Molecular dynamics simulation and pulsed-field gradient NMR studies of Bis(fluorosulfonyl)imide (FSI) and Bis[(trifluoromethyl)sulfonyl]imide (TFSI)-based ionic liquids

Article abstract of DOI:10.1021/jp911950q

The pulsed-field-gradient spin-echo NMR measurements have been performed on 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide ([emim][FSI]) and 1-ethyl-3-methylimidazolium [bis[(trifluoromethyl)sulfonyl]imide] ([emim][TFSI]) over a wide temperature range from 233 to 400 K. Molecular dynamics (MD) simulations have been performed on [emim][FSI], [emim][TFSI], [N-methyl-N-propylpyrrolidinium][FSI] ([pyr₁₃][FSI]), and [pyr ₁₃][TFSI] utilizing a many-body polarizable force field. An excellent agreement between the ion self-diffusion coefficients from MD simulations and pfg-NMR experiments has been observed for [emim][FSI] and [emim][TFSI] ILs. The structure factor of [pyr₁₃][FSI], [pyr₁₄][TFSI], and [emim][TFSI] agreed well with the previously reported X-ray diffraction data performed by Umebayashi group. Ion packing in the liquid state is compared with packing in the corresponding ionic crystal. Faster transport found in the FSI-based ILs compared to that in TFSI-based ILs is associated with the smaller size of FSI^- anion and lower cation-anion binding energies. A significant artificial increase of the barriers (by 3 kcal/mol) for the FSI ^- anion conformational transitions did not result in slowing down of ion transport, indicating that the ion dynamics is insensitive to the FSI ^- anion torsional energetic, while the same increase of the TFSI ^- anion barriers in [emim][TFSI] and [pyr₁₃][TFSI] ILs resulted in slowing down of the cation and anion transport by 40-50%. Details of ion rotational and translational motion, coupling of the rotational and translational relaxation are also discussed. ? 2010 American Chemical Society.

Full text of DOI:10.1021/jp911950q

6786
J. Phys. Chem. B 2010, 114, 6786–6798
Molecular Dynamics Simulation and Pulsed-Field Gradient NMR
Studies of Bis(fluorosulfonyl)imide (FSI) and Bis[(trifluoromethyl)sulfonyl]imide
(TFSI)-Based Ionic Liquids
Oleg Borodin,*,†,‡ W. Gorecki,§ Grant D. Smith,‡ and Michel Armand|
Wasatch Molecular Inc., 2141 St. Marys DriVe, Suite 102, Salt Lake City, Utah 84108, Department of
Materials Science & Engineering, 122 South Central Campus DriVe, Room 304, UniVersity of Utah, Salt Lake
City, Utah 84112-0560, Laboratoire de Spectrome´trie Physique, UniVersite´ Joseph Fourier, Grenoble 1-38401,
BP 87, 38402 St. Martin D’he`res Cedex, France, and Laboratoire de Re´actiVite´ et de Chimie des Solides,
UniVersite´ de Picardie Jules Verne, 33 rue Saint leu, 80039 Amiens Cedex, France
ReceiVed: December 17, 2009; ReVised Manuscript ReceiVed: April 13, 2010
The pulsed-field-gradient spin-echo NMR measurements have been performed on 1-ethyl-3-methylimidazolium
bis(fluorosulfonyl)imide ([emim][FSI]) and 1-ethyl-3-methylimidazolium [bis[(trifluoromethyl)sulfonyl]imide]
([emim][TFSI]) over a wide temperature range from 233 to 400 K. Molecular dynamics (MD) simulations
have been performed on [emim][FSI], [emim][TFSI], [N-methyl-N-propylpyrrolidinium][FSI] ([pyr13][FSI]),
and [pyr13][TFSI] utilizing a many-body polarizable force field. An excellent agreement between the ion
self-diffusion coefficients from MD simulations and pfg-NMR experiments has been observed for [emim][FSI]
and [emim][TFSI] ILs. The structure factor of [pyr13][FSI], [pyr14][TFSI], and [emim][TFSI] agreed well
with the previously reported X-ray diffraction data performed by Umebayashi group. Ion packing in the
liquid state is compared with packing in the corresponding ionic crystal. Faster transport found in the FSI-
based ILs compared to that in TFSI-based ILs is associated with the smaller size of FSI- anion and lower
cation-anion binding energies. A significant artificial increase of the barriers (by 3 kcal/mol) for the FSI-
anion conformational transitions did not result in slowing down of ion transport, indicating that the ion dynamics
is insensitive to the FSI- anion torsional energetic, while the same increase of the TFSI- anion barriers in
[emim][TFSI] and [pyr13][TFSI] ILs resulted in slowing down of the cation and anion transport by 40-50%.
Details of ion rotational and translational motion, coupling of the rotational and translational relaxation are
also discussed.
I. Introduction
which are typically slow compared to those of nonionic organic
solvents. Hence, there is much effort to develop new ILs that
maintain their useful properties but exhibit significantly lower
viscosity and increased ionic mobility. Recently, considerable
attention has been focused on ILs based on the bis(fluorosul-
fonyl)imide, or FSI, anion, illustrated in Figure 1a, combined
with 1-alkyl-3-methylimidazolium (Cnmim+) and N-alkyl-N-
methylpyrrolidinium (pyr1R+) cations, due to low viscosity, high
conductivity, and acceptable electrochemical stability.19–23 Com-
pared to extensively investigated bis[(trifluoromethyl)sulfo-
nyl]imide (TFSI or tf2N, Figure 1b) ILs, FSI analogs exhibit
significantly reduced viscosity and increased conductivity at
room temperature.18,19,22,24 The specific choice of an IL for
applications is dictated by compromise between its electro-
chemical stability, conductivity, melting point, and cost. For
example, the pyr13+ cation has a wide electrochemical window
indicating electrochemical stability better than that of ILs with
Cnmim+,19,25–28 while emim+-containing ILs have higher ionic
conductivity and lower viscosity than pyr13-based analogs.19
Analysis of the melting temperatures of [pyr1R][TFSI]29 R )
1,2,3 and [Cnmim][TFSI]17 for n ) 1, 2, 3, 4, 6 ILs as a function
of the alkyl tail length has revealed that their melting points
decrease with an initial increase of the alkyl tail for R ) 1-3
and n ) 1-4. However, longer tails result in undesirable slower
ion dynamics and reduce the volume fraction of ionic groups.17,29
Often emim+ and pyr13+ are chosen from the family of Cnmim+
Room temperature ionic liquids (ILs) have been widely
investigated for use in lithium batteries,1–4 supercapacitors,5–10
dye-sensitized solar cells,11 biphasic systems for separation and
solvents for synthetic and catalytic applications,12 and actuators13
and as a reaction media14 due to their outstanding properties
that include negligible vapor pressure, excellent thermal and
electrochemical stability, good dissolution properties with many
organic and inorganic compounds, and low flammability.
Improved IL performance for these and other applications can
be achieved by tuning the combination of cations and anions
to obtain the desired thermodynamic, solvating, and transport
properties, as well as safety characteristics. For example, it has
been observed that higher charge delocalization15,16 and small
ion size17 often reduces viscosity and improves ion transport,
while the length and nature of substituent groups on IL cations
greatly affect the IL melting temperature (Tm), glass transition
temperature (Tg), and thermal stability. The heat of vaporization,
ion sizes, and cation-anion binding energies also influence ion
transport.18
The use and performance of ILs for many applications is
limited by their transport properties and molecular dynamics,
* Corresponding author. E-mail: Oleg.Borodin@utah.edu.
† Wasatch Molecular Inc.
‡ University of Utah.
§ Universite´ Joseph Fourier.
| Universite´ de Picardie Jules Verne.
10.1021/jp911950q  2010 American Chemical Society
Published on Web 05/03/2010

