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Apr 5, 2014 - Database, Analysis, and Prediction Using a Topological Index. Method. Qiao-Li ... experimental data of thermal conductivity at different...
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Thermal Conductivity of Ionic Liquids at Atmospheric Pressure: Database, Analysis, and Prediction Using a Topological Index Method Qiao-Li Chen, Ke-Jun Wu,* and Chao-Hong He State Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China S Supporting Information *

ABSTRACT: Thermal conductivity is an important thermophysical property of ionic liquids (ILs). In this paper, a database for the thermal conductivity of ILs was established by collecting experimental data from literature covering the period from 2007 to 2013, including 359 data points, 45 ILs. The influences of temperature and the alkyl chain length of the cation on thermal conductivity were also discussed. A topological index method was proposed to estimate the thermal conductivity of ILs based on collected data which were divided into training (299 data points, 38 ILs) and testing (60 data points, 7 ILs) sets. The total average absolute deviation between the calculated and literature data was found to be 2.3%, with 2.1% for the training set and 2.9% for the testing set. The topological index method guarantees satisfactory precision with a simple form and can be easily expanded to new kinds of ILs.

1. INTRODUCTION Ionic liquids (ILs) have gained increasing attention over recent years due to their designability and various applications in industry fields.1 ILs tend to have negligibly low vapor pressures, high thermal decomposition temperatures, wide liquid temperature ranges, and excellent stability in air and water, which make them possible candidates for use as heat-transfer fluids. There have been some number of investigations2−5 on the potential of using ILs as heat-transfer fluids though not as much as that of reports on the use of ILs in chemical reactions. Knowing the thermophysical properties of ILs, such as thermal conductivity, is very important for their applications especially in field of heat-transfer fluids.2−5 The ionic liquid thermo database6 records the thermal conductivities of 17 ILs based on imidazolium-, pyrrolidinium-, phosphonium-based cations with bis(trifluoromethylsulfonyl)imide (NTf2), trifluoromethanesulfonate (OTf), ethyl sulfate (EtSO4), chloride (Cl), tetrafluoroborate (BF4), and hexafluorophosphate (PF6) as anions, from four references3,7−9 published from 2005 to 2010. There is no update since the beginning of 2010, and one reference10 published in 2007 is not included in the ionic liquid thermo database. Therefore, a new database for thermal conductivity of ILs is valuable and desired. In this paper, a database of thermal conductivity of ILs was established. Plenty of important information was provided including ILs name, abbreviation, CAS registry number, molecular formula, molecular structure, molecular weight, reference, measurement method, apparatus, and uncertainty of thermal conductivity, samples source (synthesized or obtained from different companies), purity (mass fraction of water and chloride), purification method of samples, and experimental data of thermal conductivity at different temperatures at atmospheric pressure. A total of 45 ILs, 359 data points from 11 literature covering the period from 2007 to © 2014 American Chemical Society

2013 in the temperature range of 273.15−353.15 K at atmospheric pressure are covered in this database. The number of reports on thermal conductivity of ILs is less than that on other thermophysical properties, such as density, viscosity, and melting temperature.11−15 For the existing reports, most researchers4,7−10,16−20 measured thermal conductivity of ILs based on the transient hot-wire method or the transient short-hot-wire method developed from transient hotwire method. The most typical transient hot-wire method is to put a metal wire (hot wire, such as tantalum wire, platinum wire, and tungsten wire) into the sample and heat the wire. As the temperature of the wire increases, it will transfer the heat to the sample. Thus, the temperature increase time of the wire is related to the thermal conductivity of the sample. Better precision can be obtained with a finer wire. Only one report21 used a stationary guarded parallel-plate instrument. The method needs to locate an IL layer in a narrow gap between two horizontal plates which should be totally horizontally arranged. Then, a heat which is provided by the upper plate conducts through the sample, and the thermal conductivity of the sample can be determined by the heat, effective area of the heating plate, thickness of the sample, and surface temperatures of the two plates. Since the measurement and experiment on thermal conductivity are not always easy and cheap,22 estimation of thermal conductivity of ILs is necessary. By using experimental data, models can be developed. Some simple mathematic correlations for the thermal conductivity of ILs have been carried out at the beginning. Tomida et al.10 used a Tait form equation to correlate the experimental thermal conductivity of 1-butyl-3-methylimidaReceived: Revised: Accepted: Published: 7224

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Table 1. Comparison of Four Models for the Prediction of Thermal Conductivity of Ionic Liquids: Gardas and Coutinho,24 Our Previous Work,25 Hezave et al.,22 and Shojaee et al.26 models

method

data points

ionic liquids

accuracy (%)

parameters

extra data needed

Gardas and Coutinho24 our previous work25 Hezave et al.22 Shojaee et al.26

GC GC QSPR QSPR

107 286 209 209

16 36 21 21

1.06 1.66 0.50 6.97

22 29 79 5

critical temperature melting temperature melting temperature

QSPR method can overcome the disadvantage of relying on the group divisions and the GC values. There are two models which are based on QSPR method. Hezave et al.22 proposed a model based on artificial network with 209 data points from 21 ILs based on imidazolium-, pyrrolidinium-, and phosphoniumbased cations with 10 anions. The functionality of the thermal conductivity (λ) is considered as follows:

