Perturbation TheoryâMachine Learning Study of Zeolite Materials

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Perturbation Theory-Machine Learning Study of Zeolite Materials Desilication Vincent Blay, Toshiyuki Yokoi, and Humbert González-Díaz J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.8b00383 • Publication Date (Web): 23 Aug 2018 Downloaded from http://pubs.acs.org on August 25, 2018

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Journal of Chemical Information and Modeling

Perturbation Theory-Machine Learning Study of Zeolite Materials Desilication Vincent Blaya,*, Toshiyuki Yokoib, Humbert González-Díazc,d,* a

Fisher College of Business, The Ohio State University, Gerlach Hall, 2108 Neil Ave. Columbus, OH 43210, United States.

b

Institute of Innovative Research, Chemical Resources Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan. c

Department of Organic Chemistry II, University of Basque Country UPV/EHU, 48940, Leioa, Spain. d

IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain.

ABSTRACT. Zeolites are important materials for research and industrial applications. Mesopores are often introduced by desilication but other properties are also affected, making its optimization difficult. In this work, we demonstrate that Perturbation Theory and Machine Learning can be combined in a PTML multi-output model describing the effects of desilication. The PTML model achieves a notable accuracy (R2 = 0.98) in the external validation and can be useful for the rational design of novel materials. Keywords: Zeolites; ZSM-5; Hierarchization; Desilication; Machine Learning; Perturbation Theory.

1. INTRODUCTION Zeolites are microporous crystalline silicoaluminates with an enormous economic impact. They are used extensively as adsorbents, catalysts, and cation exchangers, among others.1,2 Over two hundred different zeolite frameworks have been synthesized up to date3, but only a dozen are applied in the industry4. Among these, zeolite ZSM-5 has attracted much interest because of its stable 3-dimensional framework and its high selectivity to propylene in several processes.5 Zeolites have micropores of sub-nanometric dimensions, which allows them to act as molecular sieves and selective adsorbents of small molecules but it also makes difficult the processing of larger molecules, like those present in crude oil. In response, multiple strategies have been developed to incorporate mesopores (>2 nm) into zeolites while preserving their microporosity, thus generating so-called hierarchical materials.6 Desilication is a post-synthesis (top-down) hierarchization method of special relevance (Figure 1a) because of its versatility, scalability, and the quality of the thusgenerated mesopores7,8. Desilication is achieved by digestion of the zeolite crystals in alkaline media under controlled conditions (Figure 1b). Part of the Al dissolved from the material is re-aluminated on the external surface of the zeolite, thus decreasing the Si/Al ratio of the material and often introducing new Lewis acid sites.7 The benefits of zeolite catalysts treated by desilication in terms of activity, selectivity and/or catalytic lifetime have been demonstrated in many reactions, including isomerization, alkylation, acylation, aromatization, catalytic cracking, pyrolysis, methanol-to-hydrocarbons, etc.9 However, the behavior of the ACS Paragon Plus Environment

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alkaline-treated zeolites often depends on a balance between the introduced mesopores and the effects on other variables, like the micropore volume, that is highly dependent on the reaction to be catalyzed. Moreover, an ever-expanding range of starting materials, conditions, pore-directing agents (PDAs), and sequence of treatments to tune the properties of the final material make it increasingly difficult to define the optimal desilication conditions for a given application.7 Optimization studies are expensive and often limited by the availability of novel zeolites synthesized in the laboratory and by the growing number of variables or dimensions to consider in the treatment. And, still, since desilication dissolves valuable catalytic material (losses of 30 wt.% are common7), highly optimized treatments are necessary for them to be applicable in the industry. In this context, data analysis Machine Learning (ML) techniques can be useful to model and optimize zeolite materials and processes. In fact, ML techniques have been applied to obtain relevant descriptors of zeolite frameworks10. Recently, Perturbation Theory (PT) operators and Machine Learning techniques have been combined to create powerful PTML (PT + ML) models, which are being applied to complex problems in Medicinal Chemistry, Nanotechnology, Materials Science, etc.11-20 PTML models predict the properties of a query compound or material (q) starting with the property for a system of reference (r) and adding PT operators to measure the deviations (perturbations) from the reference.21,22 They can be used to study large datasets with multiple experimental input conditions. In this work, we report for the first time a PTML model applied to Zeolite Science. We compiled from the literature a dataset with >1000 data points from ZSM-5 materials. The data are very heterogeneous and contain different ZSM-5 starting materials (including H-ZSM-5, Na-ZSM-5, Na,K-ZSM-5, NH4-ZSM-5, etc.), multiple experimental conditions, and present multiple output properties of interest. Overall, we analyzed >50000 pairs of new and reference materials by the PTML methodology. A simple yet powerful PTML model could be developed based on multi-condition moving-average (MA) operators. The PTML model developed is a multi-output linear equation able to predict up to 8 different properties: BET area (m2 g-1), mesopore volume (cm3 g-1), micropore volume (cm3 g-1), Si/Al molar ratio, mesopore size (nm), mesopore area (m2 g-1), total volume (cm3 g-1), and treatment yield (wt.%). The present model demonstrates the usefulness of PTML in catalyst engineering and may become a versatile tool for the rational modification of ZSM-5 materials.

