State of Hydrophobic and Hydrophilic Ionic Liquids in Aqueous Solutions

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State of Hydrophobic and Hydrophilic Ionic Liquids in Aqueous Solutions: Are the Ions Fully Dissociated? Patrick Yee, Jindal K Shah, and Edward J. Maginn J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp405341m • Publication Date (Web): 12 Sep 2013 Downloaded from http://pubs.acs.org on September 15, 2013

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The Journal of Physical Chemistry

State of Hydrophobic and Hydrophilic Ionic Liquids in Aqueous Solutions: Are the Ions Fully Dissociated? Patrick Yee,† Jindal K. Shah,∗,†,‡ and Edward J. Maginn∗,† Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556 USA, and Center for Research Computing, University of Notre Dame, Notre Dame, IN 46556 USA E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556 USA ‡ Center for Research Computing, University of Notre Dame, Notre Dame, IN 46556 USA † Department

1

ACS Paragon Plus Environment


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Abstract Molecular dynamics simulations were performed for aqueous solutions of five ionic liquids (ILs): 1-ethyl-3-methylimidazolium ([C2 mim]) bis(trifluoromethanesulfonyl) imide ([NTf2 ]), 1-n-butyl-3-methylimidazolium ([C4 mim]) [NTf2 ], 1-n-hexyl-3-methylimidazolium ([C6 mim]) [NTf2 ], [C2 mim] ethylsulfate ([C2 H5 SO4 ]) and [C2 mim] chloride (Cl) in order to determine whether the ions of these ILs are associated at relatively high dilutions and whether the association is governed by hydrophobicity/hydrophilicity of the ILs. The adaptive biasing force technique was applied to calculate the potential of mean force (PMF) for each IL ion-pair. For all the ILs, the PMF is characterized by two distinct contact minima in which the ions have different relative conformations. The hydrophobic ILs bearing the anion [NTf2 ]− exist predominantly in the associative state; the strength of the association of these ILs increases with increase in the alkyl chain length. The most hydrophilic IL [C2 mim] Cl was determined to be almost fully dissociated at the concentration examined in the study. [C2 mim] [C2 H5 SO4 ] showed hydration behavior that was intermediate between that exhibited by the ILs in which the anion is substituted with either Cl− or [NTf2 ]− paired with [C2 mim]+ . Association constants for these ILs were also computed. Radial distribution functions (RDFs) calculated by constraining the ions at the contact minima showed that hydration of the anion plays the dominant role in determining the microscopic behavior of these ILs in aqueous solutions.

Keywords: Water, ionic liquids, potential of mean force, association constants, adaptive biasing force, hydration, free energy

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Introduction Ionic liquids (ILs) are unconventional solvents comprised entirely of ions and exist as a liquid phase under ambient conditions. Owing to their negligible vapor pressure, tunability for desired physical and chemical properties, low flammability, good solvation characteristics towards both polar and non-polar species and a wide electrochemical window, ILs have become a subject of intense investigations in fields as diverse as gas separations, catalysis, batteries, photovoltaic cells and biocatalysis to name a few. 1–4 Many ILs are inherently hygroscopic. The presence of water in IL samples has been shown to dramatically alter IL properties such as viscosity, 5 density, 6 diffusivity and electrical conductivity 7 and much attention has been directed at properly drying IL samples for pure property determination. However, the presence of water can also be fruitfully exploited to obtain a desired range of properties for IL-water mixtures.

In addition to the transport properties of ILs, the structure of ILs can also change with the addition of water. For example, it has been shown that the pure IL structure changes very little when water is present in low concentrations. However, as the mole (weight) fraction of water increases, ILs exhibit structural transitions from a continuous phase, to domains, to ion-pairs and finally into individual ions at high water concentrations. 8–11 However, such behavior depends on the identity of the IL. 12 The presence of micelles has been detected in aqueous solutions of imidazolium-based IL cations with long alkyl chains. 13–17 In the limit of infinite dilution it has been assumed that the IL ions exist as isolated ions and their hydration is complete. 18 However, this has not been conclusively shown either experimentally or computationally.

The concept of association and dissociation of ions along with solvation of ions or ion-pairs is usually invoked to explain the trends in physical and transport properties of mixtures of ILs with various solvents. For example, Nakakoshi et al. 18 carried out an experimental investigation of the diffusion coefficient of 1-n-butyl-3-methylimidazolium ([C4 mim] bromide (Br) in water with increasing concentration of the IL. They observed that the cation diffusion coefficient increased up 3



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to an IL mole fraction of 0.0019, beyond which the diffusion coefficient monotonically decreased. The authors assumed a complete dissociation of the IL into ions to explain the anamolous behavior. In the study by Zarrougui et al., 19 the authors reported viscosities and ionic conductivities of IL-methanol mixtures and noted that the viscosity of the mixture increases marginally up to an IL concentration of 1.5 M, but increases dramatically for concentrations exceeding this limit. Similarly, the ionic conductivity shows an increase up to 1.1 M IL concentration, beyond which the conductivity decreases. This unsual behavior was explained in terms of the dissociation of the ion pairs in the methanol-rich region. Beyond certain concentrations, the IL exists as ion-pairs, thus reducing the number of charge carriers of the solution and leading to a decrease in conductivity.

