^{1}, C. Tschirwitz

^{1}and E. A. Rössler

^{1,a)}

### Abstract

In addition to the primary α-process, some neat glass formers show a well resolved secondary β-process (type-B) or solely an excess wing (type-A). We investigate two binary glass forming systems composed of a type-A and a type-B component. ^{2}H nuclear magnetic resonance (NMR) spectroscopy is selectively applied to the type-B component in order to characterize the β-process over a large range of mole fractions *x* in the glassy state. We demonstrate that for *x* ≳ 0.75 the apparent relaxation strength is constant, i.e., all molecules of type-B participate in the β-process and the time constant τ_{β}(*T*) is independent of concentration. For *x* < 0.75, however, the apparent relaxation strength decreases abruptly, which we interpret in terms of population: below this concentration a fraction ξ of type-B molecules still exhibits essentially the β-process of the neat system (in terms of time scale and mechanism), while others have been immobilized. The arise of such a scenario is verified by 2D and spin-lattice relaxation ^{2}H NMR techniques. In selective ^{2}H NMR experiments on the type-A component we observe a contribution to the β-process of the type-B molecules at medium concentrations. The latter finding and the rather sharp threshold occurring at *x* ≈ 0.75 may indicate that the β-process is a cooperative process.

The financial support of the Deutsche Forschungsgemeinschaft through Project No. RO 907/10-1 is gratefully acknowledged. The authors would like to thank Daniele Cangialosi (San Sebastian) and Christiane Alba-Simionesco (Paris) for the supply of PCB54 and picoline-d_{7}.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. RESULTS

A. Solid-echo line-shape

B. Stimulated echoes

C. Spin-lattice relaxation

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- Nuclear magnetic resonance
- 18.0
- Dielectric relaxation
- 6.0
- Diffusion
- 6.0
- Glass transitions
- 6.0
- Dielectrics
- 5.0

## Figures

(a) Loss part ε^{″} of the dielectric permittivity of toluene/PCB54 mixtures for different mole fractions *x* at *T* = 118 K (adapted from Ref. ^{ 17 } ) including data of neat toluene from Ref. ^{ 11 } . (b) Dielectric loss for different mole fractions of toluene in picoline (*T* ≈ 116 K). (c) Concentration dependence of the glass transition temperature *T* _{ g } determined from DSC measurements for both mixtures. Lines serve as guide for the eye, *T* _{ g } of neat PCB54 from Ref. ^{ 17 } .

(a) Loss part ε^{″} of the dielectric permittivity of toluene/PCB54 mixtures for different mole fractions *x* at *T* = 118 K (adapted from Ref. ^{ 17 } ) including data of neat toluene from Ref. ^{ 11 } . (b) Dielectric loss for different mole fractions of toluene in picoline (*T* ≈ 116 K). (c) Concentration dependence of the glass transition temperature *T* _{ g } determined from DSC measurements for both mixtures. Lines serve as guide for the eye, *T* _{ g } of neat PCB54 from Ref. ^{ 17 } .

(a) Solid-echo spectra of toluene-d_{3} in PCB54 for different mole fractions *x* at similar absolute temperature *T* = (104 ± 2) K, each spectrum recorded for inter-pulse delays of *t* _{ p } = 20 μs (solid red line) and *t* _{ p } = 200 μs (dashed black line). (b) Relative spectral intensity at zero frequency with respect to the singularities R(*t* _{ p } = 200 μs) for different concentrations of toluene-d_{3} in PCB54 as a function of temperature. All lines serve as guide for the eye. Inset sketches the solid-echo pulse sequence.

(a) Solid-echo spectra of toluene-d_{3} in PCB54 for different mole fractions *x* at similar absolute temperature *T* = (104 ± 2) K, each spectrum recorded for inter-pulse delays of *t* _{ p } = 20 μs (solid red line) and *t* _{ p } = 200 μs (dashed black line). (b) Relative spectral intensity at zero frequency with respect to the singularities R(*t* _{ p } = 200 μs) for different concentrations of toluene-d_{3} in PCB54 as a function of temperature. All lines serve as guide for the eye. Inset sketches the solid-echo pulse sequence.

