# The evaluation of the passive samplers' performances.

1. INTRODUCTION

Profiles of outdoor pollutant concentrations and indoor air quality can be evaluated by a multi-location measurement using the passive samplers. The passive sampler is an integrated and relatively inexpensive type monitor, providing personal exposure data for epidemiological research because it is light, small and easy to handle. An average concentration for a certain sampling period can be obtained with the passive samplers since it collects air pollutant of interest in its collection medium, but is not equipped with a detector. The major difference between an active and a passive sampler is the sampling process of the targeted air pollutant. The active sampler transports the pollutant to the medium or detector by drawing air, while the passive sampler relies on molecular diffusion (Zabiegala et al, 2005, Ott et al, 2007).

Based upon theoretical background of the diffusion process, the paper proposes an evaluation method for the performances of the passive sampler.

2. THEORETICAL BACKGROUND

The diffusion process described by Fick's law is analogized with electric resistance. The mass flow rate, N (mole/s) is proportional to a molecular diffusion coefficient, D ([cm.sub.2]/s), a cross sectional area for diffusion, A ([cm.sub.2]) and a concentration gradient of the interested air pollutant, cD (mole/[cm.sup.3])dx, where x (cm) is the one-dimensional position.

N = A x D x (dC/dx) (1)

An eddy diffusion coefficient in bulk air ranges from 100 to 10000 ([cm.sub.2]/s). Therefore, it is a reasonable assumption that the concentration gradient exists only around the collector of the passive sampler. Integration of equation (1) with boundary conditions of X=0, C=[C.sub.0], and X=L, C= [C.sub.a] gives:

N = (AD/L) ([C.sub.a]- [C.sub.0]) (2)

If N is thought of as a current, equation (2) is similar to Ohm's law. The difference in concentration ([C.sub.a] - [C.sub.0]) which is the driving force of the flow is comparable to the voltage difference.

N [right arrow] Current, ([C.sub.a] - [C.sub.0]) [right arrow] Voltage difference (3)

The proportional coefficient of current and voltage is resistance. In our case, resistance is expressed as follows

R = L / (AD) (4)

The unit of R for mass transfer is (s/[cm.sub.2]). The reciprocal of R is a sampling rate of the passive sampler, which is equivalent to the flow rate of the active sampler, F ([cm.sup.3]/s).

F = 1/R = (AD) / L (5)

There are usually three regions around the collection medium of the passive sampler where air pollutants can diffuse by molecular diffusion. This implies that there are three types of resistance during diffusion of the air pollutant from the bulk air to the collector. Air pollutants must pass a boundary layer around the interface of the air and the passive sampler, a stagnant region produced by a diffusion barrier and a boundary layer at the collector. These resistances connect in series. By analog with electrical resistance, the overall resistance of the diffusion becomes:

[R.sub.0] = [R.sub.1] + [R.sub.2] + [R.sub.3] (6)

If a small amount of the air pollutant of interest is absorbed, it is reasonable assumption that [C.sub.0] in equation (2) is nearly equal to zero. The amount of pollutant collected, M (mole), becomes:

M = (1/[R.sub.0]) * [C.sub.a] * t = F * [C.sub.a] * t (7)

This equation allows us to easily calculate the pollutant concentration during the exposure period of t.

The diffusion resistances are functions of various physical parameters. [R.sub.1] is described by the following equation using 5 as the thickness of the boundary layer.

[R.sub.1] = [delta]/D (8)

In the same manner [R.sub.2] becomes:

[R.sub.2] = L/D (9)

in which L is the length of the diffusion barrier.

If the reaction between the air pollutant of interest and the collection medium is first order, irreversible and rapid, with a reaction rate constant of k (1/s), the third resistance becomes:

[R.sub.3] = m/[(k x [D.sub.L]).sup.1/2] (10)

in which m is Henry's constant and [D.sub.L] is the diffusion coefficient in the liquid phase.

Environmental conditions can vary these parameters, that is, the environmental conditions determine the resistances. Surface wind velocity, temperature and relative humidity are the three major environmental factors affecting those (Godish, 2004). The surface wind velocity (WV) effects on the thickness of the boundary layer, [delta] and the diffusion barrier, L. At high WV, [delta] is thin. The diffusion coefficients and the chemical reaction rate constant are functions of temperature. Kinetic theory shows that the diffusion coefficient in an ideal gas is proportional to [T.sup.3/2] where T indicates absolute temperature. The reaction rate constant increases exponentially with elevation of temperature following Arrhenius' law. If the relative humidity affects the water content of the collection medium, the diffusion coefficient in the liquid phase and the reaction rate constant may be changed. The overall resistance to the diffusion process in the passive sampler could be described as functions of these environmental factors:

[R.sub.0] (WV, T, RH) = [delta](WV)/[A.sub.1]D(T) + L(WV)/[A.sub.2]D(T) + m(T)/[A.sub.3] [{k(T, RH) x [D.sub.L](T, RH)}.sup.1/2] (11)

Only the length of the diffusion barrier, L, can be controlled easily. For very large values of L, we can suppress the variation of the first and third terms due to change in the environmental conditions. However, if the second term is very large, the sensitivity of measurements, which are proportional to the reciprocal of [R.sub.0], is lowered. Therefore, we have to determine an appropriate length for the diffusion barrier.

