Concentration-Dependent Hydrogen Bond Behavior of

Article pubs.acs.org/jced

Concentration-Dependent Hydrogen Bond Behavior of Ethylammonium Nitrate Protic Ionic Liquid−Water Mixtures Explored by Molecular Dynamics Simulations Yiping Huang,† Zheng Wan,† Zhen Yang,*,† Yuanhui Ji,*,‡ Li Li,† Deshuai Yang,† Meihua Zhu,† and Xiangshu Chen*,† †

College of Chemistry and Chemical Engineering, Jiangxi Inorganic Membrane Materials Engineering Research Center, Jiangxi Normal University, Nanchang 330022, People’s Republic of China ‡ School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, People’s Republic of China S Supporting Information *

ABSTRACT: The detailed hydrogen bond (HB) behavior of ethylammonium nitrate (EAN) ionic liquid (IL)−water mixtures with different water concentrations has been investigated at a molecular level by using classical molecular dynamics simulations. The simulation results demonstrate that the increasing water concentration can weaken considerably all cation−anion, cation−water, anion−water, and water−water HBs in EAN−water mixtures, and the corresponding HB networks around cations, anions, and water molecules also change significantly with the addition of water. Meanwhile, both the translational and the rotational motions of anions, cations, and water molecules are found to be much faster as the water concentration increases. On the other hand, the order of their HB strength is found to be cation−anion > anion−water > cation−water > water−water at low water mole fractions ( cation−water > anion−water > water−water at high water mole fractions (>38%). The opposite orders of anion−water and cation−water HBs at low and high water concentrations, as well as the different changes of HB networks around cations and anions, should be responsible for the increasing deviation in diffusion coefficient between cations and anions with the water concentration, which is favorable to the cation−anion dissociation. In addition, the competing effect between ionic mobility and ionic concentration leads to that the ionic conductivity of EAN−water mixtures initially increases with the water mole fraction and follows a sharp decrease beyond 90%. Our simulation results provide a molecular-level concentrationdependent HB networks and dynamics, as well as their relationship with unique structures and dynamics in protic IL−water mixtures.

1. INTRODUCTION Recently, ionic liquid (IL)−water mixtures have attracted more and more attention due to their unique and superior properties in comparison with those counterparts of pure ILs.1−5 More importantly, their chemical and physical properties can be drastically adjusted by the addition of a small amount of water, which further expands their range of applications.1−3 On going from pure ILs to IL−water mixtures, however, there is an considerable increase in the relevant property complexity arising from the presence of additional water molecules. Therefore, a molecular-level understanding of the influence of water concentration on IL−water mixtures is very critical to exploit such an approach.1,6 From the previous experimental observations, IL−water mixtures usually possess a much lower density, viscosity, and surface tension than the corresponding pure ILs.7−14 However, these properties of IL−water mixtures do not always vary monotonically and proportionally with the amount of water. For example, Ghoshdastidar and Senapati15 have found that the density of imidazolium acetate IL−water mixtures increases with the addition of water from low to moderate concentrations, © 2017 American Chemical Society

which is completely contrary to the trend observed in most of IL−water mixtures.7−10 Yaghini et al.16 have confirmed that the effect of water on self-diffusion is stronger at lower water concentrations compared to that at higher water concentrations. Accordingly, the viscosity decreases less significantly at higher water concentrations. On the other hand, the ionic conductivity of IL−water mixtures often initially increases up to the maximum value and follows a decrease with the increasing water concentration.17−20 In addition, the excess molar volumes against the water concentration for IL−water mixtures were found to display positive, negative, and even sinusoidal shaped curves due to the competing effect between the self-association of water and the IL−water association.21,22 Although above macroscopic properties of IL−water mixtures have been wellexplored by various experimental observations, the underlying mechanism on their variations with the addition of water is still obscure so far. Received: February 22, 2017 Accepted: July 6, 2017 Published: July 20, 2017 2340

DOI: 10.1021/acs.jced.7b00205 J. Chem. Eng. Data 2017, 62, 2340−2349

Journal of Chemical & Engineering Data

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concentration-dependent HB properties and their relationship with the other properties in EAN IL−water mixtures. The direct quantitative information on different HB dynamics, including NH 3 + −NO 3 − , NH 3 + −H 2 O, NO 3 − −H 2 O, and H2O−H2O types, is determined by calculating the continuous and the intermittent HB time correlation functions. Meanwhile, the radial distribution functions, translational and rotational motions, average HB number, and the relevant ion-pair association/dissociation dynamics are also discussed in detail. This paper is organized as follows. In Section 2, we present details of MD simulations. Then, the simulation results are shown and discussed in Section 3. Finally, we offer a few general conclusions and remarks in Section 4.