Dynamics of solvent relaxation in ionic liquid-water mixtures can be used to understand the nature of ion-water interactions. For example, in the mixture of 1-n-hexyl-3-methylimidazolium [C6 mim] hexafluorophosphate [PF6 ] with water, it was observed, from time resolved fluorescence spectroscopy, that solvation time decreases upon addition of water. However, this decrease is more pronounced for acetontirile as it cannot form hydrogen bonds with the anion. 20 Similarly, the solvation time gradually decreases when water is added to the hydrophobic IL [C4 mim][PF6 ]. 21

Ionic association can also play an important role in reactions carried out in ILs in the presence of catalysts. It has been suggested by Podgor˘sek et al. 22 that as the reactant 1,3-cyclohexadiene dissolves in the IL [C4 mim] bis(trifluoromethanesulfonyl) imide ([NTf2 ]) and 1-n-butyl-2,3-dimethylimidazolium [NTf2 ] ILs, the “ionicity” or the extent to which the ions can be considered dissociated, decreases implying stronger aggregation of ions upon reactant dissolution. Increased association and concominantly higher mobility of dissociated ions lead to enhanced reaction rates. The results of the study imply that ionic association alters properties of IL solutions.

From the technological point of view, association of ions in ILs can have a profound impact on the way these materials are utilized in the emerging field of ILs as active pharmaceutical ingredi-

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ents. 23,24 Recently, it has been hypothesized by Stoimenovski and MacFarlane that the permeation of drug-like ILs across a model cell membrane is enhanced for drug forms that can exist in undissociated states while dissociation of ILs into individual ions presents a barrier to the transport of drugs. 25 Similarly, the toxicological properties of ILs may be related to the propensity of ILs to undergo association/dissociation in water and thereby their ability to transport across a cell membrane to induce ecotoxicological response in a species. Thus, it is evident that the IL-water interactions are of utmost significance not only from a fundamental perspective but also from technical application of ILs.

Thermodynamic, transport and structural properties of water-IL mixtures have been investigated by a number of researchers using both experimental 5,26–38 and molecular simulation techniques. Here we only describe a representative set of computational studies. The interested reader is referred to an excellent review article published recently by Bhargava et al. 39 and references therein. Molecular dynamics simulations of a series of alkylimidazolium-based ILs with varying alkyl chain lengths in combination with a bromide anion revealed that the ILs with short alkyl chain cations are isotropically distributed in water. As the alkyl chain length increases, the cations exhibit a propensity for micelle formation. 40 Feng and Voth 8 published similar observations from molecular dynamics simulations of aqueous solutions of [C4 mim] tetrafluoroborate ([BF4 ]), 1-octyl-3methylimidzolium ([C8 mim]) chloride (Cl) and [C8 mim][BF4 ]. They reported that, at high water concentrations, the ionic network in [C4 mim][BF4 ] collapses. On the other hand, aggregation of [C8 mim]+ is observed leading to micellar structures. Jiang et al. 9 examined structural transitions in water- [C8 mim] nitrate ([NO3 ]) from pure IL up to a water mole fraction of 0.952 and found that with increasing water concentrations, several structural transitions are observed ranging from polar network, water network, micelle formation to a loose micellar structure.

Based on molecular dynamics simulations, Raju and Balasubramanian carried out a detailed characterization of a dilute aqueous solution of [C4 mim] hexafluorophosphate ([PF6 ]) ionic liquid in

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terms of structure, energetics and dynamics. 41 The results from the study showed faster diffusion of the anion over the cation, behavior that is in direct contrast to that in the pure IL. The authors also estimated, from the energy distribution of water molecules and radial distribution functions, that about 13% of the ions are dissociated at 0.0013 mole fraction of the IL. On the other hand, Margulis and co-workers 42 simulated the ionic liquid 1-n-hexyl-3-methylimidazolium ([C6 mim]) [PF6 ] with a small concentration of water (0.17 mole fraction). The authors observed that water molecules associate with the anion. The presence of water was found to decrease the cation-anion Coulombic interaction energies, which is reflected in faster translational and rotational dynamics of the IL.

Though the body of literature examining IL-water mixtures experimentally and computationally is growing, the nature of IL-water interactions present in very dilute solutions has only recently been addressed computationally. 43,44 In this article, we seek to elucidate such IL-water interactions in an attempt to gain insights into the question: “Are IL ions associated or dissociated in water under the conditions that may be regarded as an infinitely dilute limit?” To this end, we consider five ILs: [C2 mim]Cl, [C2 mim] ethylsulfate ([C2 H5 SO4 ]), [C2 mim][NTf2 ], [C4 mim][NTf2 ] and [C6 mim][NTf2 ]. The choice of the ILs was motivated by the fact that these ILs span the spectrum of hydrophobicity. For example, the three ILs with [C2 mim]+ exhibit increasingly hydrophobic behavior as the anion is varied from Cl− , to [C2 H5 SO4 ]− , to [NTf2 ]− . On the other hand the ILs with [NTf2 ]− enable us to examine the effect of increasing alkyl chain length on the hydration behavior of these ILs. We have applied the technique of molecular dynamics simulations to compute the potential of mean force (PMF) and hence the free energy of approach as the distance between the ions is varied. These PMFs allow one to quantify the relative populations of ions in different states as a function of separation, thereby enabling us to answer the question posed earlier. In the next section, a theoretical framework for the calculation of the PMF between the ions is presented along with the determination of association constants from the computed PMF. In the following section, information on the force field parameters and simulation details are presented. Next, re-

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sults from the simulation study are provided and discussed in the context of the available literature. The last section of the article summarizes the findings of this study.

