Multipressure Sampling for Improving the Performance of MOF-based Electronic Noses

Metal–organic frameworks (MOFs) are a promising class of porous materials for the design of gas sensing arrays, which are often called electronic noses. Due to their chemical and structural tunability, MOFs are a highly diverse class of materials that align well with the similarly diverse class of volatile organic compounds (VOCs) of interest in many gas detection applications. In principle, by choosing the right combination of cross-sensitive MOFs, layered on appropriate signal transducers, one can design an array that yields detailed information about the composition of a complex gas mixture. However, despite the vast number of MOFs from which one can choose, gas sensing arrays that rely too heavily on distinct chemistries can be impractical from the cost and complexity perspective. On the other hand, it is difficult for small arrays to have the desired selectivity and sensitivity for challenging sensing applications, such as detecting weakly adsorbing gases with weak signals, or conversely, strongly adsorbing gases that readily saturate MOF pores. In this work, we employed gas adsorption simulations to explore the use of a variable pressure sensing array as a means of improving both sensitivity and selectivity as well as increasing the information content provided by each array. We studied nine different MOFs (HKUST-1, IRMOF-1, MgMOF-74, MOF-177, MOF-801, NU-100, NU-125, UiO-66, and ZIF-8) and four different gas mixtures, each containing nitrogen, oxygen, carbon dioxide, and exactly one of the hydrogen, methane, hydrogen sulfide, or benzene. We found that by lowering the pressure, we can limit the saturation of MOFs, and by raising the pressure, we can concentrate weakly adsorbing gases, in both cases, improving gas detection with the resulting arrays. In many cases, changing the system pressure yielded a better improvement in performance (as measured by the Kullback–Liebler divergence of gas composition probability distributions) than including additional MOFs. We thus demonstrated and quantified how sensing at multiple pressures can increase information content and cross-sensitivity in MOF-based arrays while limiting the number of unique materials needed in the device.


Supporting Information -Table of Contents 1. RASPA Simulation Details
 Table S1.Physical properties of MOF structures. Table S2.Parameters of framework atoms. Table S3.Parameters of gas molecule bodies. Table S4.Critical parameters of gas molecules.To model electrostatic interactions, we assigned partial charges to the atoms of the MOF frameworks via the EQeq method. 3Similarly, the molecule parameters of the gases also included partial charges, and the forcefield which we used, TrAPPE 4 , has been shown to accurately simulate these effects.

Composition Prediction & Array Analysis
Rigid MOF structures, as well as rigid molecule structures, were assumed, and Lennard-Jones (LJ) potentials with a cutoff of 12 Å were used along with Ewald charge interactions to determine the overall energy of the structure and adsorbed gases.The equations for LJ potential are given below, where  is potential well-depth and  is radius of interaction.
The equation for Ewald coulombic potential in a periodic system is given as:

𝑖
where   and   are the charges of particle  and , respectively,   is the position of atom ,  is the volume of the cell,  is a damping factor,  is the wavelength, and erfc is the error function complement.
The information about each framework, including minimum number of unit cells, density, volumetric surface area, void fraction, and pore size (largest cavity diameter) are listed below in Table S1.Forcefield parameters (excluding partial charges, which are framework specific and can be found in the cif files) for each framework atom type are given in Table S2.

Composition Prediction & Array Analysis
In order to assign probabilities to each composition, we compare the calculated set of masses at each composition (one per sensing element) to the set of sensor outputs.One element at a time, we take the sensor output associated with that element and create a truncated normal probability curve centered about the sensor output mass, with a fixed standard deviation value representative of measurement error.The reason for using a truncated probability distribution rather than a true normal distribution is to account for the fact that adsorption will always result in an increase in mass.Consequently, the lower bound is set at 0, and the upper bound is set at infinity.
The equations which govern the truncated normal distribution are as follows: , , , ;  = 0   ≤  ,  , , , ;  =  , ;  Φ ,  2 ;  Φ ,  2 ;    <  <   , , , ;  = 0   ≤   ,  2 ;  = 1 where  ,  2 is the standard normal distribution over the interval ( -∞, + ∞), and Φ ,  2 is the cumulative distribution function over the interval ( -∞, + ∞).The variables  and  are the mean and variance of the parent normal distribution, and the variables  and  are the truncation interval. 12r each composition, we assign a probability based on where simulated mass sits on the truncated probability curve, as given by:  , =  , , , ;  , where  =   ,  = 0.10,  = 0 ,  = ∞ .Since each mass is assigned a probability independently, the sum of all probabilities does not necessarily equal 1.However, since the intention of this process is to create a set of probabilities which will subsequently be used to calculate the array probabilities, we normalize the assigned probabilities for each sensing element so that now their sum equals 1.This guarantees that all sensing elements are given equal weight in the final prediction.where   and   are the system and reference probability, respectively.The goal was to ask the question, "How much better are we predicting over random chance?", hence as a reference probability we used a simple uniform distribution, such that   = 1  for all  , with the above equation simplifying to: Note that we also dropped the ( ∥ ) notation, since our reference probability was never anything other than a uniform distribution.

Benzene Isotherm for MOF-177
The sharp increase in the adsorbed concentration of benzene at approx.10^3 Pa [0.01 bar] is consistent with the sharp increase in the adsorbion of benzene in the gas mixtures at a partial pressure for benzene of approx.0.015 bar, most noticeable in Fig. 3b.Because each of the figures is plotted on their own scale, at first glance it appears as though each MOF has enough variability to be a useful sensing material to some extent.
However, upon closer examination, we can see that the difference in the total adsorbed mass

 Figure S1 .
Mapping from mass space to probability space for a ternary gas mixture of CO2, N2, and O2. 3. Additional Results 3.1.Benzene Adsorption in NU-100  Figure S2.Ternary plots of the adsorbed mass of benzene NU-100 as a function of composition and at the following pressures: a) 0.1 bar, b) 0.5 bar, c) 1 bar, d) 5 bar, and e) 10 bar.f) shows a 2x2x2 unit cell of the MOF projected down the c-axis.3.2.Benzene Adsorption in NU-100  Figure S3.Isotherm for benzene adsorption in MOF-177 at 298K.3.3.Hydrogen Adsorption at 0.1 Bar  Figure S4.Ternary plots of the total adsorbed mass for hydrogen sensing at 0.1 bar as a function of composition.The MOFs shown are a) HKUST-1, b) IRMOF-1, c) MgMOF-74, d) MOF-801, e) MOF-177, f) NU-100, g) NU-125, h) UiO-66, and i) ZIF-8.4. References 1. RASPA Simulation Details Adsorption data was generated using RASPA, a grand canonical Monte Carlo simulation software designed by Dubbeldam et al. 1 We examined a set of 9 MOFs from the CoRe MOF database 2 and used a temperature of 298 K and pressures of 0.1, 0.5, 1, 5, and 10 bar.Simulations were conducted using 1000 initialization cycles and 5000 production cycles.A single cycle consists of n Monte Carlo steps, where n is equivalent to the number of molecules in the simulation.Note that this value fluctuates during a GCMC simulation.The simulations include the following moves: insertion, deletion, translation, regrowth (configuration is changed), and swapping.

Figure S1 .
Figure S1.Mapping from mass space to probability space for a ternary gas mixture of CO2, N2,

3. Supplemental Results 3 . 1 .Figure S2 .
Figure S2.Ternary plots of the adsorbed mass of benzene NU-100 as a function of composition

Figure S4 .
Figure S4.Ternary plots of the total adsorbed mass for hydrogen sensing at 0.1 bar as a

Table S4 .
Critical Parameters of Gas Molecules