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Investigation of Ionic Liquids by Positron Annihilation Lifetime Spectroscopy
G. Dlubek1†, Yang. Yu2, R. Krause-Rehberg2, W. Beichel3 and I. Krossing3
1 ITA Institut für Innovative Technologien, Köthen, Germany2 Martin-Luther-Universität Halle, Institut für Physik, 06099 Halle(Saale) Germany
3 Institut für Anorganische Chemie, Albert-Ludwigs-Universität Freiburg, Albertstraße 21, D-79104 Freiburg i. Br., Germany
Sep. 5th. 2011
Outline
Free volume influence to molecular transport property
Fürth theory
Ionic Liquids
Experiment results and discussion
Conclusion
Permeation properties (small molecules in polymer), viscosity, viscoelasticity, glass transition, volume recovery, mechanical properties
Fluidity: Doolittle:
Mobility: Cohen-Turnbull Equation:
Permeability coefficient:
Selectivity:
Ionic conductivity:
0exp[ / ]fA bv v
exp( / )fD A v v
P SD
/ / ( / )( / )A B A B A B A BP P S S D D
Free volume influence to molecular transport property
*exp[ ( ) / ]fc
v vT
Fürth’s hole theory: The energy required for the formation of a hole of spherical shape of
radius r in a continuum is equal to the sum of the work to be done against the surface tension and the work to be done against the pressure.
Relation between hole volume and surface tension.
Ts
P
Ref: Dlubek, G., Yu, Yang, et al., Free volume in imidazolium triflimide ([C3MIM][NTf2]) ionic liquid from positron lifetime: Amorphous, crystalline, and liquid states. The Journal of Chemical Physics, 2010. 133(12): p. 124502-10.[Fürth, R. Mathematical Proceedings of the Cambridge Philosophical Society, 1941.]
Ionic Liquids (ILs): Definition: organic salts with melting points below 100 oC or
even room temperature(RTILs).
Structure: organic cations paired with organic or inorganic anions.
[OTf]- [PF6]- [Cl]- [B(hfip)4]
-
Ionic formulae of the ionic liquids studied in this work.
[BMIM]+ [BF4]- [NTf2]
-
Experiment results and discussion
100 150 200 250 300 3500.0
0.5
1.0
1.5
2.0
2.5
3.0
coolingheating T
k=280K
3
(ns)
< 3>
(ns
)
T (K)
[BMIM][BF4]
Tg=190K
3
<3>
The mean, <3 >, and the standard deviation, 3, of
the o-Ps lifetime distribution as a function of temperature T during cooling and heating of [BMIM][BF4]. Tg indicates the glass transition
temperature and Tk the “knee” temperature.
100 150 200 250 300 3500
5
10
15
[BMIM][BF4]
I 3 (%
)
T (K)
cooling heating
The intensity I3 of the o-Ps lifetime as a function of temperature T during cooling and heating of [BMIM][BF4].
[BMIM][BF4]:
100 150 200 250 300 3500
50
100
150
Tk
coolingheating
h (
Å3 )
<v h
>(Å
3 )
T (K)
[BMIM][BF4]
Tg
Number-weighted mean <vh> (spheres) and standard deviation sh (squares) of the hole size calculated from positron lifetime.
[BMIM][BF4]:
0 50 100 1500.74
0.76
0.78
0.80
0.82
0.84
coolingheating
V (
cm3 /g
)
<vh> (Å3)
[BMIM][BF4]
Plot of the specific volume from PVT experiment under 0 MPa vs the mean hole volume at supercooled liquid state (between Tg and Tk). The line is a linear fit of the data.
Nh’ = 0.442 1021 g-1; Vocc = 0.7574 cm3/g.
[BMIM][NTf2]:
100 150 200 250 300 3500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
3 (n
s)
3 (n
s)
T (K)
[BMIM][NTf2]
filled: cooling
empty: heating
Tm=272K
Tc=205K
Tg=190K
DSC, J in et al.,T
g=186K
Tcr=232K
Tm=271K
Tk =270K
The mean, <3 > (squares), and the
standard deviation, 3 (spheres), of the o-
Ps lifetime distribution as a function of temperature T during cooling and heating of [BMIM][NTf2].