(a) Normalized inter-pulse dependence of the *R*(*t* _{ p }) value for different mole fractions of toluene-d_{5} in PCB54 at *T* = 107 K. The lines represent fits via Eq. (1) with concentrations independent values of τ, β. (b) Same representation for mixtures of toluene and picoline (*T* = (105 ± 5) K), including measurements on the type-A component (red) in its neat form and from a deuterated picoline/protonated toluene mixture.

(a) Normalized inter-pulse dependence of the *R*(*t* _{ p }) value for different mole fractions of toluene-d_{5} in PCB54 at *T* = 107 K. The lines represent fits via Eq. (1) with concentrations independent values of τ, β. (b) Same representation for mixtures of toluene and picoline (*T* = (105 ± 5) K), including measurements on the type-A component (red) in its neat form and from a deuterated picoline/protonated toluene mixture.

Concentration dependent fraction ξ of toluene molecules exhibiting a β-process in mixtures with PCB54 (full symbols) and picoline (open symbols), the line serves as guide for the eye. The results from the ⟨*T* _{1}⟩ analysis are obtained from *B*(*x*)/*B*(1) (cf. Eq. (8) ) and have not been scaled.

Concentration dependent fraction ξ of toluene molecules exhibiting a β-process in mixtures with PCB54 (full symbols) and picoline (open symbols), the line serves as guide for the eye. The results from the ⟨*T* _{1}⟩ analysis are obtained from *B*(*x*)/*B*(1) (cf. Eq. (8) ) and have not been scaled.

(a) Stimulated echo decay curves (*F* ^{cos}(*t* _{ e }; *t* _{ m })) of *x* = 0.77 and 0.59 toluene-d_{5} in PCB54 for different evolution times recorded at 97 K in comparison with data of neat toluene. ^{ 18 } The full line represents a fit via Eq. (3) , for the dashed line see text. (b) Concentration dependence of the amplitude at 97 K, a clear trend is seen for concentrations below *x* = 0.77. Lines serve as guide for the eye. (c) Concentration dependence of the geometrical factor *p*(*t* _{ e }), line serves as guide for the eye. The sketch above (c) demonstrates the employed pulse sequence.

(a) Stimulated echo decay curves (*F* ^{cos}(*t* _{ e }; *t* _{ m })) of *x* = 0.77 and 0.59 toluene-d_{5} in PCB54 for different evolution times recorded at 97 K in comparison with data of neat toluene. ^{ 18 } The full line represents a fit via Eq. (3) , for the dashed line see text. (b) Concentration dependence of the amplitude at 97 K, a clear trend is seen for concentrations below *x* = 0.77. Lines serve as guide for the eye. (c) Concentration dependence of the geometrical factor *p*(*t* _{ e }), line serves as guide for the eye. The sketch above (c) demonstrates the employed pulse sequence.

(a) Average spin-lattice relaxation times ⟨*T* _{1}⟩ for mixtures of toluene-d_{5} with PCB54 (full symbols) and picoline (open symbols). The dashed lines at low temperatures represent Arrhenius fits to ⟨*T* _{1}⟩ for *T*<*T* _{ g } (cf. Eq. (8) ). Data of neat toluene adapted from Refs. ^{ 10 } and ^{ 29 } . (b) Normalized magnetization relaxation function for samples with different concentrations of toluene-d_{5} in PCB54 recorded at 97 K. Whereas the initial slope appears approximately concentration independent, the long time “tail” of the curves becomes more pronounced at low concentrations.

(a) Average spin-lattice relaxation times ⟨*T* _{1}⟩ for mixtures of toluene-d_{5} with PCB54 (full symbols) and picoline (open symbols). The dashed lines at low temperatures represent Arrhenius fits to ⟨*T* _{1}⟩ for *T*<*T* _{ g } (cf. Eq. (8) ). Data of neat toluene adapted from Refs. ^{ 10 } and ^{ 29 } . (b) Normalized magnetization relaxation function for samples with different concentrations of toluene-d_{5} in PCB54 recorded at 97 K. Whereas the initial slope appears approximately concentration independent, the long time “tail” of the curves becomes more pronounced at low concentrations.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content