Intelligent Selection of Metal–Organic Framework Arrays for Methane

Article Cite This: ACS Sens. 2019, 4, 1586−1593

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Intelligent Selection of Metal−Organic Framework Arrays for Methane Sensing via Genetic Algorithms Jenna A. Gustafson and Christopher E. Wilmer* Department of Chemical & Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States

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S Supporting Information *

ABSTRACT: Gas sensor arrays, also called electronic noses, use many chemically diverse materials to adsorb and subsequently identify gas species in complex mixture environments. Ideally these materials should have maximally complementary adsorption profiles to achieve the best sensing performance, but in practice they are selected by trial-anderror. Thus current electronic noses do not achieve optimal detection. In this work, we employ metal−organic frameworks (MOFs) as sensing materials and leverage a genetic algorithm to identify optimal combinations of them for detecting methane leaks in air. We build on our previously reported computational design methodology, which ranked MOF arrays by their Kullback−Liebler divergence (KLD) values for probabilistically describing the concentrations of each gas species in an unknown mixture. We ran the genetic algorithm to find optimal MOF arrays of various sizes when selecting from a library of 50 different MOF materials. The genetic algorithm was able to accurately predict the best arrays of any desired size when compared to brute-force screening. Thus, this search optimization can be integrated into the efficient design of MOFbased electronic noses. KEYWORDS: metal−organic frameworks, electronic nose, optimization, methane sensing, machine learning, molecular simulations

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In our previous work, we addressed a central problem in the development of MOF-based electronic noses: choosing an array that maximizes device performance.17 We established a method for the computational screening of MOF materials for the detection of methane in air, based on how well MOF arrays could resolve gas mixtures.17 To quantify MOF array performance we used the Kullback−Liebler divergence (KLD), which measures how much information is contained in a probability distribution. A KLD value could be assigned to a particular MOF array based on how precisely it can predict the composition of an unknown gas mixture. This approach facilitates computational screening of many MOF arrays without having to laboriously construct them in an experimental setting. When both the number of MOFs to choose from and the number of unique MOFs in an array is small, it is possible to screen every array in a brute-force manner. For example, we previously were able to quantify the performance of every MOF array from a library of nine MOFs (511 arrays in total).17 However, the amount of combinations increases exponentially upon increasing both (a) the number of array elements and (b) the number of possible element types, as demonstrated in Figure 1.

lectronic nose devices are composed of many sensing elements, which operate in a cooperative manner to analyze ambient gases. Over the past several decades such devices have been implemented for a broad range of industrial applications, such as quality control in food production.1 However, there remain many challenging sensing applications that are beyond the reach of current electronic noses. For example, detection of diseases via breath analysis is an exciting future application for electronic noses, but is tremendously difficult due to the complexity and variability of human breath.2 Despite technological advances, detecting trace amounts of methane in air remains a challenging problem due to the typically complex ambient environments near natural gas leaks.3,4 Progress in electronic nose design has been driven almost exclusively by experimental trial-and-error approaches, whereas computational design has not played a significant role largely due to an inability to predict electronic nose behavior in silico. This work explores computational design and optimization of electronic noses that leverage metal−organic frameworks (MOFs). MOFs have been studied for their promise as improved sensing materials due to their extremely high internal surface areas, tunable pore geometries, and reproducibility of synthesis.5 Although the study and design of individual MOFs for sensing applications has received significant attention,5−16 relatively little work has been published on using combinations of them in gas sensing arrays.7,11,14,17−19 © 2019 American Chemical Society