zolium tetrafluoroborate with a maximum deviation of 0.6%. Later, Tomida et al.8 used the Mohanty equation23 to correlate the experimental thermal conductivities of 1-butyl-3-methylimidazolium hexafluorophosphate, 1-hexyl-3-methylimidazolium hexafluorophosphate, and 1-octyl-3-methylimidazolium hexafluorophosphate. The authors pointed out that more experimental data for the thermal conductivities for different classes of ILs were needed to develop more accurate correlations.8 Fröba et al.21 proposed a new correlation with the experimental thermal conductivities of 10 ILs, 4 cations, and 7 anions based on density and molecular weight. The authors checked this correlation with 45 data points of 36 ILs, and the average absolute deviation (AAD) was found to be 6.5%. Some predictive models with various cations or anions have been proposed in recent years. These models can be classified into two categories: group contribution (GC) method and quantitative structure property relationship (QSPR) method. There are two models which are based on GC method. Gardas and Coutinho24 first came up with the idea using group contribution method to estimate the properties of ILs. For thermal conductivity of ILs, they proposed a predictive model with 107 data points from 16 ILs based on imidazolium-, pyrrolidinium-, and phosphonium-based cations with 6 anions, and the relationship between thermal conductivity (λ) and temperature (T) can be fitted as λ = Aλ − Bλ T

λ = f (Tm , MW, T , P)

Tm is melting temperature, MW is molecular weight, and P is pressure. They found that optimum number of hidden layers was determined to be 1, with 13 neurons in the hidden layer and logarithmic-sigmoid and purelin functions as the transfer functions in the hidden and output layers, respectively. The overall AAD for this model was found to be 0.5%. However, the authors did not give a specific equation of the logarithmicsigmoid and purelin functions, which made it difficult for others to use the model to calculate thermal conductivity of ILs. Besides, this model needs 79 parameters, which is too inconvenient for application. Most recently, Shojaee et al.26 proposed a new correlation based on genetic algorithm with the same data in the paper by Hezave et al.22 Though the ratio of data points to parameters of the model is large, the AAD is fairly large too. They divided the data into training (143 data points) and testing (66 data points) sets, and the total AAD was found to be 6.97%, 5.22% for the training set and 10.76% for the testing set. A detailed comparison of these models discussed above is listed in Table 1. The deficiency of the models mentioned above can be concluded as follows. (1) Most models mentioned above need the data of melting temperature, critical temperature, density, or other physicochemical properties. Since new ILs are emerging in an endless way, it is unrealistic to get all of the physicochemical property data of ILs. (2) In the two GC models, the contributions of cations and anions are considered. However, the interactions of cations and anions are not taken into account. Moreover, the method based on GC needs complicated group division such as first-order groups, second-order groups, and third-order groups to describe isomerides. In this work, a new method was presented for estimating thermal conductivity of ILs based on the topological index method. This new topological index method overcomes the deficiency mentioned above with a simple form and can be easily expanded to new kinds of ILs.

(1)

Aλ and Bλ are fitting parameters that can be obtained from a group contribution approach. The overall AAD for this model was found to be 1.06%, which is smaller than the experimental measurement uncertainty of 2−3%. The accuracy of the model is satisfactory for the 107 data points. However, Gardas and Coutinho24 considered 1,3-dimethylimidazolium, 1,1-dimethylpyrrolidinium, tetramethylphosphonium, and all 6 anions as a group without further division. Thus, the model cannot be extended to predict the thermal conductivity of ILs with ammonium- and pyridinium-based cations or new anions such as acetate (CH3COO) and dicyanamide (DCA). In our previous work,25 a new GC model was proposed with 286 data points for 36 ILs based on imidazolium-, phosphonium-, and ammonium-based cations with 18 anions, and the relationship between thermal conductivity (λ) and temperature (T) can be expressed as λ = λ 0[1 + k 0(1 − Tr)2/3 ]

(3)

2. DATABASE The data for thermal conductivity of ILs were collected through the following steps. (1) A search of publications on the thermal conductivity of ILs was performed using SciFinder Scholar, and the search topic was “thermal conductivity, ionic liquid”, with no limit to publication year, document type, or language. (2) Redid the first step using other search engines, such as Web of Science and Google Scholar to see if there were related articles which were not found by SciFinder Scholar. (3) Search results

(2)

λ0 is obtained from group contribution method, Tr = T/Tc is the reduced temperature, and Tc is the critical temperature. The overall AAD for this model was found to be 1.66%. However, this model also has the disadvantage that all GC models have. No matter how fine the group divided, when there is a new group, the model fails. Meanwhile, this model is still not simple enough due to the dependence on critical temperature. 7225

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Table 2. van der Waals Radius, Atom Electronegativity, Atom Weight, Atom Electronic Shell Number, and Atom Outermost Electron Number for All Atoms Used in This Work van der Waals radius (0.1 nm) atom electronegativity atom weight atom electronic shell number atom outermost electron number

B

C

N

O

F

P

S

Cl

Br

I

0.98 2.04 10.81 2 3

1.80 2.55 12.01 2 4

1.50 3.04 14.01 2 5

1.40 3.44 16.00 2 6

1.35 3.98 19.00 2 7

1.90 2.19 30.97 3 5

1.85 2.58 32.07 3 6

1.85 3.16 35.45 3 7

1.95 2.96 79.90 4 7

2.15 2.66 126.90 5 7

of steps (1) and (2) were further sifted to remove publications in which no thermal conductivity data were reported or only calculated values of thermal conductivity were available. Finally, the thermal conductivity data were collected and classified into tables which included totally 359 data points, 45 ILs, 18 cations, and 22 anions, covering a wide range of temperature (273.15− 353.15 K) and thermal conductivity (0.1050−0.2137 W m−1 K−1)4,7−10,16−21 (see Supporting Information for more details). In Supporting Information Table S1, the abbreviation of ILs, full name of ILs, CAS registry number, molecular formula, molecular structure, and molecular weight are listed. In Supporting Information Table S2, the reference, measurement method, apparatus, and uncertainty of thermal conductivity, samples source (synthesized or obtained from different companies), purity (mass fraction of water and chloride), purification method of samples, and experimental data of thermal conductivity at different temperatures are listed.

