Relationship between Entropic Bottleneck in Free Energy Landscape, Nonexponential Relaxation and Fragility of Glass-Forming Liquids

A mesoscopic model is proposed to explain the anomalous dynamics in a supercooled liquid as its glass transition temperature is approached from above. The model is based on the assumption of $\beta$ organized $\alpha$ process, with the requirement of coherent excitation of a minimum critical number $N_{c}$ of $\beta$ processes in the surroundings of a total $N_{\beta}$. Numerical evaluation of the model shows that the growth in this critical number in the background of a modest $N_{\beta}$ can lead to a severe entropic bottleneck and slow down the dynamics to an extent observed near real glass transition. The fragility of the glass-forming liquid is shown to be correlated with the growth of the ratio $\gamma (= N_{c}/N_{\beta})$.