Thermal and Transport Properties of Six Ionic Liquids - American

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Thermal and Transport Properties of Six Ionic Liquids: An Experimental and Molecular Dynamics Study Hongjun Liu,† Edward Maginn,*,† Ann E. Visser,‡ Nicholas J. Bridges,‡ and Elise B. Fox*,‡ †

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States Savannah River National Laboratory, Aiken, South Carolina 29808, United States

‡

S Supporting Information *

ABSTRACT: Experimental measurements and molecular dynamics simulations are used to determine the density, heat capacity, self-diffusivity, shear viscosity, and thermal conductivity of six ionic liquids over a range of temperatures. The ionic liquids examined are 1-butyl-3-methylimidazolium bis[(perfluoroethyl)sulfonyl]imide ([bmim][Pf2N]), 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([bmim][Tf2N]), 1-butyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([bmmim][Tf2N]), 1-butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide ([bmpyr][Tf2N]), N-butyl-N,N,Ntrimethylammonium bis[(trifluoromethyl)sulfonyl]imide ([N4111][Tf2N]), and N,N,N-trimethylammonium-N-butanoic acid bis[(trifluoromethyl)sulfonyl]imide ([N4111][COOHTfN]). The results of this work suggest that several of these ionic liquids have properties that would enable them to be successful high temperature heat transfer fluids. In particular, their energy storage densities and thermal conductivities are quite favorable when compared to conventional heat transfer fluids. The low temperature viscosities of the ILs are significantly higher than conventional fluids, but the viscosities drop rapidly with increasing temperature. The simulations, which are purely predictive, agree quantitatively with the experimental data for density and qualitatively for other properties. It is shown that the simulated thermal conductivity can be adequately correlated with density and molecular weight of the [Tf2N]-based ionic liquids. transfer fluid ILs to determine their key thermal and transport properties over a wide range of temperatures. These ILs are as follows: 1-butyl-3-methylimidazolium bis[(perfluoroethyl)sulfonyl]imide ([bmim][Pf2N]), 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([bmim][Tf2N]), 1-butyl2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([bmmim][Tf2N]), 1-butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide ([bmpyr][Tf2N]), N-butyl-N,N,Ntrimethylammonium bis[(trifluoromethyl)sulfonyl]imide ([N4111][Tf2N]), and N,N,N-trimethylammonium-N-butanoic acid bis[(trifluoromethyl)sulfonyl]imide ([N4 COOH 111] [Tf2N]). The [Tf2N] and [Pf2N] anions were chosen because they have been shown to give excellent thermal stability to ILs, which is essential for heat transfer fluids. The effect of varying the nature of the cation on thermal properties was also a goal of the study. The remainder of the paper is organized as follows: the simulation and experimental methodologies are presented in section II, while the main results and discussion are provided in section III. Finally, some concluding remarks are given in section IV.

I. INTRODUCTION Heat transfer fluids are commonly used in industrial and consumer applications. The applications range from refrigeration systems at the low temperature end to solar energy collection and thermal storage at high temperatures. The physical properties of thermal fluids greatly affect the overall efficiency of the system; thus, there is a strong motivation to develop thermal fluids with improved properties. Examples of commonly used heat transfer fluids in commercial use include Dowtherm (a glycol-based liquid), SYLTHERM (a silicon oil), and Therminol (diphenyl oxide/biphenyl fluids). Ionic liquids (ILs) are a class of organic salts with melting points below 100 °C. They tend to have very low volatilities, low flammability, and high thermal stability, thereby making them possible candidates for use as high temperature thermal fluids.1−5 A great number of different ILs with a variety of physical and chemical properties can be synthesized from a combination of different cations (most commonly used are substituted imidazolium, pyridinium, and quaternary ammonium or phosphonium ions) and a host of different anions. One can judiciously select from a multitude of ILs to suit a specific application. For the rational design of ILs as heat transfer fluids, it is important to investigate the thermophysical properties such as density, heat capacity, viscosity, and thermal conductivity. Although many physical properties of ILs have been studied extensively, a lack of reliable data still exists. This is especially true for thermal properties. In particular, only limited information on the thermal conductivity of ILs is available in the literature. The aim of this study is to carry out a combined experimental and molecular simulation study of six different potential heat © 2012 American Chemical Society

