A Group Contribution Method for the Thermal Properties of Ionic

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A Group Contribution Method for the Thermal Properties of Ionic Liquids Johannes Albert, and Karsten Müller Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie503366p • Publication Date (Web): 13 Oct 2014 Downloaded from http://pubs.acs.org on October 20, 2014

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Industrial & Engineering Chemistry Research

A Group Contribution Method for the Thermal Properties of Ionic Liquids Johannes Albert, Karsten Müller* Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Institute of Separation Science and Technology, Egerlandstr. 3, 91058 Erlangen, Germany *To whom correspondence should be addressed: Karsten Müller ([email protected], Tel: +49 9131 8527455) KEYWORDS: Ionic Liquids, thermal conductivity, heat capacity, group contribution method, QSPR

ABSTRACT Missing substance properties can become a limiting factor in research and process design. Especially for Ionic Liquids experimental data are often not available and measurement is expensive and time consuming. To cope with this issue an estimation scheme for the heat capacity and the thermal conductivity of Ionic Liquids has been developed. To achieve a wide range of application first order group contributions have been chosen to describe the molecular structure of the ions. 2419 experimental heat capacity data points for 106 ILs have been used in two separate subsets for parameter fitting and testing to allow for a reliable external validation. In case of thermal conductivity 372 data points for 39 Ionic Liquids have been processed analogously. The data for Ionic Liquids from the subset not used for the fitting could be reproduced with a mean absolute error of 5.4 % in case of heat capacity and of 8.1 % in case of thermal conductivity. Using these estimation schemes it is possible to screen a huge number of potential combinations of cations and anions to find candidates suited best for a specific task before performing the experimental measurement.

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Introduction

Ionic Liquids (ILs) show great potential as tailor made solvents for many applications. 1-3 Especially the possibility to adjust their properties to the requirements of a process by combination of cation and anion principally opens a wide field of applications. To be able to profit from this feature one needs to know the properties of the ILs created by these combinations to tailor a solvent for the specific needs of a process. However, due to the incredibly high number of possible combinations experimental data are always only available for a small share of the ILs. Hence, it is necessary to have ways to determine the properties in a fast and reliable way. Solubility as a property of major importance in most applications of ILs can be estimated using models such as COSMO-RS 4 or UNIFAC 5. Data for the thermal conductivity and heat capacity are crucial for the design of many thermal processes. A number of approaches for the estimation of these properties have been published in recent years, but all of them suffer from at least one of the following drawbacks: limited application range, insufficient accuracy or huge calculation effort. Quantum chemical models as well as neuronal networks could be used, but accuracy is usually not high enough to justify the high calculation time. Furthermore, the results obtained from quantum chemistry are often only for the gas phase, which is of limited interest for ILs. The most useful techniques for property estimation can be classified into two basic types: 1. correlation with other properties and 2. methods using descriptors for the molecular structure. A correlation of the thermal conductivity to density and molar mass is an example for the first type. 6 However, the major drawback of this type of approach is the necessity to know the data for the other properties. Since experimental data for these properties are often not available (or at least not for all ILs under consideration), it is desired to access the wanted property simply based on the ions and their molecular structure. Some work groups 7-9 that used estimation schemes based on correlations with the critical data of the IL tried to obtain the critical temperature and pressure from the molecular structure using group contribution methods such as the one by Joback and Reid 10. Yet, this additional estimation step causes further calculation effort and uncertainty. Molecular descriptors that directly aim at the wanted property are therefore the most promising way. Descriptors containing much information about the ions can generally yield


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higher accuracy than descriptors containing less information. The maximum information about the ion is reached using the ion itself as the descriptor (i.e. one contribution to the property for each ion as in

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). For the heat capacity of ILs we recently developed such a method. 12

Nevertheless, the high accuracy is achieved at the cost of range of application. Only ILs consisting of the parameterized ions can be treated using such a method. Gardas and Coutinho tried to overcome this limitation by introducing additional molecular descriptors accounting for alkyl chains attached to the ions. 13, 14 The application range can thus be expanded, but due to the small number of parameterized basic ion types still stays rather small. To overcome the restrictions caused by the use of such descriptors it seems reasonable to describe the molecular structure of the ions based on the structural groups constituting them. Using such group contributions a huge number of ions can be described, while keeping most of the information about the ion. In this work we present a first order group contribution method for the heat capacity and thermal conductivity of ILs.

