VARIABILITY OF TOTAL MASS AND OTHER MEASURES OF SMALL SAMPLES OF PARTICLES

Aerosol measurement frequently requires that an aerosol sample be with drawn from its environment. The sampled mass is not strictly proportio nal 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 amount of any particle measure, w, including mass, of the s ampled 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. analys is of weight per cent of asbestos in bulk powder, and microscopical an alysis of total particle mass or projected area in a specimen. The fun damental coefficient of variation CV is also given for the special cas e of individual particle diameters having a log-normal distribution. E xact knowledge of the size distribution at the upper tail is critical in determining CV, as illustrated by calculating CV for a range of rig ht truncated log-normal distributions. A mass variability equivalent d iameter, MVED, is defined, by which the mass variability of a polydisp erse aerosol can be described,in terms of number variability (Poisson) of a monodisperse aerosol with diameter MVED. A population of airborn e particles, sized by microscopy is used to show that in order to obta in 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 particl es, N>6500, while only 100 particles would be needed if the measure wa s particle number. The variability is termed fundamental because it is the lowest achievable variability for given sample size and size dist ribution. This must be recognized, when determining overall uncertaint y budgets for analytical procedures, including use of direct reading p article mass monitors for which a simple equation is given for calcula ting CV.