Measuring diffusivity in supercooled liquid nanoscale films using inert gas permeation. I. Kinetic model and scaling methods

We describe in detail a diffusion model used to simulate inert gas transport through supercooled liquid overlayers. In recent work, the transport of the inert gas has been shown to be an effective probe of the diffusivity of supercooled liquid methanol in the experimentally challenging regime near the glass transition temperature. The model simulations accurately and quantitatively describe the inert gas permeation desorption spectra. The simulation results are used to validate universal scaling relationships between the diffusivity, overlayer thickness, and the temperature ramp rate for isothermal and temperature programmed desorption. From these scaling relationships we derive simple equations from which the diffusivity can be obtained using the peak desorption time or temperature for an isothermal or set of TPD experiments, respectively, without numerical simulation. The results presented here demonstrate that the permeation of gases through amorphous overlayers has the potential to be a powerful technique to obtain diffusivity data in deeply supercooled liquids.