Diffusion-controlled evaporation through a stagnant gas: estimating low vapour pressures from thermogravimetric data

The Langmuir vaporisation relation has been advocated for estimating vapour pressures of low-volatility compounds from thermogravimetric (TG) data. However, this equation is strictly valid only for evaporation into a vacuum. When measurements are conducted at finite pressures, diffusion must to be taken into account. For the situation where the rate of evaporation is controlled by diffusion through a stagnant gas layer, the rate of vaporisation is given by dmA/dt=(MAS/RT)PADAB. Here dmA/dt g s−1 is the TG-measured rate of mass loss; PA (Pa) the sample vapour pressure at absolute temperature T (K); R (J mol−1 K−1) the gas constant; DAB (m2 s−1) the diffusion coefficient; MA (kg kmol−1) the molar mass of the vaporising compound; and S (m) a shape factor characteristic of the system geometry. In typical TG set-ups the system geometry takes the form of a partially filled cylindrical sample cup with an inert purge gas sweeping over the top. In this particular case S=A/z, where A (m2) is the cross-sectional surface area and z (m) the depth of the gas-filled part of the sample cup.