In this derivation, the concentration of air pollutant is expressed by mole/[cm.sup.3]. If the concentration is presented by a volume to volume ratio, the temperature effect on concentration should be clarified. Since the passive sampler is designed to have large resistance at [R.sub.2] to eliminate the effect of surface wind velocity, the sampling rate is proportional to the molecular diffusion coefficient. Since the molecular diffusion coefficient theoretically depends on [T.sup.3/2], the amount of collected pollutant in the collection medium proportionally increases to [T.sup.3/2]. Whereas the amount of pollutant in a unit volume is reciprocally proportional to the square root of absolute temperature, [T.sup.1/2], as long as the concentration is expressed by the volume to volume ratio such as ppm.

Similar discussion to the temperature dependence can be done to the pressure effect. The molecular diffusion coefficient is proportional to the reciprocal of pressure, 1/P, while the amount of pollutant in a unit volume is proportional to P. The pressure dependence of measured concentration by the passive sampler is none if the concentration is indicated by ppm (Hill, 2000).

3. FACTORS TO BE EVALUATED

The passive samplers are provided with the sampling rate to get a concentration value as the volume to volume ratio. The sampling rate is determined under some representative conditions such as temperature of 20[degrees]C, relative humidity of 50%, surface wind velocity of 1 m/s and 1 atm. Environmental factors potentially change the sampling rate (Gillet et al, 2000).

The range of temperature to be examined depends on conditions of the passive sampler application. If it is used in very cold weather, the sampling rate data at -5[degrees]C may be needed. The examination data of the sampling rate at 5, 20, 30 and 40[degrees]C can be enough to cover most cases.

Effects of relative humidity on the sampling rate are difficult to predict theoretically (Akutsu et al, 2000). It can change the reaction rate and diffusion coefficient in the collecting medium. Determination of sampling rates at 20, 40, 60, 80 and 95 % of RH can cover most of the applications.

Surface wind velocity affects the thickness of the boundary layer and the effective length of the diffusion barrier. At low wind velocity (indoor), the thickness of the boundary layer is thicker than at high wind velocity. If the wind velocity is high, eddies in bulk air can penetrate into the diffusion barrier and shorten its effective length. As a result, the sampling rate on the surface wind velocity is saturated at a certain high wind velocity. Determination of sampling rates at calm, 0.5, 1, 2, and 5 m/s is sufficient to evaluate the wind effects.

As concerning the factors to determine the precision and accuracy, pressure does not affect the concentration as long as it is expressed by the volume to volume ratio. There are two kinds of potential interferences by chemicals: the interference by coexisting pollutants on quantification and the impurity and/or instability of chemicals in the collecting medium. Sun light may also affect their stabilities.

The time constant or the response time determines minimum duration of the sampling. The time constant is estimated from the diffusion coefficient of the target air pollutant (D), sampling rate (F) and cross sectional area for diffusion (A) as time constant = D/(F/[A.sup.2]). The sampling time must be long enough comparing the time constant. The working range, lower and upper detection limits, is another factor to determine the sampling time. The range is indicated by concentration*exposure time. The lower limit is defined as three times of the standard deviation of blanks. Since the capacity of the collection medium is not infinite, the response of the sampler becomes nonlinear when the amount of the collected pollutant exceeds a certain level. The maximum amount within the linear region is defined as the upper detection limit.

Variability of blanks values is more important than the absolute blank value. The blank value is the amount of the target pollutant in the non-exposed sampler. The production blank indicates the extent of contamination due to the field operation. The variability of blanks determines the lower detection limit. Precision or variability of measurements conducted under identical conditions can be obtained by duplicate measurements (Yoshizumi, 1999).

4. CONCLUSIONS

The conditions described before are representative for quality of the environmental researches using passive samplers. The passive sampler is sensitive to environmental conditions such as wind velocity, air temperature, relative humidity. When designing the survey, the time constant and working range information are necessary. Precision and accuracy show the overall performance of the passive sampler.

5. REFERENCES

Akutsu, T.; Kumagai, K.; Uchiyama, S.;Tanabe, S.(2000) Development of measurement device for aldehyde emission rates using a diffusive sampler, Proceedings of Healthy Buildings, Seppanen & Sateri (ed), vol 1, pp.477-482, ISBN 952 5236 06 4, Helsinki, Finland, August 2000

Gillet, R.W.; Kreibich, H.; Ayers G.P. (2000) Measurement of indoor formaldehyde concentrations with a passive sampler, Environ.Sci.Technol., vol. 34 (10), pp2051-2056

Godish, T (2004) Air Quality, Lewis Publishers, ISBN 1 56670 586 X, USA

Hill, M; Gehrig, R.; Dorer, V.; Weber, A.; Hofer, P. (2000) Measurements of air change rates with the PFT method biassed by sink and temperature effect, Proceedings of Healthy Buildings, Seppanen & Sateri (ed), vol 2, pp.333-338, ISBN 952 5236 06 4, Helsinki, Finland, August 2000

Ott, W.R.; Steinemann, A.C. & Wallace L.A. (ed) (2007) Exposure Analysis, CRC Press, ISBN 1 56670 663 7, USA

Yoshizumi, K.; Ishibashi, Y.; Kudo, T.; Hedge, A.; Muramatsu K. (1999). Application of passive sampling methodology to the characterization of indoor air quality, Proceedings of Indoor Air '99, vol.2, pp. 870-875, ISBN 1 86081 295 3, Edinburgh, Scotland, August 1999, CRC Press, London

Zabiegala, B.; Partyka, M.; Namiesnik, J. (2005) Passive samplers in indoor air control, Air Pollution XIII, pp.195-204, ISBN 978-1-84564-014-9, WIT Press UK