Ionic Liquids IV Not Just Solvents Anymore - American Chemical Society

Chapter 6

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 14, 2016 | http://pubs.acs.org Publication Date: August 30, 2007 | doi: 10.1021/bk-2007-0975.ch006

Force Field Refinement and Molecular Simulations of Imidazolium-Based Ionic Liquids Zhiping L i u and Wenchuan Wang Division of Molecular and Materials Simulation, Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China

Refinded force fields for imidazolium ionic liquids, proposed recently by the authors, are summarized in this paper. The procedure to optimized the parameters is described. The performance of both the all-atom and united-atom force fields is verified by molecular dynamics simulation of pure ionic liquids and their mixtures with acetonitrile.

1. Introduction Room temperature ionic liquids (RTILs) are organic salts with a melting point as low as room temperature. The major interactions in RTILs are coulombic, leading to their unique properties, compared with conventional molecular solvents. It is believed that RTILs are environmentally benign solvents with various potential applications. Furthermore, through different combinations of cations and anions, there is a tremendous variety of "designer" solvents. With great versatility of their chemical and physical properties, ionic liquids can be thus tailored and tuned for specific tasks. Computer simulations have been playing an important role in molecular design, which is especially useful for RTILs because of their tremendous diversity. Nevertheless, success of molecular simulation mainly depends on the quality of the inter- and intra-molecular potential functions, i.e. the force fields. Several force fields were proposed for the imidazolium-based RTILs by the groups of Lynden-Bell , Maginn , Stassen , Padua and our group . More 1

70

2

3

4,5

6,7

© 2007 American Chemical Society

Brennecke et al.; Ionic Liquids IV ACS Symposium Series; American Chemical Society: Washington, DC, 2007.

71 recently, ab initio molecular dynamics were also performed for RTILs without any pre-defined force field , although it is much more expensive to implement such simulations. In this paper, we report our systematical work on the force fields development and atomistic molecular simulations of RTIL systems 8,9


2. Force Field Development A n all-atom ( A A ) force field is developed for RTILs containing dialkylimidazolium cations (for their schematic structures, see Figure la). To decrease the computational intensity without reducing the accuracy, we also proposed a united-atom (UA) force field , being wholly consistent with the A A one. 6

7

bonds

angles

4*r, r

\v

J

'σ.Λ y γ \ yJ

dihedrals 6

(D

The first three terms represent the bonded interactions, i.e., bonds, angles and torsions. The non-bonded interactions are described in the last term, including van der Waals (VDW, in the Lennard-Jones (LJ) 6-12 form) and Coulombic interactions of atom-centered point charges. Electrostatic and V D W interactions are calculated between only the atoms in different molecules or for the atoms in the same molecule separated by at least three bonds. The non-bonded interactions separated by exactly three bonds (1-4 interactions) are reduced by a scale factor, which is optimized as 1/2 for V D W and 1/1.2 for electrostatic interactions. The L J parameters for unlike atoms are obtained from the LorentzBerthelot (LB) combining rule:

€

=

u V^S^

σ

υ

=

K

+CT

/2

JJ)

(2)

2.1 All-atom (AA) force field Most of the parameters in our force field are directly extracted from A M B E R by atom type matching between the imidazolium cations and



72

(b) Figure 1. Schematic structure and atom type notations of l-alkyl-3-methylimidazolium cation (amim) in (a) all-atom (AA) force field, (b) united-atom (OA) force field, this work. (Reproduced with permission from reference 7. Copyright 2006 Royal Society of Chemistry.)


73 protonated histidine (HIP). The atom charges are obtained by the oneconformation two-step R E S P method in A M B E R . Besides, three major improvements are made to describe the RTILs more accurately . (1) The V D W diameter of H5 (see Figure 1) is adjusted according to the optimized geometries of cation-anion pairs by quantum calculations (QM). The value of 2.432 Â from A M B E R results in the symmetric optimized geometry for [dmim][PF ] pair (see Figure 2b for more details), while the optimized geometry by Q M in HF/6-31+G(d) level is obvious asymmetric (see Figure 2a for more details). It is found that when the V D W diameter of H5 is reduced to 1.782 Â, the asymmetric geometry emerges (see Figure 2c for more details), which is consistent to the Q M calculation. The similar results are obtained for the ion pairs of [emim][BF ] and [bmim][PF ] . (2) Some of the force constants of the bonds and angles are adjusted by fitting the vibrational frequencies from Q M calculations and IR experiments . For example, the frequency of the imidazolium ring stretching is predicted by the original A M B E R as 1808 cm" , while the experimental value is 1574 cm" . After we reduced the bond force constants related to the imidazolium ring and the angle force constants of H4-CW-NA, H4-CW-CW and H5-CR-NA, an improved value of 1632 cm" was obtained. For more details, the readers are referred to the Table 3 of the literature . (3) Four missing torsion parameters in A M B E R related to the bond N A - C T are obtained by fitting the ab initio torsion energy profiles at MP2/631+G(d)//HF/6-31+G(d) level. Lopes et a l . have been reported these missing parameters through a similar procedure. However, it is necessary to get a set of consistent parameters for our force field, because the atom charges between the two force fields are very different. 10

