Effects of Media Non-Uniformity on Electrostatic Transfer in Electrophotography

The effects of spatial non-uniformity in material parameters on the electrostatic transfer of toners from photoreceptors to receiving media are investigated with the charge transport model of dielectric relaxation in the receiver. The parameters considered include intrinsic charge density, charge mobility, charge injection strength and permittivity of the receiving media. The detrimental effects are found to be more severe when (1) the spatial period of non-uniformity is large, and/or (2) the transfer time is short. An experimental technique for the determination of such spatial nonuniformity is demonstrated. Introduction The quality of electrophotographic images depends on the interplay of process and material involved in each step of the image formation. One of these steps is the transfer of toners on the photoreceptor to intermediate and/or final receiving media, with electrostatic forces. The process requires efficient dielectric relaxation of the media to shift most of the applied bias voltage to the toner layer. Due to the semi-insulating and non-Ohmic nature of the media, it has been suggested that the analysis of this dielectric relaxation by the traditional RC equivalent circuit equation is not adequate. Instead, a first principle charge transport model of dielectric relaxation has been formulated to investigate the process. These studies have identified the intrinsic charge density qi, the charge mobility μ, and the charge injection strength s in the media as the key parameters controlling the transfer force. In the previous analyses, the media were assumed to be homogeneous, having uniform values of these parameters. The analyses were formulated in the form of one-dimensional layer model. The present work extends the investigation to consider the effects of spatial (lateral) non-uniformity of these material parameters on the transfer force and hence, on the image quality. The charge transport model of dielectric relaxation for twodimensional analyses is described in the next section. This is followed by the presentation and discussion of numerical results. Examples of spatial non-uniformity measured with the technique introduced earlier are shown in the final section. Charge Transport Model The transfer nip is represented by a three-layer configuration consisting of the grounded photoreceptor (PR), the toner layer and the receiver as shown in Fig. 1. A small air gap that may exist between the toner layer and the receiver makes no difference of physical significance in this discussion. It is assumed that the PR in the dark and the toner layer are insulators with no mobile charges. But the toner layer has a constant and uniform volume charge density qt. The receiver is a semi-insulator that has mobile positive and negative charges with volume densities qp(x, y, t) and qn(x, y, t), respectively, which vary with position and time t. Figure 1. Three-layer model of transfer nip After the bias Vb is applied, the voltages Vk over the layers k (with k = p, t, r for PR, toner and receiver, respectively) change with time due to dielectric relaxation in the receiver. In this analysis, the dielectric relaxation is treated by the charge transport model, as briefly described below. The continuity equations for conduction currents are used to determine the time and spatial variations of charge densities, ∂qp/∂t = – div(Jp), ∂qn/∂t = – div(Jn) (1) where Jp = μqpE and Jn = μqnE are the positive and negative conduction currents. The field E is related to the total space charge density Σq and the permittivity ε by the Poisson equation, div(E) = (Σq)/ε (2) Mobile charges are also supplied by injection from the electrode at y = 0. The injection current Jinj (in the y-direction) is assumed to be proportional to the y-component of field at the electrode Ey(x, 0), with the proportionality constant s, specifying the injection strength. Jinj(x) = Jp(x, 0) = s(x)Ey(x) (3) Starting with the electrostatic initial conditions and the boundary conditions, an iterative numerical procedure for the continuity equations is used to calculate the time evolution of charge densities and the fields. The y component of field in the toner layer at the toner/PR interface is denoted as the transfer field Etr. Vb Receiver X Toners Photoreceptor