II. METHODOLOGY A. Experimental Methods. 1. Materials. [bmim][Tf2N], [bmmim][Tf2N], [bmpyr][Tf2N], and [N4111][Tf2N] were purchased as off-the-shelf chemicals from Ionic Liquid Received: Revised: Accepted: Published: 7242

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Figure 1. All-atom representations of cations and anions studied.

and allowed to equilibrate to temperature. The rheometer operation was verified by NIST standards within the viscosity ranges tested and was within 5% experimental error range. The thermal conductivity for all ILs was measured by the transient hot wire method using a Decagon KD2 thermal properties analyzer with the KS-1 sensor from 20 to 80 °C. The ILs were equilibrated at temperature in a water bath for 15 min before sample measurement. The bath was turned off during the measurements to avoid inducing convection in the IL. B. Molecular Dynamics Simulations. The extent to which a classical molecular simulation accurately predicts thermophysical properties depends on the quality of the force field. In this work, we have developed force fields having the following functional form

Technologies, Inc. [N4COOH111][Tf2N] was purchased as a custom synthesis from Ionic Liquid Technologies, Inc. [bmim][Pf2N] was synthesized by the following procedures. A 1:1 molar ratio of 1-butyl-3-methylimidazolium chloride (Aldrich) and Li bis(perfluoroethylsulfonyl)imide (3M) were mixed together and covered in 300 mL of deionized water. The mixture was allowed to stir for 30 min after all of the salts were dissolved. The solution was allowed to settle into two phases. The organic phase was washed with deionized water and allowed to settle for 30 min. This process was repeated three times. The washed organic phase was then bubbled with dry nitrogen for 24 h to dry the resulting IL. The samples were diluted and analyzed for chloride content using a Dionex RFIC3000 ion chromatography system with the following parameters: IonPac AG-19 4 mm × 50 mm guard column, IonPac AS-19 4 mm × 250 mm analytical column, and a suppressed conductivity detector. Each injection used 50 μL of sample and a 20−40 mmol KOH gradient mobile phase with a 1 mL/min flow rate. Control of the system and data acquisition used Dionex Chromeleon v.6.8 software. No residual chloride was detected for any of the ILs. 2. Measurements. The heat capacity was measured using a Netzsch DSC 404 differential scanning calorimeter with a silver furnace between 40 and 400 at 20 °C/min. The values for heat capacity were determined using ASTM defined methods.6 Approximately 20 mg of IL was loaded into aluminum crucibles and covered. Observed results were compared to a sapphire standard, and the specific heat was calculated. All measurements were conducted at least five times to ensure accuracy, and representative data are shown. The density for all ILs was measured using a Mettler Toledo DM40 density meter from 20−80 °C at 20° intervals using a flow through capillary cell. Between samples, the cell was flushed with ethanol and water and then dried using the automated drying system. Viscosity measurements were taken on a Thermo Haake Mars III rheometer from 25 to 300 °C using a 0.5° Ti cone and plate. The temperature was controlled by electric heaters. Approximately 1 mL of IL was added to the plate after zeroing

Vtot =

∑

k b(r − r0)2 +

bonds

+

∑

kθ(θ − θ0)2

angles

∑

kχ [1 + cos(nχ − δχ )]

dihedrals

+

∑

k ψ [1 + cos(nψ − δψ )]

improper

⎧ ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ ⎫ qiqj ⎪ σij ⎥ ⎪ ⎢ σij ⎬ ∑ ⎨4εij⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥ + rij ⎠ rij ⎠ 4πε0rij ⎪ ⎝ ⎝ i [bmim][Tf2N] > [bmmim][Tf2N] > [bmpyr][Tf2N] ∼ [N4111][Tf2N]. In contrast, the simulation trend is [N4COOH111][Tf2N] > [bmim][Pf2N] > [N4111][Tf2N] > [bmim][Tf2N] ∼ [bmpyr][Tf2N] > [bmmim][Tf2N]. Note that no attempt was made to adjust the force field parameters to match any experimental data. Instead, these results serve as a benchmark for the level of accuracy that one might expect to achieve over a range of ILs using purely