D = (dij) dij =

(4)

{n0

(5)

where n is the length between atoms i and j. Besides, we define six characters, which include van der Waals radius, atom electronegativity, atom weight, adjacent hydrogen number, atom electronic shell number, and atom outermost electron number to describe all sides of the molecule. These six characters are the most usual and typical atom characters to describe the atom, while their values are easy to obtain. The values of the six characters are listed in Table 2. The van der Waals radius of each atom is listed in a row just next to the distance matrix to form a combined matrix D′. Then we define a matrix as M = [D′] × [D′]T. The eigenvalues (ei) of M is calculated, and the greatest eigenvalues (emax) is one topological index we need. Five more characters including atom electronegativity, atom weight, adjacent hydrogen number, atom electronic shell number, and atom outermost electron number are handled in the same way as van der Waals radius. Thus, we get six topological indexes for one ion. The thermal conductivity of ILs is not simply the sum of the anion and the cation contributions. Interaction between the cation and the anion should also be taken into account. We define another topological index to describe the interaction. According to references,15,33,37−39 it can be expressed as

3. DEVELOPMENT OF THE METHOD Topological indexes are numerical quantities derived from a graphical theoretical representation of the molecular structure through mathematical invariants,27 such as some classical indexes: Wiener index,28 Randic index,29 Hosoya index,30 and Balaban index.31 However, these indexes mentioned above only take into account the route between apexes and the adjacency relationship of the apexes, and they are difficult to describe the molecular structures containing multiple bonds and heteroatoms.32,33 Some new topological indexes have been proposed to solve the problem. The molecular connectivity descriptor suggested by Kier and Hall34 is one of the most popular indexes.32 Atomtype AI topological indexes from the topological distance sums and vertex degree further were used to describe different structural environment of each atom type in a molecule by Ren.35 This topological index can develop high-quality models for describing six physical properties (the normal boiling point, heat of vaporization, molar volume, molar refraction, van der Waals’ constant, and Pitzer’s acentric factor) of alkanes with up to nine carbon atoms.35 Estrada36 proposed a possible solution to the problem of differentiation of heteroatoms in molecular graphs in a natural way: using weights in the nondiagonal entries of the edge adjacency matrix. Most recently, the research group of Wang and Xia15,33,37−39 proposed a new topological index based on atom characters and atom positions in the hydrogen-suppressed molecule structure to predict the surface tension, toxicity, melting point, and decomposition temperature of ILs. Their results proved that the topological index method can be used to predict properties of ILs. We proposed a new predictive model for the thermal conductivity of ILs based on topological index method. First, every atom in the ion except hydrogen is numbered. Then we get the distance matrix (D), which is defined as

eca‐an =

∑ eca,i + ∑ ean,i

(6)

So we get 18 topological indexes for one IL. Names of the 18 topological indexes are listed in Table 3. (The example of calculating topological indexes can be found in Supporting Information Table S3.) It can be found in most literature4,7−10,16−21 that thermal conductivity of ILs decreases slightly while temperature increases. Thermal conductivity (λ) of ILs can be correlated Table 3. Names of 18 Topological Indexes for One Ionic Liquid

7226

characters

cation

anion

interaction between cation and anion

van der Waal radius atom electronegativity atom weight adjacent hydrogen number atom electronic shell number atom outermost electron number

eca‑max,r eca‑max,e eca‑max,w eca‑max,h

ean‑max,r ean‑max,e ean‑max,w ean‑max,h

eca‑an,r eca‑an,e eca‑an,w eca‑an,h

eca‑max,s

ean‑max,s

eca‑an,s

eca‑max,o

ean‑max,o

eca‑an,o

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Table 4. Values of Parameters ci and di of Equations 8 and 9 for Calculating Thermal Conductivity of Ionic Liquids Based on Topological Index Method at Atmospheric Pressure parameters c0 c1 c2 c3 c4 c5 c6

values 3.2588432 −1.1320981 2.3076764 −2.7816855 −2.1707068 1.3473529 −4.8316537

parameters × × × × × × ×

10−1 10−2 10−3 10−1 10−2 10−3 10−2

values −2.1303557 4.9302866 −8.5452848 −1.8030812 −7.7400518 3.3090844 2.7042104

c7 c8 c9 c10 c11 c12 c13

10−4 10−5 10−3 10−4 10−4 10−2 10−2

values −2.2205801 2.7252882 6.3786382 −7.0758914 2.8899081 9.8952835 −1.7674225

c14 c15 c16 c17 c18 d0 d1

× × × × × × ×

10−3 10−1 10−3 10−4 10−2 10−5 10−9

N

as a function of temperature in the form of a linear equation4,9,17,19,21 λ = A − BT

parameters × × × × × × ×

AAD (%) =

(7)

∑i =p1 100(λcalc − λexp)/λexp

i

Np

(10)

where Np represents the number of data points.