Received: February 5, 2019 Accepted: May 24, 2019 Published: May 24, 2019 1586

DOI: 10.1021/acssensors.9b00268 ACS Sens. 2019, 4, 1586−1593

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methodology proposed here may be used for more realistic gas mixtures provided force field parameters are available for each gas species. Moreover, if experimental adsorption isotherms of more complex gas mixtures (i.e., two or more components) were available, additional insights could be gained as to the accuracy of simulations, as well as inform model development. It is worth noting that experimental mixed component isotherms are very rare in the literature,24 and that such data would be very valuable for the design of adsorbent-based sensors. Quantifying MOF Array Performance. Previously, we demonstrated how gas mixture compositions could be predicted using only total mass adsorbed onto each MOF in an array.17 The mass change of an individual MOF rules out certain gas mixtures, but leaves many others as possibilities, which can be described by a probability distribution. We found in earlier work that by considering input from multiple MOFs via joint probability distributions, the range of likely gas mixtures narrows substantially. Then, the performance of each MOF array could be quantified using a metric called the KLD, which measures the information content of a probability distribution. In this work, we calculate KLD values for many arrays of various sizes that can be constructed from a library of 50 different MOFs. Even though calculating a KLD value is relatively inexpensive computationally (particularly when compared to simulating gas adsorption), there are trillions of array combinations (see Figure 1) and so brute-force screening cannot be used. Our use of probabilistic predictions of gas compositions and the KLD metric to quantify array performance differs from other commonly used methods for processing electronic nose data, which typically employ pattern recognition techniques that require experimental training data in the form of fingerprint responses.20,25−27 Specifically, electronic noses are evaluated according to their classification abilities using techniques such as principle component analysis (PCA) and/or partial least-squares-discriminant analysis (PLS-DA), which do not precisely quantify complex analyte concentrations.20,26,28 In contrast, our approach uses a molecular model of gas mixture adsorption instead of fingerprints to convert sensor signals into detailed gas composition information. As applied to methane sensing, PCA and/or PLS-DA may provide adequate results for the detection of natural gas leaks. However, the KLD metric employed here is more rigorous and may have advantages for more complex sensing applications or when quantifying gas compositions is particularly important. Genetic Algorithm Implementation. Various types of evolutionary algorithms have been used previously for the screening materials, including MOFs. In a broader context, genetic algorithms have been used for search optimization for many years.29−32 Here we briefly describe our specific implementation. First, we select an encoding of the solution, called the “genome” (i.e., a string of integers), for which there is not one correct approach. Analogous to human genetics, the human genotype (DNA) is the GA encoding and the phenotype (physical features) is the solution expression of the GA. Here, each gene is an integer from 0 to 49, and the genome length corresponds to the input array size, where no duplicate genes are allowed; see Figure 2. Initially, we create a random population of possible solutions, as shown in Figure 3. For a population size of N and an array size of m,

Figure 1. Possible combinations on a log scale vs array size, varying the possible number of materials to choose from (60, 50, 40, 30, 25).

Just as it is impractical to test hundreds of sensor arrays experimentally, it is equally infeasible to screen trillions of arrays computationally. Thus, to find optimal arrays containing 30+ unique MOFs, from libraries of hundreds or thousands of possible MOFs, we must develop more efficient computational search strategies. Therefore, in this work, we have implemented a genetic algorithm (GA) for large-scale intelligent selection of arrays. In this work we apply GA methods to find optimal arrays of various sizes that can be constructed from a library of 50 MOFs. Materials were manually down-selected from the CoRE MOF database to represent a large range of surface areas while simultaneously avoiding structures with residual solvent molecules or missing atoms. The intent was to choose an arbitrary set of MOFs that nevertheless would be expected to have highly variable adsorption behaviors. Grand canonical Monte Carlo (GCMC) simulations were used to predict the adsorption of methane/air mixtures in each of the 50 MOFs. After validating that the GA approach could correctly identify the best arrays for small array sizes (i.e., less than five elements), we searched for larger optimal arrays (i.e., 25+ elements) and found a nearly linear performance increase as a function of size (as measured by the KLD value). This linear performance improvement contradicts some prior reports20 of plateauing performance for electronic noses once the number of elements exceeds about 10, which highlights the potential importance of intelligent optimization of sets of sensing materials.