III. RESULTS AND DISCUSSION A. Liquid Density. Figure 2 shows a comparison of experimental and computed liquid densities as a function of temperature. The experimental densities measured in the present work agree well with previously reported values. In general, computed liquid densities and isobaric expansivities (which can be estimated from the slope of density vs temperature) agree well with the experimental data. For example, Figure 2a−c shows that the computed and experimental densities for the imidazolium-based ILs are virtually identical. Agreement is less good but still reasonable for the pyridinium-based IL (Figure 2d), 7245

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Figure 3. Comparison of simulated molar heat capacities with experimental values for (a) [bmim][Pf2N], (b) [bmim][Tf2N], (c) [bmmim][Tf2N], (d) [bmpyr][Tf2N], (e) [N4111][Tf2N], and (f) [N4COOH111][Tf2N]. Open circles denote simulation results, and filled circles are experimental results from the present study. Other experimental data36−41 are represented by other open symbols. The lines are guides to the eye fit through the simulation results.

predictive methods to generate force fields. A listing of simulated and experimental densities is given in the Supporting Information. B. Heat Capacity. Experimental heat capacity data for these ILs are scarce. Six sets of previously published experimental data for [bmim][Tf2N] are available,36−41 and one published result is available for [bmpyr][Tf2N].40 Unfortunately, the different experimental data sets for [bmim][Tf2N] have a high degree of scatter, as can be seen in Figure 3b. A recent study42 coordinated by IUPAC on the consistency of property measurements for ILs, specifically [hmim][Tf2N], suggests that such variation in experimental heat capacity measurements is typical, even when the same sample is studied. Variations in instruments and inherent uncertainties in the methods, particularly differential scanning techniques, can lead to differences

of 6% or more for the same compound. If one accounts for variations in sample purity, the deviations can be even more pronounced. Given that the most amount of data exist for [bmim][Tf2N], we discuss this IL first. Figure 3b shows that the experimental heat capacities from the present study agree fairly well with those of Ge et al.40 but are higher than both the present set of simulations and most other experimental data. The simulation results are consistent with the experimental results of Fredlake et al.37 but overestimate the results reported by Holbrey et al.36 and underestimate other experimental data by about 6%.38,39,41 All of the results show that the heat capacity increases with increasing temperature, although the rates of change vary among the various data sets. The present experimental data have what 7246

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Figure 4. Comparison of computed self-diffusion coefficients of the six ILs with experimental data25,26,29 in a log-inverse plot for (a) [bmim][Pf2N], (b) [bmim][Tf2N], (c) [bmmim][Tf2N], (d) [bmpyr][Tf2N], (e) [N4111][Tf2N], and (f) [N4COOH111][Tf2N]. The lines are the least-squares fitting of Einstein data to an Arrhenius equation.

about 12%. Interestingly, this is about the same percentage by which the simulations underestimated Ge et al.'s heat capacities for [bmim][Tf2N]. For all other ILs, the experimental heat capacities of the present study are systematically higher than the predictions from simulations. The simulations do predict that the heat capacity increases linearly with increasing temperature at about the same rate as the experimental data. The simulated trend in molar heat capacity is [bmim][Pf2N] > [N4COOH111][Tf2N] ∼ [N4111][Tf2N] ∼ [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. The experimental trend is [bmim][Pf2N] > [bmmim][Tf2N] >[N4COOH111][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N] > [N4111][Tf2N]. A listing of simulated heat capacities is given in the Supporting Information.

