Thermophysical Properties of Homologous Tetracyanoborate-Based

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Thermophysical Properties of Homologous Tetracyanoborate Based Ionic Liquids Using Experiments and Molecular Dynamics Simulations Thomas M. Koller, Javier Ramos, Peter S. Schulz, Ioannis George Economou, Michael Heinrich Rausch, and Andreas Paul Fröba J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b12929 • Publication Date (Web): 07 Apr 2017 Downloaded from http://pubs.acs.org on April 11, 2017

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The Journal of Physical Chemistry

Thermophysical Properties of Homologous Tetracyanoborate Based Ionic Liquids Using Experiments and Molecular Dynamics Simulations Thomas M. Koller,*,a Javier Ramos,b Peter S. Schulz,c Ioannis G. Economou,d,e Michael H. Rausch,a and Andreas P. Fröbaa

a

Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in

Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, 91052 Erlangen, Germany b

BIOPHYM, Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, Serrano 113bis, 28006-Madrid, Spain

c

Department of Chemical and Biological Engineering (CBI), Institute of Chemical Reaction

Engineering, University of Erlangen-Nuremberg, Egerlandstraße 3, 91058 Erlangen, Germany d

National Centre for Scientific Research “Demokritos”, Institute of Nanoscience and

Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory, GR-15310 Aghia Paraskevi Attikis, Greece e

Texas A&M University at Qatar, Chemical Engineering Program, Education City, PO Box 23874, Doha, Qatar

__________________________ *

Author to whom correspondence should be addressed. Tel. +49-9131-85-23279, Fax +49-9131-85-

25851, E-mail [email protected]. 1 Environment ACS Paragon Plus


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ABSTRACT: Thermophysical properties of low-viscosity ionic liquids (ILs) based on the tetracyanoborate ([B(CN)4]‒) anion carrying a homologous series of 1-alkyl-3-methylimidazolium ([AMIM]+) cations [EMIM]+ (ethyl), [BMIM]+ (butyl), [HMIM]+ (hexyl), [OMIM]+ (octyl), and [DMIM]+ (decyl) were investigated by experimental methods and Molecular Dynamics (MD) simulations at atmospheric pressure and various temperatures. Spectroscopic methods based on nuclear magnetic resonance and surface light scattering were applied to measure the ion selfdiffusion coefficients and dynamic viscosity, respectively. In terms of MD simulations, a nonpolarizable molecular model for [EMIM][B(CN)4] developed by optimization to experimental data was transferred to the other homologous ILs. For the appropriate description of the inter- and intramolecular interactions, precise and approximate force fields (FFs) were tested regarding their transferability within the homologous IL series, aiming at reducing the computational effort in molecular simulations. It is shown that at comparable simulated and experimental densities, the calculated and measured data for viscosity and self-diffusion coefficients of the ILs agree well mostly within combined uncertainties, but deviate stronger for longer-chained ILs using an overly coarse FF model. For the [B(CN)4]‒-based ILs studied, a comparison with literature data, the influence of varying alkyl chain length in the cation on their structural and thermophysical properties, and a correlation between self-diffusivity and viscosity are discussed.

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INTRODUCTION Low-viscosity ionic liquids (ILs) containing the tetracyanoborate ([B(CN)4]‒) anion are potential working fluids in carbon capture1,2 or electrolyte3,4 applications. For this class of ILs, reliable thermophysical property data for viscosity and self-diffusion coefficients are necessary for engineers and scientists. The viscosity affects heat and mass transport5,6 and determines power requirements for mixers and pumps,7 while the self-diffusion coefficients of ILs can often be correlated with the viscosity using, e.g., a modified Stokes-Einstein relation.8 Experiments are required to provide a reliable database used to develop structure-property relationships, but also to optimize and validate results obtained using less resource-consuming molecular simulations. Vice versa, simulations can help understand the experimental data from a molecular point of view. In connection with the determination of dynamic properties of ILs, experimental and simulation methods are subjected to own challenges. While the self-diffusivity of ILs is rarely studied experimentally,9 relative deviations between published experimental viscosity data of up to 60% for the same IL10,11 may be attributed to unspecified experimental conditions and/or to the use of inconsistent, in most cases, routine techniques. Using Molecular Dynamics (MD) simulation, the slow dynamic behavior of ILs is often underpredicted resulting in deviations for calculated dynamic properties from the experiment by more than one order of magnitude.6,12 Such deviations can often be related to an inadequate modeling of both electrostatic and nonelectrostatic interactions occurring in ILs on different length scales.4 Dynamic light scattering (DLS) and equilibrium MD simulation give access to macroscopic fluid properties by studying microscopic fluctuations at macroscopic thermodynamic equilibrium. These methods have been used in our previous studies13-15 of thermophysical properties of the two [B(CN)4]‒-based ILs [EMIM][B(CN)4] and [HMIM][B(CN)4] carrying homologous 1-alkyl-3methylimidazolium ([AMIM]+) cations based on ethyl and hexyl chains, respectively. The nonelectrostatic force field (FF) developed for [EMIM][B(CN)4]13 was transferred to the longerchained [HMIM][B(CN)4], and the electrostatic FF of [HMIM][B(CN)4] was approximated by that 3 Environment ACS Paragon Plus


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developed for [BMIM][B(CN)4].14 The good agreement between the calculated and experimental density, surface tension, self-diffusivities, and viscosity data for [HMIM][B(CN)4] indicated the reasonable representation of molecular interactions by the approximate model for this IL.14 In the present study, a continuation of the investigation of a homologous series of [B(CN)4]‒based ILs featuring different alkyl side chain lengths is carried out by performing experiments and MD simulations at various temperatures and atmospheric pressure. The experimental viscosity and self-diffusivity data for the ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4] containing butyl, octyl, and decyl chains, respectively, served as reference for the equilibrium MD simulations. Precise and approximate FFs with respect to the electrostatic and non-electrostatic potential were tested regarding their transferability within the homologous IL series. By this, the still unresolved question in literature should be addressed whether and to which extent approximate FFs can compete with more complicated and precise FFs in predicting dynamic properties of ILs, aiming at reducing the computational effort in molecular simulations. Beside contributing to an ensured database for [B(CN)4]‒-based ILs, a further objective in this work is to investigate the influence of the alkyl side chain length on the thermophysical properties and an empirical correlation between viscosity and self-diffusivity.

