^{1}and G. Pastore

^{1}

### Abstract

The connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures was investigated. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.

The authors would like to thank A. Cavagna for useful discussions and a critical reading of the manuscript. Computational resources for the present work have been partly obtained through a grant from “Iniziativa Trasversale diCalcolo Parallelo” of the Italian *CNR-Istituto Nazionale per la Fisica della Materia* (CNR-INFM) and partly within the agreement between the University of Trieste and the Consorzio Interuniversitario CINECA (Italy).

I. INTRODUCTION

II. MODELS AND SIMULATION TECHNIQUES

III. EFFECTIVE ACTIVATION ENERGIES

IV. POTENTIAL ENERGY SURFACE

V. CONCLUSIONS

### Key Topics

- Activation energies
- 19.0
- Relaxation times
- 8.0
- Statistical properties
- 8.0
- Numerical modeling
- 6.0
- Potential energy surfaces
- 6.0

## Figures

Temperature dependence of density along isobaric quenches at for a selection of AMLJ- mixtures. From bottom to top: , 0.76, 0.70, 0.64.

Temperature dependence of density along isobaric quenches at for a selection of AMLJ- mixtures. From bottom to top: , 0.76, 0.70, 0.64.

Temperature dependence of density along isobaric quenches at for BMLJ at , , and .

Temperature dependence of density along isobaric quenches at for BMLJ at , , and .

Effective activation energies for relaxation of large particles, after removal of the high-temperature limit . The dependence of on reduced temperature is shown along isobaric quenches at . Dashed lines are fits to Eq. (3). Upper plot: AMLJ- mixtures for values of size ratio (squares), 0.70 (triangles), and 0.76 (circles). Lower plot: BMLJ (filled circles) and WAHN (open symbols). Inset of upper plot: fragility index of AMLJ- vs . Inset of lower plot: fragility index vs obtained for different isobars in BMLJ.

Effective activation energies for relaxation of large particles, after removal of the high-temperature limit . The dependence of on reduced temperature is shown along isobaric quenches at . Dashed lines are fits to Eq. (3). Upper plot: AMLJ- mixtures for values of size ratio (squares), 0.70 (triangles), and 0.76 (circles). Lower plot: BMLJ (filled circles) and WAHN (open symbols). Inset of upper plot: fragility index of AMLJ- vs . Inset of lower plot: fragility index vs obtained for different isobars in BMLJ.

Scaled effective activation energies as a function of , along the isobar . Dashed lines are fits to Eq. (3). Upper plot:AMLJ- mixtures, for (squares), (triangles), and (circles). Lower plot: BMLJ (filled circles) and WAHN (open circles).

Scaled effective activation energies as a function of , along the isobar . Dashed lines are fits to Eq. (3). Upper plot:AMLJ- mixtures, for (squares), (triangles), and (circles). Lower plot: BMLJ (filled circles) and WAHN (open circles).

Unstable branch of density of states for instantaneous configurations (i-DOS, upper plot) and saddles (s-DOS, lower plot) in BMLJ. Results are shown at four different state points at (from top to bottom, , 1.0, 0.7, 0.6). Dashed lines are fits to Eq. (5).

Unstable branch of density of states for instantaneous configurations (i-DOS, upper plot) and saddles (s-DOS, lower plot) in BMLJ. Results are shown at four different state points at (from top to bottom, , 1.0, 0.7, 0.6). Dashed lines are fits to Eq. (5).

Parameter for s-DOS obtained from fits to Eq. (5) as a function of . Upper plot: BMLJ (filled circles) and WAHN (open circles) at . Middle plot: AMLJ-0.64 (filled circles) and AMLJ-0.82 (open circles) at . Lower plot: BMLJ at different pressures, (squares), (circles), and (triangles). Dashed lines are fits of the type, with being roughly system independent.

Parameter for s-DOS obtained from fits to Eq. (5) as a function of . Upper plot: BMLJ (filled circles) and WAHN (open circles) at . Middle plot: AMLJ-0.64 (filled circles) and AMLJ-0.82 (open circles) at . Lower plot: BMLJ at different pressures, (squares), (circles), and (triangles). Dashed lines are fits of the type, with being roughly system independent.

Average frequency of stable modes (main plots) and unstable modes (insets) of saddles as a function of . Upper plot: BMLJ (filled circles) and WAHN (open circles) at . Middle plot: AMLJ-0.64 (filled circles) and AMLJ-0.82 (open circles) at . Lower plot: BMLJ at (squares), (circles), and (triangles).

Average frequency of stable modes (main plots) and unstable modes (insets) of saddles as a function of . Upper plot: BMLJ (filled circles) and WAHN (open circles) at . Middle plot: AMLJ-0.64 (filled circles) and AMLJ-0.82 (open circles) at . Lower plot: BMLJ at (squares), (circles), and (triangles).