appears to be a slight curvature with temperature, although due to the uncertainties represented by the error bars, it is not entirely clear if this curvature is real. Given the scatter in the data and the fact that differences of 6% or more are to be expected, it is difficult to assess which set of data are “right” and whether or not the computed heat capacities are accurate. At this point, about all that can be concluded is that the simulations appear to give heat capacity estimates that are reasonably consistent with experiment. Results for [bmpyr][Tf2N], the only other IL for which previous experimental heat capacity data are available, are shown in Figure 3d. The results of Ge et al.40 are at low temperatures, while the experimental results from the present study are at high temperature, with only a small amount of overlap. Within the uncertainties, the experimental results agree. The simulations underestimate the values reported by Ge et al.40 by 7247

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leading to a degree of network formation that slows the dynamics. It will be interesting if this finding is confirmed experimentally. The self-diffusivity of [bmim][Tf2N] is greater than that of [bmim][Pf2N], and the diffusivity of [bmim][Tf2N] is greater than that of [bmmim][Tf2N]. It has been argued that directional and localized hydrogen bonds fluidize imidazolium-based ILs,45,46 thereby leading to increased dynamics. This would suggest that the larger [Pf2N] associates more weakly with the [bmim] cation than [Tf2N], thereby leading to slower dynamics, consistent with the simulations. It has already been suggested that the addition of a methyl group to the C2 position of the imidazolium cation ([bmmim]) slows the dynamics of the cation relative to [bmim] via this effect. The simulation results are consistent with this observation. Experimental results from Tokuda et al. suggest that the self-diffusivities of [bmim][Pf2N] and [N4111][Tf2N] are nearly the same,25 while the simulations show that these two ILs have similar selfdiffusivities at high temperature but deviate at lower temperature. D. Shear Viscosity. As with the self-diffusivity, literature data on the shear viscosity exist for all of the ILs except the butanoic acid compound. Results of the experimental viscosity measurements and viscosity simulations are shown in Figure 5. The present set of experimental results agree quite well with literature values. The experimental trend in viscosity is that [N4COOH111][Tf2N] > [bmmim][Tf2N] ∼ [bmim][Pf2N] > [N4111][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. The simulations predict a similar trend, although the simulations overestimate the numerical value of viscosities by about 1 order of magnitude. A similar behavior has been observed in previous simulation studies18,19,47 and is thought to be due in part to a neglect of polarizability.15,48 Despite this, the temperature dependence of the viscosity is captured reasonably well by the simulations. A listing of simulated and experimental viscosities is given in the Supporting Information. Figure 5 shows that temperature has a dramatic effect on the shear viscosity. For example, [bmim][Tf2N] has a viscosity of 0.481 Pa·s at 298 K, which decreases to 47.7 mPa·s at 353 K and 5.22 mPa·s at 430 K. It is also important to note that small changes in the structure of the ILs produce large changes in viscosity. It has been suggested that the viscosity of ILs is impacted by hydrogen bonding, van der Waals forces, and molecular weight and is inversely proportional to mobility.49 A group contribution method has predicted that with a common imidazolium cation, ILs having highly symmetric or almost spherical anions are more viscous, while less symmetric anions lead to decreased viscosity.50 The simulations predict that the viscosity of [bmim][Tf2N] is greater than that of [bmim][Pf2N] over the range of 283−353 K. Given that the [Pf2N] anion is “less spherical” than the [Tf2N] anion, this seems to agree with the prediction. However, the simulated trend is reversed at temperatures above 400 K. For ILs having a common [Tf2N] anion and a similar alkyl chain length on the cation, the simulation trend in viscosity is [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. This agrees with the experimental results. Tokuda et al. showed that pyrrolidinium salts are generally more viscous than the corresponding imidazolium salts.51 Bonhote et al. suggested that replacement of a methyl group with hydrogen at the C2 position substantially decreases the viscosity of imidazoliumbased ILs.49 Again, this is thought to be due to the fact that strong, directional, and localized hydrogen bonds fluidize imidazolium-based ILs through the introduction of “defects” in the Coulomb interaction network.45,46

