Molecular Dynamics Simulations of Equilibrium and Transport

J. Phys. Chem. B 2009, 113, 8103–8113

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Molecular Dynamics Simulations of Equilibrium and Transport Properties of Amino Acid-Based Room Temperature Ionic Liquids Andrew Sirjoosingh, Saman Alavi,* and Tom K. Woo* Center for Catalysis Research and InnoVation, Department of Chemistry, UniVersity of Ottawa, Ottawa, Ontario, K1N 6N5 Canada ReceiVed: October 7, 2008; ReVised Manuscript ReceiVed: April 23, 2009

Molecular dynamics simulations are used to study liquid-state equilibrium and transport properties of the 1-ethyl-3-methylimidazolium salts of the 20 naturally occurring amino acids [emim][AA] that all form room temperature ionic liquids. These ionic liquids have been recently synthesized by Ohno and co-workers [J. Am. Chem. Soc. 2005, 127, 2398], but other than measured ionic conductivity at 25 °C, there is a dearth of quantitative measurements on the physiochemical properties of these liquids. The goal is to computationally study the density, polarity, transference number, and ionic conductivity of this family of solvents. We also study the spatial correlations among the imidazolium cation and amino acid anions in these liquids by computing atomic and charge radial distribution functions and preparing polarity maps. The microscopic dynamics behavior of these materials is determined by studying the mean square displacements (MSD) and velocity autocorrelation functions (VACF). The diffusion coefficients of the liquids are determined using the MSD and VACF, and the contributions of the anions and cations to the transport of charge in the ionic liquids are studied. Ionic liquids of this family that show strong anion-anion and anion-cation associations in the simulations are experimentally observed to show anomalously low electrical conductivities. Knowledge of the microscopic structures and dynamics of these liquids can allow for an intelligent choice of a solvent from this class that has required polarity and ionic conductivity. 1. Introduction A wide range of cation and anion families have been used to synthesize room temperature ionic liquids (RTILs).1-4 The choice of cation and anion leads to RTIL solvents with customizable physical, chemical, or biological activities.5 Ionic liquids (ILs) can be designed with specific solvent,6 electrochemical,7 energetic,8 lubricant,9 thermal,10 or optical properties11 in mind. Because the variety of ionic liquid salts that can be prepared is virtually unlimited, it becomes important to have some capabilities in predicting properties of candidate ionic liquids prior to their synthesis. An interesting class of RTILs has been recently synthesized using the 20 naturally occurring amino acids (AAs) as the anions.12 Fukumoto, Yoshizawa, and Ohno13-15 recently synthesized the 1-ethyl-3-methylimidazolium [emim]+ salts of the 20 naturally occurring AAs, all of which form RTILs. Upon cooling, these liquid salts undergo glass transitions rather than freezing and have ionic conductivities that vary over a range of 10-4 to 10-9 S/cm at 25 °C. The imidazolium cation of these ionic liquids has been coupled to polystyrene supports, and resulting immobilized ionic liquids show metal-scavenging ability.16 Ohno and co-workers13 plotted the logarithm of the measured ionic conductivity per unit volume, σ, of the [emim][AA] RTILs at 25 °C against the glass transition temperature, Tg, and observed that the AA ionic liquids segregate into two groups. The ILs of the first group have lower glass transition temperatures and show a linear decreasing trend of the log(σ)-Tg plot, as shown in Figure 2 of ref 13. This behavior (with a roughly identical slope) is shared by other classes of RTILs.17,18 The * Corresponding author e-mails: [email protected], [email protected].

second group of [emim][AA] ILs, which includes AAs with acidic, amidic, imidic, or nitrogen-containing heterocyclic side chains with higher glass transition temperatures have log(σ) values that fall below the linear correlation of the previous group. The ionic conductivities of this latter group are 2-5 orders of magnitude smaller than other ionic liquids. There are a few amino acids (such as tryptophan) with low glass transition temperatures but small ionic conductivity, so the small ionic conductivity cannot be attributed solely to the higher viscosity of these ionic liquids at 25 °C. To our knowledge, the densities of the glycine and alanine ionic liquids at 25 °C are the only other experimental measurements available for these liquids.36,37 To understand the effects of the anion structures on the properties of these ionic liquids, we study the molecular level structure and dynamics of the 20 [emim][AA] ionic liquids with molecular dynamics (MD) simulations. In particular, we direct our study to differences in polarity, ionic interaction strength, diffusion coefficients, transference numbers, and electrical conductivities of members of this class of RTILs. The amino acid anions are written as R-CH(NH2)COO-, where the substituent R side chains can be an alkyl, aryl, acid, amide, imide, alcohol, or sulfur-containing group. These side chain groups have a wide range of mass, volume, polarity, and chemical functionality. We thus expect their RTILs with [emim]+ to have a wide range of behaviors, which we aim to characterize with molecular simulations. Simulations of these solvents can provide guidelines for choosing amino acid RTILs for applications as solvents for different polar and nonpolar solutes, as components of two-phase extraction processes, and as electrolytes in electrochemical applications. The structure and dynamics of [emim]+ ionic liquids with symmetric counterions, such as [BF4]-, [PF6]-, [NO3]-, and [Cl]-, have been experimentally19 and computationally20 studied.

10.1021/jp808882s CCC: $40.75  2009 American Chemical Society Published on Web 05/19/2009

