_{n}Cl

_{4−n}, n = 0,1,2

^{1,a)}, S. C. Perez

^{1,b)}, L. C. Pardo

^{2,c)}and J. Ll. Tamarit

^{2,d)}

### Abstract

Glassy dynamics of rigid molecules is still a matter of controversy: the physics behind the relaxation process at time scales faster than that ruled by the viscosity, the so called Johari-Goldstein process, is not known. In this work we unravel the mechanism of such a process by using a simple molecular model in which the centers of mass of the molecules are forming an ordered lattice, and molecular reorientation is performed by jumps between equilibrium orientations. We have studied the dynamics of simple quasi-tetrahedral molecules CBr_{n}Cl_{4−n}, n = 0, 1, 2, in their monoclinic phases by means of dielectric spectroscopy and nuclear quadrupole resonance: the first technique allows to measure in a broad time scale but it is insensitive to molecular particularities, while the second has a restricted time window but senses the movement of each chlorine atom separately. The dynamic picture emerging from these techniques is that the secondary relaxation process is related to the different molecular surroundings around each nonequivalent atom of the molecule. Dynamical heterogeneities thus seem to be the cause of the secondary relaxation in this simple model of glass.

This work was supported by SECyT-UNC, CONICET, and FONCyT of Argentina, the Spanish Ministry of Science and Innovation (Grant No. FIS2011-24439), and the Catalan Government (Grant No. 2009SGR-1251).

I. INTRODUCTION

II. EXPERIMENTAL

III. RESULTS AND DISCUSSION

A. NQR frequency

B. Spin-lattice relaxation times

C. Spin-spin relaxation times

D. Comparison with dielectric measurements

IV. CONCLUSIONS

### Key Topics

- Relaxation times
- 22.0
- Dielectrics
- 13.0
- Glass transitions
- 10.0
- Polarization
- 8.0
- Dielectric relaxation
- 6.0

## Figures

^{35}Cl NQR spectra of CBr_{n}Cl_{4−n}, n = 0, 1, 2 at 77 K.

^{35}Cl NQR spectra of CBr_{n}Cl_{4−n}, n = 0, 1, 2 at 77 K.

^{35}Cl NQR spectra, at several temperatures, in the low-temperature monoclinic phase of CCl_{4}.

^{35}Cl NQR spectra, at several temperatures, in the low-temperature monoclinic phase of CCl_{4}.

Temperature dependence of ^{35}Cl NQR frequencies for the low-temperature monoclinic phase of CCl_{4}. Inset: Temperature dependence of the central NQR frequency for the low-temperature monoclinic phase of CBrCl_{3} (empty blue squares) compared with line 1 for CCl_{4} (brown filled circles).

Temperature dependence of ^{35}Cl NQR frequencies for the low-temperature monoclinic phase of CCl_{4}. Inset: Temperature dependence of the central NQR frequency for the low-temperature monoclinic phase of CBrCl_{3} (empty blue squares) compared with line 1 for CCl_{4} (brown filled circles).

Temperature dependence of the spin-lattice (filled symbols) and spin-spin (empty squares) relaxation times in CCl_{4}. Solid and dashed lines fitted values with Eqs. (4) and (5).

Temperature dependence of the spin-lattice (filled symbols) and spin-spin (empty squares) relaxation times in CCl_{4}. Solid and dashed lines fitted values with Eqs. (4) and (5).

^{35}Cl *T* _{1} magnetization decay curves as a function of separation between pulses at *T* = 109 K for lines 11 (orange circle), 2, 6, 8, 16 (green, brown, black, and violet squares, respectively).

^{35}Cl *T* _{1} magnetization decay curves as a function of separation between pulses at *T* = 109 K for lines 11 (orange circle), 2, 6, 8, 16 (green, brown, black, and violet squares, respectively).

^{35}Cl (filled circles) and ^{37}Cl (empty circles) spin lattice relaxation times of line 16 of CCl_{4}.

^{35}Cl (filled circles) and ^{37}Cl (empty circles) spin lattice relaxation times of line 16 of CCl_{4}.

