Variability of total mass and other measures of small samples of particles

Aerosol measurement frequently requires that an aerosol sample be withdrawn from its environment. The sampled mass is not strictly proportional to the sampled volume because mass is present in discrete entities. This introduces a fundamental variability in the estimated particle mass concentration, particularly important for small particle samples. The total amound of any particle measure, ω, including mass, of the sampled particles is described by its coefficient of variation, CV. The results also apply for sampling a volume of liquid in which particles are dispersed, and can under some conditions be used for, e.g. analysis of weight per cent of asbestos in bulk powder, and microscopical analysis of total particle mass or projected area in a specimen. The fundamental coefficient of variation CV is also given for the special case of individual particle diameters having a log-normal distribution. Exact knowledge of the size distribution at the upper tail is critical in determining CV, as illustrated by calculating CV for a range of right truncated log-normal distributions. A mass variability equivalent diameter, MVED, is defined, by which the mass variability of a polydisperse aerosol can be described in terms of number variability (Poisson) of a monodisperse aerosol with diameter MVED. A population of airborne particles, sized by microscopy is used to show that in order to obtain CV < 10% for particle mass, a sample of this particular aerosol must contain an expected mass of 0.01 mg, and an expected number of particles, N> 6500, while only 100 particles would be needed if the measure was particle number. The variability is termed fundamental because it is the lowest achievable variability for given sample size and size distribution. This must be recognized, when determining overall uncertainty budgets for analytical procedures, including use of direct reading particle mass monitors for which a simple equation is given for calculating CV.