Theory Potential of Mean Force Potential of mean force (PMF) is defined as the reversible work required to bring two atom groups at a separation r from infinite distance. In a molecular simulation, the PMF may be obtained from the radial distribution function (RDF) using the following relation 45

A(r) = −kB T ln g(r)

(1)

where A denotes the PMF in terms of Helmoltz free energy between two atom groups, kB refers to the Boltzmann constant and T is the temperature. The RDF between the atom groups is defined by g(r). The accuracy of the PMF calculated via eq. (1) depends on the accuracy with which the RDF is obtained in a simulation. Conventionally, the RDF is calculated by recording the number of times the two atom groups are observed at a given distance. However, many times determining an accurate RDF can be challenging due to the presence of free energy barriers that result in inadequate sampling of all the relevant distances. 46–49 For example, large free energy barriers in the PMF potentially limit sampling between the free energy minima, give data for only certain regions of r, cause quasi non-ergodicity within sampled timescales, or show excessive preference for one free energy minimum over another. 50 In addition to the problems associated with inadequate sampling, the calculation of RDF is especially difficult when the concentration of the species in question is low necessitating excessively large-scale systems and/or long simulations to span the entire range of relevant distances. This makes the determination of RDFs and hence the PMF from RDFs a computationally expensive and time consuming task.

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The adaptive biasing force (ABF) 48,49 method presents a useful alternative for alleviating many of the aforementioned problems in systems with reversible pathways. The ABF method is designed to compute the PMF directly by applying a mean force opposite to the force along a reaction coordinate ξ for which the PMF is to be calculated. The application of the biased force modifies the potential along ξ according to VABF (ξ ) = V (ξ ) − Abias (ti , ξ )

(2)

VABF is the biased potential experienced along ξ , V is the true potential and Abias (ti , ξ ) is the estimate of the true potential along the reaction coordinate at time t in the region i. During an ABF simulation, the force along the reaction coordinate, F(ξ ) is calculated using the following expression 49 F(ξ ) = −∇V (ξ ) · vi + kB T ∇ · vi

(3)

where vi is a vector field. The mean force along ξ , hF(ξ )i, is obtained by averaging the instantaneous force. In a simulation, the instantaneous force is calculated with eq. (3) by dividing the reaction coordinate into discrete bins so that the average force exerted in the bin k is given by

Fξ (Nstep , k) =

1 N(Nstep , k)

N(Nstep ,k)

∑

Fi (tik ).

(4)

i=1

In eq. (4), N(Nstep , k) is the number of samples collected in the bin k after Nstep simulation steps. Fi (tik ) is the computed force at iteration i and tik is the time at which the ith sample was collected in the bin k. The average force is then used to revise the estimate of the PMF using

hF(ξ )i =

dAbias (t, ξ ) . dξ

(5)

In the implementation of the ABF method, no bias is applied on the system until a user-determined number of samples is collected in each bin. 49

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The ABF method thus increases sampling by creating a gradient-free PMF along ξ . The total average force along ξ is thus mitigated causing diffusion to become the dominant transfer mechanism. 50 At sufficiently large timescales, sampling should be uniform since there is no net force between the collected variables of the ABF parameter within any range of ξ . 49

Association Constant (KA ) The association-dissociation between the ion-pair and dissociated ions may be represented by an equilibrium process as [A]+ + [B]− ⇐⇒ [AB].

(6)

Based on the above equilibrium, an association constant may be defined as

KA =

[AB] [A]+ [B]−

(7)

where KA is the association constant for the equilibrium process in eq. (6) and the square brackets represent the concentrations of each of the species at equilibrium. 51 If α is the degree of dissociation, the concentration of each of the species at equilibrium is given by [AB] = (1 − α)c, [A]+ = [B]− = αc

(8)

where c denotes the total concentration of the electrolyte. Substitution of eq. (8) in eq. (7) yields an expression for the association constant in terms of the degree of dissociation

KA =

1−α . α 2c

(9)

Following Dill and co-workers, 51 we assume that the associated state of the ions arises entirely out of the ions in contact and all other states represent dissociated ions. The number of ions in the associated state may be obtained by integrating the RDF up to a distance R. This distance is

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established by the second contact minimum in the PMF as shown below. The ratio of this number to the total number of available free ions provides an estimate of the degree of dissociation via the following equation RR

1 − α = R 0∞ 0

4πr2 ρ0 g(r)dr . 4πr2 ρ0 g(r)dr

(10)

In this equation, ρ0 is the total number density of the electrolyte. Anticipating that the PMF calculations will be carried out with only a single cation-anion pair, the full system integral must evaluate to 1 and eq. (10) simplifies to

1−α =

Z R 0

4πr2 ρ0 g(r)dr

(11)

Force Field The water-IL system was modeled using an all-atom classical force field that includes the bonded interactions described by bond stretching, angle bending, torsional and improper bending. The non-bonded interaction terms consist of the van der Waals interactions modeled by standard LennardJones 12-6 type interaction while the electrostatic interactions are given by Coulombic terms. The functional form of the total system potential is given in eq. 12

Vsystem =

∑

Kl (l − l0 )2 +

bonds

+

∑

∑

Kθ (θ − θ0 )2 +

angles Kψ (ψ − ψ0 )2

∑

Kφ (1 + cos(nφ − δ ))

dihedrals

impropers

" +

∑ ∑ 4εi j i j>i

σi j ri j

12

σi j − ri j

6 # +

qi q j ri j

(12)

where terms have their usual meanings. 52,53 The force field parameters for the cations [C6 mim]+ , [C4 mim]+ and [C2 mim]+ were taken from Shi and Maginn, 54 Cadena and Maginn 55 and Kelkar et al. 56 respectively. The parameters for [C2 H5 SO4 ]− were obtained from the work of Kelkar et al. 56

