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 dm(A)/dt = (MAS/RT) P-A D-AB. Here dm(A)/dt g s(-1) is the TG-measured rate of mass loss; P-A (Pa) the sample vapour pressure at absolute temperature T (K); R (J mol(-1) K-1) the gas constant; D-AB (m(2) s(-1)) the diffusion coefficient; M-A (kg mol(-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 (m(2)) is the cross-sectional surface area and z (m) the depth of the gas-filled part of the sample cup. (C) 2003 Elsevier Science B.V. All rights reserved.