where T is the temperature in K and A and B are positive fitting parameters. We define that A and B can be obtained from topological indexes as follows

4. RESULTS AND DISCUSSION 4.1. Effect of Temperature. The thermal conductivities of five ILs at atmospheric pressure are shown in Figure 1: 1-ethyl-

A = c0 + c1 × eca‐max,r + c 2 × ean‐max,r + c3 × eca‐an,r + c4 × eca‐max,e + c5 × ean‐max,e + c6 × eca‐an,e + c 7 × eca‐max,w + c8 × ean‐max,w + c 9 × eca‐an,w + c10 × eca‐max,h + c11 × ean‐max,h + c12 × eca‐an,h + c13 × eca‐max,s + c14 × ean‐max,s + c15 × eca‐an,s + c16 × eca‐max,o + c17 × ean‐max,o + c18 × eca‐an,o

(8)

B = d0 + d1 × (eca‐max,r + ean‐max,r + eca‐an,r + eca‐max,e + ean‐max,e + eca‐an,e + eca‐max,w + ean‐max,w + eca‐an,w + eca‐max,h + ean‐max,h + eca‐an,h + eca‐max,s + ean‐max,s + eca‐an,s + eca‐max,o + ean‐max,o + eca‐an,o)/18

(9)

Figure 1. Experimental thermal conductivities of five ionic liquids as a function of temperature at atmospheric pressure: ⧫, [C2mim][EtSO4];21 ▼, [C4mim][OTf];9 ▲, [P6,6,6,14][NTf2];9 ●, [C4mim][NPf2];4 ■, [C4mpyrr][FAP].9

where ci (i from 0 to 18) and di (i from 0 to 1) are fitting parameters. A total of 359 data points for 45 ILs (the topological indexes for the 45 ILs are listed in Supporting Information Table S4) based on imidazolium-, pyrrolidinium-, phosphonium-, ammonium-, and pyridinium-based cations with bis(trifluoromethylsulfonyl)imide (NTf2), trifluoromethanesulfonate (OTf), ethyl sulfate (EtSO4), octyl sulfate (OcSO4), tris(pentafluoroethyl)trifluorophosphate (FAP), bis(2,4,4-trimethylpentyl)phosphinate (Phosph), methyl sulfate (MeSO4), chloride (Cl), tetrafluoroborate (BF4), hexafluorophosphate (PF6), acetate (CH3COO), dicyanamide (DCA), tricyanomethanide (C(CN)3), methylphosphonate (MeOHPO2), serinate (Ser), taurinate (Tau), lysinate (Lys), threonate (Thr), prolinate (Pro), valinate (Val), cysteinate (Cys), and bis(perfluoroethylsulfonyl)imide (NPf2) as anions were divided into two sets: the training set (299 data points, 38 ILs) and the testing set (60 data points, 7 ILs). The training set was used in this work to obtain the values of ci and di, and the testing set was used to test the validity of this method. The software 1stOpt v1.5 was used for regression calculation. The Levenberg−Marquardt + Universal Global Optimization method was used to optimize the parameters, and the objective function was to minimize the sum of absolute deviation. The values of parameters ci and di are listed in Table 4. The AAD is defined as

3-methylimidazolium ethyl sulfate ([C2mim][EtSO4]),21 1butyl-3-methylimidazolium trifluoromethanesulfonate ([C4mim][OTf]),9 trihexyl(tetradecyl)phosphonium bis(trifluoromethylsulfonyl)imide ([P 6,6,6,14][NTf2]),9 1-butyl-3methylimidazolium bis(perfluoroethylsulfonyl)imide ([C4mim][NPf2]),4 and 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate ([C4mpyrr][FAP])9. As illustrated in Figure 1, for most kinds of ILs, such as [C 2 mim][EtSO 4 ], [C 4 mim][OTf], [P6,6,6,14 ][NTf 2], and [C4mpyrr][FAP], thermal conductivity decreases linearly with the increase of temperature for the whole temperature range studied. However, the temperature dependence of thermal conductivity of ILs is weak, and the influence of experimental uncertainty should not be ignored. For instance, the relationship between thermal conductivity and temperature of [C2mim][EtSO4] in the temperature range of 273.15−313.15 K is fluctuant. It is possibly due to the experimental uncertainty. However, there is an exception. For [C4mim][NPf2], the thermal conductivity increases linearly with the increase of temperature. The samples of [C4mim][NPf2] were synthesized in the lab. The thermal conductivity measurement the 7227