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6787
Figure 1. Simulated (a) bis(fluorosulfonyl)imide (FSI-) and (b) bis[(trifluoromethyl)sulfonyl]imide (TFSI-) anions and (c) 1-methyl-3-
ethylimidazolium (emim+) and (d) N-methyl-N-propylpyrrolidinium (pyr13+) cations. The coordinate basis for calculation of the rotational relaxation
function are shown.
and pyr1R+ cations as representing a good compromise between
low melting point (below room temperature) and fast transport.
In 2006, we reported ion packing and transport from
molecular dynamics (MD) simulations of [pyr13][TFSI] IL and
[pyr13][TFSI] doped with LiTFSI salt.30,31 Recently, we have
significantly extended that work and developed a transferable
quantum chemistry-based transferable polarizable force field that
allowed us to obtain from MD simulations accurate predictions
of density, heat of vaporization, ion self-diffusion coefficients,
conductivity, and viscosity for a wide range of ILs32–35 and EC:
DMC/LiPF6 liquid electrolyte.36 Unlike previous efforts by
Padua, Canongia Lopes,37–50 Maginn,51–60 and other groups,61–66
we included many-body polarization in the force field and made
consistent efforts in constructing IL force fields that would be
applicable beyond a few compounds of interest. While Yan et
al.67 and Chang et al.68 reported MD simulations of [bmim][NO3]
and dmim+ with Cl-, Br-, and I- using polarizable force fields,
it is not clear if those force fields are transferable. Canongia
Lopes and Padua developed force fields for ILs that covered a
broad set of cations and anions.37–50 While the number of ILs
included in the force field reported by Canongia Lopes and
Padua is impressive and IL density and crystal phase cell
parameters are well reproduced, the ability of this force field to
predict heat of vaporization and transport properties is much
less so. For example, the enthalpy of vaporization for
[Cnmim][TFSI] was found to be approximately 20-40 kJ/mol
higher69 than values obtained from three independent experi-
mental measurements.61 The self-diffusion coefficients obtained
from simulations using Padua’s force field were a factor of 5
smaller than experimental values for [emim][TFSI].61 A sluggish
transport has been found by in simulations by Pica´lek et al.70
of [emim][PF6], [bmim][PF6], and [bmim][BF4] and by Tsuzuki
et al.64 for 13 ILs, while a number of other nonpolarizable force
fields61,65,71–74 predicted ion transport in good agreement with
experiments.
In this manuscript we further validate the ability of our
recently developed polarizable force field to accurately predict
ion transport by comparing simulation predictions to result of
pfg-NMR experiments reported in this contribution for [emim]-
[FSI] and [emim][TFSI]. The pfg-NMR experiments reported
here for [emim][TFSI] extend the range of the previously
reported17 data for this IL to the lower temperature. We compare

6788 J. Phys. Chem. B, Vol. 114, No. 20, 2010
Borodin et al.
the structure factor with the recent X-ray data reported by the
Umebayashi group.23,63,75 The validated simulations will be used
to answer a number of questions about [emim][TFSI], [emim]-
[FSI], [pyr13][TFSI], and [pyr13][FSI] ILs, such as (a) how
different is the TFSI- anion packing around cations from the
FSI- anion packing, (b) why do pyr13+ and TFSI-based ILs have
slower transport in comparison with ILs containing emim+
cation and FSI- anion, and (c) is conformational relaxation of
TFSI- and FSI- coupled to ion translational and rotational
dynamics? Furthermore, we will discuss in detail ion rotational
and translational motion, as well as anisotropy of rotational dy-
namics. The conformational equilibrium of the TFSI- and FSI-
anion in the gas phase will be compared to that in the liquid
phase from our simulations and Raman experiments.23,76–78
The paper is organized as follows. In section II, pulsed-field
gradient spin echo NMR (pfg-NMR) results are reported
focusing on comparison between the temperature dependence
of the ion self-diffusion coefficients in [emim][FSI] and
[emim][TFSI]. MD simulation methodology and the force field
used in our simulations are briefly described in section III.
Results of MD simulations describing thermodynamic, transport
and structural properties of [emim][FSI], [pyr13][FSI], [emim]-
[TFSI], and [pyr13][TFSI] are reported in section IV.
II. Pulsed-Field Gradient NMR Measurements
Figure 2. Self-diffusion coefficient of ions in [emim][FSI] (a) and
[emim][TFSI] (b) from pfg-NMR experiments and MD simulations.
Previous pfg-NMR data by Tokuda et al.17 are also shown in (b). Lines
show the VTF fit to experimental data. (MD data have been corrected
for the finite simulation cell size using eq 3.)
Materials preparation: LiTFSI was used as received from 3
M. KFSI was a special order to Morita and was made according
to the reaction
TABLE 1: Vogel-Fulcher-Tamman Parameters Fitted to
Self-Diffusion Coefficients of IL from pfg-NMR
Experimentsa
FSO2NdCdO + FSO3H ⇒ CO2 + (FSO2)2NH
The acid was distilled and reacted with KHCO3. KFSI was
recrystallized in ethanol. For IL synthesis, emim+(C2H5OSO3)-
was obtained from the reaction of stoichiometic ethyl sulfate
(Fluka) on distilled 1-methyl-imidazole (Aldrich) in CH2Cl2 at
0 °C. This hydrophilic IL was reacted in water with a 10%
excess of either LiTFSI or KFSI, compensating a possible water
uptake for air handling of hygrosdcopic LiTFSI. The denser
phase separating immediately was diluted with CH2Cl2 and
extracted in a separating funnel and washed four times with
water, and the dichloromethane was stripped. The as prepared
ILs where heated at 120 °C under a vacuum and transferred for
handling in a helium-filled drybox (H2O, O2 <1 ppm) and used
to fill ≈1.5 cm deep o.d. 4 mm NMR tubes that were stoppered
with a Torr seal in the drybox, and later flame-sealed with a
H2/O2 torch outside. The same IL samples were measured by
the Karl Fischer technique to be e30 ppm water content.
Pulsed-field gradient NMR (pfg-NMR) experiments were
performed on these [emim][TFSI] and [emim][FSI] using a
homemade spectrometer working at Larmor frequencies in the
interval 30 MHz e ν e 300 MHz and a superconducting coil
giving a direct magnetic field of 6.6 T. The magnetic field
gradient pulses were delivered by a Techron power supply, the
maximum constant current reaching 60 A during 5 ms. Details
of the diffusion coefficient measurements have been given
elsewhere.79 Figure 2 shows the cation and anion self-diffusion
coefficients for [emim][FSI] and [emim][TFSI] obtained from
pfg-NMR measurements as a function of inverse temperature.
Comparison of our self-diffusion coefficient measurements with
previously reported data17 for [emim][TFSI] indicates that at
high temperature our results are slightly lower, while at low
temperatures our results are slightly higher. The temperature
D0 (10-10 m2 s-1
)
B (K)
T0 (K)
[emim][FSI]
91.0
60.54
emim+
FSI-
821
742.3
127.6
133.5
[emim][TFSI]
90.33
72.87
130 ( 40
100 ( 10
emim+
825.0
852.8
140.
141.3
TFSI-
emim+, Tokuda et al.
TFSI, Tokuda et al.
847 ( 119 146 ( 12
903 ( 130 146 ( 13
a Previously published parameters from Tokuda et al.17 are also
given for comparison.
dependence of the self-diffusion coefficients was fit using
Vogel-Fulcher (VF) relationship:
B
D ) D0exp -
(1)
(
)
T - T0
where T is temperature and D0, B, and T0 are fitted parameters
given in Table 1. VF fits for [emim][TFSI] and [emim][FSI]
indicate that D0 and the high temperature activation energies B
are quite similar. This similarity implies that cation motion is
essentially independent of the particular anion at high temper-
ature (T . T0). However, T0 for emim+ is lower by about 10 K
for [emim][FSI] than for [emim][TFSI], indicating the onset of
glassy behavior at lower temperature for the former IL. This
translates into increasingly faster motion of emim+ in [emim]-
[FSI] relative to that in [emim][TFSI] with decreasing temper-
ature, as illustrated in Figure 3. Similar behavior is observed

