Free volume and Phase Transitions of 1-Butyl-3-Methylimidazolium Based Ionic Liquids: Positron Lifetime

Positron Annihilation LaboratoryYu, Yang

Oct. 12th. 2011

Outline

Introduction to free volume

Positron annihilation lifetime spectroscopy (PALS)

Ionic liquids

Experiment results and discussion

Conclusion

2

Introduction to free volume Hole Free volume in molecular materials:

Vf =V –Vocc: Vf: free volume Vocc: occupied volume.

Vf=<vh>×Nh’: <vh>: average hole volume Nh’: hole number density per gram

Structural, static and dynamic disorder. Viscosity, molecular transport, structural relaxation and physical aging.

Vw: van der Waal volume; VI: interstitial volume; Vc: crystalline volume;Vocc: occupied volume; Vf: free volume; Tg: glass transition temperature; Tc: crystallization temperature; Tm: melting temperature

3

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:

Dynamics: Williams-Landel-Ferry (WLF) equation

fg = f(Tg) = 0.025

0exp[ / ]fA bv v

exp( / )fD A T 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

4

Ref: Doolittle, Journal of Applied Physics, 1951. Cohen and Turnbull, Journal of Chemical Physics, 1959. Williams, Landel, and Ferry, Journal of the American Chemical Society, 1955.

Positron Annihilation Lifetime Spectroscopy5

Positronium interaction with molecular material

Ref: G. Dlubek, Positron Annihilation Spectroscopy, in: Encyclopedia of Polymer Science and Technology, ed. by. A.Seidel, John Wiley&Sons, Hoboken, 2008.

6

Free volume from positron lifetime

Theory:Tao-Eldrup model

o

0.5211

2

1.66 A

o Ps pickoffh h

h h

nsr rsin

r r r r

r

7

0 1 2 3 4 5 6 70123456789

10

o-P

s lif

etim

e po

(ns)

hole radius rh (Å)

Tao-Eldrup Standard Model

threshold

rh

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.

Property: excellent solvating properties; no measurable vapor pressure; non-flammability; high thermal stability; low melting temperature.

Application: “green” replacement for classical organic solvents, electrolytes in batteries, solar cells and fuel cells, lubricants and heat transfer fluids.

8

Ionic Liquids (ILs):

[OTf]- [PF6]- [Cl]- [B(hfip)4]-

Ionic formulae of the ionic liquids studied in this work.

[BMIM]+ [BF4]- [NTf2]-

9

Experiment results and discussion: PALS

100 150 200 250 300 3500.0

0.5

1.0

1.5

2.0

2.5

3.0

coolingheating Tk=280K

3 (n

s)

<

3> (n

s)

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]:

10

[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 (n

s)

T (K)

[BMIM][NTf2]black: coolingred : heating

Tm=272K

Tc=205K

Tg=190K

DSC, Jin et al.,Tg=186KTcr=232KTm=271K

Tk =270K

The mean, <3> (squares), and thestandard deviation, 3 (spheres), of the o-Ps lifetime distribution as a function oftemperature T during cooling and heatingof [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 oftemperature during cooling and heatingof [BMIM][NTf2]

11

The mean, <3>, and the standard deviation, 3,of the o-Ps lifetime distribution as a function oftemperature T during cooling and heating of[BMIM][Cl]. 4 shows an additional o-Pslifetime 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]:

12

100 150 200 250 300 350 4000.00.51.01.52.02.53.03.54.0

Tk

TcrTm

3 (ns

)

< 3>

(ns)

4 (

ns)

T (K)

4

<3>

3

[BMIM][Cl]

Tg

black: coolingred: heating

290 K

350 K

335 K

230 K

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 afunction of temperature T during cooling andheating of [BMIM][PF6]. 4 shows anadditional o-Ps lifetime, which appears aftertransformation 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 (

%)

I 3 (%

)

T (K)

cooling 1heating 1heating 2heating 3

I3cr-I

Tm liquidThe two o-Ps intensities I3 and I4.