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most ILs are between 0.1000 and 0.2000 W m−1 K−1. The error of the measurement of thermal conductivity mainly comes from the error in measurements of temperature. Bhatt and Gohil40 listed that the uncertainty of the thermometers used in their study was ±0.5 K. However, Zhang et al.41 suggested that if the error of temperature ΔT was 0.5 K, the uncertainty of thermal conductivity could be 80%. Besides, they have not performed a calibration with standard substances for their equipment. Thus, we did not use the thermal conductivity data in Bhatt and Gohil.40 The reason why we did not use the data reported by Van Valkenburg et al.3 was explained in our previous work.25 The AAD results are listed in Table 5 for both the training and testing sets (more details can be found in Supporting Information Table S5). The AAD for the training and testing sets was found to be 2.1 and 2.9%, respectively. The overall AAD was found to be 2.3% with a maximum deviation of 10.5%. It is observed that 29.2% of the estimated thermal conductivities were within absolute deviation of 0.0−1.0%, 63.0% were within 1.0−5.0%, 7.2% were within 5.0−10.0%, and only 0.6% were greater than 10.0%. We noticed that the maximum deviation was found between the calculated data and experimental data of [C4mim][NPf2] at 296.14 K from Liu et al.,4 and the calculated data were 10.5% greater than the experimental data. The thermal conductivities of [C4mim][NPf2] at 296.14, 314.35, and 332.36 K are 0.1110, 0.1155, and 0.1185 W m−1 K−1, respectively, reported by Liu et al.4 However, in most reports,7−10,16−21 the thermal conductivity of ILs decreases slightly with the increase of temperature. There are no other reports about the thermal conductivity of [C4mim][NPf2] at different temperatures, so the thermal conductivity of [C4mim][NPf2] needs further research. A detailed deviation analysis of this work, Gardas and Coutinho,24 our previous work,25 and Shojaee et al.26 is given in Table 5. We did not compare the model proposed by Hezave et al.22 though the AAD of their model was found to be only 0.5% and the reasons are stated as follows. (1) The 79 parameters of the model were obtained according to 209 data points and might not be applicable to plenty types of ILs. (2) The melting point needed in the model is not always available for ILs, such as [C2mim][MeOHPO2], [N4,4,4,1][Tau], and [P4,4,4,4][Cys]. (3) The authors did not give a specific equation of the logarithmic-sigmoid and purelin functions, which made it difficult for others to use the model to calculate thermal conductivity of ILs. As we can see from Table 5, the model proposed by Gardas and Coutinho24 can only predict the thermal conductivities of 16 ILs in 45 ILs. It is clear that the limitations of this model lie in the group division principle that they considered 1,3dimethylimidazolium, 1,1-dimethylpyrrolidinium, tetramethylphosphonium, and all of the six anions as a group without further division, which means that this model cannot be extended to other ILs with the new group. Moreover, the data points including the types of cations and anions they used are not as much as other models. The AAD result (3.9%) of this model presented in Table 5 was found to be larger than that in their original paper. It can be explained by the reason that some data in Table 5 are not available at the time Gardas and Coutinho24 proposed the model. For instance, the AAD of [C6mim][BF4] reported by Nieto et al.7 and Tomida et al.18 and [C8mim][BF4] reported by Tomida et al.18 were found to be 23.1, 15.9, and 18.1%, respectively. Our previous work25 defined 25 detailed groups to describe the ILs, and the AAD of the model was found to be 2.5% for 42

researchers used was a Decagon KD2 Thermal Properties Analyzer, and only three data points from 296.15 to 336.15 K were reported. As the authors suggested, the temperature range is small in the experiment and the uncertainties are fairly large, so it is difficult to draw hard conclusion from the trend. Meanwhile, the authors did not analyze the water content of [C4mim][NPf2], which has significant influence on thermal conductivity.7−10,16−21 More experiments are needed to confirm this result. 4.2. Effect of the Alkyl Chain Length of the Cation. Figure 2 shows the thermal conductivities of ILs with

Figure 2. Experimental thermal conductivities for four ionic liquids with different C numbers in alkyl chain at 293.15 K at atmospheric pressure: ▲, [Cnpy][BF4];16 ▼, [Cnmim][BF4];10,18 ●, [Cnmim][PF6];8 ■, [Cnmim][NTf2].9

pyridinium-based cation and tetrafluoroborate (BF4) as anion:16 [C4py][BF4], [C6py][BF4], and [C8py][BF4], ILs with imidazolium-based cation; and tetrafluoroborate (BF4) as anion:10,18 [C4mim][BF4], [C6mim][BF4], and [C8mim][BF4], ILs with imidazolium-based cation; and hexafluorophosphate (PF6) as anion:8 [C4mim][PF6], [C6mim][PF6], [C8mim][PF6]; and ILs with imidazolium-based cation; and bis(trifluoromethylsulfonyl)imide (NTf2) as anion:9 [C2mim][NTf2], [C 4 mim][NTf 2 ], [C 6 mim][NTf 2 ], [C 8 mim][NTf 2 ], and [C10mim][NTf2] at 293 K at atmospheric pressure. It is observed that for [Cnpy][BF4] and [Cnmim][BF4], the thermal conductivity decreases slightly with the increase of the alkyl chain length. For [Cnmim][PF6] and [Cnmim][NTf2], the alkyl chain length has no significant influence on the thermal conductivity. So the types of anions should be considered when it comes to the effect of the alkyl chain length. 4.3. Topological Index Method. The experimental data of the ILs’ thermal conductivity, for both training and testing sets, used to estimate the parameters for the topological index correlation and test the validity of this method, were collected from literature and summarized in Table 5. Limited number of available accurate experimental data on thermal conductivity and discrepant results on the same kind of IL made the removal of doubtful literature very difficult. Therefore, we took all the literature into account except two.3,40 Bhatt and Gohil40 calculated the thermal conductivities of [N4,4,4,4][HCO3], [N4,4,4,4][BF4], [N4,4,4,4][PF6], [N4,4,4,4][BrO3], [N4,4,4,4][NO3], [N4,4,4,4][NO2], [N4,4,4,4][SCN], and [N4,4,4,4][IO3] using a method proposed by Zhang et al.41 The thermal conductivities of the eight kinds of ILs are in the range of 0.381−0.954 W m−1 K−1, which is extremely large since the thermal conductivities of 7228

