Theoretical approach to non-constant uptake rates for tube-type diffusive samplers

A simple theoretical model was developed for evaluating the validity of the simplified uptake model of diffusive sampling. In the model based on the plate theory diffusion to the adsorbent surface, phase equilibrium of the adsorbate and mass transport in the adsorbent bed were considered. It was found that in the early stage of sampling, the rate of sampling is close to its theoretical value. As sampling progresses, the concentration increases and the mass transfer front gradually moves into the adsorbent layer. Above a certain threshold limit, the mass uptake becomes a steady state process in which the diffusion in the air gap and the mass transport in the adsorbent bed are balanced. As uptake is a cumulative process, sampling should continue long enough to render the effects of these initial changes negligible. That is why constant uptake rates can still be obtained above a critical exposure dose. This critical exposure dose should be exceeded both in the determination of uptake rates and outdoor measurements, to obtain consistent and reliable analytical data. Evaluation of the time and concentration dependence of uptake rate in laboratory experiments and the time dependence of uptake rate in filed test was performed to justify the model results. Since the determination of uptake rates always takes places in the laboratory, where the exposure time is much shorter and the concentration is much higher than in the environment, the uptake rates are thus overestimated by 10–30%. Therefore, the uptake rates should be determined in the field under ambient conditions by means of an independent reference method.