Contribution of the Individual Ions to the Heat Capacity of Ionic Liquids

Article pubs.acs.org/IECR

Contribution of the Individual Ions to the Heat Capacity of Ionic Liquids Karsten Müller* and Johannes Albert Institute of Separation Science and Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Egerlandstr. 3, 91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Heat capacity is a crucial parameter for process design. Ionic liquids (ILs) offer the opportunity to tailor the relevant properties for many processes, but heat capacity data often are not available. In this work, temperature-dependent contributions to the heat capacity for 39 cations and 32 anions are proposed. A database containing 104 ILs with 2443 data points was used for the development of this model. The experimental data in the test set could be reproduced with a mean relative error of 4.4%. This allows for a systematic screening of a huge IL database to determine the solvent best-suited for a task without the necessity to measure all the missing data. Furthermore, an optimization taking different substance properties into account by using respective mathematical tools is possible by combination with prediction models for other properties.

1. INTRODUCTION Ionic liquids (IL) are a substance class that has drawn much attention, since their negligible vapor pressure and other properties make them interesting fluids for many applications. Options under consideration, among others, include their use as solvents for absorption heat pumps,1 CO2 removal from gas streams,2,3 and purification of biomaterials.4 One of the most interesting features of ILs is the opportunity to tailor their properties by combining different cations and anions to obtain an IL with optimized properties. A rather small number of different ions can be combined to form thousands of ILs, not considering mixtures containing more than one cation or anion, respectively. Because of this high number, it is challenging, if not impossible, to determine the IL best-suited for a task by pure experimental means. Even though the number of experimental data available in the literature has grown significantly in recent years, it is still far from comprehensive. Hence, a two-step screening is advisible: (i) “theoretical” screening of a list of potential ILs, and (ii) experimental validation. In the “theoretical” screening, the properties relevant for the respective process are estimated based on information available about the IL, such as the ions comprising it. For the selection of a solvent, a major criterion is the solubility of gases or other substances in the IL that can, e.g., be accessed predictively, using the model COSMO-RS.5,6 However, only optimizing the IL concerning solubility is insufficient for a tailor-made solvent, since other properties can have significant influence on the process performance. The heat capacity is a crucial parameter for the energy balance in all processes that include a change of the solvent temperature (e.g., absorption heat pumps or CO2 removal with chemisorption). Therefore, the assessment of this value is essential for a reasonable tailoring of the solvent properties. Many works have already been focused on estimating the heat capacity of ILs. Gardas and Coutinho7 estimated the heat capacity using contributions of the structural groups that © 2014 American Chemical Society

constitute the ions, as well as by a correlation with the molar volume. The prediction quality in their work seems to be higher for the method based on the structural groups. However, since the results were only compared to the data used for the fitting and not validated on a separate test set, no definite conclusion can be drawn. Ge et al.8 used the group contributions published by Joback and Reid9 to estimate the hypothetical gas-phase heat capacity of ILs, which are transferred to the liquid phase based on a corresponding state model. The critical parameters needed in this approach are also derived from the Joback and Reid model. The effort needed for this approach is greater than that needed for the pure group contribution method by Gardas and Coutinho,7 but the experimental values could be reproduced with a mean deviation of only ∼2.9%. A similar prediction quality has been achieved by Valderrama et al.,10 who fitted parameters for contributions of structural groups that are further corrected by a so-called mass connectivity index describing the degree of branching in the ion. The major drawback of all these models is the limited applicability due to missing parameters or rather small databases for the fitting and/ or testing of the methods. Sattari et al.11 tried to overcome the problem of limited applicability by developing a 16-parameter model. This model is based on a combination of contributions by atom numbers, ring types, and forms of bonds. The experimental data could be reproduced with a mean deviation of 1.7%. For a systematic search for the best combination of cation and anion, it would be desirable to have a simple model that gives the heat capacities of the individual ions. Soriano et al.12 analyzed 32 ILs to derive the heat capacities of 10 cations and 14 anions. The heat capacity contributions of the ions were able to describe the experimental heat capacities of the ILs pretty Received: Revised: Accepted: Published: 10343

April 17, 2014 May 24, 2014 May 30, 2014 May 30, 2014 dx.doi.org/10.1021/ie501575n | Ind. Eng. Chem. Res. 2014, 53, 10343−10346

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the charge balance, the sum of all xi and all xj each must be unity). The parameter fitting has been done on the training set, using the Levenberg−Marquardt algorithm for nonlinear leastsquares minimization.15

well. However, because of the limited number of ions, only 140 pure ILs can be described using this model. In order to make this approach usable for a higher number of ILs, we evaluated the heat capacities of 39 cations and 32 anions. Based on these data, the heat capacities of 1248 pure ILs can be calculated.