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Table 5. Average Absolute Deviation (AAD) for the Estimation of Thermal Conductivity Based on Topological Index Method at Atmospheric Pressure ionic liquids [C4mim][NTf2] [C6mim][NTf2] [C8mim][NTf2] [C10mim][NTf2] [C4mim][OTf] [C2mim][EtSO4]

[C2mim][OcSO4] [C4mpyrr][FAP] [C4mpyrr][NTf2]

[P6,6,6,14][NTf2] [P6,6,6,14][Phosph] [P6,6,6,14][Cl] [C4mim][BF4] [C6mim][BF4] [C8mim][BF4] [C4mim][PF6] [C6mim][PF6] [C8mim][PF6] [C2mim][CH3COO] [C2mim][DCA] [C2mim][MeOHPO2] [C4bim][NTf2] [N8,8,8,1][NTf2] [N4,4,4,1][Tau] [N4,4,4,1][Lys] [N4,4,4,1][Thr] [P4,4,4,4][Ser] [P4,4,4,4][Tau] [P4,4,4,4][Lys] [P4,4,4,4][Thr] [P4,4,4,4][Pro] [P4,4,4,4][Val] [C4mim][NPf2] [N4,1,1,1][NTf2] [N4COOH,1,1,1][NTf2] [C4mmim][NTf2] [C6py][BF4] [C8py][BF4] [C2mim][NTf2]a [P6,6,6,14][FAP]a [P4,4,4,1][MeSO4]a [C2mim][C(CN)3]a [N4,4,4,1][Ser]a [P4,4,4,4][Cys]a [C4py][BF4]a total for training set total for testing set

T (K)

data points

AAD (%) (this work)

AAD (%) (Gardas and Coutinho24)

AAD (%) (our previous work25)

AAD (%) (Shojaee et al.26)

ref

293.00−353.00 296.24−332.36 293.00−353.00 273.15−353.15 293.00−353.00 293.00−353.00 293.00−353.00 293.00−353.00 293.00−353.00 273.15−353.15 283.11−352.82 273.15−353.15 293.00−353.00 293.00−323.00 293.00−333.00 296.15−332.40 293.00−353.00 285.65−333.55 282.47−353.62 293.00−353.00 294.70−334.90 293.00−353.00 294.20−334.40 294.20−334.40 293.00−353.00 294.90−335.10 293.00−353.00 294.10−335.20 295.10−335.20 273.15−353.15 273.15−353.15 273.15−353.15 273.15−353.15 273.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 298.15−353.15 313.15−353.15 296.14−332.36 296.69−332.21 295.70−331.03 296.18−333.16 294.20−334.30 294.20−334.30 293.00−353.00 273.15−353.15 282.19−355.07 283.34−353.51 273.15−353.15 298.15−353.15 298.15−353.15 294.20−334.30 273.15−353.15 273.15−353.15

7 3 7 9 7 7 7 7 7 9 8 9 7 4 5 3 7 7 9 7 3 7 3 3 7 3 7 3 3 9 9 9 9 9 7 7 7 7 7 7 7 7 5 3 3 3 3 3 3 7 9 9 9 9 7 7 3 299 60

3.6 2.2 4.0 1.3 0.8 2.4 2.5 6.0 1.9 0.7 0.8 0.8 1.1 1.7 3.6 3.2 1.4 2.8 1.0 2.0 0.7 3.7 2.4 0.3 1.9 2.0 0.6 3.4 0.7 2.2 1.2 1.3 1.8 0.7 0.5 3.8 3.1 1.5 1.7 3.6 0.7 5.6 0.7 5.2 3.8 7.6 4.9 1.3 2.2 3.6 4.7 0.6 5.2 1.1 1.5 3.4 3.7 2.1 2.9

1.3 2.2 1.4 5.3 1.1 0.8 0.2 3.5 0.2 2.5 2.5 − − 0.2 5.8 1.8 0.7 4.8 − 0.2 13.2 23.1 15.9 18.1 1.0 0.7 4.3 0.9 1.2 − − − − − − − − − − − − − − − − − − − − 1.6 6.4 − − − − − − − −

1.0 0.3 2.0 1.9 3.0 5.2 0.4 3.1 1.3 1.1 1.3 0.7 1.9 0.8 4.8 2.2 0.3 4.4 − 0.2 5.4 1.2 4.3 4.2 1.6 1.4 1.5 1.8 3.0 0.9 0.6 − 4.5 0.8 0.2 0.2 0.1 1.5 3.3 0.1 0.2 0.1 0.1 6.1 1.6 2.3 1.8 2.4 1.9 2.3 5.8 24.1 5.3 0.7 0.4 − 4.5 − −

3.3 4.2 3.7 7.2 − 5.1 1.9 3.8 9.3 10.9 11.2 14.7 − 6.1 10.9 5.9 16.3 9.1 − 22.1 1.1 0.8 4.8 − 2.3 2.6 2.3 3.1 4.9 6.5 5.3 − − − − − − − − − − − 17.3 − 8.2 − 4.5 − − 3.7 11.2 − − 2.2 − − 0.8 − −

9 4 9 21 9 9 9 7 9 21 17 21 9 9 7 4 9 20 20 9 10 7 18 18 7 8 7 8 8 21 21 21 21 21 19 19 19 19 19 19 19 19 19 4 4 4 4 16 16 9 21 20 20 21 19 19 16 − −

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Table 5. continued ionic liquids total a

T (K)

data points

AAD (%) (this work)

AAD (%) (Gardas and Coutinho24)

AAD (%) (our previous work25)

AAD (%) (Shojaee et al.26)

ref

273.15−353.15

359

2.3

3.9

2.5

7.2

−

Testing set in this work.

