^{1,2,a)}, Yang Yu

^{1}, R. Krause-Rehberg

^{1}, W. Beichel

^{3}, S. Bulut

^{3}, N. Pogodina

^{3}, I. Krossing

^{3}and Ch. Friedrich

^{3}

### Abstract

Positron annihilation lifetime spectroscopy (PALS) is used to study the ionic liquid 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide in the temperature range between 150 and 320 K. The positron decay spectra are analyzed using the routine LifeTime-9.0 and the size distribution of local free volumes (subnanometer-size holes) is calculated. This distribution is in good agreement with Fürth’s classical hole theory of liquids when taking into account Fürth’s hole coalescence hypothesis. During cooling, the liquid sample remains in a supercooled, amorphous state and shows the glass transition in the ortho-positronium lifetime at 187 K. The mean hole volume varies between at 150 K and at 265–300 K. From a comparison with the macroscopic volume, the hole density is estimated to be constant at corresponding to at 265 K. The hole free volume fraction varies from 0.023 at 185 K to 0.073 at and can be estimated to be 0.17 at 430 K. It is shown that the viscosity follows perfectly the Cohen–Turnbull free volume theory when using the free volume determined here. The heating run clearly shows crystallization at 200 K by an abrupt decrease in the mean and standard deviation of the lifetime distribution and an increase in the intensity . The parameters of the second lifetime component and behave parallel to the parameters, which also shows the positron’s response to structural changes. During melting at 253 K, all lifetime parameters recover to the initial values of the liquid. An abrupt decrease in is attributed to the solvation of and particles. Different possible interpretations of the lifetime in the crystalline state are briefly discussed.

Dirk Pfefferkorn from the Institute of Chemistry of the Martin-Luther-University Halle-Wittenberg is acknowledged for performing the PVT experiments. We thank also Jerzy Kansy, Institute of Materials Science, Silesian University, Katowice, for supplying the analyzing routine LifeTime (LT) and the simulation routine simLT.

I. INTRODUCTION

II. EXPERIMENTAL

III. RESULTS AND DISCUSSION

A. Positron decay spectrum analysis

B. Ps lifetimes and size distribution of local free volumes (holes)

C. Temperature dependence of the hole free volume

D. Crystallization and melting

E. Free volume and viscosity

IV. CONCLUSIONS

## Figures

The mean and standard deviation of the lifetime distribution for . The lines through the data points are a visual aid; the arrows show the glass transition, the crystallization, the melting and the knee temperature of the sample. Filled symbols: decreasing ; empty symbols: increasing .

The mean and standard deviation of the lifetime distribution for . The lines through the data points are a visual aid; the arrows show the glass transition, the crystallization, the melting and the knee temperature of the sample. Filled symbols: decreasing ; empty symbols: increasing .

Hole radius distribution of for four selected temperatures: 160 and 185 K (glass), 220 K (supercooled liquid), and 265 K (liquid). The distributions are normalized to the unity area below the curve. Vertical lines show the effective radius of ions (dotted) and (dashed).

Hole radius distribution of for four selected temperatures: 160 and 185 K (glass), 220 K (supercooled liquid), and 265 K (liquid). The distributions are normalized to the unity area below the curve. Vertical lines show the effective radius of ions (dotted) and (dashed).

Hole volume distribution from PALS (line) and from the complex-hole theory of Fürth (Ref. 3) (line with dots) for at 265 K. gives the fractional number of holes of sizes between and and has been here normalized to . The surface tension in Fürth’s theory was chosen to in order to get the best agreement of Fürth’s distribution with the experimental curve from PALS. The value denotes the number of individual holes in a complex hole of Fürth’s theory.

Hole volume distribution from PALS (line) and from the complex-hole theory of Fürth (Ref. 3) (line with dots) for at 265 K. gives the fractional number of holes of sizes between and and has been here normalized to . The surface tension in Fürth’s theory was chosen to in order to get the best agreement of Fürth’s distribution with the experimental curve from PALS. The value denotes the number of individual holes in a complex hole of Fürth’s theory.

The same as for Fig. 1, except for the mean and standard deviation of the hole size distribution (squares and circles). is the specific volume at zero pressure from PVT experiments (stars) and its extrapolation to low temperatures is shown by a dashed-dotted line. The rhomb symbols show the mean hole size calculated from Fürth’s complex-hole theory (Ref. 3). For clarity, we have omitted the error flags.

The same as for Fig. 1, except for the mean and standard deviation of the hole size distribution (squares and circles). is the specific volume at zero pressure from PVT experiments (stars) and its extrapolation to low temperatures is shown by a dashed-dotted line. The rhomb symbols show the mean hole size calculated from Fürth’s complex-hole theory (Ref. 3). For clarity, we have omitted the error flags.

Plot of the specific volume of calculated from the fit in Fig. 3 vs the mean hole volume for the temperature range above . The line is a linear fit to the data of the supercooled liquid in the temperature range between 185 K and 265 K (filled symbols).

Plot of the specific volume of calculated from the fit in Fig. 3 vs the mean hole volume for the temperature range above . The line is a linear fit to the data of the supercooled liquid in the temperature range between 185 K and 265 K (filled symbols).

The same as for Fig. 1, but the intensity .

The same as for Fig. 1, but the intensity .

The same as for Fig. 1, but the mean lifetime and standard deviation of the lifetime distribution.

The same as for Fig. 1, but the mean lifetime and standard deviation of the lifetime distribution.

Arrhenius plot (squares: bottom -axis and left -axis) and Cohen–Turnbull plot (circles: top -axis and right -axis) of the value , where is the viscosity and the absolute temperature for . The lines are VFT and Cohen–Turnbull (CT) fits to the data in the temperature range between 253.3 and 353.3 K.

Arrhenius plot (squares: bottom -axis and left -axis) and Cohen–Turnbull plot (circles: top -axis and right -axis) of the value , where is the viscosity and the absolute temperature for . The lines are VFT and Cohen–Turnbull (CT) fits to the data in the temperature range between 253.3 and 353.3 K.

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