Modeling Toner Transfer
in Electrophotography
(seminar II)
Tao Wu
Supervisor: Nikolas Provatas
Collaborator: XRCC
1
Outline
• Introduction to electrophotographic process
• Physics in toner transfer process
• Modeling platform
- Paper structure simulation
- Electric field calculation
• Simulate toner transfer distribution
• Time dependent transfer process
• Conclusion
2
Electrophotographic printing
* Edgar M. Williams, The physics and technology of xerographic processes, New york,1984
3
Form image on photoconductor
light
Image
corona
+++++++++++++++++++++++++++++++
Photoreceptor (PC)
4
Image development on photoconductor
−
− −
− − − −
−
+
Charged area on +
+
photoreceptor +
+
+
Non-charged area
Toner layer
−−− −−
++++++++
− − −
−
− −−−
−
− −
−
− −
−
− −
− −
− − − −
−
Toner developer
(Tribological methods)
The negative toner particles stick to the
positively charged areas on the
selenium plate.
The toner doesn’t stick to the neutral
parts of the plate and falls off.
5
Transferring toner onto paper
corona
+
++++++++++++++++++++++++
paper
F
V
− − − −
+++++
-
Toner layer
Photoreceptor
Applied voltage
facilitates transfer
r r
F=qE
Electrostatic field drives toner to paper
6
The physics of toner transfer
y
z
Corona charge
Paper property
+ + + + + + + + + + + + + + + ++++
x
Toner charge density
σf
σt
F
- ------++++++
V
hd
h
p
---------------------------
Photoreceptor
*Simula, S. ,et al. Imag.Sci and Tech, 43(5),472 (1999)
7
Print mottle
Toner clusters
8
Project objective
Develop model to predict toner distribution
Predict effects of paper structure on
Electrophotographic printing quality
Identify main attributes affect non-uniform
print density variation in Electrophotography
9
Modeling platform
Paper structure model
Phase 1
Virtual Paper Structure
Toner Transfer model
Multi-Grid Simulations of
Electrostatic Field Distribution
Phase 2
Toner Density Distribution
10
Non-uniformity of paper structure
Top view
fibre
filler
Cellulose fibre
200 um
SEM Micrograph of
paper cross section
11
Paper structure simulation
Fibre dimensions
Fibre quantity
Fibre orientations
L
W
Flexibility
In-plane spatial
distribution
Fibre collapsibility
filler
Formation index
*Provatas et al, Journal of Pulp and Paper Science,vol.29,No.10, 2003
12
Different paper structure
Low collapse of fibre
High collapse of fibre
Flexible fibre
Stiff fibre
High rejection-random
Low rejection-uniform
13
Consolidation of paper
Before compression of Network
After compression of Network
*N. Provatas and T. Uesaka, Pulp and Paper Report 1554, 2001
14
Dielectric distribution of paper
9
fibre
=
3
filler
=
air
=1
Paper Structure Model:
-Fibre locations
Individual dielectric properties
ε ( x, y , z )
Dielectric distribution of
paper
-filler
- porosity
15
Electric field calculation
r
ε (x)
Boundary condition:
V ( x, y, 0) = 0
V ( x, y , d1 + d 2 + d 3 + d 4 ) = Va
16
Electric field calculation
Gauss’ Law
r
r
∇ ⋅ D( x ) = ρ ( x )
r
r
E ( x ) = −∇V ( x )
r
r
r
D( x ) = ε ( x ) E ( x )
r
r
r
∇ ⋅ (ε ( x )( −∇V ( x ))) = ρ ( x )
Determine from Paper structure model
17
Multi-Grid finite volume scheme
Finite volume discretization
-Gauss divergence theorem
r
r
∫∫∫ ∇⋅ (ε ( x ) ∇φ )dV = − ∫ ∫ ∫ ρ ( x )dV
r
r
r
∫ ∫ ε ( x )∇φ ⋅ dS = − ∫ ∫ ∫ ρ ( x )dV
Conservation of flux
Fw
Fe − Fw + Fn − Fs + Ft − F = − ρ × hx × hy × hz
P
b
Fn
Fe
Cell P
Fs
Fe denotes the flux across surfaces of cell P normal to the east
18
Full Multi-Grid (FMG)
Iteration
Methods(3D)
Number of
iterations
Gaussian
elimination
N6
Jacobi
N6
Gauss-Seidel
N6
Fourier Transform