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Figure 1. a) Publications per year indexed in Scopus® on zeolite hierarchization and desilication. b) Illustration of desilication of zeolite ZSM-5. Adapted from ref. 8 with permission of The Royal Society of Chemistry.

2. MATERIALS AND METHODS Dataset. In this work, we studied a dataset of 1019 data points collected from the literature and investigated here as a benchmark dataset for the first time. These 1019 values come from experiments measuring properties/parameters εij for the alkaline desilication of ZSM-5 materials. These parameters depend on a series of experimental conditions cj= (c1, c2, …cn). The data also present variations in multiple conditions: c0 = property of interest of the material, c1 = starting raw material used, to characterize the micropore specific volume of the starting material,

c2 = method used

c3 = method used to characterize

the mesopore specific surface area of the starting material, c4 = base/PDA/acid combination used, c5 = base/PDA/acid used in step 1, c6 = base/PDA/acid used in step 2, c7 = method used to characterize the micropore specific volume of the treated materials, c8 = method used to characterize the mesopore specific


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surface area of the treated materials, etc. The 8 output properties/parameters εij of the materials studied are: BET surface area (m2 g-1), Mesopore volume (cm3 g-1), Micropore volume (cm3 g-1), Si/Al, Mesopore size (nm), Mesopore area (m2 g-1), Total volume (cm3 g-1), and Treatment yield (wt.%). Detailed information about this dataset is provided as Supporting Information file SI01.xlsx.

Monte Carlo pseudo-random number generation of data pairs. Using this original (raw data) set we generated >4000 pairs of new vs. reference materials. In order to generate the pairs of materials, we have taken the following steps. Firstly, we labeled each material in the dataset with a number (ni = 1 to 1019). Secondly, we sorted the data using two criteria: (1) sort by property (from A to Z), and (2) sort the by value of the property from the highest to the lowest value. Next, using a pseudo-random number generator, we sampled nnew = 5000 values of ni for the new materials. In particular, we used the version of the Wichmann-Hill algorithm as implemented in Microsoft Excel. This algorithm is useful for pseudo-random number generation in Monte Carlo (MC) simulations.23 The function used has the form nnew = Random(npstart;

np-last), with arguments np-start and np-last equal to the first and the last label ni for the values belonging to

the same experimental property p. Next, we sampled other nref =5000 values out of ni to label the reference material in the pair. In this case, we used the same MC pseudo-random number generator with a modification. The modification was nref = nnew + Random(1; 5). Consequently, we sampled both nref and nnew that belong to materials with a similar value of the property p. This procedure is aimed to sample pairs with low perturbations in the ouput/input values. As the initial data ni = 1019 < nref = nnew = 5000, a given value of ni was sampled more than once. Finally, we deleted all duplicated pairs (with the same nref and nnew) and/or different properties (if any) to avoid duplicated and/or cross-property pairs. Detailed information about the dataset generated, including observed values, input variables, etc. is available as Supporting Information file SI02.xlsx.

