## Q

— — exp(-at) (1.23) qo where q0 is the initial amount of analyte loaded on the fibre coating, and Q is the amount of analyte remaining on the fibre after exposure to the sample matrix for sampling time t. The constant a in Eqs. (1.22) and (1.23) has the same definition. In other words, the value of constant a should be the same for both the absorption and the desorption of anal-yte under the same experimental conditions (sample bulk velocity and temperature). This implies the isotropy of the absorption and the desorption of an analyte onto and from an SPME fibre, which can be demonstrated by rearranging Eq. (1.22) (absorption) into n

The left side of Eq. (1.23) represents the fraction of the analyte remaining on the fibre after desorption time t, while the left side of Eq. (1.24) represents the fraction of the analyte absorbed on the fibre after absorption time t. When constant a has the same value for the absorption and the desorption, the sum of Q/q0 (desorption) and n/n0 (absorption) should be 1 at any desorption/absorption time.

The simultaneous absorption of toluene and desorption of deuterat-ed toluene (d-8) proved the isotropy of the absorption and the desorption of an analyte onto and from an SPME fibre (Fig. 1.11) [30]. An important implication of this is that if the behaviour of either absorption or desorption is known, the behaviour of the other will also be understood. The application of this conclusion is clear. To determine the concentration of an analyte in a sample matrix, a certain amount of isotopically labelled analogue is loaded onto an SPME liquid coating fibre. Then, the fibre is exposed to the sample matrix for a certain time period, during which a part of the isotopically labelled analogue is des-orbed from the fibre and a certain amount of the analyte is absorbed onto the fibre. The value n0 can be obtained using the isotropic relationship (Q/q0+n/n0 — 1), by knowing the initial amount (q0) of the isotopically labelled analogue loaded onto the fibre, the amount (Q) of

Time (min)

Fig. 1.11. The isotropy of absorption and desorption in SPME. Simultaneous absorption of toluene ( x ) and desorption of deuterated toluene (d-8) (o) onto and from a 100-mm PDMS fibre into water of 0.25 cm s"1 at 25°C. (▲) represents the sum of Q/q0 and n/n0.

Time (min)

Fig. 1.11. The isotropy of absorption and desorption in SPME. Simultaneous absorption of toluene ( x ) and desorption of deuterated toluene (d-8) (o) onto and from a 100-mm PDMS fibre into water of 0.25 cm s"1 at 25°C. (▲) represents the sum of Q/q0 and n/n0.

the isotopically labeled analogue remaining on the fibre, and the amount (n) of analyte absorbed on the fibre after sampling time t. Since n0 is expressed as (KVfVs/(KVf+Vs))C0, the concentration of the analyte (C0) can readily be determined.

1.2.5.3 Time-weighted average passive sampling Consideration of different arrangements of the extraction phase is beneficial. For example, extension of the boundary layer by a protective shield that restricts convection would result in a TWA measurement of the analyte concentration. A variety of diffusive samplers has been developed based on this principle. One system consists of an externally coated fibre with the extraction phase withdrawn into the needle (Fig. 1.12).

When the extraction phase in an SPME device is not exposed directly to the sample, but is contained within a protective tubing (a needle) without any flow of sample through it, diffusive transfer of analytes occurs via the static sample (gas phase or other matrix) trapped in the needle. This geometric arrangement provides the basis of a very simple method, capable of generating a response proportional to the integral of the analyte concentration over time and space (when the needle is moved through space) [31]. Under these conditions, the only mechanism of analyte transport to the extracting phase is diffusion through the matrix contained in the needle.

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