Non-injective gas sensor arrays: identifying undetectable composition changes

A gravimetric, MOF-based (MOF = metal-organic framework) sensor array functions by measuring the mass of gas adsorbed in an array of MOFs. Changes in the gas composition are expected to produce detectable changes in the mass of gas adsorbed in the MOFs. In practical settings, multiple components of the gas adsorb into the MOFs. As a result, the map from gas compositions to sensor response vectors will be non-injective (many-to-one). Here, we outline a mathematical method to determine undetectable changes in gas composition to which non-injective gas sensor arrays are unresponsive. This is important for understanding their limitations and vulnerabilities. Our method relies on a mixed-gas adsorption model in the MOFs comprising the sensor array. We illustrate the identification of unresponsive subspaces and ranked responsive directions for gas sensor arrays based on Co-MOF-74 and HKUST-1 aimed at quantitative sensing of CH4/N2/CO2/C2H6 mixtures (relevant to the natural gas industry).