Development of a group contribution method for estimating the thermal decomposition temperature of ionic liquids

Fluid Phase Equilibria 355 (2013) 81–86

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Development of a group contribution method for estimating the thermal decomposition temperature of ionic liquids Farhad Gharagheizi a , Poorandokht Ilani-Kashkouli a , Amir H. Mohammadi a,b,∗ , Deresh Ramjugernath a,∗∗ , Dominique Richon a,c a Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa b Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France c Department of Biotechnology and Chemical Technology, School of Science and Technology, Aalto University, P.O. Box 16100, 00076 Aalto, Finland

a r t i c l e

i n f o

Article history: Received 30 January 2013 Received in revised form 22 June 2013 Accepted 28 June 2013 Available online 8 July 2013 Keywords: Thermal decomposition temperature Ionic liquid (ILs) Group contribution Reliable model Dataset

a b s t r a c t In this communication, a reliable group contribution (GC) method is presented for the estimation of the thermal decomposition temperature (Td ) of ionic liquids. A dataset comprising experimental Td data for 613 ionic liquids (ILs) that covers a temperature range from 374 to 740 K was collated from various literature sources. Approximately 80% of the dataset (Td data for 489 ILs) was used to develop the model and the remaining 20% (Td data for 124 ILs) was implemented to evaluate the predictive capability of the obtained model. The method uses a total of 30 substructures or structural functional groups to estimate the Td . In order to distinguish the effects of the anion and cation on the Td , 10 sub-structures related to the chemical structure of the anion, and 20 substructures related to the chemical structure of the cation were implemented. The results of this method show an average relative deviation (AARD%) of about 4.4% from dataset values. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Ionic liquids (ILs) are special salts, which are typically liquid below the normal boiling point of water or in case of room temperature ILs, below room temperature. These ILs which are entirely composed of ions generally consist of a combination of a large organic cation with smaller sized and more symmetrical anion. Their most important characteristic is that their properties can be significantly manipulated for any particular application by changing their combination of anion and cation. This latter attribute makes them “designable materials” [1,2]. In order to design a new IL, one of the first steps requires the estimation of the elementary physico-chemical properties of the substance. One of the most significant properties of ILs, which determines their processing temperature range, is their liquidus range which is bounded by their normal melting temperature (Tm ) as the lower limit and their thermal decomposition temperature (Td ) as the upper limit of temperature. Although the Tm of ILs has been carefully studied and numerous models have been suggested

∗ Corresponding author at: Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France. ∗∗ Corresponding author. E-mail addresses: [email protected], amir h [email protected] (A.H. Mohammadi), [email protected] (D. Ramjugernath). 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.06.054

to date for its prediction [3–16], Td has not been appropriately investigated and only two models have been recently proposed for its estimation [17,18]. One of the estimation methods mentioned above, which was developed by Lazuss [17], is a group contribution method (GC). The model is based on a dataset containing 198 experimental Td data for correlation and prediction (120 data points for developing the model and tuning the model parameters, and the remaining 78 for its validation). Using a combination of a genetic algorithm as an optimizer method and least square error as an objective function, the method introduced a collection of 58 sub-structures (27 cationbased and 31 anion-based) to estimate the Td . The average absolute relative deviations of the model results from experimental data for the correlation set and the prediction set were calculated as 4.3% and 4.2%, respectively. The second estimation method which was proposed by Yan et al. [18] is a quantitative structure–property relationship (QSPR) model using a dataset of 158 experimental Td data (126 data points for developing the model and tuning the model parameters, and the remaining 32 values for its validation). The average absolute relative deviations of this 25-parameter model from experimental data for the training set and the test set were approximated as 3.1% and 3.5%, respectively. In addition to reviewing the estimation methods available for Td , an extensive literature survey undertaken during this study

F. Gharagheizi et al. / Fluid Phase Equilibria 355 (2013) 81–86

revealed that the available experimental Td data in the literature was considerably more than those used in the aforementioned studies. Consequently, as part of this study an extensive data collection exercise was conducted to collate a comprehensive experimental Td database which would aid in the development of a more general model for the prediction of Td of ILs. Since, GC methods have proved their capability in accurate estimation of various physical properties [16,19], this method was employed in this estimation study. 2. Methodology