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There is strong ion-pair association in these liquids, the magnitude of which depends on the relative size and charge distributions of the cations and anions. In the [emim][X] ionic liquids, anions were found to generally have larger initial mean square displacements, whereas the cations were found to have larger diffusion coefficients and transference numbers. The ionic conductivities of these liquids have also been studied, and larger (e.g., PF6-) and flatter anions (e.g., NO3-) were observed to have larger σ values. The ionic conductivities of some of these ionic liquids show large deviations from the Kohlrausch (Nernst-Einstein) behavior (see below), which is an indication of strong ion-pair correlations in the liquids. The effects of relative mass and ionic radii on the anion and cation diffusion and the ionic conductivity of ionic liquids have been calculated for simple repulsive soft-core spheres by Harada et al.21 and for charged Lennard-Jones spheres by Spohr and Patey22 using MD simulations. Harada et al.21 determined that increasing the relative mass of the anion to the cation by a factor of 2 can decrease the anion and increase the cation diffusion coefficients by ∼5% and increase the ionic conductivity by ∼10%. Spohr and Patey24 observed that for a system of fixed total radius, the ionic liquids with greater size disparity have larger diffusion coefficients and viscosities, which is the result of weaker ion-pair formation in these systems. Further studies22 show that noncentral alignment of the charges on the cation and anion will lead to stronger association among the ions. Many experimental measurements19 and theoretical calculations20 of the mass, radius, and temperature dependence of specific room temperature ionic liquid transport coefficients have recently appeared in the literature. Ionic liquids with amino acid anions and the tetrabutylphosphonium cation [P(C4)4][AA] have been recently synthesized.23,24 Zhou et al. developed an AMBER-based force field for this family of ILs.25 The authors adapted the AMBER intermolecular Lennard-Jones parameters and many of the intramolecular force field constants for this group of amino acid-based ionic liquids. Molecular dynamics simulations were performed, and the force field was validated by comparison with experimental density and heat capacity data. They also studied the structure (radial distribution functions) of the ionic liquids, but no simulations of transport properties were presented in this work. In this work, we use MD simulations with an AMBER-based force field to compare equilibrium and dynamic properties of the 20 [emim][AA] room temperature ionic liquids. The 20 naturally occurring amino acids vary greatly in their size and mass and the polarity of their side chain. This family of ILs is therefore expected to have a very wide range of values for ionpair strength, transference numbers, ionic conductivity, polarity, and viscosity, as well as other physiochemical properties. We aim to provide some molecular level insight into the properties of the members of this family of RTIL and show the wide range of properties obtainable from them. 2. Computational Methods 2.1. The Force Field. The general AMBER force field (GAFF)26 is used to determine the intra- and intermolecular force constants for the [AA]- and [emim]+ ions of the [emim][AA] ionic liquids. Because there is a very large variety of organic anions and cations that form ionic liquids, one of our goals was to test the performance of a general, “off the shelf”, force field in studying properties of a family of ionic liquids. Given the use of the AMBER force field for other families of amino acidbased ionic liquids,25 we decided to use this force field for our simulations. The internal structure of the anions and cations was

Sirjoosingh et al.

Figure 1. Atom labels in [emim][AA] RTILs based on the standard AMBER force field atom types.

considered flexible, and the intramolecular bond stretching constants (kr), angle bending constants (kθ), and dihedral potential parameters are taken directly from the AMBER force field. The equilibrium values of bond lengths (req) and bond angles (θeq) were determined by optimizing the structures of [emim]+ and [AA]- ions at the B3LYP/6-311++G(d,p) level with the Gaussian 03 suite of programs.27 The functional form of the AMBER intramolecular force field is given in the Supporting Information. The intermolecular potential is a sum of pairwise additive atom-atom 12-6 Lennard-Jones (LJ) potentials for the van der Waals interactions and Coulombic interactions between point charges centered on the atoms, N-1

V(inter) )

N

∑∑ i)1

j>i

{ [( ) ( ) ] 4εij

σij rij

12

-

σij rij

6

+

qiqj 4πε0rij

}

(1)

where εij and σij are the energy and distance parameters for the LJ interactions for atom pairs i and j, and N is the number of distinct intermolecular interactions in the system. The LJ parameters for like-atom interactions for the cation and anions were taken directly from the AMBER force field and are reproduced in Table S1 of the Supporting Information. The labels for the atom types in the cation and anion are shown in Figure 1. Parameters for i * j interactions are obtained from the standard combination rules, εij ) (εiiεjj)1/2 and σij ) (σii+σjj)/ 2. The partial charges on atoms i and j, qi and qj, are determined using the CHELPG algorithm28 on the ions optimized at the B3LYP/6-311++G(d,p) level, and ε0 is the dielectric permittivity of vacuum. The CHELPG point charges on the cation and anion atoms are given in Table S2 of the Supporting Information. 2.2. Molecular Dynamics Calculations. Constant pressure and temperature (NpT) molecular dynamics simulations with the modified Nose´-Hoover barostat algorithm29 of liquid [emim][AA] with 512 ion pairs were performed with the DL_POLY program, version 2.17.30 Thermostat and barostat relaxation times of 0.1 and 0.5 ps, respectively were used because these values lead to well-converged energies and volumes in the simulations. The equations of motion were integrated using the Verlet leapfrog scheme using a time step of 1 fs.31,32 For structural and dynamics calculations, all

AA-Based RTIL Equilibrium, Transport Properties

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intermolecular interactions between the atoms in the simulation box and the nearest image sites were calculated within a cutoff distance of 14 Å for the simulation cell. A larger cutoff of 20 Å was used in simulations to determine the radial distribution functions (RDFs). The Coulombic long-range interactions were calculated using Ewald’s method31,32 with a precision of 1 × 10-6. The Ewald convergence parameter was taken as R ) 0.225 Å-1, and maximum k vector indices of 12 were used in the Ewald summation. We performed MD calculations at 298 K for each liquid at an ambient pressure of 1.013 × 105 Pa. An arbitrary single ion-pair configuration was replicated 512 times in a simulation cell to generate starting configurations for the simulation for each ionic liquid. These configurations were randomized by annealing simulations at 700 K for 1 ns, followed by cooling in two sequential 1 ns simulations, first to 500 K and then to the target 298 K. Dynamic properties were determined with constant volume and energy, NVE, simulations on the equilibrated systems obtained from NpT simulations. The mean square displacement (MSD), velocity autocorrelation function (VACF), current autocorrelation function (CACF), and mean square dipole moment (∆M2) were calculated, and transport coefficients were determined. For the amino acids, the MSD and ∆M2 plots were obtained from averaging five simulation trajectories of 500 ps. For MSD calculations, data from the trajectories was saved every 1 ps. The slopes of these plots were determined from data in the range of 200-400 ps (MSD) and 100-300 ps (∆M2). The VACF and CACF plots for each AA were obtained by averaging 5-10 simulation trajectories of 40 ps duration. For the VACF and CACF trajectories, data was saved every 0.025 ps. Averages over all ions and over multiple time origins was used in calculating the MSD, VACF, CACF, and ∆M(t)2 curves. 2.3. Transport Coefficients. The ensemble average of the mean square displacement of the center of mass of each ion i cm 2 in the liquid, MSDi(t) ) 〈|rcm i (t) - ri (0)| 〉, generally has power law time-dependence, i.e. MSDi(t) ∝ tβ. There are generally three different time scales for the MSD that are distinguished by computing the exponent β from