It is of interest to compare the heat capacities of the ILs with a common heat transfer fluid such as TherminolVP-1. It has been reported that TherminolVP-1 has a heat capacity of 295.5 J·mol−1·K−1 at 373 K and 265.6 J·mol−1·K−1 at 313 K.43 Molar heat capacities of the ILs are almost twice as high as that of TherminolVP-1. More relevant for engineering purposes is the specific heat capacities. TherminolVP-1 has a specific heat capacity of 2.0 J·g−1·K−1 at 450 K, while the specific heat capacity of the ILs is in the range of 1.4−1.7 J·g−1·K−1 at 450 K. For heat transfer fluids, a critical parameter is the energy storage density, which is the product of the specific heat capacity and gravimetric density. The ILs compare favorably with TherminolVP-1. The energy storage density of [bmim][Tf2N] is calculated to be 1.91 MJ·m−3·K−1 at 373 K as compared to 1.78 MJ·m−3·K−1 for TherminolVP-1. Experimentally,44 the energy storage density of [bmmim][Tf2N] is 2.37 MJ·m−3·K−1 at 473 K versus 1.90 MJ·m−3·K−1 for TherminolVP-1. This suggests that on a volumetric basis, ILs are better thermal energy storage fluids than conventional heat transfer fluids. C. Self-Diffusivity. Figure 4 shows the computed selfdiffusion coefficients for the anions and cations of each IL as a function of temperature. Results are reported for the application of eqs 3 and 4. Previously reported experimental self-diffusivities25,26,29 are available for all but the butanoic acid IL. No self-diffusivities were measured in the present study. Computed self-diffusivities are given in the Supporting Information and tend to be lower than the experimental values by about a factor of 2. The simulations capture the temperature dependence very well and agree with experiments in that for all but the butanoic acid IL, the cations have a higher selfdiffusivity than anions. Self-diffusivities estimated from the Green−Kubo method are consistently higher than those computed from the Einstein relation. Such an observation has been found in other studies.18,19 The differences are most apparent at lower temperatures where dynamic heterogeneity is observed. On the basis of previous studies, we believe that the Einstein method gives the most reliable estimates, due to numerical imprecision associated with the Green−Kubo approach at long times. As expected, the self-diffusion coefficient increases with increasing temperature, and a linear behavior of log D vs 1/T indicates an Arrhenius temperature dependence of the self-diffusion coefficients. The activation energies from the Arrhenius equation fitting are reported in Table 1. Note that the simulated activation energies compare well with the experimental values (see Figure 4). Table 1. Activation Energies from the Arrhenius Equation D = D0 exp(−ED/RT) Fitting to the Simulated D Data kJ mol−1 ILs

ED+

ED−

[bmim][Pf2N] [bmim][Tf2N] [bmmim][Tf2N] [bmpyr][Tf2N] [N4111][Tf2N] [N4COOH111][Tf2N]

32.5 34.6 32.2 32.5 37.8 36.5

32.4 35.2 31.4 31.7 37.2 35.5

The simulations predict that the self-diffusivity of [N4111][Tf2N] is greater than that of [N4COOH111][Tf2N]. This may be due to the fact that the carboxyl group is capable of forming additional associations among cations and anions, thereby 7248

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Figure 5. Comparison of computed shear viscosities (open circles) of ILs with experimental data from the present study (filled circles) and other experimental data25,26,29,31,35,56−58 (other open symbols) as a function of temperature for (a) [bmim][Pf2N], (b) [bmim][Tf2N], (c) [bmmim][Tf2N], (d) [bmpyr][Tf2N], (e) [N4111][Tf2N], and (f) [N4COOH111][Tf2N]. The lines are least-squares fits of the Einstein data to an Arrhenius equation.

where reff is the effective hydrodynamic radius of a molecule. One can always adjust reff to yield a particular viscosity from the self-diffusivity, but because ILs are not spherical, this is a somewhat ill-defined measure. Instead, a fractional Stokes−Einstein relation of the following form is investigated