1 Training set Test set

0.9 0.8 0.7 The mean distance

82

0.6 0.5 0.4 0.3

2.1. Data preparation 0.2

A database of experimental Td data for 613 ILs was collected from open literature. In order to assess the quality of the data when comparing them in case of multiple reported data, their experimental reported uncertainties were considered. The ILs within the dataset were categorized into 20 groups containing 1,3-dialkyl imidazolium, 1-alkyl imidazolium, amino acids, ammonium, double imidazolium, guanidinium, morpholinium, oxazolidinium, phosphonium, piperidinium, pyridazinium, pyridinium, pyrrolidinium, quinary alkyl imidazolium, sulfonium, tetra-alkyl imidazolium, tetrazolium, tri-alkyl imidazolium, triazolium, and uronium. The information about the names, abbreviations, and the original reference for each data point are presented as supplementary materials. It should be noted that the ILs within the gathered database comprise 58 anions and 313 cations. The chemical structures of the anions and cations are also presented as supplementary materials. Before moving to the next step, namely, developing the model, the dataset should be divided into two sub-datasets; one for developing the model (training set), and the other one for its testing (test set). The division of the data can be performed randomly; however, this may lead to an inappropriate allocation of compounds to each sub-dataset. In other words, all of the larger Td values might end up in the test set. As a result, it would be of great interest if we could split the main dataset so that both the training set and the test set are uniform and have almost the same ranges and means. In order to take the aforementioned points into account, the K-means clustering technique was used to split the dataset into two subdatasets [20,21]. This technique is used to partition a dataset into k sub-datasets in which each data belongs to the cluster with the nearest mean. As a result, nearly 20% of the data (124 data points) were kept out to test the model [22]. The remaining data (489 data points) were implemented for the model development. 2.2. Development of a new group contribution model To develop a reliable GC model, the chemical structures of all the ILs were examined thoroughly to find out the most efficient sub-structures for the estimation of the Td . In order to improve the understanding of the effects of anions and cations on the Td , the contributions of anions and cations were independently investigated. Therefore, in total 30 chemical sub-structures (10 for anions and 20 for cations) were found to be most efficient for the prediction of the Td of ILs. The sub-structures were used, in addition to their number of occurrences in chemical structures of anions and cations for each IL, as the model parameters. They are presented as supplementary materials. To ensure the diversity of ILs present in both the training and test sets, a diversity test was conducted in this study [23]. There are many approaches to measure diversity, owing to its many definitions. In this study, the Euclidean distance approach was applied to measure the diversity of the ILs studied. In this approach, each IL

0.1 0 350

400

450

500

550 Td

exp

600

650

700

750

/K

Fig. 1. Diversity of training and test sets.

(Xi ) is described by a vector of corresponding sub-structures incorporating both anion and cation (xim ) as its elements where m is number of all total substructures: Xi = (xi1 , xi2 , xi3 , ..., xim )

(1)

The distance between two different ILs (dij ) is defined as follows:

  m    dij = Xi − Xj  =  (xik − xjk )2

(2)

k=1

Next, the mean distance of one sample to the remaining ones (di ) is calculated as follows:

n di =

d j=1 i,j

n−1

(3)

where n refers to number of all ILs. Then, the calculated mean distances are normalized according to following definition:

di

Norm

=

di − dmin dmax − dmin

(4)

diNorm indicates the structural diversity of ILs (i) in comparison to others. Fig. 1 presents the values of the diversity test for both the test and training sets.

2.3. Optimization of group contributions In order to generate the GC model, the Td of ILs should be correlated using the aforementioned parameters. The conventional method for this purpose is the assumption of an existence of a multi-linear relationship between these groups and the desired property (here the Td of ILs). This technique is conventionally used to develop most of the GC methods [16,24]. As a result, the collection of 30 sub-structures is introduced to develop the model (input parameters). To calculate the contribution of these parameters, the well-known least square method is employed.

