Supporting Information: Structures and Dynamics of Silicon Substituted Ionic Liquids
Boning Wu,1 Yuki Yamashita,2 Takatsugu Endo,2 Kenji Takahashi,2, a) and Edward W.
Castner Jr.1, a)
1)
Department of Chemistry and Chemical Biology, Rutgers,
The State University of New Jersey, Piscataway, NJ
2)
Institute of Science and Engineering, Kanazawa University, Kakuma-machi,
Kanazawa, 920-1192, Japan
a)
08854. United States
Electronic mail: [email protected], [email protected]
1
I.
MD SIMULATION METHODS
The ionic liquids (ILs) are simulated using cubic boxes containing 1000 ion pairs. Pe-
riodic boundary conditions are used in each direction. The leap-frog algorithm is used for
integration at a time step of 1 fs. Initial conditions for the boxes were obtained from several simulations of 300 picoseconds, in which fractional charge was applied to the ions, and
the charges are gradually increased to the full charge values. These simulations are done
under Berendsen pressure and temperature coupling.1 Subsequently an 8 ns long simulated
annealing was applied, during which the temperature is increased from 298 to 598 K then
annealed back to 298 K. The final equilibration at 1 bar and 298 K continues for another
10 ns of simulation. The production MD run is done at the same temperature and pressure
as the final equilibration run. During the production run, the coordinates are saved every
1 ps for 2 ns and the radial distributions g(r) and spatial distributions are averaged over
these 2001 snapshots. The Nosé-Hoover thermostat2,3 and Parrinello-Rahman barostat4 are
used during the simulated annealing, final equilibration and production run. The cutoffs
for Coulomb and Lennard-Jones potentials are all set to 1.5 nm. Long range electrostatic
potentials are treated using the Particle Mesh Ewald (PME) method5,6 , the interpolation
order is set to 6 and FFT grid spacing is set to 0.08 nm.
II.
FORCE FIELD FOR MD SIMULATIONS OF IONIC LIQUIDS
In this work, we used the modified OPLS-AA force field7 for ionic liquids by Lopes and
Pádua, called the CL&P force field,8 while adding new parameters for silicon based on
our previous work.9 The parameters for cations are parameterized based on the method in
literature10,11 and our previous work.9 The parameters for anions are directly taken from
the Lopes and Pádua’s force field,11,12 and the parameters for perfluoroalkyl chains are
from OPLS-AA force field.13 The total potential of the system is the sum of the bonded
interactions and non-bonded interactions:
Vtotal = Vbonded + Vnon−bonded
(1)
where the bonded parameters include contributions from bonds, angles, proper dihedral
angles and improper dihedral angles:
2
Vbonded =
Vbond + Vangle + Vdih + Vimdih
X1
=
kb (rb − rb0 )2
2
b
X1
+
kaθ (θa − θa0 )2
2
a
+
5
XX
Cn (cos(φd ))n
n=0
d
+
(2)
X
kφ (1 + cos(nφ − φs ))
imd
and non-bonded parameters include Lennard-Jones (L-J) type van der Waals parameters
and Coulomb interactions:
Vnon−bonded = VLJ + Vcoulomb
XX
σij
σij
1 qi qj
=
4ij (( )12 − ( )6 ) +
ij
ij
4π0 rij
i
j
(3)
the L-J force between different atoms were combined using the combining rule given in Eq.
4. The intra-molecular non-bonded potential between atoms that are connected by bonds
or angles are excluded, and all non-bonded 1,4 interactions are scaled by a factor of 0.5.
σij = (σi σj )1/2 ; ij = (i j )1/2
angle Si-C-C-C
15
angle C-Si-C-C
)lom/Jk( ygrenE
10
5
0
0
50
100
150
Dihedral angle (degree)
FIG. 1. The fitting of two dihedral angles for the trimethylsilylpropyl group.
3
(4)
HC
HA
H1
HC
H1
HC
HC
CSi
H1
CR
H1
C1
NA
C1
C3
C2
NA
+
H1
HC
Si
CSi
HC
HA
HC
CSi
HC
CW
CW
HC
HA
HC
HC
HC
HC
Si-C3-mim+
H1
H1
HC
HC
H1
C2
HC
HC
H1
C1
C1
CSi
H1
C2
C1
C2
C1
H1
HC
H1
HC
C3
NT
HC
HC
HC
Si
HC
H1
HC
CSi
HC
H1
CSi
HC
HC
HC
HC
HC
Si-C3-pyrr+
FIG. 2. Atom labels for the Si-C3 -mim+ and Si-C3 -Pyrr+ cations.
