How does the diffusive sampler work?

The diffusive sampler is a closed box, usually cylindrical. Of its two opposite sides, one is “transparent” to gaseous molecules which cross it, and are adsorbed onto the second side. The former side is named diffusive surface, the latter is the adsorbing surface (marked with S and A in the figure).
Driven by the concentration gradient dC/dl, the gaseous molecules cross S and diffuse towards A along the path l, parallel to the axis of the cylindrical box. The molecules, which can be trapped by the adsorbing material, are eventually adsorbed onto A according to the diffusive:

where dm is the adsorbed mass during time dt and D is the diffusion coefficient.
Let C be the concentration at the diffusive surface and C0 the concentration at the adsorbing surface, the integral of [1] becomes:

If the concentration at the adsorbing surface is negligible, the equation can be approximated to:

Q is the sampling rate and has the dimensions of a gaseous flow (if m is expressed in µg, t in minutes and C in µg·l-1, Q is expressed in l·min-1).
Therefore, if Q is constant and measured, to calculate the ambient air concentration you need only to quantify the mass of analyte trapped by the adsorbing material and to keep note of the time of exposure of the diffusive sampler.

In the diffusive sampler, the adsorbing and the diffusive surfaces are two opposing plane of a closed box.
Driven by the concentration radient, the gaseus molecules (coloured in the figure) pass through the diffusive surface and are trapped from the adsorbing surface.

The geometrical constant

To improve the analytical sensitivity the collected mass m should be increased by enlarging Q. As D is a constant term, one can only try to improve the S/l ratio, namely the geometrical constant of the sampler. Unfortunately, in the common axial simmetry sampler, if S is enlarged, the adsorbing surface A must be enlarged too, in order to keep the two parallel surfaces at a fixed distance. Since the analytes can be recovered from the axial sampler only by solvent extraction, any increase of A lead to a proportional increase of the extraction solvent volume, thus the improvement of Q is canceled out by the effect of dilution

The value of distance l could also be reduced, but under the critical value of about 8 mm the diffusion law is no longer valid in the case of low air velocity values, since adsorption rate becomes higher than supplying rate of analyte molecules at the diffusive surface.

Cannot we improve Q then?
The answer is to improve the sampler geometry to a radial design.
From this idea the radiello sampler has been developed, its cylindrical outer surface acting as diffusive membrane: the gaseus molecules move axially parallel towards an adsorbent bed which is cylindrical too and coaxial to the diffusive surface.

When compared to the axial sampler, radiello shows a much higher diffusive surface without increase of the adsorbing material amount. Even if the adsorbing surface is quite smaller then the diffusive one, each point of the diffusive layer faces the diffusion barrier at the same distance.

The radial simmetry

As S=2prh (where h is the height of the cylinder) and the diffusive path is as long as the radius r, we can then axpress equation [1] as follows:

The integral of equation [4] from rd (radius of the diffusive cylindrical surface) to ra (radius of the adsorbing surface) becomes

the ratio

is the geometrical constant of radiello. The calculated uptake rate [5] is therefore proportional to the height of the diffusive cylinder and inversely proportional to the logarithm of the ratio of diffusive vs adsorbing cylinder radii.
While ra can be easily measured, rd can only be calculated by exposure experiments. In fact, in order to obtain a sample device of small dimensions which respect of the diffusion laws, the diffusive barrier has been designed with a thick tubular microporous layer. The actual diffusive path length is therefore much longer than the distance among the diffusive and adsorbing surfaces due to the tortuosity of the path through the pores. A diffusive cylinder of external diameter 8 mm, thickness 1.7 mm and average porosity of 25 µm, coupled to an adsorbing cartridge with radius 2.9 mm creates a diffusive path of 18 mm instead of the straight line path estimation of (8-2.9) = 5.1 mm.

The microporous sintered polyethylene diffusive barrier of radiello photographed at the electron microscope; the path length is much longer than the barrier thickness due to the tortuosity of the pores.

Meteorological parameters

The sampling rate Q is function of diffusive coefficient D, which is a thermodynamic property of each chemical substance. D varies with temperature (T) and pressure (p); therefore also the sampling rate is a function of those variables according to:

Q = f(T,P)

Q values that will be quoted in the following have been measured at 25 °C and 1013 hPa. As a consequence, they should be corrected so as to reflect the actual sampling conditions.
The correction of Q for atmospheric pressure is usually negligible since its dependence is linear and very seldom we face variations of more than 30 hPa about the average value of 1013 hPa. In the worst case, if corrections for pressure are ignored you make an error of ±3%, usually it is within ±1.5%.
On the other hand, Q depends exponentially on temperature variations, therefore more relevant errors can be introduced if average temperatures very different from 25 °C are ignored. Moreover, when chemiadsorbing cartridge are used kinetic effects (variations of reaction velocities between analyte and chemiadsorbing substrate) can be evident, apart from thermodynamic ones (variation of D).
As an example, when volatile organic compounds are sampled onto activated charcoal an experimental variation of ±5% of Q is measured corresponding to a variation of T of ±10 °C from 25 °C, but when nitrogen dioxide is sampled on triethanolamine the variation of Q increases up to 21% for a similar variation of temperature.
It is therefore very important to know the average temperature in order to ensure accuracy of experimental data. See page thermometer how you can perform on-field temperature measurements.

Even if some cartridge adsorb large quantities of water if exposed for a long time in wet atmosphere, generally this does not affect sampling by radiello. Some consequences, neverthless, can sometimes be felt on the analysis. As an example, a very wet graphitised charcoal cartridge could generate ice plugs during cryogenic focusing of thermally desorbed compounds or blow out a FID flame.
It is therefore important to protect radiello from bad weather. See page shelter how this can be easily done.