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Table 1 The group contributions. No

GC

Chemical structure

Td0

–

Comment

GC value 524.5031

−30.7764

1

Tda1

Number of ketones (aliphatic)

2

Tda2

Number of nitro groups (aromatic) Al = aromatic group linked through carbon

13.62521

3

Tda3

Number of sulfonates (thio-/dithio-) Y = O or S

28.5994

−12.4228 48.86072 −68.3122 −27.5444 −2.00812 11.85731 14.33442

4 5 6 7 8 9 10

Tda4 Tda5 Tda6 Tda7 Tda8 Tda9 Tda10

CH3 R or CH4 CHX3 CHR R C( X) X or R C#X or X C X Ha attached to C1 (sp3) or C0 (sp2) O Fa attached to C2 (sp2) C4 (sp2) or 1 C (sp) or C4 (sp3) or X

11

Tdc1

12

Tdc2

13

Tdc3

19.0942

14

Tdc4

34.18349

15

Tdc5

Sum of the hydrogens linked to all of the Os and Ns in the molecule

16 17 18 19 20 21

Tdc6 Tdc7 Tdc8 Tdc9 Tdc10 Tdc11

CH2 X2 CH2 CHR R–CH–R X–CX–X R C( X) X or R C#X or X C X

Number of ring tertiary C(sp3) Y = H or any heteroatom

−84.9426

−75.4884

C CH2 X

Number of donor atoms for H-bonds (N and O)

−10.0274

−16.6531 −17.2874 −25.5953 −11.4046 −95.7805 −11.1804

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Table 1 (Continued) No

GC

Chemical structure

22 23 24 25 26 27 28 29 30

Tdc12 Tdc13 Tdc14 Tdc15 Tdc16 Tdc17 Tdc18 Tdc19 Tdc20

X–CH..X H attached to alpha-Cb O O–c RCO N< or >N X X R#N or R N R- -N- -Rd or R- -N- -X Fa attached to C1 (sp3) R2 S or RS SR

Comment

GC value 19.02173 9.677203 −37.5977 −27.8545 −41.5379 −48.2145 −27.1901 38.92751 −23.6962

R represents any group linked through carbon; X represents any electronegative atom (O, N, S, P, Se, halogens); Al and Ar represent aliphatic and aromatic groups, respectively; represents a double bond; # represents a triple bond; - - represents an aromatic bond as in benzene or delocalized bonds such as the N O bond in a nitro group; .. represents aromatic single bonds as the C N bond in pyrrole. a The superscript represents the formal oxidation number. b An alpha-C may be defined as a C attached through a single bond with C X, C#X, C–X. c As in nitro, N-oxides. d Pyridine-type structure.

According to the aforementioned procedure, the contribution of each of the 30 sub-structures was determined using the training set. The proposed model for estimation of the Td of ILs is as follows: Td =

10 

Nai Tdai +

20 

i=1

Nci Tdci + Td0

(5)

i=1

where Nai , Nci , Tdai , Tdci , and Td0 are, respectively, the number of occurrence of ith sub-structure of anions and cations, the Table 2 The statistical parameters of the developed model for the training, the test, and the total datasets. Statistical parameter

0.851 4.5 31.86 32.05 489

Test set R2 Average absolute relative deviation Standard deviation error Root mean square error Ne

0.857 4.3 31.05 31.17 124

Total R2 Average absolute relative deviation Standard deviation error Root mean square error N

0.852 4.4 31.67 31.87 613

i

b

%AARD =

100 N

(Calc.(i)/Est.(i)−average(exp .(i)))

N 

2

.

|Calc.(i)/Est.(i)−exp .(i)| . exp .(i)

c

Std =

1 N

 N

Calc.(i) Est.(i)

− average

Calc.(i)

2

i

d

RMSE =

i=1

(Calc(i)/Est.(i)−exp(i))2 N

700 650 600 550 500 450

i

N  

750

Td

a

N (Calc.(i)/Est.(i)−exp .(i))2 R2 = 1 − N i

800

pred

Training set R2 a Average absolute deviationb Standard deviation errorc Root mean square errord Ne

contribution of the ith sub-structure of anions and cations, and the intercept of Eq. (5). The computed group contributions, namely Tdai , Tdci , and Td0 , are presented in Table 1. The predicted Td values and their absolute relative deviations from experimental values are presented as supplementary materials. The statistical parameters of the model are presented in Table 2. As can be seen, the experimental Td data are well described using this GC method. The average AARD% of the model results from experimental values for the training set and the test are 4.5% and 4.3%, respectively. The model results show an AARD% of 4.4% from experimental Td values for the 613 ILs. Among all the ILs studied, tricaprylmethylammonium benzoatetrifluoromethyltrifluoroborate, with approximately 15%, shows the maximum AARD%. The deviation of the model results from experimental data for different chemical classes of ILs is presented in Table 3. As can be observed, the highest AARD% values are related to tetrazolium and tetra-alkyl imidazolium ILs. This may be due to the small number of ILs within this classes that cannot efficiently tune the model to predict their Td well. The predicted Td values in comparison with their corresponding experimental values are depicted in Fig. 2. Additionally, the relative

/K

3. Results and discussion

Est.(i)

400 .