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METHODS

Predicting Gas Adsorption in MOFs. In a continuation of our previous work, we are designing MOF arrays for sensing methane-inair mixtures, which we represent as compositions of methane, oxygen, and nitrogen. Since the focus of this work is on the development of an optimization methodology, we are not considering some additional gas species found in air such as water, carbon dioxide, and so forth. We performed grand canonical Monte Carlo (GCMC) simulations using the software package RASPA,21 calculating adsorption for all mixtures of methane, oxygen, and nitrogen, in 2% increments of each gas. This resulted in 1326 mixtures whose adsorption was simulated in 50 MOF structures at 298 K and 1 bar. These 50 MOF structures were manually chosen to represent a broad range of surface areas from the CoRE MOF Database (manual inspection and selection facilitated the exclusion of certain structures that were duplicates, had left over solvent species, or were otherwise unsuitable).22 Please see section S1 in the Supporting Information for a list of structures and further simulation details. It is important to note that these simulation techniques have been widely used to predict gas adsorption of these gases in MOFs.6,15,23 However, for modeling more complex gas mixtures, new force field parameters (or potentials) may need to be developed. Although this work employs a simplified gas mixture environment, the same

Figure 2. Example of an encoded array of six MOFs in a genetic algorithm. First, MOFs are randomly chosen for a specified array size then checked for duplicates. The final array is a set of unique integers. 1587

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taken until enough children are created to make up the next generation. During the crossover process, each array is again checked for duplicates and if found they are replaced with a different random MOF. Once the next generation of children has been created, each child undergoes mutation. We used a 0.1% mutation rate unless otherwise specified (in the Results section we discuss the influence of varying the mutation rate on optimization efficiency). In our implementation, if an element is selected for mutation then a random number (from 0 to 49) is selected to replace it, and then the array is checked for duplicates (as in crossover). After mutation, the fitness for each solution in the new population is evaluated, and the process repeats for a user-specified number of generations. After each generation, we save the top performing result, which in the end we expect to be a high-performance array. Optimization of the parameters used in genetic algorithms often requires trial-and-error. In this study, we evaluate a range of parameter values to achieve the most efficient optimization strategy for predicting the best MOF arrays.

Figure 3. Procedure for creating the first population of arrays. we choose random numbers from 0 to 49 m times to construct each array. The result is a set of N lists of length m, where we impose the constraint of no duplicate MOFs in an array. If a duplicate MOF occurs, another MOF is randomly chosen until there are no remaining duplicates. Note that order does not matter and we do not use any canonical ordering scheme. The next step is to evaluate the “fitness” of each array solution, defined here as a product of three KLD values from a candidate array (eqs 1 and 2). Each KLD value is the result of an array’s probabilistic prediction of one gas in a mixture; thus, since we are testing three component mixtures there are three KLD values for each array. N

Pi Qi

(1)

fitness = KLDCH4 × KLDO2 × KLDN2

(2)

KLD =

∑ Pi log i

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RESULTS AND DISCUSSION Comparison to Brute-Force Analysis. Initially, we compare the genetic algorithm results to a known correct result to validate its ability for predicting the best MOF arrays (which is only possible for small array sizes). Therefore, we evaluate 1, 2, 3, and 4 MOF arrays (from a library of 50 MOFs) for which we can easily compute KLD values for all possible combinations (See Figure 4). MOF array performance is quantified by its ability to predict an “unknown” gas mixture of 10% methane, 20% oxygen, and 70% nitrogen, which we have chosen to represent methane in air. First, we immediately see that a small percentage of arrays have significantly better performance than the rest of the set. Please note that all reported KLD values are in units of bits3 throughout the study. Subsequently, we compare the top MOF arrays from our genetic algorithm to the known correct results, as shown above in Figure 4. The GA was run for array sizes of 1, 2, 3, and 4, where each run included 50 generations with a population size of 100 and a mutation rate of 0.1%. The black points in Figure 4 represent the best array found in each of five GA runs for each array size. We see that algorithm clearly performs well, having found the global best array for each array size, in some cases in all five runs. Specifically, the GA found the global best

The probability at each mole fraction is represented by Pi, and a reference probability of Qi is a probability equivalent to 1/N (i.e., a uniform probability distribution), where N is the number of points (mole fractions) we have from 0 to 1 for each gas (see section S2 in the Supporting Information for a detailed calculation of the fitness function). Consequently, the array with the highest product of KLD values is saved as the best result in its generation, and the next generation of candidate arrays is created. To do this, we first keep the top 20% of solutions as parents and then randomly select another 20% of the population as additional parents to ensure genetic diversity and avoid local optima. Importantly, parents are combined to create the next generation, their “children”, using an established method called crossover. Each child inherits pieces from both parents, so we select MOFs from each parent array for the child to retain. Specifically, our approach is to randomly retain each array element from one parent or the other, giving equal probability to each parent. The result is a new array with a mix of elements from each parent. Combinations of parents are