6


6

6

4

6

11

1

1

1

6

4

2.2 United-atom (UA) force field 7

The U A force field is derived from the above A A model . It is essential to define the united atoms by using a coarse-grained method for the imidazolium cation. Because the three H atoms on the ring are very important to the hydrogen-bond formation in RTILs, the detailed structure between the cations and anions would be lost if the C H groups in the ring are treated as united atoms. Therefore, only CH3 and CH2 in alkyl chains can be treated as united atoms here (see Fig. 1). Consequently, four kinds of united atoms are defined in this work, i.e. CN2, CN3, CT2 and CT3 (see Fig. lb), since there are two kinds of H on the alkyl chains, i.e. H I and HC. The V D W parameters of the united atoms are obtained by mapping the interaction energies of a pair of them. The energies between united atom pairs 6



74

Figure 2. Optimized geometries of [dmim][PF ] pair from (a) quantum calculation, (b) the original AMBER force field, and (c) the refinedforce field presented in this work. Use with permission from J. Phys. Chem. Β 2004, 108, 12978 (Liu, Huang and Wang) 6



75

Figure 2. Continued.

7

were calculated by a Monte Carlo algorithm , i.e., the U A groups are rotated randomly to obtain the average interaction energies. It is noticed that in the published U A force fields ' ' , the charges of the united atoms were all obtained by simply adding the corresponding atom charges. In fact, the atom charges would be determined to reproduce the electric field around a molecule. Therefore, it is more reasonable to refit the charges in the U A force field. The method used is R E S P , the same algorithm used for the A A force field. The difference in the U A force field here is that all the H atoms in the alkyl chains were removed in the fitting procedure. The parameters of our A A and U A force fields can be found in our previous work ' . 1 12 13

10

6 7

3. Molecular Dynamics Simulations To obtain macro-properties of RTIL systems from the A A and U A force field developed by our group, the molecular dynamics simulations were performed by the package M D y n a M i x . The typical systems include 128 ion pairs or more. The typical length of M D in this work is 400ps. More details of the simulations can be found in the literature . The results from U A force field agree well with those from A A force field. However, the computational cost of the former 14

6,7,15


76 deceases significantly. For example, the time for the simulations of [bmim][PF ] by U A is about 1/4 of that by A A . 6


3.1 Pure ionic liquids Some of the simulated results for pure RTILs are listed in Table 1. More results are referred to the literature [6] and [7]. For brevity, only the liquid densities and inter-molecular energies are presented here.

3.1.1 Densities The densities of the ionic liquids are one of the most accurate sources of experimental data. Therefore, it is important to predict the densities by simulations for the validation of the proposed force field. The simulated results show that both our force fields can describe the densities of pure RTILs rather accurately, with the absolute relative deviations less than 2% . For example, the densities of [C„mim][PF ] are predicted from our U A force field, as is shown in Figure 3. Besides, a correlation between liquid density and the carbon atom number of [C mim][PF ] is proposed by fitting our simulated data with n=5~7, given by 6,7

6

n

6

/? = 1.483 - 0 . 0 2 9 5 Η

(3) 3

where ρ is the liquid density of [C mim][PF ], g/cm , η is the carbon number of the alkyl chain in [C mim] . Furthermore, the densities of [C mim][PF ] and [C mim][PF ] are predicted by the correlation. It is found in Figure 2 that the predicted densities for the two liquids are in good agreement with the experimental data. n