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6789
TABLE 2: Length of Simulation Production Runs and IL
Properties from MD Simulations and Previously Published
Experiments (in Parentheses)
run length (ns)
ionic liquid
Nion pairs
393 K
333 K
298 K
273 K
[emim][TFSI]
[emim][FSI]
[pyr13][TFSI]
[pyr13][FSI]
150
125
216
216
15.3
16.0
8.6
14.4
16.2
9.3
16.8
18
9.3
18
18
9.7
10.1
10.2
density (kg m-3
)
ionic liquid
393 K
1435
333 K
298 K
273 K
Figure 3. The ratio of the ion self-diffusion coefficients in [emim][FSI]
to that in [emim][TFSI] from pfg-NMR experiments and MD simulations.
[emim][TFSI]
1488
1521 (1522a,
1545
(1487)a
1395
1517b)
(1547)a
1449
[emim][FSI]
[pyr13][TFSI]
1347
1358
1426
1434
1407
(1408-1447)c
1339 (1339)d
when FSI- and TFSI- self-diffusion coefficients are compared,
as shown in Figure 3. However, in contrast to emim+, the high
temperature activation energy for the anion does depend upon
the particular anion, with that for TFSI- being greater than that
for FSI-. Hence, even at temperatures well above the glass
transition temperature, FSI- and TFSI- motions remain different.
[pyr13][FSI]
1266
1308
viscosity (mPa s)
333 K
ionic liquid
393 K
298 K
[emim][TFSI]
[emim][FSI]
[pyr13][TFSI]
[pyr13][FSI]
3.6
3.6
4.8
6.3
10.4
6.7
18.2
18.5
13.3
63.0
III. Simulation Methodology
a Reference 17. b Reference 75. c References 26 and 28.
d Reference 23.
Simulations were performed using an improved version
(f1e24) of the many-body polarizable force field,32,35 that
demonstrated consistently accurate predictions of IL density,
ion self-diffusion coefficients, conductivity, and viscosity.32–34
The crystal structure of four selected ionic crystals was also
accurately predicted32 together with the conductivity of EC:
DMC/LiPF6 liquid electrolytes36 and properties of semifluori-
nated alkanes,80 alkyl nitrate liquids, and PETN energetic
crystal.81 This force field (APPLE&P version f1e) has an
improved transferability and allowed better prediction of ion
transport compared to the previous force field generations
developed by us82–85 that have been used in simulations of
carbonate liquid electrolytes, polymer electrolytes, [pyr13][TFSI],
and [pyr13][TFSI] doped with LiTFSI.82,83,85–88 Main force field
features are briefly described here, while development meth-
odology is outlined in detail elsewhere.32 Molecules were fully
flexible with bending, and a conformational energetics were fit
to quantum chemistry data, while bond lengths were constrained.
Polarization was incorporated via an isotropic atomic dipole
formalism using Thole screening (aT ) 0.2), while the electro-
static potential around molecules is described via permanent
charges located on atoms and off-atom sites. For the TFSI and
FSI- anions, an extended charge (denoted as Lp, Figure 1a) in
the S-N-S plane was included in the modified force field
(f1e24) to provide an improved description of the electrostatic
potential around anions as obtained from quantum chemistry
calculations performed on the MP2/cc-pvTz level. Inclusion of
this charge center in the force field has only a minor effect on
the density and transport properties of ionic liquids reported
here, but it is expected to be important for describing the FSI-
and TFSI- interactions with the lithium cations. Interestingly,
placing two additional force centers at the positions where lone
pairs are expected on the nitrogen atom yielded a less significant
improvement than was found for the single extended charge
located within the S-N-S bend. In the f1e24 version of the
force field the R* (position of the minimum) of the repulsive-
dispersive interactions was reduced by 6% for the F · · ·F pair
in the FSI- anion, while R* for the S · · ·S pair was reduced by
3% from the corresponding parameters in the f1e1 force field
to improve the density description of the ILs. The resulting
densities from MD simulations are compared with experimental
data in Table 2, demonstrating excellent agreement between the
two.
A version of the MD simulation package Lucretius that
includes many-body polarization was used for all MD simula-
tions.89 A three-dimensional, periodic cubic simulation cell
consisted of 125-216 ion pairs as shown in Table 2. The IL
initial configurations were created in the gas phase correspond-
ing to a cell (linear) dimension of approximately 75-90 Å. The
dimensions of the simulation cells were reduced to yield
estimated densities at 393 K followed by 0.8-2 ns NPT run.
The average box sizes from the NPT runs were utilized in the
subsequent NVT production runs. The length of production runs
was always long enough to achieve the diffusive regime in ILs
and is given in Table 2. Additional simulations 4-5 ns long
were performed with the barriers for the anion conformational
transitions increased by 12.5 kJ/mol at 298 K.
The Ewald summation method was used for electrostatic
interactions between partial charges with partial charges and
partial charges with induced dipole moments using k3 from 63
to 83 k-vectors, and R from 8.5 to 12 Å depending on the system
size. The interaction between an induced dipole and a partial
charge separated by 3 bonds was scaled by 0.8, providing an
improved description of the electrostatic potential around the
molecules. Multiple time step integration with an inner time
step of 0.5 fs (bonded interactions), a central time step of 1.5
fs for all nonbonded interactions within a truncation of 7.0 Å
and an outer time step of 3.0 fs for all nonbonded between 7.0
Å and the nonbonded truncation distance of 10.5 or 11 Å as
well as for the reciprocal part of Ewald was employed. A
Nose-Hoover thermostat (NPT and NVT simulations) and a
barostat (NPT simulations) were used to control the temperature
and pressure with the associated frequencies of 10-2 and 0.5 ×
10-3 fs. Induced dipoles were calculated via a direct iteration
with a predictor method. Pressure tensor and virial were
calculated using atom-based with bond (constrained) forces
every 3 fs and saved every 9 fs for viscosity calculation.

