Numerical simulation aided relative optical density analysis of TEM images for soot morphology determination

The relative optical density (ROD) method provides a means to measure three-dimensional information about soot aggregates from two-dimensional transmission electron microscopy (TEM) micrographs of soot. The method is dependent on accurate calibration of the relationship between the measured soot ROD in TEM images and the actual soot thickness perpendicular to the imaging plane. A novel calibration method based on the comparison between probability distributions of measured soot ROD in TEM images and that of virtual soot thickness of numerically simulated soot is introduced. Soot aggregates of various prescribed fractal structure parameters were numerically generated using a tunable cluster–cluster aggregation model. The probability histograms of the local soot thickness for the simulated soot aggregates and ROD of the TEM images of flame generated soot aggregates were found to be quite similar and were used as a basis to establish a quantitative relationship between ROD and the local soot thickness. The calibration constant obtained from the analysis of the simulated soot was found to be insensitive to the fractal structure parameters over a wide range. The calibrated ROD method is successfully applied to the morphology analysis of soot aggregates generated in an atmospheric laminar co-flow ethylene–air diffusion flame based on thermophoretic sampling (TS) and TEM analysis techniques. With the ROD method, an overlap coefficient is introduced to identify and eliminate non-soot-aggregate structures and the selection of a cut-off overlap coefficient was found to have little influence on the final results over a relatively wide range. ROD is independent of empirical constants and human judgments and has been found to be an accurate and reliable TEM image analysis method for studying the morphology of soot aggregates.