PTML linear model. PTML modeling techniques are useful to quantify the effect of perturbations in complex biomolecular systems.21,24 The aim of the PTML model proposed here is to predict the value εk(mi, cj) of a property εk of type k of a material under experimental conditions cj. The model starts using as input the value εk('mi, 'cj)ref of the same property εk for a material of reference 'mi measured under similar experimental conditions 'cj. Next, the model adds up the values of PT operators to account for the effect of differences between the new material and the material of reference. These PT operators are differences of moving averages21,22 with the following form ∆∆Vk(mi, cj) = [(Vk(mj) - )new - (Vk('mi) - ) to account for the differences on the experimental conditions (cj ACS Paragon Plus Environment

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and 'cj) of the procedures used to modify and characterize the new material and the material of reference, respectively. We a Multivariate Linear Regression (MLR) algorithm to seek the model25. Figure 2 shows the general workflow and the main steps taken in this work to develop the PTML model. The compact and extended forms of the equations for a PTML linear model are as follows:

,

,

, a ′ , ′ a V a

! , #

e a !′ , ′ #

a

,

,

∆∆V !c #

a V

%!V & 〈V !c #〉#

& !V ′ & 〈V !′c #〉#

)

Figure 2. General workflow used to develop the PTML model.


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3. RESULTS AND DISCUSSION In the present Materials Chemistry problem we analyzed ntotal = 4975 pairs of new and reference materials. Specifically, 3732 pairs of materials were used to train the model and 1243 pairs were used as the validation series. These cases are labeled with a t = train or a v = validation in the Supporting Information file SI02.xlsx. The first input variable is the value εk(mi, cj) of the property εk of one material of reference measured under the same experimental conditions cj= (c1, c2, …c8) as the new material. In order to seek the PTML model, we collected the values of 10 different input variables, Vk. These variables represent properties of the starting materials as well as information about the treatments used in the experimental methods. The variables studied in this work are: V01 = Si/Al molar ratio before treatment (b.t.), V02 = Crystal size b.t. (µm), V03 = BET surface area b.t. (m2 g-1), V04 = Total volume b.t. (cm3 g-1), V05 = Micropore volume b.t. (cm3 g-1), V06 = Mesopore volume

b.t. (cm3 g-1), V07 = Mesopore area b.t. (cm2 g-1), V08 = NaOH

concentration (M), V09 = TPAOH concentration

(M), V10 = MCTAB concentration (M),

V11

=

Temperature of treatment (°C), V12 = Time of treatment (min), V13 = No. of steps in the treatment, V14 = Solid weight (g), V15 = Solution volume (mL). All these variables Vk are input variables measured previously or during the treatment and must not be confused with the output variables εk(mi, cj) measured after the treatment. After collecting the values of the original input variables Vk, we used them to calculate the values of the PT operators. The most common PT operators used in PTML models are the one-condition moving-average (MA) operators. These MA operators are analogous to the MA used in Box-Jenkins’s ARIMA models for time series analysis.26 However, we can also develop PTML models using multi-condition PT operators (moving averages).27 In a multi-condition PT operator, we use the same moving-average idea: ∆Vk(cj) = Vk - . In Table 1, we also show the average values for two of these properties, and , which resulted relevant to the model. Note that, in our model, the average calculation does not run over one single condition but over multiple conditions. For instance, we can calculate a triplecondition average for the input variable Vk for all the cases with the same set of conditions c1, c2, c3 as instead of calculating three separated one-condition averages as , , and . In this case, the PT operator ∆Vk(c1, c2, c3) = [Vk - ] quantifies at the same time the structure of the system in terms of Vk and three boundary conditions with . The detailed list of multi-condition averages is available as Supporting Information file SI03.xlsx. We found a simple yet powerful linear PTML model using only two PT multi-condition operators. The PT operators used codify changes in 8 different experimental conditions at the same time: BET surface area (m2 g-1), Mesopore volume (cm3 g-1), Micropore volume (cm3 g-1), Si/Al molar ratio, Mesopore size (nm),


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Mesopore area (m2 g-1), Total volume (cm3 g-1), and Treatment yield (wt.%). The equation of the resulting model is the following:

, &0.22881 1.02864 ′ , ′ 0.02792 V 67.29053 V

0.01264 ∆∆V c , c5 , c6 , c7 , c8 , c9 , c: 0.05753 ∆∆V9 c , c5 , c6 , c7 , c8 , c9 , c:

n 5 train 0.980 > 5 val 0.985 F1,3730 228700 p < 0.05

The model outputs the values εk(mi, cj) of the property εk of the material measured under different experimental conditions cj= (c1, c2, …c8). They refer to the same properties as some of the input variables but measured after the treatment. In this model, the output property predicted is always of the same type as the property already known for the system of reference (knew = kref). Table 1 shows the different properties under study, εk(mi, cj), the number of materials in the original dataset with these properties, nk, and their expected output, . Detailed information of each case, including observed value, predicted value, residuals, values of reference, etc., is provided in the Supporting Information file SI02.xlsx.