β(t) )

d log(MSD(t)) d log(t)

(2)

The diffusion coefficient can also be calculated from the ensemble average of the normalized velocity autocorrelation cm cm cm function, Ci(t) ) 〈vcm i (t) · vi (0)〉/〈 vi (0) · vi (0)〉, through the corresponding Green-Kubo relation,35

Di )

6Di ) lim tf∞

d〈|ricm(t) - ricm(0)| 2〉 dt

(3)

The angular brackets indicate an ensemble average over ions in the system and over time origins.

∫0∞ Ci(t) dt

(4)

cm The vcm i (0) and vi (t) are the velocities of the center of mass of ions i at times 0 and t, respectively. For 1:1 electrolytes, the relative contributions of the cations and anions to the total conductivity are characterized by transference numbers of the cation and anion,

t+ )

D+ (D+ + D-)

and

t- )

D(D+ + D-)

(5)

where t+ + t- ) 1 and 0 e t+, t- e 1. The transference or transport numbers show the relative mobility of the ions in an electrolyte. In electrolytes with t+ > 0.5, the cation will diffuse more quickly and have a larger contribution to the ionic conductivity of the electrolyte than the anion. The electric current in an ionic liquid is defined as j(t) ) e ∑i zivcm i , where the sum is over both cations and anions in the liquid, and zi is the fractional electronic charge on ion i. The ionic conductivity per unit volume is related to the electrical current autocorrelation function, J(t) ) 〈j(0) · j(t)〉, by a Green-Kubo relation,

σGK )

1 3kTV

∫0∞ J(t) dt

(6)

where the system molar volume is V. The current autocorrelation function can decomposed into20b N

At short times (a few picoseconds), the ions undergo quasiballistic motion in the cages formed by their counterions and β ) 2. In the intermediate time range (a few picoseconds to nanoseconds, depending on the fluid), the motion of the ions obeys subdiffusive dynamics similar to a supercooled liquid.33,34 In this time range, β < 1 and the ions can be viewed as breaking out of their initial solvation cages and exchanging sets of nearest neighbors. For strongly associated ionic liquids or highly viscous liquids, the time scale of the diffusive dynamics may become very long. At long times, the systems exhibit linear diffusive behavior after the molecules have undergone many collisions, and β ) 1. In the long-time limit, the slope of the MSD curve with time is related to the diffusion coefficient, Di, through the Einstein relation,

kT m

J(t) ) e2

N

∑ ∑ 〈zizj vicm(t) · vjcm(t)〉 ) Z(t) + i)1 j)1 N N 2

e

∑ ∑

〈zizj vicm(t) · vjcm(t)〉 ) Z(t) + ∆(t) (7)

i)1 j)1,j*i

where Z(t) includes terms in the summation that have i ) j and is proportional to the sum of the VACFs for the cations and anions, and ∆(t) is cross-correlation terms in the CACF. Here, N is the total number of ions (both anions and cations) in the system. If the cross term in eq 7 is neglected, the Nernst-Einstein equation for the ionic conductivity33 is obtained. For the 1:1 salts of this study, the ionic conductivity from the Nernst-Einstein approximation becomes

σNE )

e2F 2 (z D + z-2D-) kT + +

(8)

The mean-square dipole displacement for 1:1 salts is given by

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〈| ∑

Sirjoosingh et al. TABLE 1: Anion Mass (g mol-1); Experimental Glass Temperatures, Tg (°C);b and Density at 25°C (g cm-3) for the 20 [emim][AA] Ionic Liquidsc a

N/2

∆M(t)2 ) e2

(ricm,+(t) - ricm,+(0))

i)1

N/2

-

|〉

∑ (rjcm,-(t) - rjcm,-(0)) 2 j)1

(9)

where the sum over i runs over all cations and the sum over j runs over all anions. ∆M(t)2 can be related to the ionic conductivity through its long-time slope by the following,21

σD )

d∆M(t)2 1 lim 6kTV tf∞ dt

(10)

The conductivity obtained from ∆M(t)2 in eq 10 takes correlations between ions into account and is rigorously equivalent to eq 6 for σGK. 3. Results and Discussion 3.1. Equilibrium Properties. The calculated densities of the 20 [emim][AA] ionic liquids at 25 °C are given in Table 1. The densities of the [emim][AA] ionic liquids are greater than that of water, in contrast to the densities of the [P(C4)4][AA] family, which are generally FALA > FVAL > FLEU ≈ FILE, FSER > FTHR, and FASP > FGLU. The effect of functional groups of the amino acid anion on the density of the ionic liquid is not straightforward to predict. In general, the presence of polar groups on the amino acid side chain increases the density; for example, FSER > FALA, FTHR > FVAL, and FTYR > FPHE. The RDF, g(rij), for the atom pairs i and j on different molecules can be used to characterize the structure of the ionic liquids. In ionic liquids, electrostatic forces are a very strong factor in determining the local liquid structure. As seen in Table S2 of the Supporting Information, electrostatic charges on both [emim]+ and the amino acid anions are predominantly localized on certain regions of the molecules. In [emim]+, most of the positive charge resides in the five-membered ring. In the amino acid anions, most of the negative charge resides in the amino acid -CH(NH2)COO- moiety. To study electrostatic association between the cation and anion, we have chosen to examine RDFs between the charge centers of the two ions, rather than the RDFs between the centers of mass of the ions. This is because in amino acids with large R-substituent groups (such as phenylalanine and glutamine), the location of the [AA]center of mass is significantly displaced from the local center of charge. In this case, the RDFs based on the center of mass would not properly reflect the inhomogeneous nature of the ionic interactions in the [emim][AA] pairs, which are localized at the amino acid moiety in the [AA]- anions. Spohr and Patey have

