Investigation of Ionic Liquids by Positron Annihilation Lifetime Spectroscopy

Positron Annihilation LaboratoryYu, Yang

Jul. 20th. 2011

Outline

Introduction to free volume concept

Positron annihilation lifetime spectroscopy (PALS) technology

Ionic Liquids

Experiment results and discussion

Conclusion

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.

Free volume, dynamics and transport: Mobility: Cohen-Turnbull Equation Diffusion constant:

v*: minimum required volume of the void; A and : constants for a single substance.

Idea: statistical redistribution of the free volume occasionally opens up voids large enough for diffusive displacement.

Hard sphere model. Van der Waals simple liquid:

0.66v0<v*<0.86v0 for =1; 1.32v0<v*<1.7v0 for =1/2; v0:Van der Waals volume.

Liquid metal:v* in most cases near the volume of ion core for =1.

Amorphous phase according to which the liquid and glassy states of a given substance together comprise a single thermodynamically well-defined phase. In this model the transition to the glass state results ideally from the freezing out of the free volume, and hence the configurational entropy of the liquid.

exp( / )fD A v v

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

Molecular mobility and free volume

*exp[ ( ) / ]fc v vT

Variation of . with the reciprocal mean local free volume / in poly(ethylene oxide) doped with LiClO4. Dash-dotted line: Cohen-Turnbull fit. Crosses: as obtained from extrapolation of the linear fit in the range T<Tk. [Bamford, D., et al., Journal of Chemical Physics, 2003.]

Free volume from the equation of state(eos) Tait equation:

Coefficients:

Thermal expansion: Isothermal compressibility:

Free volume from the equation of state(eos) Sanchez-Lacombe equation of state: SL eos

[Sanchez, I.C. and R.H. Lacombe. Journal of Physical Chemistry, 1976.]

Free volume from the equation of state(eos) Simha-Somcynsky equation of state(S-S eos):

y: fraction of occupied lattice sites; s: number of segments per chain of molar mass M; 3c: number of external degrees of freedom per chain; M0: segmental molar mass M/s; v*: molar repulsion volume between segment pair; *: molar attraction energy between segment pair; qz=s(z-2)+2: number of intermolecular contacts; A, B, and z: constants equal respectively, 1.011, 1.2045, and 12; Q= 1/ and 2 / / are dimensionless quantities.

Local free volume (hole) concentration and hole size distributions Fürth’s hole theory:

P Ts

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.

Positron Annihilation Lifetime Spectroscopy

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.

Data Analysis

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

220 K

[C3MIM][NTf2]

n(r h) (

Å-1)

rh (Å)

265 K (Tm+10)

185 K (Tg)

160 K Theory:Tao-Eldrup model

0 1 2 3 4 5 6 70123456789

10

o-Ps

life

time po

(ns)

hole radius rh (Å)

Tao-Eldrup Standard Model

threshold

rh

o

0.5211

2

1.66 A

o Ps pickoffh h

h h

nsr rSin

r r r r

r

1/ 22

( )

[ ( ) ( ) ]

fh h n h h

h

h h h n h h

Vv v g v dv

N

v v g v dv

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 result and discussion

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]:

100 150 200 250 300 3500

50

100

150

Tkcoolingheating

h (Å3 )

<v h>(

Å3 )

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 (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 (n

s)

T (K)

[BMIM][NTf2]filled: coolingempty: 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]

[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 ¥ 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=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 (half step) 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 3500.00.51.01.52.02.53.03.54.04.5

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.

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 PVTexperiment under 0 MPa vs the meanhole volume at supercooled liquid state.The line is a linear fit of the data.

Nh’ = 0.376 ¥ 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

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 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]:

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 PVTexperiment under 0 MPa vs the mean holevolume at supercooled liquid state. The line is alinear fit of the data.

Nh’ = 0.584 ¥ 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 (n

s)

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)

0.030190

0.034188

0.022190

fh(Tk) 0.070(335)

0.079(280)

0.088(285)

0.061(270)

Summarized parameter from experiment result 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>

(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). The straight lines arelinear fits constrained to pass zero, thedashed 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.]

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> and its dispersion 3 show 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 local free volume from PALS displays a systematic relationship with molecular volume.

Conclusion

More Results:

http://positron.physik.uni-halle.de/

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