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while those for the anion [NTf2 ]− were those reported by Lopes et al. 57 The model proposed by Jensen and Jorgensen was used for Cl− . 58 A non-rigid water model was employed in the study for which the non-bonded interaction parameters were set identical to those of the SPC water model by Berendsen. 59 The bond stretching and angle bending parameters for the water model were adopted from the work by Shi and Maginn. 60 Intramolecular non-bonded interactions between the atoms separated by exactly three bonds were scaled by a factor 0.5. Interactions between the atoms separated by fewer than three bonds was fully accounted by the bonded interactions. Interactions between all the other atoms were computed with a scaling factor of 1.0. A complete listing of the bonded and non-bonded interaction parameters for the ionic liquids is provided in the Supporting Information.

Simulation Details Molecular dynamics (MD) simulations were performed in the canonical (NVT), isothermal-isobaric (NPT) and microcanonical (NVE) ensembles. Langevin dynamics was used for the temperature and pressure control in NVT and NPT ensembles. The temperature coupling coefficient was set to 1 ps−1 . The pressure was maintained at 1 bar by setting the barostat oscillation timescale to 200 fs and the barostat damping timescale to 100 fs. Volume was set to vary isotropically in the NPT ensemble. Non-bonded interactions were truncted at 16 Å with a switching function starting at 14.5 Å. Electrostatic interactions were calculated with the particle mesh Ewald (PME) method with a PME grid size of ∼ 0.9 Å in each of the X, Y and Z directions. The equations of motion were integrated with a timestep of 1 fs.

Simulations were conducted with NAMD 2.7b2. 53 Simulations of the water-IL systems were carried out at four temperatures: 300 K, 320 K, 340 K and 400 K. Each simulation contained 3150 water molecules and one IL cation-anion pair such that the ionic liquid mole fraction was ∼ 0.0003. Complete coordinate files for the IL ion pairs were first created from individual ion coor-

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Figure 1: Atomic labeling schemes for the cations and anions. (a) [C2 mim]+ , (b) [C4 mim]+ , (c) [C6 mim]+ , (d) Cl− , (e) [NTf2 ]− , (f) [C2 H5 SO4 ]− . The PMF, for each IL ion pair, was calculated by varying the distance between the atoms identified with ∗ . dinate files. The cation-anion pair was then solvated by water molecules using the solvate utility in VMD. 61 The mixtures were subsequently subjected to a 5000 step steepest-descent minimization followed by 20 ps NVT equilibration. The resulting configuration was then subjected to 500 ps NPT equilibration and a final 500 ps NVE equilibration. Each water-IL solution yielded a density close to that of water at the system’s temperature after equilibration, which is expected considering the fact that system contained only one IL cation-anion pair. The equilibrated configurations were then used as inputs for ABF simulations (see below).

ABF MD simulations The ABF method was employed to estimate the PMF of the IL ions pairs. The reaction coordinate, ξ was represented by the distance between two atoms, one on each of the ions (Figure 1). ABF simulations were conducted over five non-overlapping windows of 2 Å each such that values of ξ

12


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ranged from 2 Å to 12 Å. PMF data were collected in bins of 0.05 Å width in each of the windows. A potential was applied outside the bounds of ξ to constrain the ions within the sampling range in each window as given by eq. 13

Vbound =

   41.84 kJ/mol     0      41.84 kJ/mol

ξ ≤ ξupper ξlower ≤ ξ ≤ ξupper

(13)

ξ ≥ ξlower

where ξupper and ξlower are the upper and lower bounds of ξ respectively and Vbound is the potential applied at the boundaries of ξ .

Each ABF simulation was performed for 30 ns in the NVT ensemble. 20,000 samples of the mean force were collected in each bin in order to obtain a relatively accurate estimate of the PMF prior to applying the biasing force. The geometric entropy term (Jacobian) was omitted from the PMF calculation as is conventional in the ABF method when computing the PMF based on distance. 62

To verify the consistency of the PMF obtained by combining results from five windows and that obtained from a single ABF simulation, an additional ABF calculation was carried out over the distance covering the first two minima observed in the PMF reconstructed from multiple window ABF simulations.

Constrained MD simulation To obtain better insight into the organization of water molecules at the PMF minima, unbiased 4 ns MD simulations were conducted in the NVT ensemble for three representative ILs: [C2 mim]Cl, [C2 mim][C2 H5 SO4 ] and [C4 mim][NTf2 ]. In these simulations the distance between the atom groups for which the PMF was calculated were constrained to that corresponding to the minima in the PMF profile. Trajectories were saved every 500 fs for the RDF analysis between various atom

13



groups on each ion and the oxygen in water.

Results and Discussion Potential of Mean Force The PMFs obtained from the ABF simulations are plotted in Figure 2. The corresponding RDFs obtained using eq. (1) are given in Figure 3. The five PMFs are characterized by two distinct free energy minima. These free energy minima correspond to the ions that are in direct contact and will be referred to as the first contact minimum (CM1) and the second contact minimum (CM2). The two contact minima arise due to the fact that the bulky ions can exist in different conformational states. Note that this IL behavior is in direct contrast with that observed for spherical ions exhibiting two minima corresponding to contact minimum and a solvent separated minimum. 63

[C2mim]Cl [C2mim][C2H5SO4] [C2mim][NTf2] [C4mim][NTf2] [C6mim][NTf2]

4

PMF(ξ) (kJ/mol)

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0

-4

-8

0

3

6

9

12

15

ξ (Å) Figure 2: PMFs obtained for the five ILs at 300 K from the ABF simulations. The locations of the CM1 and CM2 are fairly consistent across all the five ILs and occur between 3 to 4 Å and 5 to 6 Å, respectively. The depth of the free energy minima and the height of free energy barriers, however, vary significantly across the ILs suggesting different hydration 14


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behavior.