EXPERIMENTAL SECTION This section includes the essential information on the sample preparation of the [B(CN)4]‒-based ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4] as well as the experimental methods used to determine their self-diffusion coefficients, surface tension, and viscosity at atmospheric pressure. A more detailed description of the fundamentals and experimental realization of the employed techniques, especially in connection with their application to ILs, is given in literature.15-17 The ILs [BMIM][B(CN)4] (molar mass M = 254.10 g·mol−1), [OMIM][B(CN)4] (M = 310.21 g·mol−1), and [DMIM][B(CN)4] (M = 338.26 g·mol−1) were synthesized from their corresponding 4 Environment ACS Paragon Plus

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chloride salts [BMIM][Cl], [OMIM][Cl], and [DMIM][Cl]. These salts were purchased from Merck KGaA and washed with acetone before use. Using potassium tetracyanoborate ([K][B(CN)4]) obtained from Merck KGaA and used as received, the chloride was substituted by tetracyanoborate in an anion exchange reaction. Equimolar amounts of a 0.5 mol·kg−1 aqueous solution of the halide salt and [K][B(CN)4] were suspended in distilled water under rigorous stirring at ambient temperature. The formed upper aqueous phase was decanted while the lower IL phase was diluted with dichloromethane and washed with distilled water several times. After drying the IL-rich phase over magnesium sulfate, dichloromethane was removed from the IL product under a vacuum atmosphere. The purities of the [B(CN)4]−-based ILs of larger than 99 mol-% were verified by 1H nuclear magnetic resonance (NMR) analysis (JEOL, ECX +400 spectrometer). The water concentration was determined by Karl-Fischer coulometric titration (Metrohm, 756 KF Coulometer) after the sample preparation and after the experiments. The mean water mass fractions averaged from the values before and after the measurements are 365 ppm for [BMIM][B(CN)4], 676 ppm for [OMIM][B(CN)4], and 535 ppm for [DMIM][B(CN)4]. Their expanded uncertainties (k = 2) are estimated to be less than ±20%. The self-diffusion coefficients D of the cation (D+) and anion (D−) at atmospheric pressure were derived from pulsed-field gradient spin-echo NMR measurements. The 1H nuclei in the methyl and alkyl chains of the cation and the 11B nucleus in the anion were used as NMR active species. The temperature stability during the experiments performed between (293.15 and 313.15) K in steps of 5 K was better than ±0.5 K, and the absolute uncertainty in the temperature measurement was ±0.05 K. The expanded uncertainty (k = 2) of the experimental self-diffusivity data is estimated to be less than ±10%. The surface tension or, strictly speaking,18 the interfacial tension σref was measured at a single temperature Tref close to room temperature (293 K) inside an optical glass cell for photometry



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(Hellma, 402.000) under argon atmosphere using a pendant drop apparatus (OEG, SURFTENS universal). The uncertainty of the temperature measurement is within ±0.1 K. For the surface tension data σref, the expanded uncertainty (k = 2) can be specified with ±1%. To evaluate the dynamic viscosity from surface light scattering (SLS) in the case of an overdamped behavior of surface fluctuations, temperature-dependent surface tension data were predicted by the McLeod-Sudgen correlation scheme19,20 according to 4

 ρ (T )   . σ (T ) = σ ref  ρ ( T )  ref ref 

(1)

In eq 1, ρ(T) and ρref(Tref) are the densities at variable temperature T and at the reference temperature Tref. The proposed scheme predicts the surface tension of high viscosity fluids with a typical uncertainty of less than 2%.21 In the case of an overdamped behavior of surface fluctuations at lower temperatures, at a first approximation SLS could only give access to the ratio of surface tension σ to dynamic viscosity η of the [B(CN)4]−-based ILs. Here, η is evaluated based on the results from the SLS technique and the pendant drop method combined with eq 1. At larger temperatures resulting in an oscillatory behavior, surface tension and viscosity of the ILs could be determined simultaneously by SLS. In both cases, the experimental ηSLS and σSLS data were obtained by an exact numerical solution of the dispersion equation for a free liquid surface. The expanded uncertainty (k = 2) for the η values at temperatures corresponding to an overdamped behavior is estimated to be ±3%. For higher temperatures, the expanded uncertainties (k = 2) for dynamic viscosity and surface tension are estimated to be less than ±6% and less than ±11%. The larger uncertainties for η and σ at the temperature conditions where the surface fluctuations change between an overdamped and oscillatory behavior are related to the experimental complexity in this region.


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For the analysis of the SLS and pendant drop measurements as well as the prediction of σ according to eq 1, the densities ρ measured by the oscillating U-tube densimeter with an expanded uncertainty of 0.02% (k = 2) were used. These data are given in our previous publications.14,15,22

MOLECULAR DYNAMICS (MD) SIMULATION For the MD simulations of ILs, both electrostatic and non-electrostatic interactions need to be considered. In a previous study, a non-polarizable hybrid all-atom (AA) and united-atom (UA) FF with reduced charges was developed and optimized for [EMIM][B(CN)4] (abbreviated as FF-E3 in the reference13 where E stands for the ethyl homologue and 3 for the third FF developed). The FF is characterized by the potential energy function U in terms of bond stretching, bond angle bending, proper and improper dihedral torsion, and non-bonded intra- and intermolecular interactions caused by dispersive non-electrostatic and fixed-charge electrostatic interactions. The detailed functional form of the FF and the sources for the various parameters are given in Ref. 13. Based on the reduction of the electrostatic charges and an optimization of some of the non-electrostatic parameters for [EMIM][B(CN)4], an accurate prediction of equilibrium and dynamic properties was obtained when compared with the experimental data.13 The non-electrostatic terms, i.e. all FF contributions except of the electrostatic term, were transferred from [EMIM][B(CN)4] to [HMIM][B(CN)4] (FF-HB).14 The electrostatic part of [HMIM][B(CN)4] was modeled using the electrostatic charges from the IL [BMIM][B(CN)4].14 The letter B in the abbreviation FF-HB indicates such approximation. In the present study, the transfer of FF parts to various homologous ILs is carried out in different ways. The transferability of the optimized non-electrostatic FF terms for [EMIM][B(CN)4] (FF-E3) to the longer-chained ILs [BMIM][B(CN)4], [HMIM][B(CN)4], and [OMIM][B(CN)4] is tested. Concerning the electrostatic part of the potential, two different approaches are used. First, for the IL [HMIM][B(CN)4], the electrostatic potential given in the model FF-H is obtained from



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quantum mechanical (QM) calculations in a similar manner as for [EMIM][B(CN)4]13 and [BMIM][B(CN)4].14 In a second approach, based on the electrostatic charges for [BMIM][B(CN)4], an electrostatic FF for [OMIM][B(CN)4] (FF-OB) was approximated in the same way as conducted previously14 for [HMIM][B(CN)4] (FF-HB). Quantum calculations on [DMIM][B(CN)4] for calculating its electrostatic charges would require an enormous effort due to the large number of conformations. Since the transferability of the electrostatic part is addressed sufficiently by [HMIM][B(CN)4] and [OMIM][B(CN)4], investigations on the next IL in the homologous series given by [DMIM][B(CN)4] are not carried out here. The essential information on the nonelectrostatic and electrostatic FFs developed is given below. To implement the non-electrostatic FF of [BMIM][B(CN)4] and [OMIM][B(CN)4], the parameter set optimized for the MD simulations with [EMIM][B(CN)4] (FF-E3)13 was directly transferred. The additional UAs for the butyl and octyl chains in the [BMIM]+ and [OMIM]+ cations were treated according to the method proposed by Liu et al.23 All anion parameters were transferred from [EMIM][B(CN)4] to the longer-chained ILs except of the Lennard-Jones (LJ) size parameters

