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Absorption

Adsorption

Adsorption t=te

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Fig. 1.8. Extraction using absorptive (a) and adsorptive (b) extraction phases immediately after exposure of the phase to the sample (t — 0) and after completion of the extraction (t — te).

extraction phase, resulting in a possible source of nonlinearity. This is rarely observed, because extraction/enrichment techniques are typically used for the analysis of trace contaminants.

One way to overcome this fundamental limitation of porous coatings in a microextraction application is through the use of an extraction time that is much less than the equilibration time. Thus the total amount of analytes accumulated by the porous coating is substantially less than the saturation value. When such experiments are performed, not only is it critical to control the extraction times precisely, but convection conditions must also be controlled because they determine the thickness of the diffusion layer. One way of eliminating the need to compensate for differences in convection is to normalize (use consistent) agitation conditions. The short-term exposure measurement has the advantage that the rate of extraction is defined by the diffusivity of analytes through the boundary layer of the sample matrix, and thus the corresponding diffusion coefficients, rather than by distribution constants. This situation is illustrated in Fig. 1.9 for a cylindrical geometry of the extraction phase dispersed on the supporting rod.

The analyte concentration in the bulk of the matrix can be regarded as constant when a short sampling time is used and there is a constant supply of analyte as a result of convection. The volume of the sample is much greater than the volume of the interface and the extraction process does not affect the bulk sample concentration. In addition, adsorption binding is frequently instantaneous and essentially irreversible.

Fig. 1.9. Schematic diagram of the diffusion-based calibration model for cylindrical geometry. The terms are defined in the text.

The solid coating can be treated as a 'perfect sink' for analytes. The analyte concentration on the coating surface is far from saturation and can be assumed to be negligible for short sampling times and relatively low analyte concentrations. The analyte concentration profile can be assumed to be linear from Cg to C0. The relationship between the mass of the extracted analyte and the sampling time can be described [25] by the following equation:

where n is the mass of analyte extracted (ng) in a sampling time (t), Dg is the gas-phase molecular diffusion coefficient, A is the outer surface area of the sorbent, d is the thickness of the boundary surrounding the extraction phase, B3 is a geometric factor, and Cg is the analyte concentration in the bulk of the sample. It can be assumed that the analyte concentration is constant for very short sampling times and, therefore, Eq. (1.14) can be further reduced to n(t) =

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