Figure 4. KLD (in bits3) vs ranking of every MOF array for size of (a) 1 MOF, (b) 2 MOFs, (c) 3 MOFs, and (d) 4 MOFs. Black points represent best arrays found from the GA over five runs, where some are overlapping. 1588

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Figure 5. Probability density versus mole fraction of CH4, O2, and N2 for array sizes of 1, 2, 3, and 4 for predicting 0.1 CH4, 0.2 O2, and 0.7 N2. Results are from the best arrays all on the left, and subsequent arrays are evenly spaced based on decreasing performance (100th, 66th, 33rd, 0th percentile, from left to right).

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array three out of five times for arrays of 1 and 4 MOFs, and five out of five times for arrays of 2 and 3 MOFs. This gives reasonable confidence that the GA will yield high-performing arrays when considering larger sizes as well. It is important to note that the top arrays for sizes of one through four reported here differ from the top MOF arrays reported in our previous work.17 The full list of best arrays of these sizes are reported in Table S8 in the Supporting Information. In this study we are (1) searching a much larger materials space (50 compared to 9 previously) and (2) considering a different test gas mixture, and therefore we cannot make a direct comparison in array performance. We can display the improvement of arrays’ abilities to predict gas mixture compositions by showing probability density versus mole fraction relative to each gas, as the array performance decreases (see Figure 5). Again, we chose an “unknown” mixture composition of 10% methane, 20% oxygen, and 70% nitrogen. The probability density plots correspond to arrays evenly spaced from best to worst along the analogous plots in Figure 4 above. The trends in probability validate the KLD ranking metric as a tool for informing the selection of sensing materials relative to electronic nose design.

GENETIC ALGORITHM PARAMETER ANALYSIS

Varying Population Size. In the interest of optimizing the GA parameters to maximize computational efficiency, we investigated the trade-off between the algorithm’s convergence time and performance by varying the population size. Displayed in Figure 6 is a plot of the KLD value, averaged over multiple GA runs, against population size, for predicting the best 4 MOF arrays, using a 0.1% mutation rate and 50

Figure 6. Plot of KLD (in bits3, averaged over 10 GA runs) versus population size, for selecting the best 4 MOF arrays. The dashed line is the KLD of the best possible 4 MOF array. 1589

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population of 75 works well in the full algorithm implementation. Varying Mutation Strength. Whereas increasing the population size reliably improves the KLD values of the best arrays (up to a point), the influence of mutation rate is more complicated. Using a population size of 75, for 50 generations, a variety of mutation rates were tested for array sizes of 4, 10, and 25 MOFs. In Figure 9, we show the average KLD values normalized relative to the highest KLD found for that size array versus the mutation rate for a range from 0% to 20%.

generations. The KLD steadily increases with population size from 10 up to around 40 arrays, then maintains approximately the same value for populations up to 150. Additionally, error bars indicate the deviation of the KLD from the average, showing less deviation in the GA result between runs with larger population sizes, therefore indicating an improvement in the GA reliability. The dashed line represents the best four MOF arrays, at a KLD of 8.062 bits.3 Further, we can show the range of KLD values obtained over the range of one GA run, averaged over multiple runs, and plotted versus generation (Figure 7). We compare population

Figure 9. Plot of KLD values normalized, relative to the highest KLD for that array size, versus mutation rate in percent for 4, 10, and 25 MOF arrays.

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Figure 7. Plot of average KLD (in bits ) with the range of possible values shaded versus the generation for selecting 4 MOF arrays with a population size of 50 and 100 arrays. The upper bound peaks at the KLD for the best possible 4 MOF array.