It is well-known that the solvent properties of IL−water mixture are definitely determined by the interactions between ILs and water molecules. Furthermore, the interaction can be further divided into the electrostatic and van der Waals interactions, as well as hydrogen bonds (HBs). The HB interaction between the IL anion and water has been experimentally addressed through ATR-IR spectroscopy, and water molecules were found to mainly form HBs with the anions, such as NO3− and CF3CO2−.23 Compared to other two kinds of interactions, furthermore, experimental observations of the HB interaction in IL−water mixtures are often fraught with enormous difficulties owing to its localized and directional characters.24−26 For instance, the spectroscopic assignments in the HB vibrational region can be very complicated experimentally even for pure ILs, as shown in the detailed studies of both far-IR spectroscopy and density functional theory (DFT) calulations proposed by Ludwig and co-workers.25 More complicated phenomena of the spectroscopic assignments can be observed in IL−water mixtures since the characteristic peaks of different HBs may be tightly coupled with one another. Therefore, relatively few experimental studies were reported on the HB behavior in IL−water mixtures up to now.27 As a powerful complementary analysis tool, molecular dynamics (MD) simulation can offer a direct and deep insight into the structure, dynamics, and HB properties of IL−water mixtures at a molecular level.1,28−36 For example, Niazi et al.34 have studied structural and diffusion properties of imidazoliumbased IL−water in detail by using MD simulations, showing that the diffusivity of both cations and anions begins with a rapid increase with the water concentration until the mixing system transforms into an aqueous solution with the IL as the solute (approximately 70 mol % water). Migliorati et al.36,37 have combined the MD simulation method with the extended X-ray adsorption fine structure (EXAFS) spectroscopy to explore the aggregation behavior in [C4mim]Br/water mixtures, where the cations and the anions are found to be not completely separate, but rather solvent-shared ion pairs are formed in spite of the amount of water. Although recent MD simulations have provided much detailed information on the structure and dynamics properties of various IL−water mixtures, few simulations focus on the HB behavior in IL−water mixtures.31,33−35 It should be emphasized that the HB behavior may be significantly responsible for the exotic properties of IL−water mixtures. Furthermore, the protic IL−water mixtures have received much less attention than the aprotic IL−water mixtures.38−40 As an important subset of the ILs, the protic ILs are formed through the proton transferring from the Brønsted acid to the Brønsted base, resulting in the presence of protondonor and proton-acceptor sites of protic ILs. Consequently, there must be various HBs in protic IL−water mixtures including cation−anion, cation−water, anion−water, and water−water HBs, and different HBs should also compete fiercely with one another. Clearly, much more work is needed to understand the HB behavior of protic IL−water mixtures as well as its relations to other properties. This present work attempts to provide some contributions toward this issue. In this work, a series of MD simulations have been carried out to investigate the HB behavior of various IL−water mixtures with 19 different water concentrations. A prototype protic IL of ethylammonium nitrate (EAN) is considered here, which is one of the oldest discovered and most extensively studied protic ILs. Meanwhile, the EAN IL can be completely miscible with water. Herein, we mainly focus on the

2. SIMULATION DETAILS To explore the influence of water concentration, we first constructed 19 EAN IL−water mixture systems in this work, where the number of EAN ion pairs is fixed at 512 while that of water molecules is from 64 to 15360, as shown in Table S1 of the Supporting Information. Namely, the mole fraction of water molecules in the EAN IL−water mixtures is approximately from 11% to 97%. Also, the details about the setup of initial configurations are shown in the Supporting Information. Then, an all-atom OPLS model developed recently by Acevedo and Tirado-Rives was employed for the EAN IL.41,42 To estimate the validity of this EAN force field, we have made a comparison in density and ionic conductivity of pure EAN between our MD simulations and available experimental data,43 as shown in Figure S1 of the Supporting Information. The comparison results showed that our simulation results failed to accurately provide an quantitative data (especially for the ionic conductivity) but are at least qualitatively reasonable for all simulated data. Furthermore, it should be emphasized that most of simulated ionic conductivities based on current force fields are often less than the corresponding experimental data by about 1 order of magnitude, as shown in previous MD simulations.44,45 Meanwhile, the water molecules were represented by using the TIP3P model,46 which is compatible with the all−atom OPLS model. On the basis of these force fields, the nonbonded interactions were described by the combination of electrostatic and Lennard−Jones (L−J) interactions. All L−J parameters and partial atomic charges used in this work were summarized and listed in Table S2 of the Supporting Information. Furthermore, the mixed L−J parameters, including the collision diameter σij and the well depth εij, were derived from self-parameters using the mixing rule of geometric mean. Next, a series of MD simulations have been carried out for the EAN IL−water systems in isothermal−isobaric ensemble (NPT) with the temperature of 353 K and the pressure of 1.0 atm. For each system, an NPT MD simulation of 10 ns was first performed for equilibration, and then another NPT MD simulation of 10 ns was performed for data analysis with the trajectories stored every 100 fs. The Newton’s equations of motion were integrated by using the velocity-Verlet algorithm with a time step of 1 fs, and the periodic boundary condition was used in all three directions. The cutoff distance of nonbonded interactions was set to 12 Å, and the long-range electrostatic interactions were calculated by using the particlemesh Ewald (PME) method.47 Both the temperature and the pressure were controlled by using the Berendsen algorithm with coupling times of 0.4 and 2.0 ps, respectively. In addition, another NPT MD simulation of 500 ps following the above final configuration was performed for each EAN IL−water 2341