The force field parameters for the Si-C3 -mim+ and Si-C3 -Pyrr+ cations are shown in
Table I, with the atom labels defined in Fig. 2. The bonded and non-bonded potentials
for non-silicon parts are all taken from CL&P force field.10,11 The partial charges on silicon
atoms and its connected structure are proposed using the method by Sun,14,15 in which a
silicon atom will donates 0.135 electrons to each carbon it is bonded to. The Lennard-Jones
parameters are taken from OPLS-AA force field, which is originally copied from Gromos53a6
force field.16 Some bond and angle parameters by the force field for silane by Frierson et al. 15
To obtain the torsion profiles for the two needed dihedral angles, CT-CT-CT-Si and
CT-CT-Si-CT, the same methods used in our previous work are adopted here.9 A virtual
molecule, trimethylpropylsilane (CH3 CH2 CH2 Si(CH3 )3 ) is proposed for dihedral scanning.
The torsion barriers for the selected dihedral angles are obtained by subtracting total energy
and the contribution of non-bonded parameters. The total quantum energy is from a relaxed
scan with a step length of 10 degree at MP2/cc-pVTZ level, and the non-bonded contribution
4
is obtained using a single molecule molecular dynamics simulations in which the atomic
positions are fixed at the result of relaxed optimization. The 1,4 interactions are scaled by a
factor of 0.5 in this scan. The scan and fits of energy profile is shown in Fig. 1. The red curve
is the result of fits of Si-C-C-C angle in CH3 CH2 CH2 Si(CH3 )3 , which contains one CT-CTCT-Si angle, 4 HC-CT-CT-HC angles, two HC-CT-CT-CT angles and two Si-CT-CT-HC
angles. The blue curve is for the C-Si-C-C angle, which can be split to six Ct-Si-CT-HC and
three CT-Si-CT-CT angles. The profiles of HC-CT-CT-HC, HC-CT-CT-CT, Si-CT-CT-HC
and Ct-Si-CT-HC can be obtained from OPLS-AA force field7 and previous work,9 , therefore
our desired angle, CT-CT-CT-Si and CT-CT-Si-CT can be obtained after subtracting them.
TABLE I. Force field parameters used for Si-C3 -mim+ and Si-C3 -Pyrr+ cations.
L-J parameters
Atomtype
σ
q
Source
Atomtype
σ
C1
0.350
0.27614
-0.170
Ref. 10
C2
0.350 0.27614
0.010
Ref. 10
C3
0.350
0.27614
-0.255
Ref. 10,14
CSi
0.350 0.27614
-0.315
Ref. 10,14
CW
0.355
0.29288
-0.130
Ref. 10
CR
0.355 0.29288
-0.110
Ref. 10
NA
0.325
0.71128
0.150
Ref. 10
HA
0.242 0.12552
0.210
Ref. 10
HC
0.250
0.12552
0.060
Ref. 10
Si
0.339 2.44704
0.540
OPLS-AAa , Ref. 14
H1
0.250
0.12552
0.130
Ref. 10
NT
0.325 0.71128
0.120
Ref. 11
Bond and angle parameters
Bond type
rb0
kb
Source of rb0 Source of kb Bond type
C3-Si
0.1907 359000
this work
CSi-HC
0.1090 284500
CL&P
Angle type
θa0
ka
d
worke
C2-C3-Si
113.8
488.3
this
110.7
450.0
this worke
193.3
worke
110.8
Si-CSi
this
C0
Source
Source of rb0
Source of kb
0.1870 359000 Gromos53a6
Gromos53a6
kb
CL&P
OPLS-AA
θa0
ka
Source of θa0
worke
C3-Si-CSi
108.2
450.0
this
Gromos53a6 HC-C3-Si
108.3
193.3
this worke
Source of ka
Gromos53a6
Ref. 15
Ref. 15
Dihedral angle parameters
Dihedral angle type
q
a
rb0
Source of θa0 Source of ka Angle type
CSi-Si-CSi
Si-CSi-HC
Gromos53a6
a,b
C1
C2
C3
Source
CT-Si-CT-HC
0.3358
1.0074
0.0000
-1.3432
this work
CT-CT-CT-Si
-1.2584
-1.5312
4.8460
-2.0564
this work
CT-CT-Si-CT
0.4923
1.4771
0.0000
-1.9692
this work
0 : nm ; k b : kJ mol−1 nm−2 ; k θ
−1 rad−2 ;
Units: σ: nm ; : kJ mol−1 ; rij
ij
ijk : kJ mol
a
Only can’t be found in CL&P force field8,10,11 are listed here
5
b
C1, C2, C3 and CSi are all count as CT here
III.