6

+

n

8

4

6

6

3.1.2 Inter-molecular Energies The inter-molecular energy, Uint, is another characteristic property for condensed phases. In addition, it can be directly extracted from the molecular simulation. It is shown by our calculations that the electrostatic interactions are about four times as large as the V D W interactions, indicating the "ionic feature" of these solvents. 6,7



f

vap

18 b

UA -498.6 -508.6 -519.8 -509.5 -511.5 -533.0

UA 1.365 1.308 1.258 1.264 1.208 1.126

19 c

-509.6 -506.8

U^/kJmor AA -493.8

1.284 1.194

3

ρ gem' AA 1.350

1

e

b

4

exp. 1.363 1.307' 1.237" 1.279 1.211

17 d

anion 0.6 0.8 0.6 2.0 0.6 0.6

20

e

AH^/kJmor' AA UA 186.7 190.4 199.0 208.2 175.9 175.8 174.7 179.1 198.7

cation 1.2 0.8 0.6 2.1 0.9 0.8

UA

ll

2

e

203

e

exp. 191

1.1 1.2

16

UA 902.6 822.8 765.9 1105.8 937.4 782.4

0.9 0.8

10 D/m s" AA cation anion 1.0 1.2

Notes: * from reference , from reference , from reference , from reference , from reference .

[bmim][PF6] [hmim][PF6] [omim][PF6] [emim][BF4] [bmim][BF4] [omim][BF4]

RTIL

[bmim][PF6] [hmim][PF6] [omim][PF6] [emim][BF4] [bmim][BF4] [omim][BF4]

RTIL

b

1124.6 906.2

c / J cm" AA 875.0

d

4.9 1.4

cation 0.7"

3

exp. a

998

e

e

exp. 912

4.2* 1.3*

anion 0.5

Table 1. Densities (ρ), self diffusion coefficients (D), intermolecular energies ( U ) heats of vaporization ( A H ) and the cohesive energy densities (c) for some pure room temperature ionic liquids (RTILs) simulated by using the A A and U A force field proposed in this work.

int


78


1.40

J

I

4

I

5

I

6

7

L 8

Number of C atom in alkyl Figure 3. A correlation between the simulated liquid density and the carbon number of alkyl chain in [C„mim][PF ] for n=5~7 (see equation (3) in section 3.1). The predictive liquid densities for n-4 and 8 are also presented. (Reproduced with permission from reference 7. Copyright 2006 Royal Society of Chemistry.) 6

The enthalpy of vaporization, AHvap, and cohesive energy density, c, are calculated by 6

AH

= RT

vap

c

= (y

- (f/

int

-

U

)

ionpair

(4)

-U )/V

ionpair

int

(5)

m

lonpmr

where V is the molar volume o f the liquid. R is the gas constant, JJ represents the average intermolecular energy of ionic pairs at the ideal gas state, which can be simulated in term of a single ion pair at the same temperature with a simulation box large enough . It is difficult to measure the enthalpy o f vaporization directly from experiment, since RTILs are all nonvolatile. However, Swiderski et a l . reported the values for several ionic liquids estimated from the bimolecular rate constant experiments very recently. The internal energies of vaporization estimated for [bmim][PF ] and [bmim][BF ] are 189±20 and 201±20 kJ/mol, respectively, m

2,15

16

6

4


79 which are in fair agreement with the simulated values of 190.4 and 179.1 kJ/mol from our U A force field. In addition, they also estimated the cohesive energy densities for [bmim][PF ] and [bmim][BF ], which are 912±100 and 998±100 J/cm , respectively. The values coincide well with our simulated values, 902.6 and 937.4 J/cm . 6

4

3

3

3.2 Mixtures of [bmim][BF ] and acetonitrile (CH CN) Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 14, 2016 | http://pubs.acs.org Publication Date: August 30, 2007 | doi: 10.1021/bk-2007-0975.ch006

4

3

A rigorous test for our force fields is the interactions between RTILs and other molecules, therefore, we performed molecular dynamics of the mixtures of [bmim][BF ] and acetonitrile . Some of the simulation results for different concentrations of the mixtures are shown in Table 2. It is also noticed that the values from U A and A A force fields are very close. 4

3.2.1 Excess volumetric and energetic properties The nonideality of mixture can be depicted by the excess properties. From our simulation, both the excess molar volume (see Figure 4) and excess molar enthalpy (see Figure 5) exhibit negative deviations and show a minimum in the concentration range of x^O.3-0.4, which is consistent with the corresponding experimental results . 17

3.2.2 Viscosities The experimental values of viscosity for both pure ionic liquids and the mixtures are frequently reported in the literature. In contrast, it is more difficult to measure the diffusion coefficients accurately by experiment. In molecular dynamics, it needs much longer time in simulation to calculate the viscosity than self-diffusion coefficient by either the Green-Kubo or Einstein methods. Here we assumed that the Stokes-Einstein relation holds for the mixture, in which 2

