Curating Metal-Organic Frameworks to Compose Robust Gas Sensor Arrays in Dilute Conditions

Metal-organic frameworks (MOFs)-- tunable, nano-porous materials-- are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from <i>gas composition space</i> to <i>sensor array response space</i> defined by the matrix <b>H</b> of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of <b>H </b>is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO<sub>2</sub> and SO<sub>2</sub> in the gas phase.