Table 1. Output properties predicted by the PTML model. k 1 2

Property εk(mi, cj) (units) 2

-1

BET area (m g )

nk

S.D.

139

424.26

117.17

79.170

0.005

3

-1

139

0.26

0.14

79.170

0.005

3

-1

Mesopore volume (cm g )

3

Micropore volume (cm g )

139

0.12

0.04

79.170

0.005

4

Si/Al molar ratio

138

47.71

86.96

79.439

0.005

5

Mesopore size (nm)

130

9.78

3.70

83.515

0.005

6

Mesopore area(m2 g-1)

123

181.48

121.51

87.026

0.006

7

Total volume (cm3 g-1)

123

0.53

0.15

87.026

0.006

8

Treatment yield (wt.%)

88

51.91

13.17

47.082

0.008

Table 2 summarizes some figures of merit for the best PTML linear model obtained using multi-condition PT operators. The model achieves a high value of R2 = 0.980, F(1, 3730) = 228700, and p < 0.05 in the training series. Notably, the model also has very high value R2 = 0.985 in the validation series. Figure 3 illustrates the strong linear relationship existing between the input and output variables for both the training and validation series. In addition, the model presents low values (in the range 19.5-22.5) for the standard error of the estimate (SEE) and the standard deviation of the error of the prediction (SDEP) for both the training and the validation series. To better assess the quality and predictive power of the model, we also


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calculated the values of the statistical parameter GH5 for the training and external validation series.28 This parameter was proposed by Roy et al. to solve some problems presented by the index q2 (see discussion by Golbraikh and Tropsha29). The threshold value for GH5 is equal to 0.5, with acceptable models falling in the 5 range 0.5-1.0. The value calculated for the validation series is GHIJI = 0.923 (Table 2).

Table 2. Results of the linear PTML model. Sampling

Coefficient

Std. Error

t

p

-95.00%/+95.00%

Set-01

a0 εijref V01new V10new DDV01(cj) DDV07(cj)

-0.22881 1.02864 0.02792 67.29053 0.01264 0.05753

0.46129 0.00240 0.00226 16.53283 0.00220 0.02603

-0.4960 429.0550 12.3701 4.0701 5.7480 2.2099

0.619916 0.000000 0.000000 0.000048 0.000000 0.027173

-1.13/0.68 1.02/1.03 0.02/0.03 34.9/99.7 0.01/0.02 0.01/0.11

Sampling

Parametera

Training

Validation

Parametera

Training

Validation

3732 0.980 0.980 0.911

1243 0.985 0.985 0.923

SEE SDEP F(1, 3730) p

22.450 22.444 228700 10 nm dark red. This kind of predictions may help to obtain new mesopore-containing materials useful in the industry with minimal loss of microporosity. We are working to expland our PTML approach to a wider range of conditions, materials, and properties of interest to zeolites and materials chemistry.


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Figure 4. Predicted values of εk(mi, cj)pred = mesopore size (nm) for >1000 data points.

4. CONCLUSION Mesopore-containing zeolites may offer better performance over conventional zeolites in multiple applications, including heterogeneous catalysis. Given its flexibility, desilication in alkaline media is often attempted as a method to introduce these mesopores. However, this same flexibility makes it difficult to select the proper treatment conditions, as multiple treatment variables have to be decided. At the same time, multiple properties of the materials are likely to be affected and experimental studies are often restricted to a limited number of these. Therefore, the development of multi-input, multi-output models that could harmonize the discrete pieces of information on zeolite hierarchization in the literature, although challenging, would have great interest. For this proof-of-concept, we compiled a dataset from the literature with >1000 data points of ZSM-5 materials. The data contain different types of starting materials and present variations in multiple treatment conditions. This generates a large number of combinations of initial conditions to be optimized in the treatment. We analyzed >4000 pairs of new and reference materials and found a simple but powerful PTML model based on multi-condition moving averages. This PTML model is a multi-output linear equation able to predict up to 8 different properties: BET surface area (m2 g-1), Mesopore volume (cm3 g-1), Micropore volume (cm3 g-1), Si/Al molar ratio, Mesopore size (nm), Mesopore area (m2 g-1), Total volume (cm3 g-1), and Treatment yield (wt.%). The model yields R2 = 0.98, F(1, 3730) = 228700, and p < 0.05 in the training series, and R2 = 0.98 in an external validation series never used to train the model. This work thus demonstrates that Perturbation Theory and Machine Learning methods can be combined in a useful model for the rational design of novel materials.