VP^VJDJ

(6)

where 7J , η., D- and D. represent the viscosity and self-diffusion coefficient i

of the two systems i and j , respectively, at the same temperature and pressure. B y using equation (6) and the simulated values of the self-diffusion coefficient, the viscosities of the mixture can be estimated. The calculation


Brennecke et al.; Ionic Liquids IV ACS Symposium Series; American Chemical Society: Washington, DC, 2007. 4

3

0 0.20 0.30 0.40 0.60 0.80 1

Χι

AA 54.86 79.52 92.30 105.61 133.87 161.77 190.57

m

s m

V lc 1

mor UA 54.86 79.00 91.60 104.60 131.99 158.98 187.35

1

(/"'/kJmor AA UA -30.75 -30.75 -129.29 -130.23 -176.37 -177.69 -224.98 -223.26 -319.51 -322.93 -411.52 -415.75 -507.42 -512.59

Λ / Γ * 7 kJ m o f UA AA 33.22 33.22 64.48 63.82 78.24 79.13 93.62 92.46 123.17 120.57 150.55 147.45 179.15 175.40

m

φ

Notes: V is the molar volume of the mixture; if" is the intermolecular energy of the system; ΔΗ" is enthalpy of vaporization and c is the cohesive energy density of the system. SOURCE: Reproduced with permission from reference 7. Copyright 2006 Royal Society of Canada.

2

System size N N, 0 210 52 204 77 179 102 154 118 78 102 52 0 256

Table 2. Sizes of the systems and the results of simulations for the mixture [bmim][BF ] (1) + C H C N (2) from the A A and U A force field presented in this work


81 0.5 0.0 -0.5 -1.0 -1.5 -

/ /

Γ '

-2.0 Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 14, 2016 | http://pubs.acs.org Publication Date: August 30, 2007 | doi: 10.1021/bk-2007-0975.ch006

-2.5

/ /

Γ

\

_

γτ

•

^)

/

/

λ)

/

/

/

/

\ /

/

/ —· —UA --0--ΑΑ

-3.0

•δ-

-3.5 ι

I

0.0

I

.,ι,

0.2

..ι.

0.4

-J

ι

0.6

exp. .

I

0.8

1.0

Figure 4. Excess molar volumes of the mixtures of [bmim][BF ](l) - CH CN(2) from simulations by the all-atom (AA) and united-atom (UA) model. (Reproduced with permission from reference 7. Copyright 2006 Royal Society of Chemistry.) 4

-3 0 '

0.0

.

«

0.2

«

»

•

0.4

1

0.6 X

•

3

l _ — — ι

0.8

1.0

»

Figure 5. Excess molar enthalpies of the mixtures of [bmim][BF ](l) CH CN(2) from our simulations by the all-atom (AA) and united-atom (UA) model. (Reproduced with permission from reference 7. Copyright 2006 Royal Society of Chemistry.) 4

3


82 15

details can be referred to the the literature . Impressively, as is shown in Figure 6, the U A force field even presents better results, especially for the viscosity at Xg =0.8.


3.2.3 Microscopic structures The microscopic structural information of liquids can be extracted from molecular simulation. The radial distribution function (RDF) is often presented in the literature. However, it is difficult to describe the three-dimensional distribution of particles by RDF. In contrast, the space distribution function (SDF) is a more intuitive method to represent the distribution of particles around a central molecule . The distribution contour surfaces of the [bmim] , [BF ]" and C H C N molecules around a C H C N molecule are shown in Figures 7a to 7c, respectively. The cations distribute like a cap adjacent to the Ν atoms of C H C N , while the anions and the Ν atoms in C H C N distribute like a ring surrounding the C H C N near the side of C H . In Figures 7a and 7b, both the distributions of cations and anions exhibit a minimum at x\=03. As is seen in Figure 7c, the distribution of C H C N shows a maximum at the same concentration. These results coincide well with the analyses of the RDFs (see Figures 10-12 in the literature ). It is shown intuitively by the distributions of different species in the mixture that the liquid structure at χχ=03 is significant different, which causes the maximal negative deviation of excess properties of the mixtures near this concentration. 6

+

4

3

3

3

3

3

3

3

15

4. Conclusions We developed a refined all-atom force field and the corresponding unitedatom one for RTILs with imidazolium cations. Comprehensive tests on the force field were presented for the liquid densities, inter-molecular energies, transport properties. It is found that both the pure RTILs and mixtures can be described quite accurately by the force fields. This work provides a good start to the molecular design of RTILs. In future work, we will focus our attentions on the task-specific RTILs, such as ionic liquids with guanidinuim cations , the promising solvents in flue gas desulfurization. 21

Acknowledgements This work was supported by the National Basic Research Program (No. G2000048010), the National Natural Science Foundation of China (No. 20236010) and the Postdoctoral Scientific Foundation of China (No. 2003033095).