THE VAN DER WAALS VOLUME AND RADIUS OF IONIC LIQUID
CATIONS AND ANIONS
The van-der Waals volumes and radii are calculated the total electron density via Monte
Carlo integration using Gaussian09 D01 package at a HF/6-31g(d) theory level with structures optimized at the same level. The SiOSi-mim+ cation is calculated at the MP2/cc-pVTZ
level. The radius is calculated assuming spherical molecules. The van der Waals volume of
the molecule is defined by the value at which the electron density is larger than 0.002 e/a30 .
5000 test points per a30 for each molecule is used in Monte Carlo integration. The volumes
and radius are shown in Table II.
TABLE II. The calculated Van der Waals volume and radius of all ions calculated using Monte
Carlo method at hf/6-31g(d) level of theory
Ion
Volume (Å3 ) Radius (Å)
Volume (Å3 ) Radius (Å)
-mim+
238.2
3.85
241.6
3.86
Si-C3 -Pyrr+
257.8
3.95
C-mim+
183.4
3.52
Pyrr+
4,1
183.2
3.52
Pyrr+
3,1
164.8
3.40
195.6
3.60
SiOSi-mim+
281.9
4.07
Si-pyrr+
Si-C3
216.4
3.72
N
N
CnH2n+1
125.9
165.3
207.8
N+
3.11
112.1
2.99
3.40
NTf−
2
167.7
3.42
3.67
BETI−
221.9
3.76
FTFSI−
138.1
3.21
O
CnH2n+1
Pyrrn,1+
Volume (Å3 ) Radius (Å)
Ion
FSI−
O
N
S
F
Imn,1+
IV.
Ion
Im+
2,1
Im+
4,1
Im+
6,1
Im+
8,1
Si-mim+
S
O O
CF3
FTFSI-
DIFFUSIVITIES AND VISCOSITIES OF IONIC LIQUIDS FROM
THIS WORK AND FROM LITERATURE
The diffusion coefficients of eight ionic liquids measured in this work at three different
temperatures are shown in Table III. The viscosities are fit into Vogel-Fulcher-Tammann
(VFT) equations, and the parameters of these ILs are shown in Table IV.
6
TABLE III. Diffusion coefficients of silicon ionic liquids and C-mim+ / NTf−
2 measured in this work
298.15 K 303.15 K 308.15 K
in 10−7 cm2 /s
a
Si-mim+ / NTf−
2
Dcation
1.351
1.593
1.884
Danion
1.306
1.581
1.894
a
C-mim+ / NTf−
2
Dcation
0.681
0.868
1.075
Danion
0.644
0.792
0.998
Dcation
Si-C3 -mim+ / NTf−
2
0.799
1.014
1.218
Danion
0.912
1.120
1.406
Dcation
1.104
1.334
1.644
Danion
1.472
1.707
2.121
Dcation
0.363
0.471
0.572
Danion
0.364
0.471
0.603
Si-C3
Si-C3
-mim+ / FSI−
-mim+ / BETI−
Si-C3 -Pyrr+ / NTf−
2
Dcation
0.361
0.456
0.552
Danion
0.466
0.578
0.743
a D
SiOSi-mim+ / NTf−
cation
2
1.190
1.418
1.670
Danion
1.485
1.808
2.178
Si-pyrr+ / NTf−
2
a
Dcation
0.728
0.830
0.996
Danion
0.768
0.965
1.284
A little off from the values in Reference 17, with an acceptable error ;
TABLE IV. VFT of silicon ionic liquids and C-mim+ / NTf−
2 from literature or this work in the
range from 293 K to 363 K
ln(η) = ln(η0 )+(D × T0 /(T − T0 ))
ln(η0 ) (ln(cP))
a
Si-mim+ / NTf−
2
a
C-mim+ / NTf−
2
−a
+
Si-mim / BF4
a
C-mim+ / BF−
4
−b
+
Si-pyrr / NTf2
Si-C3 -mim+ / NTf−
2
Si-C3 -mim+ / FSI−
Si-C3
a
Data from Ref. 18, VFT fits see
-mim+ / BETI−
D
T0 (K)
-2.036
4.43
176.5
-2.264
4.979
175.8
-3.166
5.886
183.1
-5.914
10.226
172.1
-1.6122
3.9897
187.83
-2.8358
6.1764
165.29
-2.5488
6.5794
154.47
-4.6048
12.608
133.8
Si-C3 -Pyrr+ / NTf−
2
-4.1765
10.252
144.68
c
SiOSi-mim+ / NTf−
2
-2.5051
6.5644
151.61
Ref.17,19
;
b
VFT parameters from previous work9 ;
c
Data from this work. Though VFT
parameters are very different in Ref. 19, the viscosity vs. temperature curve it reproduced is very similar in the measured
temperature range
7
The VFT fits of diffusion coefficients and viscosities of ILs with hydrocarbon side chains
are shown in Table V and VI, respectively. For better comparison, all diffusion coefficients
here are used PG-SE NMR technique. The diffusivities or viscosities at different temperatures are extracted from VFT fits, if the fit parameters are available.
