Gantzler Nickolas, Henle E Adrian, Thallapally Praveen K, Fern Xiaoli Z, Simon Cory M
Department of Physics, Oregon State University, Corvallis, OR, United States of America.
School of Chemical, Biological, and Environmental Engineering, Oregon State University, Corvallis, OR, United States of America.
J Phys Condens Matter. 2021 Sep 7;33(46). doi: 10.1088/1361-648X/ac1e49.
Metal-organic frameworks (MOFs) are nanoporous materials with good prospects as recognition elements for gas sensors owing to their adsorptive sensitivity and selectivity. A gravimetric, MOF-based sensor functions by measuring the mass of gas adsorbed in a MOF. Changes in the gas composition are expected to produce detectable changes in the mass of gas adsorbed in the MOF. In practical settings, multiple components of the gas adsorb into the MOF and contribute to the sensor response. As a result, there are typically many distinct gas compositions that produce the same single-sensor response. The response vector of a gas sensor array places multiple constraints on the gas composition. Still, if the number of degrees of freedom in the gas composition is greater than the number of MOFs in the sensor array, the map from gas compositions to 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. We focus on gravimetric, MOF-based gas sensor arrays. Our method relies on a mixed-gas adsorption model in the MOFs comprising the sensor array, which gives the mass of gas adsorbed in each MOF as a function of the gas composition. The singular value decomposition of the Jacobian matrix of the adsorption model uncovers (i) the unresponsive directions and (ii) the responsive directions, ranked by sensitivity, in gas composition space. 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 CH/N/CO/CHmixtures relevant to natural gas sensing.
金属有机框架（MOF）是具有纳米孔的材料，由于其吸附敏感性和选择性，作为气体传感器的识别元件具有良好的前景。基于MOF的重量传感器通过测量吸附在MOF中的气体质量来发挥作用。预计气体成分的变化会在吸附在MOF中的气体质量上产生可检测到的变化。在实际应用中，气体的多种成分会吸附到MOF中并对传感器响应产生影响。因此，通常有许多不同的气体成分会产生相同的单传感器响应。气体传感器阵列的响应向量对气体成分施加了多个约束。然而，如果气体成分中的自由度数量大于传感器阵列中MOF的数量，那么从气体成分到响应向量的映射将是非单射的（多对一）。在此，我们概述一种数学方法，以确定非单射气体传感器阵列无响应的气体成分中无法检测到的变化。这对于理解它们的局限性和脆弱性很重要。我们专注于基于MOF的重量气体传感器阵列。我们的方法依赖于构成传感器阵列的MOF中的混合气体吸附模型，该模型给出了吸附在每个MOF中的气体质量作为气体成分的函数。吸附模型的雅可比矩阵的奇异值分解揭示了（i）气体成分空间中的无响应方向和（ii）按灵敏度排序的响应方向。我们说明了基于Co-MOF-74和HKUST-1的气体传感器阵列的无响应子空间和排序响应方向的识别，旨在对与天然气传感相关的CH₄/N₂/CO₂/CH₃OH混合物进行定量传感。
