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.

TsP

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

3.0coolingheating Tk=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

Tkcoolingheating

h (Å

3 )

<

v h>(Å

3 )

T (K)

[BMIM][BF4]

Tg

Number-weighted mean <vh> (spheres) and standard deviation h (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 (c

m3 /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 (ns

)

3 (

ns)

T (K)

[BMIM][NTf2]filled: coolingempty: heating

Tm=272K

Tc=205K

Tg=190K

DSC, J in et al.,Tg=186KTcr=232KTm=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: coolingempty: 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 (c

m3 /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 3000.00.51.01.52.02.53.03.54.0

Tm=285KTcr

3 (n

s)

< 3

> (n

s) 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 30005

101520253035

Tm

BMIM-OTf

I 3 (%

)T (K)

coolingheating

Tcr

The o-Ps intensity I3.

150 200 250 300 3500.00.51.01.52.02.53.03.54.04.5

Tmcr-II

h3

h2, glass

h1

<3>

3

4

3 (ns

)

< 3>

(ns)

4

(ns)

T (K)

cooling 1heating 1heating 2heating 3

[BMIM][PF6]

c1

cr-ITg

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 35005

101520253035

h2, glass

cr-II

I4

[BMIM][PF6]

h3

c1

h1I 4

(%)

I 3 (

%)

T (K)

cooling 1heating 1heating 2heating 3

I3cr-I

Tm liquidThe 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

(cm3 /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 4000.00.51.01.52.02.53.03.54.0

Tk

TcrTm

coolingheating

3 (ns

)

< 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 (%

)

I 3(%)

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 (c

m3 /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

1.01.5

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, 3, 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  

Tk 335 ± 5 K 280±5 K  285 ± 5 K    270±5 K  

Tg/Tk 0.687 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

50100150200250300350

<vh>

(Å3 )

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

<vh>

(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 ) (

Pas

/K0.

5 )

1000/T (K-1)

[C4MIM][BF4]

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 ) (

Pas

/K0.

5 )

2.0 2.5 3.0 3.5 4.0 4.5-202468

101214

Ln(

T1/2 ) (

mS/

cm)

1000/T (K-1)

CT: = CT -1/2eV*/Vf

[C4MIM][BF4]

VFT: = 0T -1/2eB/(T-T0)

4 8 12 16 20 24

-6

-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 3.8 4.0-8

-7

-6

-5

-4

-3

-2

-1

Ln(T

-1/2 ) (

Pas

/K0.

5 )

1000/T (K-1)

VFT: = 0T1/2eB/(T-T0)

12 16 20 24 28

-11-10-9-8-7-6-5-4-3-2

Ln(T

-1/2 ) (

Pas

/K0.

5 ) 1/Vf (g/cm3)

[C4MIM][NTf2]

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(T

1/2 ) (

mS/

cm)

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(T

1/2 ) (

mS/

cm)

[C4MIM][NTf2]

CT: = CT -1/2eV*/Vf

VFT: = 0T -1/2eB/(T-T0)

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][PF6]

CT: = CT1/2e(V*/Vf)

VFT: = 0T1/2eB/(T-T0)

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][PF6]

CT: = CT -1/2eV*/Vf

VFT: = 0T-1/2eB/(T-T0)

6 8 10 12 14 16 18

-4

-2

0

2

4

6

8

10

1/Vf (g/cm3)

Ln(

T1/

2 ) (m

S/cm

)

2.8 3.0 3.2 3.4 3.6-6

-4

-2

0

2

4

6

Ln(

T -1/2) (

Pas

/K0.

5 )

1000/T (K-1)

CT: = CT1/2e(V*/Vf)

VFT: = 0T1/2eB/(T-T0)

12 14 16 18 20 22 24

-9

-6

-3

0

3 1/Vf (g/cm3)

Ln(T

-1/2) (

Pas

/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][BF4]

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][NTf2] = -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

-14-12-10-8-6-4-202

Relaxation time VFT fitting

Ln (

s)

T (K)

[C4MIM][PF6]

= -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