[AA]-

mass

Tg

F25, calc (exptl)

Gly Ala Val Leu Ile Phe Tyr Trp Asp Asn Glu Gln Lys His Arg Ser Thr Met Cys Pro

74.1 88.1 116.1 130.2 130.2 164.2 180.2 203.2 132.1 131.1 146.1 145.1 145.2 154.2 173.2 104.1 118.1 148.2 120.2 115.1

-65 -57 -52 -51 -52 -36 -23 -31 +5 -16 +6 -12 -47 -24 -18 -49 -40 -57 -19 -48

1.219 (1.1589)d 1.171 (1.1209)e 1.101 1.077 1.067 1.136 1.144 1.193 1.280 1.250 1.226 1.237 1.111 1.213 1.190 1.243 1.161 1.173 1.260 1.140

a The molecular mass of the [emim]+ cation is 111 g mol-1. Experimental result, from ref 13. c The error in the calculated densities is ( 0.003 g cm-3. d Experimental result at 25 °C, from ref 36. e Experimental result at 25 °C, from ref 37. b

discussed this point further, with studies of charged LennardJones particles with noncentral distributions of electrostatic charge.22 As shown in Figure 1, the cation NA atoms are the nitrogen atoms of the imidazolium ring and the anion N3 atoms are from the NH2 groups of the amino acid. Figure 2 shows the RDFs for the interactions of the polar atom pairs N3-N3, N3-NA, and NA-NA for simulations at 298 K for selected [emim][AA] ionic liquids with hydrocarbon (alkyl and aryl) side chains. The N3-N3, N3-NA, and NA-NA RDFs roughly correspond to anion-anion, anion-cation, and cation-cation positional correlations. The RDFs for the anion-anion negative charge centers show a peak near 7 Å, and the RDFs for the cation-cation positive centers have a wide peak between 6 and 9 Å. The anion-cation charge center RDF contains two sharper peaks. As expected, the cation-anion peaks are out-of-phase with respect to the spacing of the anion-anion and cation-cation interactions. To study spatial correlations between the nonpolar ends of the anions, the RDFs between the methyl groups of different alanine anions are shown in the upper panel of Figure 2 by the red dashed line. The van der Waals interactions between these -CH3 groups leads to a peak in the RDF between 2.5 and 4 Å. The dashed line in the middle panel shows the alanine methyl CH3-cation NA correlations. There are no specific correlations between the nonpolar methyl group of alanine and the charge-carrying atoms of the imidazolium ring. In Figure 2, the peaks in the charge-center RDFs for different alkyl and aryl group RDFs are generally similar. This indicates that the strong cation-anion interactions among the nearest neighbor ion pairs are localized in the -CH(NH2)COObackbone of the amino acid anions. With the exception of [emim][GLY], which has an additional peak at ∼5 Å in the anion-anion (NA-NA) RDF, the nature of the R group does not appear to affect the electrostatic interactions in the nearest neighbor shell. A similar observation was made by Zhou et al. for the [P(C4)4][AA] ionic liquids.25 From Figure 2, it is seen that after ∼14 Å, the spatial correlations between the anion-anion, anion-cation, and cation-cation pairs are weak.

AA-Based RTIL Equilibrium, Transport Properties

Figure 2. Radial distribution functions for atom pairs of the alkyl class of ILs at 298 K. The upper panel shows RDFs for N3-N3 anion-anion interactions (solid lines). The dashed line represents the RDF of the methyl groups of alanine. The middle panel shows RDFs for N3-NA anion-cation interactions as (solid lines). The dashed line represents the RDF of the methyl groups of alanine and the NA of the cation. The lower panel shows RDFs for NA-NA cation-cation interactions. The atom labels are defined in Figure 1.

Figure 3. Radial distribution functions for atom pairs for aspartic acid, asparagine, glutamic acid, and glutamine ILs at 298 K. The upper panel shows RDFs for N3-N3 anion-anion interactions (solid lines). The black dashed line represents the RDF of the carboxylic acid -OH of aspartic acid. The red dashed line represents the RDF of the amide HNd of asparagine. The bottom panel shows RDFs for N3-NA anion-cation interactions (solid lines). The black dashed line represents the RDF of the carboxylic acid -OH of aspartic acid and the NA of the cation. The red dashed line represents the RDF of the amide HNd of asparagine and the NA of the cation. The RDFs for NA-NA cation-cation interactions are similar to those shown in Figure 2 and are not reproduced. The atom labels are defined in Figure 1.

However, from the discussion of the radial charge distribution function given below, we shall see that there are significant correlations up to ∼20 Å. The RDFs of the acid and amide amino acid ionic liquids aspartic acid, asparagine, glutamic acid, and glutamine are shown in Figure 3. The cation-cation correlations are similar to Figure 2 and are not reproduced. The descriptions of the anion-anion and cation-cation interactions in Figure 3 are generally similar to those of Figure 2. Additional RDFs between O · · · HO groups in the carboxylic acid segment of aspartic acid and O · · · HNd amide groups of asparagine are shown in the anion-anion panel of Figure 3. Correlations between NA · · · O (carboxylic acid) and NA · · · O (amide) are shown by dashed lines in the anion-cation panel of Figure 3. These additional spatial correlations reveal there are additional strong bindings between these functional groups among the different acid and amide

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Figure 4. The radial charge distribution function for several [emim][AA] ionic liquids. Long-range correlations of the charged particles are seen in these liquids.

amino acid anions. This is due to hydrogen bonding between two carboxylic acid or amide functional groups in adjacent aspartic acid and asparagine molecules, respectively. Moreover, in the bottom panel, we see that these secondary anion groups also have strong correlations with the positive charge center of the imidazolium ring. The acid and amide class of anion interact electrostatically with the cation from two ends, thus enhancing the strength of the electrostatic ion-pair interactions in these ionic liquids, as compared to the alkyl- or aryl-substituted amino acids shown in Figure 2. The acid and amide amino acids are among the class that does not follow the linear log(σ)-Tg trend observed for other ionic liquids. The additional cation-anion and anion-anion bonding in this class of amino acids can be one of the factors contributing to a lowering of the ionic conductivity and an increase in the glass temperature and viscosity of these ionic liquids. The RDFs for the other amino acid ionic liquids are given in the Supporting Information. The radial charge distribution function, Q(r) is defined as22,38