3. RESULTS AND DISCUSSION The estimation of the heat capacity is demonstrated using the example of 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([C4mim][CF3SO3]). The heat capacity of the cation can be calculated as

2. MODEL DEVELOPMENT The NIST Standard Reference database 14713,14 was used to gather heat capacity data for ILs. To allow for a reliable parametrization data with an uncertainty higher than 10% (for a level of confidence of 95%) were not used for our database. If data from different authors were available for one IL, they were only used if they were consistent. Otherwise, unreasonable data have been removed. Data for 104 ILs in their liquid state with 2443 experimental data points have been collected and split into a training set that is used for fitting the parameters and a test set that is used for validating the result. Eighty four (84) ILs have been assigned to the training set and 20 ILs to the test set. The temperature dependency of the heat capacity was described using a polynomial function. The degree of the equation was selected using cross validation. Thereby different degrees have been tested. A quadratic equation, as used by Soriano et al.,12 proved to be best-suited for this task (see Figure 1). Prediction quality using a constant or linear form is

cP,C4mim = 290.79 J/(mol K) − ⎡⎣0.84477 J/(mol K2)⎤⎦T + ⎡⎣1.89659 × 10−3 J/(mol K3)⎤⎦T 2

(3)

and that of the anion can be calculated as cP,CF3SO3 = −178.25 J/(mol K) + ⎡⎣2.12498 J/(mol K2)⎤⎦T − ⎡⎣2.65331 × 10−3 J/(mol K3)⎤⎦T 2 −1

(4) −1

At 313.15 K, a heat capacity of 212.2 J mol K is obtained for C4mim and a heat capacity of 227.0 J mol−1 K−1 is observed for CF3SO3. The heat capacity of the IL can thus be estimated as 439.2 J mol−1 K−1 (compared to an experimental value of 432.4 J mol−1 K−1)16 (i.e., a deviation of 1.6%). As expected, the molar heat capacity increases as the chain length of functional groups connected to the ion increases (for the example of 1-alkyl-3-methylimidazolium cations, see Figure 2). For different ions, the mean increase per additional CH2

Figure 1. Comparison of different degrees of polynomial functions and introduction of a logarithmic term for describing the temperature dependency (relative error from cross-validation). Figure 2. Heat capacities of different 1-alkyl-3-methylimidazolium cations (Cnmim) at 298.15 K.

rather poor, while a cubic equation did not yield a significant increase in prediction quality, compared to the quadratic form. Expanding a quadratic equation by a fourth parameter multiplied by the logarithm of temperature has been tested as well, but the prediction could not be improved considerably. Therefore, the heat capacity of the ions is described as cP,ion = A + BT + CT 2

group (n) in a side chain is 30.7 J mol−1 K−1 n−1 at 298.15 K (which is similar to the value of 32.17 J mol−1 K−1 n−1 observed by Paulechka17 for methylimidazolium-based ions). The experimental data in the training set could be reproduced with an absolute average error of 1.4%. However, to evaluate the suitability of the model for extrapolation to ILs not used for the parameter fitting, the errors for the test set are most meaningful. For the 209 data points for the 20 ILs in the test set, an absolute average error of 4.4% was observed (see Table 1). This deviation is within the accuracy range of the experimental data, for which a maximum uncertainty of 10% was allowed in our database. No distinct outliers have been observed (see Figure 3). The cation for which the biggest errors occur is 1-butyl-1methylpyrrolidinium (ILs containing this cation show a mean

(1)

The parameters for eq 1 are given as Supporting Information. The heat capacity of the IL is derived by summing the heat capacity contributions of the cation and the anion. If an IL contains more than one cation or anion, the heat capacity is calculated as cP ,IL = ∑i = cations xicP , i + Σj = anionsxjcP , j

(2)

with xi and xj being the molar shares of the cation or anion on all cations or anions, respectively (keep in mind that, because of 10344