100 150 200 250 300 35010
12
14
16
18
20
22
24
26
28
30
[BMIM][NTf2]
filled: cooling
empty: heating
I 3 (
%)
T (K)
The o-Ps intensity I3 as a function of
temperature during cooling and heating of [BMIM][NTf2]
[BMIM][NTf2]:
0 50 100 150 200 2500.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
V (
cm3 /g
)
<vh> (Å3)
[BMIM][NTf2]
supercooled liquid during cooling
Plot of the specific volume from PVT experiment under 0 MPa vs the mean hole volume at supercooled liquid state (between Tg and Tk). The line is a linear fit
of the data.
Nh’ = 0.179 x 1021 g-1 Vocc = 0.6405 cm3/g.
[BMIM][OTf]:
150 200 250 3000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Tm=285KT
cr
3 (n
s)
< 3>
(ns) BMIM-OTf
T (K)
coolingheating
The mean, <3>, and the standard deviation,
3, of the o-Ps lifetime distribution as a
function of temperature T during cooling and heating of [BMIM][OTf]. Tcr and Tm show the
temperatures of crystallization (during cooling) and melting.
150 200 250 3000
5
10
15
20
25
30
35
Tm
BMIM-OTf
I 3 (%
)T (K)
coolingheating
Tcr
The o-Ps intensity I3.
150 200 250 300 3500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Tm
cr-II
h3
h2, glass
h1
<3>
3
4
3 (n
s)
< 3>
(ns
)
4
(ns
)
T (K)
cooling 1heating 1heating 2heating 3
[BMIM][PF6]
c1
cr-IT
g
liquid
The mean, <3>, and the standard deviation, 3,
of the o-Ps lifetime distribution as a function of temperature T during cooling and heating of [BMIM][PF6]. 4 shows an additional o-Ps
lifetime, which appears after transformation of the cr-II into the cr-I phase.
[BMIM][PF6]:
150 200 250 300 3500
5
10
15
20
25
30
35
h2, glass
cr-II
I4
[BMIM][PF6]
h3
c1
h1I 4
(%
)
I3
(%)
T (K)
cooling 1heating 1heating 2heating 3
I3cr-I
Tm liquid
The two o-Ps intensities I3 and I4.
0 20 40 60 80 100 120 140 160 180 2000.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
coolingheating linear fitV
(cm
3 /g)
<vh> (Å3)
[BMIM][PF6]
Plot of the specific volume from PVT experiment under 0 MPa vs the mean hole volume at supercooled liquid state. The line is a linear fit of the data.
Nh’ = 0.376 x 1021 g-1
Vocc = 0.6670 cm3/g.
[BMIM][PF6]:
100 150 200 250 300 350 4000.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Tk
Tcr
Tm
coolingheating
3 (n
s) < 3>
(ns)
4
(ns)
T (K)
4
<3>
3
[BMIM][Cl]
Tg
The mean, <3>, and the standard deviation, 3,
of the o-Ps lifetime distribution as a function of temperature T during cooling and heating of [BMIM][Cl]. 4 shows an additional o-Ps
lifetime which appears after crystallization.
100 150 200 250 300 350 4000
5
10
15
20
25
30
[BMIM][Cl]
coolingheating
I 4 (%
)
I3(
%)
T (K)
The two o-Ps intensities I3 and I4.
[BMIM][Cl]:
0 20 40 60 80 100 120
0.86
0.88
0.90
0.92
0.94
cooling heating
V (
cm3/g
)
<vh>
[BMIM][Cl] Plot of the specific volume from PVT experiment under 0 MPa vs the mean hole volume at supercooled liquid state. The line is a linear fit of the data.
Nh’ = 0.584 x 1021 g-1 Vocc = 0.8822 cm3/g.
[BMIM][Cl]:
150 200 250 300 3500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
3 (ns)
3
(ns)
T (K)
heatingcoolingheating after fast cooling
from 340 to 150 K
[BMIM][B(hfip)4]
crystalline solid
liquid
3
3
The mean, <3>, and the standard deviation,
s3, of the o-Ps lifetime distribution as a
function of temperature T during cooling and heating of [BMIM][B(hfip)4].
