2944 J. Phys. Chem. B, Vol. 109, No. 7, 2005
Saito et al.
-
-
from the anion (IH(anion), IF(anion)) of RMIm(HF)2.3F exhibited
c (a + b + c ) 1) for (HF)3F , (HF)2F , and HF, respectively,
2
an exponential decay with δ , indicating random walk migration
as
of the species in the molten salts.11 Therefore, apparent diffusion
coefficients DH(cation), DH(anion), and DF(anion) were estimated from
the slope of log plots of IH(cation), IH(anion), and IF(anion), respec-
3
a
2b
DH(anion)
)
)
D
(HF)3F-
+
+
D
(HF)2F-
+
3
a + 2b + c
3a + 2b + c
2
2
2
2 15
c
tively, against γ g δ (4∆ - δ)/π . Figure 1 shows the
DHF
temperature dependence of apparent diffusion coefficients
3a + 2b + c
(DH(cation), DH(anion), DF(anion)) of the cation and anion species of
4
a
3b
EMIm(HF)2.3F, BMIm(HF)2.3F, and HMIm(HF)2.3F molten salts.
These results demonstrate several characteristic features. One
is that, in each salt, activation energies (Ea) of diffusion
estimated from the slopes are almost the same independent of
the cation, anion, and probed nuclei. This indicates that the
carrier migration mechanism is essentially the same between
the cation and anion of RMIm(HF)2.3F. Cation and anion species
would migrate randomly by colliding and exchanging positions
with each other. This result explicitly rules out the possibility
of another peculiar migration mechanism such as proton hopping
DF(anion)
D
(HF)3F-
D
(HF)2F-
+
4
a + 3b + c
4a + 3b + c
c
DHF (4)
4a + 3b + c
As a result,
DH(anion) - DF(anion) ∝ a(b - c)D
(HF)3F-
- b(a + c)D
(HF)2F-
+
c(a + b)DHF (5)
1
6
Considering the atomic fraction of H:F ) 2.3:3.3, which was
confirmed by the chemical analyses for this type of salt, 0 e a
e 0.3, 0 e b e 0.77, 0 e c e 0.23 (10/13 e a + b e 1) are
held simultaneously. The contribution of DHF, which is expected
to be larger than D(HF) F , leads to DH(anion) > DF(anion) consistent
with the observed results in Figure 1. IR spectroscopy did not
give the evidence of HF except for two independent species,
HF)2F and (HF)3F . Furthermore, this kind of salt is chemi-
represented by Grotthus proton transfer among anion species.
The larger value of DH(anion) or DF(anion) compared with DH(cation)
for all salts reflects the greater size of the cation than that of
the anion. That is, the smaller the size of the species, the faster
it could migrate according to the Stokes-Einstein relation when
-
2
weight and charge densities are constant.1
7,18
It is also anomalous
that DH(anion) and DF(anion) did not necessarily agree with each
other because the observed diffusion coefficient should be
independent of the probed nucleus if the observed species are
identical. This result is consistent with the observation of the
-
-
(
cally stable without any volatility and corrosive action to glass.
These results indicate that the lifetime (probability of existence)
of HF, corresponding to the pre-factor of DHF in eq 4, is too
small to be confirmed in the IR spectra which represent the
equilibrium state, but the inherent diffusion coefficient, DHF, is
fairly large enough to affect the observed diffusion values under
the condition of DH(anion) > DF(anion).
-
-
IR spectra that (HF)2F and (HF)3F coexist as the anion species
5
in the salts. The difference in the composition ratio of H to F
-
-
between (HF)2F (2:3) and (HF)3F (3:4) and the fast exchange
between the two species through HF resulted in independent
observed values of DH(anion) and DF(anion). Taking into account
the order of magnitude of the inherent diffusion coefficient,
2
. Interpretation of Ionic State Based on the Dissociation
Degree of the Salt. a. Validity of the HaVen Ratio (Λimp/ΛNMR)
for EValuation of the Dissociation Degree of the Salt. Table 1
lists electrical conductivity, viscosity, and observed and esti-
mated diffusion coefficients of each ionic species and several
physical parameters of RMIm(HF)2.3F at 25 °C. With increasing
molecular weight of the salt caused by extension of the side
chain of the cation, Λimp and Dtotal decreased almost monotoni-
cally although the reverse order was observed between DMIm-
-
-
D(HF) F > D(HF) F , that is expected from the order of the anion
2
3
size, r(HF)2F- < r(HF) F , the observed DF(anion) should be larger
-
3
than DH(anion) on the assumption of that only the two species,
-
-
(
HF)2F and (HF)3F , contribute to the observed diffusion
values. This is because DH(anion) and DF(anion), under the situation
of two anion species coexisting, can be represented explicitly
as
(
HF)2.3F and EMIm(HF)2.3F. This general feature is attributed
3
a
2b
3a + 2b
DH(anion)
)
)
D
(HF)3F-
+
+
D
(HF)2F-
(HF)2F-
to the fact that an increase in cation size leads to the viscosity
increase of the molten salts.
The ratio of molar conductivities estimated from impedance
technique (Λimp) to diffusion coefficient from PGSE-NMR
3
a + 2b
4a
3b
4a + 3b
DF(anion)
D
(HF)3F-
D
(2)
4
a + 3b
1
9
(
ΛNMR), which is called the Haven ratio, was not unity and
-
depended on the sample shown in Table 1. This indicates that
the salt does not completely dissociate to isolated ions.19 It is
expected that the ionization state depends on the structure and
combination of the cation and anion species. We then first
speculate the static feature of ions of the molten salts before
evaluating the ionic migration mechanism.
where a and b ()1 - a) are the molar fraction of (HF)3F and
-
(
HF)2F in the salt, respectively. This relation leads to
DF(anion) - DH(anion)
)
ab
4a + 3b)(3a + 2b)
(D(
HF)2F-
- D
(HF)3F-
) (3)
(
One of the ways of representing the ionization state in RTMS
is to apply the idea of “degree of dissociation of the salt” that
is conventional for the dissolved salt in a solvent. We here
assume that at any moment a molten salt is, in some degree,
dissociated into ions and partially maintains the associated
condition between the cation and anion forming ion pairs. This
situation could be characterized by the degree of dissociation,
x, that represents a fraction of ions in the total (ions and ion-
pairs) species in the salt. Under the equilibrium condition, the
ion and ion pair exchange with each other very fast compared
Considering the situation of D(HF)2F- > D(HF) F- mentioned
above, eq 3 has to be greater than 0. The opposite experimental
result of DH(anion) g DF(anion), independent of the kind of cation,
suggests the existence of another fast diffusive species. Con-
sidering the situation of anion species, (HF)2F and (HF)3F ,
coexisting under the equilibrium condition, the exchanging
species, HF, between the two anions can be a candidate as the
third diffusive component of the diffusion values. In this case,
eq 2 can be modified by using the molar fraction of a, b, and
3
-
-
9
with the time taken for a diffusion measurement. As a result,