13

[BMIM][OTf]:

150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Tm=285KTcr

3 (ns

)

<

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 3000

5

10

15

20

25

30

35

Tm

BMIM-OTf

I 3 (%

)T (K)

coolingheating

Tcr

The o-Ps intensity I3.

14

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 (n

s)

T (K)

heatingcooling

[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]:

15

0 40 80 120 160 200 240

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

V sp (c

m3 /g

)

<vh> (Å3)

Cooling, [BF4] Heating, [BF4] Cooling, [NTf2] Cooling, [PF

6]

Heating, [PF6]

Cooling, [Cl] Heating, [Cl]

Plot of the specific volume frompressure-volume-temperature (PVT)experiment under 0 MPa vs the meanhole volume at supercooled liquid state(between Tg and Tk). The line is a linearfit of the data.

[C4MIM]+ [Cl]　 [BF4]　 [PF6]　 [NTf2]　

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

Occupied volume and number density

V

16

[BMIM]+ [Cl]- [BF4]- [PF6]- [OTf]- [NTf2]- [B(hfip)4]-

Tg(K)(DSC) 225 188-190 190-194 186

Tm/Tcr(DSC)

341/290 283/220 286/254 271/232 328/300

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.

17

180 200 220 240 260-18

-15

-12

-9

-6

-3

0

3

[BF4] [NTf2] [PF6] [Cl] VFT fitting

Ln

(s)

T (K)

[C4MIM]+ [Cl]　 [BF4]　 [PF6]　 [NTf2]　

Ln(t0)(s)BT0(K)

-26.71561128

-29.71339140.8

-34.02250132

-25.8731156

max_o-ps (ns) 2.5 2.85 3 3.5

T( = max_o-ps ) (K) 354 274 289 271

Tk (K) 335±5 280±5 285±5 270±5

ln ln

Vogel-Fulcher-Tamman (VFT) equation:

Dynamic spectroscopy18

Ref: Vogel, Phys. Z., 1921. Fulcher, Journal of the American Ceramic Society, 1925. Tammann, G. and W. Hesse, Zeitschrift für anorganischeund allgemeine Chemie, 1926

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>

(Å3 )

Vm (Å3)

The hole volumes of various ILs in the liquid(filled circles) and in the glass (140 K, emptycircles) states as function of the molecularvolume Vm = V(A+X).

19

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 (p). 4

Relation between hole volume ( ) and surface tension ( ).

0.68 / 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.]

20

Fig. Comparison of hole volume from Fürth theory (squares) and PALS (circles). V (stars) is specific volume from PVT experiment.

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.]

21

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 )

T: 188 K ~ 293 K

2.0 2.5 3.0 3.5 4.0 4.5

-2

0

2

4

6

8

10

12

14

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)

T: 238.1 K ~ 468.1 K

22

CT: / exp ∗/

CT: σ ∗ /

VFT: / exp /

VFT: / exp /

Viscosity:

Conductiity:

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(

T1/2 ) (

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(

T1/2 ) (

mS

/cm

)

[C4MIM][NTf2]

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

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

23

CT: / exp ∗/

VFT: / exp /

Viscosity:

CT: σ ∗ /

VFT: / exp /

Conductiity:

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(T

1/2 ) (

mS/

cm)

2.8 3.0 3.2 3.4 3.6-6

-4

-2

0

2

4

6

Ln(

T -1/2) (

Pa

s/K

0.5 )

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]

24

[BMIM]+ [Cl]　 [BF4]　 [PF6]　 [NTf2]　

Ln( )(Pa*s)BT0Viscosity_VFT

-16.52256162.1

-13.21154149.8

-12.51094166.2

-11.9810164.9

Ln(C)γ ∗

Viscosity_CT

-13.50.673

-11.00.462

-13.90.683

-11.40.313

Ln( )(mS/cm)BT0Conductivity_VFT

10.72888163.6

10.52914172.5

9.40666170.5

Ln(C)γ ∗

Conductivity_CT

10.950.516

11.580.593

9.300.283

γ ∗/NM/Vm 0.813629 0.6447660.720126

1.05710.9178

0.5096120.460619

25

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 coincides 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.

Conclusion26

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