[BMIM][B(hfip)4]:
[BMIM]+ [Cl]- [BF4]- [PF6]- [OTf]- [NTf2]- [B(hfip)4]-
Tg(K)(DSC) 225 188-190 190-194 186
Tm/Tcr
(DSC)341/290 283/220 286/254 271/232
Tg(PALS) 230 ± 5 K 190±3 K 188 ± 3 K 190±5K
Tk335 ± 5 K 280±5 K 285 ± 5 K 270±5 K
Tg/Tk0.687 0.679 0.660 0.704
Vocc_sp(cm3/g)(PALS)
0.8822 0.7574 0.6670 0.6405
Nf(1021 g-1) 0.584 0.442 0.376 0.179
Vocc(Å3)(PALS) 256 284 315 446
fh
(Tg)0.025(230 K)
0.030(190 K)
0.034(188 K)
0.022(190 K)
fh
(Tk)0.070(335 K)
0.079(280 K)
0.088(285 K)
0.061(270 K)
Summarized parameters from experiment results for the ionic liquids.
Hole volumes comparison with molecular volume[BMIM]+ [Cl]
[BF4]
[PF6]
[OTf]
[NTf2]
[B(hfip)4]
Vm = V(A+X) (Å3) 240 26930 30529 32736 42836 759V([X]) (Å3) 47±13 739 10710 1297 23215 556liquid (<3>, ns; <vh>, Å3)
2.501155
2.851505
3.031805
3.282155
3.5052405
4.353405
glass, 140 K (3, ns ;<vh>, Å3))
1.25363
1.40473
1.60613
1.60613
crystal (<3> ns) 0.78 - 1.50/1.25 1.70 1.45 1.70 - 2.00
0 100 200 300 400 500 600 700 800 9000
50
100
150
200
250
300
350
<vh>
(Å
3 )
Vm (Å3)
The hole volumes of various ILs in the liquid (filled circles) and in the glass (140 K, empty circles) states as function of the molecular volume Vm = V(A+X). The straight lines are
linear fits constrained to pass zero, the dashed line shows a quadratic fit.
Comparison of the mean hole volumes <vh> for the liquid or supercooled liquid and glassy
states of the ionic liquids under investigation. Filled symbols: cooling, empty symbols: heating. Free volume calculated by Fürth theory is shown as line in the graph.
Hole volume comparison with Fürth theory
100 150 200 250 300 350 4000
100
200
300
400
<v h>
(Å3 )
T (K)
B(hipf)4
-
NTf2
-
OTf-
PF6
-
BF4
-
Cl-
[NTf2]
[BF4]
[Cl]
[PF6]
[Fürth, R. Mathematical Proceedings of the Cambridge Philosophical Society, 1941.]
Viscosity and conductivity
3.6 4.0 4.4 4.8 5.2
0
10
20
30
Ln(
T -
1/2)
(Pa
s/K
0.5)
1000/T (K-1)
[C4MIM][BF
4]
CT: = CT1/2 e(V*/Vf)
VFT:=0T1/2 eB/(T-T0)
10 20 30 40 50 60
-18
-9
0
9
18
1/Vf (g/cm3)
Ln(
T -
1/2)
(Pa
s/K
0.5)
2.0 2.5 3.0 3.5 4.0 4.5
-2
0
2
4
6
8
10
12
14
Ln(
T1/
2) (m
S/c
m)
1000/T (K-1)
CT: = CT -1/2eV*/Vf
[C4MIM][BF
4]
VFT: = 0T -1/2eB/(T-T
0)
4 8 12 16 20 24
-6
-4
-2
0
2
4
6
8
10
1/Vf (g/cm3)
Ln(
T1/
2) (m
S/c
m)
2.8 3.0 3.2 3.4 3.6 3.8 4.0-8
-7
-6
-5
-4
-3
-2
-1
Ln(
T -
1/2)
(Pa
s/K
0.5)
1000/T (K-1)
VFT: = 0T1/2eB/(T-T
0)
12 16 20 24 28
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2Ln(
T -
1/2)
(Pa
s/K
0.5)
1/Vf (g/cm3)
[C4MIM][NTf
2]
CT: = CT1/2e(V*/Vf)
2.6 2.8 3.0 3.2 3.4 3.6 3.82
3
4
5
6
7
8
9
Ln(
T1/2) (m
S/c
m)
1000/T (K-1)
10 12 14 16 18 20 22 24 26
0
1
2
3
4
5
6
7
1/Vf (g/cm3)
Ln(
T1/2) (m
S/c
m)
[C4MIM][NTf
2]
CT: = CT -1/2eV*/Vf
VFT: = 0T -1/2eB/(T-T
0)
3.1 3.2 3.3 3.4
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0
Ln(
T -
1/2)
(Pas
/K0.