σLJ of the nitrogen (NC) atoms. A slight modification of σLJ,NC given by

σ LJ,NC / nm = 0.3200 + 0.0025 ⋅ nCT 2

(2)

was necessary to adjust the simulated to the experimental densities at (293.15 or 298.15) K. In eq 2, nCT2 is the number of methylene groups of type CT2 in the alkyl chain of [EMIM][B(CN)4] (nCT2 = 0), [BMIM][B(CN)4] (nCT2 = 2), [HMIM][B(CN)4] (nCT2 = 4), and [OMIM][B(CN)4] (nCT2 = 6). Increasing σLJ,NC values with increasing nCT2 decreases the attractive dispersive interactions. This outweighs the effect that the densities calculated for the homologous series carrying the [BMIM]+, [HMIM]+, and [OMIM]+ cations were found to be between (1 and 2)% larger compared to the experimental data. For the development of the electrostatic FF terms of [HMIM][B(CN)4] (FF-H), QM calculations of different ion pairs and a subsequent charge fitting applying the ensemble averaged


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restrained electrostatic potential (EA-RESP) method on the most stable ion pairs were carried out in a similar way as performed for [EMIM][B(CN)4]13 and [BMIM][B(CN)4].14 With increasing alkyl chain length of the cation, the number of dihedral conformations in the chain increases exponentially, causing very time-consuming calculations. For [HMIM][B(CN)4], 7776×3 different initial ion pair configurations were built in accordance to the methodology used for [BMIM][B(CN)4].14 For the 25 most stable configurations, the EA-RESP method was applied to compute the electrostatic charges of [HMIM][B(CN)4]. Using this method, an ensemble of structures was used, where the anion was located in different spatial regions with respect to the cation. By this technique, the surrounding electrostatic effects of the cation on the anion are captured on average, which provides a way to account in some degree for electrostatic polarizability effects within non-polarizable force fields as employed in this study. In Table S1 in the Supporting Information, the atomistic charges calculated from the most stable ion pair configurations are summarized for the homologous series of [B(CN)4]−-based ILs. The overall reduced total charges of cation and anion of the different homologous ILs are comparable around ±0.85 e. Significant variations in the electronic charge distributions of the cations of the ILs can only be found for alkyl chain variations from ethyl in [EMIM][B(CN)4] to butyl in [BMIM][B(CN)4]. Here, the aliphatic methylene groups located close to the imidazolium rings seem to shift electrons from the chain into the aromatic ring more strongly in [BMIM]+ than in [EMIM]+. Comparing the partial charges for [BMIM][B(CN)4] and [HMIM][B(CN)4], the atoms in the imidazolium ring are not subject to further electrostatic influence from the non-polar alkyl chain for nCT2

≥

2. The effect of the changing charge distribution of the short-chained cations of the

[B(CN)4]–-based ILs on the corresponding charge distribution in the anion is also relatively weak where detectable changes are also only found between [EMIM][B(CN)4] and [BMIM][B(CN)4]. The calculations presented suggest that it may be more efficient to transfer the partial charges of the IL with the corresponding alkyl side chain length for which the manifestation of the charge distribution starts to all homologous ILs with longer alkyl chains. To test the transferability of the 9 Environment ACS Paragon Plus


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electrostatic potential of ILs, the partial charges derived from [BMIM][B(CN)4] (FF-B) were transferred to the approximate models (FF-HB) [HMIM][B(CN)4] in our previous work14 and FFOB ([OMIM][B(CN)4]) within this study. The respective charges sets are listed in Table S1. In detail, for the two or four additional UAs in the hexyl or octyl chains of the [HMIM]+ or [OMIM]+ cations compared to [BMIM]+, the partial charges were assumed to be 0. This assumption seems to be straightforward as the electrostatic potential decrease strongly for long alkyl side chains, a fact which is confirmed by the EA-RESP calculations. A comparison of the thermophysical properties computed for [HMIM][B(CN)4] using the precise (FF-H) or approximate (FF-HB) partial electrostatic charges while keeping the non-electrostatic potential constant serves to illustrate the role of the electrostatic potential. The computational methods and the evaluation techniques used for [BMIM][B(CN)4] (FF-B), [HMIM][B(CN)4] (FF-H), and [OMIM][B(CN)4] (FF-OB) are identical to those used for [EMIM][B(CN)4] (FF-E3)13 and [HMIM][B(CN)4] (FF-HB).14 Thus, only the basic information is summarized here. The Gromacs 4.0.7 simulation package24 was used in all simulations performed for temperatures between (293.15 and 363.15) K at a pressure of p = 1 bar. The simulated systems represent cubic simulation boxes of volume V containing N = 58 ion pairs, i.e. more than 1200 atoms. Simulations with up to a factor of three larger numbers of molecules showed no significant differences in the computed properties within statistical uncertainties to the results based on 58 ion pairs. A time step of 2 fs was used employing periodic boundary conditions in all directions. Four different initial IL configurations obtained from the quantum calculations were energetically minimized for each temperature and equilibrated in the NVT and NpT ensemble. Thereafter, NpT simulations on the order of 5 ns were performed to determine the density ρ and to analyze the liquid bulk structure of the systems by calculating radial distribution functions between different ion types. The self-diffusion coefficients for the cation D+ and the anion D– were computed from subsequent NVT runs in the order of 20 ns based on the mean square displacement (MSD) of each ion in the linear Fickian diffusive regime where the Einstein equation25 is valid. To calculate the dynamic 10 Environment ACS Paragon Plus

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viscosity η with the equilibrium Green-Kubo method25 by analyzing the pressure autocorrelation function of the off-diagonal elements of the stress tensor, the simulation time in the NVT ensemble was extended up to 50 ns. For all simulated properties, the statistical uncertainties given in the corresponding tables and figures represent the double standard deviation of four independent runs with different initial configurations.

RESULTS AND DISCUSSION Thermophysical properties of [B(CN)4]–-based ILs were investigated by experiments and MD simulation. First, microscopic structural properties of the IL systems studied by MD simulations help support the analysis of the macroscopic behavior. Then, the results for density, surface tension, self-diffusion coefficients, and dynamic viscosity are discussed. In the corresponding subsections, the simulation results are compared to the experimental data. To obtain a full picture about the FF transferability within the homologous IL series, our previous results for [EMIM][B(CN)4]13,15 and [HMIM][B(CN)4]14 are also incorporated here. In addition to a data comparison with available literature data, the relation between self-diffusivity and viscosity of the ILs studied is investigated. Structural Properties. To analyze the liquid bulk structure of the IL systems, radial distribution functions (RDFs) were employed. The RDF, gij(r), is a probability function between particles of type i and j in terms of the number density ρN = N/V. It describes the average number density of type j, ρ N, j (r ) , at a distance r around type i, relative to the mean density of type j, ρ N, j

av

, averaged over all r-dependent spheres around type i, given by26 g ij (r ) =

ρ N, j (r ) ρ N, j

.

(3)

av

While gij(r) = 1 indicates a uniform random distribution at a given distance r between i and j, gij(r) > 1 or gij(r) < 1 denotes a local ordering or depletion in the structure, respectively.