ILs in 45 ILs. The thermal conductivity is considered as a function of critical temperature in the model. Our previous work25 calculated the critical temperature of ILs using the GC method Valderrama et al.42 proposed. However, the method did not contain the group of −PO and −SH which is the component of [P6,6,6,14][Phosph], [C2mim][MeOHPO2], and [P4,4,4,4][Cys]. Thus, the thermal conductivities of 3 ILs, [P6,6,6,14][Phosph], [C2mim][MeOHPO2], and [P4,4,4,4][Cys], cannot be calculated. The AAD of the model proposed by Shojaee et al.26 was found to be 7.2%, which is much larger than any other models. Besides, it can only predict the thermal conductivity of ILs with known Tm. A comparison between the experimental thermal conductivities and calculated thermal conductivities by four models for [C2mim][EtSO4], [C4mpyrr][NTf2], [C6mim][BF4], and [C8mim][PF6] is given in Figure 3. It can be observed that

Figure 4. Linear relationship between experimental thermal conductivity (λexp) and calculated thermal conductivity (λcalc) for ionic liquids: ○, the training set; ●, the testing set.

for the training and testing sets, and the overall AAD was found to be 2.3%.

Figure 3. Comparison of relative deviations between experimental thermal conductivities (λexp) and calculated thermal conductivities (λcalc) by four models (□, this work; ○, Gardas and Coutinho;24 Δ, our previous work;25 ∇, Shojaee et al.26) for four kinds of ionic liquids: (a) [C2mim][EtSO4] (Ge et al.,9 Fröba et al.,21 Chen et al.17); (b) [C4mpyrr][NTf2] (Ge et al.,9 Nieto et al.,7 Liu et al.4); (c) [C6mim][BF4] (Nieto et al.,7 Tomida et al.18); (d) [C8mim][PF6] (Tomida et al.8).

Figure 5. Relative deviations between experimental thermal conductivity (λexp) and calculated thermal conductivity (λcalc) for ionic liquids: ○, the training set; ●, the testing set.

These results show clearly that this topological index method can be applicable to other ILs with 18 topological indexes. This new topological index method describes isomerides in a simple way and takes into account the interactions of cations and anions. Moreover, the model needs no other physicochemical property data but only characters of atoms composed in the IL. Theoretically, this topological index method can predict the thermal conductivity of all kinds of ILs. The 18 topological indexes of hundreds of ILs and formula to calculate thermal conductivity at different temperatures are given in Supporting Information Table S6. When new experimental data are reported, the accuracy and feasibility of the method this work proposed can be further proved. In brief, the model guarantees satisfactory precision with a simple form and can be easily expanded to new kinds of ILs.

the model proposed by this work has satisfactory precision. The calculated thermal conductivity (λcalc) of ILs using the topological index method presents a good agreement with the experimental data (λexp) for both the training and testing sets: λcalc = (0.9795 ± 0.00318)λexp (the training set) and λcalc = (0.9344 ± 0.00854)λexp (the testing set), at 95% level of confidence, as shown in Figure 4. Relative deviations between the calculated and experimental thermal conductivity data are shown in Figure 5. The AAD was found to be 2.1 and 2.9% with maximum deviations equal to 10.5 and 7.0%, respectively, 7230