6790 J. Phys. Chem. B, Vol. 114, No. 20, 2010
Borodin et al.
self-diffusion coefficients are similar for the corresponding FSI-
and TFSI-based ILs.
D. Conductivity and Correlated Ion Motion. Ionic con-
ductivity can be calculated from MD simulations using the
Einstein relation91
N
e2
λ ) lim λ(t) ) lim
z z ([R (t) -
〈
i j i
∑
tf∞
tf∞
6tVkBT
i,j
R (0)])([R (t) - R (0)]) (3)
〉
i
j
j
Figure 4. Ion self-diffusion coefficients of ILs obtained from MD
simulations (corrected for the finite simulation cell size).
where e is the electron charge, V is the volume of the simulation
box, zi and zj are the charges over ions i and j in electrons, Ri(t)
is the displacement of the ion i during time t, the summation is
performed over all ions N in the simulation cell, 〈 〉 denote the
ensemble average. Here λ(t) is the apparent time-dependent
conductivity whose long-time limit corresponds to the equilib-
rium dc conductivity of an electrolyte. Conductivity can be
decomposed into an “ideal” conductivity that would be realized
if ion motion were uncorrelated, denoted λuncor, and the degree
to which ion motion is in fact uncorrelated, or Rd. The apparent
degree of uncorrelated ion motion Rd(t) is given as the ratio of
the apparent collective (total) charge transport λ(t) to the
apparent charge transport due to self-diffusion only λuncor(t),
hence
IV. Simulation Results
A. Ion Self-Diffusion Coefficients. The self-diffusion coef-
ficient Di for species i was calculated using the Einstein relation,
by fitting the slope on the mean-square displacement MSD(t)
in the linear diffusive regime and dividing by six. The MSD(t)
and a + btꢀ local fits to the MSD(t) for [emim][FSI] and
[pyr13][FSI] are shown in Supporting Information. These MSD(t)
and the local a + btꢀ fits to the MSD(t) segments (a, b, and ꢀ
are fit parameters) indicate that at 298 K the subdiffusive regime
(ꢀ < 1) extends up to ∼0.8 ns for [pyr13][FSI] and 0.3 ns for
[emim][FSI].
Due to the finite size of the simulation cell, long-range
hydrodynamic interactions restrict diffusion.90 The leading order
finite size correction (FSC) to the self-diffusion coefficient
(∆DFSC) was found to be inversely proportional to the simulation
box and is given by90
N
e2
λuncor ) lim λuncor(t) ) lim
z 2 [R (t) -
〈
∑
i
i
tf∞
tf∞
6tVkBT
i
e2
VkBT
R (0)]2
)
(n+Da+pp + n-Da-pp
)
(4)
(5)
〉
i
2.837kBT
∆DFSC
)
(2)
6πηL
λ
λ(t)
λuncor(t)
Rd )
) lim Rd(t) ) lim
tf∞ tf∞
λuncor
where L is a linear dimension of the cubic simulation periodic
cell, T is temperature, and η is viscosity. We utilized viscosity
from MD simulations shown in Table 2 for calculating ∆DFSC
when possible. Viscosity was extracted using the Einstein
relation, as described in our previous work.32 At low temper-
atures where the viscosity value from MD simulations was not
available due to insufficient run length, the FSC correction from
the high temperature was used. The finite size correction was
10-21% for the simulated ILs depending on the system size.
Figure 2 shows the finite size corrected self-diffusion coef-
ficients from MD simulations are in excellent agreement with
pfg-NMR data for [emim][FSI] and [emim][TFSI]. MD simula-
tions also correctly predict that the cation is diffusing slightly
faster than the anion for [emim][FSI] and noticeably faster for
[emim][TFSI] IL. Figure 3 shows that MD simulations ad-
equately describe the enhancement of the ion diffusion coef-
ficients in [emim][FSI] relative to the cation and anion diffusion
coefficients in [emim][TFSI]. Consistent with experiments, we
observed that the anion diffusion coefficient is largely respon-
sible for the faster ion transport in [emim][FSI] compared to
that in [emim][TFSI].
Here ni is the number of ions of type i. A degree of ion
uncorrelated motion Rd(t) ) 1 corresponds to completely
uncorrelated ion motion, while Rd(t) ) 0 if all of the cations
only move together with anions (which corresponds to λ ) 0,
i.e., zero ionic conductivity). Determining the long-time limit
of λ(t) using eq 3 is problematic because of poor statistics in
the diffusive regime. Instead, we determine the IL conductivity
as a product of λuncor derived from self-diffusion coefficients
using eq 4 and Rd extracted from the sub diffusive regime but
with good statistics. An example of Rd(t) for [emim][FSI] IL is
shown in Supporting Information, Figure S3. We observe an
initial increase of the Rd value followed by the plateau indicating
degrease of ion correlation with time as ions escape the cages.
Our experience indicates that Rd(t) results are accurate only up
to the times approximately 2-5% of the total simulation run,
consistent with similar claims for extracting viscosity from MD
simulations;92 therefore we extracted Rd value from the plateau
of Rd(t) in the region of 100-200 ps. The Rd values for simulated
ILs are in the region of 0.55-0.75. Similar values of Rd(0.52-0.78)
have been reported from the coordinated pfg-NMR and conduc-
tivity measurements16,17,93 of [emim][TFSI], [bmim][PF6], [bmim]-
[BF4], [bmim][TFSI], [bmim][CF3SO3], [C6mim][TFSI], [pyr14]-
[TFSI], [N1114][TFSI], and simulations.70 Nicotera et al.28 also
reported unusually low value Rd of 0.28 for [pyr13][TFSI] at
333 K, while MD simulations predict Rd of 0.63 at 333 K, which
is in line with the Rd ) 0.7 experimentally found by Tokuda et
al.93 for [pyr14][TFSI].
Figure 4 compares ion self-diffusion coefficients for all for
simulated ILs. Ion self-diffusion coefficients roughly follow the
order [emim][FSI] > [emim][TFSI] > [pyr13][FSI] > [pyr13]-
[TFSI]. In contrast to a significantly faster anion dynamics in
[emim][FSI] than in [emim][TFSI], the difference between the
ion diffusion coefficients in [pyr13][TFSI] and [pyr13][FSI] is
less pronounced. Replacing the TFSI- with FSI- results in a
significant enhancement of the anion diffusion, while the cation