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Figure 1 shows the center-of-mass (COM) RDFs for the pairs (a) cation-anion, g+ ‒(r), (b) anion-anion, g‒ ‒(r), and (c) cation-cation g++(r) of the four [B(CN)4]–-based ILs studied. To investigate the influence of the electrostatic potential, the corresponding RDFs for [HMIM][B(CN)4] are compared using the precise FF-H and the approximate FF-HB and shown in Figure 1d. The results are obtained from NpT simulations at (333.15 or 338.15) K and 1 bar.

Figure 1. Computed COM-RDFs between (a) cation-anion, (b) anion-anion and (c) cation-cation of [EMIM][B(CN)4] (FF-E3) at 338.15 K, [BMIM][B(CN)4] (FF-B) at 333.15 K, [HMIM][B(CN)4] (FF-HB) at 338.15 K, and [OMIM][B(CN)4] (FF-OB) at 333.15 K. All three types of RDFs are compared for [HMIM][B(CN)4] using the precise (FF-H) and approximate (FF-HB) electrostatic potentials (d). The results are calculated from NpT simulations at 1 bar.

For all types of ion interactions in the [B(CN)4]–-based ILs studied, the typical long-range ordering of ILs caused by the long-range nature of electrostatic interactions12 can be observed. The cation-anion RDFs shown in Figure 1a display a first relatively large peak at about between (0.52 and 0.58) nm (g+ ‒ ≈ 1.6-2.2). This indicates the expected preferential cation-anion interaction over anion-anion and cation-cation interactions. An increase in the alkyl chain length does not


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significantly affect peak height and width in relation to the [EMIM]+, [BMIM]+, and [HMIM]+ homologues, while a distinctly smaller and broader peak is observed for the [OMIM]+-based IL. This behavior is in accordance with the findings for the familiar ILs based on the tricyanomethanide ([C(CN)3]–) anion27 and can be related to the larger delocalization of the center of mass position of the cation with increasing alkyl chain length. Longer alkyl tails have a larger flexibility than shorter chains, which causes a broader spatial distribution of the chains. Furthermore, the electrostatic interactions between cation and anion become smaller for longer-chained ILs. The resulting reduction and broadening of the cation-anion RDF peaks, which seems to start from [OMIM]+based ILs, is also found in the work of Logotheti et al.28 that examined the corresponding [NTf2]–based systems. Considering the peaks of cation-anion RDFs, the counter ion interactions for [B(CN)4]–-based ILs are similar to those for [C(CN)3]–-based ILs and lower than those for [AMIM]+-based ILs carrying other anions.29,30 This is an indication of the low coordination between cations and anions in the cyano-based ILs investigated. The anion-anion RDFs of the [B(CN)4]–-based ILs exhibit two characteristic peaks. The first peak at about 0.56 nm (g‒ ‒ ≈ 0.8-0.9) has a lower intensity than the second peak at about (0.900.95) nm (g‒ ‒ ≈ 1.4). The existence of two peaks is similar to the anion-anion RDFs calculated for [AMIM][C(CN)3]-based ILs27 and different to those calculated for the homologous ILs carrying the, e.g., larger bis(trifluoromethylsulfonyl)imide ([NTf2]–) anion.31 According to Vergadou et al.,27 the small size of the [C(CN)3]– anion and the weak interaction between the counter ions enables a more uniform anion distribution around the cation compared to the bulky [NTf2]‒ anion. The broadest distribution can be found for the cation-cation RDFs of the [B(CN)4]–-based ILs. The smaller peak magnitudes observed in the cation-cation RDF compared to those in the anionanion RDF is a result of the larger flexibility of the cation.32 With increasing alkyl chain of the [B(CN)4]–-based ILs, the first peak decreases and shifts to larger distances, which is also found for [C(CN)3]–-based ILs.27 The shoulder in the cation-cation RDFs observable for [HMIM][B(CN)4]



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and especially for [OMIM][B(CN)4] at distances before the first peak may indicate the formation of increasing dispersive van der Waals interactions with increasing alkyl side chain length. A similar trend though less strongly pronounced can also be observed for the series of [C(CN)3]–-based ILs in Ref. 27. The simulations of Logotheti et al.28 produced the same phenomenon in terms of the appearance of a distinct shoulder for the [OMIM]+-based IL carrying the [NTf2]–. Another interesting feature is that the IL [EMIM][B(CN)4] shows a smaller second cation-cation peak at a distance of about 1.1 nm. This observation is in agreement with the MD simulations on the liquid structure of the same IL performed by Dhungana et al.33 Based on their investigations on several [EMIM]+-based ILs carrying varying-sized anions with different numbers of cyano groups between one and four, an increasing anion volume has shown to prevent stacking of the cationic rings. The [C(CN)3]– and especially the [B(CN)4]– anion block the access of [EMIM]+ cations to other cations, which seems to be indicated by the spatial separation of the cation-cation distribution function into two peaks found in Figure 1c. Furthermore, the results in Figure 1d indicate no significant influence of the slightly different charge distribution in the precise (FF-H) and approximate (FF-HB) electrostatic potential on the various types of computed RDFs of [HMIM][B(CN)4]. This behavior is reasonable because the liquid structure of ILs is even not affected significantly using full or reduced total charges.12 In Figure 2, three-dimensional snapshots of the simulation boxes for the four homologous [B(CN)4]–-based ILs under study, which carry (a) [EMIM]+, (b) [BMIM]+, (c) [HMIM]+, and (d) [OMIM]+ at (293.15 or 298.15) K and 1 bar are visualized by the open-source graphics program "Visual Molecular Dynamics" (VMD).34 For the systems obtained after NpT production runs, the non-polar alkyl groups of the cations and the polar segments related to the imidazolium ring of the cation and to the anion are illustrated in yellow and red, respectively.


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Figure 2. Visualization of the simulation boxes of the systems (a) [EMIM][B(CN)4] (FF-E3) at 298.15 K, (b) [BMIM][B(CN)4] (FF-B) at 293.15 K, (c) [HMIM][B(CN)4] (FF-HB) at 298.15 K, and (d) [OMIM][B(CN)4] (FF-OB) at 293.15 K after NpT simulation runs for a pressure of 1 bar using the VMD program.34 Non-polar and polar domains are shown in yellow and red, respectively.