In the case of the most hydrophobic IL [C6 mim][NTf2 ], the CM1 is the deepest with a PMF of ∼ -6 kJ/mol. The CM1 is connected to the CM2 by a small barrier height of about 1 kJ/mol in either direction. The free energy of the CM2 is nearly identical to that of the CM1. The presence of two deep minima of approximately the same magnitude and with a small barrier between them imply that the most stable configurations are when IL ion pairs are in contact. As the alkyl chain length decreases the CM1 and CM2 shift upward indicating a decrease in the associative strength of these ILs when the alkyl chain length is shortened. However, the shape of the PMFs is preserved. The free energy at the CM1 for [C2 mim][C2 H5 SO4 ] is -4.5 kJ/mol while that of the CM2 is -2.5 kJ/mol. The two free energy minima are separated by a barrier of about 2 kJ/mol in going from the CM1 to the CM2 while the barrier height is only 0.5 kJ/mol in traversing from the CM2 to the CM1. In comparison to the ILs bearing [NTf2 ]− anion, however, the PMF decays rapidly to zero for this IL. The free energy minima in the case of [C2 mim]Cl are the most shallow; the CM1 is about -1 kJ/mol and CM2 is approximately -1.5 kJ/mol with a barrier between the two free energy minima of 2.5 kJ/mol. In addition, the PMF approaches zero within 1 Å of the CM2 indicating that the ions are practically solvated beyond 7 Å. The ions in [C2 mim][C2 H5 SO4 ] may also be regarded as completely solvated beyond 7 Å.

Radial Distribution Functions The association patterns of the IL ions are clearly illustrated in the RDF depicted in Figure 3. The first two peaks in these RDFs correspond to the CM1 and the CM2 respectively. The first peak height of the RDF of [C6 mim][NTf2 ] is close to 15 suggesting strong aggregation of the ions; the second peak height is also comparable (∼12). Similarly, the peak heights in the RDF of [C4 mim][NTf2 ] are ∼11 and ∼9 at the CM1 and CM2, respectively, implying a strong propensity for association for this IL. The ionic liquid [C2 mim][NTf2 ], however, displays RDF peak heights that are considerably lower - ∼5 at both the CM1 and CM2 - an observation that is consistent 15



with the decreasing strength of association with decrease in the alkyl chain length. In contrast to these observations, the peak heights at the CM1 and the CM2 for [C2 mim][C2 H5 SO4 ] are ∼5 and ∼2, respectively, pointing to the fact that the tendency for association of these ions is much less pronounced than that for [C6 mim][NTf2 ] and [C4 min][NTf2 ]. The association strength for the [C2 mim][C2 H5 SO4 ] is similar to that of [C2 mim][NTf2 ], albeit lower as indicated by a factor of 2.5 reduction in the peak height at CM2. The peaks in the RDF of the most hydrophilic IL are close to 1 suggesting that the ions in [C2 mim]Cl do not exhibit preference for association.

Bernardes et al. 64 recently performed a molecular dynamics study of pure [C2 mim][C2 H5 SO4 ] 20


15

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10

5

0

2

4

6

8

10

12

r (Å) Figure 3: RDFs calculated fromt the PMFs obtained from the ABF simulations by inverting eq. (1). and its mixture with water from a water mole fraction of 0.5 all the way up to 0.996. Their RDF results between the H2 (the hydrogen attached to C2 in Figure 1 of the cation and S1 (Figure 1) of the anion showed, at all IL concentrations, the presence of two peaks representing the CM1 and the CM2. The RDFs obtained in this work are consistent with the results of the present study. The peak height at the CM1 obtained in the present work, however, is higher than that of the highest dilution solution in the study by Bernardes et al. 64 due to the fact that the RDFs are computed 16


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between the C2 and S1 sites in our work while they were calculated for H2 and S1 in the work by Bernardes et al.. Another key difference is that the concentration of IL in the present study is approximately 10 times lower than the highest dilution of the IL investigated by Bernades et al. Given that the first peak height increased with increasing dilution of the IL while that of the CM2 remained nearly constant upon dilution of the IL, our results are consistent with those of Bernardes et al.. In the present study, unbiased simulations were also carried out to determine the RDFs of three representative ILs. The RDFs obtained from these simulations showed qualitatively similar behavior to those depicted in Figure 3. However, due to the very low concentration of ILs investigated in the present study, the RDFs were much noisier (see Supporting Information Figure S1).

