Time constant of the extraction process

The time constant is mainly determined by diffusion processes towards and inside the membrane. The time constant t is the time which is needed to reach 1-1/e of the final concentration. The solution of Fick s law with suitable boundary conditions gives a relation for the time constant  

In most polymers the diffusion coefficients have magnitudes from 10 10 cm s at 20 °C. For a membrane thickness of 25 pm the resulting time constants are between 3000 and 0.3 seconds. For PDMS the diffusion coefficients are between 10 and 10 cm s at 20 °C for most organic substances. The time constants experimentally determined for gaseous samples are of the order 1 to 100 s (Table 6.5-3). Because the diffusion is greatly affected by temperature it is necessary to control the temperature of the membrane to have reproducible results. 

For gaseous samples the quadratic relation of the time constant to the membrane thickness can be verified by experiment. For aqueous solutions the measured relation is often only directly proportional to the membrane thickness and sometimes up to 50 times larger than 

The kinematic viscosity of dilute aqueous solutions is ca. 0.01 cm s. So Nernst diffusion layers 5/v between 200 and 30 pm result at flow velocities between 5 and 100 cm s. For small molecules like benzene, tetrachloroethene, etc. the diffusion coefficients in water and in the PDMS membrane are of the same order. Then the time constant is approximately  

Therefore, altering cIm effects the time constant less than expected without the Nernst diffusion layer. The time con.stants r for the enrichment from aqueous samples in a PDMS membrane are of the order of 10 to 600 s for small molecules like benzene derivatives and up to e.g. 3600 s for 2-chlorobiphenyl (Table 6.5-4). 

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