A gradually occurring nano-segregation with increasing alkyl chain length is observed for the [B(CN)4]–-based ILs as it was also found by Canongia Lopes et al.35,36 for other IL types. While for the short-chained ILs [EMIM][B(CN)4] and [BMIM][B(CN)4], no clear aggregation of polar and non-polar domain occurs, the longer-chained [HMIM][B(CN)4] and [OMIM][B(CN)4] form distinct segregated areas, which is especially visible for the non-polar domains. Aggregated alkyl groups seem to exclude [B(CN)4]– anions from the aliphatic domains and push them closer to the imidazolium rings where the main positive charge is located. Surface Tension. For the three [B(CN)4]–-based ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4], surface tension data σref were measured at a reference temperature Tref by the pendant drop method and, in combination with the prediction scheme according to eq 1, used to evaluate the dynamic viscosity based on SLS measurements in the overdamped regime. In the oscillatory regime, also surface tension results σSLS for [BMIM][B(CN)4] and [OMIM][B(CN)4] could be directly accessed by SLS at large temperatures. These data sets are given in Table S2 in the Supporting Information. The σSLS data obtained using SLS at larger temperature agree within



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combined uncertainties with the simple correlation method in the form of eq 1 using the σref data as reference points. In the following comparison with literature data for the ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4], the effect of slightly different but relatively small water contents of the rather hydrophobic [B(CN)4]−-based IL samples on the experimental σ values can be neglected.37 For all three ILs investigated here, the σref values obtained by the pendant drop method and the σSLS values measured by SLS agree within combined uncertainties with our temperaturedependent data38 determined with the pendant drop method for different samples of same purities. Only for [OMIM][B(CN)4], an additional data point measured by Kolbeck et al.18 at 298.15 K for a different sample using the same setup as employed here is found. This value deviates by about +4% compared to the σref value determined in this study. A comparison between literature data for the further [B(CN)4]−-based ILs [EMIM][B(CN)4] and [HMIM][B(CN)4] is given in our previous work.14 The decrease of the surface tension of the [B(CN)4]−-based ILs with increasing alkyl side chain length is generally found in literature for ILs. The relatively large surface tension values of ILs containing the [B(CN)4]− anion can be related to the strong charge delocalization in its relatively small anion. For a detailed discussion about the influence of cation and anion on the surface tension of the [B(CN)4]−-based ILs and ILs in general from a microscopic level, the reader is referred to our previous publication.38 Density. The simulated density data ρsim for [BMIM][B(CN)4] (FF-B), [HMIM][B(CN)4] (FFH), and [OMIM][B(CN)4] (FF-OB) obtained for temperatures between (293.15 and 363.15) K and at a pressure of about 1 bar are summarized in Table S3 in the Supporting Information. Our corresponding simulation results for [EMIM][B(CN)4] (FF-E3)13 and [HMIM][B(CN)4] (FF-HB)14 can be found in the literature. Figure 3 presents the relative deviation of the simulated densities of


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the [B(CN)4]‒-based ILs from the corresponding data ρfit obtained by a second-order polynomial fit to our experimental data with respect to temperature.

Figure 3. Relative deviations for the simulated densities ρsim of [B(CN)4]–-based ILs from fits ρfit based on experimental data as a function of temperature at about 1 bar. Statistical uncertainties (k = 2) of the data are shown as error bars. For data comparison, the results for [EMIM][B(CN)4] from MD simulations by Liu et al.39 and Borodin40 are shown in the plot in the upper right part.

The MD calculations for density for the different ILs deviate from the experimental values by less than 0.8% and typically by less than 0.3% within combined expanded uncertainties. This is an accurate prediction of the density over a broad temperature range. In all cases, the root mean square (rms) deviation of the computed data from the correlated experimental data is less than 0.4%. The slightly larger temperature dependence of the simulated densities compared to that of the experimental densities might be related to the use of temperature-invariant FF parameters. Taking into account the results from the precise FFs, in terms of electrostatic potential, for the ILs [EMIM][B(CN)4] (FF-E3), [BMIM][B(CN)4] (FF-B), and [HMIM][B(CN)4] (FF-H), very good agreement between the computed and experimental density data is found over the broad temperature range, as shown in Figure 3. This was obtained without any FF parameter adjustment for the non-electrostatic FF of the cations. Only the LJ size parameters of the nitrogen atoms of the



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anion were slightly modified according to eq 2 to reproduce the experimental densities at (293.15 or 298.15) K adequately reliable. A transfer of the electrostatic FF from [BMIM][B(CN)4] to the approximate FFs used for [HMIM][B(CN)4] (FF-HB)14 and for [OMIM][B(CN)4] (FF-HB) still exhibits very good agreement with the experimental values. Comparing the results for [HMIM][B(CN)4] using the precise or approximate FF, agreement within uncertainties is found in most cases. The approximate FF provides slightly larger values that are closer to experimental values since this model was optimized in terms of the LJ potential. The matching of the densities obtained using the two models for [HMIM][B(CN)4] is consistent with the congruent observations made in relation to the investigation of structural properties in Figure 1d. Thus, the use of a precise or approximate electrostatic FF seems to have no significant influence on the density of [AMIM][B(CN)4]-based ILs carrying sufficiently large but still relatively short alkyl chains. The marginal differences in the total charge and charge distribution of the ILs under study given in Table 1 may be responsible for this behavior. To conclude, the models partially transferred from [EMIM][B(CN)4] to the homologous ILs are capable of predicting reliable temperature-dependent data for the equilibrium property density. This is a first indication of the good quality of the FFs developed. Only two further MD simulation studies on the thermophysical properties of [B(CN)4]–-based ILs investigated in this study were found, which considered the IL [EMIM][B(CN)4]. Liu et al.39 used a different non-polarizable FF with uniformly scaled reduced charges of ±0.8 e, while Borodin40 employed a polarizable model. Most probably due to the fact that no FF parameters were manipulated to match ρ in both sources, the simulated densities deviate by more than +2% in the case of Borodin40 and by more than −5% in the case of Liu et al.39 with respect to the experimental densities (see Figure 3). These deviations are distinctly larger than those determined in the present study. For a better quantitative calculation of dynamic properties of ILs, it is recommended to aim


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to reproduce the equilibrium density well since already small variations in ρ can cause distinct deviations in, e.g., viscosity and self-diffusion coefficients. The densities of the studied [B(CN)4]–-based ILs are among the lowest for imidazolium-based ILs9 and affected rather by the anion than by the cation. In terms of the influence of cation variation on the experimental density data, the trend observed for the [B(CN)4]–-based ILs, i.e., that an increasing alkyl side chain length results in a decreasing density, concurs with several investigations of [AMIM]+-based ILs carrying the same or other anions.17,41-43 An increase in the alkyl chain length increases the sizes of the cations, leading to less dense packing and lower mass densities of the ILs. More information on the influence of the alkyl chain length in the cation and the anion on the density of [AMIM]+-based ILs is provided in our previous studies.14,15,22 Self-Diffusion Coefficients. The self-diffusion coefficients of the cations (D+) and of the anion (D–) for the [B(CN)4]–-based ILs under investigation in this study obtained by experiment and MD simulation are reported in Tables S4 and S5 in the Supporting Information. These data including our corresponding data obtained for [EMIM][B(CN)4]13,15 and [HMIM][B(CN)4]14 are shown in Figure 4 in an Arrhenius-like plot. Relatively large self-diffusivities in the order of (10–1110–10) m2·s–1 are found, which increase exponentially with increasing T and decrease with increasing alkyl chain length. For the limited temperature ranges, the experimental data are correlated well by Arrhenius-type fits D±,fit which are indicated by the lines in Figure 4. In a corresponding regression, each data point related to an IL was considered with the same statistical weight. With the exception of one value for the IL [OMIM][B(CN)4] at 293.15 K, all measured selfdiffusivities are in agreement with the corresponding Arrhenius-like correlations within the experimental uncertainty. The rms deviations of the experimental data from the fits are less than 8.7% for all [B(CN)4]–-based ILs investigated. No further experimental literature data for the selfdiffusion coefficients of [B(CN)4]–-based ILs investigated in this study are available in literature. Experimental results measured by Sanchez-Ramirez et al.44 for other [B(CN)4]–-based ILs containing a butyl side chain connected to piperidinium or pyrrolidinium cores show a factor of 19 Environment ACS Paragon Plus


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about two lower ion self-diffusion coefficients than the imidazolium-based [BMIM][B(CN)4] at comparable temperatures. This behavior is in line with the reciprocal trend of the dynamic viscosities discussed later.