The hydrophobic behavior of the [NTf2 ]− containing ionic liquids can be further understood from the temperature dependent PMF profiles. As shown in Figure 4, the PMFs, for a representative [C4 mim][NTf2 ] ionic liquid, show that raising the temperature causes the free energy at the CM1 to increase; the free energy at the CM2, however, becomes more favorable with increase in temperature. The PMF behavior suggests that with increasing temperature there is a shift in the conformations of ions yielding the minimum in free energy. Better hydration and corresponding higher solubility of [C4 mim][NTf2 ] is characteristic of hydrophobic hydration 65 of this ionic liquid. The increase in aqueous solubility of the ionic liquid based on the PMF profiles is also consistent with the liquid-liquid equilibrium study of water and the ionic liquid where it was found that the solubility of the ionic liquid increases as the temperature was raised from 288.15 K to 318.15 K. 66

Coordination Number The RDFs obtained from the ABF calculations and provided in Figure 3 may be used to calculate the number (N(r)) of anions around a cation from the relation Z r

N(r) = 0

4πr2 ρ0 g(r)dr. 17


(14)


Page 18 of 38

-4.4

300 K 320 K 340 K 400 K

-4.8

PMF(ξ) (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-5.2

-5.6

-6

-6.4

3

3.5

4

4.5

5

5.5

6

ξ (Å) Figure 4: Temperature dependent PMFs for the IL [C4 mim][NTf2 ] calculated from the ABF simulations. Figure 5 presents the calculations of the coordination number as a function of the reaction coordinate. Note that in the absence of any force exerted on the pair (i.e. g(r) = 1), the coordination number varies as the cube of the separation between the IL pair. Such an ideal distribution is included as a dashed line in Figure 5. The coordination number obtained from this distribution serves as the reference from which enhancement or depletion of the IL pair at a given distance may be compared. In the case of the ILs [C6 mim][NTf2 ], [C4 mim][NTf2 ], and [C2 mim][NTf2 ], the coordination numbers are much higher than that obtained from the ideal distribution for distance up to 8 Å. This is a direct consequence of the fact that the ions of these ILs are found to be predominantly in the associative state. Beyond this distance, the coordination numbers, though higher than that for an ideal distribution, begin to follow the ideal distribution behavior. The coordination number calculated for the IL [C2 mim][C2 H5 SO4 ] is about a factor of 2 higher than that for the ideal scenario. The number of anions surrounding the cation for the IL [C2 mim]Cl follows closely that obtained for the ideal distribution suggesting that the ions are most likely, among the five ILs, to be found in dissociative states.

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0.25

Coordination Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2 0.15 0.1 0.05 0

2

4

6

8

10

12

r (Å) Figure 5: Anion coordination number around the cation for the five ILs at 300 K obtained from eq. (14).

Association Constants The ion-ion pairing in the five ILs can be further examined by determining their association constants using eq. (9) in conjuction with the eq. (11). For these calculations, the ions are considered to be associated if they are separated by a distance less than the position of the CM2; if this distance is greater than the CM2 position, they are regarded as dissociated. The distance of association and the association constant of each of the ILs are presented in Table 1. The association constants are in the range 0.5-3.6 dm3 · mol−1 and follow the order: [C6 mim][NTf2 ] > [C4 mim][NTf2 ] > [C2 mim][NTf2 ] > [C2 mim][C2 H5 SO4 ] > [C2 mim]Cl. The order of KA is consistent with the hydrophobicity/hydrophilicity of the IL.

Association constants may be estimated experimentally using electrical conductivity measurements, or dielectric relaxation spectroscopy of the aqueous solutions of ILs. A three parameter model such as the low concentration Chemical model 67 or a Lee-Wheaton model 68 is used to fit the molar conductivity data measurements. The three parameters correspond to the limiting

19



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Table 1: Association constants of the three ILs at 300 K. The distance of the association for the maximum separating the CM and SSM is given by R. KA is the association constant. IL

R (Å) [C6 mim][NTf2 ] 5.2 [C4 mim][NTf2 ] 5.15 [C2 mim][NTf2 ] 5.2 [C2 mim][C2 H5 SO4 ] 6.1 [C2 mim]Cl 5.2

(dm3 ·

KA −1 mol ) 3.62 2.69 1.61 1.33 0.48

conductivity at infinite dilution, the association constant and a distance parameter related to the distance of closest approach of a ions in the solvent. Depending on the studied concentration range and the selection of a given model, the association constant estimated by such a procedure can vary by a factor of 10-15. For example, the association constants of [C4 mim]Br extracted using the Lee-Wheaton model is 66 dm3 · mol−1 69 while that obtained with the low concentration chemical model is 6.0 dm3 · mol−1 . 70 Electrophoretic mobilities of ions have also been used to determine the association constants of ILs. 71 Application of these different approaches can lead to conflicting trends that substitution of a hydrophobic anion by a hydrophilic anion does not alter the association constant while small variation in both the cation and anion identities can alter the association constant by several orders of magnitude. For example, Katsuta et al., 71 based on electrophoretic mobility measurements, reported the association constant of [C4 mim][NTf2 ] to be 8.0 dm3 · mol−1 which is nearly identical to the association constant of 7.92 dm3 · mol−1 determined by Shekaari and Mousavi 70 for [C4 mim]Cl using the low concentration Chemical model. On the other hand, Be˘ster-Roga˘c et al. 72 estimated, based on electrical conductivity measurements, that the association constant of [C2 mim][C2 H5 SO4 ] is 0.008 dm3 · mol−1 , a value that is three orders of magnitude smaller that of [C4 mim]Cl and [C4 mim][NTf2 ].