Q(r) ) F[gAA + gCC - 2gAC]

(11)

where gAA, gCC, and gAC are the anion-anion, cation-cation, and anion-cation radial distribution functions, respectively. For ionic liquids composed of spherical ions, the gAA, gCC, and gAC functions are drawn with reference to the centers of mass of the anions and cations.22,38 In the [emim][AA] systems, we have chosen the amino nitrogen atoms (N3) of the amino acid anions and the heterocyclic nitrogen atoms (NA) of the [emim]+ cations as reference sites to determine the gAA, gCC, and gAC functions. It is the vicinity of these charge-bearing groups that primarily participates in the cation-anion electrostatic interactions in the [emim][AA] liquids. The radial charge distribution functions for several [emim][AA] ionic liquids are shown in Figure 4. The systems show the decaying oscillations characteristic of strongly coupled systems. At short distances between 3 and 6 Å, the ions of opposite charge surround each ion. The successive shells of charge can be seen in the ionic liquids as we move further out from the central ion. The shell structure is seen to be more regular in the upper panel, where amino acids with alkyl R groups are plotted. Due to more complex anion-anion and anion-cation correlations in the aspartic and glutamic acid cases (see Figure 3), the structure of the outer-more shells is less

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Sirjoosingh et al.

Figure 6. The normalized VACF C(t) of the [emim][AA] ionic liquids for amino acids with alkyl side chains. The top panel shows the cation VACFs, and the bottom panel, the anion VACFs.

Figure 5. Snapshots of the equilibrated alkyl ionic liquids at 298 K and ambient pressure. Polar components of the anion and cations are shown by the dark color and nonpolar components are shown by the light color. The size of the nonpolar component increases from the glycine to phenylalanine ILs.

regular in these amino acid ionic liquids. In both cases, it can be seen that significant charge correlations are maintained up to distances of ∼20 Å. Snapshots of the liquid simulations at 298 K for selected alkyl amino acids are shown in Figure 5. The representations are similar to those introduced by Padua´ and co-workers,39 where the polar components of each ion are shown by the dark segments, and the nonpolar components, by the light segments of the representations. In the [emim]+ cation, the methyl group of the C2H5 moiety is considered nonpolar, and in the [AA]anions with alkyl substituents, the R substituent groups are considered nonpolar. The polar and nonpolar groups of the ions cluster separately to form islands of distinct polarity in the liquid. As the R substituent group becomes larger, the size of the nonpolar portion of the RTIL becomes larger, and presumably, the hydrophobicity of the solvent increases. For other ionic liquids of the [emim][AA] family, the R substituents may themselves contain polar groups. The RDF plots of Figure 3 show that the -COO- functional group of the aspartic acid side chain associates strongly with the [emim]+ and with -COO- groups of other [ASP]- anions. Compared to the amino acids with alkyl R groups, these ionic liquids are more polar. 3.2. Dynamic Properties and Transport Coefficients. The only dynamic properties of the AA ionic liquids measured

experimentally are the ionic conductivities, σ, at 25 °C.13 When log(σ) is plotted against the glass transition temperature, the AA ionic liquids segregate into two groups. The VACFs for the ion center of mass of the 20 [emim][AA] ionic liquids are shown in Figure S5 of the Supporting Information, with the anions indicated by the solid lines, and the cations, by the dashed lines. The detailed behaviors of the VACFs for the alkyl R-substituted amino acids are shown in Figure 6. The normalized VACF plots are averages over a minimum of five simulation trajectories. The x intersect of the VACFs appears quickly after 0.1-0.2 ps, which corresponds to the mean collision time of the ions in the liquid. The masses of the anions are given in Table 1, and generally, the lighter partner of the anion/cation pair has a shorter mean collision time. After the mean collision time (x intercept), the VACFs show a negative region where the ions are reflected backward in the encapsulated cages made predominantly by their counterions. The encapsulating cage breaks up, and the VACF for the anions and cations decays to 0 at times >1 ps. At this time, as a result of multiple collisions, the velocities of the ions have been randomized. The anions and cations generally will not have the same velocity randomization times, with the lighter species randomizing more quickly. Between the mean collision and velocity randomization times, the VACF of the lighter of the two ions oscillates. These oscillations have been seen in other RTILs.20 The [emim]+ cation (top panel) has the same mean collision time (∼0.1 ps) and velocity randomization time (∼1 ps) in all ionic liquids in this class. The mean collision and velocity randomization times of anions in this family (bottom panel), however, increase with the mass of the anion. The VACFs of the lighter of the pair of ions in each RTIL show oscillations in the intermediate time range, which are due to the rattling motion of the lighter ion in the encapsulating cage of the heavier ions.34 The oscillatory behavior of the VACF for the lighter component of an ion pair in the ionic liquids is observed for [emim]+ ionic liquids with other counterions such as Cl-, NO3-, and PF6-.19 The VACF for other [emim][AA] ionic liquids are shown in the Supporting Information. In simple liquids, the VACFs show a long-time, slowly decaying tail that is due to collective, hydrostatic motions in the liquid.32,33 Evidence of long-time tails in the VACFs of the [emim][AA] ionic liquids is not observed. This may be due to the high viscosity of the ionic liquids and the bulky structures of the anions and cations, which prevent the hydrodynamic flow

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TABLE 2: Calculated Anion and Cation Diffusion Coefficients (10-11 m2/s) and Transference Numbers at 25°C for the 20 Liquid AA Ionic Liquids from the VACFa VACF [AA]Gly Ala Val Leu Ile Phe Tyr Trp Asp Asn Glu Gln Lys His Arg Ser Thr Met Cys Pro a

Dcat (error)

Dan (error)

1.07 0.95 1.33 1.30 0.95 1.71 1.35 1.05 0.72 0.91 1.76 0.40 1.37 1.62 0.92 0.48 1.29 1.36 1.45 1.77

