Different on-line submicron particle sizing techniques report different "equivalent diameters." For example differential mobility analyzers (DMAs) report electrical mobility diameter (d m ), while a number of recently developed instruments (such as the Aerodyne Aerosol Mass Spectrometer, or AMS) measure vacuum aerodynamic diameter (d va ). Particle density and physical morphology (shape) have important effects on diameter measurements. Here a framework is presented for combining the information

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... content of different equivalent diameter measurements into a single coherent mathematical description of the particles. We first present a review of the mathematical formulations used in the literature and their relationships. We then show that combining d m and d va measurements for the same particle population allows the placing of constraints on particle density, dynamic shape factor (χ), and fraction of internal void space. The amount of information that can be deduced from the combination of d m and d va measurements for various particle types is shown. With additional measurements and/or some assumptions, all relevant parameters can be determined. Specifically, particle mass can be determined from d m and d va measurements if the particle density is known and an assumption about χ is made. Even if χ and density are not known, particle mass can be estimated within about a factor of 2 from d m and d va measurements alone. The mass of a fractal particle can also be estimated under certain conditions. The meaning of various definitions of "effective density" used in the literature is placed in the context of the theory. This theoretical framework is applied to measurements of fractal (soot-like) particles by using experimental results from the literature as additional constraints.