Figure 4. Self-diffusion coefficients from experiment (Dexp) and from MD simulations (Dsim) for (a) the cations (D+,exp or D+,sim) and (b) the anions (D+,exp or D+,sim) of the homologous [B(CN)4]–-based ILs as a function of temperature at 1 bar. The MD simulation results for the cation and anion of [EMIM][B(CN)4] obtained by Liu et al.39 and Borodin40 are also shown.

Given the small temperature range accessible by the NMR experiments, the Arrhenius fits were not extrapolated to larger temperatures where MD simulations were also performed. Figure 4 shows that the simulation results for the ILs using the optimized models FF-E3,13 FF-B, and FF-H as well as the transferred models FF-HB14 and FF-OB agree very well with the experimental data, often within combined expanded uncertainties. The relative deviations between the simulation data and the fits based on the experimental data for same temperature range between –65% for the anion of [OMIM][B(CN)4] and +2% for the cation of [EMIM][B(CN)4]. Furthermore, based on simulations using FF-H or FF-HB, the influence of the electrostatic FF on the computed selfdiffusivities for [HMIM][B(CN)4] is also negligible for dynamic properties. The results based on the different charge models agree within combined statistical uncertainties.


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In general, the simulations provide slightly lower self-diffusivity values than the experiments. This is more pronounced for ILs with longer alkyl chain length, particularly for [OMIM][B(CN)4]. While for the ILs [EMIM][B(CN)4], [BMIM][B(CN)4], and [HMIM][B(CN)4], deviations of typically smaller than 30% and often within the uncertainties of the simulated data can be achieved, the calculated results for [OMIM][B(CN)4] using FF-OB are distinctly larger, especially at low temperatures of (293.15 and 313.15) K. The deviations might originate from different sources, such as the more sluggish dynamics for longer-chained ILs, the impact of the UA approximation which increases with increasing alkyl chain, and the FF parameters. Regarding the latter, the transfer of the non-electrostatic FF optimized for [EMIM][B(CN)4] (FF-E3) and of the electrostatic FF obtained for [BMIM][B(CN)4] (FF-B) are simplifications which are considered to be responsible for the somewhat larger deviations between simulation and experiment concerning [OMIM][B(CN)4]. Nevertheless, the satisfactory reproduction of self-diffusivities for the homologous [B(CN)4]–-based ILs in the simulations presented verifies the sound quality of the precise and approximated FF contributions transferred from shorter- to longer-chained ILs. In addition, the reliable reproduction of the self-diffusion coefficients is accompanied by a very good prediction of the density by the simulations. For the reference system [EMIM][B(CN)4], the deviations between the simulated and the experimental data are smaller than 20% for both ions,13 taking into consideration the experimental uncertainty of ±10% (k = 2). In comparison, Figure 4 depicts that the self-diffusivities of [EMIM][B(CN)4] computed by Borodin38 are between –(35 and 48)% lower than our simulated results. This may be influenced by the larger liquid densities obtained in his simulations, which tends to result in slower dynamics. The good agreement between the self-diffusivities calculated by Liu et al.39 and those calculated in our study13 seems to be related to their more than 5% lower density values with respect to experimental data. No further simulation data for the self-diffusion coefficient are available for the [B(CN)4]–-based ILs studied in this work.



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In agreement with the NMR data, the present MD simulations compute similar self-diffusion coefficients of the cations and anions for the different [B(CN)4]–-based ILs over the complete temperature ranges, in most cases also within combined uncertainties. Though the cation is larger and heavier than the anion, this behavior can be attributed to a preferential movement of the cation parallel to the plane of the imidazolium ring. In this case, the long bulky alkyl chains of the [AMIM]+ cations are in the same plane as the imidazolium ring, which facilitates the motion of the cations in the direction within this plane. In contrast, the three-dimensional tetrahedral structure of the [B(CN)4]– anion sterically hinders the diffusion in the bulk. For increasing alkyl side chains, the self-diffusion of the cations tends to be lower than that of the anions. This can be influenced by the entanglement of longer chains and the increasing differences in the molecular weights, impeding cationic diffusion. Furthermore, the nanosegration of the aliphatic chains as shown in Figure 2 decelerates the mobility of the cations additionally. Similar trends as discussed above were also observed for the self-diffusivities in other imidazolium-based ILs.27,45,46 The experimental and simulated data show that the self-diffusion coefficients for both ions of the [B(CN)4]–-based ILs decrease with increasing alkyl chain length. In detail, the relative differences in the experimental data between [DMIM][B(CN)4] and the reference [EMIM][B(CN)4] are about −80% within the temperature range between (293.15 and 308.15) K. This trend is expected given the fact that the viscosity increases for longer-chained cations and can be related to the same intermolecular and sterical effects which are discussed in connection with this property in the next section. It should be noted that the relevant effects associated with longer-chained cations, such as the more pronounced sterical hindrances and stronger dispersive interactions, reduce not only the mobility of the cation, but also that of the anion. For different [NTF2]−-based ILs with varying [AMIM]+ cations, Tokuda et al.46 also reported that increasing the alkyl chain length implies smaller self-diffusion coefficients for both ions. The relatively high self-diffusivities of the [B(CN)4]–-based ILs are in accordance with their low viscosities and strongly associated with the nature of the anion. To study the anion effect, ILs 22 Environment ACS Paragon Plus

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featuring the [EMIM]+ cation should be compared in terms of the self-diffusivity values because comparable trends are also found for the homologous [AMIM]+-based ILs. [EMIM][B(CN)4] exhibits higher D+ and D– values than [EMIM][NTf2],46 which might be related to the smaller size of [B(CN)4]– than [NTf2]–. In addition, the comparatively weak intermolecular interactions between [B(CN)4]– and [EMIM]+, which are indicated by the small peak in the radial distributions functions and the low densities as discussed in the previous chapters, seem to enhance the self-diffusion of both ions. Even [EMIM][BF4], which has a smaller but geometrically similar anion as [EMIM][B(CN)4], shows lower self-diffusivities,47 confirming the large influence of the weak interactions in [EMIM][B(CN)4] on the self-diffusivities. The cation of [EMIM][C(CN)3]48 has an approximately 50% larger D+ value than the cation of [EMIM][B(CN)4] at 298.15 K. This is in agreement with the by 20% lower viscosity of [EMIM][C(CN)3] compared to [EMIM][B(CN)4].49 For five [BMIM]+-based ILs consisting of various anions, Tokuda et al.45 observed the same qualitative trends between self-diffusivity and viscosity. Dynamic Viscosity. The dynamic viscosities ηSLS of the three homologous [B(CN)4]–-based ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4] under investigation in this work and their corresponding uncertainties, ∆ηSLS (k = 2), measured by SLS at temperatures between (283.15 and 363.15) K at atmospheric pressure are listed in Table S6 in the Supporting Information. These data as well as our corresponding SLS results for [EMIM][B(CN)4]15 and [HMIM][B(CN)4]14 are shown in the form of an Arrhenius plot in Figure 5.