From this, it is evident that array size is an important consideration for deciding the best mutation rate. Mutation rates above 5% yield good results for a 4 MOF array, but for 10 and 25 MOFs the algorithm performance steadily drops as the rate increases. Interestingly, the trends do not show a monotonic relationship with array size (i.e., the drop in performance is greater for 10-MOF arrays than for 25 MOF arrays in this example). Nevertheless, we found the optimal mutation rate to be around 1% across these array sizes (and 0.1%, which was used for the majority of this study, also yielded satisfactory results). Increasing Array Sizes. Finally, we report results for MOF array sizes ranging from 1 to 50, where, as we have previously reported,17,18 the KLD values increase with increasing array size (Figure 10). For arrays with five or more elements, we do

sizes of 50 and 100, where the larger population again yields a consistently high-performing MOF array prediction. The shaded region is the range of KLD values obtained at each generation, where the population size of 100 shows little variation compared to 50. From this, we see that the algorithm converges well before 50 generations for a population size of 100, where the best array is consistently obtained around generation 13. Thus, to improve efficiency in practical implementation, the number of generations may be lowered to reduce algorithm time. Finally, the ideal population size would minimize the variation in KLD values for a high KLD, while also minimizing the algorithm time. Moreover, minimizing the variation will give more confidence in each GA result, so one GA run will be enough to predict the best array. In Figure 8, we look at these metrics on the same plot, where the values of KLD and deviation from average KLD have been normalized relative to their highest possible values. We determine the optimal population is the smallest at which we obtain the maximum KLD values with little deviation; thus, we see that using a

Figure 10. Plot of best KLD value (in bits3) versus array size, using a population size of 100 and a mutation rate of 0.1% (black points), compared to random arrays averaged over 10 runs (red).

not have known best solutions to compare to, but we are able to benchmark all of the GA solutions against a theoretical maximum fitness value. Namely, from eqs 1 and 2, one can show that the maximum fitness occurs as the probability approaches the limit of 100% for one gas mixture vs 0% for all other gas mixtures and yields a value of around 180 bits3 (see section S4 in the Supporting Information for a detailed explanation of the theoretical limits of the KLD).

Figure 8. Plot of normalized values for KLD (in bits3) and deviation in KLD versus the population size, for selecting 4 MOF arrays over 50 generations. 1590

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Figure 11. Plots of probability density versus mole fraction of CH4, O2, and N2 for the best predicted arrays of (a) 5, (b) 10, (c) 15, (d) 20, (e) 25, (f) 30, (g) 35, (h) 40, and (i) 45.

individual MOFs/arrays, so predicting the best MOFs to add is not trivial. Additionally, it is important to emphasize the improvement in GA array optimization compared to random MOF combinations, as shown in Figure 10. Thus, we are confident that the algorithm yields the best performing arrays and is always going to produce a better result than random array selection. Lastly, we compare probability densities from each of the best arrays for array sizes of 5 through 45 MOFs (see Figure 11), using the same arbitrarily chosen gas mixture as before: 0.1 CH4, 0.2 O2, and 0.7 N2. As the array size increases, the probability also increases in a concentrated area, with the results steadily improving up to 50 arrays. These probability density results show that our GA accurately produces high performing arrays, in that we achieve a precise prediction of the unknown gas mixture. At an array size of forty-five we see the highest probability density at one gas mixture, rather than a cluster of mixtures.

In previous work we demonstrated that array performance stopped increasing at an array size of five and remained the same for a study of up to nine MOFs.17 Here, our results show a steady linear increase in performance up to 50 MOFs; however, we anticipate an eventual plateau if even larger arrays were considered. The maximum possible KLD value for this analysis is 180 bits.3 However, as can be seen in Figure 10, we are only reaching 45 bits3 at 50 MOFs, so we are still in the linear regime. As expected, the slope of the GA optimized arrays is larger than that for the randomly selected MOFs, although they both converge to the same value once all 50 MOFs are used. One counterintuitive aspect of assembling complementary materials into arrays for sensing is that the contribution of individual elements can be latent, that is, not observable until a later point. For example, given three hypothetical materials, A, B, and C, one can construct pairs (AB, BC, or AC) that yield identical information content to the individual materials, but where all three have a much higher KLD value. Thus, one can progress from A to AB without any increase in KLD score, but then ABC may have a large increase. Thus, when choosing at random, an array can be increasing its latent potential for information gain that is only realized once the array gets sufficiently large. In contrast, an optimized array (using our methods) will always aim to increase its KLD with size. As MOFs are added to an array, one may intuitively assume that the best arrays of smaller sizes are always contained within arrays of larger sizes. This is generally not the case: the best 6 MOF array may not contain any of the MOFs from the best 5 MOF array. However, once arrays are sufficiently large (and of course, once all 50 MOFs are used), the best small-MOF arrays are observed within the larger (10 and above) ones. Hence, it is not always a matter of combining the best ranked