(NlogN)3
Multigrid
N3
V circle
interpolation
Restriction
Coarse mesh
L. B. William, A Multigrid Tutorial
Finer mesh
19
Electrostatic field simulation
Paper surface
5mm*5mm
Electric field
5mm*5mm
20
Power spectra mode analysis
Low frequency
sin x + sin 2 x + sin 3 x
High frequency
sin 4 x + sin 5 x + sin 6 x
f x = ∑ Ak sin kx
(k =0,1,2,3……)
k
21
Effect from surface roughness
Surface:
H = H + ∑ Ak sin(2π k x x Lx ) (kx=2,5,20,40,60)
kx
22
Effect from Surface Roughness and
Filler Particles
Surface:
H = H + ∑ Ak sin(2π k x x Lx ) (kx=5,10,60)
kx
23
Effect from Filler Particles
Filler put in long wavelength valley will greatly affect the Electric field.
24
Conclusion (part 1)
• Power spectral analysis showed that long wavelength variations
of the electrostatic transfer field corresponded almost exactly to
the same length scales of variation in the paper surface.
Conversely, surface variations on smaller length scales did not
display any relevant effect on the electrostatic field.
• Surface filler distributed on small wavelengths across the surface
does not alter the electrostatic “signature” created by surface height
variations alone. Conversely, surface filler distributed in the long
wavelength valleys of the surface leads to mode mixing, which
actually reduces peak-to-peak fluctuations of the electrostatic field.
25
Toner distribution (experiments)
Handsheet paper (Chemistry department, McMaster Univ.)
•Two kinds of fibre: 75wt% hardwood fibre and 25wt%
softwood fibre
•TAPPI standard method
•Handsheets property
- Cut size(10cm*10cm)
- Baseweight (38g/m2)
- Thickness (80um)
26
Toner distribution (experiments)
SEM image for toner layer
Power spectrum
1
Magnitude
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
K
Scan results
27
Paper structure simulation
• Simulate the paper structure-fibre property
100X Magnification
28
Paper structure simulation
Properties
Samples
Simulation
Mean Mass
0.922mg
(5% water)
0.876mg
Mean Thickness
80um
79.49um
Covariance of thickness
1.697
1.698
Covariance of formation
(10^(-3) mg m-1)
1.219
1.266
29
Two-point correlation function
•2-Point density-density correlation function (inverse
fourier transform of structure factor)
•1D example:
G ( r ) = m( x )m( x + r )
Spatial correlation of quantity
m(x) at two different positions
Spatially random quantity
separated by distance r
at positions x and x+r
*P.M.Chaikin and T.C.Lubensky,”Principles of Condensed Mater
Physics”, Cambirdge University Press, 1995
30
Correlation function and length scales
Identifies typical scale of
correlated mass clusters
ξ
31
Comparing mass-mass correlation function
Experiments,β radiography, Syracuse, NY
Simulation
32
Comparing height-height correlation function
Experiments
Simulation
33
Effect from thickness vs. formation
1
Electric field
formation
surface
Magnitude
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
k
34
Toner distribution Vs. simulated
electric field
1
Toner distribution
Electric Field
Magnitude
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
k
35
Adhesion Force: FA
Van der waals force
between toner and
photoreceptor
Coulomb forces
between toner
particles
Toner particle
Van der waals force
between toner and
paper
Electrostatic
transfer (or “bias”)
field
Toner drag force: FG
36
Schematics of new toner transfer
platform
37
Determination of strain-hardening from
handsheets sample
Ao
Tip
h1
h2
Paper
Silicon Chip
ε = (h2-h*)/(h2-h1)
= F/Ao
38
Determination of strain-hardening from
handsheets sample
• Tip material: quartz glass