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Figure 5. Experimental dynamic viscosities ηSLS of the homologous series of [B(CN)4]– based ILs at a pressure of 1 bar as a function of temperature obtained using SLS. The lines represent fits to the experimental data according to eq 4.

Compared to other imidazolium-based ILs and ILs in general,9 the measured viscosities of the five homologous [B(CN)4]–-based ILs ranging between (3 and 230) mPa·s are very low. As generally observed for ILs, the viscosity exhibits strong dependence on temperature. The dynamic viscosity data of each IL can be represented well in the form of a Vogel-type equation,

η fit (T ) = η0 exp( B /(T − C )) ,

(4)

where T is the temperature in K, and η0, B, and C are the fit parameters. For the data correlation, the same statistical weights are assumed for all data points considered. For the ILs [BMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4], the fit parameters and the rms deviation of the dynamic viscosity data from the fits are summarized in Table 1. For all data points, these deviations are smaller than the expanded uncertainties (k = 2) of the viscosity results.


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Table 1. Coefficients of eq 4 and Rms Deviation of the Experimental Dynamic Viscosity Data ηSLS from the Corresponding Correlation for the ILs Investigated in this Study. IL [BMIM][B(CN)4] [OMIM][B(CN)4] [DMIM][B(CN)4]

η0 / mPa·s 0.08641 0.06349 0.04184

B/K 770.050 890.271 1096.88

C/K 168.182 170.543 155.687

rms / % 1.79 2.04 0.73

A comparison with other experimental data available in literature for the ILs [EMIM][B(CN)4]15 and [HMIM][B(CN)4]14,49 can be found in our previous studies. Further data published in connection with [B(CN)4]–-based ILs exist only for [BMIM][B(CN)4] investigated in our recent study49 based on dynamic light scattering (DLS) with the aid of dispersed particles. Good agreement between the SLS and DLS data within combined uncertainties is observed in the temperature range from (283 to 333) K. From (333 up to 353) K, the DLS data deviate increasingly from the SLS data, with the value at 353 K being outside combined uncertainties. Different water contents cannot explain this behavior because the larger average water fraction of the DLS sample at 1650 ppm compared to that of the SLS sample at 365 ppm rather decreases viscosity. The increasing discrepancy of the DLS data to the SLS data is probably attributed to weak particle agglomeration at larger temperatures. The simulation results for the viscosity ηsim of the [B(CN)4]–-based ILs [BMIM][B(CN)4] (FF-B), [HMIM][B(CN)4] (FF-H), and [OMIM][B(CN)4] (FF-OB) as a function of the temperature at a pressure of about 1 bar are given in Table S7 in the Supporting Information. Figure 6 shows the relative deviations of the simulated viscosities from the correlations according to eq 4 based on the SLS measurements at the various temperatures studied. Deviations are also depicted in Figure 6 for [EMIM][B(CN)4] (FF-E3)13 and [HMIM][B(CN)4] (FF-HB).14



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Figure 6. Relative deviations of simulated dynamic viscosities ηsim of homologous [B(CN)4]–-based ILs from fitted values ηfit according to eq 4 based on SLS data as a function of temperature at 1 bar. Statistical uncertainties (k = 2) of the data are shown as error bars. For comparison, the results for [EMIM][B(CN)4] from MD simulations performed by Borodin39 are also shown.

Overall, the viscosity of ILs is captured reasonably well by the simulations using the reducedcharge FF models. The relative deviations between simulation and fit based on the experimental data range between +(3 and 172)% and are in most cases below +50%. This fair agreement is a result of the FF optimization in FF-E3 for [EMIM][B(CN)4] by using an electrostatic term with a reduced charge and optimizing the non-electrostatic term.13 For this IL, deviations of less than 20% within statistical uncertainties could be found over the whole temperature range, while reproducing the experimental densities well at the same time. As illustrated in Figure 6, the data for [EMIM][B(CN)4] calculated by Borodin40 deviate by +107% at 298 K and by +65% at 333 K with respect to the experimental data. These deviations are larger than those obtained with the refined model FF-E3. The viscosities obtained by the simulations are generally larger than the experimental values. Larger deviations can be found for ILs with longer alkyl chain length, especially for [OMIM][B(CN)4] where the FF is approximated at the most. This behavior is consistent with the findings for the self-diffusivity and can be related to the same sources as discussed above in connection with the self-diffusion coefficients. The analogy can be justified because the two 26 Environment ACS Paragon Plus

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dynamic properties viscosity and self-diffusivity of ILs behave almost reciprocally, which will be further discussed later. In this context, it is also reasonable that the viscosities for [HMIM][B(CN)4] calculated in this study on basis of the precise FF-H model are in agreement with those data calculated using the approximated FF-HB model.14 This is a further indication that the use of approximated electrostatic and non-electrostatic terms in the FF works well for ILs carrying cations with relatively similar alkyl side chain length. In conclusion, the dynamics of the homologous [B(CN)4]–-based ILs represented by the self-diffusion coefficients and the viscosity are fairly well predicted by the MD simulations applying transferable molecular models. This is consistent with the simultaneous very good prediction of the density by the simulations. The viscosity of the [B(CN)4]–-based ILs is remarkably low for ILs carrying the same cations. Structural aspects such as the entanglement of the molecules as well as intermolecular effects caused by van der Waals (vdW) interactions, hydrogen bonding, and Coulombic forces have to be considered. Regarding the cation influence, the viscosity of the [B(CN)4]–-based ILs increases with increasing alkyl chain length, an effect that becomes stronger at lower temperature. While electrostatic interactions tend to decrease, longer aliphatic chains enhance both the formation of attractive vdW forces resulting in the aggregation of non-polar parts, and the probability of entanglement between neighboring cations in the bulk of the ILs. In consequence, the ion dynamics reduces and larger viscosities are found. Increasing η values with increasing cationic alkyl chain length were also observed for [B(CN)4]–-based ILs by other authors43,50 and for [AMIM]+-based ILs carrying other anions, such as the cyano-based thiocyanate ([SCN]–),43 dicyanamide ([N(CN)2]–),43 and [C(CN)3]– anion43,50 or the fluorinated tetrafluoroborate ([BF4]–)51 and [NTf2]– anion.46 In connection with the influence of the anion, Bonhôte et al.52 stated that charge delocalization within the anion weakens intermolecular electrostatic interactions and hydrogen bonding with the cation, yielding lower viscosities if not overcompensated by vdW interactions. The latter effect seems to be responsible for the anomalous behavior of the [B(CN)4]–-based ILs compared to the [C(CN)3]–-based ILs, which was also found by Neves et al.43 Moreover, the bulky 27 Environment ACS Paragon Plus


