LID Development

Ink Design

& Fabrication

Benchtop

Ink

Characterization Characterization

Model

Fixture

Fixture

Models

• Mobility (ELS/LDV)

• Charging (SC/PO)

• Size Measurement

• etc.(ESA, light scattering,

light transmission

Model verification

Ink characterization

Plate-Out Cell Setup

Ink Characteristic

Cu

rren

t d

ensi

ty(a

mp

/m2)

Ink Charge Properties•Number of charge species

•Mobility of each species

•Charge density of each species

•Q/M of toner

Time (sec)

Ink Characterization

Ink Characterization Model

Eu

ut

i

i

ii

µ

ρφε

ρ∂

∂ρ

=

−=∇

=•∇+

∑2

0)( Conservation of Charge

(Charge transport equation)

Gauss’ Law

(Poisson equation for potential)

Fluid velocity + Electrophoretic velocity

[ ]2

1

0

,

0

1,,1

0

,

0

1 )......()...( ∑=

−=N

k

nn

M

k

E

kn eef ρρµµρρ

Automatic Curve Fitting --- An Optimization Problem

Minimize

Subject to

00 ≥iρ

Restate in the form of an unconstrained optimization problem with

a penalty function

∑

∈

+=Jj

jnn Rff ||)...()...(ˆ 00,

01

0,

01 ρρρρρ

R is the penalty parameter

J identifies the set of violated constraints (i.e., 00 <jρ for all Jj ∈ )

Optimization Algorithm

initial guess

x

x

x

Powell’s Conjugate Direction Method

•Needs only function value, not gradient.

•For quadratic object function,

predetermined steps to reach optimal.

01ρ

02ρ

Conductivity =

∑∑∑∑(Charge Density*Mobility)

SUMMARY:

• A charge characterization process based on the charge transport model is developed.

• The process determines charge density and mobility distribution of simple dispersions.

• For liquid inks, the apparent charge densities of the toner particles do not stay constant.

• To better characterize liquid inks, a quantitative understanding and modeling of charge generation is needed.