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where the cutoff radius rc is usually chosen to be the first local minimum of corresponding RDF, that is, the first solvation shell. However, the RDFs used for N(r) are based on the centers of mass of cations, anions, and water molecules, as shown in Figure S3 of the Supporting Information. Herein, the values of rc are chosen to 6.0, 6.0, 4.8, and 3.8 Å for the cation−anion, cation−water, anion−water, and water−water cases, respectively. Then, Figure 2 presents the corresponding

system to calculate the corresponding continuous HB dynamics. The trajectories stored every 5 fs instead of 100 fs, which is short enough to accurately calculate continuous HB dynamics. In this work, all NPT MD simulations were performed by using the Tinker 7.0 code.48

3. RESULTS AND DISCUSSION To explore the effect of water concentration on the structural properties, we first present the site−site radial distribution functions (RDFs) for EAN−water mixtures at different water mole fractions in Figure 1. The RDF g(r) is defined as the ratio

Figure 2. Coordination numbers of cation−anion, cation−water, anion−water, and water−water in EAN−water mixtures as a function of water mole fractions, xw (%). For comparison, the corresponding water−water value of pure bulk water is also shown here.

coordination numbers of cation−anion, cation−water, anion− water, and water−water in EAN−water mixtures with different water concentrations. The cation−anion value expectedly displays an obvious decrease, but other values increase as the water concentration increases. Furthermore, both cation− water and anion−water values are obviously larger than the water−water value, suggesting that the interactions between ions and water molecules are stronger than those between water molecules. By further comparisons, the cation−water value is found to be much larger than the anion−water value, which may arise from the stronger cation−water HBs than the anion−water HBs at high water mole fractions. Similarly, ab initio MD study proposed by Kirchner and co-workers have revealed that strong directional HBs allow a strong coordination of the cation to water for the mixture of monomethylammonium nitrate and water.39 On the other hand, the hydrophobic ethyl group in cations could induce the formation of a cage-like hydration shell (see the illustration in Figure S4 of the Supporting Information), which is favorable for water molecules to aggregate around cations. This assumption can be supported through the recent experiment proposed by Hayes et al., where the hydrophobic ethyl group in EA+ cations can lead to a local apolar and a polar domain structures when the water molecules are added into the pure EAN IL.40 Actually, such cage-like hydration shell can also be observed even for the shorter methyl group. For example, the MD simulation results proposed by Kusalik et al. showed that the hydrophobic methyl groups can also induce the formation of a cage-like hydration shell for the methylamine/water mixtures.50 Figure 3 presents the translational motions (i.e., diffusion behavior) of cations, anions, and water molecules in EAN− water mixtures at different water mole fractions, which can be directly studied through the mean square displacement (MSD) of their centers of mass. Accordingly, their diffusion coefficients can be determined using the Einstein’s formulation34,36,51

Figure 1. RDF curves of (a) cation−anion, (b) cation−water, (c) anion−water, and (d) water−water in EAN−water mixtures with different water mole fractions, xw (%). For comparison, the corresponding curve of pure bulk water is also shown here.

of local density ρ(r) within a spherical shell at position r in the radial direction to the corresponding partial bulk density ρbulk, that is, g(r) = ρ(r)/ρbulk. Furthermore, it should be noted that the partial bulk densities ρbulk for ions and water molecules are different from each other. Herein, the nitrogen atoms in both cations and anions, as well as the oxygen atom in water molecules, are taken as reference sites to calculate the corresponding site−site RDFs. Then, we can see clearly from Figure 1 that the peak height of cation−anion RDF is the largest compared to other kinds of RDFs regardless of the water concentration, suggesting the interactions between anions and cations are the strongest owing to the presence of both electrostatic interactions and HBs. As the water concentration increases, the first peaks of anion−water, cation−water, and water−water RDFs become lower and lower, while that of cation−anion RDF shows an obvious increase, indicating the cation−anion pairs prefer to aggregate together at high water concentrations. Such opposite variations with the water concentration between cation− anion and other RDFs have also been observed for other IL−water mixtures.34−36,49 These opposite variations are mainly due to an increase of the partial bulk density ρbulk for water molecules, while a decrease of the partial bulk density for cations and anions, as shown in Figure S2 of the Supporting Information. On the other hand, we calculate the relevant coordination numbers N(r) by numerically integrating the RDFs, which are expressed as6,38 N (r ) =