TABLE V. Diffusion coefficients of non-silicon ionic liquids from literature
D0
−
Im+
2,1 / NTf2
−
Im+
4,1 / NTf2
−
Im+
6,1 / NTf2
−
Im+
8,1 / NTf2
−
Im+
4,1 / BETI
−
Pyrr+
3,1 / FTFSI
VFT parameters
Diffusivity (10−7 cm2 /s)a
D = D0 exp[−B/(T − T0 )]
at different temperatures
(10−4
cm2 s−1 )
B (K) T0 (K) 298.15K 303.15K 308.15K 305K Reference
Dcation
1.10
816
147
4.98
5.91
6.95
20
Danion
0.90
857
147
3.10
3.72
4.41
20
Dcation
1.10
845
157
2.76
3.39
4.11
20
Danion
1.30
933
152
2.20
2.71
3.30
20
Dcation
1.50
965
156
1.69
2.13
2.64
20
Danion
1.70
1010
154
1.54
1.95
2.43
20
Dcation
3.10
1246
140
1.17
1.49
1.88
20
Danion
2.50
1167
146
1.17
1.49
1.87
20
Dcation
1.70
995
160
1.27
1.63
2.06
21
Danion
1.90
1109
154
0.87
1.12
1.43
21
Dcation
3.84
22
Danion
3.53
22
−
Pyrr+
4,1 / FTFSI
Dcation
2.94
22
−
Pyrr+
4,1 / NTf2
Dcation
1.20
914
164
1.32
1.68
2.12
Danion
1.30
961
161
1.18
1.51
1.90
Danion
2.83
22
− D
Pyrr+
cation
4,1 / BETI
23
0.90
Danion
0.62
−
Im+
2,1 / BF4
Dcation
1.60
970
Danion
1.60
−
Im+
4,1 / BF4
Dcation
1.40
Danion
2.80
a
23
5.90
6.91
24
24
130
5.00
1000
130
4.18
4.97
5.84
25
935
162
1.46
1.86
2.33
21
1108
153
1.36
1.75
2.22
21
Numbers are extracted from VFT fitting when VFT parameters are available ;
8
25
TABLE VI. Viscosity from literature
VFT parameters
Viscosity (cP)
η = η0 exp[B/(T − T0 )]
at different temperatures
D0 (cP) B (K) T0 (K) 298.15K 303.15K 308.15K 305K Reference
a
−
Im+
2,1 / NTf2
0.4
509
182
32.0
26.7
22.6
20
−
Im+
4,1 / NTf2
+
Im6,1 / NTf−
2
−
Im+
8,1 / NTf2
+
Im4,1 / BETI−
−
Pyrr+
3,1 / FTFSI
−
Pyrr+
4,1 / FTFSI
−
+
Pyrr4,1 / NTf2
−
Pyrr+
4,1 / BETI
+
−
Im2,1 / BF4
−
Im+
4,1 / BF4
0.25
625
180
49.6
40.0
32.8
20
0.16
757
173
67.8
53.7
43.3
20
0.15
802
173
91.0
71.2
56.7
20
0.17
763
180
108.4
83.4
65.5
21
0.383
580.2
169
34.2
28.9
24.8
22
0.249
725.7
160
47.6
39.6
33.4
22
0.45
534
199
98.2
75.8
60.0
23
0.2
750
150
31.6
26.8
22.9
25
0.21
697
185
99.4
76.6
60.3
21
200
Note that this equation is slight different from what we used in Table IV ;
b
VFT parameters are available ;
9
24
Numbers are extracted from VFT fitting when
The linear fitting results between the measured diffusivities using PG-SE NMR method
and estimated diffusivities using Stokes-Einstein Equation are shown in Table VII. The
anions have a similar slope of both silicon and carbon ionic liquids, but the slope for cations
are very different.
TABLE VII. The relation between measured diffusivity and Stokes-Einstein diffusivity.
Dexp = a + bDS-E
a
Anion Carbon ILs 0.75 ± 0.61 ×
Silicon ILs
b
10−10
1.52 ± 0.04
1.27 ± 0.49 × 10−10 1.48 ± 0.06
Cation Carbon ILs −2.27 ± 1.18 × 10−10 2.17 ± 0.08
Silicon ILs
1.02 ± 0.46 × 10−10 1.46 ± 0.03
10
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