The viscosity of TherminolVP-1 is 2.6 mPa·s at 313 K and 0.985 mPa·s at 373 K.43 For comparison, this is about an order of magnitude less than the viscosity of the ILs investigated here. In addition, the simulations predict that the addition of a carboxyl group to the cation increases the viscosity even more. This suggests that additional strategies aimed at lowering the viscosity of ILs should be pursued. Note that the viscosity trend of the ILs generally coincides with the reverse order of selfdiffusivity, as would be expected for a fluid that obeys a Stokes− Einstein relation of the following form D=

kBT 6πηreff

D ∝ (Tη−1)β

(10)

where β = 1 for a conventional Stokes fluid. It has been found that β ∼ 0.8 for some molten salts 52 and β ∼ 0.92 for the IL [bmim][PF6].53 A log−log plot of D vs Tη −1 is shown in Figure 6, and the estimates of β taken from a linear regression of the simulation results are given in Table 2.

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temperature. The accessible temperature range is small in the experiments, however, and the uncertainties are fairly large, so it is difficult to draw hard conclusions from these trends. The simulations predict that changing the anion from [Tf2N] to [Pf2N] lowers the thermal conductivity by 0.015 W·m−1·K−1, with a very similar temperature dependence, while varying the cation from [bmim] to [bmmim] hardly changes the thermal conductivity. There is a slight decrease in thermal conductivity when the cation is changed from [bmim] to [bmpyr]. The simulations and experiments agree that the addition of a carboxyl group to the cation increases the thermal conductivity. Of all of the ILs studied, [N4COOH111][Tf2N] appears to have the highest thermal conductivity, with a simulated value of 0.128 W·m−1·K−1 and an experimental value of 0.135 W·m−1·K−1 at 300 K. These values of the thermal conductivity are similar to those of common organics but only 20% as large as that of water. The overall trend of simulated thermal conductivity is [N4COOH111][Tf2N] > [N4111][Tf2N] > [bmim][Tf2N] ∼ [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Pf2N]. The experimental trend is [N4COOH111][Tf2N] > [bmmim][Tf2N] > [bmim][Tf2N] > [bmpyr][Tf2N] > [N4111][Tf2N] > [bmim][Pf2N]. The relative position of each compound in these two trends is consistent, with the exception of [N4111][Tf2N], which has a lower thermal conductivity in the experimental trend. It is assumed that heat is conducted through a liquid via longitudinal oscillations and that the thermal conductivity of the liquid decreases as the average distance between the centers of molecules is increased. Although the ILs have significantly higher densities than most molecular liquids, this is offset by the large size of their ions. On the basis of the computed radial distribution functions (not shown), all of the ILs have cation−anion center of mass distances greater than 5 Å. This may be why their thermal conductivities are lower than expected from their high gravimetric densities. The ILs also have thermal conductivities that are similar to TherminolVP-1. The computed temperature dependence of the thermal conductivity can be represented by the following linear equation: 1,59

Figure 6. Parity plot of the Stokes−Einstein relation for cations (open symbols) and anions (filled symbols) of ILs. All results are for simulations. Most of the liquids fall below the equivalence line, indicating that viscosities are larger than the Stokes−Einstein model suggests.

Table 2. Fractional Stokes−Einstein Relation of ILs D ∝ (Tη−1)β ILs

β+

β−

[bmim][Pf2N] [bmim][Tf2N] [bmmim][Tf2N] [bmpyr][Tf2N] [N4111][Tf2N] [N4COOH111][Tf2N]

