Comparison of triboelectric measurements of two-component xerographic developers with the continuous and patchy charge models

The two-component xerographic developer charging model of Gutman and Hartmann offers two alternative formulations of the interfacial electric field between toner and carrier, based on the assumption of either a continuous charge distribution on the surface of the toner, or a non-uniform patchy charge distribution. They found that m/q:C measurements on some developers were better described by one version of the model, while measurements on other developers were better described by the other version. In this study, we investigate when each version is applicable. We do this by comparing the two versions of the model with measurements of many different developers prepared with toners and carriers having different physical and chemical formulations that alter how charge is distributed throughout the developer. We found that the carrier surface formulation does not influence which version of the model better fits the data, nor does toner polarity. The main influence is the toner formulation, which creates different toner surface structures that presumably have intrinsically different toner surface charge distributions. We find that the patchy charge version fits the measurements if the carbon black is a minor component on the toner surface and an extremum in the triboelectric series. In contrast, the continuous charge version fits the data if the resin is a major component on the toner surface and also an extremum in the triboelectric series. Also, the continuous charge version of the model fits measurements of toners formulated with a charge control additive (CCA), consistent with the assumption that the particular CCA is uniformly distributed over the toner surface. In addition, we compare the two versions of the model to previously published measurements on a variety of toners with structures similar to those mentioned above, and find that the two versions fit the measurements in a similar pattern.