Given that the experimental determination of association constant is somewhat arbitrary and can lead to variation over several orders of magnitude, one should not expect an absolute agreement between the association constants determined from simulations and those reported based on in20


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direct experimental measurements. Notwithstanding, the simulation results indicate a trend that increasing alkyl chain length leads to an increase in association constants in line with experimental observations. 69,70

It is to be noted that predictions of the association constants are based on the accuracy with which the PMFs can be obtained, which in turn are sensitive to the choice of IL force field parameters. The role of force field parameters in the calculations of the association constant was clearly elucidated in a comprehensive study focusing on ion pair formation in aqueous solution of alkali halides by Fennell et al.. 51 The authors examined a number of ion force fields in combination with five different water models. The results from the study demonstrated that it is possible, depending on the selection of force field parameters, to change the behavior of ions from an associative state to the one in which the ions are predicted to be completely dissociated. However, the ion parameters optimized for a given water model predict association constants that are in good agreement with those derived from experimental measurements. In the case of ILs, however, the force field parameters are developed to match the pure IL properties and it is not clear if these parameters can adequately describe the interaction between ions and water. It has already been shown by Kelkar et al. 56 that although the force field parameters for the IL [C2 mim][C5 H2 SO4 ] capture the pure IL thermodynamic properties satisfactorily, the application of these parameters for accurate prediction of thermodynamic properties of mixtures of ILs with water requires modification of partial charges in the water model. Given these limitations, the association constant results of the present study should be taken as preliminary. A systematic study of the effect of water and IL models needs to be carried out.

Constrained Simulations Constrained simulations of the ILs at CM1, CM2 and isolated pair (IP) separations were performed to gain a better understanding of the hydration of the ions. The IP is defined as the distance at which

21



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Page 22 of 38

the two atom groups are sufficiently far apart so that they may be assumed to be a completely dissociated pair. In the constrained simulations, the IP distance was set over 20 Å, which is outside the cutoff range of the Lennard-Jones potential. From these simulations, the radial distribution functions (RDFs) were computed between the oxygen site in water and various atomic sites in the cations and anions.

Figure 6 displays the most prominent RDFs for different anions in [C4 mim][NTf2 ], [C2 mim][C2 H5 SO4 ] and [C2 mim]Cl. Among the three anions, water interacts strongly with Cl− as can be deduced from the first peak height (∼ 3.6) at a separation of 3.2 Å. In comparison, the first peak heights for the atom groups for the other anions shown in Figure 6 are considerably lower. For example, the first peak height in the RDF of the O2 site in [C2 H5 SO4 ] is close to 1.5 while that for F5 site in [NTf2 ] is merely ∼ 1.0. The strong hydration of Cl− in comparison to the other ions is a direct consequence of its spherical shape and small size leading to high charge density. In addition, the spherical nature of the Cl− anion is also favorable for hydrogen bonding with water molecules. Note that, however, the RDF in Figure 6 does not directly provide information on the hydrogen bonds between water and the anion atom groups, as the presence of a hydrogen bond is usually detected based on the distance between the donor and acceptor atoms and the angle donor-hydrogen-acceptor. 73

In addition to the first peak heights, the RDFs also point to several distinctions in the hydration shells of the anions. The distance between the first two peaks is greater for the RDF in [C2 H5 SO4 ]− in comparison to that of Cl− . This observations suggests that the second hydration shell is more disordered in the case of the former anion. This effect may be attributed to the bulky nature of the anion and the fact that the negative charge is dispersed over a number of sites. The RDF values for the F5 site are below 1 for distances up to 9 Å indicating that the presence of [NTf2 ]− induces a long-range depletion of water in the vicinity of the anion resulting in the weakest hydration among the three anions. The depletion in water density around the anion is in line with the hydrophobic nature of the anion. Poor hydration of the anion may also explain why CM1 and CM2 states are

22


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4

F5-OH O2-OH Cl-OH

3

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

1

0

2

4

6

8

10

r (Å) Figure 6: RDFs between atoms in the three anions in [C4 mim][NTf2 ], [C2 mim][C2 H5 SO4 ] and [C2 mim]Cl and oxygen in water at 300 K. The RDFs were calculated from constrained simulations in which the distance between the atoms indicated with * in Figure 1 was the same as the first minimum (CM1) in the PMF of each of the ILs. The O2 -OH and F5 -OH RDFs are shifted upwards by 1 and 2, respectively, for clarity.

23



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more stable than the IP states as these configurations tend to minimize the solvent accessible surface area.

The simulation results of these RDFs suggest that water interacts primarily with the anion of an IL, an observation that has been reported in a number of simulation 42,74–77 and experimental studies. 78,79 The trends in the RDFs identified at the CM2 and IP were similar to those reported here for the CM1 and hence are not shown.

When the results of the RDFs in Figure 6 are compared against the cation-anion RDFs plotted in Figure 3, it becomes readily apparent that the first peak height in the water-anion RDF is inversely related to that in the cation-anion RDF. For example, the height of the first peak in the ion-ion RDF in [C4 mim][NTf2 ] is ∼ 11 while the corresponding value for water-anion RDF barely approaches 1. On the other hand, the first peak is almost nonexistent in the cation-anion RDF in [C4 mim]Cl in contrast to a peak value of > 3 for water-anion RDF. The implication of this observation is that the microscopic description of dilute ILs is determined by a subtle interplay between cation-anion interactions and anion-water interactions.

Although RDF plots in Figure 6 show the most relevant atom group of each IL pair, the RDFs of other atom groups in the ILs were calculated to obtain a complete picture of the hydration of ions in the ILs. As before, cation groups are not included as they are not informative due to small RDF values over the entire range of distances. This finding supports previously reported observation that the hydrogen bonding between imidzaolium cations and water is very weak. 41,80 Results of the RDF of [NTf2 ]− with water determined at the CM1 are provided in Figure 7. It is evident that water localization is practically non-existent around any of the atom groups of the anion. An important conclusion from these RDFs is that the hydrophobic nature of this IL originates not because of the long alkyl chain in the cation, but because water does not effectively hydrate any of the atom groups in the anion. Figure 8 displays the RDFs of [C2 H5 SO4 ]− atom groups at the CM1.