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6791
Figure 6. Distribution of conformational populations for FSI- and
TFSI- anions around F-S· · ·S-F and C-S· · ·S-C dihedrals for ILs
at 298 K.
Figure 5. Conductivity of ILs obtained from MD simulations and the
following experiments: [pyr13][FSI] from Zhou et al.;22 [pyr13][TFSI]
from Nicotera et al.;28 [emim][FSI] from Guerfi et al.24 (black filled
circle), Kikuta et al.94 (yellow filled circle), and Matsumoto et al.19
(semifilled circle); [emim][TFSI] from Tokuda et al.17
TABLE 3: Apparent Activation Energy (in kJ/mol) for IL
Transport Properties: Diffusion (Ediff), Conformational
Relaxation Measured via Torsional ACF (Etor), and the
Trans Conformer Populations for Anions (Etrans
)
The resulting ionic conductivities from MD simulations are
compared with experiments17,19,22,24,28,94 in Figure 5. At room
temperature an excellent agreement between experimental and
simulation conductivity has been observed for all simulated ILs.
The predicted [emim][FSI] conductivity agrees perfectly with
the experimental data by Guerfi et al.,24 which is slightly higher
than the values reported by Kikuta et al.94 and Matsumoto et
al.19 MD simulations also predicted the temperature dependence
of [emim][TFSI], [pyr13][FSI], and [emim][FSI] in good agree-
ment with experiments.17,22,94 The temperature dependence of
[pyr13][TFSI] from experiments differs from that observed in
MD simulations; however, we previously reported an excellent
prediction of the temperature dependence of ion conductivity
and self-diffusion coefficients for the closely related
[pyr14][TFSI], giving us additional confidence in the accuracy
of our predictions for [pyr13][TFSI]. It is probably that the
unusually low Rd of 0.28 for [pyr13][TFSI] reported by Nicoreta
et al.28 stems from the low experimental conductivity of
[pyr13][TFSI] at 333 K shown in Figure 5. Further examination
of Figure 5 indicates that conductivity of ILs are ordered as
follows at room temperature: [emim][FSI] > [emim][TFSI] >
[pyr13][FSI] > [pyr13][TFSI]. While the ordering of conductivities
is similar to the ordering of the ion self-diffusion coefficients
shown in Figure 4, the enhancement of conductivity upon
replacing TFSI- and FSI- is more pronounced than the effect
observed for the ion self-diffusion coefficients because the
smaller size of the FSI- anion compared to that for TFSI- results
in a higher ion number density leading to an additional
enhancement of the conductivity for the FSI-based ILs. Lower
activation energy is seen for [emim][FSI] than for [emim][TFSI],
and [pyr13][FSI] than for [pyr13][TFSI], which is consistent with
the analysis of the temperature dependence of ion self-diffusion
coefficients presented in Figures 3 and 4.
Ediff
Etor
Etrans
D+
D-
τtor
anion
[emim][FSI]
[emim][TFSI]
[pyr13][FSI]
[pyr13][TFSI]
17.8
19.8
23.5
24.8
17.6
21.7
21.8
26.7
16.8
21.4
17.8
22.8
2.1
2.1
2.4
3.3
indicates that the TFSI- and FSI- conformational populations
are the same for the emim+-containing IL and pyr13+-containing
ILs. Moreover, the anion conformational populations were found
to be similar in the gas phase and liquid phases. However, we
observed a significantly higher peak for the FSI- trans conformer
at 150° than for the cis conformer at 0°, while Canongia Lopes
et al.50 have reported a similar magnitude for those peaks.
Similarly, the peak for the TFSI- trans conformer is about a
factor of 3 larger than the peak for the cis conformer located
around 40°, while in Canongia Lopes et al.37 simulations the
difference was less than 1.5 for [pyr14][FSI] at 298 K. The trans
populations were calculated by integrating distributions from
90° to 180° for FSI-based ILs and from 130° to 180° for the
TFSI-based ILs. We obtained for following populations of trans
conformers at 298 K: 0.643 for [emim][FSI], 0.632 for
[pyr13][FSI], 0.565 for [emim][TFSI], and 0.468 for
[pyr13][TFSI]. These conformational populations are in agree-
ment with the analysis of Raman measurements for
[pyr13][TFSI],96 [pyr13][FSI],23 and [emim][TFSI]23 that indicated
that a similar fraction of cis and trans conformers were found
in these ILs near room temperature. In agreement with analysis
of Raman experiments,23,96 MD simulations predict that the
fraction of trans conformers increases with decreasing temper-
ature. The activation energies were calculated for the trans
conformational populations by fitting populations vs inverse
temperature to the Arrhenius behavior and are given in Table
3. These activation energies are in agreement with the fits to
Raman measurements for [pyr13][TFSI],96 [pyr13][FSI],23 and
[emim][TFSI].23
C. Conformational Populations and Dynamics. The TFSI-
and FSI- anions have two low energy conformations gg and
g+g-,75 where conformations are given around the F-S-N-S
and CF3-S-N-S dihedral angles. These conformers are also
referred to as trans and cis conformations around F-S· · ·S-F
and C-S· · ·S-C dihedrals for FSI- and TFSI- anions, respec-
tively. The trans conformer is more stable than the cis conformer
by about 1 kcal/mol (4.184 kJ/mol) for both TFSI- and FSI-
anions according to quantum chemistry calculations32,50,95 and
analysis of Raman spectra.76,95 The distribution of TFSI- and
FSI- conformational populations in ILs from MD simulations
is shown in Figure 6. The FSI- and TFSI- anion conformational
populations indicate a significant difference between each other,
which is consistent with previous reports.38,50 Figure 6 also
We have monitored the dynamics of anion conformational
transitions via torsional autocorrelation function (ACF) given
by eq 6.
2
〈
〉
〈
〉
cos(ꢁ(t)) cos(ꢁ(0)) - cos(ꢁ(0))
PACF(t) )
(6)
2
2
〈
〉
〈
〉
cos (ꢁ(t)) - cos(ꢁ(0))
where φ(t) is the O-S-N-S dihedral angle, t is time, and the
brackets denote an ensemble and time average over all dihedrals.

