Kinetics

The kinetic theory is useful to optimize the extraction conditions by identifying 'bottlenecks' in SPME and indicating strategies to increase extraction speed. In the discussion below we will limit our consideration to direct extraction (Figure 3).

Perfect agitation Let us first consider the case where the liquid or gaseous sample is well agitated. In other words, the sample phase moves rapidly with respect to the fibre, so that all the analytes present in the sample have access to the fibre coating. In this case, the equilibration time, defined as the time required to extract 95% of the equilibrium amount (Figure 4) of an analyte from the sample, corresponds to:

Using this equation one can estimate the shortest equilibration time possible for a practical system by substituting appropriate data for the diffusion coefficient of an analyte in the coating (Df) and the fibre-coating thickness (b — a). For example, the equilibration time for the extraction of benzene from a highly agitated aqueous solution with a 100 |im PDMS film is expected to be about 20 s assuming diffusion coefficient of 10~5 cm2 s"1 in PDMS. Equilibration times close to those predicted for agitated samples have

Figure 3 Graphic representation of the SPME/sample system configuration, with dimensions and parameters labelled as follows: a, fibre coating inner radius; b, fibre coating outer radius; L, fibre coating length; d vial inner radius; Cf, analyte concentration in the fibre coating; Df, analyte diffusion coefficient in the fibre coating; Cs, analyte concentration in the sample; Ds, analyte diffusion coefficient in the sample; f analyte distribution coefficient between fibre coating and sample; Kfs = Cf/Cs. (With permission from Louch etal. (1992) AnalyticalChemistry 64: 1187.)

Figure 3 Graphic representation of the SPME/sample system configuration, with dimensions and parameters labelled as follows: a, fibre coating inner radius; b, fibre coating outer radius; L, fibre coating length; d vial inner radius; Cf, analyte concentration in the fibre coating; Df, analyte diffusion coefficient in the fibre coating; Cs, analyte concentration in the sample; Ds, analyte diffusion coefficient in the sample; f analyte distribution coefficient between fibre coating and sample; Kfs = Cf/Cs. (With permission from Louch etal. (1992) AnalyticalChemistry 64: 1187.)

Figure 4 Mass absorbed versus time for a well-agitated solution of infinite volume. (With permission from Louch etal. (1992) AnalyticalChemistry 64: 1187.)

model mass transport, the gradation in fluid motion and convection of molecules in the space surrounding the fibre surface can be simplified by a zone of a defined thickness in which no convection occurs, and perfect agitation in the bulk of the fluid everywhere else. This static layer zone is called the Prandtl boundary layer (Figure 5). Its thickness is determined by the agitation conditions and the viscosity of the fluid.

The equilibration time can be estimated for practical cases from the equation below:

Figure 4 Mass absorbed versus time for a well-agitated solution of infinite volume. (With permission from Louch etal. (1992) AnalyticalChemistry 64: 1187.)

been obtained experimentally for extraction of analytes from air samples (because of high diffusion coefficients in gases) or when high sonication power is used to facilitate mass transfer in aqueous samples. However, in practice there is always a layer of unstirred water around the fibre, although a high stirring rate will reduce its thickness.

Practical agitation Independently of the level of agitation, fluid contacting the fibre surface is always stationary, and as the distance from the surface increases, the fluid movement gradually increases until it corresponds to the bulk flow in the sample. To where (b — a) is the coating thickness on the fibre, Ds is the diffusion coefficient of the analyte in the sample fluid, Kfs is the distribution constant of the analyte between the fibre and the sample and 5 is a boundary layer thickness. This equation can be used to predict equilibration times when the extraction rate is controlled by the diffusion in the boundary layer. The extraction time calculated using eqn [8] must be longer than the corresponding time predicted by eqn [7].

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Solar Panel Basics

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