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Model development

Experimental data of ILs have been collected using the NIST Standard Reference Database #147 15, 16. To allow for a reliable parameterization data with an uncertainty higher than 10 % (for a level of confidence of 95 %) as well as non-experimental data have not been added to our database. If more than one source was available the data have been checked for consistency and inconsistent data have been removed. Heat capacity data for 106 ILs in their liquid state with a total of 2419 data points at different temperatures have been gathered. Concerning the thermal conductivity less data have been available. So data for 39 ILs in their liquid state with a total of 372 data points have been collected here. The data points covered a temperature range from 190 K to 663.1 K for heat capacity and from 273.15 K to 390 K for thermal conductivity. The parameter fitting has been done by nonlinear least-square minimization. 17 To be able to not only check the accuracy of the reproduction of the data used for the parameter fitting, but also to test the predictive quality of the model for unknown substances, each of the data bases has been split into two subset. The training set, containing the majority of the data points, was used to calculate the parameters. However, if only the training set would have been used no reliable testing of the correlation would be possible. 18 Hence, one part of the data points (representing


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about 20 % of the ILs) has been assigned to the test set. This subset only contained data for ILs not present in the training set and was used to evaluate the validity of extrapolation to unknown ILs. Heat capacity and thermal conductivity both are temperature dependent properties. To determine the best-suited function for describing this dependency different equations have been compared in a cross validation. The equations yielding the lowest error have been selected. Polynomial functions with a degree of two and one respectively proved to be suited best for describing this dependency: , = + + + ∙ + + ∙ ²

(1)

and = + − + ∙ .

(2)

The parameters A, B and C are calculated from the contributions of the structural groups constituting the respective ion: =

with

!

∑= ∙ +

(3)

being the number of occurrences of the specific group in the ion and "! being the

contribution of the group. is an additional contribution accounting for the type of ion or the structure of rings (e.g. for 1,2-diethylpyridinium the correction heteroatom (aromatic) would be applied once). Parameter B and C are calculated analogously. The values for the group contributions can be found in the supporting information. The method is demonstrated on the example of N,N-dibutyl-N-methyl-1-butanaminium L-threoninate [N4,4,4,1][Thr] (an IL from the test sets for both properties). The combined parameter + for the heat capacity can be calculated as + = #$ + % ∙ &' + ( ∙ &) + ) ∙ & + *& + ** + #&) = +)). -. / ∙ 0+ ∙ 10+

Correspondingly the combined parameters B and C is calculated as + = '. %'23 / ∙ −+ ∙ 1−)

and + = −-. --34'.4 / ∙ −+ ∙ 1−' . The temperature

dependent heat capacity for [N4,4,4,1][Thr] is therefore estimated as = +)). -. / ∙ −+ ∙ 1−+ + '. %'23 / ∙ −+ ∙ 1−) ∙ + −-. --34'.4 / ∙ −+ ∙ 1−' ∙ ².


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At 298.15 K a heat capacity of 746.4 J mol-1 K-1 is obtained (compared to an experimental value of 753 J mol-1 K-1 19; i.e. a deviation of 0.9 %). The analogous procedure for thermal conductivity yields = -. +4''(' 5 ∙ 0+ ∙ 10+ − +. -)2+ ∙ +-03 5 ∙ 0+ ∙ 10) ∙ .

At 298.15 K a thermal conductivity of 0.1528 W m-1 K-1 is obtained (compared to an experimental value of 0.160 W m-1 K-1 19; i.e. a deviation of 4.5 %).

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Results and discussion

Heat capacity The heat capacity data have been split into a training set with 86 ILs covering 2210 data points and a test set with 20 ILs covering 209 data points. The data used for the parameter fitting (i.e. from the training set) could be reproduced with a mean absolute deviation of 2.58 % (compare table 1). As expected the deviation from the experimental values is higher for unknown substances (5.44 % for the test set), but still within the maximum uncertainty of the experimental data. Since experimental uncertainty and estimation error in worst case can add up it is insufficient to just look at the deviation between experimental and estimated data. The accuracy of an estimation tool can be evaluated by an error propagation combining both errors. A combined experimental and predictive uncertainty of 7.58 % for data points not used in the fitting was reached. This value can be assumed as the mean actual accuracy of the proposed group contribution method. (The mathematical definition of the error types is given as supporting information). table 1: Errors for the estimation of the heat capacity using the proposed method

test set

training set

absolute average error (AAE) * / J mol-1 K-1

30.9

14.6

absolute average percentage error (AAPE) /%

5.44

2.58

root mean square deviation (RMSD) * / J mol-1 K-1

47.0

36.0


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coefficient of determination (R²) /-

