Society for Imaging Science and Technology's 15th Non-Impact Printing (NIP15), Orlando, FL, October 17 - 22, 1999.

1. 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

2. Liquid Toner Chemical Model: The Anatomy of an
Ink
-
-
-
+ + -
+
- Inverse
+ +
Micelle
11/ 96, file: LTM_NHT.PPT

3. Liquid Inks Contain:
1) Charged toner particles: Field dependent
2) Co-Ions: charged micelle with same polarity
of toner
3) Counter-Ions: charged micelle with opposite
polarity of toner
4) Carrier Liquid

4. Big Picture
Work Process to Study LID Development
Ink Design Model verification
& Fabrication Ink characterization
Benchtop
Ink
Characterization Characterization
Model
• Mobility (ELS/LDV)
• Charging (SC/PO) Fixture
• Size Measurement Models
• etc.(ESA, light scattering,
light transmission Fixture

5. Plate-Out Cell Setup

6. Ink Characteristic
Ink Characterization
Current density(amp/m2 )
Ink Charge Properties
•Number of charge species
•Mobility of each species
•Charge density of each species
•Q/M of toner
Time (sec)

7. Ink Characterization Model
∂ρ i
+ ∇ • ( ρ i u ) = 0 Conservation of Charge
∂t (Charge transport equation)
ε ∇ φ = − ∑ ρ i Gauss’ Law
2
i (Poisson equation for potential)
u = µE Fluid velocity + Electrophoretic velocity

8. Automatic Curve Fitting
--- An Optimization Problem
Minimize 2
N
f ( ρ 10 , ... ρ n ) =
0
∑ [e
k =1
E
k − e kM ( µ 1 , ... µ n, ρ 10 , ... ρ n0 ) ]
Subject to
ρ i0 ≥ 0
Restate in the form of an unconstrained optimization problem with
a penalty function
ˆ 0
f ( ρ1 , ... ρ n ) = f ( ρ1 , ... ρ n ) + R ∑ | ρ 0 |
0 0 0
j
j∈ J
R is the penalty parameter
0
J identifies the set of violated constraints (i.e., ρ j < 0 for all j ∈ J )

9. Optimization Algorithm
x
Powell’s Conjugate Direction Method
0 x •Needs only function value, not gradient.
ρ2 initial guess
x •For quadratic object function,
predetermined steps to reach optimal.
ρ10

14. Conductivity =
∑(Charge Density*Mobility)

17. 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.