Evaluating the Fitness of Combinations of Adsorbents for Quantitative Gas Sensor Arrays

Robust, high-performance gas-sensing technology has applications in industrial process monitoring and control, air quality monitoring, food quality assessment, medical diagnosis, and security threat detection. Nanoporous materials (NPMs) could be utilized as recognition elements in a gas sensor because they selectively adsorb gas. Imitating mammalian olfaction, sensor arrays of NPMs use measurements of the adsorbed mass of gas in a set of distinct NPMs to infer the gas composition. Modular and adjustable NPMs, such as metal-organic frameworks (MOFs), offer a vast material space to sample for combinations to comprise a sensor array that produces a response pattern rich with information about the gas composition. Herein, we frame quantitative gas sensing, using arrays of NPMs, as an inverse problem, which equips us with a method to evaluate the fitness of a proposed combination of NPMs in a sensor array. While the (routine) forward problem is to use an adsorption model to predict the mass of gas adsorbed in each NPM when immersed in a gas mixture of a given composition, the inverse problem is to predict the gas composition from the observed masses of adsorbed gas in the NPMs of the array. The fitness of a given combination of NPMs for gas sensing is then determined by the conditioning of its inverse problem: the prediction of the gas composition provided by a fit (unfit) combination of NPMs is insensitive (sensitive) to inevitable errors in the measurements of the mass of gas adsorbed in the NPMs. For illustration, we use experimentally measured adsorption data to analyze the conditioning of the inverse problem associated with a (IRMOF-1 and HKUST-1) CH₄/CO₂ sensor array.