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(2) Chen, H.; He, Y.; Zhu, J.; Alias, H.; Ding, Y.; Nancarrow, P.; Hardacre, C.; Rooney, D.; Tan, C. Rheological and Heat Transfer Behaviour of the Ionic Liquid, [C4mim][NTf2]. Int. J. Heat Fluid Flow 2008, 29, 149. (3) Van Valkenburg, M. E.; Vaughn, R. L.; Williams, M.; Wilkes, J. S. Thermochemistry of Ionic Liquid Heat-Transfer Fluids. Thermochim. Acta 2005, 425, 181. (4) Liu, H.; Maginn, E.; Visser, A. E.; Bridges, N. J.; Fox, E. B. Thermal and Transport Properties of Six Ionic Liquids: An Experimental and Molecular Dynamics Study. Ind. Eng. Chem. Res. 2012, 51, 7242. (5) Nakata, Y.; Kohara, K.; Matsumoto, K.; Hagiwara, R. Thermal Properties of Ionic Liquid + Water Binary Systems Applied to Heat Pipes. J. Chem. Eng. Data 2011, 56, 1840. (6) ILThermo; http://ilthermo.boulder.nist.gov/ILThermo/ mainmenu.uix (accessed September 17, 2013). (7) Nieto De Castro, C. A.; Lourenco, M. J. V.; Ribeiro, A. P. C.; Langa, E.; Vieira, S. I. C.; Goodrich, P.; Hardacre, C. Thermal Properties of Ionic Liquids and Ionanofluids of Imidazolium and Pyrrolidinium Liquids. J. Chem. Eng. Data 2010, 55, 653. (8) Tomida, D.; Kenmochi, S.; Tsukada, T.; Qiao, K.; Yokoyama, C. Thermal Conductivities of [bmim][PF6], [hmim][PF6], and [omim][PF6] from 294 to 335 K at Pressures up to 20 MPa. Int. J. Thermophys. 2007, 28, 1147. (9) Ge, R.; Hardacre, C.; Nancarrow, P.; Rooney, D. W. Thermal Conductivities of Ionic Liquids over the Temperature Range from 293 to 353 K. J. Chem. Eng. Data 2007, 52, 1819. (10) Tomida, D.; Kenmochi, S.; Tsukada, T.; Yokoyama, C. Measurements of Thermal Conductivity of 1-Butyl-3-methylimidazolium Tetrafluoroborate at High Pressure. Heat TransferAsian Res. 2007, 36, 361. (11) Wu, K.; Chen, Q.; He, C. Speed of Sound of Ionic Liquids: Database, Estimation, and Its Application for Thermal Conductivity Prediction. AIChE J. 2014, 60, 1120. (12) Gharagheizi, F.; Ilani-Kashkouli, P.; Mohammadi, A. H.; Ramjugernath, D.; Richon, D. Development of a Group Contribution Method for Determination of Viscosity of Ionic Liquids at Atmospheric Pressure. Chem. Eng. Sci. 2012, 80, 326. (13) Gharagheizi, F.; Sattari, M.; Ilani-Kashkouli, P.; Mohammadi, A. H.; Ramjugernath, D.; Richon, D. Quantitative Structure−Property Relationship for Thermal Decomposition Temperature of Ionic Liquids. Chem. Eng. Sci. 2012, 84, 557. (14) Ji, X.; Adidharma, H. Thermodynamic Modeling of Ionic Liquid Density with Heterosegmented Statistical Associating Fluid Theory. Chem. Eng. Sci. 2009, 64, 1985. (15) Yan, F.; Xia, S.; Wang, Q.; Yang, Z.; Ma, P. Predicting the Melting Points of Ionic Liquids by the Quantitative Structure Property Relationship Method Using a Topological Index. J. Chem. Thermodyn. 2013, 62, 196. (16) Tomida, D.; Kenmochi, S.; Qiao, K.; Tsukada, T.; Yokoyama, C. Densities and Thermal Conductivities of N-Alkylpyridinium Tetrafluoroborates at High Pressure. Fluid Phase Equilib. 2013, 340, 31. (17) Chen, Q.; Wu, K.; He, C. Thermal Conductivities of [EMIM][EtSO4], [EMIM][EtSO4] + C2H5OH, [EMIM][EtSO4] + H2O, and [EMIM][EtSO4] + C2H5OH + H2O at T = (283.15 to 343.15) K. J. Chem. Eng. Data 2013, 58, 2058. (18) Tomida, D.; Kenmochi, S.; Tsukada, T.; Qiao, K.; Bao, Q. X.; Yokoyama, C. Viscosity and Thermal Conductivity of 1-Hexyl-3methylimidazolium Tetrafluoroborate and 1-Octyl-3-methylimidazolium Tetrafluoroborate at Pressures up to 20 MPa. Int. J. Thermophys. 2012, 33, 959. (19) Gardas, R. L.; Ge, R.; Goodrich, P.; Hardacre, C.; Hussain, A.; Rooney, D. W. Thermophysical Properties of Amino Acid-Based Ionic Liquids. J. Chem. Eng. Data 2010, 55, 1505. (20) Ferreira, A. G. M.; Simões, P. N.; Ferreira, A. F.; Fonseca, M. A.; Oliveira, M. S. A.; Trino, A. S. M. Transport and Thermal Properties of Quaternary Phosphonium Ionic Liquids and IoNanofluids. J. Chem. Thermodyn. 2013, 64, 80.

5. CONCLUSION Thermal conductivity is a vital thermophysical property for ILs. In this paper, a database for the thermal conductivity of ILs was established. Plenty of important information was provided including IL name, abbreviation, CAS registry number, molecular formula, molecular structure, molecular weight, reference, measurement method, apparatus, and uncertainty of thermal conductivity, samples source (synthesized or obtained from different companies), purity (mass fraction of water and chloride), purification method of samples, and experimental data of thermal conductivity at different temperatures at atmospheric pressure. A total of 45 ILs, 359 data points in the temperature range of 273.15−353.15 K are covered in this database. The influences of temperature and the alkyl chain length of the cation on thermal conductivity were also discussed. Moreover, a simple but broad practicability topological index method was developed in this paper to estimate the thermal conductivity of ILs with good precision. A database of 359 data points for 45 ILs was divided into training and testing sets. The training set was used in this work to obtain the values of parameters, and the testing set was used to test the validity of this method. The calculated thermal conductivity agrees well with experimental data with a total AAD of 2.3%, with 2.1% for training set and 2.9% for testing set, which confirmed the validity of the model. These results show clearly that this topological index method can be applicable to other ILs with 18 topological indexes we proposed.

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ASSOCIATED CONTENT

S Supporting Information *

The abbreviation of ILs, full name of ILs, CAS registry number, molecular formula, molecular structure, and molecular weight are listed in Table S1. The reference, measurement method, apparatus, and uncertainty of thermal conductivity, samples source, purity, purification method of samples, and experimental data of thermal conductivity at different temperatures are listed in Table S2. The example of calculating topological indexes is listed in Table S3. The topological indexes for the 45 ILs are listed in Table S4. The details of deviation between λexp and λcalc for both the training and testing sets are listed in Table S5. The 18 topological indexes of hundreds of ILs and formula to calculate thermal conductivity at different temperatures are listed in Table S6. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Fax: +86 571 87951742. Phone: +86 571 87952709. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the National Natural Science Foundation of People’s Republic of China (Project Nos. 21176206 and 21306167) is gratefully acknowledged.

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REFERENCES

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