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tetrahedral [B(CN)4]− seems to cause reduced mobility in the bulk compared to the flat trigonal [C(CN)3]−, which also tends to increase η. Nonetheless, the combination of the relatively smallsized [B(CN)4]– anion and the still weak coordination between anion and cation results in the lowest viscosity of [EMIM][B(CN)4] compared to numerous other [EMIM]+-based ILs containing the smaller [BF4]–,51 [SCN]–,43 and [N(CN)2]– anion43 or the larger [NTf2]– anion.46 Correlation between Self-Diffusion Coefficients and Dynamic Viscosities. The widely known correlation for the two dynamic properties diffusion coefficient and viscosity is the StokesEinstein equation53 in the hydrodynamic regime. The equation is based on the assumption of large macroscopic spheres diffusing in a continuum of small solvent molecules. However, the relation is not appropriate for the diffusion of molecules54 such as ILs which additionally show a non-spherical nature.8 Instead, Liu et al.8 suggested a fractional Stokes-Einstein equation in the form of

D ± ∝ (T η ) β ,

(5)

where the fractional Stokes-Einstein coefficient β is 1 for a Stokes-Einstein fluid and 0.8 for some molten salts.53 Eq 5 is applied for the ions of the five homologous [B(CN)4]–-based ILs in a doublelogarithmic plot of D± versus Tη−1 in Figure 7 using the T-dependent NMR data for D±,exp and the SLS-based viscosities ηfit calculated by eq 4 at the respective temperatures. From linear fits of the data indicated as dashed and solid lines for the cations and anions, respectively, β values were deduced and are listed in Table 3. Here, the absolute uncertainties for β (k = 2) resulting from the regression procedures are also included. For each ILs studied, corresponding β values obtained from the simulated self-diffusivity and viscosity data agree with the results derived from the experiments within expanded uncertainties. This is a further indication that the simulated dynamic properties are consistent.


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Figure 7. Double-logarithmic plot of the experimental self-diffusion coefficients D±,exp for cations and anions of the [B(CN)4]–-based ILs studied at various temperatures T versus the product Tηfit−1 using the SLS-based viscosities ηfit calculated according to eq. 4. The corresponding data for [EMIM][B(CN)4]13,15 and [HMIM][B(CN)4]14 are taken from our previous publications. The bisecting line is an arbitrary form of eq 5 with β = 1 and does not represent a fit of the data.

Table 2. Fractional Stokes-Einstein Coefficients of Cations (β+) and Anions (β–) from experimental data for the [B(CN)4]–-Based ILs Studied as well as their Corresponding Uncertainties, ∆β± (k = 2). IL [EMIM][B(CN)4] [BMIM][B(CN)4] [HMIM][B(CN)4] [OMIM][B(CN)4] [DMIM][B(CN)4]

β+ ± ∆β+

β – ± ∆β–

0.83 ± 0.06 1.05 ± 0.10 0.95 ± 0.03 0.77 ± 0.69 0.94 ± 0.08

0.75 ± 0.15 1.01 ± 0.10 0.91 ± 0.06 0.83 ± 0.04 1.10 ± 0.11

Table 2 shows that the studied ILs do not follow the Stokes-Einstein model, but are in a range between molten salts and molecular liquids with β values ranging from 0.75 up to 1.10 and are generally smaller than 1. Taking into account the uncertainties of the experimental data and of the fits, significant dependencies of β with respect to the alkyl chain length of the cation or the cation and anion themselves cannot be detected. The present results are similar to those derived from



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experiments of Kanakubo et al.55 for the hexafluorophosphate ([PF6]−)-based IL [BMIM][PF6] and from simulations of Liu et al.8 for six different ILs, where β values mainly between 0.8 and 1 were reported.

CONCLUSIONS Low-viscosity ILs carrying the [B(CN)4]− anion and possessing different alkyl chain length in the imidazolium-based cation were investigated with respect to structural, equilibrium, and dynamic properties as a function of temperature at atmospheric pressure. Conventional techniques in the form of a pendant drop apparatus and NMR spectroscopy were used to determine the surface tension and ion self-diffusion coefficients, respectively. Using SLS the dynamic viscosity and, for larger temperatures, also the surface tension could be measured at macroscopic thermodynamic equilibrium in an absolute way. At such condition, MD simulations were performed based on molecular models which account for the electrostatic and non-electrostatic interactions differently. While the non-electrostatic part optimized for [EMIM][B(CN)4] using experimental data was partially transferred to all [B(CN)4]−-based ILs, the electrostatic part derived from quantum calculations was transferred from [BMIM][B(CN)4] to the longer-chained ILs in our previous studies13,14 and in the present work. Comparison of the experimental and simulated results for the homologous [B(CN)4]−-based ILs displays good agreement generally within combined uncertainties, which indicates a solid transferability of both FF contributions from shorter to longer alkyl chains for ILs. Only for a very coarse transfer from [BMIM][B(CN)4] to [OMIM][B(CN)4], more distinct deviations between simulated and experimental dynamic properties could be found at low temperatures. The matching results for [HMIM][B(CN)4] calculated on the basis of its precise electrostatic charges and the charges approximated from [BMIM][B(CN)4] denote no distinct influence of the varying electrostatic potential in the alkyl chain of the cation on the IL properties. This observation suggests that the charges associated with relatively short-chained ILs are transferable to longer-chained homologues without a significant loss in accuracy. A


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nanosegregation in the bulk of the fluid gradually occurring with increasing alkyl chain length in the cation as well as a correlation between self-diffusivity and viscosity, which were both observed for the [B(CN)4]−-based ILs, agree with the findings reported for ILs in literature.

ACKNOWLEDGEMENTS This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative. In addition, financial support from the 7th European Commission Framework Program for Research and Technological Development for the project "Novel Ionic Liquid and Supported Ionic Liquid Solvents for Reversible Capture of CO2" (IOLICAP project no. 283077) is gratefully acknowledged. J. Ramos acknowledges financial support through the Ramón y Cajal program (MINECO, Spain, Contract RYC-2011-09585).

SUPPORTING INFORMATION Partial charges for the electrostatic force fields of the ILs [EMIM][B(CN)4], [BMIM][B(CN)4], [HMIM][B(CN)4], and [OMIM][B(CN)4] as well as experimental and simulation results for the surface tension, density, self-diffusion coefficients, and dynamic viscosity of the ILs [BMIM][B(CN)4], [HMIM][B(CN)4], [OMIM][B(CN)4], and [DMIM][B(CN)4]. This material is available free of charge via the Internet at http://pubs.acs.org.

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Thermophysical Properties of Homologous Tetracyanoborate-Based

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