Upper plot: scatter plot of the fraction of unstable modes against energy of single saddles. Results are shown for WAHN at for three different state points: (squares), (circles), and (triangles). Linear fits of the type (solid lines) are used to estimate the derivative in Eq. (11), i.e., . Lower plot: parametric plot of average unstable modes of saddles against energy of saddles , for WAHN at .

Upper plot: scatter plot of the fraction of unstable modes against energy of single saddles. Results are shown for WAHN at for three different state points: (squares), (circles), and (triangles). Linear fits of the type (solid lines) are used to estimate the derivative in Eq. (11), i.e., . Lower plot: parametric plot of average unstable modes of saddles against energy of saddles , for WAHN at .

Effective energy barriers as a function of reduced temperature (left column) and as a function of (right column). Upper plots: WAHN (open circles) and BMLJ (filled circles) at . Lower plots: AMLJ-0.82 (open circles) and AMLJ-0.64 (filled circles) at .

Effective energy barriers as a function of reduced temperature (left column) and as a function of (right column). Upper plots: WAHN (open circles) and BMLJ (filled circles) at . Lower plots: AMLJ-0.82 (open circles) and AMLJ-0.64 (filled circles) at .

Effective energy barriers as a function of reduced temperature for BMLJ at (squares), (circles), and (triangles). Dashed lines represent linear fits.

Effective energy barriers as a function of reduced temperature for BMLJ at (squares), (circles), and (triangles). Dashed lines represent linear fits.

Participation ratio of average squared displacements on unstable modes as a function of reduced temperature at . Insets show the reduced gyration radius against . Upper plot: AMLJ-0.82 (white squares) and AMLJ-0.64 (black squares). Lower plot: WAHN (white circles) and BMLJ (black circles).

Participation ratio of average squared displacements on unstable modes as a function of reduced temperature at . Insets show the reduced gyration radius against . Upper plot: AMLJ-0.82 (white squares) and AMLJ-0.64 (black squares). Lower plot: WAHN (white circles) and BMLJ (black circles).

Distribution of average squared displacements on unstable modes of saddles. Results are shown for small particles (dotted lines), large particles (dashed lines), and irrespective of chemical species (solid lines). Normalization is such that the area under each curve is proportional to the corresponding number concentration. Arrows indicate the average values of for large and small particles. Upper plot: WAHN at , . Lower plot: BMLJ at , .

Distribution of average squared displacements on unstable modes of saddles. Results are shown for small particles (dotted lines), large particles (dashed lines), and irrespective of chemical species (solid lines). Normalization is such that the area under each curve is proportional to the corresponding number concentration. Arrows indicate the average values of for large and small particles. Upper plot: WAHN at , . Lower plot: BMLJ at , .

Selection of three unstable modes of a quasisaddle sampled in BMLJ at , . The nearly zero mode of the quasisaddle has been ignored. A fourth unstable mode, not shown, is very similar in extension and shape to that shown in (b). For clarity, only particles having square displacements larger than 0.004 are shown, and eigenvectors are scaled logarithmically. Large and small particles are shown as pale large spheres and small darker spheres, respectively. Note the strong localization of mode (a) and the existence of distinct stringlike instabilities of large particles in modes (b) and (c).

Selection of three unstable modes of a quasisaddle sampled in BMLJ at , . The nearly zero mode of the quasisaddle has been ignored. A fourth unstable mode, not shown, is very similar in extension and shape to that shown in (b). For clarity, only particles having square displacements larger than 0.004 are shown, and eigenvectors are scaled logarithmically. Large and small particles are shown as pale large spheres and small darker spheres, respectively. Note the strong localization of mode (a) and the existence of distinct stringlike instabilities of large particles in modes (b) and (c).

## Tables

Summary of thermal histories and simulation details. Also shown are the number concentration of large particles , the cutoff scheme used (see the text for definitions), and the value of the cutoff radius . In the case of AMLJ- mixtures, the following values of have been considered: , 0.64, 0.70, 0.73, 0.76, 0.82.

Summary of thermal histories and simulation details. Also shown are the number concentration of large particles , the cutoff scheme used (see the text for definitions), and the value of the cutoff radius . In the case of AMLJ- mixtures, the following values of have been considered: , 0.64, 0.70, 0.73, 0.76, 0.82.

Parameters of fits to Eq. (3) for effective activation energies of large and small species. The reference temperature and the onset temperature are described in the text.

Parameters of fits to Eq. (3) for effective activation energies of large and small species. The reference temperature and the onset temperature are described in the text.

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