Fig. 1: Thermal perturbation of the adsorption equilibrium and transient capacitive measurement.

a Illustration of the temperature dependence of adsorption isotherms. b Zoom-in on the low-concentration isotherm region most relevant for sensing. The arrows indicate two ways to transition between equilibrium states with adsorbed amounts \({q}_{1}\) and \({q}_{2}\). c Perturbation of the adsorption equilibrium by a sudden temperature step triggers desorption upon heating and adsorption upon cooling. While the change \(\Delta q\left(T\right)\) is equal for the heating and cooling steps, \({\tau }_{2}\) is longer than \({\tau }_{1}\) because diffusion is thermally activated. d Schematic representation of a thin-film capacitor featuring a nanoporous dielectric layer and a gas-permeable top electrode with l film thickness and w film width. e Simulated adsorbate distribution profiles in a nanoporous film with an arbitrary thickness of 1 μm at different time points after initiating desorption. The top part illustrates individual capacitance contributions by adsorbate (full green circles). f Comparison of normalized mass and capacitance transients during desorption. The capacitance measured at equilibrium is approximately proportional to the adsorbed quantity. The largest divergence occurs at \({t}^{1/2} \sim 3\) s^1/2, when the adsorbate distribution is the most inhomogeneous (cf. panel e).