0.94

0.98

combined experimental and predictive uncertainty (CEPU) / %

7.58

5.19

* Compared to a mean value of 569 J mol-1 K-1 in the training set and 524 J mol-1 K-1 in the test set

The estimation for the majority of the heat capacity data was close to the experimental data (figure 1), but some outliers have to be noted. Within the training set the biggest error is observed for 1-methyl-3-octylimidazolium chloride. However, the deviances examined in the test set were usually higher. 1-hexyl-3-methylimidazolium dicyanamide ([C6mim][Dca]) showed the highest deviation followed by tetrabutylphosphonium L-lysinate ([P4,4,4,4][Lys]) and N,N-dibutylN-methyl-1-butanaminium 2-aminoethanesulfonate ([N4,4,4,1][Tau]). It should be considered in this context that the experimental data for the latter two exhibited uncertainties close to the maximum allowed in the data base (10 %). Their deviation to the experimental value was 15.5 % and 13.2 %. Taking the error bars into account the deviation is within the average error range observed for the test set. Concluding on the performance of the method on specific substance classes is therefore not meaningful.

figure 1: Estimated heat capacities versus experimental data for the training set (a) and the test set (b)

Data points for temperatures up to 663.1 K have been used for the parameter fitting. Hence, the parameters should be suited for estimations up to this temperature. Nevertheless, above about 420 K the number of data points in the test set was rather small. Therefore, the use of the method


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is only recommended up to 420 K, since external validation above this temperature is not granted. A comparison to approaches found in the literature is shown in figure 2 (a temperature of 293 K was chosen since most experimental data were available for this temperature). The model of Soriano et al. 11 gives the best value for two of the nine ILs under consideration, but does not work on two third of the substances. Gardas and Coutinho 13 reach the best results for one IL, but cannot be applied to the other eight. Besides the proposed method only that of Sattari et al. 20, Ge et al. 9 and Valderrama et al. 21 work on all nine ILs. The mean absolute error on these nine ILs was 6.88 % for the proposed method compared to 7.6 %, 9.0 % and 10.2 %, respectively for the methods from literature. From the methods that work on all ILs the proposed one reached the best result on five of these ILs, Sattari et al. for three, Ge et al. for one and Valderrama et al. for none of them.

figure 2: Comparison of the proposed method for the heat capacity at 293 K to models found in the literature

Thermal conductivity Due to the limited data availability concerning thermal conductivity the training and test set are smaller than for the heat capacity evaluation. The data have been split into a training set with 32 ILs covering 316 data points and a test set with 7 ILs covering 59 data points. The data used for the parameter fitting could be reproduced with a mean absolute deviation of 2.49 % (compare table 2). Again the deviation from the experimental values is higher for unknown substances (8.09 % for the test set), but still within the maximum uncertainty of the experimental data.


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The accuracy of the estimation was further evaluated by an error propagation to combine the experimental and the estimation errors. A combined uncertainty of 10.7 % for data points not used in the fitting was reached. This value should be assumed as the mean accuracy for this group contribution method. table 2: Errors for the estimation of the thermal conductivity using the proposed method

test set

training set

absolute average error (AAE) * / W m-1 K-1

0.0120

0.00373

absolute average percentage error (AAPE) /%

8.09

2.49

root mean square deviation (RMSD) * / W m-1 K-1

0.0158

0.00499

coefficient of determination (R²) /-

0.74

0.95

combined experimental and predictive uncertainty (CEPU) / %

10.7

5.22

* Compared to a mean value of 0.154 W m-1 K-1 in the training set and 0.162 W m-1 K-1 in the test set

The estimation of the thermal conductivity data did not yield significant outliers within the training set (figure 3). For the test set the deviation between experimental and estimated data was bigger in some cases. 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate ([C4MPyr][Fap]) showed the highest deviation followed by tetrabutylphosphonium L-serinate ([P4,4,4,4][Ser]) and 1-ethyl-3-methylimidazolium tetrafluoroborate ([C2mim][BF4]). Similar to the outliers for heat capacity some of the highest deviations occur on substances with rather high experimental uncertainties. Especially in case of [C4MPyr][Fap] one can further observe a namable dependency of prediction quality on temperature. Estimation is rather good at room temperature, but is getting poorer with increasing temperature.