∫0

rc

4πρbulk r 2g (r ) dr

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We can find clearly from Figure 3 that increasing water concentration obviously speed up the translational motions of cations, anions, and water molecules, which agrees well with the previous simulation results in other IL−water mixtures.32,35,52 Meanwhile, the MSD value of water molecules increases much faster than the values of both cations and anions as the water concentration increases. Accordingly, Table 1 shows that the diffusion coefficients of cations, anions, and water molecules are 1.09 × 10−7, 1.89 × 10−7, and 12.59 × 10−7 cm2/s in turn at the water mole fraction of 11%, while these corresponding values increase up to 293.47 × 10−7, 350.33 × 10−7, and 659.53 × 10−7 cm2/s at 97%, respectively. Moreover, their diffusion coefficient always show the order of water > anion > cation over the whole concentration range.32 It should be noted that although the EAN−water mixtures also display an identical subdiffusive behavior to the pure EAN IL.53 However, the diffusion coefficients in this work are calculated in the time interval of 2000 ps, which far exceeds the bend point of 0.5 ps in the MSD curves, as shown in Figure S5 of the Supporting Information. In addition, Table 1 shows that the deviation in diffusion coefficient between cations and anions is only 0.80 × 10−7 cm2/ s at 11%, while this deviation is up to 56.86 × 10−7 cm2/s at 97%, which is 2 orders of magnitude more than the corresponding deviation of pure EAN IL (0.51 × 10−7 cm2/s).53 Similar phenomena have also been observed in NMR experiments54 and MD simulations.28,34,51,55 Such a small deviation in pure EAN IL suggests that the strong interaction between anions and cations considerably enhances the cation−anion association so that both anions and cations almost displays the same diffusion motions.53 However, the decreasing ionic concentration with the addition of water is expected to significantly weaken the whole electrostatic interactions between cations and anions in EAN−water mixtures. Besides, the strength of cation−anion HBs is found to be weaker as the water concentration increases in the following discussion. Therefore, the cation−anion dissociation can be considerably promoted by the addition of water due to the weakened electrostatic interactions and HBs between cations and anions.34,52

Figure 3. MSD curves of (a) cations, (b) anions, and (c) water molecules in EAN−water mixtures with different mole fractions, xw (%). For comparison, the corresponding curve of pure bulk water is also shown here.

Di = lim

t →∞

⟨[ri(t ) − ri(0)]2 ⟩ 6t

(2)

where ⟨[ri(t) − ri(0)]2⟩ is the MSD of cations, anions, and water molecules in EAN−water mixtures at a certain time t, respectively.

Table 1. Diffusion Coefficients (10−7 cm2/s) of Cations, Anions, and Water Molecules in EAN−Water Mixtures with Different Water Mole Fractions, xw (%) xw (%) 11 27 33 38 43 47 50 55 59 62 65 68 71 75 79 83 88 94 97 bulk water

Dca (EA+) 1.09 2.79 3.75 4.73 6.42 7.73 9.22 11.59 14.69 16.97 22.79 26.99 34.58 44.42 59.38 81.65 126.98 202.99 293.47

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.01 0.05 0.04 0.05 0.08 0.07 0.08 0.17 0.14 0.13 0.28 0.24 0.50 0.38 0.79 0.68 1.07 1.62 1.35

Dan (NO3−) 1.89 4.49 6.00 7.48 9.79 11.69 13.94 16.84 21.54 26.17 32.24 38.04 46.75 60.08 76.71 101.65 152.25 251.79 350.33

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.02 0.04 0.07 0.05 0.13 0.11 0.13 0.14 0.20 0.34 0.29 0.33 0.40 0.51 0.64 1.32 1.29 2.01 1.80

2343

Dw (H2O) 12.59 22.62 26.31 32.83 38.73 46.10 50.64 59.52 73.64 81.36 97.81 110.68 133.19 161.29 198.94 260.68 350.24 526.72 659.53 910.73