1.09 0.94 1.18 1.00 0.90 0.82

1.09 0.95 1.15 0.97 0.89 0.80

From these results, it appears that there is no universal Stokes−Einstein relation for these ILs, but rather, ILs fall in a range between conventional molten salts and molecular liquids. For instance, β ∼ 0.94 and 0.95 for cations and anions of [bmim][Tf2N], respectively, while it equals 0.82 and 0.80 for cations and anions of [N4COOH111][Tf2N]. These estimates are close to the experimental values by Kanakubo et al. 53 and are consistent with previous simulation results that have shown that the Stokes−Einstein equation is invalid for ILs.54,55 E. Thermal Conductivity. As with the heat capacity, previous thermal conductivity data only exist for [bmim][T2N] and [bmpyr][Tf2N]. As shown in Figure 7, the experimental results from the present study agree very well with the data of Ge et al.59 for [bmim][T2N] and [bmpyr][Tf2N], but they are about 10% higher than the results of Nieto de Castro et al. for [bmpyr][Tf2N].60 The simulations predict that the ILs have similar thermal conductivities, each within the range of 0.09− 0.13 W·m−1·K−1, with the thermal conductivity decreasing with increasing temperature. In general, the experimental thermal conductivities of the present study are higher than the simulations by 10−15%. The weak temperature dependence of thermal conductivity observed in the simulations has been reported in other experimental studies of ILs.1,3,59 The experimental results for four of the six ILs show that the thermal conductivity decreases slightly with increasing temperature, in agreement with the simulations. For [bmim][Pf2N] and [N4COOH111][Tf2N], however, the experiments predict that the thermal conductivity increases slightly with increasing

λ = aT + b

(11)

which is useful for engineering design calculations. The fit parameters a abnd b for the simulation results are given in Table 3. Note that the variance of the fits does not exceed 0.8%. Because of the limited temperature range, fitting was not performed on the experimental data. Figure 8 shows how the thermal conductivity of all of the ILs and TherminolVP-1 vary with temperature. Relating thermal conductivity to particular molecular level properties is significantly more difficult for ILs because of the presence of two types of ion, the presence of strong intermolecular Coulombic interactions, possible hydrogen bonding interactions, and heterogeneous aggregation of polar and nonpolar regions.61 To better understand the trend in thermal conductivity, the simulation results were correlated using several empirical models.2,4 Figure 9 shows the computed thermal conductivities for the six ILs correlated in various ways. The simple correlation of thermal conductivity and molecular weight shows a slight decrease of thermal conductivity with increasing molecular weight for the ILs at a given temperature 400 K. [N4COOH111][Tf2N] is an exception. The scattered data suggest that the correlation shown in the second panel of Figure 9 between λM/η and M is lacking, although Tomida et al. 7250

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Figure 7. Comparison of simulated thermal conductivities (open circles) of the six ILs with experimental data from the present work (filled squares) and published experimental data (filled triangles) as a function of temperature for (a) [bmim][Pf2N], (b) [bmim][Tf2N], (c) [bmmim][Tf2N], (d) [bmpyr][Tf2N], (e) [N4111][Tf2N], and (f) [N4COOH111][Tf2N]. The lines are linear regression fits to the simulation results.

found that the correlation log(λM/η) = A − BM worked well for their experimental data set (imidazolium hexafluorophosphates) and normal alkanes.2 Froda et al. have suggested a simple relationship between thermal conductivity, molecular weight, and density.4 The third and fourth panels of Figure 9 show that there is a linear trend for both λM versus M and λMρ versus M for ILs, again with [N4COOH111][Tf2N] being an outliner. These latter two correlations appear to work well, especially for [Tf2N]-based ILs, and could be used to predict thermal conductivities for ILs when no data exist.

Table 3. Temperature Parameters for Thermal Conductivity of the Six ILs Obtained from Simulations

7251

ILs

−105a (W·m−1·K−2)

b (W·m−1·K−1)

[bmim][Pf2N] [bmim][Tf2N] [bmmim][Tf2N] [bmpyr][Tf2N] [N4111][Tf2N] [N4COOH111][Tf2N]