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figure 3: Estimated thermal conductivities versus experimental data for the training set (a) and the test set (b)

Above about 350 K the test set contained only a small number of data points. Consequently, the application of the method is only recommended up to this temperature, since external validation beyond that point is not granted (even though the parameters are fitted up to 390 K). A number of possible ways to estimate the thermal conductivity of ILs can be found in the literature, but most of them can only be applied to a small share of the ILs 7, 14, 22 (figure 4). The correlation proposed by Fröba et al. 6 was applicable to all six ILs for which experimental data at 303.15 K were available (303.15 K was the temperature with the highest number of experimental data points for thermal conductivity). However, besides its dependency on density data as additional input parameter the accuracy was rather low (mean error of 9.0 %). From the models applicable to all six ILs, the model of Wu et al. 8 gave the best result for four of the six ILs and that proposed in this work two. The absolute average percentage error of 0.7 % on these six compounds for Wu et al. was lower than that for this work (4.2 %), but is has to be kept in mind that all six ILs have been used in the parameter fitting by Wu et al..


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figure 4: Comparison of the proposed method for the thermal conductivity at 303.15 K to models found in the literature

Despite the rather good performance of the estimation, one should keep in mind that the data base for thermal conductivity was significantly smaller than for heat capacity. As a consequence the training set was also smaller and the parameters thus fitted to less data points. Furthermore, and maybe more important, the test set contained only 7 ILs with 56 data points. The validation based on the test set therefore supports reliability of the method, but complete confidence cannot be achieved with the number of data currently available.

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Conclusion

An incremental method for the estimation of thermal properties of ILs was developed and externally validated. First order groups have been used as molecular descriptors to describe the ions. This allows for a wide range of application and high accuracy at the same time. Experimental heat capacity data for 106 ILs and thermal conductivity data for 39 ILs have been collected and used for the development. A maximum experimental uncertainty of 10 % was allowed in the data base. Extrapolation to unknown experimental data could be done with a mean absolute deviation of 5.4 % for the heat capacity and of 8.1 % for the thermal conductivity. An error propagation in the test set taking experimental and estimation uncertainty into account gave combined uncertainties of 7.6 % and 10.7 %, respectively. Acknowledgments The authors wish to thank Prof. Wolfgang Arlt for valuable discussion. Supporting Information Available


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The contributions of the groups and a complete list of the ILs studied as well as a definition of the errors used is presented as supplementary information. This information is available free of charge via the Internet at http://pubs.acs.org/

References (1) Seiler, M.; Jork, C.; Kavarnou, A.; Arlt, W.; Hirsch, R. Separation of azeotropic mixtures using hyperbranched polymers or ionic liquids. AIChE Journal 2004, 50, (10), 2439-2454. (2) Predel, T.; Schlücker, E.; Wasserscheid, P.; Gerhard, D.; Arlt, W. Ionic Liquids as Operating Fluids in High Pressure Applications. Chemical Engineering & Technology 2007, 30, (11), 1475-1480. (3) Preißinger, M.; Pöllinger, S.; Brüggemann, D. Ionic liquid based absorption chillers for usage of low grade waste heat in industry. International Journal of Energy Research 2013, 37, (11), 1382-1388. (4) Völkl, J.; Müller, K.; Mokrushina, L.; Arlt, W. A Priori Property Estimation of Physical and Reactive CO2 Absorbents. Chemical Engineering & Technology 2012, 35, (3), 579-583. (5) Kato, R.; Gmehling, J. Systems with ionic liquids: Measurement of VLE and γ∞ data and prediction of their thermodynamic behavior using original UNIFAC, mod. UNIFAC(Do) and COSMO-RS(Ol). The Journal of Chemical Thermodynamics 2005, 37, (6), 603-619. (6) Fröba, A. P.; Rausch, M. H.; Krzeminski, K.; Assenbaum, D.; Wasserscheid, P.; Leipertz, A. Thermal Conductivity of Ionic Liquids: Measurement and Prediction. International Journal of Thermophysics 2010, 31, (11-12), 2059-2077. (7) Huang, Y.; Dong, H.; Zhang, X.; Li, C.; Zhang, S. A new fragment contributioncorresponding states method for physicochemical properties prediction of ionic liquids. AIChE Journal 2013, 59, (4), 1348-1359. (8) Wu, K.-J.; Zhao, C.-X.; He, C.-H. Development of a group contribution method for determination of thermal conductivity of ionic liquids. Fluid Phase Equilibria 2013, 339, (0), 1014. (9) Ge, R.; Hardacre, C.; Jacquemin, J.; Nancarrow, P.; Rooney, D. W. Heat Capacities of Ionic Liquids as a Function of Temperature at 0.1 MPa. Measurement and Prediction. Journal of Chemical & Engineering Data 2008, 53, (9), 2148-2153. (10) Joback, K. G.; Reid, R. C. ESTIMATION OF PURE-COMPONENT PROPERTIES FROM GROUP-CONTRIBUTIONS. Chemical Engineering Communications 1987, 57, (1-6), 233-243. (11) Soriano, A. N.; Agapito, A. M.; Lagumbay, L. J. L. I.; Caparanga, A. R.; Li, M.-H. A simple approach to predict molar heat capacity of ionic liquids using group-additivity method. Journal of the Taiwan Institute of Chemical Engineers 2010, 41, (3), 307-314. (12) Müller, K.; Albert, J. Contribution of the Individual Ions to the Heat Capacity of Ionic Liquids. Industrial & Engineering Chemistry Research 2014, 53, (25), 10343-10346. (13) Gardas, R. L.; Coutinho, J. A. P. A Group Contribution Method for Heat Capacity Estimation of Ionic Liquids. Industrial & Engineering Chemistry Research 2008, 47, (15), 57515757.