1.23 1.10 1.17 1.06 0.88 1.60 0.88 0.86 0.45 0.60 1.06 0.33 1.18 1.18 0.63 0.40 0.75 1.13 1.14 1.32

(0.52) (0.67) (0.54) (0.68) (0.78) (1.21) (0.83) (0.45) (0.75) (0.59) (0.58) (0.61) (0.51) (0.58) (0.51) (0.42) (0.60) (0.44) (0.78) (0.84)

(0.59) (0.74) (0.58) (0.63) (0.93) (1.21) (0.73) (0.63) (0.64) (0.62) (0.64) (0.71) (0.56) (0.82) (0.70) (0.48) (0.47) (0.57) (0.89) (0.78)

MSD T+ 0.46 0.46 0.52 0.55 0.52 0.52 0.60 0.54 0.62 0.60 0.62 0.54 0.54 0.58 0.59 0.54 0.63 0.63 0.56 0.57

Dcat(β) 0.104 0.196 0.238 0.105 0.130 0.207 0.219

(0.57) (0.33) (0.39) (0.30) (0.21) (0.29) (0.71)

Dan(β) 0.095 0.172 0.273 0.130 0.105 0.200 0.123

T+

(0.52) (0.27) (0.38) (0.26) (0.17) (0.29) (0.69)

0.52 0.53 0.53 0.55 0.55 0.51 0.63

0.098 (0.25) 0.278 (0.47)

0.083 (0.24) 0.186 (0.42)

0.54 0.60

0.203 (0.39)

0.233 (0.37)

0.53

Selected diffusion coefficients from the MSD curves are also given.

associated with the long-time tails. The relatively small number of ions (512) in the simulations may also be a factor in not observing the long-time tails. The simulation cells are large (∼50 Å per side) and have a large number of atoms (∼15 000), but the small number of ions and imposition of periodic boundary conditions may not allow the establishment of the long-time tails. Diffusion coefficients can be calculated from the integration of the normalized VACF, eq 4, or from the long-time slope of the MSD, eq 3. Although eqs 3 and 4 are rigorously equivalent pathways for determining the diffusion coefficients, the two methods have different numerical accuracies. If a diffusive regime can be established at long simulation times, values of the diffusion coefficient from the MSD plots will generally be numerically more accurate. To calculate the diffusion coefficient from the VACF plots of Figure 6 and eq 4, time integration from t ) 0 to t ) 25 ps was performed. The results are shown in Table 2. The integration of the normalized anion and cation VACFs for glycine are shown in Figure S7 of the Supporting Information. As can be seen from the inset of Figure S7, for glycine, the uncertainty in ∫C(t) dt ∼ 0.0002 ps, which gives an uncertainty in the diffusion coefficient of ∼0.5 × 10-11 m2/s. This magnitude of numerical uncertainty in the diffusion coefficient is despite the fact that the C(t) curve is an average from five different trajectories. The uncertainties in the cation and anion diffusion coefficients for other [emim][AA] ionic liquids at 25 °C are given in Table 2. The diffusion coefficients from eq 3 can be directly obtained from the long-time slope of the MSD plot. As seen in Table 1, a number of the [emim][AA] ionic liquids have glass transition temperatures that are only a few degrees below the simulation temperature (298 K). As mentioned above, the dynamics of ionic liquids are generally glassy and subdiffusive,34,40 and it is difficult to perform simulations long enough to capture the diffusive regime in the amino acid ionic liquids with their bulky anion and cation structures. For the [emim][GLY] ionic liquid, we ran MSD plots to 2 ns, and the resulting MSD plots are shown in Figure 7. Given

the large number of molecules in the simulation and the trajectory-averaging required to obtain the data, these calculations are computationally expensive to perform. According to eq 3, the MSD appears linear within the time range of 1 and 2 ns, and the corresponding linear fits, which are shown by dashed lines, are hardly discernible from the curves. Logarithmic plots of the data are prepared and shown in the top panel of Figure 7. The slope of the line β equals 1 in the diffusive regime. However, in Figure 7, in the range of 1-2 ns, we obtain β values of 0.52 and 0.57 for [GLY]- and [emim]+, respectively. These β values are far from 1, which shows that within this time frame, the dynamics of this ionic liquid are glassy and subdiffusive. Kelkar and Maginn41 show that times much longer than 1 ns are required to observe diffusive dynamics in equilibrium MD simulations, and they recommend the use of nonequilibrium MD simulations to extract transport coefficients for ionic liquids. In

Figure 7. The long time behavior of the MSD for [emim][GLY] (bottom panel). The black curve represents the MSD of the anion, and the red curve, the cation. The linear fit of the MSDs with time between 1 and 2 ns are shown by the dashed lines. The log-log plot for the MSD against time for [emim][GLY] for times between 1 and 2 ns (top panel). The linear fit of the curves is shown by dashed lines.

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Figure 8. The mean-square displacement curves for the RTILs of amino acids with alkyl side chains. The solid lines are the MSD curves of the anions, and the dashed lines are the MSD curves of the cations.

the following, we calculate the “apparent” diffusion coefficients for the ions in the liquids and note that these values are lower limits to the true diffusion coefficients. The mean square displacement curves for times up to 450 ps for the anion and cation centers of mass of amino acids with alkyl side chains are shown in Figure 8. These curves are the results of averaging the MSDs of five simulation trajectories. In all cases, the [emim]+ cation species have larger long-time MSD slopes, which results in cations of this family having larger transference numbers than the anions (see below). The faster diffusion of [emim]+ is likely due to its relative planarity and enhanced diffusion in the direction parallel to the plane of the imidazolium ring and has been observed in other families of [emim]+ ionic liquids.19 The MSD curves shown in Figure 8 appear to be relatively linear, and the slopes of the MSD curves in the time range of 250-450 ps are used to calculate the β values and apparent diffusion coefficients of the [emim][AA] ionic liquids, which are given in Table 2. The β values for the cations and anions are less than 1, which, as stated, is common for equilibrium simulations of RTILs. As seen from the values given in Table 2, the diffusion coefficients determined from integrating the VACF plots are up to a factor of 10 larger than those calculated from the slopes of MSD plots. The discrepancy is due to two factors. The first factor is the larger numerical uncertainty of the integration procedure of eq 4, where the positive and negative contributions of the VACFs (shown in Figures 9 and S7 of the Supporting Information) nearly cancel producing a small diffusion coefficient value. The bulky nature of the cations and anions and the glassy dynamics in the systems add noise to the VACF curves, making it difficult to attain a smoothly converging integral. As mentioned, the velocity autocorrelation functions appear to decay quickly, and there is no evidence of the longtime slowly decaying tails in the VACF that would affect the integration procedure. The second factor affecting the discrepancy of the VACF and MSD diffusion coefficients is the subdiffusive dynamics observed for the MSD plots in the time range of the simulations. This leads to smaller-than-expected apparent diffusion coefficients from the MSD plots. The cation transference numbers, t+ ) D+/(D++D-), calculated from the VACF and MSD diffusion coefficients, are given in Table 2. Within the range of error of the diffusion coefficients, the transference numbers obtained from the two methods are

Sirjoosingh et al.