6792 J. Phys. Chem. B, Vol. 114, No. 20, 2010
Borodin et al.
The torsional ACFs were fit with Kohlrausch-Williams-Watts
(KWW) stretched expontial functions for PACF(t) > 0.01 given
by eq 7
weak, between the TFSI- conformational relaxation, ion dif-
fusion and matrix relaxation.
E. Rotational Relaxation. We investigated the rotational
motion of ion by examining the motion of the three vectors
shown in Figure 1. P1(t) rotational ACF of the vectors are given
by
ꢀ
t
PKWW(t) ) A exp -
(7)
(
)
[
]
τKWW
P1(t) ) 〈be(t)·be(0)〉
(8)
where ꢀ determines the degree of stretching characterizing the
broadness of the relaxation process, and the Α prefactor allows
us to account for decay that occurs in a time span significantly
faster than our minimum data collection rate of 1 ps-1. A is
typically 0.95-1.0. The stretched exponential fits yielded the
degree of the relaxation process broadness ꢀ of 0.9 for the FSI-
anion in [emim][FSI] and [pyr13][FSI], while ꢀ for the TFSI-
anion was around 0.6 for [emim][TFSI] and [pyr13][TFSI],
indicating a much broader relaxation spectrum for the latter.
The torsional relaxation times were calculates as integrals of
PKWW(t) fits from zero to infinity. The apparent activation
energies for the torsional relaxation times (Etor) were calculated
and are compared in Table 3 with the apparent activation energy
for the average self-diffusion coefficients. The activation energy
and absolute values for torsional relaxation time for the FSI-
anion in [emim][FSI] and [pyr13][FSI] are essentially identical
despite a significant difference observed between the ion self-
diffusion coefficients in these two ILs. While the activation
energy for torsional relaxation of FSI- is only slightly less than
the activation energy for the anion self-diffusion coefficient for
[emim][FSI], a significantly smaller activation energy for the
torsional relaxation Etor compared to the activation energy for
diffusion was observed for [pyr13][FSI], suggesting a decoupling
between the FSI- conformational relaxation and diffusion. A
large ꢀ-broadness parameter of 0.91-0.94 for the stretched
exponent fit is also consistent with decoupling of torsional
relaxation from the matrix relaxation. For example, a high
ꢀ-broadness parameter and low activation energy for the
torsional relaxation time was found for isolated polyethylene
chains compared to the case for the polyethylene melt.97 Unlike
the FSI- anion conformational relaxation, the TFSI- anion
conformational relaxation is characterized by a ꢀ-broadness
parameter of 0.6-0.65, indicative of the TFSI- conformational
relaxation coupled to the matrix relaxation.
where be(t)is a unit vector corresponding to one of the three
vectors shown in Figure 1. Decay of the P1(t) autocorrelation
functions to 0.01 obtained from MD simulations was ap-
proximated by a stretched exponential expression given by
eq 7.
Rotational autocorrelation times τ1 were calculated as the time
integrals of the KWW fits to P1(t) from zero to infinity. The τ1
autocorrelation times are shown in Figure 7 as a function of
inverse temperature. Rotation of the emim+ x-axis, pyr13+ y-axis,
and FSI- and TFSI- x-axis are the slowest as the molecules
are the longest in these directions, as roughly indicated by
components of the mean-square radii of gyration for emim+
+
(3.24, 0.80, 0.274 Å), pyr13 (0.87, 3.06, 1.17 Å), FSI- (2.59,
0.51, 0.61 Å), and TFSI- (3.83, 0.85, 1.76 Å) ions. Replacement
of the TFSI- anion with FSI- only slightly increases rotation
relaxation of catons, while rotational relaxation of the FSI- anion
is much faster than that of the TFSI- anion in accord with the
trends observed for the self-diffusion coefficients. The apparent
activation energies for the rotational relaxation time were
calculated from Arrhenius fits to τ1 autocorrelation times and
were found to be similar (within 3 kJ/mol) to the apparent
activation energies for the ion self-diffusion coefficients shown
in Table 3.
Further comparison between temperature dependence of the
rotational and translational relaxations was achieved by inves-
tigation of the product of the ion self-diffusion coefficient and
rotational relaxation time (τRD) shown in Figure 8 as a function
of temperature. All plots were scaled to bring them to 1.0 at
393 K. If the product of τRD does not change with temperature,
it indicates that the translational and rotational relaxation have
the same temperature dependence. A decrease of the (τRD)
product with decreasing temperature indicates that the ion self-
diffusion coefficient decreases faster than the rotational relax-
ation time increases with temperature decrease. We observe that
for all ILs the (τRD) product slightly decreases with decreasing
temperature, thus indicating that the ion rotational relaxation
has a slightly weaker temperature dependence that the transla-
tional relaxation, but the effect is not large. The smallest
deviation of the product from unity was observed for the emim+
cation in [emim][FSI] followed by the emim+ cation in
[emim][TFSI], while the largest deviation from unity was
observed for the y-axis (see Figure 1) of TFSI. Thus, the fastest
rotation of the TFSI- anion shows the largest decoupling from
the translational ion relaxation.
To confirm our supposition about decoupling of the FSI-
anion conformation relaxation from ion diffusion and understand
the extent to which TFSI- conformational dynamics is coupled
to ion diffusion, we have performed MD simulations of
[emim][FSI], [pyr13][FSI], [emim][FSI], and [pyr13][TFSI] ILs
with the FSI- and TFSI- conformation relaxation slowed down
by approximately a factor of 100-200. This was achieved by
increasing the barriers for conformational transitions by 12.5
kJ/mol, without influencing the relative conformational energies
of the trans and cis conformers of anions. In [emim][FSI] with
the increased FSI- barriers the estimated O-S-N-S dihedral
relaxation time increased from 0.145 ns to ∼18 ns, allowing
FSI to diffuse 680 Å2 during this time, indicating that anions
diffuse long distances without undergoing conformational
relaxation and, therefore, could be considered as rigid anions.
We found that the cation and anion self-diffusion coefficients
of [emim][FSI] and [pyr13][TFSI] remained unchanged when
the FSI- anion conformational relaxation was significantly
retarded, thus confirming that the FSI- conformational relaxation
is indeed decoupled from the ion translational motion. Slowing
down the TFSI- conformational relaxation, on the other hand,
resulted in a slowing down of the ion diffusion in [emim][TFSI]
and [pyr13][TFSI] by 40-50%, thus confirming coupling, albeit
F. Structural Properties. Structure factor was calculated
using eq 9 for ILs,
S(k) ) 1 +
rc
sin(rk)
rk
x x f (k) f (k)4π
(gRꢀ(r) - 1)r2
dr
∫
∑
R
ꢀ R
ꢀ
0
Rꢀ
(9)
(
x f (k))2
∑
R R
R

