Mathematical Models of Ink Mileage Curves of Dry Toners in Electrophotography


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Renmei Xu and Celeste M. Calkins


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An ink mileage curve is a plot of the reflection density of an ink film printed on a substrate as a function of the ink film thickness. It is helpful to predict how much ink is needed to achieve a target density and has been studied for many years. It was found that it was affected by both paper properties and ink properties. However, previous research was done for liquid inks used in conventional printing processes, such as offset and gravure printing. Non-impact printing (NIP) technologies have grown rapidly in the last several decades. Electrophotography (EP), as one of the major NIP technologies, mostly uses dry toners. Their ink mileage behaviors are still not well understood. In this study, four different substrates were printed on a dry-toner color production EP press, a Xerox iGen3. The print layout contains patches with different CMYK tonal values from 10% to 100%. Toner amounts on cyan patches were measured using an analytical method. Printed patches and unprinted paper samples as well as dry toners were dissolved in nitric acid and the copper concentrations in the solutions were analyzed by a Zeeman graphite furnace atomic absorption spectrometer (AAS). Analytical results were calculated to determine the toner amounts on paper for different tonal values. Their corresponding reflection densities were also measured. All the data were plotted in OriginPro(r) 8 software and four mathematical models were used for curve fitting. It is found that C-S model fits the experimental data of the two uncoated papers slightly better than the other three models. None of the four models fit the experimental data of the two coated papers well, while the linear model is found to fit the data well. So linear fitting is best in the practical density region for the two coated papers. Ink mileage curves obtained from curve fitting can be used to estimate how much ink is required to achieve a target density and hence the ink mileage can be calculated. The effect of paper properties on ink mileage was studied. It is found that the rougher the paper surface is, the higher ink film weight is required, and then the lower the ink mileage is.

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