Supporting Information Supporting information files SI01.xlsx, SI02.xlsx, SI03.xlsx, and SI04.xlsx include the references and original dataset compiled, the data used to fit the PTML model and the results of the same, the computed multi-condition moving averages, and the results of the predictive study, respectively. This material is available free of charge via the Internet at http://pubs.acs.org.

Corresponding Author: *E-mail: [email protected] (V.B.), [email protected] (H.G.-D.)


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Notes The authors declare no competing financial interests.

Acknowledgements Ministerio de Economía y Competitividad (FEDER CTQ2016-74881-P) and (CTQ2013-41229-P) and Basque Government (IT1045-16) are gratefully acknowledged for their financial support. V. B. thanks the support from The Ohio State University. ■ REFERENCES

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21. Gonzalez-Diaz, H.; Arrasate, S.; Gomez-SanJuan, A.; Sotomayor, N.; Lete, E.; Besada-Porto, L.; Ruso, J. M. General Theory for Multiple Input-Output Perturbations in Complex Molecular Systems. 1. Linear QSPR Electronegativity Models in Physical, Organic, and Medicinal Chemistry. Curr. Top. Med. Chem. 2013, 13, 1713-1741. 22. Martinez, S. G.; Tenorio-Borroto, E.; Barbabosa Pliego, A.; Diaz-Albiter, H.; Vazquez-Chagoyan, J. C.; Gonzalez-Diaz, H. PTML Model for Proteome Mining of B-cell Epitopes and Theoretic-Experimental Study of Bm86 Protein Sequences from Colima Mexico. J. Proteome Res. 2017, 16, 4093-4103. 23. McCullough, B. D. Microsoft Excel’s ‘Not The Wichmann-Hill’ random number generators. Comput. Stat. Data Anal. 2008, 52, 4587-4593. 24. Gonzalez-Diaz, H.; Perez-Montoto, L. G.; Ubeira, F. M. Model for Vaccine Design by Prediction of Bepitopes of IEDB given Perturbations in Peptide Sequence, In Vivo Process, Experimental Techniques, and Source or Host organisms. J. Immunol. Res. 2014, 2014, 768515. 25. Hill, T.; Lewicki, P. Statistics: Methods and Applications. A Comprehensive Reference for Science, Industry and Data Mining. StatSoft: Tulsa, 2006 Vol. 1, p 813. 26. Box, G. E. P.; Jenkins, G. M. Time Series Analysis: Forecasting and Control. Holden-Day: San Francisco, CA, 1970; p 575. 27. Garcia, I.; Fall, Y.; Gomez, G.; Gonzalez-Diaz, H. First Computational Chemistry Multi-target Model for Anti-Alzheimer, Anti-parasitic, Anti-fungi, and Anti-bacterial Activity of GSK-3 Inhibitors In Vitro, In Vivo, and In Different Cellular Lines. Mol. Divers. 2011, 15, 561-567. 28. Pratim Roy, P.; Paul, S.; Mitra, I.; Roy, K. On Two Novel Parameters for Validation of Predictive QSAR Models. Molecules 2009, 14, 1660-1701. 29. Golbraikh, A.; Tropsha, A. Beware of q2! J. Mol. Graph. Model. 2002, 20, 269-76. 30. Simón-Vidal L, García-Calvo O, Oteo U, Arrasate S, Lete E, Sotomayor N, González-Díaz H. Perturbation-Theory and Machine Learning (PTML) Model for High-Throughput Screening of Parham Reactions: Experimental and Theoretical Studies. J. Chem. Inf. Model. 2018, 58(7):1384-1396. 31. Golub, Gene; Charles F. Van Loan. Matrix Computations – Third Edition. The Johns Hopkins University Press: Baltimore, 1996; p. 728.


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Perturbation TheoryâMachine Learning Study of Zeolite Materials

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