Modeling analyte permeation in cylindrical hollow fiber membrane introduction mass spectrometry

The time-resolved signal generated from membrane introduction mass spectrometry (MIMS) has been modeled in cylindrical coordinates to analyze the data from MIMS experiments, in which a capillary hollow fiber selectively passes a low molar mass analyte dissolved in an aqueous solution to a mass spectrometer. Two approximate solutions are developed to Fick's second law for a step change in upstream concentration. The first, found by a finite Fourier transform, gives an accurate description of the MIMS signal at relatively long times while the second, found via Laplace transform, gives an accurate description at short times. Together with the steady-state solution, the results allow straightforward determination from data of the analyte's diffusivity in the membrane as well as the analyte partition coefficient between the upstream solution and the membrane. Analysis of data for trace levels of toluene in aqueous solution passed through a polydimethylsiloxane (PDMS) hollow fiber yields the diffusion coefficient, partition coefficient, and their temperature dependences for the toluene/PDMS system.