5)
1000/T (K-1)
[C4MIM][PF
6]
CT: = CT1/2e(V*/Vf)
VFT: = 0T1/2eB/(T-T
0)
12.0 12.5 13.0 13.5 14.0 14.5
-6.3
-5.6
-4.9
-4.2
1/Vf (g/cm3)
Ln(
T -
1/2)
(Pas
/K0.
5)
2.0 2.5 3.0 3.50
2
4
6
8
10
12
Ln(
T1/
2)
(mS
/cm
)
1000/T (K-1)
[C4MIM][PF
6]
CT: = CT -1/2eV*/Vf
VFT: = 0T-1/2eB/(T-T
0)
6 8 10 12 14 16 18
-4
-2
0
2
4
6
8
10
1/Vf (g/cm3)
Ln(
T1/
2)
(mS
/cm
)
2.8 3.0 3.2 3.4 3.6-6
-4
-2
0
2
4
6
Ln(
T -
1/2) (P
as/
K0.
5)
1000/T (K-1)
CT: = CT1/2e(V*/Vf)
VFT: = 0T1/2eB/(T-T
0)
12 14 16 18 20 22 24
-9
-6
-3
0
3
1/Vf (g/cm3)
Ln(
T -
1/2) (P
as/
K0.
5)
[C4MIM][Cl]
[BMIM]+ [Cl] [BF4] [PF6] [NTf2]
Ln()(Pa*s)BT0
Viscosity_VFT
-16.52256162.1
-13.21154149.8
-12.51094166.2
-11.9810164.9
Ln(C) Viscosity_CT
-13.50.673
-11.00.462
-13.90.683
-11.40.313
Ln()(mS/cm)BT0
Conductivity_VFT
10.72888163.6
10.52914172.5
9.40666170.5
Ln(C) Conductivity_CT
10.950.516
11.580.593
9.300.283
/NM/Vm 0.813629 0.6447660.720126
1.05710.9178
0.5096120.460619
Important information of the local free volume in the amorphous (glass,
supercooled liquid, true liquid) and crystalline phases of ionic liquids as well as the corresponding phase transitions can be obtained from PALS.
The o-Ps mean lifetime <3> shows different behaviour indicating different phases (smaller values in crystalline phase due to dense packing of the material).
The parameters I3 also responds to phase transition by sharp value change. Low value in supercooled and true liquid, due to solvation of e+, precursor of Ps.
The knee temperature Tk coincidents with melting temperature of corresponding crystalline structure for [NTf2], [PF6] and [Cl] samples.
The local free volume from PALS displays a systematic relationship with molecular volume.
Fitting result of viscosity and conductivity by CT equation shows the free volume influence to molecular transport property.
Conclusion
More Results:
http://positron.physik.uni-halle.de/
Thanks for your time and patience!
Structural dynamic:
180 190 200 210 220 230 240
-16
-12
-8
-4
0
4
Relaxation time VFT fitting
Ln
(s)
T (K)
[C4MIM][BF
4]
Vogel-Fulcher-Tamman (VFT) equation:
= -29.7, B = 1339 and T0 = 140.8.
T(=max_o-Ps=2.85 ns)=274 KTk=280 K
180 190 200 210 220 230
-16
-12
-8
-4
0
Relaxation time VFT fitting
Ln
(s)
T (K)
C4MIM][NTf
2]
= -25.8, B = 731 and T0 = 156.
T(=max_o-Ps=3.5 ns)=271 K Tk=270 K
190 200 210 220 230 240 250
-14
-12
-10
-8
-6
-4
-2
0
2
Relaxation time VFT fitting
Ln (
s)
T (K)
[C4MIM][PF
6]
= -34.0, B = 2250 and T0 = 132.
T(=max_o-Ps=3 ns)=289 KTk=285 K
180 200 220 240 260 280
-16
-12
-8
-4
0
Relaxation time VTF fitting
Ln
(s)
T (K)
[C4MIM][Cl]
= -26.7, B = 1561 and T0 = 128.
T(=max_o-Ps=2.5 ns)=354 KTk=335 K