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6793
Figure 7. Rotational relaxation times of IL from MD simulations. Arrows point to the same cation and anion rotational modes in the FSI-based
ILs (open symbols) and TFSI-based ILs (filled symbols).
the magnitude of the second peak also increases upon replacing
emim+ with pyr13+. To understand which ion correlations
contribute to the first and second peaks, the cation-cation,
anion-anion, and cation-cation contributions to the IL structure
factor were calculated and are shown in Figure 10. The
cation-cation and anion-anion correlations contribute to the
first S(k) peak, while the cation-anion correlations make a large
negative contribution to the first peak. The cation-anion
correlations make the most significant contribution to the second
S(k) peak shown in Figure 10, while for [emim][FSI] and
[pyr13][FSI] the FSI-FSI correlations also contribute to the
second peak around 1.2 Å-1
.
The neutron weighted structure factors were calculated for
ILs by assuming complete deuteration of cations and are
compared with the X-ray weighted S(k) in Figure 11. A
significant difference between the X-ray and neutron S(k) were
observed, particularly for the FSI- anion-containing ILs. For
pyr13+-containing ILs the magnitude of the first peak is larger
for the neutron S(k) than for the X-ray S(k), while the opposite
behavior was observed for the second peak. We associate this
difference between the neutron and X-ray S(k) with the
significantly larger contribution of sulfur to the X-ray S(k) than
to the neutron weighted S(k). In fact, making sulfur form factor
f(k) zero reduces the [pyr13][FSI] second X-ray weighted S(k)
peak by a factor of 3. On the other hand, setting the neutron
scattering length of sulfur to zero essentially does not change
the second peak while slightly increasing the first peak.
Examination of the [emim][TFSI] and [emim][FSI] S(k) indi-
cates that the magnitudes of the first peak for the neutron S(k)
is smaller than the magnitudes for the X-ray S(k).
Figure 8. Product of the rotational relaxation time and the ion self-
We continue comparison of structure in the four ILs by
analyzing the center of mass radial distribution functions (RDFs)
shown in Figure 12. We found very little difference for RDFs
calculated from simulations with 216 and 100 ion pairs for
[pyr13][TFSI], indicating that artifacts due to the finite simulation
box are not expected to occur for the investigated box sizes.
The cation-cation center of mass RDF shows a higher first peak
for the FSI-based ILs compared to that for TFSI-based ILs, while
the magnitude of the first anion-cation peak is similar to those
for the FSI-based and TFSI-based ILs. The magnitude of the
first anion-cation peak is larger for the pyr13+-based ILs than
for the emim+-based ILs, suggesting a stronger structuring of
the anion-cation in the pyr13+-based ILs than in the emim+-
based ILs. The TFSI-TFSI-RDF first peak is consistently higher
than the FSI-FSI- one, while the FSI- anions exhibit closer
approaches to each other than the TFSI- anions due to the
smaller size of the FSI- anion. The smaller size of the FSI-
diffusion coefficients.
where xR and xꢀ are the fractions of atoms of type R and ꢀ,
gRꢀ(r) is the radial distribution function (RDF) for R and ꢀ atom
types, k is the wave vector, fR(k) is the form factor for species
R, and rc is the cutoff for integration equal to half of the
simulations box. Parts a and b of Figure 9 show the structure
factor for ILs calculated from MD simulations and X-ray
diffraction measurements. An excellent agreement between
simulation predictions and X-ray measurements has been
observed for [emim][TFSI], [pyr13][FSI], and [pyr14][TFSI],
further demonstrating the ability of the developed force fields
to accurately capture the ionic liquid structure, including the
presence of two peaks in the low k value region (0.8-1.4 Å-1).
A more detailed examination of Figure 9b indicates that
replacement of TFSI- with FSI- results in a significant increase
of the second peak for both emim+- and pyr13+-based ILs, while

6794 J. Phys. Chem. B, Vol. 114, No. 20, 2010
Borodin et al.
Figure 9. X-ray weighted structure factor S(k) at 298 K from MD simulations and experiments.23,63,75
Figure 11. Neutron (deuterated) and X-ray weighted structure factors
S(k) for ILs at 298 K calculated from MD simulations.
magnitude of the first peak for the O-H RDF for [emim][TFSI]
compared to that for [emim][FSI] the coordination number of
oxygen atoms from FSI- and TFSI- anions near emim+ ring
hydrogen atoms is essentially the same: at 3.3 Å cutoff, 1.2
anion oxygen atoms are coordinating H(C4) and H(C5) hydro-
gens, and 1.7 anion oxygen atoms are coordinating H(C2)
hydrogen.
Figure 10. Cation-cation, anion-anion, and cation-anion contribu-
tions to the X-ray weighted structure factor S(k) at 298 K from MD
simulations.
anion is consistent with the shift of the S(k) first and second
peak positions to higher wave vectors, as shown in Figure 9.
The RDFs for the oxygen atom of FSI- and TFSI- with the
emim+ ring hydrogen are shown in Figure 13. The positions of
the first peak are similar for [emim][TFSI] and [emim][FSI],
whereas the magnitude of the first peak is larger for the
[emim][TFSI] than for the [emim][FSI]. Despite the larger
The 3D distributions of anion oxygen atoms are shown in
Figure 14. The isosurfaces for the TFSI- oxygen atoms have
been scaled by the ratio of the number densities of [emim][FSI]/
[emim][TFSI] and [pyr13][FSI]/[pyr13][TFSI] to reflect the
coordination number of the oxygen atoms. Figure 14 clearly
shows that the FSI- and TFSI- anion oxygen atoms pack
(coordinate) in a very similar way around emim+ and pyr13
+

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6795
Figure 14. Isosurface of O atom of FSI- (blue solid surface) and TFSI-
(red wirefarme) anions around emim+ and pyr13+ at 298 K for F/Frandom
) 5 (volume distribution function yielding 5 times the bulk average
oxygen atom density) for [emim][FSI] and [pyr13][FSI]. For the TFSI-
based IL, F/Frandom ) 6.2 for [emim][TFSI] and F/Frandom ) 6.07 for
[pyr13][TFSI] were used to correct for the difference in bulk oxygen
density in the FSI- and TFSI-based ILs.
Figure 12. Center of mass radial distribution functions from MD
simulations at 298 K.
Figure 13. Radial distribution functions for [emim][FSI] and [emim]-
[TFSI] from MD simulations at 298 K.
cations; specifically, not only the locations of the anion oxygen
atoms around cations are the same but also the magnitudes of
the scaled isosurfaces are indicative of the same coordination
numbers.
Next we consider the relation between ion packing in the
crystal phase to that in the liquid. While the most detailed
information of the ion packing is typically obtained from X-ray
diffraction measurements in the crystal phase, most IL liquids
are utilized in the liquid phase that is more challenging to
characterize experimentally at the same level of detail. MD
simulations allow a detailed characterization of the structure in
both the crystal and liquid phases. Here we utilize our
simulations to understand differences in the crystal and liquid
state ion packing. Figure 15 shows the position of anion oxygen
atoms in the crystal phase from our previous simulations32 as a
red wireframe and their positions in the liquid as green
isosurfaces. While there is some overlap between the oxygen
Figure 15. Positions of the TFSI- anion oxygen atoms around emim+
and pyr13 cations from MD simulations of [emim][TFSI] and
[pyr13][TFSI] in the liquid (green isosurface F/Frandom ) 5) and the crystal
(red isosurface F/Frandom ) 5). The most probable positions of TFSI-
anion oxygen atoms from X-ray experiments for [pyr13][TFSI] are
shown in blue.98
+
positions in the crystal phase and in the liquid, little resemblance
is found between the anion packing in the crystal and liquid
phases; thus, X-ray crystal data should be used with caution
for gleaning the insight into ion packing in the liquid phase.