1/2 .

350 300 300

Training set Test set 400

500

600 T

d

e N: number of data points in each sub-dataset (the training, the test, and the total sets).

exp

700

/K

Fig. 2. Comparison between the experimental and predicted Td of ILs.

800

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85

Table 3 The average absolute relative deviation (%AARD) of the model results from experimental Td data for each IL; the temperature range and the experimental and predicted Td rages, in addition to the number of experimental data for each IL (N ) for each IL. No.

Family

%AARD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1,3-Dialkyl imidazolium 1-Alkyl imidazolium Amino acids Ammonium Double imidazolium Guanidinium Morpholinium Oxazolidinium Phosphonium Piperidinium Pyridazinium Pyridinium Pyrrolidinium Quinary alkyl imidazolium Sulfonium Tetra-alkyl imidazolium Tetrazolium Tri-alkyl imidazolium Triazolium Uronium

4.8 2.9 4.1 4.8 3.8 5.1 4.3 4.0 3.5 4.5 1.2 1.8 5.5 1.1 1.4 6.6 8.0 5.4 4.5 1.8

AARD% range 0.0–14.8 0.1–7.7 0.0–12.7 0.0–14.9 0.3–8.4 1.0–10.7 0.2–14.5 0.3–11.3 0.5–13.0 0.0–13.9 1.2–1.2 0.3–4.3 0.2–12.3 0.4–2.3 0.8–2.3 3.0–11.5 2.8–13.7 0.7–14.5 0.0–13.5 1.8–1.8

15 10 Relative deviation %

436.15–725.15 461.15–686.15 392.15–514.15 374.15–693.15 508.15–715.15 463.15–587.15 413.15–685.15 446.15–620.15 457.15–693.15 473.15–696.15 573.15–573.15 500.35–677.00 523.15–690.15 606.15–739.15 449.15–456.15 439.15–580.15 455.15–588.15 526.15–730.19 382.15–698.15 493.15–493.15

Td pred range 389.35–735.58 478.63–664.69 399.53–541.68 387.22–724.66 512.00–693.38 469.41–560.07 417.61–657.94 451.91–641.29 464.56–657.94 469.41–657.94 579.86–579.86 494.36–664.93 550.85–657.94 603.50–742.80 445.72–445.72 489.73–599.23 452.88–507.54 479.72–684.73 393.36–647.91 484.43–484.43

N 96 42 32 139 28 16 32 18 22 18 2 5 20 3 8 6 3 31 91 1

general group contribution model. A collection of 30 chemical substructures was implemented as model inputs from which 10 were anion-based, and the other 20 were cation-based. Using this model, a training set comprised of 489 data points was correlated with a low AARD of 4.5%. A test set consisting of 124 data points was employed to test its capability. The model shows an AARD of 4.3% for the test set. As a result, the model proposed here is reliable and may be conveniently used to predict the thermal decomposition temperature of ILs.

20

5 0

Acknowledgements

−5

This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation.

−10 −15 −20 300

Td exp range

Training set Test set 400

500

600 Td

exp

700

800

Appendix A. Supplementary data

/K

Fig. 3. Relative deviation of the model from the experimental Td data.

deviation of the model results from experimental data is shown in Fig. 3. A comparison between the proposed model and those recently presented in literature indicates that the database used in this study (613 ILs) is much more comprehensive than those previously implemented by Lazuss [17] (198 ILs) and Yan et al. [18] (158 ILs). Furthermore, the number of parameters used in the model (30 molecular descriptors) is much lower than those of Lazuss [17] (58 GCs) and very close to that of Yan et al. [18] (25 molecular descriptors). Of course, counting GCs is much simpler than computation of molecular descriptors that needs at least elementary knowledge of molecular simulation. Therefore, the model may be superior to the previous models. Thus, the model is predictive (within 4.4%) and may be conveniently used to predict the Td of ILs. 4. Conclusion A group contribution method has been successfully developed for estimation of the thermal decomposition temperature of ILs. A comprehensive dataset of experimental Td data for 613 ILs consisting of 58 anions and 313 cations were used to develop a

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