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.55 0.34 0.42 0.46 0.09 0.22 0.13 0.23 0.48 1.05 0.43 0.38 0.30 0.24 0.23 0.52 0.77 0.35 0.23 0.08

Dan−Dca 0.80 1.70 2.25 2.75 3.37 3.96 4.72 5.25 6.85 9.20 9.45 11.05 12.17 15.66 17.33 20.00 25.27 48.80 56.86

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.03 0.09 0.11 0.10 0.21 0.18 0.21 0.31 0.34 0.47 0.57 0.57 0.90 0.89 1.43 2.00 2.36 3.63 3.15



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To confirm the deduction above, the ion-pair dissociation dynamics between cations and anions is characterized through the corresponding time correlation functions (TCFs), which can be expressed as53,56 S (t ) =

⟨p(0)P(t )⟩ ⟨p(0)p(0)⟩

(3)

⟨p(0)p(t )⟩ ⟨p(0)p(0)⟩

(4)

and C(t ) =

where the variable P(t) is unity when the ion is always in contact from time 0 to time t, and zero otherwise. On the other hand, the population variable of p(t) is unit when the ion is in contact at time t and zero otherwise. It should be emphasized that an “ion pair” means a cation in contact with an anion (i.e., within the first solvation shell) and a cation or anion can form several ion pairs at the same time. According to the definition, the S(t) function provides a more accurate ion-pair lifetime than the C(t) function while the C(t) function allows the reassociation of dissociated ion pairs in the interval of time t so that it can provide much information on the structural relaxation of ion pairs. In other words, the relaxation times of S(t) and C(t) represent the average lifetime τdis S and the structural relaxation time τdis C , respectively. As shown in our previous work, the dissociation for an ion pair occurs when the distance between the cation’s and anion’s centers of mass is larger than 6.1 Å and association otherwise.53 Then, we can see from Figure 4 that each C(t) curve obviously decays much slower than the corresponding S(t) curve at all water concentrations, since the S(t) curve represents the first-time breaking of an ion pair while the C(t) curve corresponds to a long-time structure relaxation. Meanwhile, all S(t) and C(t) curves decay much faster as the water concentration increases. To obtain the average lifetime τdis S and the structural relaxation time τdis , the S(t) and the C(t) curves are fitted by the three C weighed exponentials, which is expressed as53,56

Figure 4. (a) Continuous and (b) intermittent TCFs for the anion− cation dissociation in EAN−water mixtures with different mole fractions, xw (%).

Cr(t ) = A exp( −t /τa) + B exp(−t /τb) + C exp(−t /τc) (5)

Figure 5. Average lifetimes τdis S (ps) of cation−anion dissociation in EAN−water mixtures as a function of water mole fraction, xw (%). The inset shows the corresponding structural relaxation times τdis C (ps).

and then τR = Aτa + Bτb + Cτc

(6)

where A, B, and C are the fitting parameters, and A + B + C = 1, τa, τb, and τc are the time constants. As shown in Figure 5, dis both τdis S and τC values initially decrease more sharply and follows a slow decrease with the addition of water. By comdis parisons, both τdis S and τC values at 11% are more than those at 97% by approximately 1 order of magnitude. To further explore the relationship of the ionic conductivity with the water mole fractions in EAN−water mixtures, the ionic conductivity is calculated through the Nernst−Einstein equation using the self-diffusion coefficients of anions and cations57 σNE =

Npair VkBT

(q+2D+ + q−2D−)

formula, but qualitatively correct at least.57 Meanwhile, the simulated values at 298 K are also calculated for comparison with the available experimental data.58 We can find from this figure that the deviation between experimental and simulated ionic conductivities at 298 K is large due to the inaccuracy of EAN force field (see Figure S1 of the Supporting Information) and decreases with the water concentration. But the simulated transition point is found to be consistent with that from the relevant experiment. Then, the calculated ionic conductivities and concentrations in EAN−water mixtures with different water mole fractions at 353 K are shown in Figure 6. We can see from this figure that the ionic conductivity initially increases with the water mole fractions and follows a sharp decrease beyond 90%, which is identical with the common phenomena observed in previous experiments and simulations.19,20,29 Such a tendency of the ionic conductivity in IL−water mixtures is mainly due to the competing effect between ionic mobility and ionic concentration.20 Expectedly, Figure 3 illustrates that the addition of water can accelerate significantly the translational

(7)

where Npair is the number of ion pairs and V is the volume of simulation box. It should be noted that the correlation motion between cations and anions is not considered in the Nernst− Einstein equation so that the calculated ionic conductivities may be somewhat overestimated compared to the Green−Kubo 2344



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motions of cations and anions, which is favorable to increasing the ionic conductivities of EAN−water mixtures. On the contrary, Figure 6 shows that the addition of water can gradually

