Computer simulation of the development process in electrophotography

A formulation for the toner deposition time constant
W
was derived and the effect of each of the variables appearing in it or the toner deposition equation was studied by computer simulation. The simulations were performed using toners containing 10 and 20 particle sizes over a range of size frequency distributions. It was found that the effect of each variable was quite dependent upon the values of the other variables. The variables were: depletion-rate constant
K
time
T
, capacitance
C
, electrode spacing
G
, toner particle concentration
N
, particle diameter
PD
, charge per particle
CP
, and three choices of thickness of the diffuse double layer:
WC
--very diffuse-coupled with the charge per particle varying with the diameter of the particle,
WB
--normal-coupled with the charge per particle varying with the surface area of the particle, and
WA
-- tightly bound-coupled with the charge per particle varying with the volume of the particle. When the variables were such that the maximum in the distribution function for the deposited toner particles was at the lower end of the particle size range, increase in the depletion-rate constant shifted the maximum toward the upper end of the particle size range when the
KT
product became greater than 0.1 and decreased the rate of deposition. However, when the variables were such that the maximum in the distribution function for the deposited toner particles was at the upper end of the particle size range, increase in
K
merely decreased the rate of deposition without affecting particle size distribution. In general, large values of
K
, small values of
N
, short time periods, large values of
C
, and large values of
G
tended to push the distribution of the deposited toner toward the upper end of the particle size range. Large values of
N
, large values of
T
(restricted to
KT < 1
), and small values of
C
,
G
, and
K
tended to push the distribution maximum toward the lower end of the particle size range. The variables
K
,
N
, and
PD
strongly affected the magnitude of
W
while
T
did not affect the magnitude of
W
unless
KT
>0.1. For a given particle size range, the ratio of
W
for the smallest particle to
W
for the largest particle was invariant with respect to the magnitude of
W
. The range of
W
for a given particle size range was much less for the very diffuse layer (charge was a linear function of the diameter) than for the normal layer (charge was a linear function of the surface area) and even less than for the tightly bound layer (charge was a linear function of the volume). Change in particle size range affected the ratio of
W
for the smallest to largest particle in the range. Size frequency distributions with a maximum at some particle size or sizes tended to control the distribution of deposited particles at short deposition times (
t<1 \micro s
), but could not control the distribution of deposited particles at long deposition times (
t > 1
ms). The choice of diffuse double layer and coupled charge dependency had very large effects on the magnitude of
W
and the effect of some of the variables on
W
. The input-output tests showed that for a density range of 0 to 1.5, the response of the photoconductor in the present model was unsatisfactory and that a better simulation of latent image formation is required.