Figure 9. The time decay of the current autocorrelation function J(t), Z(t), and -∆(t) terms of eq 10 for [emim][ALA]. Initially, J(t) decays faster than the self-term, Z(t). The Z(t) function decays quickly, but the many-body CACF shows long-lived oscillations.

similar in magnitude. Transference numbers can be experimentally measured using the Hittorf42 or moving boundary method42 or by means of measuring the cation and anion diffusion coefficients using pulse-gradient spin echo NMR (PGSENMR).43 The values of the transference numbers and the ionic conductivities (see below) are both important in determining the behavior of ionic liquids as electrolytes.44 Transference numbers quantify the relative contribution of the cations and anions to the total conductivities. A transference number >0.5 indicates that the cations are more mobile than the anions and contribute more to the ionic conductivity. Similar to the present family of RTILs, in the 1-alkyl,3-methylimidazolium (alkyl ) methyl, ethyl, propyl, butyl) family of ionic liquids with Cl-, NO3-, and PF6counterions, the cations have larger diffusion coefficients than the anions. This is related to the planar structure of the imidazolium ring, which gives it a smaller activation energy for diffusion in directions parallel to the ring.20,43 In the alkyl AA groups, the cation transference numbers increase with the inclusion of polar functionality on the anions, which increases anion-anion interactions. The anion and cation diffusion coefficients can be used to calculate the ionic conductivity according to the Nernst-Einstein (NE) relation, eq 8. Diffusion coefficients obtained from both the integration of the VACFs and the long-time slopes of the MSD curves are used in the Nernst-Einstein relation. The results are given in Table 3. Due to the subdiffusive nature of the MSD plots, the predicted NE conductivity from the MSDs will be lower than VACF values. The NE equation neglects ion-pair formation and assumes independent (uncorrelated) motion of the cation and anion in the electric field. As expected, predictions for σNE shown in Table 3 overestimate the experimental ionic conductivity. The ionic current autocorrelation function, J(t), for alanine along with self-current, Z(t) and deviation terms -∆(t) ) Z(t) - J(t) of eq 7 are shown in Figure 9. The curves are averages over five simulation trajectories. The initial decay of the J(t) function is faster than Z(t), which is an indication of the existence of dynamic correlations between the ion pairs at short times. The Z(t) function is a sum of one-particle time correlation functions and varies more smoothly with time than the manyparticle J(t) function. The oscillations in J(t) do not show noticeable decays for trajectories up to 25 ps. The integration

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TABLE 3: Calculated Ionic Conductivity (S/cm) at 25°C for the 20 [emim][AA] Ionic Liquids σNE [AA]Gly Ala Val Leu Ile Phe Tyr Trp Asp Asn Glu Gln Lys His Arg Ser Thr Met Cys Pro

MSDa 4.9 8.1 9.3 4.0 3.9 6.4 5.0

× × × × × × ×

VACFb -4

10 10-4 10-4 10-4 10-4 10-4 10-4

3.9 × 10-4 8.8 × 10-4 9.0 × 10-4

6.6 4.0 4.6 3.3 2.6 6.2 2.1 1.6 2.1 3.0 4.6 1.3 3.7 3.9 2.3 1.5 3.6 3.3 5.0 4.7

× × × × × × × × × × × × × × × × × × × ×

-3

10 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3

σDc 5.4 6.7 2.6 3.5 9.4 2.8

× × × × × ×

σexptld -4

10 10-4 10-4 10-4 10-5 10-4

2.9 × 10-4 5.6 × 10-4 6.6 × 10-4

5.7 6.4 8.8 8.1 6.9 6.0 4.0 9.1 1.7 1.1 5.0 1.7 7.8 1.0 9.0 6.5 1.0 2.4 3.5 1.6

× × × × × × × × × × × × × × × × × × × ×

10-4 10-4 10-5 10-5 10-5 10-5 10-8 10-9 10-9 10-6 10-7 10-7 10-5 10-7 10-7 10-4 10-4 10-4 10-5 10-4

a Calculated using diffusion coefficients calculated from eq 3. Calculated using diffusion coefficients calculated from eq 4. c Calculated from eq 10. d From Fukumoto et al., ref 12. b

averaging process. Linear regression was performed between 100 and 300 ps. The calculated values of σD are tabulated in Table 3. We observe that, for the ionic liquids studied, σD < σNE, as expected, since the former considers ion-pair correlations that are neglected in the Nernst-Einstein relation. The values of σD are systematically larger than experimental values of the ionic conductivity. Longer simulation times, larger systems, and more trajectories are needed to achieve a better converged data for the mean-square dipole displacement data. This is especially true for the amino acids with experimental conductivities on the order of 10-7-10-9 S cm-1. Previous simulations of ionic conductivity were performed on ionic liquids that are heated to temperatures at ∼100 K higher than the melting/glass temperature.20c,22,45,46 However, many of the ionic liquids in this study have low glass temperatures (Table 1) and are viscous at 25 °C. This factor combined with the irregularly shaped, strongly binding amino acid anions makes the calculation of well-converged ionic conductivities using eqs 6 and 10 very difficult for these ionic liquids. Experimentally, the [emim][AA] ionic liquids with ionic conductivities smaller than 10-5 S cm-1 have additional functional groups in the R side chains that interact strongly with the cations. For example, the amino acids with acidic and amide functional groups shown in Figure 3 have strong anion side chain-cation and anion-anion hydrogen bonding, which lowers the ionic conductivities in these ionic liquids. The same [emim][AA] ionic liquids often have high glass transition temperatures and high viscosities at 25 °C, which also contribute to their low measured ionic conductivities. We have studied the trends in the VACF and MSD for amino acids in the same class. Quantitatively, different values for the diffusion coefficients are obtained from integration of the VACF and the slope of the MSD curves, but both routes give similar values for the cation transference numbers in different ionic liquids. Ionic conductivities have been calculated from the Nernst-Einstein relation and directly from the time integration of the current autocorrelation functions and slope of the meansquare dipole displacement vector. 4. Summary and Conclusions