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Table 1. Errors for the Estimation of Heat Capacities of ILs Using the Proposed Method training set absolute average percentage error combined uncertainty (experimental/ estimation) absolute average errora root-mean-square deviationa

test set

1.4% 4.2%

4.4% 7.2%

7.28 J mol−1 K−1 13.2 J mol−1 K−1

21.7 J mol−1 K−1 30.1 J mol−1 K−1

Compared to an average heat capacity of 564.1 J mol−1 K−1 within the database. a

deviation of 4.8%). The anion with the biggest error is dicyanamide (4.8%). The error propagation of the experimental uncertainty for the individual data points and the deviation between experimental and calculated values gives an overall error of 4.2% in the training set and 7.2% in the test set. Hence, the conclusion that the model yields an accuracy range for the estimation of unknown ILs within the maximum uncertainty range for the experimental data of 10% seems to be justified. The database contained data points with temperatures up to 663.1 K. However, above ∼545 K, the number of data points significantly decreases, leading to a weak parametrization above this temperature. The highest temperature evaluated in the test set was 425.15 K. Therefore, even if the parameters should be well-fitted up to ∼545 K, the reliability of the model can only be assured up to 425 K. In Figure 4, the errors for the estimation of the heat capacities at 293.15 K for ILs taken from our test set are compared to the methods found in the literature (the method of Gardas and Coutinho7 has not been added, since the available parameters only allow application on one of the ILs). The method by Soriano et al. could only be applied to three of the nine ILs, because of missing parameters (but is still considered in the diagram). The method proposed in this work gives the best results for four of the nine ILs. For [C2mim][MeSO3], Sattari et al.11 reached the best prediction, Soriano et al.12 gave the best result for [C2mim][OAc] (however, this IL was part of their training set), Ge et al.8 reached the best results for [C6mim][BF4] and [N4,4,4,1][Thr] (it is unknown if these ILs are part of their training set), and Valderrama et al.10 reached the best result for [P4,4,4,4][Ser].

Figure 4. Comparison of the prediction based on the proposed method and methods from the literature for ILs from our test set at 293.15 K.

The average deviation on the data points tested was 5.6% for the method proposed in this work, 7.6% for the method of Sattari et al.,11 9.0% for the method of Ge et al.,8 and 10.2% for the method of Valderrama et al.10 (for the method of Soriano et al.,12 an average value is not reasonable, because of the missing parameters for most substances under consideration). Mixtures of ILs with molecular fluids such as water or ethanol have been tested as well. The heat capacity of the pure IL has been estimated using the proposed method; for the pure solute, experimental data have been used. By weighting these molar heat capacities by their molar fraction and setting the excess heat capacity to zero, the experimental data for the mixture could be reproduced with a mean accuracy of 4.1%, which is within the accuracy range of the proposed method for pure ILs.

4. CONCLUSION In this work, we presented temperature-dependent contributions of the individual ions to the heat capacity of ionic liquids (ILs). Based on these contributions, the experimental data for the heat capacity of ILs not used for the parameter fitting can be reproduced with an accuracy of 4.4%. Even by taking the combined uncertainty of the experimental data and the estimation into account, a deviation of only 7.2% for ILs not used for the parameter fitting can be achieved. A quadratic

Figure 3. Estimated values over the experimental values for (a) the training set and (b) the test set. 10345

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147: NIST Ionic Liquids Database(ILThermo), Version 2.0; available via the Internet at http://ilthermo.boulder.nist.gov. (14) 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. J. Chem. Eng. Data 2007, 52 (4), 1151−1159. (15) Seber, G. A. F.; Wild, C. J. Nonlinear Regression; Wiley: Hoboken, NJ, 2003. (16) García-Miaja, G.; Troncoso, J.; Romaní, L. Excess properties for binary systems ionic liquid + ethanol: Experimental results and theoretical description using the ERAS model. Fluid Phase Equilib. 2008, 274 (1−2), 59−67. (17) Paulechka, Y. U. Heat Capacity of Room-Temperature Ionic Liquids: A Critical Review. J. Phys. Chem. Ref. Data 2010, 39 (3), 033108 (DOI: 10.1063/1.3463478).

equation turned out to be best-suited for describing the temperature dependency. The derived temperature correlation has been validated up to 152 °C.

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ASSOCIATED CONTENT

* Supporting Information S

The parameters for eq 1, the mathematical definitions of the error types given in Table 1, and a complete list of the ILs and structural formulas for all ions are presented as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 9131 8527455. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank Prof. Wolfgang Arlt for valuable discussion. REFERENCES

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