6796 J. Phys. Chem. B, Vol. 114, No. 20, 2010
Borodin et al.
TABLE 4: Ionic Liquid Structural and Thermodynamic
Properties (Definitions in Text)
GOmax(r) Hvap (kJ/mol) E( (kJ/mol) Vm (nm-3
)
[emim][TFSI]
[emim][FSI]
[pyr13][TFSI]
[pyr13][FSI]
15.3
11.7
35.2
25.5
123.9
134.6
137.3
143.9
342.9
330.7
334.2
326.5
0.427
0.339
0.473
0.382
G. Relation between Ion Transport with Thermodynamic
Properties and Ionic Liquid Structure. Self-diffusion coef-
ficients are different by a factor of 5 between four ILs
considered. What accounts for such a difference of the self-
diffusion coefficient for emim+-based vs pyr13+-based IL or for
TFSI- and FSI--based ILs? Four parameters that can potentially
influence ion self-diffusion are (a) ion size, (b) cation-anion
binding energy, (c) enthalpy of vaporization, and (d) packing
of ions in IL. Analysis of the 3-D distributions shown in Figure
14 shows that the anion oxygen atoms are located in the four
well-separated zones around pyr13+, while only three discon-
nected locations of the anion oxygen atoms are observed around
emim+. Moreover, a large connected zone (domain) of anion
oxygens around the C2 carbon of emim+ indicates that the anion
can easily explore a large area without significant free energy
Figure 16. Correlation between the ion average self-diffusion coef-
ficient (D) multiplied by the volume of the ion pair vs the enthalpy of
vaporization (Hvap) plus the cation-anion binding energy (E() at 298
K: (1) [emim][TFSI]; (2) [emim][FSI]; (3) [pyr13][TFSI]; (4) [pyr13]-
[FSI].
V. Conclusions
The pfg-NMR measurements have been performed over a
wide temperature range on [emim][TFSI] and [emim][FSI] ILs
focusing on the influence of anion on the ion dynamics.
Replacing the TFSI- anion in [emim][TFSI] IL with FSI-
resulted in a much faster diffusion of the anion in [emim][FSI]
compared to that in [emim][TFSI], while the emim+ cation
dynamics increased to a much smaller extent. Because of a lower
apparent activation energy for the temperature dependence of
the ion self-diffusion coefficients in [emim][FSI] compared to
those in [emim][TFSI], the ratio of the ion diffusion coefficients
in [emim][TFSI] to those in [emim][FSI] increases with
decreasing temperature.
+
barriers, while for an anion to relax (move) around pyr13 it
should jump from one domain to another via the region with a
low probability. A significantly larger first peak of the
cation-anion RDF shown in Figure 13 for the pyr13+-based ILs
compared to that for the emim+-based ILs also indicates a
stronger free energy for the cation-anion interaction in a liquid
for the former. The maximum of the 3-D distribution function
of the anion oxygen atom (denoted as GOmax in Table 4) is also
significantly larger for pyr13+-based ILs than for emim+-based
MD simulations were performed on [emim][TFSI], [emim]-
[FSI], [pyr13][TFSI], and [pyr13][FSI] ILs. An excellent agree-
ment was obtained between the ion self-diffusion coefficients
of [emim][FSI] and [pyr13][TFSI] extracted from MD simula-
tions with the measured values from pfg-NMR experiments and
available conductivity data. The X-ray structure factor for
[emim][TFSI], [pyr13][FSI], and [pyr14][TFSI] from MD simula-
tions agreed well with results of X-ray diffraction measurements.
+
ILs, further indicating stronger anion coordination around pyr13
than around emim+. A comparison of GOmax for [emim][TFSI]
with [emim][FSI] and [pyr13][TFSI] with [pyr13][FSI] yields the
ratios of GOmax[emim][FSI]/GOmax[emim][TFSI] ) 0.76 and
GOmax[pyr13][FSI]/GOmax[pyr13][TFSI] ) 0.72. However, after
correction for the difference of the oxygen atom number density
in TFSI- and FSI-based ILs, these ratios become 0.95 and 0.87,
indicating that the coordinations of cations by TFSI- and FSI-
are similar, which is in accord with the above discussion and
3-D distributions shown in Figure 14. We conclude that the
ion packing considerations cannot explain faster dynamics in
[emim][FSI] compared to those in [emim][TFSI]. A smaller size
of the FSI- anion than for the TFSI- anion (see Table 4),
however, is most likely a reason behind the faster transport in
[emim][FSI] than in [emim][TFSI], as the smaller size of the
The pyr13 and emim+ cation coordination by TFSI- anions
+
closely resembled the cation coordination by FSI- anions. The
anion coordination around cations in the liquid phase was
significantly different from the ion packing observed in the
crystal phase.
A smaller size of the FSI- anion compared to that of the
TFSI- anion and a lower cation-anion binding energy were
responsible for the faster transport in [emim][FSI] than in
[emim][TFSI]. The smaller size of the emim+ cation compared
emim+ cation compared to that of the pyr13 cation is also
+
consistent with the faster transport in emim+-based ILs com-
pared to that in pyr13+-based ILs.
+
to that of the pyr13 cation, the lower heat of vaporization of
emim+-based IL compared to those of pyr13+-based ILs, and
the way the anion is distributed around the cations were
suggested as the three primary reasons why ion transport in
emim+-based ILs is faster compared to that in pyr13+-based ILs.
Analysis of the ion transport indicated that the FSI- confor-
mational relaxation was found to be decoupled from the ion
translational motion, while the TFSI- conformation dynamics
showed some coupling with the ion transport. A slowing down
of the TFSI- conformational motion by 2 orders of magnitude
reduced ion transport only by 40-50%.
In our recent work we investigated a number of correlations
between the heat of vaporization Hvap, cation-anion binding
energy (E(), ion sizes expressed through molar volumes (Vm),
and the self-diffusion coefficient (D) for 29 ionic liquids. A
significant correlation between D and Hvap has been found, while
the best correlation was found for -log((DVm)) vs Hvap
+
0.28E(, where the term Hvap + 0.28E( serves as a measure of
the effective cohesive energy for ionic liquids. Table 4 suggests
that diffusion trends for the FSI- and TFSI-based ILs cannot
be correlated with Hvap; however, we found that Hvap + E(
correlates well with (DVm), as shown in Figure 15, suggesting
that the faster diffusion in [emim][FSI] than in [emim][TFSI]
could be attributed to the lower cation/anion binding energy
and smaller size of FSI- compared to those for TFSI-.
Acknowledgment. We are grateful for financial support of
this work by Air Force Office of Scientific Research, Department
of the Air Force, contract number FA9550-09-C-0110 to
Wasatch Molecular Inc. and the Department of Energy under

FSI- and TFSI-Based Ionic Liquids
J. Phys. Chem. B, Vol. 114, No. 20, 2010 6797
(33) Borodin, O.; Smith, G. D.; Kim, H. J. Phys. Chem. B 2009, 113,
4771–4774.
Contract Nos. DE-SC0001912 and DE-AC02-05CH11231 on
PO No. 6838611 to University of Utah. Opinions, interpreta-
tions, conclusions, and recommendations are those of the authors
and are not necessarily endorsed by the United States Air Force
and DOE. An allocation of computer time from the Center for
High Performance Computing at the University of Utah is
gratefully acknowledged. We also would like to thank John Kerr
and Wesley Henderson for numerous stimulating discussions.
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Supporting Information Available: Apparent degree of ion
uncorrelated motion, mean-square displacements, and their fits.
This material is available free of charge via the Internet at http://
pubs.acs.org.
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