Figure 10. The mean square dipole displacement curves for selected [emim][AA] RTILs.

of J(t) will therefore have large numerical uncertainty. Accurate values for the integral cannot be obtained, since the fluctuations (on the order of 10-4 S cm-1) are significant when compared to experimental conductivity values (on the order of 10-3-10-9 S cm-1). Larger simulations and a greater number of trajectories would be needed to obtain well-converged ionic conductivities with orders of magnitude in the experimentally observed range of 10-4-10-9 S cm-1. The ionic current autocorrelation functions for the amino acid ionic liquids with alkyl side chains are shown in Figure S8 of the Supporting Information. A rigorously equivalent method uses the slope of the meansquare dipole displacement to calculate the ionic conductivity, σD, as shown in eqs 9 and 10. The relation between eqs 10 and 6 for calculating the ionic conductivity is parallel to the relation between eqs 3 and 4 for calculating the diffusion coefficient. The ∆M(t)2 plots were averaged over a minimum of five runs and are displayed in Figure 10 for the amino acids with alkyl side chains. The ∆M(t)2 curves are many-body ensemble properties and exhibit considerably more fluctuation than the single-particle MSD plots, and off-lying trajectories for ∆M(t)2 that exhibit anomalous time behaviors were discarded from the

Structural features and dynamic properties are calculated for the 20 [emim][AA] ionic liquids with molecular dynamics and the AMBER force field. The amino acid anions of this class of ionic liquids have different polar/nonpolar moieties. Studies of the structure of the ionic liquids show that the polar fragments of the anions and cations are spatially correlated. Well-defined polar and nonpolar islands are formed in the ionic liquid. On the basis of size and the nature of the R substituent group of the amino acid, the ionic liquid may have large nonpolar pockets or may be predominantly polar. This aspect may determine the miscibility of the different members of this family with polar or nonpolar solvents in a two-phase extraction process. It also is relevant to the solubility of the different solutes in the ionic liquid. The calculated range of diffusion coefficients of the anions and cations of this family varies within a factor of 2. This is due to the widely different chemical nature of the amino acid side chain groups. Amino acids with side chains containing hydrogen bonding groups have low anion diffusion coefficients and high cation transference numbers. The experimental ionic conductivities of the 20 [emim][AA] ionic liquids vary over a range of 5 orders of magnitude. The ionic conductivities calculated using the Nernst-Einstein relation (which neglects ion pair formation) do not vary over such

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a wide range. This indicates that strong ion-pair formation is an important contributor to the small ionic conductivity of some of these ionic liquids. Stronger ion pairs form when the functional group R on the amino acid side chain includes polar groups that can interact electrostatically with the cation from two polar functional groups on the molecule, strengthening the interaction between positive and negative ions. Ionic conductivity values at 25 °C were calculated using the mean-square dipole displacement and CACF for the amino acids with alkyl-substituted side chains that have relatively low glass transition temperatures. Reasonable agreement with experimental values is obtained for ionic liquids with low glass transition temperatures. Ionic liquids with higher glass transition temperatures, low conductivities, or both require longer simulation times, larger simulation systems, and more trajectory averaging and have not been attempted in this work. We believe the strong ion-pair correlations from two functional groups on different sides of the amino acid anions, such as those shown in Figure 3, contribute to deviations from the linear log(σ)-vs-glass transition temperature observed for [emim] ionic liquids with Trp, Tyr, His, Arg, Asn, Asp, Gln, and Glu. Evidence for the strong ion-pair formation may be seen directly from the RDF plots. The strength of the electrostatic interactions and ion-pair correlations can also be discerned from the charge radial distribution function. The presence of long-range electrostatic correlations indicates that all [emim][AA] ionic liquids are in the strongly coupled regime. With the variety of functional groups, R, available on the amino acid side chains, it is possible to combine different solvent properties in this family. For example, in the case of [emim][ASP], we have strong ion-pair formation in the solvent, a high calculated cationic transference number, and fairly small nonpolar islands in the liquid capable of accommodating nonpolar solutes. On the other hand, [emim][LEU] has weaker ion-pair formation, a lower cationic transference number and larger nonpolar domains, and an ionic conductivity roughly 4 orders of magnitude larger than the aspartic acid analog. We have used the generally available AMBER force field to model the equilibrium and dynamical properties of this class of room temperature ionic liquids. Better numerical agreement between simulation and experimental values could be obtained using a custom-designed force field for the amino acid anions25 and the emim cation.47 With the exception of [emim][CYS], all other members of the [emim][AA] family are stable up to 200 °C.13 To further understand this class of ionic liquids, experiments and simulations at higher temperatures would be useful. The effect of glassy dynamics for the high-Tg ionic liquids would be decreased, simulations of all the ionic liquids could be carried out with similar accuracy, and the effect of viscosity on ionic conductivity could be minimized. The inclusion of polarizability in the force field20c or the performance of nonequilibrium molecular dynamics41 have been considered important in quantitatively calculating the transport coefficients of room temperature ionic liquids. If further higher-temperature experimental data becomes available on these systems, we will be able to subject the details of the force field to more rigorous testing. Acknowledgment. We gratefully acknowledge the Natural Science and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs Program for financial support. We also acknowledge funding from the Canada Foundation for Innovation, the Ontario Research Fund, and IBM Canada for computing resources. We also thank A. A. H. Padua´ for guidance in preparing Figure 5.

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