Hongsuk Kang, T. R. Kirkpatrick, D. Thirumalai
We use Brownian dynamics simulations of a binary mixture of highly charged spherical colloidal particles to illustrate many of the implications of the Random First Order Transition (RFOT) theory (Phys. Rev. A. 40 1045 (1989)), which is the only theory that provides a unified description of both the statics and dynamics of the liquid to glass transition. In accord with the RFOT predictions, we find that as the volume fraction of the colloidal particles $\phi$, the natural variable that controls glass formation in colloidal systems, approaches $\phi_A$ there is an effective ergodic to non-ergodic dynamical transition, which is signalled by a dramatic slowing down of diffusion. Using the energy metric (a measure to probe ergodicity breaking in classical many body systems) we show that the system becomes non-ergodic as $\phi_A$ is approached. The time $t^*$, at which the four-point dynamical susceptibility achieves a maximum, also diverges as a power law near $\phi_A$. The translation diffusion constant, the ergodic diffusion constant, and $(t^*)^{-1}$ all vanish as $(\phi_A - \phi)^{\gamma}$ with both $\phi_A$ and $\gamma$ being the roughly the same for all three quantities. Below $\phi_A$ transport involves crossing suitable free energy barriers. In this regime, the density-density correlation function decays as a stretched exponential. The $\phi$-dependence of the relaxation time $\tau_{\alpha}$ is well fit using the VTF law with the ideal glass transition occurring at $\phi_K \approx 0.47$. By using an approximate measure of the local entropy ($s_3$) we show that below $\phi_A$ the law of large numbers, which states that the distribution of $s_3$ for a large subsample should be identical to the whole sample, is violated. The subsample-to-subsample variations results in dynamical heterogeneity, which a consequence of violation of law of large numbers.
View original:
http://arxiv.org/abs/1212.6284
No comments:
Post a Comment