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CONCLUSIONS Despite their attractive properties for gas sensing, limited attention so far has been given to building gas sensor arrays with MOFs in the 20 years they have been studied. Here we have built on prior work by ranking larger arrays of MOFs for methane-in-air detection than had been considered previously, using a novel genetic algorithm. As more MOFs are considered as candidates for use in a sensor array, their optimal selection becomes an exponentially more computationally expensive problem. We have implemented a genetic algorithm and shown that it can efficiently search for optimal array configurations when considering a library of 50 MOF structures and sensing among 1,326 gas mixtures of methane, oxygen, and nitrogen. 1591

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ACS Sensors Notes

After comparing different GA parameters for a range of array sizes, we concluded that a population of 75 arrays and a mutation rate of around 1% yields the best results, regardless of array size. Additionally, it was found that the average KLD values for the best arrays increase as MOFs are added to the array, all the way up to 50 MOFs (i.e., as opposed to saturating much earlier, as had been suggested by prior studies). We believe this contradiction occurs for two possible reasons: (1) MOFs are more structurally diverse materials than polymers and metal-oxides, therefore they will perform better in a complementary array fashion; and (2) since MOFs can be simulated, we are able to test more array configurations, where if every polymer array was tested there may be a continual increase in performance with size. As previously noted, we have not included water or other interferents in our simulations to simplify the considered systems and develop a clear methodology for predictive array selection. Water, in particularly, is well-known in the molecular simulation community as prohibitively costly for adsorption calculations and this was an important consideration in our deferring this important adsorbate to future studies. However, we acknowledge that water is known to strongly adsorb to many MOFs and thus its inclusion in our adsorption simulations may have significantly altered the observed arrayinformation-content responses. In particular, it may be the case that above certain ambient water concentrations (i.e., high humidities), the probability distributions for all other gas components might broaden significantly and thus decreasing sensor array performance. Simulating mixtures that accurately represent those in real world ambient conditions will be necessary in future work. Importantly, we have shown that optimal MOF arrays can be found in minutes, using a GA, whereas for the same size of array it would have taken thousands of years to do an exhaustive search. We hope that these tools may be used to inform experimental design of MOF sensors going forward. In future work, we will expand to larger databases of MOFs and more complex ambient gas mixtures. Depending on the MOFs from which one can choose, there may be 10 that perform better than all 50 from this study. Thus, we anticipate that casting as wide a net as possible will ultimately lead to the discovery of the best possible gas sensor array.

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The authors declare the following competing financial interest(s): Christopher E. Wilmer has a financial interest in the start-up company NuMat Technologies, which is seeking to commercialize metal-organic frameworks.

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ACKNOWLEDGMENTS J.A.G. and C.E.W. gratefully acknowledge support from the Chemical & Petroleum Engineering Department and Clinical and Translational Science Institute at the University of Pittsburgh. J.A.G. gratefully acknowledges support from a D.O.E. Office of Science Graduate Student Research (SCGSR) award. We also thank the Center for Research Computing at the University of Pittsburgh for their computational resources.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssensors.9b00268. Molecular simulation parameters, MOF properties, as well as an explanation of the statistical and genetic algorithm methodology in further detail (PDF)

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REFERENCES

All of the MOF files used in simulations as crystallographic information files (ZIP)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jenna A. Gustafson: 0000-0002-3092-8745 Christopher E. Wilmer: 0000-0002-7440-5727 1592

DOI: 10.1021/acssensors.9b00268 ACS Sens. 2019, 4, 1586−1593

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DOI: 10.1021/acssensors.9b00268 ACS Sens. 2019, 4, 1586−1593