Figure 6. Ionic conductivity and ion pair concentration of EAN−water mixtures as a function of water mole fractions, xw (%). Here the ionic conductivity is obtained from the Nernst−Einstein equation, and the corresponding values are shown in Table S4 of the Supporting Information. For comparison, the experimental values are taken from the literature proposed by ref 58.

lead a decrease of ionic concentration, which is a negative effect on the ionic conductivities. Therefore, there must be a maximum point in the curve of ionic conductivities as a function of water concentration for all IL−water mixtures. Besides the translational motions, the rotational motions of cations, anions, and water molecules in EAN−water mixtures are also investigated through the relevant time correlation functions (TCFs). As shown in our previous work,50 the orientation of each anion is determined by the vector from the N atom to the geometric center of three O atoms, and that of each cation is represented by a vector pointing from its center of mass to the N atom of ammonium group. The orientation of each water molecule is represented by its dipole vector. It should be noted that the three O atoms of the NO3− anion are no longer coplanar with the N atom in EAN−water mixtures, which is very different from that in the gas phase (see Figures S6 and S7 of the Supporting Information). Then, the corresponding TCFs Cr(t) of ions and water molecules can be calculated as53,59,60 Cr(t ) =

⎛1 Pl ⎜⎜ ⎝N

N

⎞

i=1

⎠

∑ ui(t )ui(0)⎟⎟

Figure 7. Rotational TCFs of (a) cations, (b) anions, and (c) water molecules in EAN−water mixtures with different water mole fractions, xw (%). Here the rotational TCFs are constructed using the secondorder Legendre polynomial. For comparison, the corresponding curve of pure bulk water is also shown here.

and then τC = Aτs + Bτl

where A and B are the fitting parameters, and A + B = 1, while τs and τl are the time constants of shorter and longer relaxation time scales, respectively. Then, Table 2 illustrates that all rotational relaxation times of cations, anions, and water molecules decreases rapidly as the water concentration increases, and the rotational relaxation time of cations is always much larger than those of anions and water molecules at all water mole fractions. For example, the values of cations, anions, and water molecules decrease from 186.62, 133.35, and 103.20 ps at 11% to 114.99, 75.21, and 44.28 ps at 27%, respectively. When the water mole fractions is up to 97%, their values even decrease to 2.95, 0.66, and 0.60 ps, which are less than those at 11% by about 2 orders of magnitude. Unlike the translational motions, it is well-known that the rotational motions of ions and water molecules are dominated by the local and directional HBs.50,53 In EAN−water mixtures, there are four major kinds of HBs among cations, anions, and water molecules, that is, NH3+−NO3−, NH3+−H2O, NO3−− H2O, and H2O−H2O HBs. As shown in Figure 8, the presence

(8)

where Pl is the lth rank Legendre polynomial (l = 2) and N is the number of ions and water molecules in this system as well as ui is the unit vector of the ith ions or water molecules at time t. The angular bracket means that the ensemble averaging is taken over the tagged ions or water molecules at different reference initial times. As shown in Figure 7, all rotational Cr(t) curves of cations, anions, and water molecules decay faster and faster as the water concentration increases, indicating that increasing water concentration also speed up the rotational motions of both ions and water molecules. Furthermore, the Cr(t) decay of cations is found to be much slower than those of both anions and water molecules regardless of the water mole fractions. To further determine the rotational relaxation times of anions, cations, and water molecules, the Cr(t) curves are fitted by a double exponentials53,61,62 Cr(t ) = A exp( −t /τs) + B exp(−t /τl)

(10)

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Table 2. Rotational Relaxation Times τC(ps) of Cations, Anions, and Water Molecules in EAN−Water Mixtures with Different Water Mole Fractions, xw (%)a

SHB(t ) =

11 27 33 38 43 47 50 55 59 62 65 68 71 75 79 83 88 94 97 bulk water

cation (τCca) 186.62 114.99 111.61 94.77 61.38 61.30 55.27 36.14 28.31 26.37 21.68 17.08 14.31 12.31 9.72 7.84 5.37 3.53 2.95

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

5.83 4.46 4.53 4.27 3.95 3.69 4.02 3.30 2.46 2.58 2.12 1.83 0.31 0.58 0.23 0.19 0.03 0.05 0.02

anion (τCan) 133.35 75.21 63.75 54.19 44.78 37.43 34.30 25.44 21.97 18.05 16.69 15.02 12.92 11.19 8.80 2.56 1.64 0.84 0.66