Temperature dependence of spin-lattice (empty triangle) and spin-spin (empty circle) relaxation times in CBrCl_{3} (blue), CBr_{2}Cl_{2} (orange). For comparison *T* _{1} (filled symbols) and *T* _{2} (empty symbols) of some CCl_{4} NQR lines are presented (brown: line 1, red: line 14, and violet: line 6).

Temperature dependence of spin-lattice (empty triangle) and spin-spin (empty circle) relaxation times in CBrCl_{3} (blue), CBr_{2}Cl_{2} (orange). For comparison *T* _{1} (filled symbols) and *T* _{2} (empty symbols) of some CCl_{4} NQR lines are presented (brown: line 1, red: line 14, and violet: line 6).

Reorientational correlations times obtained from *T* _{1} of CCl_{4} and the ratio between the different sets.

Reorientational correlations times obtained from *T* _{1} of CCl_{4} and the ratio between the different sets.

Tetrahedral molecule: The four C_{3} axes and the jump probabilities *w* _{ i } around these axes are shown.

Tetrahedral molecule: The four C_{3} axes and the jump probabilities *w* _{ i } around these axes are shown.

Decay constants τ = λ^{−1} (λ being the eigenvalues of **Λ**) for different ratios *w* _{2}/*w* _{1}: (a) *w* _{2}/*w* _{1} = 20, (b) *w* _{2}/*w* _{1} = 1, (c) *w* _{2}/*w* _{1} = 0.05.

Decay constants τ = λ^{−1} (λ being the eigenvalues of **Λ**) for different ratios *w* _{2}/*w* _{1}: (a) *w* _{2}/*w* _{1} = 20, (b) *w* _{2}/*w* _{1} = 1, (c) *w* _{2}/*w* _{1} = 0.05.

Spin polarization decay for different ratios *w* _{ i }/*w* _{1} and initial conditions. Exponential decays with the four eigenvalues of Λ shown in Fig. 11 correspond to the black lines. Blue, red, cyan, and green refer to polarization of sites 1, 2, 3, and 4, respectively. (a) and (b) Full and dashed lines: saturating one and two sites at *t* = 0. (c) Full, dashed, and dotted lines: saturating one, two, or three nuclear sites at *t* = 0.

Spin polarization decay for different ratios *w* _{ i }/*w* _{1} and initial conditions. Exponential decays with the four eigenvalues of Λ shown in Fig. 11 correspond to the black lines. Blue, red, cyan, and green refer to polarization of sites 1, 2, 3, and 4, respectively. (a) and (b) Full and dashed lines: saturating one and two sites at *t* = 0. (c) Full, dashed, and dotted lines: saturating one, two, or three nuclear sites at *t* = 0.

Dielectric relaxation times: Empty squares (τ_{α}) and circles (τ_{β}) for CBr_{2}Cl_{2} (red) and CBrCl_{3} (black) from Ref. 9. NQR τ_{c} correlation times for CCl_{4}: Filled squares from lines 2, 6, 8, 14, and 16; filled circles from lines 1, 7, 11, 12, 13, and 15. Empty blue and orange triangles NQR correlation times for CBrCl_{3} and CBr_{2}Cl_{2}.

Dielectric relaxation times: Empty squares (τ_{α}) and circles (τ_{β}) for CBr_{2}Cl_{2} (red) and CBrCl_{3} (black) from Ref. 9. NQR τ_{c} correlation times for CCl_{4}: Filled squares from lines 2, 6, 8, 14, and 16; filled circles from lines 1, 7, 11, 12, 13, and 15. Empty blue and orange triangles NQR correlation times for CBrCl_{3} and CBr_{2}Cl_{2}.

β_{KWW} stretched exponent of the stretched relaxation function for CBrCl_{3} (empty black squares) and CBr_{2}Cl_{2} (empty red squares). Blue filled triangles stretching parameter determined from the NQR correlation times.

β_{KWW} stretched exponent of the stretched relaxation function for CBrCl_{3} (empty black squares) and CBr_{2}Cl_{2} (empty red squares). Blue filled triangles stretching parameter determined from the NQR correlation times.

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