A model for two-component developers, where the charging process is an equilibrium of the transfer of charge between a toner and a carrier, was refined, giving the relations of the toner-carrier mass ratio (
mt/mc=Ct) to the carrier charge-to-mass ratio (
qec) and to the apparent tribocharging-rate constants (
kobsd):
1/
qec=-1/
qlimt[(
k-1st/
k1sc)+1/
Ct] and
kobsd=
k1[1+(
k-1st/
k1sc)
Ct],
where
qlimt is the limiting charge (the tribocharge when no charge transfers to the toner from the carrier,
k-1=0),
st and
sc are specific surface areas of the toner and the carrier, respectively,
kobsd is the apparent tribocharging-rate constant, and
k1 and
k-1 are pseudo-first order rate constants of the transfer of charge from the toner to the carrier and from the carrier to the toner, respectively.
These relationships were confirmed to apply in our experiment using a model toner: The values of
qlimt and
k1sc/
k-1stobtained from the two equations were in good agreement with those obtained previously from the relationship between the toner charge-to-mass ratio (
qet) and
mt/mc=Ct. Furthermore, the 1.0% CCA toner-to-0.5% CCA toner ratios in
k1 and
k-1 were not only comparable with each other but also with the CCA weight ratio and with the ratio of the frequency factors,
Z, for the two toners estimated from the Arrhenius equation. These results show that our model consistently joins the dynamic and the static states and is valid.
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