24


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Page 25 of 38

The most prominent atom groups for which the RDF was higher than 1 are O2 and C5 atom groups. The O2 group was chosen for the above analysis due to the fact that the distance at which the first peak in the RDF appears is relevant for hydrogen bonding interactions. On the other hand, it is likely that the peak in the C5 RDF is induced as a consequence of ordering around the O2 moiety. 2.0

1.6

1.2

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8

O3-OH F5-OH N1-OH

0.4

0.0

2

4

6

8

10

r (Å) Figure 7: RDFs between various atoms in the anion [NTf2 ]− and oxygen in water at 300 K. The RDFs were determined by constraining the distance between N1 of the anion and C2 in [C4 mim]+ at a distance corresponding to the first minimum (CM1) in the PMF of the IL. Refer to Figure 1 for the labeling scheme. The RDF O3 -OH and F5 -OH are shifted upwards by 0.4 and 0.8 units respectively for clarity.

Conclusions The microscopic behavior of five different ILs with varying hydrophobicity was investigated by computing the potential of mean force between the cation and anion of each IL. The PMFs were obtained using the adaptive biasing force simulations. The results indicated that the ILs show two distinct free energy minima in their PMFs under the condition of high dilution. These free energy minima were attributed to the ions in direct contact.

25



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Page 26 of 38

2.4 2.0 1.6

g(r) 1.2

O2-OH O3-OH C4-OH C5-OH

0.8 0.4 0.0

2

4

6

8

10

r/Å Figure 8: RDFs between various atoms in the anion [C2 H5 SO4 ]− and oxygen in water at 300 K. The RDFs were calculated by constraining the distance between S1 in the anion and C2 in [C2 mim]+ at the distance corresponding to the first minimum (CM1) in the PMF of the IL. The RDFs are shifted upwards for clarity. Refer to Figure 1 for the labeling scheme. The free energy minimum at the shortest distance between cation and anion was referred to as CM1 and occurred between 3-4 Å separation for all the ILs. The second free energy minimum appearing at 5-6 Å was attributed to the cation-anion in different conformations and was labeled as CM2. The relative depths of these minima and free energy barriers separating these minima provided an indication of association/dissociation of the ILs. In the case of [C6 mim][NTf2 ], [C4 mim][NTf2 ] and [C2 mim]NTf2 ], both minima are deep, have a low free energy barrier separating these minima and the PMF exhibits a large free energy penalty for dissociation, features suggestive of association of ions even under very dilute conditions examined in the present study. In contrast, the PMF of [C2 mim]Cl is characterized by very weak free energy minima, a large barrier between the minima and practically no free energy penalty for dissociation. Collectively, these PMF features imply that [C2 mim]Cl is likely to be dissociated when diluted at a very low concentration. [C2 mim][C2 H5 SO4 ] exhibits characteristics in between those of [C2 mim][NTf2 ] and [C2 mim]Cl, since the PMF has a low free energy penalty for dissociation but a deep CM. The ten-

26


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dency of each IL to dissociate therefore increases in the order: [C6 mim][NTf2 ] < [C4 mim][NTf2 ] < [C2 mim][NTf2 ] < [C2 mim][C2 H5 SO4 ] < [C2 mim]Cl in accordance to solubility trends for these ILs. It is evident that the IL preference for dissociation decreases with increase in the alkyl chain length on the cation when the identity of the anion is held constant. Similarly, for a given cation, the tendency for dissociation increases when the anionic nature of the IL is more hydrophilic. The picture that emerges from such observations is that the association of the ions is correlated with the hydrophobicity/hydrophilicity of ILs.

An estimate of the association constants of ions was also obtained from the PMF profiles. Consistent with the hydrophobic and hydrophillic nature of the ILs, the association constants follow the order: [C6 mim][NTf2 ] > [C4 mim][NTf2 ] > [C2 mim][NTf2 ] > [C2 mim][C2 H5 SO4 ] > [C2 mim]Cl and range from 3.6 - 0.5 dm3 ·mol−1 .

The distribution of water around the ions constrained at the distances corresponding to the CM1, CM2 and IP were analyzed in terms of the RDFs. These distribution functions suggest that the interactions of water predominantly take place with the anion atom groups. All the atom groups of [NTf2 ]− showed a clear long-range depletion of water suggesting unfavorable hydration of the anion. The RDF of water around the atom group O2 in [C2 H5 SO4 ]− is characterized by a welldefined peak suggestive of a more favorable hydration of the anion. The Cl− anion was found to have the most favorable hydration characteristics among the three anions, as evidenced by a strong peak in the RDF of oxygen in water and the anion. Based on the observation that there was no noticeable difference in the RDFs determined at the CM2 and IP distances, hydration patterns of the anions are independent of the state of the ion-pair.

Acknowledgement The authors thank the Center for Research Computing at Notre Dame for providing computational resources. J. K. S. gratefully acknowledges financial support from the Center for Research 27



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Computing at Notre Dame. Additionally, a part of the study was supported by the NSF grant CBET-1134238.

Supporting Information Available The RDFs obtained from unbiased molecular dynamics simulations are provided. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Ionic liquid 1-Ethyl-3-Methylimidazolium Ethyl Sulfate and Water. J. Phys. Chem. B 2010, 114, 4747–4754.

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State of Hydrophobic and Hydrophilic Ionic Liquids in Aqueous Solutions

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