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

7.36 4.33 3.88 4.11 4.25 3.64 1.97 2.62 2.35 2.09 1.82 1.45 0.56 0.81 0.32 0.27 0.09 0.03 0.02

water (τCw) 103.20 44.28 35.01 29.45 21.55 18.40 16.43 13.76 12.88 10.98 9.94 8.82 7.90 6.84 5.68 4.67 1.10 0.74 0.60 0.43

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

5.41 6.07 4.21 3.82 4.16 2.99 3.23 3.44 1.23 1.78 0.96 1.25 1.10 0.88 0.43 0.16 0.07 0.04 0.01 0.01

Figure 9. Continuous TCFs SHB(t) for (a) NH3+−NO3−, (b) NH3+− H2O, (c) NO3−−H2O, and (d) H2O−H2O HBs in EAN−water mixtures with different water mole fractions, xw (%). For comparison, the corresponding curve of pure bulk water is also shown here.

a

Here the rotational TCFs are constructed using the second-order Legendre polynomial.

NO3−, NH3+−H2O, NO3−−H2O, and H2O−H2O HBs are found to decay faster and faster as the water concentration increases, indicating that increasing water concentration can weaken all kinds of HBs in EAN−water mixtures. This is due to that the addition of water can significantly increase the competition of different HBs. Compared to cations and anions, smaller and lighter water molecules have faster translational and rotational motions, which can be clearly supported by the results of Tables 1 and 2. Such faster translational and rotational motions are favorable to breaking the HBs with water molecules, and then these free water molecules, cations, and anions will force other HBs breaking and reformation. Therefore, all kinds of HB lifetimes in EAN−water mixtures decrease with the addition of water. Accordingly, Table 3 + − illustrates that the corresponding τHB S values of NH3 −NO3 HBs decreases from 3.55 to 1.55 ps and those of H2O−H2O HBs reduces from 2.13 to 0.55 ps when the water mole fraction increases from 11 to 97%. Such concentration-dependent HB strength may be partly responsible for the faster translational and rotational motions of cations, anions, and water molecules at higher water concentrations (see Figures 3 and 7). Meanwhile, further comparisons reveal that average lifetimes of all kinds of HBs shows the order of NH3+−NO3− > NO3−−H2O > NH3+−H2O > H2O−H2O types at low water mole fractions ( NO3−−H2O > NH3+−H2O > H2O−H2O types when the water mole fractions is less than 38%. Nevertheless, the strength order of these HBs is found to be NH3+−NO3− > NH3+−H2O > NO3−−H2O > H2O−H2O types when the water mole fractions is more than 38%. To characterize the changes of the HB networks around cations, anions, and water molecules, Figure 10 presents the proportions of different HBs with cations, anions, and water

Figure 8. Schematic illustrations for the HB definition of (a) NH3+− NO3−, (b) NH3+−H2O, (c) NO3−−H2O, and (d) H2O−H2O in EAN−water mixtures.

of HBs in this work are defined in terms of the following distance distance and angular criteria58,63 R XY < R CXY

and

θ XYH < θCXYH

(12)

where the variable H(t) is unity when the tagged HB pair is continuously kept from time 0 to time t, and zero otherwise. Then, the corresponding average lifetimes (τHB S ) are calculated by fitting the SHB(t) decay curves through three weighed exponentials, As shown in Figure 9, all SHB(t) curves of NH3+−

τC(ps) xw (%)

⟨h(0)H(t )⟩ ⟨h(0)h(0)⟩

(11)

where X is the atom of HB acceptor and Y is the non-hydrogen atom of HB donor. RXY is the distance of X and Y atoms, and XYH θXYH is the angle. Accordingly, RXY are the upper limit C and θC distance and angle of HB formation, respectively. Herein, the RXY values of NH3+−H2O, NO3−−H2O, and H2O−H2O HBs are set to 3.5 Å, while that of NH3+−NO3− HB is 3.7 Å which are obtained from the first minimum of the corresponding RDFs.38,53 The θXYH values are always fixed at 30° for all kinds of HBs.53,63,64 To determine the strength of different kinds of HBs in EAN−water mixtures, their HB lifetimes have been characterized accurately through the relevant continuous SHB(t) TCFs in this work, which are defined as the following expressions53,59,64 2346



Article

+ − + Table 3. Average Lifetimes τHB S (ps) of NH3 −NO3 , NH3 − H2O, NO3−−H2O, and H2O−H2O HBs in EAN−Water Mixtures with Different Water Mole Fractions, xw (%)a

a

xw (%)

NH3+−NO3−

NH3+−H2O

NO3−−H2O

H2O−H2O

11 27 33 38 43 47 50 55 59 62 65 68 71 75 79 83 88 94 97 bulk water

3.55 3.28 3.10 3.03 2.92 2.79 2.73 2.50 2.49 2.43 2.39 2.28 2.21 2.12 1.98 1.93 1.79 1.63 1.55