120

—J

0.0

1

I

0.2

ι

I

ι

0.4

I

ι

0.6 X

I

ι

0.8

L _

1.0

l

Figure 6. Viscosity of the mixtures of[bmim][BF ](l) - CH CN(2) at T=298 K, P=0.1 MP a. The solid line represents experimental date? . The circles are estimated by the Stokes-Einstein relation and our simulations. (Reproduced with permission from reference 7. Copyright 2006 Royal Society of Chemistry.) 4

3

7



84

Figure 7. The orientational distributions of the CR atoms in cation (a), the Β atoms in anion (b) and the Ν atoms in CH CN (c) around CH3CN in the mixtures [bmim][BF ](l) - CH CN(2). From left to right, the molarfractions of the mixture x are 0.2, 0.3 and 0.4. The contour levels in (a), (b) and (c) are 2.5, 4.5 and 3.0, respectively. (Reproduced with permission from reference 15. Copyright 2005 Royal Society of Canada.) 3

4

3

l


85

References


1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M . Mol. Phys., 2001, 99, 801. Morrow, T. I.; Maginn, E. J. J. Phys. Chem. B, 2002, 106, 12807. de Andrade, J.; Boes, E. S.; Stassen, H . J. Phys. Chem. B, 2002, 106, 3546. Lopes, J. N . C.; Deschamps, J.; Padua, Α. A . H . J. Phys. Chem. B, 2004, 108, 2038. Lopes, J. N . C.; Padua, Α. A . H . J. Phys. Chem. B, 2004, 108, 16893. Liu, Z. P.; Huang, S. P.; Wang, W. C. J. Phys. Chem. B, 2004, 108, 12978. Liu, Z. P.; Wu, X . P.; Wang, W. C. Phys. Chem. Chem. Phys., 2006, 8, 1096. Del Popolo, M . G.; Lynden-Bell, R. M . ; Kohanoff, J. J. Phys. Chem. B, 2005, 109, 5895. Buhl, M . ; Chaumont, Α.; Schurhammer, R.; Wipff, G J. Phys. Chem. B, 2005, 109, 18591. Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Kollman, P. A . J. Am. Chem. Soc. 1993, 115, 9620. Paulechka, Y. U . ; Kabo, G. J.; Blokhin, Α. V.; Vydrov, Ο. Α.; Magee, J. W.; Frenkel, M . J. Chem. Eng. Data, 2003, 48, 457. Shah, J. K . ; Brennecke, J. F.; Maginn, E. J. Green Chem., 2002, 4, 112. Urahata, S. M . ; Ribeiro, M . C. C. J. Chem. Phys., 2004, 120, 1855. Lyubartsev, A . P.; Laaksonen, A . Comp. Phys. Comm., 2000, 128, 565-589. Wu, X . P.; Liu, Z. P.; Wang, W. C. Phys. Chem. Chem. Phys., 2005, 7, 2771. Swiderski, K . ; McLean, Α.; Gordon, C. M . ; Vaughan, D . H . Chem. Comm., 2004, 2178. Wang, J. J.; Tian, Y.; Zhao, Y ; Zhuo, K. Green Chem., 2003, 5, 618. Chun, S.; Dzyuba, S. V.; Bartsch, R. A . Anal. Chem., 2001, 73, 3737. Noda, Α.; Hayamizu, K.; Watanabe, M . J. Phys. Chem. B, 2001, 105, 4603. Tokuda, H . ; Ishii, K.; Hayamizu, K . ; Susan, Μ. Α. Β. H . ; Watanabe, M . J. Phys. Chem. B, 2004, 108, 16593. Wu, W. Z.; Han, Β. X . ; Gao, Η. X . ; Liu, Ζ. M . ; Jiang, T.; Huang, J. Angew. Chem.-Int. Edit, 2004, 43, 2415. f


Ionic Liquids IV Not Just Solvents Anymore - American Chemical Society

Recommend Documents