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(14) Gardas, R. L.; Coutinho, J. A. P. Group contribution methods for the prediction of thermophysical and transport properties of ionic liquids. AIChE Journal 2009, 55, (5), 12741290. (15) Kazakov, A.; Magee, J. W.; Chirico, R. D.; Diky, V.; Muzny, C. D.; Kroenlein, K.; Frenkel, M. "NIST Standard Reference Database 147: NIST Ionic Liquids Database (ILThermo)", Version 2.0,. http://ilthermo.boulder.nist.gov (16) Dong, Q.; Muzny, C. D.; Kazakov, A.; Diky, V.; Magee, J. W.; Widegren, J. A.; Chirico, R. D.; Marsh, K. N.; Frenkel, M. ILThermo: A Free-Access Web Database for Thermodynamic Properties of Ionic Liquids. Journal of Chemical & Engineering Data 2007, 52, (4), 1151-1159. (17) Seber, G. A. F.; Wild, C. J. Nonlinear Regression. Wiley: 2003. (18) Gramatica, P. Principles of QSAR models validation: internal and external. QSAR & Combinatorial Science 2007, 26, (5), 694-701. (19) Gardas, R. L.; Ge, R.; Goodrich, P.; Hardacre, C.; Hussain, A.; Rooney, D. W. Thermophysical Properties of Amino Acid-Based Ionic Liquids. Journal of Chemical & Engineering Data 2009, 55, (4), 1505-1515. (20) Sattari, M.; Gharagheizi, F.; Ilani-Kashkouli, P.; Mohammadi, A.; Ramjugernath, D. Development of a group contribution method for the estimation of heat capacities of ionic liquids. Journal of Thermal Analysis and Calorimetry 2014, 115, (2), 1863-1882. (21) Valderrama, J. O.; Toro, A.; Rojas, R. E. Prediction of the heat capacity of ionic liquids using the mass connectivity index and a group contribution method. The Journal of Chemical Thermodynamics 2011, 43, (7), 1068-1073. (22) Shojaee, S. A.; Farzam, S.; Hezave, A. Z.; Lashkarbolooki, M.; Ayatollahi, S. A new correlation for estimating thermal conductivity of pure ionic liquids. Fluid Phase Equilibria 2013, 354, (0), 199-206.


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figure 1a Estimated heat capacities versus experimental data for the training set (a) and the test set (b) 58x53mm (300 x 300 DPI)



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figure 1b Estimated heat capacities versus experimental data for the training set (a) and the test set (b) 58x53mm (300 x 300 DPI)


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figure 2 Comparison of the proposed method for the heat capacity at 293 K to models found in the literature 82x53mm (300 x 300 DPI)



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figure 3a Estimated thermal conductivities versus experimental data for the training set (a) and the test set (b) 57x53mm (300 x 300 DPI)


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figure 3b Estimated thermal conductivities versus experimental data for the training set (a) and the test set (b) 57x53mm (300 x 300 DPI)



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figure 4 Comparison of the proposed method for the thermal conductivity at 303.15 K to models found in the literature 82x53mm (300 x 300 DPI)


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A Group Contribution Method for the Thermal Properties of Ionic

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