The response time of permeation passive samplers is determined by the rate of analyte transport through permeation barrier, which in turn, depends on the magnitude of the diffusion coefficient of the analyte in the material of the barrier (the semi-permeable membrane). For permeation passive sampler the response time is defined as:

where tR is the residence time (s) of a compound in the permeation zone.

If the membrane of permeation passive samplers is thin enough (^100 mm), the response time is typically in the order of seconds. Thus, it is negligibly small compared to overall sampling time (typically weeks).

Temperature is also an important parameter in permeation passive sampling. However, the effect of temperature on sampling rate is much smaller for permeation passive samplers than for diffusive samplers.

The temperature dependence of the permeability coefficient, S, can be described by the relationship:

where S0 is the standard permeability coefficient and EP is the activation energy for permeation (Jmol-1), which is the sum of the heat of solution of the analyte in the membrane material (DH) (Jmol-1) and the activation energy for diffusion (ED) (Jmol-1). Since ED is typically small (^41.9kJmol-1), either a very weak or virtually no temperature dependence of the sampling rate is usually observed in the ambient temperature range.

4.2.1 Membrane

In general, the membrane is a selective barrier that permits the separation of certain species by a combination of sieving and sorption diffusion mechanism. It can selectively separate components over a wide range of particle sizes and masses. In the case of permeation passive samplers, the non-porous membrane constitutes a diffusive barrier for analyte transport and defines the rate at which analyte molecules are collected at a given concentration, which is crucial for quantitative analysis [4,9]. The membrane of permeation passive samplers should eliminate or minimize the effect of external factors (such as the velocity of the sampled medium at the face of the sampler, humidity and temperature) on the sampling rate, thus, the material it is made of should meet specific requirements:

• It should be characterized by a high overall mass transfer coefficient for analytes of interest. The coefficient determines the concentration drop within the membrane. Permeation rates through a thick membrane made of the material characterized by a high mass transfer coefficient and through a thin membrane with a low coefficient can be quite close.

• It should be selective with respect to various compounds present in sampled air.

• It should be hydrophobic and hence poorly permeable for water vapour. In case of hydrophobic membranes, permeation rates do not depend on the humidity of the sampled air since water does not penetrate the membrane and hence it does not affect membrane properties. Moreover, with very hydrophobic membranes, sorbents with high water affinity can be used to trap analytes without the risk of excessive water absorption.

• It should be homogenous so that permeation rates for samplers used in replicate measurements were not different.

Membranes are made of various polymer materials. Poly-dimethylsiloxane (PDMS) has been proven to have the best performance, therefore, is the material of choice for permeation passive samplers.

The process of permeation of analytes through a membrane can be described by a three-step solution-diffusion mechanism [10]:

• Sorption of the analyte on the surface of the membrane.

• Dissolution in the membrane material and diffusion of the dissolved analyte through the membrane. Dissolution is governed by the solubility of the analyte in the membrane material.

• Desorption of the analyte on the opposite side of the membrane. In order to extract effectively the analyte from the membrane into the sorption medium and to obtain high recoveries, the analyte distribution ratio between the membrane and the sorption medium should be small.

When analyte flux obeys Fick's law, permeability of a polymer is given by [7,10]:

where N is the steady-state analyte flux through the polymer (kg cm-2. min), p0 is analyte partial pressure near the outer surface of the membrane, P1 is the analyte partial pressure near the inner surface of the membrane (Pa), C'0 is the analyte concentration in the polymer at the outer surface of the membrane (Pa), C1 is its concentration in the polymer at the inner surface of the membrane and D is concentration-averaged diffusivity (cm2 min-1).

When P1 is much lower than P0 (which is normally the case for passive samplers, as the sorbent in the sampler should trap the analyte molecules quantitatively), the term in parentheses in e.g. Eq. (4.8) becomes C'0/p0, which is the analyte solubility coefficient S at pressure P0. Consequently, Eq. (4.8) can be rewritten as:

At the same time, for rubbery polymers with liquid-like properties (such as PDMS), the term C'0/p0 is equivalent to Henry's law constant KH of an analyte between polymer and air, which can be converted to the dimensionless Henry's constant KH:

where K is the gas-membrane partition coefficient.

According to Eq. (4.9), the permeation rate is controlled by the combination of analyte solubility in the membrane material and its diffu-sivity within the membrane. The solubility at constant operating conditions (temperature, pressure and composition) is mainly a function of analyte condensability, which can be characterized for example by the normal boiling point temperature [10]. Diffusivity is inversely related to the size of the molecule. Larger molecules are typically more condensable, which leads to a trade-off in the overall magnitude of the permeability coefficient. However, the liquid-like matrix of PDMS has a poor ability to sieve molecules based on their size, therefore differences between the permeability coefficients of different molecules are mostly governed by the differences in their solubility in PDMS [10]. The solubility, in turn, determines the magnitude of the partition coefficient between the air and the membrane material. Consequently, permeability through the membrane is often described by the following equation [11]:

where De is the effective diffusion coefficient of the analyte in the membrane material and K is the partition coefficient of the analyte between the membrane material and ambient air.

Often, effective diffusion coefficients of the analytes in the membrane material are unavailable; therefore, the analyte permeability has to be determined experimentally for each individual analyte (because the membrane of the permeation passive sampler has a well-defined surface area, the permeability is typically expressed through the calibration constant k—see Eq. (4.3)). This requirement constitutes the most important drawback of permeation passive samplers. Only target analytes, for which the calibration constants were determined in advance in model experiments, can be quantified using this technique.

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