Fragility and elastic behavior of a supercooled liquid

A model for the supercooled liquid is considered by taking into account its solidlike properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) 431, 961 (2004)] that the fragility index $m$ of a glass forming material is linearly related to the corresponding ratio $K∕G$ of the bulk and the shear moduli.

Figure 1

Relevant one loop diagrams which contribute to the effective viscosity as nonlinear corrections.

Figure 2

(Color online) $c_1$ vs $c_2$ and the solid line displays the dynamic transition line. The circles (joined with a solid line to indicate continuity) shown in the nonergodic phase correspond to the states for which the results of Figs. 5, 7 are obtained $({\Delta }_0=1.7)$. These circles refer to different values of the ratio $K∕G$ of bulk and shear moduli with the adjacent number to a circle indicating the corresponding value of $K∕G$.

Figure 3

(Color online) Log of relaxation time $\tau$ in units of ${\Gamma }_0∕\left({\rho }_0{c}_L^2\right)$ vs ${\Delta }_0$ (see text). The constant $K∕G$ value corresponding to each curve is also displayed adjacent to it in the figure. The dashed and dotted lines are, respectively, the power law and exponential fits to the corresponding curve.

Figure 4

(Color online) The inverse slope $\tilde{m}$ (see text) vs ratio $K∕G$ of bulk and shear moduli at different ${\lambda }_0$ values, displayed in the figure.

Figure 5

(Color online) Nonergodicity parameter $f$ vs the ratio $K∕G$ of bulk and shear moduli from the present model $({\Delta }_0=1.7)$.

Figure 6

(Color online) Experimental data (points) and best fit (line) to the experimental data Ref. 21 linking fragility index $m$ with $f$. The inset shows ${\alpha }_0=(1-f)∕f$ vs fragility index $m$ (solid line) (using the experimental best fit) and x-ray Brillouin scattering data (solid triangles) [22].

Figure 7

(Color online) Fragility index $m$ vs ratio $K∕G$ of bulk and shear moduli from the present model at different ${\lambda }_0$ values (solid lines) $({\Delta }_0=1.7)$, experimental data of Ref. 4 (points).

Figure 8

(Color online) Stretched exponential exponent $\beta$ vs Poisson’s ratio $\sigma$ $({\Delta }_0=0.885)$.

Figure 9

(Color online) Power law exponent $a$ vs the ratio $K∕G$ of bulk and shear moduli $({\Delta }_0=1.7)$. Inset shows normalized density correlation function $\varphi \left(t\right)$ vs $t$ in units of ${\Gamma }_0∕\left({\rho }_0{c}_L^2\right)$ (see text). The dashed curve is the power law fit with the exponent value shown as a dot on the main figure.