2.29 2.10 1.99 1.91 1.91 1.89 1.87 1.72 1.66 1.64 1.58 1.51 1.48 1.40 1.34 1.27 1.18 1.08 1.04

2.49 2.19 2.14 1.99 1.87 1.82 1.77 1.63 1.56 1.50 1.43 1.37 1.30 1.21 1.15 1.05 0.96 0.85 0.79

2.13 1.92 1.81 1.74 1.60 1.50 1.46 1.38 1.29 1.21 1.14 1.08 1.00 0.91 0.84 0.76 0.67 0.59 0.55 0.49

All standard deviations here are less than ±0.02 ps.

molecules as a function of water mass fraction. We can find from this figure that both cations and anions are dominated by the NH3+−NO3− HBs anions at low water concentrations but form more NH3+−H2O and NO3−−H2O HBs than the NH3+−NO3− HBs at high concentrations, respectively. For example, more than 90% of both cations and anions form the NH3+−NO3− HBs at 11%, while more than 80% of both cations and anions form the NH3+−H2O and the NO3−−H2O HBs at 97%. Different HB networks around cations and anions at low and high water mole fractions, as well as above opposite orders of NO3−−H2O and NH3+−H2O HBs, can be responsible for the increasing deviation in diffusion coefficient between cations and anions with water concentration (see Table 1). On the other hand, there are mainly both NH3+−H2O and NO3−−H2O HBs around each water molecule at low water concentrations while the H2O−H2O HBs are mainly around each water molecules at high concentrations (more than about 80%). Besides the small size and mass, the water molecules rotate much faster than both cations and anions at low water concentrations partly owing to the strength of NH3+−NO3− HBs much stronger than those of NH3+−H2O and NO3−−H2O HBs.

Figure 10. Proportions of different HBs with (a) cations, (b) anions, and (c) water molecules in EAN−water mixtures as a function of water mole fraction, xw (%).

conductivity of EAN−water mixtures initially increases with the water mole fraction and follows a sharp decrease beyond 90%. On the other hand, the order of these HB strength is NH3+− NO3− > NO3−−H2O > NH3+−H2O > H2O−H2O at the water mole fractions less than 38%, while the corresponding order is NH3+−NO3− > NH3+−H2O > NO3−−H2O > H2O−H2O at the water mole fractions more than 38%. Furthermore, the addition of water can significantly change the HB networks around cations and anions in EAN−water mixtures, where both cations and anions are dominated by the NH3+−NO3− HBs at low water concentrations but by NH3+−H2O and NO3−− H2O HBs at high concentrations, respectively. Combining different evolutions of HB networks around cations and anions, with the opposite orders of NO3−−H2O and NH3+− H2O HBs at low and high water mole fractions, results in the deviation in the diffusion coefficient between cations and anions increasing with the water concentration, which is favorable to the cation−anion dissociation as the water mole fraction increases. The concentration-dependent HB networks and dynamics of EAN−water mixtures studied in this work can be of great benefit for experimental scientists to understand the unique behavior of protic IL−water mixtures at a molecular level.

4. CONCLUSIONS In this work, we have systematically investigated the HB networks and dynamics around cations, anions, and water molecules in EAN−water mixtures with 19 different water concentrations (the water mole fraction from 11% to 97%) by using classical MD simulations. Our simulation results showed that increasing water concentration can weaken considerably all NH3+−NO3−, NH3+−H2O, NO3−−H2O, and H2O−H2O HBs in EAN−water mixtures. Accordingly, both the translational and the rotational motions of anions, cations, and water molecules are found to be much faster as the water concentration increases. Furthermore, the competing effect between ionic mobility and ionic concentration lead to that the ionic

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00205. 2347



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Article

1. Simulation systems used in this work; 2. Force field used in this work; 3. Comparison between RDF curves and radial density profiles; 4. RDF curves based on the centers of mass; 5. Schematic illustration of the cage-like hydration shell; 6. Subdiffusive behavior of EAN−water mixtures; 7. Calculated values of ionic conductivity; 8. Geometrical structure of anions (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Z. Y.). *E-mail: [email protected] (Y.H.J.). *E-mail: [email protected] (X.S.C.). ORCID

Zhen Yang: 0000-0002-5205-3281 Notes

The authors declare no competing financial interest. Funding

This work was supported by the National Natural Science Foundation of China (nos. 21463011, 21606043, and 21476099), Natural Science Foundation of Jiangxi Province (nos. 20171BAB203012 and 20151BAB203014), Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University.

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