• E = 73 GPa1 > Ec = 10 GPa2
• Diameters obtained:
• 100 µm, 200 µm, 300 µm, 1mm
• Jigs created to ensure a flat surface
- Tips were polished using SiC paper
1 – W. Callister, Materials Science and Engineering (2000)
2 – M. Ashby, Cellular Solids (2001)
39
Tip size and paper thickness effect
1 mm Indenter head
1mm Indenter Head
1000000
900000
800000
47.16 g/m2
62.53 g/m2
99.63 g/m2
600000
500000
Baseweight 40g/m2
2
Average Density: 62.53 g/m
400000
50000000
300000
45000000
200000
1mm
1mm
40000000
100000
1mm
1mm
35000000
0
0
0.2
0.4
0.6
Strain
0.8
1
1.2
Stress (Pa) - normalized
Stress (Pa)
700000
300micron
300micron
30000000
300micron
25000000
300micron
200micron
20000000
200micron
200micron
15000000
200micron
100micron
10000000
100micron
100micron
5000000
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Strain
40
Scaling with additional effect h
F
F
σ=
=
A0 π R 2
F
F
σ=
=
2
A0 π ( R + h)
41
Scaling results
2
Average Density: 62.53
g/m
Baseweight
40g/m2
2000000
1800000
1mm
1mm
1600000
1mm
1mm
Stress (Pa) - normalized
1400000
300micron
1200000
300micron
300micron
1000000
300micron
200micron
800000
200micron
200micron
600000
200micron
100micron
400000
100micron
100micron
200000
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Strain
42
Toner density vs. compressed surface
1
Toner experiments
1
toner simulation
0.8
Toner distribution
new surface
0.6
Magnitude
Magnitude
0.8
0.4
0.6
0.4
0.2
0.2
0
0
0
10
20
30
k
40
50
60
0
10
20
30
40
50
60
k
Surface variation controls the toner distribution.
43
Conclusion (part 2)
• The paper structure model can simulate real paper
by setting up proper parameters
• Surface variation (Long wavelength) controls the
distribution of electrostatic transfer force, not
formation
• New transfer platform has been set up, which can
predict toner density distribution
44
The physics of electrostatic transfer
0
Photoreceptor
Toner particles
Paper layer
r r
F=qE
r
r
E ( x ) = −∇V ( x )
+V
1000 v!?
Corona charging!!
45
Corona charging
800
600
(V) 400
corona
200
0
-1
0
1
2
3
(S)
+++++++++++++++++++++++++++++++
Paper sheets
The charge density change with time
Paper structure
- paper formation, paper surface, filler distribution
Ambient area
- Temperature, Relative humidity
46
Voltage decay with time
800
handsheet1_177um
handsheet2_213um
handsheet3_143um
handsheet4_97um
600
(V)
400
200
0
-1
0
1
2
3
(s)
47
Voltage decay for different paper
800
commercial paper
handsheets paper
600
(V)
400
200
0
-1
0
1
2
3
(S)
48
Future Work
• Study the discharging property of paper
• Study the influence of charge distribution
49
Conclusion
• New toner transfer platform has been set up,
which combined the 3D paper network model
with an efficient 3D electrostatic solver to
predict the electrostatic transfer forces and
toner density distribution for certain paper
structures;
• 3D paper network model has been calibrated
according to a laboratory made handsheet
paper, which proves that the 3D model can
simulate real paper structure;
50
Conclusion
• The effect from paper microstructure (paper
surface, filler distribution, formation variation)
has been studied with the help of the new
platform;
• The stress-strain property of handsheet paper
has been obtained;
• The toner transfer experiments have been
done at the XRCC, and it was compared with
simulation results.
51
Acknowledgement
•
•
•
•
Dr. N. Provatas
Gordon Sisler (Xerox)
Dr. Chaohui Tong
Dr. Igor Zhitomirsky
Special thanks for use of laboratory facilities:
• Dr. R.H.Pelton
• Dr. Kari Dalnoki-Veress
• Dr. D.S.Keller
52
Thanks!
53