4.443 6.494 4.387 4.129 9.947 4.004

0.1058 0.1261 0.1183 0.1151 0.1442 0.1374

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limited amount of experimental data for thermal conductivity and the small temperature range over which measurements were made make it difficult to assess the accuracy of the simulations. Densities decrease while heat capacities increase linearly with increasing temperature. The trend in heat capacity is [bmim][Pf2N] > [N4COOH111][Tf2N] ∼ [N4111][Tf2N] ∼ [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. Molar heat capacities of ILs are almost twice as large as that of the commercial heat transfer fluid TherminolVP-1. ILs compare favorably with TherminolVP-1 with respect to energy storage density; for [bmim][Tf2N], the energy storage density at 373 K is 1.91 MJ·m−3·K−1, while for TherminolVP-1, the corresponding value is 1.78 MJ·m−3·K−1. The viscosities of the ILs decrease significantly with increasing temperature. The temperature dependence can be described with an Arrhenius equation. The experimental trend in viscosity is that [N4COOH111][Tf2N] > [bmmim][Tf2N] ∼ [bmim][Pf2N] > [N4111][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. The simulations predict a similar trend. For ILs having a common [Tf2N] anion and a similar alkyl chain length on the cation, the trend in viscosity is [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Tf2N]. The viscosity trend of ILs generally coincides with the reverse order of self-diffusivity, which suggests that the microscopic ion dynamics reflects the macroscopic physical properties. ILs have at least 1 order of magnitude higher viscosity than TherminolVP-1. The simulations predict that the thermal conductivities of the ILs are within the range of 0.09−0.13 W·m−1·K−1, which is about 10−20% lower than the experimental values reported here and about one-fifth that of water. There is a weak linear dependence of the thermal conductivity on temperature. The thermal conductivities of the ILs are comparable with TherminolVP-1. The overall trend in thermal conductivity is [N4COOH111][Tf2N] > [N4111][Tf2N] > [bmim][Tf2N] ∼ [bmmim][Tf2N] > [bmpyr][Tf2N] > [bmim][Pf2N]. The thermal conductivities of the [Tf2N]-based ILs can be correlated with linear expressions involving thermal conductivity, molecular weight, and density.

Figure 8. Simulated thermal conductivities (open symbols) of the six ILs as a function of temperature as compared with the data of TherminolVP-1.43 The straight lines are linear regressions.

Figure 9. Computed thermal conductivities and its combination with other thermophysical properties of ILs at 400 K as a function of the molecular weight M. First panel, thermal conductivity λ in the unit of W·m−1·K−1; second panel, λ times M divided by shear viscosity η in the unit of W·g·mPa−1·s−1·m−1·K−1·mol−1; third panel, λM in the unit of W·g·m−1·K−1·mol−1; and fourth panel, λM times density ρ in the unit of W·g2·m−1·K−1·mol−1·cm−3. The letter A stands for [bmim][Pf2N], B for [bmim][Tf2N], C for [bmmim][Tf2N], D for [bmpyr][Tf2N], E for [N4111][Tf2N], and F for [N4COOH111][Tf2N]. The lines are from the linear regression.

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ASSOCIATED CONTENT

S Supporting Information *

A listing of the simulated and experimental data and some comparison figures, along with a complete listing of force field parameters. This material is available free of charge via the Internet at http://pubs.acs.org.

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IV. CONCLUSIONS We have carried out experimental property measurements and molecular dynamics simulations on six ILs over a range of temperatures to determine the thermal and transport properties relevant for their use as heat transfer fluids. Properties examined include density, heat capacity, self-diffusivity, viscosity, and thermal conductivity. Overall, there is good agreement between the current experimental results and the previous studies, although some differences were observed for the heat capacity and thermal conductivity. The simulations also generally agree with the experimental data. Agreement is best for density and heat capacity. The simulations tend to underestimate the selfdiffusivity and overestimate the viscosity, a phenomenon observed in many other studies. Relative trends and the temperature dependence of these quantities is captured well. The rather

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (E.M.) or [email protected] (E.B.F.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this work is from the DOE-EERE Solar Energy Techology Program. Savannah River National Laboratory is operated by Savannah River Nuclear Solutions. This document was prepared in conjunction with work accomplished under Contract No. DEAC09-08SR22470 with the U.S. Department of Energy. We thank Dr. Craig Tenney for help with force field development. Computational resources were provided by Notre Dame's Center for Research Computing. 7252

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